Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Set Volumes 1 and 2 [1, 1 ed.] 111945834X, 9781119458340

Citation preview

Position, Navigation, and Timing Technologies in the 21st Century

IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Ekram Hossain, Editor in Chief Jón Atli Benediktsson Xiaoou Li Saeid Nahavandi Sarah Spurgeon

David Alan Grier Peter Lian Jeffrey Reed Ahmet Murat Tekalp

Elya B. Joffe Andreas Molisch Diomidis Spinellis

Position, Navigation, and Timing Technologies in the 21st Century Integrated Satellite Navigation, Sensor Systems, and Civil Applications

Volume 1

Edited by Y. T. Jade Morton, University of Colorado Boulder Frank van Diggelen, Google James J. Spilker, Jr., Stanford University Bradford W. Parkinson, Stanford University

Associate Editors:

Sherman Lo, Stanford University Grace Gao, Stanford University

Copyright © 2021 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data is available. The CiP data for ISBN 9781119458340 has been applied. Cover Design: Wiley Cover Images: Global telecommunication network © NicoElNino/Getty Images, GPS Satellite © BlackJack3D/iStockphoto Set in 9.5/12.5pt STIXTwoText by SPi Global, Pondicherry, India 10 9 8 7 6 5 4 3 2 1

In Memory of: Ronald L. Beard Per Enge Ronald Hatch David Last James J. Spilker, Jr. James B. Y. Tsui

vii

Contents Preface xiii Contributors xv

Part A

ftoc.3d 7

1

Satellite Navigation Systems

1

Introduction, Early History, and Assuring PNT (PTA) 3 Bradford W. Parkinson, Y.T. Jade Morton, Frank van Diggelen, and James J. Spilker Jr.

2

Fundamentals of Satellite-Based Navigation and Timing John W. Betz

3

The Navstar Global Positioning System John W. Betz

4

GLONASS 87 S. Karutin, N. Testoedov, A. Tyulin, and A. Bolkunov

5

GALILEO 105 José Ángel Ávila Rodríguez, Jörg Hahn, Miguel Manteiga Bautista, and Eric Chatre

6

BeiDou Navigation Satellite System Mingquan Lu and Zheng Yao

7

IRNSS 171 Vyasaraj Rao

8

Quasi-Zenith Satellite System 187 Satoshi Kogure, Yasuhiko Kawazu, and Takeyasu Sakai

9

GNSS Interoperability Thomas A. Stansell, Jr.

10

GNSS Signal Quality Monitoring 215 Frank van Graas and Sabrina Ugazio

11

GNSS Orbit Determination and Time Synchronization Oliver Montenbruck and Peter Steigenberger

12

Ground-Based Augmentation System Boris Pervan

43

65

143

205

233

259

15/12/2020 6:59:11 PM

viii

Contents

13

Satellite-Based Augmentation Systems (SBASs) Todd Walter

Part B

307 309

14

Fundamentals and Overview of GNSS Receivers Sanjeev Gunawardena and Y.T. Jade Morton

15

GNSS Receiver Signal Tracking 339 Y.T. Jade Morton, R. Yang, and B. Breitsch

16

Vector Processing 377 Matthew V. Lashley, Scott Martin, and James Sennott

17

Assisted GNSS 419 Frank van Diggelen

18

High-Sensitivity GNSS Frank van Diggelen

19

Relative Positioning and Real-Time Kinematic (RTK) Sunil Bisnath

20

GNSS Precise Point Positioning Peter J.G. Teunissen

21

Direct Position Estimation Pau Closas and Grace Gao

22

Robust Positioning in the Presence of Multipath and NLOS GNSS Signals Gary A. McGraw, Paul D. Groves, and Benjamin W. Ashman

23

GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM) Sam Pullen and Mathieu Joerger

24

Interference: Origins, Effects, and Mitigation Logan Scott

25

Civilian GNSS Spoofing, Detection, and Recovery Mark Psiaki and Todd Humphreys

26

GNSS Receiver Antennas and Antenna Array Signal Processing Andrew O’Brien, Chi-Chih Chen and Inder J. Gupta

Part C

ftoc.3d 8

Satellite Navigation Technologies

277

445

481

503

529

551

591

619

655

681

Satellite Navigation for Engineering and Scientific Applications

717

27

Global Geodesy and Reference Frames 719 Chris Rizos, Zuheir Altamimi, and Gary Johnston

28

GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment Yehuda Bock and Shimon Wdowinski

741

15/12/2020 6:59:24 PM

Contents

ftoc.3d 9

821

29

Distributing Time and Frequency Information Judah Levine

30

GNSS for Neutral Atmosphere and Severe Weather Monitoring Hugues Brenot

31

Ionospheric Effects, Monitoring, and Mitigation Techniques 879 Y. Jade Morton, Zhe Yang, Brian Breitsch, Harrison Bourne, and Charles Rino

32

GNSS Observation for Detection, Monitoring, and Forecasting Natural and Man-Made Hazardous Events Panagiotis Vergados, Attila Komjathy, and Xing Meng

33

GNSS Radio Occultation 971 Anthony J. Mannucci, Chi O. Ao, and Walton Williamson

34

GNSS Reflectometry for Earth Remote Sensing 1015 James Garrison, Valery U. Zavorotny, Alejandro Egido, Kristine M. Larson, Felipe Nievinski, Antonio Mollfulleda, Giulio Ruffini, Francisco Martin, and Christine Gommenginger

Part D

ix

849

Position, Navigation, and Timing Using Radio Signals-of-Opportunity

939

1115

1117

35

Overview of Volume 2: Integrated PNT Technologies and Applications John F. Raquet

36

Nonlinear Recursive Estimation for Integrated Navigation Systems Michael J. Veth

37

Overview of Indoor Navigation Techniques Sudeep Pasricha

38

Navigation with Cellular Signals of Opportunity Zaher (Zak) M. Kassas

39

Position, Navigation and Timing with Dedicated Metropolitan Beacon Systems Subbu Meiyappan, Arun Raghupathy, and Ganesh Pattabiraman

40

Navigation with Terrestrial Digital Broadcasting Signals Chun Yang

41

Navigation with Low-Frequency Radio Signals Wouter Pelgrum and Charles Schue

42

Adaptive Radar Navigation Kyle Kauffman

43

Navigation from Low Earth Orbit 1359 Part 1: Concept, Current Capability, and Future Promise Tyler G.R. Reid, Todd Walter, Per K. Enge, David Lawrence, H. Stewart Cobb, Greg Gutt, Michael O’Conner, and David Whelan

43

Navigation from Low-Earth Orbit 1381 Part 2: Models, Implementation, and Performance Zaher (Zak) M. Kassas

1121

1141

1171

1225

1243

1281

1335

15/12/2020 6:59:25 PM

x

Contents

Part E

1413

1415

44

Inertial Navigation Sensors Stephen P. Smith

45

MEMS Inertial Sensors Alissa M. Fitzgerald

46

GNSS-INS Integration 1447 Part 1: Fundamentals of GNSS-INS Integration Andrey Soloviev

46

GNSS-INS Integration 1481 Part 2: GNSS/IMU Integration Using a Segmented Approach James Farrell and Maarten Uijt Haag

47

Atomic Clocks for GNSS Leo Hollberg

48

Positioning Using Magnetic Fields Aaron Canciani and John F. Raquet

49

Laser-Based Navigation 1541 Maarten Uijt de Haag, Zhen Zhu, and Jacob Campbell

50

Image-Aided Navigation – Concepts and Applications Michael J. Veth and John F. Raquet

51

Digital Photogrammetry 1597 Charles Toth and Zoltan Koppanyi

52

Navigation Using Pulsars and Other Variable Celestial Sources Suneel Sheikh

53

Neuroscience of Navigation 1669 Meredith E. Minear and Tesalee K. Sensibaugh

54

Orientation and Navigation in the Animal World Gillian Durieux and Miriam Liedvogel

Part F

ftoc.3d 10

Position, Navigation, and Timing Using Non-Radio signals of Opportunity

1435

1497

1521

1571

1635

1689

Position, Navigation, and Timing for Consumer and Commercial Applications

1711

1713

55

GNSS Applications in Surveying and Mobile Mapping Naser El-Sheimy and Zahra Lari

56

Precision Agriculture 1735 Arthur F. Lange and John Peake

57

Wearables 1749 Mark Gretton and Peter Frans Pauwels

58

Navigation in Advanced Driver Assistance Systems and Automated Driving David Bevly and Scott Martin

1769

15/12/2020 6:59:25 PM

Contents

Train Control and Rail Traffic Management Systems Alessandro Neri

60

Commercial Unmanned Aircraft Systems (UAS) 1839 Maarten Uijt de Haag, Evan Dill, Steven Young, and Mathieu Joerger

61

Navigation for Aviation Sherman Lo

62

Orbit Determination with GNSS Yoaz Bar-Sever

63

Satellite Formation Flying and Rendezvous Simone D’Amico and J. Russell Carpenter

64

Navigation in the Arctic 1947 Tyler G. R. Reid, Todd Walter, Robert Guinness, Sarang Thombre, Heidi Kuusniemi, and Norvald Kjerstad

1871

1893

1921

Glossary, Definitions, and Notation Conventions

ftoc.3d 11

1811

59

Index

xi

1971

I1

15/12/2020 6:59:25 PM

xiii

Preface The ability to navigate has been an essential skill for survival throughout human history. As navigation has advanced, it has become almost inseparable from the ability to tell time. Today, position, navigation, and timing (PNT) technologies play an essential role in our modern society. Much of our reliance on PNT is the result of the availability of the Global Positioning System (GPS) and the growing family of Global Navigation Satellite Systems (GNSSs). Satellite-based navigation and other PNT technologies are being used in the many fast-growing, widespread, civilian applications worldwide. A report sponsored by the US National Institute of Standards and Technology (NIST) on the economic benefits of GPS indicated that GPS alone has generated a $1.4 trillion economic benefit in the private sector by 2019, and that the loss of GPS service would have a $1 billion per-day negative impact.1 PNT has become a pillar of our modern society. Knowledge and education are essential for the continued advancement of PNT technologies to meet the increasing demand from society. That is the rationale that led to the creation of this book. While there are many publications and several outstanding books on satellite navigation technologies and related subjects, this two-volume set offers a uniquely comprehensive coverage of the latest developments in the broad field of PNT and has been written by world-renowned experts in each chapter’s subject area. It is written for researchers, engineers, scientists, and students who are interested in learning about the latest developments in satellite-based PNT technologies and civilian applications. It also examines alternative navigation technologies based on other signals and sensors and offers a comprehensive treatment of integrated PNT systems for consumer and commercial applications. The two-volume set contains 64 chapters organized into six parts. Each volume contains three parts. Volume 1 focuses on satellite navigation systems, technologies, and 1 RTI International Final Report, Sponsored by the US National Institute of Standards and Technology, “Economic Benefits of the Global Positioning System (GPS),” June 2019.

applications. It starts with a historical perspective of GPS and other related PNT developments. Part A consists of 12 chapters that describe the fundamental principles and latest developments of all global and regional navigation satellite systems (GNSSs and RNSSs), design strategies that enable their coexistence and mutual benefits, their signal quality monitoring, satellite orbit and time synchronization, and satellite- and ground-based systems that provide augmentation information to improve the accuracy of navigation solutions. Part B contains 13 chapters. These provide a comprehensive review of recent progress in satellite navigation receiver technologies such as receiver architecture, signal tracking, vector processing, assisted and high-sensitivity GNSS, precise point positioning and realtime kinematic (RTK) systems, direct position estimation techniques, and GNSS antennas and array signal processing. Also covered are topics on the challenges of multipath-rich urban environments, in handling spoofing and interference, and in ensuring PNT integrity. Part C finishes the volume with 8 chapters on satellite navigation for engineering and scientific applications. A review of global geodesy and reference frames sets the stage for discussions on the broad field of geodetic sciences, followed by a chapter on the important subject of GNSS-based time and frequency distribution. GNSS signals have provided a popular passive sensing tool for troposphere, ionosphere, and Earth surface monitoring. Three chapters are dedicated to severe weather, ionospheric effects, and hazardous event monitoring. Finally, a comprehensive treatment of GNSS radio occultation and reflectometry is provided. The three parts in Volume 2 address PNT using alternative signals and sensors and integrated PNT technologies for consumer and commercial applications. An overview chapter provides the motivation and organization of the volume, followed by a chapter on nonlinear estimation methods which are often employed in navigation system modeling and sensor integration. Part D devotes 7 chapters to using various radio signals transmitted from sources on the ground, from aircraft, or from low Earth orbit (LEO) satellites for PNT purposes. Many of these signals were

xiv

Preface

intended for other functions, such as broadcasting, networking, and imaging and surveillance. In Part E, there are 8 chapters covering a broad range of non-radio frequency sensors operating in both passive and active modes to produce navigation solutions, including MEMS inertial sensors, advances in clock technologies, magnetometers, imaging, LiDAR, digital photogrammetry, and signals received from celestial bodies. A tutorial-style chapter on multiple approaches to GNSS/INS integration methods is included in Part E. Also included in Part E are chapters on the neuroscience of navigation and animal navigation. Finally, Part F presents a collection of work on contemporary PNT applications such as surveying and mobile mapping, precision agriculture, wearable systems, automated driving, train control, commercial unmanned aircraft systems, aviation, satellite orbit determination and formation flying, and navigation in the unique Arctic environment. The chapters in this book were written by 131 authors from 18 countries over a period of 5 years. Because of the diverse nature of the authorship and the topics covered in the two volumes, the chapters were written in a variety of styles. Some are presented as high-level reviews of progress in specific subject areas, while others are tutorials with detailed quantitative analysis. A few chapters include links to MATLAB or Python example code as well as test data for those readers who desire to have hands-on practice. The collective goal is to appeal to industry professionals, researchers, and academics involved with the science, engineering, and application of PNT technologies. A website, pnt21book.com, provides chapter summaries; downloadable code examples, data, worked homework examples, select high-resolution figures, errata, and a way for readers to provide feedback. A comprehensive project of this scale would not be possible without the collective efforts of the GNSS and PNT community. We appreciate the leading experts in the field taking time from their busy schedules to answer the call in contributing to this book. Some of the authors also

provided valuable input and comments to other chapters in the book. We also sought input from graduate students and postdocs in the field as they will be the primary users and represent the future of the field. We want to acknowledge the following individuals who have supported or encouraged the effort and/or helped to improve the contents of the set: Michael Armatys, Penina Axelrad, John Betz, Rebecca Bishop, Michael Brassch, Brian Breitsch, Phil Brunner, Russell Carpenter, Charles Carrano, Ian Collett, Anthea Coster, Mark Crews, Patricia Doherty, Chip Eschenfelder, Hugo Fruehauf, Gaylord Green, Richard Greenspan, Yu Jiao, Kyle Kauffman, Tom Langenstein, Gerard Lachapelle, Richard Langley, Robert Lutwak, Jake Mashburn, James J. Miller, Mikel Miller, Pratap Misra, Oliver Montenbruck, Sam Pullen, Stuart Riley, Chuck Schue, Logan Scott, Steve Taylor, Peter Teunissen, Jim Torley, A. J. van Dierendonck, Eric Vinande, Jun Wang, Pai Wang, Yang Wang, Phil Ward, Dongyang Xu, Rong Yang, and Zhe Yang. The Wiley-IEEE Press team has demonstrated great patience and flexibility throughout the five-year gestation period of this project. And our families have shown great understanding, generously allowing us to spend a seemingly endless amount of time to complete the set. This project was the brainchild of Dr. James Spilker, Jr. He remained a fervent supporter until his passing in October 2019. A pioneer of GPS civil signal structure and receiver technologies, Dr. Spilker was truly the inspiration behind this effort. During the writing of this book set, several pioneers in the field of GNSS and PNT, including Ronald Beard, Per Enge, Ronald Hatch, David Last, and James Tsui also passed away. This set is dedicated to these heroes and all those who laid the foundation for the field of PNT. Jade Morton Frank van Diggelen Bradford Parkinson Sherman Lo Grace Gao

xv

Contributors Zuheir Altamimi Institut National de l’Information Géographique et Forestière, France Chi O. Ao Jet Propulsion Laboratory, United States Benjamin W. Ashman National Aeronautics and Space Administration, United States Yoaz Bar-Sever Jet Propulsion Lab, United States Miguel Manteiga Bautista European Space Agency, the Netherlands John W. Betz The MITRE Corporation, United States David Bevly Auburn University, United States Sunil Bisnath York University, Canada

Jacob Campbell Air Force Research Laboratory, United States Aaron Canciani Air Force Institute of Technology, United States J. Russell Carpenter National Aeronautics and Space Administration, United States Eric Châtre European Commission, Belgium Chi-Chih Chen The Ohio State University, United States Pau Closas Northeastern University, United States H. Stewart Cobb Satelles, United States Simone D’Amico Stanford University, United States

Yehuda Bock Scripps Institution of Oceanography, United States

Evan Dill National Aeronautics and Space Administration, United States

Alexei Bolkunov PNT Center, Russia

Gillian Durieux Max Plank Institute for Evolutionary Biology, Germany

Harrison Bourne University of Colorado Boulder, United States

Alejandro Egido Starlab, Spain

Brian Breitsch University of Colorado Boulder, United States

Naser El-Sheimy University of Calgary, Canada

Hugues Brenot Royal Belgian Institute for Space Aeronomy, Belgium

Per K. Enge Stanford University, United States

xvi

Contributors

James Farrell Vigil Inc., United States

Zaher (Zak) M. Kassas University of California Irvine, United States

Alissa M. Fitzgerald A.M. Fitzgerald & Associates, LLC, United States

Kyle Kauffman Integrated Solutions for Systems, United States

Grace Gao Stanford University, United States

Yasuhiko Kawazu National Space Policy Secretariat, Japan

James Garrison Purdue University, United States

Norvald Kjerstad Norwegian University of Science and Technology, Norway

Christine Gommenginger National Oceanography Centre, United Kingdom Mark Gretton TomTom, United Kingdom Paul D. Groves University College London, United Kingdom Robert Guinness Finnish Geospatial Research Institute, Finland Sanjeev Gunawardena Air Force Institute of Technology, United States Inder J. Gupta The Ohio State University, United States Greg Gutt Satelles, United States Maarten Uijt de Haag Technische Universität Berlin, Germany Jörg Hahn European Space Agency, the Netherlands Leo Hollberg Stanford University, United States Todd Humphreys University of Texas–Austin, United States

Satoshi Kogure National Space Policy Secretariat, Japan Attila Komjathy Jet Propulsion Laboratory, United States Zoltan Koppanyi The Ohio State University, United States Heidi Kuusniemi Finnish Geospatial Research Institute, Finland Arthur F. Lange Trimble Navigation, United States Zahra Lari Leica Geosystems Inc., Canada Kristine M. Larson University of Colorado Boulder, United States Matthew V. Lashley Georgia Tech Research Institute, United States David Lawrence Satelles, United States Judah Levine National Institute of Standard and Technology, United States

Mathieu Joerger Virginia Tech, United States

Miriam Liedvogel Max Plank Institute for Evolutionary Biology, Germany

Gary Johnson Geoscience Australia, Australia

Sherman Lo Stanford University, United States

Sergey Karutin PNT Center, Russia

Mingquan Lu Tsinghua University, China

Contributors

Anthony J. Mannucci Jet Propulsion Laboratory, United States

Peter Frans Pauwels TomTom, the Netherlands

Francisco Martin Starlab, Spain

John Peake Trimble Navigation, United States

Scott Martin Auburn University, United States

Wouter Pelgrum Blue Origin LLC, United States

Gary A. McGraw Collins Aerospace, United States Subbu Meiyappan NextNav LLC, United States Xing Meng Jet Propulsion Laboratory, United States Meredith E. Minear University of Wyoming, United States Antonio Mollfulleda Starlab, Spain Oliver Montenbruck German Aerospace Center, Germany Y.T. Jade Morton University of Colorado Boulder, United States Alessandro Neri University of Roma TRE, Italy Felipe Nievinski UFRGS, Brazil Andrew O’Brien The Ohio State University, United States Michael O’Conner Satelles, United States

Boris Pervan Illinois Institute of Technology, United States Mark Psiaki Virginia Tech, United States Sam Pullen Stanford University, United States Arun Raghupathy NextNav LLC, United States Vyasaraj Rao Accord Software and Systems, India John F. Raquet Integrated Solutions for Systems, United States Tyler G. R. Reid Stanford University, United States Charles Rino University of Colorado Boulder, United States Chris Rizos University of New South Wales, Australia José Ángel Ávila Rodríguez European Space Agency, the Netherlands Giulio Ruffini Starlab, Spain

Bradford W. Parkinson Stanford University, United States

Takeyasu Sakai National Institute of Maritime, Port, and Aviation Technology, Japan

Sudeep Pasricha Colorado State University, United States

Charles Schue, III UrsaNav, Inc., United States

Ganesh Pattabiraman NextNav LLC, United States

Logan Scott LS Consulting, United States

xvii

xviii

Contributors

James Sennott Tracking and Imaging Systems, United States

Frank van Graas Ohio University, United States

Tesalee K. Sensibaugh University of Wyoming, United States

Panagiotis Vergados Jet Propulsion Laboratory, United States

Suneel Sheikh ASTER Labs, Inc., United States

Michael J. Veth Veth Research Associates, United States

Stephen P. Smith The Charles Stark Draper Laboratory Inc., United States Andrey Soloviev QuNav, United States James J. Spilker Jr. Stanford University, United States Thomas A. Stansell, Jr. Stansell Consulting, United States Peter Steigenberger German Aerospace Center, Germany Nikolai Testoedov PNT Center, Russia Peter J. G. Teunissen Curtin University, Australia and Delft University of Technology, The Netherlands Sarang Thombre Finnish Geospatial Research Institute, Finland Charles Toth The Ohio State University, United States Andrei Tyulin PNT Center, Russia Sabrina Ugazio Ohio University, United States Frank van Diggelen Google, United States

Todd Walter Stanford University, United States Shimon Wdowinski Florida International University, United States David Whelan University of California San Diego, United States Walton Williamson Jet Propulsion Laboratory, United States Chun Yang Sigtem Technology Inc., United States Rong Yang University of Colorado Boulder, United States Zhe Yang University of Colorado Boulder, United States Zheng Yao Tsinghua University, China Steven Young National Aeronautics and Space Administration, United States Valery U. Zavorotny National Oceanic and Atmospheric Administration, United States; University of Colorado Boulder, United States Zhen Zhu East Carolina University, United States

1

Part A Satellite Navigation Systems

3

1 Introduction, Early History, and Assuring PNT (PTA) Bradford W. Parkinson1, Y.T. Jade Morton2, Frank van Diggelen3, and James J. Spilker Jr.1 1

Stanford University, United States University of Colorado Boulder, United States 3 Google, United States 2

1.1

Introduction

Knowledge of your current location is now taken for granted by people worldwide. This is largely due to the advent of satellite-based navigation systems, particularly the Global Positioning System (GPS). These global navigation satellite systems (GNSSs) are still rapidly evolving with more capability and even greater robustness. Their fundamental purpose is determining location in four dimensions – three geographical positions plus time. A user is indifferent to the source of location knowledge – any technique will do if it is reliable. While much of this book is devoted to satellite-based navigation systems (satnavs), we intend to give full explanations of virtually all modern sources of position, navigation, and timing (PNT). The classical definition of navigation is the act, activity, science, method, or process of finding a route to get to a place when you are traveling in a ship, car, airplane, etc. It involves the determination of position, course, and distance traveled [1]. A more contemporary, formal definition of navigation is determining positions, orientations, velocities, and accelerations, all in three dimensions and in a stated coordinate system, and time, as well as planning, finding, and following a route. The goal for most satnav users is assured PNT; providers recognize that combining dissimilar sources of basic PNT information leads to a much more robust positioning capability – that is, greater PNT assurance. The United States Federal Aviation Administration (FAA) uses four criteria to measure PNT capability. These are (i) Availability, (ii) Accuracy, (iii) Integrity, and (iv) Continuity of operations. They are useful measures for all users and all applications, not just aviation. In particular, compounding or augmenting systems (e.g. satnav + inertial) leads to greater assurance of PNT in the face of deliberate or inadvertent radio interference. Thus, another purpose of this book is

to illustrate such interconnecting relationships and the benefits that accrue to the user. Application Explosion For the user, GPS is simply a technique to assure PNT; there are significant other ways to find location today, and more will become available in the near future. This book will explore both current and future techniques, especially the other GNSSs and regional navigation satellite systems (RNSSs). But GPS is now a name familiar to nearly every cell phone user in the world. By the year 2015, over 2 billion receiver sets had been produced, and, driven by cell phone applications, these are increasing by over 1.4 billion per year. Besides ubiquitous cell phones, GPS has stealthily crept into virtually every corner of our society. Even the early developers have been amazed by the countless applications. Table 1.1 presents a partial list of application areas. Clearly, any attempt to explore all applications of satnav and PNT would require many volumes and be outdated as soon as it was published. However, we do intend to describe representative current and future applications for PNT in this book. GPS has been called “The Stealth Utility” because many applications are usually invisible to the user. Operationally, GPS availability has been over 99.9%, on a worldwide basis [2]. This pervasive availability drives the enormous GPS benefits in terms of safety, productivity, and convenience. For example, there are now over 3600 certified GPS runway approaches for aircraft in the United States. An economic study for the US National Space-Based PNT Advisory Board (PNTAB) calculated the mid-range value of GPS at over $65 billion per year for the United States alone [3]. These broad benefits have led to GPS being properly described as “a system for humanity.” As such, GPS raises some historical questions. How did it come into being and what applications are likely to be developed in the

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

4

1 Introduction, Early History, and Assuring PNT (PTA)

Table 1.1 Twelve major application areas for satnav Areas

Example application

Aviation

Area navigation, approach, landing up to Cat III, NextGen

Agriculture

Autofarming: crop spraying, precision cultivating, yield assessment

Automotive

Turn-by-turn guidance, concierge services, driverless cars

Emergency and Rescue Services

911, ambulance, fire, police, rescue helicopters, emergency beacons, airplane and ship locaters

Intelligent Transportation

Train control and management, UAVs

Military

Rescue, precision weapon delivery, unit and individual location

Recreation

Geocaching, drones, hiking, boating, fitness

Robotics and Machine Control

Bulldozers, earth graders, mining trucks, oil drilling

Scientific

Earth movement and shape, atmosphere, weather forecasting, climate modeling, ionosphere, space weather, tsunami warning, soil moisture, ocean roughness and salinity, wind velocity, snow, ice, foliage coverage, etc.

Survey and GIS

Mapping, environmental monitoring, tagging disease outbreaks

Timing

Cell phone towers, banking, power grid

Tracking

Fleets, assets, equipment, shipments, children, Alzheimer’s patients, wildlife, livestock, pets, law enforcement, criminals, parolees, etc.

future? The history will be addressed in this introductory chapter‚ and selected applications will be summarized here, but expanded in later chapters. While GPS has been the pioneer in satnav, other nations are in the process of fielding their own systems. Three examples of newer Global satnavs are the upgraded GLONASS built by the Russians, the EU-sponsored system called Galileo,1 and the Chinese system, called BeiDou (formerly: Compass). In addition, a number of countries are fielding Regional satnav systems (RNSSs). In Volume I, Part A of this book, we devote a chapter to each of these global and regional systems. With these systems, an individual user is able to use well over 40 satellites simultaneously for determining position. The key enabler for the user is that the satnav systems are at least interoperable, if not interchangeable. The similarities and differences among the GNSSs as well as the challenges for interoperability are also addressed in this book. Reliance on satnav alone is imprudent for many users. What techniques and processes can be used to increase robustness and accuracy? This first chapter will introduce the topic‚ and later chapters will expand on this in depth. The program to ensure PNT availability has been a major subject for the US PNTAB and is called “PTA.” PTA stands for Protect, Toughen, and Augment and will be further elaborated in this introduction. An example of GNSS augmentation is the US FAA’s Wide Area Augmentation System (WAAS). Driven by the need to 1 The recent Brexit will probably change Galileo management. There is the possibility of an added British navigation satellite constellation.

ensure integrity for aviation, WAAS became operational on 10 July 2003. This pioneering system performs real-time measurements of all GPS satellites and sends the user an integrity message in near real time that also corrects any real-time ranging errors. An example of the GPS measurement accuracy performance: for the 22 WAAS ground stations in the third quarter of 2015, it was better than 2.2 m of horizontal error at the 95th percentile [4]. The European Geostationary Navigation Overlay Service (EGNOS) and Japanese Multi-functional Transport Satellite (MTSAT) Space-based Augmentation System (MSAS) perform similar functions. All of these are examples of satellite-based augmentation systems (SBAS) for satnavs. A similar, more local augmentation technique, called the Local Area Augmentation System (LAAS), and other ground-based augmentation systems (GBAS) and techniques are designed for high-integrity, blind landing of aircraft. Furthermore, numerous ground-based accuracy augmentation networks, such as the Continuously Operating Reference Station (CORS) networks, are the results of combined efforts by government organizations, self-funding agencies, universities, and research institutions from over 100 countries [5–7]. These networks and their combined super-networks play a fundamental role in enabling broad areas of applications. These essential GNSS augmentation systems will be discussed in this book. Numerous innovative PNT algorithms and methodologies have been developed since the inception of the GPS concept. Volume I of this book focuses on the progress made and future trends in satnav technologies

1.2 A Brief History Prior to SatNav

and applications, while Volume II focuses on non-GNSS sensors, integrated PNT systems, and applications. The fundamental purposes of these volumes are to offer technical explanations of the many satnav and other techniques that provide civil PNT and to explore selected applications that are useful to the global community. The chapters have been written by world-class experts on the current state of the art of these PNT technologies.

1.2

A Brief History Prior to SatNav

1.2.1

Early Navigation Techniques

As humans migrated across the globe, the ability to navigate was an absolute prerequisite to survival. The Polynesians developed techniques of using the observation of stars and planets to navigate across vast areas of the Pacific Ocean with legendary accuracy. In 1976, these voyages were replicated using a newly built war canoe of ancient Polynesian design. This vessel, named the Hokulea, was navigated solely by the stars from Hawaii to Tahiti. It is a fascinating story that elaborates on the ancient techniques of using the heavenly bodies [8]. About 1000 years ago, the Chinese introduced the magnetic compass‚ which was particularly useful for voyages in overcast conditions. On cloudy days, the Vikings may have used cordierite or some other birefringent crystal to determine the Sun’s direction and elevation from the polarization of daylight through cloudy skies. Then a series of techniques were developed to measure the altitude (angle above the horizon) of stars and other heavenly bodies to calculate position, culminating in the invention of the sextant by British Vice-Admiral John Campbell in 1757. Latitude could be determined by the elevation of the Sun above the horizon at high noon or the elevation of the star Polaris, but longitude required accurate time, synchronized to an observatory that had published a nautical almanac. The challenging requirement for synchronized time soon led to the development of highly accurate shipborne clocks (called chronometers), with the initial successful version by a Yorkshire carpenter, John Harrison‚ in 1761. His clock was accurate to better than 1 second per day. This history was documented in the excellent book Longitude by Dava Sobel [9].

1.2.2

Radio Navigation

With the discovery and exploitation of radio waves, new navigation techniques could be developed. Perhaps the most elementary is radio direction finding (RDF), which allows a user to determine the line of bearing to a radio

source with a known location. Practical RDF devices were in use by the early 20th century. RDF is an example of bearing-measurement systems that includes the modern VHF omni-directional range (VOR) used by FAA. The other four classes of radio navigation system are beam systems, transponder systems (including distance measuring equipment (DME)), hyperbolic systems, and satnavs. The most well known of the hyperbolic systems is probably LORAN (Long-Range Navigation). A modernized variant of this is eLORAN (enhanced LORAN). The underlying technique is to measure the difference in time of arrival (TOA) between pairs of transmitted pulses. Each station pair produces a hyperbolic line of position. The user’s location is determined by the intersection of two or more such lines. This system is only two-dimensional (2D) with accuracies of about 20 m in a calibrated differential mode. It is appealing as an augmentation for GPS because its powerful RF signal is in an entirely different radio spectrum band.

1.2.3

Inertial Navigation

Inertial navigation is another method of providing positioning information. During World War II, the Germans deployed an elementary guidance system for the V-2 rocket, but this was not a generally useful configuration. The first purely inertial, generalized system was invented and developed by Dr. Charles Stark Draper at MIT in the early 1950s [10]. The basic idea is to mount very precise accelerometers on a gyroscopically stabilized platform (in strapped-down mode‚ such stabilization is maintained in software). By doubly integrating the accelerometer outputs and correcting for the effect of gravity, which cannot be sensed, position can be determined. This requires very accurate initial conditions (both position and velocity) as well as careful alignment with an inertial coordinate frame. The nature of double integration magnifies small sensor biases into error growth that is proportional to time or time squared, so periodic reset is essential for most applications. Draper’s inertial navigation systems were very successful and quickly became the basic navigation device for the Navy’s ballistic missile submarines. Professor Walter Wrigley has written a history of inertial navigation and said: “Notwithstanding the work of those previously discussed, the MIT Instrumentation Laboratory under Professor C. S. Draper was the main spearhead in the development of inertial navigation systems and components for aircraft, ships, missiles, and spacecraft” [11]. Professor Wrigley bases this statement on an earlier article in the American Journal of the Institute of Navigation by H. Hellman [12]. These state-of-the-art inertial navigators still required periodic updates of position and velocity to maintain the

5

6

1 Introduction, Early History, and Assuring PNT (PTA)

desired accuracy. This led to the first space-based radio navigation system‚ called Transit, which is discussed below. Modern micro-electro-mechanical systems (MEMS) which measure accelerations and rotations are now common in many applications including automobiles. Major efforts are being made to improve the accuracy and stability of these devices. A parallel development of chip-scale atomic clocks, which are both inexpensive and accurate, is also a major advance. MEMS devices and these clock technologies are discussed in Volume II.

1.3 Initial GPS Development: Key Milestones in the Early Development of Worldwide 3D satnav for PNT Figure 1.1 depicts the major events in GPS and related developments in two major segments: 1957–1983 and 1989–2020. The focus of this chapter is on the early history and development of GPS. While major events related to other GNSSs and RNSSs and future development are touched upon as well, these topics are fully addressed in later chapters.

GPS DEVELOPMENT: 1957–1983 Getting, Aerospace Corp Proposed 3D satnav system

CDMA signal structure & Gold Code

Woodford & Nakamura, US Air Force 621B study

Pentagon “Lonely Halls” meeting. GPS defined DSARC approved GPS

White Sands tests, Inverted ranges

57 58

1960

66 67

62

Transit, US Navy Guier & Weiffenbach World’s first track satellite using Doppler. satnav system Transit conceived.

First GPS satellite launched

US Air Force designated to develop Joint Navigation System

73

1970

Initial operational control system 6 satellites in space Median accuracy 7m

78 79 1980

74

President Regan formally guaranteed GPS civil signal availability

82 83

NTS-1, NRL First attempt to place First GLONASS atomic clock in space Cicada, satellite launched Experienced early radiation-induced failure USSR

Timation (quartz oscillator) Navy Research Labs (NRL)

Sputnik, USSR

RELATED DEVELOPMENT

GPS DEVELOPMENT: 1989–2020 GPS declared fully operational

First Block IIR President Clinton satellite discontinued Selective Availability broadcasting L1M, L2C, L2M signals launched

First Block IIF satellite broadcasting L5 signals launched First GPS III satellite broadcasting L1C launched

24 satellites in space 19 GPS satellites launched

89 1990

93

Began broadcasting CNAV messages

SPS PS RMS 4m SPS PS RMS 6m

95 96

GLONASS: 24 satellites in space operational

2000 01

Beidou I: limited test system

Galileo: first test satellite GIOVE-A launched

05

08

2010

12

QZSS: first satellite launched Galileo: first operational satellite launched

OTHER GNSS & RNSS DEVELOPMENT Figure 1.1 Timeline of major development in GPS, GNSS, RNSS, and related technologies.

13 14

17 18

2020

NavIC: Galileo, 7 satellites NavIC, QZSS launched operational Beidou II: 14 satellites in space Beidou III operational global operation

1.4 The Seminal System Study of Alternatives for Satellite-Based Navigation Sponsored by the Air Force and Ivan Getting

The first development occurred on 4 October 1957, when the entire world was fascinated by the launch of the Russian Sputnik satellite. The American public greeted this event with both apprehension and curiosity. In 1958, the Applied Physics Laboratory (APL) of Johns Hopkins University employed an extremely competent team of engineers and scientists. Two of those scientists, Drs. William Guier and George Weiffenbach, began to study the orbits of the new Sputnik satellites. The satellites were broadcasting a continuous tone signal, so their velocity, relative to the ground, created a Doppler shift of the signal that was unique. After some innovative work, Guier and Weiffenbach discovered they could determine the Sputnik’s orbit with a single pass of the vehicle. At that point, Frank McClure of APL made a very creative suggestion: why not turn the problem upside down? Using a known satellite position, a navigator could determine their location anywhere in the world after receiving and processing the satellite signal for 15 minutes. His insight became the basis for the Navy’s Transit satellite program, also known as the Navy Navigation Satellite System. This pioneering satellite system was developed under the leadership of Dr. Richard Kershner, head of APL (see his photo with Dr. Bradford Parkinson, who led the development of GPS in Figure 1.2). Transit’s main purpose was to provide position updates to the inertial

Table 1.2 Transit characteristics First operational prototype

1962

Operational

1964–1996

Orbit

Circular polar orbit at ~1000 km altitude in 5+ nominal orbital planes

Transmit frequencies

150 and 400 MHz to correct for ionospheric delays

Time for a position fix

~15 min

Time between fix

Periodic, ~90 min

2D accuracy

For moving ship, 200 to 500 m, needs velocity correction For stationary user, 80 m

navigators of the United States Submarine Ballistic Missile Force then being deployed. These submarines were a major deterrent during the Cold War. Transit was first tested in 1960 and by 1964 the system was operational. Although limited in scope as a 2D shipboard navigation satellite system, Transit was a major contributor to satellite navigation as the first worldwide operational navigation satellite system. Table 1.2 lists key information on Transit.

1.4 The Seminal System Study of Alternatives for Satellite-Based Navigation Sponsored by the Air Force and Ivan Getting [13]

Figure 1.2 Dr. Richard Kershner (left) who led the development of Transit. On his right is Col. Bradford Parkinson, who led the development of GPS.

New Satellite-Based Navigation Systems Proposed 1962–1970 By 1962, Dr. Ivan Getting, president of the Aerospace Corporation, saw the need for a new satellite-based navigation system. While he did not have a specific implementation, he envisioned a more accurate positioning system that would be available in 3 dimensions, 24 hours a day, 7 days a week. He had direct access to the highest levels of the Pentagon and was a tireless advocate for his vision. Getting’s energy and foresight in the early 1960s were essential to gaining Air Force support to study system alternatives. As a result, the Air Force formed a new satellite navigation program that was later named 621B. His efforts were recognized in 2003 when he shared the Charles Stark Draper Prize of the National Academy of Engineering (known as the “Engineer’s Nobel”) with Dr. Bradford Parkinson.

7

8

1 Introduction, Early History, and Assuring PNT (PTA)

By 1962, engineers at Aerospace, under Air Force sponsorship, were heavily immersed in studying the system alternatives for a new navigational satellite system. From 1964 to 1966, the Air Force directed Aerospace to perform an extensive, formal system study whose principal authors were James Woodford and Hiroshi Nakamura, both highly regarded space-systems engineers. The Woodford/Nakamura study was summarized as a DoD (Department of Defense) secret briefing in August 1966. As a result of the classification, it was unavailable to anyone outside the project until 13 years later in 1979, when it was finally declassified. Figure 1.3 shows the front page of the GPS system study.

USAF/621B 1964 Study of 12 Alternative GNSS Architectures

Competing NRL proposal–User required an atomic clock

2 12

GPS selected the most Challenging of 12 Alternatives – 4D Position with no user need for an atomic clock (Demonstrated by USAF 621B– 1971)

Figure 1.4 Key summary of alternatives for satellite-based navigation systems. The USAF Program Office selected the 12th alternative. The competing Naval Research Laboratory (NRL) proposal (Option #2) was two-dimensional and relied on an atomic clock at the user’s station.

Figure 1.3 Front page of the seminal GPS system study performed from 1964 to 1966 by USAF 621B program. Originally classified SECRET, it was declassified after the initial GPS constellation had been launched. This was the essential foundation for the GPS design concept.

with “X.” “A” shows that the user needs an atomic clock. “X” shows the user needs only a crystal clock. The option that was later selected for GPS is #12, designated with the green box. This technique is the 3 Δρ (four satellites) that eliminated the need for the user’s atomic clock and provided three-dimensional positioning (really fourdimensional since it also captured time). This technique is illustrated in Figure 1.5 (taken from [14]).

1.4.1 This report was a very complete system study that examined the following topics:

• • •

Capabilities and limitations of then current DoD navigation systems. Tactical applications and utility of improved positioning accuracy. Comprehensive analysis of alternative system configurations and techniques for positioning using satellites.

Since the full survey of alternative system configurations was extremely important in selecting an optimum system configuration for GPS, we reproduce the summarizing figure in Figure 1.4. Twelve major alternatives were studied. Note that the “COMPUTATION PERFORMED BY USER” is split into two columns. The reader should focus on the columns of the 1-WAY passive ranging techniques with the red outline. These alternatives can have an unlimited number of users – i.e. there is no system constraint. In this column, there are two “user boxes,” one with “A” and one

The 621B Era – Additional USAF Studies

From 1966 to 1972, program 621B continued with trade-off studies including signal modulation, user data processing techniques, orbital configuration, orbital prediction, receiver accuracy, error analysis, system cost, and comprehensive estimates of the tactical mission benefits. In late 1968, the Air Force’s NavSat program in the Plans Office (XR) at the Space and Missile Systems Organization (SAMSO) in Los Angeles was re-designated as 621B. All of the various proposals that went forward from SAMSO to Headquarters came henceforth from the 621B office in XR. Over 90 NavSat reports completed by USAF/Aerospace during this period were filed in the Aerospace Corporation library.

1.4.2 The Code Division Multiple Access (CDMA) or PRN Signal Structure Of these studies, the most important were those aimed at selecting the best passive ranging technique for the navigation signal. By 1967, it appeared that the best method was

1.4 The Seminal System Study of Alternatives for Satellite-Based Navigation Sponsored by the Air Force and Ivan Getting

(x|, y|, z|) R|

RN

R1 b + (x, y, z)

Measurements: Pseudoranges {R|} Given: Satellite positions {(x|, y|, z|)} Ri =

(x| – x)2 + (y| – y)2+ (z| – z)2 – b i = 1, 2,...., N

Unknown: User Position (x, y, z) Receiver clock Bias b

Figure 1.5 Illustration of the principle of satellite navigation (from [14]). The user-satellite ranging measurements are based on the times of transmission and receipt of signals. They are biased by a common time offset and are called pseudoranges. Four pseudoranges are required. Source: Reproduced with permission of Ganga-Jamuna Press.

pseudorandom noise because the encoded (but repeated) sequence appears to be random transitions of +1 and −1. It is called Code Division because each satellite is assigned its own coded signal. Each was a binary (digital) sequence selected to be uncorrelated with other signals and also uncorrelated with time shifts of the signal itself. The expected, powerful advantage of this technique was that all satellites would broadcast on exactly the same frequency. It was clear that it would lend itself to digital signal processing. Furthermore, and very importantly, any time shifts induced by the receiver for the various satellite signals would be identical and effectively eliminated. However, there were still a number of significant questions concerning CDMA that needed to be resolved. These included the following:

Figure 1.6 Dr. James Spilker Jr., one of the creative engineers who led development of the GPS digital signal structure.

a variation of a new communications modulation known as CDMA. Pioneering this signal were several outstanding scientists and engineers, including Dr. James Spilker (Figure 1.6) and Dr. Fran Natali (both of Stanford Telecom), as well as Dr. Charlie Cahn and Bert Glaser (both of Magnavox). This signal has many names. In addition to CDMA, it is sometimes called “spread spectrum” or “spreading code” since the energy of the signal was spread over a wide range of spectrum frequencies. It is also sometimes called PRN or

1) Could such a signal be easily acquired in the face of time uncertainty and Doppler shifts? 2) Was there a technique to encrypt the military signal so that unauthorized users could not gain access? 3) How would the codes be easily selected to avoid a false lock and also allow additional satellites to be added without interfering with existing satellite signals? 4) Would the anticipated complexity of the receiver drive costs to unacceptable levels? 5) Was the signal resistant to accidental or deliberate interference? 6) Could this signal accommodate communication capability for satellite location, satellite clock correction, and other parameters? Fortunately, in 1967, a technique for selecting orthogonal codes was invented by an accomplished applied

9

10

1 Introduction, Early History, and Assuring PNT (PTA)

mathematician, Dr. Robert Gold of the Magnavox Corp. Naturally these are now known as the Gold codes, and they partially resolved the third CDMA issue stated above. But that was not the whole story.

1.4.3 The White Sands Missile Range Tests and Confirmation 1970–1972 To address the remaining problems, the USAF 621B program developed two prototype versions of CDMA navigation receivers (Magnavox and Hazeltine) for testing at the White Sands Missile Range (WSMR). For the tests, 621B arranged four transmitters in a configuration known as the Inverted Range. These transmitters broadcast CDMA signals from locations that were geometrically similar to a satellite configuration except that they were broadcast from the ground, i.e. “upside down.” By 1972, program 621B had successfully proven the effectiveness and accuracy of the CDMA signal by demonstrating that such a configuration would achieve 5 m, three-dimensional navigational accuracy. These test results answered most of the remaining questions regarding the CDMA signal. The tests confirmed the enormous technical value of the modulated signal by showing that all satellite signals could, indeed, be received simultaneously on the same frequency. These tests also corroborated the expectation that ranging to four satellites eliminated the need for a highly precise user atomic clock, while still supporting full, threedimensional navigation. This became an extremely important feature of GPS. If each user had required an atomicclock-class frequency standard, no inexpensive user equipment could have been produced within the technology horizon visible at that time. This is still true today. All this evidence supported CDMA as the passive ranging signal of choice and was available to the Air Force’s 621B team when the system configuration was selected at the September 1973 meeting that will be discussed later.

1.4.4 Distinguishing Between the 621B Demo Configuration and the 621B Preferred Operational Configuration From the time of the 1966 Woodford/Nakamura study on, the Air Force and Aerospace advocated the use of atomic clocks in the operational satellites with the modulation also originating in the satellites. There were two significant risks to placing atomic clocks on the satellites: first, the technology readiness risk (no radiation-hardened atomic clocks had ever been designed and flown), and second, the political and budgeting risk associated with gaining approval for a development/demonstration program of the full

capability. To reduce both of these risks, the Air Force had developed a plan. This included a proposal in early 1972 to deploy a foursatellite “demonstration system.” This proposal addressed both risks. It would reduce the technological readiness risk in the clocks by launching simple L-band transponders. The navigation signal would be generated on the ground and transponded to users with a “bent-pipe” in the satellite. At the same time, it would save substantial money, thereby reducing the political and budgeting risk. In many circles, this proposal was erroneously thought of as the 621B operational proposal because it came from that office. In fact, the operational concept for 621B never contemplated or advocated using transponders in the final operational system. The use of transponders had been rejected for the operational system because they could be easily jammed from the ground. Such a jamming signal would overpower the transponder and steer all of the transmitted energy away from the transponded navigational signal. This enemy jamming would shut down the entire system, clearly an unacceptable risk. 621B Proposed Initial Satellite Constellation To demonstrate four-satellite, passive ranging capability, 621B had studied a number of orbital configurations, including geosynchronous and inclined, lower orbits. They proposed placing a constellation of four synchronous satellites in orbits over the United States. This array would allow extended periods of four-satellite testing without committing to a full global employment. If this demonstration were successful, the next step would have been to add three more longitudinal sectors, each with its own array. Again, the principal redeeming feature of this approach was that there was some hope of it being funded. The Air Force in the Pentagon was placing enormous pressure on the 621B program to come up with the absolutely cheapest way to demonstrate the four-satellite approach. In addition, they wanted any initial configuration to provide the beginning of a full global system. This proposed constellation design was a reasonable compromise, given the boundary conditions of a foursatellite demonstration and absolutely minimal cost. It is interesting that the Japanese, with a requirement to supplement GPS with satellite signals to improve coverage in urban areas (where there are high shading angles), have been deploying a very similar constellation. The Japanese configuration is intended to improve coverage restricted to their longitudinal sector of the globe. The new system is called Quasi-Zenith Satellite System (QZSS), and the Japanese have announced the four-satellite constellation is now operational (2018) [15]. The system is further described in Chapter 8.

1.5 Competition, Parkinson Appointed Program Director, the Encounter with Dr. Currie, the “Lonely Halls” meeting, and GPS Approved

1.5 Competition, Parkinson Appointed Program Director, the Encounter with Dr. Currie, the “Lonely Halls” meeting, and GPS Approved 1.5.1

NRL and the Timation Satellite

In 1964, the US Navy initiated a second Navy Navigation and Timing satellite program, called Timation, under the direction of Roger L. Easton Sr., a longtime member of the NRL staff. The NRL’s Timation project was aimed at exploring techniques for passive ranging to satellites as well as time transfer between various timing centers around the world. It subsequently developed a number of experimental satellites, the first of which was called Timation 1. This was a small satellite, weighing 85 pounds and producing 6 W of power. It was launched on 30 May 1967 (Figure 1.7). The key feature of Timation 1 was that it included a very stable quartz clock. The fundamental ranging technique was to synchronize a clock at the user’s location with the clock on the satellite and use a passive ranging signal structure called Side Tone Ranging. By 1968, NRL demonstrated single-satellite position fixes, accurate to about 0.3 nautical miles, that required about 15 minutes of measurements. NRL engineers encountered two significant problems during their testing. First, solar radiation caused shifts in the satellite clock’s frequency, and, second, the ionospheric group delay created ranging errors. A second Timation satellite, called Timation II, was developed and launched into a 500 nautical mile orbit on 30 September 1969. To calibrate the ionospheric group delay, the satellite broadcast on two frequencies: the same technique pioneered by the Transit program. Its quartz

Figure 1.7

The Navy’s Timation satellite included a quartz clock.

oscillator was expected to be somewhat more stable – about 1 part in 1011. Again, a large frequency shift observed in the clocks was finally traced to a solar proton storm. NRL was able to demonstrate ranging accuracies of approximately 200 feet to a fixed location with dual frequency and extended measurement times.

1.5.2

Competition

By 1972 some authorities in the Pentagon had already recognized that a new satellite-based navigation system would be valuable. There were literally hundreds of different positioning and navigation systems currently used by the DoD that were expensive to maintain and upgrade. Obviously, a single replacement system offered significant cost savings. Understandably, the two competing concepts (621B and NRL) apparently confused the decision-makers and led to a very acrimonious competition. As a result of the competition and a reluctance to commit the necessary monies, any decision was delayed. In November 1972, Col. Bradford Parkinson was the Director of Engineering for the Advanced Ballistic ReEntry Systems Program (ABRES) at SAMSO. Brig. Gen. William Dunn, who led the advance planning group (XR), identified Col. Parkinson as a potential candidate to head the floundering 621B program. At Dunn’s behest, Lt. Gen. Kenneth Schultz, commander of SAMSO, asked Parkinson if he would like to be assigned to the 621B program. Col. Parkinson had a very relevant background in navigation, guidance, and control that included a PhD from Stanford in Astronautics. The background was a match, but Parkinson expressed an unwillingness to volunteer for the assignment without assurance that he would be the Program Director. At that point, General Schultz said he could not make that promise, but, immediately after Parkinson left his office the General reassigned him to the 621B program and effectively made him the Director. Beginning in December 1972, Col. Parkinson, immediately after he assumed control of 621B, instituted a series of 7 a.m. educational meetings. At these gatherings, the program re-examined every aspect of the proposed 621B program, including alternatives. This educational process was key to having everyone in the Program Office completely understand the technical issues they faced. During this period, Gen. Schultz supported the program in every way that he could. In particular, Parkinson was allowed to recruit Air Force officers whose background and experience were aligned with the needs of the fledgling program. All had advanced engineering degrees from the very best universities in the country including MIT, Michigan, and Stanford. In addition, virtually every officer had experience in developing hardware or in testing inertial

11

12

1 Introduction, Early History, and Assuring PNT (PTA)

Figure 1.8 Major Gaylord Green. His creativity on modified orbits ensured the success of GPS. Figure 1.9 Dr. Malcolm Currie. His support was essential to GPS approval.

guidance systems. The first officer Col. Parkinson brought aboard was Air Force Major Gaylord Green (Figure 1.8), who had worked for him on ABRES. Maj. Green’s creativity, focused on satellites and orbits, had an extremely important impact on the success of GPS. The result of Parkinson’s hunting license was a cadre of about 25 of the best and brightest people that the Air Force had to offer. Many names and photos of these and other “GPS heroes” can be found in the GPS World magazine article “The Origins of GPS” in the issues of May and June 2010. In addition, there was a small, hand-selected group of Aerospace technical support personnel led by Walter Melton. This fine group of engineers and scientists was experienced in all technical aspects of Space Navigation Programs and particularly skilled at issues relating to signal modulation, satellite position prediction, and building long-life satellites. The Aerospace contingent continued to enjoy the strong support of the president of the Aerospace Corporation, Ivan Getting. During early spring of 1973, the newly appointed Director of Defense Research and Engineering (DDRE), Dr. Malcolm Currie, formerly of Hughes Aircraft, would fly round-trip to Los Angeles from Washington, D.C., on most weekends (Figure 1.9). His secondary purpose was to oversee the relocation of his family, but he needed an “official” reason to travel to Los Angeles. So, each Friday afternoon he would visit SAMSO in Los Angeles for a presentation. After a few weekends, Gen. Schultz, his host, ran out of subjects to present and instead invited Dr. Currie to spend an afternoon with his new program director, Col. Parkinson.

Gen. Schultz’s invitation resulted in an astonishing meeting because a newly promoted colonel does not usually have the opportunity to confer with the number three person in the DoD over an uninterrupted three- or four-hour period. This informal one-on-one meeting was held in private, in a very small cubicle within Parkinson’s Program’s offices. Currie, with his PhD in physics, was a very quick study, so the interaction was lively and deep, delving into every aspect of the 621B proposal. After that meeting, Dr. Currie became a good friend to and a sponsor of the new satellite-based navigation program. He later played a critical role in ensuring DoD support for GPS, especially, during the Air Force’s subsequent attempts to cancel the infant program. On 17 April 1973, the Deputy Secretary of Defense issued a memorandum which designated the Air Force as the executive service in an effort to develop a Joint Service navigation system. This would build on the technological achievements of the predecessor Air Force and Navy programs, and also incorporate the position/navigation requirements of the US Army and Defense Mapping Agency (DMA). The Navstar Joint Program Office (JPO), still located at SAMSO in El Segundo, California, was the first Joint Services Development Program. In addition to the US Air Force Program Manager, the JPO initially included Deputy Program Managers representing the Army, Navy, Marine Corps, and the DMA. DSARC 1 and Failure On 17 August 1973, Parkinson was invited to the Defense Systems Acquisition Review

1.5 Competition, Parkinson Appointed Program Director, the Encounter with Dr. Currie, the “Lonely Halls” meeting, and GPS Approved

Council meeting to make a presentation on 621B. The meeting’s purpose was to determine whether to proceed with the concept demonstration program. It was held in the Pentagon, and attended by general officers of all services, with Dr. Currie presiding. At the meeting’s conclusion, the Council voted against approving the 612B program. Dr. Currie immediately invited Parkinson into his private office and told him he wanted Parkinson to develop a new system proposal that would incorporate the best features of all the technical alternatives. He emphasized the need for a joint program involving all services. Regrouping: The “Lonely Halls” of the Pentagon Meeting Parkinson immediately called a meeting in the Pentagon over Labor Day weekend in September 1973. The purpose of the meeting was to define modifications to the 621B proposal that would meet Dr. Currie’s directive. Parkinson wanted the 2500-mile isolation (from his home base) to ensure unfettered creativity in defining the new proposal. Leading up to this, an updated systems study had been performed by The Analytical Sciences Corporation (TASC) under the guidance of (then USAF Major) Gaylord Green. This study was a review and update of the earlier systems study directed by Jim Woodford and H. Nakamura for project 621B in 1964–1966. Over that weekend, the world’s largest office building seemed to be a series of poorly lit, uninhabited tunnels because almost everyone was away on holiday. The light at end of those tunnels, both figuratively and literally, was in a small conference room, on the top floor, D-ring, seating about a dozen attendees. All were Air Force officer/ engineers from Parkinson’s Los Angeles Office except for three Aerospace Corporation engineers. Lt. Col Steve Gilbert (USAF Deputy), Captain Robert Rennard (the Deputy Chief Systems Engineer), and Major Gaylord Green (Satellite Project Manager) were essential contributors to the discussion and definition of GPS. After Parkinson’s team had completed the modified design, they met with NRL officials to disclose the result and request that NRL continue their clock development under his program office, which they agreed to do.

1.5.3

Definition and Design of GPS

After much intense discussion over that weekend, the Parkinson-led team defined GPS with the following 10 facets: 1) The fundamental USAF 621B concept of simultaneous passive ranging to four satellites would be the underlying principle of the new system proposal, ensuring that user equipment would not require a synchronized atomic clock.

2) The signal structure would be the 621B CDMA modulation (also called pseudorandom noise or spread spectrum). It would include a clear (i.e. unencrypted) acquisition modulation (C/A) and a precision military modulation (P/Y). The C/A modulation was to be freely available to civil users throughout the world. 3) There would be two GPS broadcast frequencies in the L band using the same dual frequency technique that Transit had employed to correct for the ionospheric group delay as well as provide redundancy. The use of L-band signals instead of Transit’s UHF substantially reduces the ionosphere group delay, which is inversely proportional to the square of frequency. 4) Based on the progress that NRL had made in satellite clocks, the program would commit to space-hardened atomic clocks on the first operational/demonstration GPS satellites (called Navigation Development Satellites–NDS). At the “Lonely Halls” meeting, Parkinson had concluded that the NRL technology was relatively low risk, obviating the need to use the ground-relay, experimental demonstration scheme that 621B had previously proposed. It later turned out that the NRL development was not as mature as it appeared, but the USAF/JPO backup clocks (by Rockwell) were available in time for the first launches. 5) The nominal constellation would be 24 satellites in three rings of eight each. The orbits for the satellites were to be circular and inclined at 62 and not geosynchronous. NRL had advocated similar 8- or 12-hour inclined orbits. Because of the need for an extensive testing program on an instrumented range, exact 8or 12-hour orbits would have been unsatisfactory, because those orbits would continuously shift relative to Earth. Instead Green proposed 11 hour 58 minute (sidereal synchronous) orbits that gave about two hours of testing over the same United States test area each day. While these orbits resembled those advocated by NRL, Green’s modification was critical to the success of the testing program. The corresponding high altitude for these 11h 58m orbits (approximately 20,200 km) helped minimize the number of satellites that were needed for Earth coverage. It also was the maximum altitude that the selected booster could achieve with the expected mass of the first-generation satellites. 6) Orbit prediction would be handled with modifications to the Transit-developed orbit-prediction programs called Celeste. 7) The initial test constellation would include four operational satellites, competitively procured, one of

13

14

1 Introduction, Early History, and Assuring PNT (PTA)

which would be a refurbished Qualification Model. They would be launched on refurbished Atlas-Fs, which were retired intercontinental ballistic missiles (ICBMs), to minimize cost, although they limited the number of solar panels that could be carried because of weight. As a result of that power limitation, the second frequency signal to calibrate the ionosphere could not be transmitted with both the civilian and the military modulations at once. There was a switch allowing either to be selected, but the second civilian signal was seldom turned on. 8) A family of user equipment prototypes would be procured competitively. This equipment would span all normal military uses, and also include a low-cost set that would prototype civilian use. Where they were affordable, competitive contracts would be used. Particular attention would be devoted to user equipment integration with inertial navigation units and demonstration of anti-jam capabilities. 9) The master control/upload station and its backup would be on United States soil with monitor stations located all around the world. 10) The testing would be principally performed at the US Army’s Yuma test range with accuracy measured from a trilateration laser configuration. Using three laser ranging devices at the same time would ensure that all test vehicles could be measured to about a meter of positioning error in three dimensions. It was expected (and later proved) that this technique could even precisely locate an Air Force or Navy fighter aircraft flying close to Mach 1. Testing would make use of the inverted range concept with satellites replacing each range transmitter as each newly launched GPS satellite became operational on orbit. This technique allowed the tests to begin with the first orbiting satellite in 1978 (and three pseudolites on the desert floor at Yuma). GPS Made Available to Both Military and Civilian from the Beginning Contrary to some inaccurate versions of history, from the very beginning, GPS was configured to be a “dual-use” system. Civilian users were to be given full access to the C/A signal for PVT.2 To enable widespread civil use, the detailed code structure was published as a specification document and freely distributed worldwide. (The interesting consequence was that the first civil receiver to lock onto the first GPS satellite was developed by students at the University of Leeds in England in 1978.) 2 The inherent accuracy was expected to be about 10 times worse than the military signal, but innovative techniques (e.g. the Hatch/ Eschenbach filter), developed by civil contractors, very quickly demonstrated about the same accuracy.

1.6

GPS Approval – December 1973

That Labor Day weekend of September 1973 had been a very busy three days. With help from the Air Staff Program Element Monitor (PEM), Lt. Col. Paul Martin, the “Lonely Halls” gathering developed a seven-page Decision Coordinating Paper (DCP) and a presentation of the new concept. Over the next two and a half months‚ there was a flurry of activity as Col. Parkinson made presentations and defended the concept before all those who could block the proposal in the Pentagon. This effort culminated with Parkinson’s second presentation to the DSARC. He was given approval to proceed on 14 December 1973. There were no significant modifications to the proposal that had been developed during the “Lonely Halls” meeting in the Pentagon. Parkinson, during the whole Phase I development, resolved to avoid any conflict with the other original competitors to build a satellite-based navigation system. He deliberately ignored claims of invention and statements regarding the origins of technology. He felt the real purpose was to build the system, not to reopen the earlier fight. His silence may have precipitated a recent article that suggested the Air Force and JPO provided nothing in terms of technology and system concept. Aware that this was a false statement and denigrated the people who had first analyzed, advocated, and demonstrated the fundamental concept, as well as built the system, he resolved to correct the record. The list of corroborators for this history includes virtually all of the major Phase I development leaders who are still alive. See coauthors of the previously mentioned, May 2010 GPS World article on GPS origins.

1.7 The Three Essential GPS Innovations and Their Sources The 10 points described above provide an outline of the GPS design. A more complete technical description of GPS and other satnavs will be provided in later chapters. However, there were three key innovations in the fundamental design that deserve elaboration. These have withstood the test of time – all non-US satnavs have now adopted the same three GPS innovations.3

3 The Russian GNSS system called GLONASS has finally accepted the value of CDMA, and announced that the latest series of their satellites will include a CDMA signal.

1.7 The Three Essential GPS Innovations and Their Sources

1.7.1 Innovation #1: The CDMA Signal and Selection of Frequencies, Verified in the White Sands Test – This Enabled Centimeter Accuracy The most significant innovation of GPS may be the CDMAbased passive ranging signal technique. There are three reasons that support this bold statement. First, this choice allowed all signals to be broadcast on exactly the same frequency, eliminating all inter-frequency biases that could occur in a multi-frequency technique, such as that advocated in competing designs. Second, the CDMA spreading codes enabled a signal processing technique with a processing gain, which gave substantial resistance to interference, whether it came from natural sources or was deliberate. Third, the particular implementation chosen dictated phase coherence among the code, the carrier, and the data [16]. This led to the unprecedented accuracy in the radio navigation ranging measurement. By reconstructing the L-band carrier, the receiver could perform measurements with accuracy better than a millimeter. This corresponded to measuring radio signal arrivals with a timing precision of about 1% of 1 ns. A noteworthy use for this precision and accuracy is the direct measurement of tectonic plate motion in three dimensions, to fractions of a millimeter. Later chapters will describe this application in greater detail. The Russian GLONASS has operated without CDMA thus far. It uses different frequencies on different satellites in view, and the identical PRN code on all satellites. This PRN code allows it to achieve the necessary processing gain. And, with differential techniques, GLONASS provides accuracy approaching GPS. The frequency division does give an added measure of robustness to narrow band interference, but the overall argument of the relative benefits of CDMA has been settled with the Russian decision to use single-frequency CDMA in the modernized GLONASS system now under development. While the fundamental decision to select CDMA had been made during the “Lonely Halls” meeting, a vast number of details had yet to be worked out. Perhaps the most important detail was the decision that the carrier, code, and data of the GPS signal would all be phase coherent, as mentioned. Dr. James Spilker‚ who had also written a

seminal reference book on digital satellite communications [17], was an author of a key initial study and developed a near-optimal method of locking the GPS user’s receiver to satellite signals [18, 19]. Dr. Charles Cahn, Nat Fran Natali, Burt Glazer, Ed Martin, and Dr. Robert Gold, a consultant to Magnavox‚ all made significant contributions. The Gold-developed theory guaranteeing code orthogonality assumed no Doppler shifts between signals, but that clearly was not the case. This is due to both satellite orbital motion and the velocity of the user (including Earth’s rotation). Selection of the optimal code length (in the face of these Doppler shifts) required extensive computer simulation at a time when existing computers were quite puny compared to the current capability. This problem was pointed out and solved by Dr. James Spilker. The selection of the optimal Gold code length was shown to be 1023 (considering the limitations of the user’s digital electronics in 1973). A summary of the key trade-off is shown in Table 1.3, developed by Dr. Spilker. The optimum (lowest probability) is circled in red. On each of the two carrier frequencies, called L1 and L2, two different signals, named C/A (Clear Acquisition) and P/Y (Precise Military), were modulated in phase quadrature. As mentioned earlier, the C/A signal on L1 was freely available for civil use as well as for acquiring the military signal. Again, these dual frequencies enabled a direct measurement of the ionospheric group delay for correction of the ranging signal. The civil L2 signal was seldom available due to power restrictions on the first family of GPS satellites. The latest generations of GPS satellites not only broadcast the civil L2C signal, but also the new L5 civil signal in a fully-protected radio authorization band. The data message was integrated into both signals through inversion of their codes every 20 ms. The data stream, therefore, came down at 50 bits per second. Through this tiny pipe of information all the precision data for GPS had to pass. It included the space vehicle orbit position information (ephemerides), system time, space vehicle clock prediction data, transmitter status information, and C/A signal handover time for P/Y code acquisition. Also, as a part of the message, ionospheric propagation delay models were

Table 1.3 Key trade-off figures for three different Gold code lengths Code Length Parameters

511

1023

2047

Peak cross-correlation (any Doppler shift) (dB)

−18.6

−21.6

−24.6

Peak cross-correlation (zero Doppler shift) (dB)

−23.8

−23.6

−29.8

0.5

0.25

0.5

Probability of near-worst-case cross-correlation (zero Doppler)

15

16

1 Introduction, Early History, and Assuring PNT (PTA) Carrier at 1575.42 MHz (L1) 1227.60 MHz (L2)

19 cm (L1)

Code at 1.023 Mcps (C/A) 10.23 Mcps (P(Y))

300 m (CA)

Navigation data at 50 bps

6000 km

Figure 1.10 GPS signals were designed to be all phase-aligned as transmitted (i.e. coherent) [14]. Source: Reproduced with permission of Ganga-Jamuna Press.

incorporated for the single-frequency user. In addition, to aid the rapid acquisition of new satellites just rising over the horizon, the ephemerides of all other satellites in the whole constellation had to be included. Each digital word had to be defined in terms of scaling, bias offset, and precision in terms of the number of bits transmitted. About 95% of the GPS message has endured with no changes needed at all. In a few cases, because the newer user equipment is more accurate, greater precision is desirable (i.e. more bits). It is a great tribute to the dedicated engineers and scientists, who designed the signal structure in 1975 that it has endured for over 45 years with so little need for modification (Figure 1.10).

1.7.2 Innovation #2: Four-Satellite Instantaneous Measurement, Allowing Inexpensive User Receivers to Solve for Three Dimensions of Position Plus Time The genesis of the four-satellite concept was clearly the USAF/621B Woodford/Nakamura study of 1964 to 1966. The use of four satellites for four-dimensional positioning had been confirmed by the previously described tests that were run by program USAF/621B at the WSMR with the help of Joe Clifford, Bill Fees, and Larry Hagerman, all from the Aerospace Corporation. This enabled inexpensive user receivers without resorting to expensive user atomic clocks.

1.7.3 Innovation #3: Space-Hardened, Long-Life (Space-Based) Atomic Clocks to Allow Long Periods of Satellite Autonomy without Significant Inaccuracy In 1966, both the Air Force and the Navy recognized that developing a precise, stable time base for generating the

one-way (passive) navigation ranging signal in the satellite would be extremely useful. To use GPS required knowledge of the satellites’ location and system time to nanoseconds. With very stable clocks, position and time could be predicted for periods of 12 hours or more with only a small growth in ranging errors. This prediction could be uploaded to each satellite for future use without the need for continuous satellite uploads. An obvious choice to ensure timing stability was a spaceborne atomic clock. Cesium atomic clocks had been invented, demonstrated, and offered for commercial sale by the middle of the 1950s, well before the space age. Unfortunately for satellite applications, they tended to be bulky, power hungry, and not hardened against space radiation. Particularly challenging, the orbits for GPS were to be in the upper Van Allen belt, which is an extremely intense radiation zone and required special hardening of the clocks. An unshielded human would receive a lethal dose in less than 10 seconds. For laboratory use, a new clock based on the rubidium atom was commercially being developed that was much smaller and drew less power. Because this development was for ground-based civilian use, it did not contemplate launch vibration, radiation hardening, or the extreme temperature variations encountered in space. The USAF Woodford/Nakamura study advocated a technology program to space-harden the existing clock technology, but it was not pursued by the Air Force at that time. However, the NRL did institute a program in 1964 with a series of satellites that have already been mentioned. The first Timation satellite, launched in May 1967, carried a quartz clock, but the temperature-induced variations in frequency were unacceptable. The second Timation satellite also contained a quartz clock, as well as a temperature controller and showed improved operation, but the results were still far short of operational requirements. This last satellite in the original Timation series was launched in July 1974. By that time the Timation program had been placed under the GPS JPO in Los Angeles, reporting through the JPO Navy Deputy, Cdr. William Huston, to the Program Director Col. Bradford Parkinson. The JPO had renamed the satellite as Navigation Technology Satellite4 (NTS-1). The gross weight had been increased to 650 pounds with a power requirement of 125 watts. Developed by Peter Wilhelm of NRL, this satellite was 4 The NTS satellites were strictly technology-testing satellites. For many reasons‚ they had no role in the development of the operational satellites by the JPO and Rockwell. The latter were operational satellites and were called NDS satellites (Navigation Development Satellites). They were the only ones used in the operational testing during Phase I of GPS.

1.7 The Three Essential GPS Innovations and Their Sources

Figure 1.11 NTS-I included first, but unhardened, cesium clocks. Space-qualified cesium clocks were not successful until the fifth GPS operational satellite. Source: https://www.nrl.navy.mil/news/ releases/first-gps-navstar-satellite-goes-display. Reproduced with permission of U.S. Naval Research.

placed at an orbital altitude of 7500 nautical miles (Figure 1.11). The renamed NTS-1 included two small, lightweight rubidium oscillators as clocks. A German commercial company called Efratom had independently developed these models. Amazing at the time, they consumed only about 13 watts of power and weighed some four pounds each. Efratom will be further discussed later. While NRL made some electronic modifications, the clocks were unable to withstand the radiation of the GPS orbits. Because of this, the NTS-1 clocks could not be used as prototypes for the operational GPS satellites. Tests run at NRL also showed that the modified rubidium clocks had an unacceptable level of sensitivity to temperature variations. Al Bartholemew of the NRL later wrote “the lack of attitude stabilization system on NTS-1 resulted in large temperature variations which ultimately masked any quantitative evaluation of Rubidium standard performance” [20]. This apparently occurred because the satellite used a two-axis gravity gradient stabilization system that did not function well at these altitudes. Later, NRL developed their last satellite (NTS-II) for the GPS Program Office. The vehicle included two modified cesium beam oscillators developed by Frequency and Time Systems Inc. (FTS) of Danvers, Massachusetts. The key clock developer was the engineer and creative entrepreneur, Robert Kern. This clock showed great initial promise, but it was not yet a space prototype in terms of radiation hardening and parts life. In addition, the USAF/JPO

provided a Rockwell-developed Navigation Payload for NTS-II that the JPO had developed for the operational GPS satellites. This would enable the NRL satellite to broadcast the GPS CDMA signal and participate in the initial GPS test constellation. NTS-II was launched on 23 June 1977 from Vandenberg AFB. Unfortunately, the NRL ranging transmitter in NTSII failed, rendering the NRL satellite unusable for the Yuma Proving Ground testing. “Of the two experimental Cesium standards carried on NTS-II,” Ron Beard wrote, “one experienced a power supply failure after a period of satisfactory operation.” The other cesium clock continued to operate for over a year, but quantitative drift rates on orbit were never available. As a result of these failures, these cesium clock tests were inconclusive [21]. Only tests with the first four JPO/Rockwell (NDS) satellites were available to support the full-scale GPS development approval on 5 June 1979. For the next step, NRL defined a radiation hardening program and then contracted with FTS to develop a hardened cesium clock. This new clock was flown on the fourth operational GPS satellite (NDS 4, launched 10 December 1978). Unfortunately, the clock also suffered a premature failure of the power supply after only 12 hours of operation. FTS soon found the root cause and fixed the design. Beginning with NDS 5, the on-board cesium clocks performed as well or better than the rubidium clocks. Based on the progress that NRL had made, the JPO, during the 1973 “Lonely Halls” meeting, had earlier decided to commit to atomic clocks in the first operational GPS satellites. Ironically, it was only the backup clocks independently developed by the JPO/Rockwell that were operational on the initial NDS satellites. First Operational GPS Clocks The operational GPS space-based rubidium atomic clock technology was derived from a unit produced by Efratom, the same German company that had originally worked with NRL. This breakthrough laboratory device was designed by two brilliant German Engineers, Ernst Jechart and Gerhard Huebner. By the summer of 1974, the JPO selected Rockwell International to build the GPS operational satellites, including a separate development of space-hardened rubidium clocks as a backup to the NRL cesium clock effort in case the NRL effort faltered. Hugo Fruehauf of Rockwell had independently discovered and directly contacted Efratom, and his interaction with Efratom was totally independent of that of the NRL. In addition, Fruehauf’s relationship with Efratom was simplified because of his fluency in German, since Jechart was not an English speaker. A summary of the early clock program is shown in Table 1.4. In spite of NRL’s development difficulties, GPS users owe a debt to NRL for pursuit of this technology. It

17

18

1 Introduction, Early History, and Assuring PNT (PTA)

Table 1.4 Satellite navigation clock history to GPS # of Sats / Nav Method

Nav Dim

Clocks

Ops Status

1964 to ~1990 1967 and 1969 Launch July 1974

(7) Sats; Doppler meas. (2) Sats; Ranging tones (1) Sat; Hazeltine 621B Transm., No Data; Ranging tones

2D

(1) Quartz oscillator

Was fully operational

2D

(1) Quartz oscillator

Experimental

2D

(2) Efratom Com’l Rb’s, modified by NRL to perform in space, +(1) Quartz

Experimental: (1) Rb operated for more than one year; (1) Rb failed early

NTS-2; (Navy-NRL); USAF/JPO provided Nav. payload

Launch July 1977

(1) Sat; ITT Engg. PRN Nav. Pkg. from USAF-JPO; + Ranging tones

2D

(2) Proto space qualified FTS Cs + (2) Quartz oscillators

Although intended to be part of the initial (4) Satellite nav. testing, NTS-2 failed before nav. testing began

GPS Operational Prototypes, awarded to Rockwell in 1974 by USAF-JPO, now “GPS Wing”; named GPS in Dec 1973; DNSDPa during early proposal effort

Devlpmt. 1973-75; Rockwell Block-I launches began Feb. 1978

(4) Sats, Production ITT PRN Nav. Pkg

3D

(3) RI-Efratom Rb’s on the 1st (3) GPS Sats; 4th Sat & up, (3) RI-Efratom Rb’s + (1) 2nd gen. FTS Csb. 1st Cs on GPS 4 failed after 12 hrs; Cs ok - GPS-5 & up

GPS Constellation of (4) Rockwell Block-I GPS Satellites for the initial Navigation Test Program +(1) NRL NTS-2 Sat, but failed before nav. testing began (see above)

Program / (Service)

Dates

NNSS (Transit); (Navy-JHU/APL) Timation I & II; (Navy- NRL) Navigation Technology Satellite-1 (NTS-1) (Navy- NRL)

a

Defense Navigation Satellite Development Program. Later, Block-II and -IIA, flew (2) Rb and (2) Cs. Source: From B. W. Parkinson and S. T. Powers, The origins of GPS, Fighting to Survive, Part 2, Figure 3, GPS World, June 1, 2010. Reproduced with permission of GPS World.

b

was NRL’s apparent progress in developing atomic clocks that induced the JPO’s critical decision at the “Lonely Halls” meeting to depend on atomic clocks from the beginning. The support of Ron Beard of NRL in this joint effort has been invaluable to the program over many years. Over 450 atomic frequency standards have now flown in space. By far the greatest user has been GPS.

1.8 The GPS Development Process and Additional Major Challenges The GPS Phase I program formal approval on 22 December 1973 meant that the real work could begin. By January 1974, the GPS program at the JPO was well underway. With only about 30 officers in the program, the workload was enormous. Fortunately, the Aerospace cadre of about 25 engineers was also making extraordinary contributions. In a flurry of activities, the team developed Requests for Proposals (RFPs), drew up top-level specifications‚ and published initial interface control documents (ICDs). The

work of converting viewgraphs into real hardware, as many know, is an exacting and sometimes painful process. By June 1974 (only 5 months after program approval), the satellite contract had been awarded to Rockwell of Seal Beach, California. At the same time, the Air Force generally did not support the GPS development, and the yearly budget was in constant jeopardy. To shore up support, Col. Parkinson had to spend many hours and trips back to Washington DC to avoid serious budget cuts, while at the same time directing the overall program and making key technical decisions. Of course, there were many additional development challenges, but three of them, principally engineering, stand out as being particularly formidable. These were 1) Achieving rapid and accurate satellite orbit prediction 2) Ensuring and demonstrating spacecraft longevity approaching 10 years 3) Developing a full family of GPS user equipment Each of these challenges will be discussed in some detail, including the names of those who were most instrumental in meeting them.

1.8 The GPS Development Process and Additional Major Challenges

1.8.1 Achieving Rapid and Accurate Satellite Orbit Prediction – to within a Few Meters User Ranging Error (URE) in 160,000 km of Travel Since the GPS system architecture only had upload stations on US soil, the satellites were out of sight for many hours, thus making accurate prediction of their orbits and clock drift essential. To achieve the expected positioning accuracy, the orbit prediction had to contribute less than a few meters ranging error after 160,000 km of travel (one complete orbit, bringing the satellite over an upload station). Achieving this standard was a major challenge in the early days of GPS. Such a prediction must account for the complications of Earth pole wander, Earth gravitational fields, Earth tides, general and special relativity, the noon turn maneuver of the satellites, solar and Earth radiation, the reference station’s location, as well as the drift in the clock. An example of these problems is shown in Figure 1.12 as the plot of the Earth’s polar axis wander. The pole axis of Earth moves in an irregular, but roughly circular way, occasionally reversing phase 180 . This effect, known as the Chandler Wobble, has approximately a 400day period and an amplitude of over 10 m. It is important if a PNT user would like sub-meter level accuracies. Fortunately, the Transit program had pioneered precise orbit prediction and had taken most of these effects into account. Their program, called Astro/Celeste, was developed by Robert Hill and Richard Anderle at the Naval Surface Weapons Center in Dahlgren, Virginia. For

Pole coordinates (xp, –yp) –150

Observatoire de Paris – SYRTE

08/12/1

–190

towards 90° East

–230

05/1/1

–270

06/7/27

–310 –350 –390

09/9/17

08/2/19 05/10/14

–430 y (mas)

Transit, the measurements taken by the reference stations had been batch-processed. Unfortunately, this processing would take too long to provide timely predictions for GPS. The JPO devised a modification that included partial derivatives of predictions relative to reference station measurements. These calculations allowed an extended (linearized) Kalman filter to be used for near-real-time optimal prediction. Implementers of these techniques included Bill Feess of Aerospace, Walt Melton of General Dynamics‚ and Sherman Francisco of IBM. These calculations were made in the initial master control and uploaded from Vandenberg Air Force Base. Primary control has since been moved to Schriever Air Force Base in Colorado Springs, and more recently a backup master control station has been reestablished at Vandenberg. Another important enabler to achieve rapid and accurate orbit determination is the operational GPS control segment, which performs precision pseudorange tracking of the satellites for GPS satellite orbit and clock measurements. The team of General Dynamics, IBM Federal Systems and Stanford Telecommunications won the contract for the GPS Operational Control Segment, which both tracked the GPS satellites and estimated the satellite clock offset and precise orbit. Dr. James Spilker recommended that the best GPS control segment performance could be obtained by tracking each GPS satellite from multiple monitor stations with precision receivers that coherently tracked both code and carrier (which are transmitted from each satellite coherently) as the satellites appear on one horizon and disappear on the other and, furthermore, track the carrier for each satellite without ever producing a carrier cycle slip. He and his team successfully achieved this objective with extreme precision. The root-mean-square (rms) pseudorange error in these monitor station code/ carrier tracking loop receivers was only 7 mm, indeed an excellent performance for the 1980s time frame [22].

–470

10 Meters

–510 –550 –590 –630 –150.00

–70.00

10.00

90.00

170.00

x (mas)

250.00

330.00

towards Greenwhich

Figure 1.12 Earth’s polar axis wander and example of effects calibrated by GPS.

1.8.2 Ensuring and Demonstrating Spacecraft Longevity Approaching 10 Years (Driving GPS Affordability) The issue was simply that sustaining a constellation of 24 satellites would be prohibitively expensive if the satellites did not have long lives. Again, the Air Force/621B study by Woodford and Nakamura in 1966 focused on the problem: “the most specific change in satellite technology is the increase of Mean Time Before Failure (MTBF), MTBFs on the order of 3 to 5 years can now be considered feasible.” Amazingly, some of the recent GPS satellites have orbital lifetimes of over 25 years. With a 24-satellite constellation, the annual launch rate is 24 divided by the average

19

1 Introduction, Early History, and Assuring PNT (PTA)

satellite lifetime. The problem of short lifetimes is easily illustrated in Figure 1.13. The light blue line shows the trade-off between the average satellite lifetime, L, and the required number of satellites per year for a 24-satellite constellation (it is a plot of 24/L). The yellow box illustrates the US GPS experience of lifetimes of 10 years or more, which requires only two to three launches per year. Also shown is the initial experience of GPS during Phase I. Even the first 10 GPS satellites had an average age of 7.6 years. This is an enormous credit to Rockwell International, particularly the Program Manager Richard Schwartz. GLONASS, the Russian system similar to GPS, had the early experience shown in the darker blue box. With satellite lifetimes averaging two to three years, the corresponding requirement for GLONASS was 8 to 12 satellite launches per year. GLONASS satellites now have design lifetimes of 10 years. The following are the keys to long-lived GNSS satellites:

•

Designs with carefully selected redundancy (e. g. clocks, power amplifiers).

14.00 Required Satellites per year

20

• •

Enforcing a rigorous part selection program including the de-rating of parts (class S or equivalent). “Testing as you fly” and insisting on an in-depth analysis of all failures.

Demonstrating long lifetimes was an essential key to GPS affordability, which helped win both approval and support.

1.8.3 Developing a Full Family of GPS User Equipment That Capitalizes on the Digital Signal (Leading to Inexpensive Digital Implementation) and Spans Most Fundamental Military Uses, as well as Demonstrating Civilian Feasibility The last, but certainly equally difficult‚ of these three engineering challenges was the development of nine different types of GPS user equipment in less than four years. These sets cost $250,000 or more each and had only 1 to 5 receiver channels to make satellite ranging measurements. Figure 1.14 shows some early GPS receivers: the Magnavox X-set for GPS Phase 1 validation in 1974–1975 (left); the first Rockwell Collins GPS receiver from 1976 (center left);

Early Russian GLONASS 2–3 Year Lifetime Requires 8–12/Year (working to correct)

12.00 10.00

#3 –#10 Satellites 9.1 Years Life

8.00 6.00

US GPS 10–12 Year Lifetime Requires 2–3/Year

4.00 First 10 GPS Satellites 7.6 Years Life

2.00 0.00

2

3

4

5 6 7 8 9 Average Satellite Life – “L” (Year)

10

11

12

Figure 1.13 Sustainment of 24-satellite constellation. The plot shows the enormous penalty for short satellite lifetimes. GPS had to launch about 1/4 of the satellites that the Russians would have needed to maintain a 24-satellite constellation. The current GLONASS satellites have lifetimes of approximately 10 years.

Figure 1.14 Early GPS receivers. The Magnavox X-set (left) was manufactured in 1974–1975 for GPS Phase 1 validation. The first Rockwell Collins GPS receiver was from 1976 (center left). The GPS Manpack was carried by solders in 1978 (center right). The TI 4100 GS Navigator (right) was the first GPS commercial receiver by Texas Instrument in 1981. Source: (Left) Photo provided by Vito Calbi. Reproduced with permission of Institute of Navigation. (Center Left) Photo courtesy of Rockwell Collins. Reproduced with permission of Rockwell Collins. (Center Right) US Air Force photo. (Right) Photo courtesy of Phil Ward. Reproduced with permission of Phil Ward.

1.8 The GPS Development Process and Additional Major Challenges

Table 1.5 User equipment developed from 1974 to 1978 User Equipment Set

Description

X Unaided

Four channels, high-performance, military

Magnavox

X Aided

Four channels, inertial-aided, military

Magnavox

Y Unaided

Single channel, sequential, military

Magnavox

Y Aided

Single channel, sequential, inertial-aided, military

Magnavox

HDUE-High Dynamic

Five channels, high-performance, military

Texas Instruments

MVUE-Manpack Vehicular

Single channel Manpack/ground vehicle military

Texas Instruments

GDM-Generalized Development Model

Five channels, high anti-jam military

Collins Radio of Rockwell International

MP-Manpack

Single channel Manpack/ground vehicle military

Magnavox

Z

Single channel, low-cost civil prototype

Magnavox

the GPS Manpack receivers carried by solders in 1978 (center right); the TI 4100 GPS Navigator was the first commercial GPS receiver by Texas Instruments first offered for sale in 1981 (right). Now, more than 35 years later, consumer GNSS chips have over 100 channels and cost about one dollar. The Phase One user equipment had applications across a wide variety of military uses. Another major goal was demonstrating a very low-cost GPS receiver. In the interest of brevity, we will not describe each of these development efforts. Table 1.5 summarizes the development of user equipment from 1974 to 1978.

1.8.4

Controversy: Origins of the GPS Concept

Over the past decade, a number of published reports have attributed the origins of GPS to the NRL and Mr. Roger Easton. These claims are understandable, since the NRL was evidently unaware of the earlier USAF/Aerospace (Woodford/Nakamura) study performed from 1964 to 1966 because it was classified SECRET. This section will clarify the historical antecedents of GPS. In October 1970, Mr. Roger Easton applied for a patent titled Navigation System using Satellites and Passive Ranging Techniques that was awarded in January 1974 (#3789409) [23]. This apparently is the preferred concept for a new satellite navigation system that Mr. Easton and NRL advocated and is the basis of the claim of GPS invention. Note that the patent application was four years after the completed, definitive USAF study by Woodford/Nakamura. The NRL proposal used a ranging signal technique called side-tone ranging that required satellites to broadcast on different frequencies. By the time of the NRL patent application, the USAF/ Aerospace was already embarked on studying and building

Manufacturer

CDMA user receivers using the much-preferred PRN/ CDMA signal later adopted by GPS. In its design, the Navy system was apparently focused on two-dimensional navigation; furthermore, the patent did not use the GPS four pseudorange calculation to eliminate the need for a precise (atomic) user clock. Instead it called for the user to have a clock with stability equivalent to the satellite: “a navigator’s station including: receiving means for receiving said broadcast multifrequency signals; signal generating means including a second extremely stable oscillator for producing multifrequency signals the same as said broadcast signals …”. It is shown on the USAF 621B study summary (figure 4) as #2, and was already described 4 years before Mr. Easton’s patent application, but again Mr. Easton was probably unaware of this work because of classification at the time. Thus, this patent and the NRL design cannot be described as the source of GPS in any sense. It did not describe the foursatellite technique to eliminate the ultra-stable user clock, and it used an unsuitable ranging technique that was specifically rejected by Col. Parkinson in the GPS design meeting. Lastly, it was filed four years after the Woodford/Nakamura (then classified) study that did describe the GPS technique (as well as describing the technique used by Mr. Easton in his patent). Finally, there is no record of the technique actually being experimentally verified, whereas the GPS concept was confirmed with both the White Sands (1969–1972) and Yuma testing (1978–1980; see below).

1.8.5 Verification of GPS and the Yuma Test Results [24, 25] By the spring of 1979, six satellites had been launched, nine types of GPS user equipment built, and extensive test results were available from over 650 individual tests. The

21

22

1 Introduction, Early History, and Assuring PNT (PTA)

4-CHANNEL SET C-141 F-4 UH-IH

100 ft 25

33 ft ILS WINDOW AT DECISION HT. – 526 ft

526 ft – 400 ft

– 200 ft

200 ft

400 ft

– 33 ft 200 ft DECISION HEIGHT (SIMULATED) GPS performance during landing approaches.

Figure 1.15

Errors at “decision height” for 25 GPS landing approaches.

summary test results confirmed GPS system accuracies of 7 m at the 50th percentile and 17 m at the 90th percentile. An indication of the system capability is shown in Figure 1.15, which plots the errors at “decision height” for 25 GPS landing approaches. These results are for three different types of aircraft: a large transport (C-141), a fighter type airplane (F4), and a helicopter (UH – 1H). Note that these displacements are a combination of GPS and pilot errors. There was no GPS receiver specifically designed for time transfer, but an initial test was also performed on this capability. A synchronized cesium clock was flown from Washington, DC, to Vandenberg Air Force Base for this evaluation. The result was a measured capability of about 50 ns. This error included any drift in the cesium clock between the time it was synchronized at the Naval Observatory in Washington, DC, and the comparison at the Yuma Proving Ground. Of course, GPS time transfer receivers of today have capabilities better than 10 ns. For the details of these results, please consult [24, 25]. In summary, virtually every performance claim in the original GPS proposal of 1973 was met.

1.9 GPS Declared Fully Operational 17 July 1995 Twenty-one years and six months after initial approval for a demonstration system, GPS was finally declared fully operational. If the production line for the initial satellites had been extended, full system capability could have been

attained in half that time. Unfortunately, the Air Force was ambivalent about its requirements for the system and on a number of occasions recommended a budget that would have canceled the project. The events leading up to that operational date are described below. The 11 block I satellites were followed by a series of block II, IIR, IIRM, and IIF satellites with the characteristics shown in Figure 1.16. Of the 72 satellites launched since 1978, at this time, over 40% of them are still operational. In fact, many of the satellites have demonstrated lifetimes of over 20 years, which attests to the spacecraft engineering skills of their manufacturers (Figure 1.17). From February 1989 through March 1993, 19 GPS satellites were launched in 49 months. Thus, the system was close to operational in the early portions of the Bosnian war. This was a significant milestone because the precision bombing capability of GPS was clearly established in the minds of the operational Air Force. GPS was declared fully operational (FOC) on 17 July 1995: “The Air Force announced today that the Global Positioning System satellite constellation has met all requirements for full operational capability. FOC status means that the system meets all the requirements specified in a variety of formal performance and requirements documents.” The GPS operational configuration is shown in Figure 1.18 with six inclined orbital planes; each plane hosts four to six satellites. A full description of GPS accuracy standards can be found in [26]. Table 1.6 is extracted from the December 2015 report to show civil capability (“Standard Service”).

1.9 GPS Declared Fully Operational 17 July 1995

Legacy Satellites

Modernized Satellites

Block IIA

Block IIR

Block IIR(M)

Block IIF

GPS III

0 operational

12 operational

7 operational

11 operational

3 in testing 7 in production

• Coarse Acquisition (C/A) code on L1 frequency for civil users

• C/A code on L1 • P(Y) code on L1 & L2

• Precise P(Y) code on L1 & L2 frequencies for military users

• 7.5-year design lifespan

• 7.5-year design lifespan

• On-board clock monitoring

• All Block IIR(M) signals

• All legacy signals •

2nd

civil signal (L2C)

• New military M code signals for enhanced jam resistance

• Launched in 19972004

• Launched in 19901997 • Last one decommissioned in 2016

• Flexible power levels for military signals • 7.5-year design lifespan

3rd

• civil signal on L5 • Advanced atomic clocks • Improved accuracy, signal strength, and quality • 12-year design lifespan

• Launched in 20052009

• Launched in 20102016

• All Block IIF signals • 4th civil signal on L1 (L1C) • Enhanced signal reliability, accuracy, and integrity • No SA • Satellites 11+: laser reflectors; search & rescue payload • 15-year design lifespan • 1st launch 2018, 2nd in 2019, last launch expected 2023

Figure 1.16 A summary of GPS satellites’ statistics and key parameters.

Block

Launched

Operational

Testing/ Reserve

Unhealthy

Retired

Launch Failures

Block I

11

0

0

0

10

1

Block II*

9

0

0

0

9

0

Block IIA

19

0

8

0

11

0

Block IIR

13

12

0

0

0

1

Block IIRM

8

7

1

0

0

0

Block IIF

12

12

1

0

0

0

Block IIIA

3

0

2

0

0

0

Total

75

31

4

0

30

2

*One Block II prototype was never launched.

Figure 1.17 Summary of the number of satellites launched, operational, testing/reserve, unhealthy, retired, and launch failures for different blocks.

The specifications on GPS service are extremely conservative; all independent test data indicate very comfortable margins against all parameters. It is hard to make an exact comparison of existing measurement data against the specifications. The GPS specifications are for a worldwide distribution and include certain assumptions about the Age of

Data, which is the time since the last upload for a particular satellite. In addition, the geometric distribution of satellite ranging can drive the accuracy by factors of 10 or more. However, the FAA Technical Center publishes a quarterly evaluation of GPS performance as measured by their WAAS North American monitoring stations [27]. A monthly report

23

24

1 Introduction, Early History, and Assuring PNT (PTA)

1.9.1 Presidential Decisions Helping to Assure GPS for Humanity There were two presidential decisions that were a substantial boost to the usefulness of GPS and growth of its applications. These were the decisions by President Reagan and President Clinton to ensure that GPS was available for all of humanity with no restrictions on accuracy. 1.9.1.1 President Reagan Guarantees GPS to be Freely Available to Benefit Humanity

Figure 1.18 Current GPS operational configuration showing six inclined planes with four to six satellites per plane. Source: Schriever AFB. Reproduced with permission of Schriever AFB.

from January 2019 is shown in Table 1.7. This report showed that the median horizontal accuracy (95%) has been better than 3 m. It is a tribute to the United States Air Force operators that the historical trends of GPS Signal-in-Space (SIS) ranging errors (SISRE) have been steadily improving. SISRE is defined as the accuracy considering satellite location and timing errors as well as the ionospheric correction. While it does not include user-centered errors, such as multipath and troposphere, it represents the foundation system capability. Against the 4 m Standard Positioning Service (SPS) Performance Standard (see Figure 1.19), recent measurements show accuracies that are at least four times better.

President Reagan’s Address to the Nation on the Soviet Attack on a Korean Airliner (KAL 007) on 5 September 1983 [28] foreshadowed his orders that GPS would be made available and supported for civilians throughout the world. This event has been misconstrued by many reporters. In fact, the signal had been freely usable for civilians since 1978, as discussed earlier, on a use-at-your-own-risk basis. President Reagan’s announcement, however, formally guaranteed civil-signal availability for an indefinite period with a statement that any termination would have a 10-year advanced warning. Thus, a signal which could be used only at risk was converted to a signal with the backing and guarantee of the US government. In fact, by 1983, a major market was already developing for the use of GPS in precision survey and mapping. 1.9.1.2 President Clinton Directs Cessation of Deliberate Civil-Signal Degradation

A different president, Bill Clinton, also made an announcement that affected civil use. It was recognized, after the initial testing, that the civilian signal was virtually as accurate as the precision military signal, which was encrypted. There was a fear that such civil capability might be used against the United States during periods of hostility. Therefore, the DoD decided to deliberately degrade the accuracy of the civil signal with a technique known as Selective Availability (SA). This was done by perturbing the ranging

Table 1.6 GPS accuracy standards for civil capability (Standard Service) Position Service Availability Standard

Conditions and Constraints

≥ 99% Horizontal service availability, average location

17 m horizontal (SIS only) 95% threshold

≥ 99% Vertical service availability, average location ≥ 90% Horizontal service availability, worst-case location ≥ 90% Vertical service availability, worst-case location SIS = Signal-in-Space

37 m vertical (SIS only) 95% threshold Defined for a position/time solution meeting the representative user conditions and operating within the service volume over any 24-hour interval. 17 m horizontal (SIS only) 95% threshold 37 m vertical (SIS only) 95% threshold Defined for a position/time solution meeting the representative user conditions and operating within the service volume over any 24-hour interval

1.9 GPS Declared Fully Operational 17 July 1995

Table 1.7 FAA Monthly Civil Report Card on GPS performance published in January 2019 [27] Operational Performance Parameter

CY 2018

Dec 2018

Jan 2019

Average number of satellites usable

30.77

30.66

30.97

Average number of satellites usable in primary slots

23.83 (99.29%)

23.98 (99.90%)

23.98 (99.91%)

Average availability of 6 satellites in view

100%

100%

100%

Area Median

1.4

1.4

1.4

Worst site

8.0

9.4

7.5

Area Median

2.4

2.4

2.4

Worst site

35.4

39.3

26.8

Area Median

2.7

2.7

2.7

Worst site

36.5

40.4

27.6

NPA Service Area (NSA)

63.36%

47.05%

36.53%

World

65.93%

58.36%

56.45%

Availability Parameters

99.99% Horizontal DOP

99.99% Vertical DOP

99.99% Position DOP (PDOP)

100% RAIM Availability (HAL = 185m)

Accuracy Parameters RMS Single Frequency User Range Error Constellation Median

1.66

1.69

1.65

Worst Satellite

10.96

10.90

10.92

1.70

1.68

1.70

95% Horizontal Error Area Median Worst Site

2.99

2.87

2.69

Availability (% 99.8

13/12/2020 10:19:51 AM

114

5 GALILEO

•

•

•

OS: This is a free timing and positioning service that can be used by anyone. In the E1/L1 frequency band, the E1 OS signals are highly interoperable with the GPS L1 Civil signal (L1C) thanks to the common MBOC modulation that allows users to profit from the enhanced geometry and availability that results from the combined use of Galileo and GPS constellations. The timing service is synchronized to UTC, as seen in Section 5.3. PRS: This is a robust and access-controlled positioning and timing service that is only available through the Competent PRS Authorities (CPAs) of users authorized by Member States of the EU, the Council, the EC, the EEAS, and duly authorized Union agencies in accordance with Decision No 1104/2011/EU. PRS provides encrypted signals with protection against jamming and spoofing, and is intended to support critical transport and emergency services, law enforcement, border control, peace missions, and other governmental operations. The PRS provides users with enhanced protection against diverse threats, thus ensuring high continuous availability. Commercial Service (CS): This service addresses highperformance or liability-critical applications. The access to added-value data is controlled by an encryption mechanism that grants access only to those users that have paid a fee. A Precise Point Positioning (PPP) service is included as well as strong authentication feature offering additional robustness over Open Service Navigation Message Authentication.

In addition to the navigation services described above, Galileo also provides an additional service that supports the COSPAS-SARSAT system, the SAR service.

•

SAR: Galileo relays the signals coming from emergency beacons down to the ground, where the SAR ground segment calculates the actual location of the transmitter. It represents Europe’s contribution to COSPASSARSAT, the international satellite-based search and rescue distress alert detection system. Galileo further enhances the system with the additional feature of informing receivers equipped with Galileo through the so-called return link that the distress alert was well received. The SAR distress signals are detected by the Galileo satellites in the UHF band of 406-406.1 MHz and then relayed to the Medium Earth Orbit Local User Terminal (MEOLUT) in the L6 band (1544-1545 MHz). The alert acknowledgment of distress alerts and coordination of rescue teams is embedded as part of the OS data transmitted in the E1 carrier frequency.

0004815226.3D 114

5.5

Galileo Space Segment

This section provides details on the two fundamental elements of the Galileo space segment:

••

Launch vehicles and constellation Spacecraft (platform and payload)

5.5.1

Launch Vehicles and Constellation

This section introduces first the family of Galileo launchers and continues with an overview of the planned Galileo constellation. 5.5.1.1 Galileo Launchers

Europe currently employs Soyuz and Ariane launchers to place the Galileo satellites into space from the Guiana Space Centre, which is Europe’s Spaceport and is located in French Guiana. The first 14 satellites were placed using Soyuz launchers, in a series of dual launches in October 2011, October 2012, August 2014, March, September and December 2015, and May 2016. The latest launch from November 2016 (Figure 5.9) employed for the very first time an Ariane 5 launcher and placed four satellites at a time. In total, Galileo has already 18 fully operational satellites as of today. The Soyuz launcher is the jewel of the Russian space program. It was introduced in 1966, and is derived from the Vostok launcher, which in turn was based on the 8K74 or R-7a intercontinental ballistic missile that launched Sputnik 1 in 1957 in a modified form. Soyuz has performed more than 1000 manned and unmanned missions and is designed to achieve extremely high reliability levels for its use in manned missions. For the particular case of Galileo, a special version of the Soyuz launcher is employed. It is the more powerful Soyuz ST-B version, which includes a Fregat-MT upper stage that can be ignited again. This stage was used for the first time to deliver the GIOVE-A and -B experimental satellites and carries an additional 900 kg of propellant. For launches from French Guiana, which is the standard for Galileo, the Soyuz three-stage rocket plus Fregat upper stage is assembled horizontally following the traditional Russian approach. Then it is erected vertically before the payload mates with the launcher from above in the standard European way. Given the particular approach that combines European and Russian procedures, a new mobile launch gantry was built to facilitate this process. The dedicated gantry also helps protect the satellites and the launcher from the humid tropical environment that reigns in French Guiana.

13/12/2020 10:19:51 AM

5.5 Galileo Space Segment

115

Figure 5.9 First Galileo launch with Ariane 5 carrying four satellites on 17 November 2017. Source: © ESA – S. Corvaja.

In addition to Soyuz, Galileo also has Ariane rockets to place satellites into space. Galileo uses a re-qualified version of the Ariane 5 ES that can deploy up to four Galileo satellites into MEO orbit at a time. Ariane 5 ES is an evolution of the initial Ariane 5 generic launcher that was upgraded to allow re-ignition and long coast phases as those required in Galileo to inject the four Galileo satellites into their operational orbits. Furthermore, re-ignition is required to allow the last launcher stage to vacate the injection orbit once the payload has been released so that the last stage is placed at the graveyard orbit, far away from the nominal Galileo orbit. The first such fourfold launch occurred on 17 November 2016 and another two Ariane 5 launches followed end of 2017 and in 2018 to complete the Galileo constellation. Figure 5.10 shows Galileo’s baseline launch plan to achieve Full Operations in 2020. 5.5.1.2 Galileo Constellation

The fully deployed Galileo system consists of 30 satellites (24 operational + 6 in-orbit spares), positioned in three circular MEO planes at a nominal average orbit semi-major axis of 29,599.801 km, and at an inclination of the orbital planes of 56 with reference to the equatorial plane. Once

0004815226.3D 115

FOC is achieved, the Galileo navigation signals will provide good coverage even at latitudes up to 75 north and 75 south. The Galileo constellation was the result of detailed studies and optimization efforts conducted toward the objectives of achieving good accuracy and availability performance at high latitudes also [3]. An additional factor taken into consideration at the moment of the selection of the Galileo constellation geometry was the capability to deploy it fast and reduce the costs related to constellation maintenance. In fact, the finally retained three-plane configuration is consistent with the European launch capabilities, which can place multiple satellites in orbit at a time: as said, Ariane 5 can launch up to four Galileo satellites and Soyuz one pair of them. Table 5.3 summarizes the finally selected basic Galileo reference constellation parameters [13, 14]. The Galileo constellation slots are depicted in Figure 5.11. The position of the spare satellites is indicative, as their actual position is decided at the time of deployment. Furthermore, we can recognize the pair of satellites from the launch anomaly of Launch 3 (L3) and their relative location with respect to the rest of the constellation. Due

13/12/2020 10:19:51 AM

116

5 GALILEO

IOV 2011

FOC 2012 2013

2

2015

2014

4

6

Figure 5.10

10

8

2017

2016

12

18

14

22

Parameter

Value

Constellation type

Walker 24/3/1 + 6 in-orbit spares

Semi-major axis (km)

29,599.801

Inclination

56

Period

14h04m42s

more than 8 satellites above 5 of elevation. This reference constellation is complemented with another six spare satellites, resulting in worldwide geometries with typical vertical dilution of precision (VDOP) and horizontal dilution of precision (HDOP) values of approximately 2.3 and 1.3, respectively [15]. Finally, another important aspect to which Galileo has paid particular attention is the disposal of the satellites after the end of their operational life. This is important not only in terms of international agreements on control of space debris, but also because debris avoidance maneuvers have an impact on the availability of operational satellites, and ultimately on the provision of the service. Galileo satellites are designed to be removed from the nominal Galileo orbits after they have reached the end of their operational life. At that point in time‚ they are moved to a graveyard orbit which is at least 300 km higher than the operational Galileo

Ground track repeat cycle 10 sidereal days/17 orbits

to the different plane inclination, this relative location evolves with time, so the figure is only indicative. The Galileo selected reference constellation of 24 satellites allows users worldwide to have between 6 to 11 Galileo satellites in view at any time, being the average visibility of

18 0

°

A5

°

C4

13 5

B4 C3

°

A3

B3

°

C2

45

A2

B2

A1

27 5° 22

0004815226.3D 116

C1

B1 120°

0°

31 5°

0°

Re la

tiv e

0°

Me

an

An

om

aly

90

C5

B5

A4

A8

240° C8

Relative RAAn

B8 C7

A7

Figure 5.11

26

Galileo launch plan toward FOC.

Table 5.3 Galileo reference constellation parameters

A6

2018

B7 C6 B6

Galileo FOC Reference Geometry Slot FOC L3 Satellites (Snapshot–Relative Location will evolve over time)

Galileo FOC constellation slots.

13/12/2020 10:19:52 AM

5.5 Galileo Space Segment

orbit. The same logic applies to the launcher stages that remain after injection of the satellite into orbit.

5.5.2

good health. In spite of the non-nominal orbit, the performance was fully in line with the expectations and, in fact, these satellites have since then broadcast navigation signals and been used for clock technology validation. Unfortunately, and due to the fact that the new orbit could not be fully fit into the nominal navigation message, the other satellites cannot yet transmit almanac details on these two satellites. GSAT0201 and GSAT0202 are, however, healthy‚ and currently efforts are running to fully incorporate them into the ground processing. After the initial mishap, the following dual launches in March 2015, September 2015, December 2015‚ and May 2016 were fully successful with injection in the planned orbits, the satellites thus becoming part of the nominal constellation.

Galileo Spacecraft

The Galileo operational constellation consists of a mix of two families of satellites:

•

•

The first four Galileo satellites were manufactured by EADS Astrium GmbH as prime contractor and launched with two Soyuz rockets. This family of satellites is still operational today and was used for system validation in the IOV phase. The first dual launch occurred on 21 October 2011 and placed satellites GSAT0101 and GSAT0102 into orbital plane A. The second launch followed on 12 October and placed satellites GSAT0103 and GSAT0104 in orbital plane B. Due to a permanent on-board failure, GSAT0104 does not transmit in E5/ E6 nor broadcast navigation messages in E1 (only dummy data). However, the Search and Rescue Transponder (SART) is fully in use, using TGVF processing for ephemeris determination. The second family of Galileo satellites is manufactured by OHB System AG as prime contractor [16]. To differentiate these satellites from those of the other family, its numbering follows the sequence GSAT02xx. A total of 22 satellites have been produced under this order. The first dual launch of this family took place in August 2014 and was impaired by a malfunction in the Fregat stage of the Soyuz launcher that led to the so-called injection anomaly of Launch 3. Once GSAT0201 and GSAT0202 reached the new corrected target orbit, the navigation payloads were activated and subject to IOT. This allowed the technology and performance of the new family of satellites to be validated, confirming their

117

Figure 5.12 provides with details of the two families of Galileo satellites‚ and further details on platform and payload are provided separately in Table 5.4, according to the standard separation applied in space system engineering. 5.5.2.1 Galileo Platform

The Galileo platform comprises all subsystems for on-board data handling and control, attitude and orbit control including propulsion, power generation and distribution, thermal control, telemetry, and a laser retro reflector:

•

Attitude and Orbit Control System (AOCS): Galileo uses 3-axis attitude control during all phases and for all maneuvers [17]. Depending on the actual mission status, several modes of operation are applicable: – Launch and Early Orbit Phase (LEOP) as well as in contingency situations and safe modes: For this mode, dedicated acquisition modes are used for Earth or Sun acquisition.

Figure 5.12 Artist’s impression of Galileo satellites in orbit (left GSAT010x and right GSAT02xx). Source: © ESA – P. Carril.

0004815226.3D 117

13/12/2020 10:19:53 AM

118

5 GALILEO

Table 5.4 Overview of main Galileo satellite characteristics [16] GSAT010x

GSAT02xx

S/C Prime contractor

EADS Astrium GmbH

OHB System AG

Number of satellites

4

22

Mass at launch (kg)

700

733

Size with solar array deployed

2.7 m × 1.6 m × 14.5 m

2.5 m × 1.1 m × 14.7 m

Design lifetime (years) 12

12

Available power (kW) 1.420

1.900

Source: Pauly, K., “Galileo FOC–Design, Production, Early Operations after 1st Launch, and Project Status,” Proc. IAC-14-B2.2.1, 65th International Astronautical Congress (IAC 2014), Toronto, Canada, September 2014.

• •

•

– Orbit acquisition, station-keeping maneuvers, and endof-life (EOL) decommissioning: This mode is expected to require very few station-keeping maneuvers [18, 19]. – Nominal operational mode: This mode uses yaw steering to orient the solar panels toward the Sun with full nadir pointing performance and to support the thermal control of the satellite. In this mode, the AOCS sensor/actuator configuration is based on Earth and Sun sensors that continuously keep the satellite pointed toward Earth. Propulsion subsystem: Galileo is typically equipped with eight monopropellant hydrazine thrusters, each of which provides a nominal thrust of 1 N at the beginning of life (BOL). Since both families of satellites (GSAT010x and GSAT02xx) are designed for direct injection into the final MEO orbit, their propulsion subsystems only need to provide the delta-velocity required for orbit correction maneuvers during the operational life. Power Subsystem: It is based on a classical regulated 50 V bus architecture that consists of – A power conditioning and distribution unit (PCDU) that provides electrical power to all units on-board the spacecraft – Two solar array wings that supply electrical power to the spacecraft during Sun exposition and in parallel charge the battery after the eclipse phases – A Li-Ion battery that stores the power provided by the solar arrays during the Sun phases and feeds it back during the eclipse phases TT&C Subsystem: Galileo satellites use redundant command reception and telemetry transmission at S band, with two modes of operation: ESA standard TT&C mode and spread-spectrum mode. When the S-band transponder is operated in coherent mode, accurate range-rate

0004815226.3D 118

•

(Doppler) measurements are possible. The S-band Telemetry, Telecommand and Control (TT&C) hemisphericalcoverage helix antennas are located on opposite sides of the satellite, providing omnidirectional coverage for reception and transmission. Ranging operation is performed simultaneously with telemetry transmission. Laser Retro Reflector (LRR): Galileo’s cat eye reflector array is located on the nadir panels close to the navigation transmit antenna and allows the measurement of the satellite’s distance to within a few centimeters. Laser ranging campaigns using Galileo’s LRR are planned on average once a year, with altitude measurements via S-band telemetry and telecommand link in between.

5.5.2.2 Galileo Payload

Galileo’s payload comprises a fully redundant triple-band navigation payload and a SAR repeater [20]. Functionally, the navigation payload can be split into the mission uplink data handling system, the timing subsystem, and the signal generation and transmitter subsystem:

• •

Mission uplink data handling system: It receives the navigation message data and all related support data by means of a dedicated CDMA C-band uplink from the uplink stations (ULSs) of the Galileo ground segment. Timing subsystem: It generates the on-board frequency reference based on two different clock technologies: the Rubidium Atomic Frequency Standard (RAFS) and the passive hydrogen maser (PHM) (Figure 5.13). Every Galileo satellite flies two units of each; thus, there are four clocks in all. The Clock Monitoring and Control Unit (CMCU) provides the interface between these four clocks and the Navigation Signal Generation Unit (NSGU), guaranteeing synchronization between the master clock and the active spare clock that operates as hot redundant spare (the other two clocks remain as cold spares) [21, 22]. This ultimately allows the ground segment to command one spare clock to take over seamlessly should the master clock fail or simply in case of maintenance operations.

The stability of the on-board reference frequency is one of the core performance parameters for the quality of the navigation payload. Example Allan Deviation (ADEV) measurements from September 2017 are shown in Figure 5.14, covering exemplary RAFS and PHM results from different Galileo satellites (except those of Launch L3). The superior performance of the PHM clock technology can also be appreciated. Indeed, at the moment of the measurement most of the operating clocks were PHM except for E11-GSAT0101 and E22-GSAT0204, which were run under RAFS.

13/12/2020 10:19:53 AM

5.5 Galileo Space Segment

119

Figure 5.13 Galileo passive hydrogen maser clock (left) and Rubidium Atomic Frequency Standard (right). Source: © Spectratime.

From 2017/09/06 19:00:00 to 2017/09/20 19:00:00

10−10

FREQUENCY STABILITY Allan Deviation PHM ground specs RAFS ground specs E01– GSAT0210 E02– GSAT0211 E03– GSAT0213 E04– GSAT0213 E05– GSAT0214 E07– GSAT0207 E08– GSAT0208 E09– GSAT0209 E11– GSAT0101 E12– GSAT0102 E14– GSAT0202 E18– GSAT0201 E19– GSAT0203 E22– GSAT0204 E24– GSAT0205 E26– GSAT0203 E30– GSAT0206

ADEV, σ(τ)

10−11

10−12

10−13

10−14

10−15 102

103

τ(s)

104

105

Figure 5.14 Galileo PHM and RAFS frequency stability.

•

0004815226.3D 119

Navigation payload: It provides navigation signals that are coherent to the common frequency reference generated by the timing subsystem. Galileo transmits on three L-band carriers – E1, E6, and E5 – and is the first navigation system that provides a wideband signal of more than 50 MHz bandwidth, namely‚ AltBOC, which is emitted on the E5 band. All navigation signals are radiated through a dual-band transmit antenna that uses a common antenna subsystem for E5 and E6 [23, 24].

•

SAR: Galileo provides an enhanced distress localization functionality as part of the COSPAS-SARSAT MEOSAR System and is interoperable with other MEOSAR repeaters from GLONASS and future GPS satellites [25]. Galileo’s SAR transponder is able to receive distress alerts coming from COSPAS-SARSAT beacons operating in the 406.0–406.1 MHz band and further downlinks them at 1544 MHz to dedicated ground stations, the so-called MEOLUT. These perform the beacon localization in near real time based on difference of arrival (DOA)

13/12/2020 10:19:53 AM

120

5 GALILEO

measurements of time and frequency [26]. In addition, Galileo also provides a so-called SAR return link service, which confirms the alerting beacon that the distress message has been received by the COSPAS-SARSAT system. This acknowledgment is embedded in the navigation message [27]. The Council of COSPAS-SARSAT declared MEOSAR services on 9 December 2016. With this declaration, Galileo has become the largest worldwide contributor to this unique international SAR infrastructure‚ supporting on average over 2000 rescue operations every year and eventually saving many human lives.

5.6

Galileo Ground Segment

The Galileo Ground Segment is composed of two functional parts:

• •

Ground Control Segment (GCS): It performs all functions related to command and control of the satellite constellation and provides global coverage. It comprises a worldwide network of S-band TT&C stations hosted on Galileo remote sites. Ground Mission Segment (GMS): It is responsible for service-related tasks. It measures and monitors the Galileo navigation signals and uses them to estimate, predict, and build the navigation message. The navigation message is further uplinked to the satellites for later relay to the users via the L-band downlink signals. The basic content of the navigation message is composed of satellite specific orbit and clock corrections, which are estimated in batches by the Orbit Determination and Time Synchronization (ODTS) process every 10 min based on E1-E5a observables for F/NAV products, E1-E5b observables for I/NAV products‚ and E1-E6 observables for PRS products. To successfully perform this task, the GMS counts with two worldwide networks of stations: – L-band GSS: In charge of collecting ranging measurements of the Galileo navigation signals, for ODTS and monitoring of the signal in space. – C-band ULSs: Five stations are in charge of up-linking mission data to the satellites (e.g. ephemerides and clock prediction, SAR return link‚ and commercial service data). Each station can operate up to four uplink antennas in order to provide the whole constellation with timely navigation message updates.

Further, the Galileo ground segment is the interface to the satellites and provides a large number of functions ranging from on-board software maintenance, to operations support and telemetry analysis as well as support to

0004815226.3D 120

eventual troubleshooting of the satellite platform and payload units. Galileo has two GCCs in Oberpfaffenhofen (Germany) and Fucino (Italy) that hold the core facilities of the GCS and the GMS. These are further connected to all ground facilities through a global data dissemination network that is equipped with redundant links to guarantee service and operations continuity. The LEOP Control Centres (LOCCs) located in Toulouse (French Space Agency, CNES) and Darmstadt (ESA Operations Centre, ESOC) are in charge of taking control of the satellites after their separation from the launch vehicle and until they have reached their position within the assigned orbital slots. Once the satellites achieve their final orbital position, IOT of the new satellites starts. During this phase, the Redu station in Belgium performs all necessary tests required to verify that the satellite payload survived the launch and that it is in good health. Redu counts with a calibrated high-gain antenna, an L-band measurement system for navigation signals, and testing equipment and transmitters for the C-band and SAR UHF RF links. In addition to system-specific tasks such as those briefly mentioned above, the GCS is also responsible of interfacing with several external entities involved in the provision of Galileo services. These service providers are procured, coordinated‚ and operated by the GSA. They are listed next and briefly introduced:

• • • • •

GNSS Service Centre (GSC): This center interfaces with the Galileo OS users and the Galileo CS external data providers. The GSC facility is located near Madrid, Spain. GSMC: This center provides system security monitoring and management of the PRS user segment. It interfaces with national CPAs. Given its critical nature, the GSMC relies on two hot redundant facilities. Time Service Provider (TSP) and Geodetic Reference Service Providers (GRSP): These centers monitor and steer the GST and the GTRF in order to align it to international meteorological standards. SAR Galileo Data Service Provider (SAR GDSP): This center determines the position of the distress alert emitted by the SAR beacons and generates the SAR Return Link Messages to be later disseminated through the Galileo navigation signals. The SAR GDSP premises are located in Toulouse, France. Galileo Reference Centre (GRC): This center provides independent performance monitoring of the Galileo services. The GRC facility is located in Noordwijk, the Netherlands.

13/12/2020 10:19:54 AM

5.7 Galileo Signal Plan

121

Figure 5.15 Galileo ground segment overview.

Figure 5.15 provides an overview of the Galileo ground segment and gives a good feeling for the long list of assets required to provide the service.

5.7

Galileo Signal Plan

5.7.1

Galileo Spectrum and Frequency Plan

As introduced in Section 5.1, the signal plan of Galileo has been the product of many years of technical discussions and optimization trade-offs that culminated in the frequencies and signals that Galileo transmits today. Galileo’s signal plan in general and the waveform and message structure in particular are also a consequence of the political efforts of Europe to promote the combined interoperable use of GPS and Galileo, a result of the agreement between the United States and the European Union on the promotion, provision, and use of both systems and their related applications [28]. The agreement also paved the way for the very final modification in the open signals of E1, and introduced what de facto has become the new standard waveform for GNSS open signals at 1575.42 MHz: MBOC. Interoperability between Galileo and GPS ultimately aims at easing the efforts at the receiver level to use signals from both constellations and profit from their combined geometry. The fact that Galileo and GPS share the

0004815226.3D 121

frequency carriers E5a/L5 and E1/L1 with equivalent modulations and that both ensure a guaranteed link to UTC and the ITRF are indeed a proof of that. But the concept goes far beyond this and also includes the comparable definition of message concepts such as ephemeris, almanac, clock correction, GST- UTC, bias group delay, common receiver algorithms, and even software. Galileo satellites transmit coherent signals on three different navigation carriers, namely‚ E1, E5‚ and E6, and each of these signals contains several components, with at least one pair of pilot and data streams. As shown in Figure 5.16, the E1 band refers to the carrier frequency in the upper L band of 1575.42 MHz, and is also denoted as E2-L1-E1 in other books. It is the same L1 carrier frequency used by GPS. E6 is in the upper part of the lower L band and has a carrier frequency of 1278.75 MHz. E5 designates the lower part of the lower L band and is subdivided into E5b and E5a. The E5 carrier frequency is 1191.795 MHz, while the E5b and E5a carrier frequencies are respectively 1207.14 MHz and 1176.45 MHz. E5a coincides with the L5 frequency of GPS. All Galileo signals use RHCP‚ and according to the Galileo SIS ICD [5], the minimum received power is specified for satellite signals received at 5 of elevation at an output of a 0 dBic circularly polarized antenna situated around the surface of Earth. The definition does not include excess atmospheric attenuation. The power spectral densities of

13/12/2020 10:19:54 AM

122

5 GALILEO

E5a

E5b

1164 MHz

1189 MHz

1176.45 MHz

E6

1214 MHz

1278.75 MHz

1260 MHz

E1

1300 MHz

1544 MHz

1559 MHz

1544.2 MHz

1207.14 MHz

SAR OS Data AltBOC(15,10) Data 50 sps

OS/SoL/CS Data AltBOC(15,10) Data 250 sps

CS Data BPSK(5) Data 1000 sps

1575.42 MHz

1563 MHz

1591 MHz 1587 MHz

OS/SoL/CS Data MBOC(6,1,1/11) Data 250 sps Pilot Channel

PRS Data BOCcos(15,2.5)

PRS Data BOCcos(10,5)

OS Pilot AltBOC(15,10) BPSK(10)

BPSK(10)

CS Pilot BPSK(5)

Galileo Assigned Frequency Band GPS L5 Band GPS L1 Band Glonass L3 Band SAR Downlink Carrier Frequencies Signals accesible to all users, with data partly encrypted Signals to which access is controlled through the use of encryption for ranging codes and data Signals to which access is restricted through the use of encryption for ranging codes and data

Figure 5.16

Galileo frequency plan, signals‚ and components.

the Galileo signals and the respective carriers introduced above are shown in Figure 5.16: Each of the signals in E1 and E5 provides at least one free open access pair of pilot and data components. In particular, E5 is composed of two pilot–data pairs at ±15.345 MHz

0004815226.3D 122

around the E5 carrier frequency (E5b at +15.345 and E5a at −15.345). The sidebands of E5 fulfill a dual purpose. On the one hand, they serve users that track each of the sidebands individually due to bandwidth limitations‚ while on the other hand they allow more sophisticated receivers to profit

13/12/2020 10:19:54 AM

5.7 Galileo Signal Plan

from the coherent generation of the two sidebands and achieve an excellent performance, equivalent to that of using one single and very large bandwidth, namely‚ that of the whole E5 with at least 51.15 MHz (50 × 1.023 MHz). The coherent generation of the E5 sidebands is achieved by means of the AltBOC multiplex [5], which we describe in further detail next.

5.7.2

• •

Table 5.5 summarizes the mapping between Galileo navigation services and signals [3]. All Galileo signals are coherently derived from a common reference time. The signal definitions in the next few subsections are specified without the effect of band-limiting filters and payload imperfections. Furthermore, although the actual values vary from application to application, some recommendations for receiver bandwidths are provided.

Galileo Signals and Services

Section 5.4 introduced the Galileo services and planned user communities. In this section, we provide further details on the main signal characteristics of Galileo in each frequency band and the mapping between signals and services:

•

123

OS: OS is provided in two modes: single-frequency and dual-frequency. The single-frequency (SF) OS is provided by each of the three OS signals transmitted in E1B&C, E5a‚ and E5b. The dual-frequency (DF) OS is provided by the dual-frequency signal combinations E1B&C-E5a and E1B&C-E5b. CS: CS is provided by the E6B&C signal in combination with the OS signals of E1B&C, E5a, and E5b. The E6B&C signal contains value-added data transmitted at a high data rate, and it is combined with OS signals for improved performance. PRS: PRS is provided by the E1A and E6A signals, which have been specially designed to be resistant to intentional and non-intentional interference.

5.7.3

Galileo E1 Band

Galileo provides two services on the E1 band: the E1 OS and the E1 PRS. E1 OS is served by two signal components, E1B and E1C, while PRS uses the third signal component, namely‚ E1A. The E1 OS modulation is called CBOC (Composite Binary Offset Carrier) and is a particular implementation of MBOC (Multiplexed BOC) [3]. MBOC(6,1,1/11) is the result of multiplexing a wideband signal – BOC(6,1) – with a narrowband signal – BOC(1,1) – in such a way that 1/11 of the power is allocated, on average, to the high-frequency component. This signal was finalized in 2007 in collaboration with GPS and was the last signal to be completely defined in the Galileo frequency plan. The normalized (unit power) power spectral density is given by GMBOC 6,1,1

11

f =

10 GBOC 1,1 11

f +

1 GBOC 6,1 11

f 51

Table 5.5 Galileo navigation services mapped to signals Service Signal

Open Service

Commercial Service

Public Regulated Service

E5a OS E5b IM E5 E6A

E6B,C E1A

E1B,C

0004815226.3D 123

13/12/2020 10:19:55 AM

124

5 GALILEO

CBOC is a particular case of the more general Composite Binary Coded Symbols (CBCS) [3] modulation and can be expressed as follows: cD t cos θ1 sBOC 1,1 t + cos θ2 sBOC 6,1 t + 2 cP t cos θ1 sBOC 1,1 t − cos θ2 sBOC 6,1 t + s t =A + 2 sin θ1 + sin θ2 + sIM t + j sPRS t 2

Another interesting property of CBOC becomes evident if we rearrange the terms in Eq. (5.2) above and express the combined signal as a pseudorandom time-multiplexed alternation of BOC(1,1) and BOC(6,1) chips that are modulated by the non-binary code that results from adding the data and pilot ranging codes: cD t + cP t cos θ1 sBOC 1,1 t + 2 cD t − cP t cos θ2 sBOC 6,1 t + s t =A + 2 sin θ1 + sin θ2 + j sPRS t + sIM t 2

52 sIM t = − j cD t cP t sPRS t

sin θ1 − sin θ2 2 53

where

• • • • • • •

A is the amplitude of the modulation envelope, which is the sum of the OS data (D) and pilot (P), PRS and intermodulation product IM.A = 2PT , where PT is the total power of the multiplexed signal. θ1 and θ2 describe the angular distance of points of the 8PSK modulation. This depends on the percentage of power that is placed on the BOC(6,1) component. sBOC(1, 1)(t) represents the BOC(1,1) modulation with a chip rate of 1.023 MHz. sBOC(6, 1)(t) represents the BOC(6,1) modulation with a chip rate of 6 × 1.023 MHz. sPRS(t) is the PRS modulation with a chip rate of 2.5 × 1.023 MHz. sIM(t) is the IM product signal, which is added to the useful signals above to guarantee that their sum produces a constant envelope. cD(t) and cP(t) are the data and pilot codes‚ respectively. It is important to note that cD(t) accounts for the effect of the data bits.

The high-frequency BOC(6,1) component is placed on both the data and pilot components‚ and both data and pilot have equal power following a 1:1 data to pilot power ratio. Moreover, each of the data and pilot streams is spread by a linear combination of BOC(1,1) and BOC(6,1) spreading symbols, with coefficients such that 10/11 of the power falls on BOC(6,1) and 1/11 on BOC(6,1). It is also important in the definition of CBOC that data and pilot components are in anti-phase, since the subcarriers add with opposite sign for the data and the pilot component. This results in a fourlevel time domain signal that differs slightly for the CBOC data and pilot components and consequently also differs slightly for the autocorrelation functions of data and pilot. The pilot CBOC signal has indeed a narrower peak and consequently a better tracking and multipath mitigation performance.

0004815226.3D 124

54 If we carefully look at the expression above, we can observe the following: if cD(t) = = if cD(t) = = if cD(t) = = if cD(t) = =

+ 1 and cP(t) = + 1, then 2 and cD(t) − cP(t) = 0 + 1 and cP(t) = − 1, then 0 and cD(t) − cP(t) = 2 − 1 and cP(t) = + 1, then 0 and cD(t) − cP(t) = − 2 − 1 and cP(t) = − 1, then − 2 and cD(t) − cP(t) = 0

cD(t) + cP(t) cD(t) + cP(t) cD(t) + cP(t)

(5.5)

cD(t) + cP(t)

Accordingly, whatever the value of cD(t) and cP(t), the coefficients of sBOC(1, 1)(t) and sBOC(6, 1)(t) will always be nonzero at different but complementary slots in time. This proves the time-multiplex nature of this equation since the BOC(1,1) subcarrier is transmitted at different but complementary time slots to those of the BOC(6,1) subcarrier. Another interesting effect from the introduction of the low-power BOC(6,1) component is that the number of phase points increases to eight from the original six that were necessary when only BOC(1,1) was transmitted [3]. For the same reason, the power spent in the IM product signal sIM(t) is considerably reduced, thus improving the efficiency of the multiplex. It is also important to note that the quadrature component (the PRS signal) is left unaffected by this new scheme, except for its relative amplitude. A detailed description of the public Galileo modulations is available in the Galileo public Open Service Signal in Space Interface Control Document [5]. A generic view of the E1 OS signal generation is depicted in Figure 5.17 [3]. The whole transmitted Galileo E1 signal consists of the multiplexing of the following three components:

•

The E1 OS data component eE1−B(t) is generated from the I/NAV navigation data stream DE1−B(t) and the ranging code CE1−B(t), which are then modulated with

13/12/2020 10:19:55 AM

5.7 Galileo Signal Plan

CE1–B(t)

four-level correlators at the receiver with amplitude values

10/ 11scE1–BOC(1,1)(t) + 1/ 11scE1–BOC(6,1)(t)

DE1–B(t) X

eE1–B(t)

of ±

X

Primary

CE1–C

1 2 X

+ – X

Secondary

CE1–C

CE1–C(t)

eE1–C(t)

sE1(t)

X

10/ 11scE1–BOC(1,1)(t) – 1/ 11scE1–BOC(6,1)(t)

Figure 5.17 CBOC modulation block diagram.

• •

the subcarriers scE1−BOC(1, 1)(t) and scE1−BOC(6, 1)(t) of BOC(1,1) and BOC(6,1), respectively. The E1 OS pilot component eE1−C(t) is generated from the ranging code CE1−C(t), including its secondary code, which is then modulated with the subcarriers scE1−BOC(1, 1)(t) and scE1−BOC(6, 1)(t) in anti-phase. The E1 PRS signal, also denoted as E1-A, which results from the modulo-two addition (product if we consider the physical bipolar representation of the signal) of the PRS data stream DPRS(t), the PRS code sequence CPRS(t), and the subcarrier scPRS(t). This subcarrier consists of a BOC(15,2.5) in cosine phasing.

Figure 5.5 shows the power spectral density of all Galileo E1 signals. It is important to note that the E1 band is the notation used by Galileo to refer to the L1 band of GPS or B1 of BeiDou. The E1 OS codes are, as well as the E6 CS codes that we will see later, also random memory codes. The plain number of choices to set the 0s and 1s for the whole code family is enormous‚ and thus special algorithms have to be applied to generate random codes efficiently [3, 32, 33]. The codes can be driven to fulfill special properties such as balance and weakened balance, where the probability of 0s and 1s must not be identical but within a well-defined range, or to realize the autocorrelation sidelobe zero (ASZ) property. This latter property guarantees that the autocorrelation values of every code correlate to zero with a delayed version of itself, shifted by one chip. The technical characteristics of all the Galileo signals in E1 are summarized in Table 5.6. In the same manner as the CBOC expression admits many different interpretations of its nature, it does also offer a wide range of possible tracking strategies to exploit its intrinsic properties. Ideal direct CBOC tracking would require

0004815226.3D 125

125

10 11 +

1 11 and ±

10 11 −

1 11 to

be optimum. Some applications‚ however‚ do not need to achieve maximum possible performance of the signal and could instead, at the cost of a suboptimum implementation, use a two-bit representation. For low-cost applications, receivers of limited bandwidth might also consider using a conventional binary BOC(1,1) de-spreading at the cost of a negligible 0.4 dB loss (the actual value will be a function of the selected receiver bandwidth). Other techniques suggest the possibility of combining separate binary correlators for the BOC(6,1) and BOC(1,1) parts [29–31], demonstrating the feasibility of efficient and simplified CBOC tracking architectures. The E1B,C CBOC signal was designed to permit receivers to explore different tracking strategies depending on the envisaged complexity and performance. For receivers targeting to minimize the receiver bandwidth, it is expected that only the BOC(1,1) component of CBOC is processed. In this case, the minimum necessary receiver (doublesided) bandwidth to capture the main lobes of BOC(1,1) would be approximately 4.0 MHz, although narrower bandwidth are possible as long as enough power falls within it. The recommended bandwidth is between approximately 2.0 MHz and 24.552 MHz, and the maximum receiver bandwidth is suggested to not be larger than 31 MHz. Intermediate values are possible in steps of 2.046 MHz to capture full secondary lobes. Another category of receivers processing CBOC is expected to target the best tracking performance and multipath robustness by exploiting the BOC(6,1) component. These receivers would require a minimum of approximately 14.3 MHz to capture the BOC(6,1) main lobe.

5.7.4

Galileo E6 Band

As shown in [5], the transmitted Galileo E6 signal consists of the following three components:

• • •

E6 CS data component: This modulating signal is the modulo-two addition of the E6 CS navigation data stream DCS(t) with the CS data component code sequence C DCS t . This last one is already modulated by a BPSK(5) at 5.115 MHz. E6 CS pilot component: This modulating signal is the modulo-two addition of the E6 CS pilot component code CPCS t with a BPSK(5) at 5.115 MHz. E6 PRS signal component: It is the modulo-two addition of the E6 PRS navigation data stream DPRS(t) with the PRS code sequence CPRS(t) at 5.115 MHz. This signal is further modulated by a subcarrier of 10.23 MHz in cosine phasing.

13/12/2020 10:19:55 AM

126

5 GALILEO

Table 5.6 Galileo E1 signal technical characteristics Frequency band

E1

Carrier frequency

1575.42 MHz

Access technique

CDMA

Multiplexing

Interplex

Component name

E1-A

E1-B

E1-C

Service

PRS

OS/SAR

OS

Spreading modulation

BOCc(15,2.5)

CBOC(6,1,1/11)

CBOC(6,1,1/11)

Data/pilot

Data+PilotTime Mux

Data

Pilot

Subcarrier rate (MHz)

15.345

1.023

1.023

Primary code type

Encrypted

Memory code

Memory code

Primary PRN code duration (ms) Primary PRN code rate (Mcps) Primary PRN code length (chips)

2.5575

Secondary PRN code type

4

4

1.023

1.023

4092

4092

Memory code

Memory code

Secondary PRN code rate (cps)

250

Secondary PRN code length (chips)

25

PRN code repetition (ms)

4

100

Spectral line spacing (Hz)

250

10

Data fraction of power (%)

50

Data symbol duration (ms)

4

Data rate (sps)

250

Data rate (bps)

125

Interleaver

Block 30 × 8

Error correction

Convolutional codes r = 1/2, k = 7 CRC-24

Error detection Keying

Binary

Message

G/NAV

−157.25

I/NAV 30 s subframes, divided into 2 s pages (even + odd parts). Each page part: 10 sync + 2∗ (114 bits+ 6 tail bits) −160.25

Min Power (at 5 el.) (dBW)

−160.25

Max power (dBW)

−152.00

−157.00

−157.00

This is graphically shown in Figure 5.18. Moreover, the spectrum of the different E6 signals is as shown in Figure 5.19. The E6 CS codes are also random codes like E1OS codes [32, 33]. The signal characteristics of E6 are summarized in Table 5.7.

0004815226.3D 126

For the processing of the E6B,C signal, a minimum receiver (double-sided) bandwidth of 10.2 MHz is required, while the recommended bandwidth ranges between approximately 10.2 MHz and 20.5 MHz. The maximum receiver bandwidth is suggested to not be larger than 41 MHz. Intermediate values are possible in steps of 10.23 MHz to capture full secondary lobes.

13/12/2020 10:19:55 AM

5.7 Galileo Signal Plan

DCS(t) SD(t)

X

D CCS (t)

1 2 +

X –

P

CS

SE6 (t)

SP (t)

CCS (t)

In-Phase PSD [dBW/Hz]

Figure 5.18 Modulation scheme for the Galileo E6 signals.

Galileo E6 CS Data & Pilot Galileo E6 PRS

–60 –70 –80 –90

–100 –20 –10 Frequen 0 cy Offse 10 t with re spect to 20 the carr ier [MH z]

Figure 5.19

5.7.5

–90 –80

D

–70

se

PS

–100 z] /H W [dB

a Ph

ra-

ad

Qu

Spectra of Galileo signals in E6.

Galileo E5 Band

The different Galileo E5 signal components are generated according to the following [5]:

• • • •

The E5a data component: This component is the modulotwo addition of the E5a navigation data stream DE5a(t) with the E5a data PRN code sequence C DE5a t of the chipping rate 10.23 MHz. The E5a pilot component: This component is the E5a pilot PRN code sequence C PE5a t of the chipping rate 10.23 MHz. The E5b data component: This component is the modulotwo addition of the E5b navigation data stream DE5b(t) with the E5b data PRN code sequence C DE5b t of the chipping rate 10.23 MHz. The E5b pilot component: This component is the E5b pilot PRN code sequence C PE5b t of the chipping rate 10.23 MHz.

The E5 modulation is AltBOC. It is a wideband modified version of the BOC, transmitted at 1191.795 MHz with a code rate of 10.23 MHz and a subcarrier frequency of 15.345 MHz.

0004815226.3D 127

127

AltBOC is conceptually similar to the well-known BOC modulation but with the remarkable advantage that it also provides high spectral isolation between the two upper main lobes and the two lower main lobes (considering the I and Q phases separately). This is accomplished by using differentiated codes for each of the main lobes. This interesting property allows keeping the same implementation principles of a typical BOC receiver while at the same time allowing the lobes to be differentiated [34]. The AltBOC modulation is generally denoted as AltBOC(m, n) for simplicity, which is technically equivalent to an AltBOC(fs, fc) with fs = m 1.023 and fc = n 1.023. Conceptually, the AltBOC modulation is inspired by the idea of using a complex subcarrier to shift the power from the carrier to higher and lower frequencies so that the resulting spectrum does not split up and carry the same information on both main sides. The resulting wideband complex modulation can be then represented in baseband as the sum of coherently generated and individually quadrature modulated complex upper (E5b) and lower (E5a) subcarriers. However, as [3] discusses in detail, if no other additional terms were introduced, the resulting composite signal would not guarantee a constant envelope in the end. The technical solution to this problem came from [35–37], where a new signal term called the Inter Modulation (IM) product was proposed. This term does not contain any useful navigation information but ensures that the AltBOC modulation keeps all the phase points of the constellation diagram within the circle and with a non-constant allocation of the eight phase states as in a classical 8-PSK modulation, which obviously is an ideally constant envelope [38]. The final selected modified constant envelope AltBOC was proposed around 2002/2003 in [37]. Applied to the Galileo particular case of AltBOC in E5 and following the Galileo ICD notation, the previous expressions simplify to the following:

sAltBOC t =

1 8

cDE5a + j cPE5a

scd t − j scd t −

cDE5b + j cPE5b

scd t + j scd t −

cDE5a + j cPE5a cDE5b + j cPE5b

scp t − j scp

Ts 4

+

Ts 4 Ts t− 4

scp t + j scp t −

Signal + + IM

Ts 4

56 where Ts is the period of the AltBOC subcarrier. Moreover, cDE5a = cPE5b cDE5b cPE5a

cPE5a = cDE5b cPE5b cDE5a

cDE5b = cDE5a cPE5b cPE5a

cPE5b = cDE5b cDE5a cPE5a 57

13/12/2020 10:19:56 AM

128

5 GALILEO

Table 5.7 Galileo E6 signal technical characteristics Frequency band

E6

Carrier frequency

1278.750 MHz

Access technique

CDMA

Multiplexing

Interplex

Component name

E6-A

E6-B

E6-C

Service

PRS

CS

CS

Spreading modulation

BOCc(10,5)

BPSK(5)

BPSK(5)

Data/pilot

Data+Pilot Time Mux

Data

Pilot

Subcarrier rate

10.230 MHz

Primary code type

Encrypted

Primary PRN code duration (ms) Primary PRN code rate (Mcps)

2.5575

Encrypted

Encrypted

1

1

1.023

1.023

Primary PRN code length Secondary PRN code type Secondary PRN code rate (cps)

1000

Secondary PRN code length (chips)

100

PRN code repetition (ms)

1

100

Spectral line spacing (Hz)

1000

10

Data fraction of power (%)

50

Data symbol duration (ms)

1

Data rate (sps)

1000

Data rate (bps)

500

Interleaver

Block 123 × 8

Error correction

Convolutional codes r = 1/2, k = 7 CRC-24

Error detection Keying

Binary

Message

G/NAV

Min power (at 5 el.) (dBW)

−155.25

C/NAV 15 s subframes divided into 15 pages. Each page made of: 16 sync + 2∗ (486 bits + 6 tail bits) −158.25

Max power (dBW)

−152.00

−155.00

and the data and pilot subcarriers can be expressed as follows: scd t =

2 π sign cos 2 π f s t − 4 4

+

2 π + sign cos 2 π f s t + 4 4

0004815226.3D 128

1 sign cos 2 π f s t 2

58

scp t =

−

2 π sign cos 2π f s t − 4 4

−

2 π sign cos 2 π f s t + 4 4

+

−158.25 −155.00

1 sign cos 2 π f s t 2

59

As we can observe, all the IM terms are the result of triple products of the nominal spreading sequences. Since the IM power is ultimately wasted power, it is important to note

13/12/2020 10:19:56 AM

5.7 Galileo Signal Plan

also that most of the power of the IM is located around and beyond the 3fs MHz offset from the E5 carrier, which is far outside the recommended AltBOC receiver bandwidth. Moreover, the IM terms are uncorrelated with any single signal or component of interest and their power within the receiver bandwidth is much lower than the total noise power. Thus, the IM can safely be neglected for the purpose of AltBOC tracking. Furthermore, while in the original conception the complex subcarrier was composed of a cosine-phased rectangular signal for the real part and a sine-phased rectangular signal for the complex part, now both the real and complex part are a mixture of both sine and cosine delayed and early rectangular waveforms. The time representation of the data and pilot AltBOC subcarriers is depicted in Figure 5.20. As we can recognize, they are discrete multi-level signals with period Ts= (15.345 MHz)−1. Figure 5.21 shows the generic generation of the Galileo E5 signal modulation.

AltBOC Subcarriers 2+1 2 1 2

2–1 2

–1 2

–

– SCd SCp

2+1 2 Ts 8

0

2

Ts 8

3

Ts 8

4

Ts 8

5

Ts 8

6

Ts 8

7

Ts 8

2–1 2

Ts

Figure 5.20 Galileo E5 data and pilot subcarriers.

D

CE5a (t)

X DE5a (t)

F/NAV P

CE5a (t) D

AltBOC(15,10) X

CE5b (t) I/NAV

DE5b (t) P CE5b (t)

Figure 5.21 Galileo E5 modulation scheme.

0004815226.3D 129

sE5(t)

129

Taking the terms of the previous lines, one can show that the power spectral density for the constant envelope AltBOC modulation is as follows:

Φ

odd,c f = GAltBOC

2 4 f c cos π 2 f 2 cos 2

− cos

πf fc πf 2 fs

cos 2

πf 2fs

πf πf πf − 2 cos cos 2fs 2fs 4fs

+2 5 10

This expression actually corresponds to the odd variant of AltBOC, where (2fs/fc) is odd in the case of Galileo’s AltBOC(15,10) constant envelope modulation. The resulting spectrum of the E5 signal modulation is shown in Figure 5.22. As shown in the figure above, the spectrum of the AltBOC(15,10) modulation is very similar to that of two QPSK(10) signals shifted by 15 MHz to the left and right of the carrier frequency. Indeed, since to acquire all the main lobes of the modulation a very wide bandwidth is necessary, many receivers are expected to correlate the AltBOC signal with two shifted QPSK(10) replicas, allowing acquisition and tracking of each of the data and pilot of both E5a and E5b individually, with a minimum receiver (doublesided) bandwidth of approximately 20.5 MHz and centred on the E5a and/or E5b carriers. Larger bandwidths are possible, but values beyond approximately 41 MHz – which corresponds to the main lobe plus the secondary lobe at each side – will not bring significant improvements. Furthermore, intermediate values for receiver bandwidth should capture full main and secondary lobes. For the full processing of the whole AltBOC signal, a minimum receiver (double-sided) bandwidth of 51.2 MHz and centred at 1191.795 MHz is recommended. For bandwidths beyond this value, the benefits do not seem to compensate for the increased complexity and power consumption. Also, it is important to recall that E5a and E5b are generated fully coherently within AltBOC. Other tracking concepts have been proposed for wideband AltBOC processing‚ and all basically require AltBOC replica generation. To mention one that is considered as a benchmarking baseline, [6] suggests the possibility of generating the replica using a lookup table and accounts for aspects of receiver implementation. Nevertheless, new concepts are expected to be proposed in the coming years as the use of Galileo becomes more widespread. The E5 primary codes can be generated with shift registers. Indeed, the outputs of two parallel registers are modulo-two added to generate the primary codes. For more

13/12/2020 10:19:56 AM

130

5 GALILEO Galileo E5a Band Galileo E5 I Galileo E5 Q

E5a I

Galileo E5b Band E5b I

–75 –80

Figure 5.22

–35

–25 –15 0 Frequency Offset with respect

15 25 35 to the carrier [MHz]

Galileo Spreading Codes and Sequences

Every Galileo signal component is spread with unique sequences called pseudorandom noise (PRN) codes that are specific to every satellite. As a general rule:

•

The length of the spreading sequences for the Galileo data components was selected so as to exactly fit within one symbol of the data component. However, if the resulting length was larger than 10,230 chips, a twotiered code structure was chosen. The tiered code is based on the construction of a primary spreading sequence

0004815226.3D 130

45

dB

ase

Power spectral densities of Galileo signals in E5.

details on the start values of the primary codes and the corresponding secondary codes of each satellite, refer to [5]. Finally, some details on the technical characteristics of the E5 signal are presented in Table 5.8. One final remark to make on the AltBOC signal is that while Galileo transmits content in the navigation message for E5a and E5b individually, it does not provide a dedicated message for the whole AltBOC signal (composed of both E5a and E5b). This is relevant for the clock correction of the E5 carrier if the whole E5 band is exploited, since the clock correction values transmitted in the navigation message are optimized for the dual-frequency reception of E1 and E5a (F/NAV message) and for the dual-frequency reception of E1 and E5b (I/NAV message). As a good approximation, the average of the I/NAV and the F/NAV clock corrections could be used instead. In addition, for the sole reception of the E5 signal, the I/NAV and F/ NAV Bias Group Delays (BGDs) would be necessary too.

5.7.6

–80

E5b Q

Ph

E5a Q

ra-

–100 –45

ad

–95

PS

–90

D[

–90

W/

Hz ]

–100

–85

Qu

In-Phase PSD [dBW/Hz]

–70

•

overlaid with a slower secondary code. The primary code length was the result of many trade-offs‚ but essentially the selected length of 10,230 chips is a good compromise between the correlation properties of families in that length range and reasonable complexity during acquisition. The spreading sequences of the Galileo pilot component are also based on the two-tiered construction. In this case, the length of the primary code is equal to that of its associated data component while the length of the secondary code is chosen so as to produce a non-repetitive pilot spreading (tiered-code) sequence of 100 ms in total. This pilot code period was selected to allow receivers to resolve the code phase relative to the GST within an initial uncertainty of 100 ms, which is approximately the delay between any visible satellite of the nominal Galileo constellation and a terrestrial user and more than four times the difference between the propagation delays of that same satellite to the closest and the farthest user on Earth. Thus, the selected Galileo codes allow users on the surface of Earth to derive time-free position solutions using only code phase measurements, provided the receiver already had the ephemeris and clock correction available in memory.

The effect of modulating the spreading waveforms of data and pilot components with the PRN sequences that result from the two-tiered code construction mechanism is similar to that of modulating with pseudodata. In this case, the secondary code plays the role of the a priori known symbol modulation and is clocked to have a duration equal to the

13/12/2020 10:19:56 AM

5.7 Galileo Signal Plan

131

Table 5.8 Galileo E5 signal technical characteristics Frequency band

E5

Carrier frequency

1191.795 MHz

Access technique

CDMA

Multiplexing

AltBOC

Component name

E5a-I

E5a-Q

E5b-I

E5b-Q

Service

OS

OS

OS

OS

Spreading modulation

BPSK(10)

BPSK (10)

BPSK(10)

BPSK(10)

Data/pilot

Data

Pilot

Data

Pilot

Primary code type

Memory code

Memory code

Memory code

Memory code

Primary PRN code duration (ms)

1

1

1

1

Primary PRN code rate (Mcps)

10.23

10.23

10.23

10.23

Primary PRN code length (chips)

10,230

10,230

10,230

10,230

Secondary PRN code type

Memory code

Memory code

Memory code

Memory code

Secondary PRN code rate (cps)

1000

1000

250

1000

Secondary PRN code length (chips)

20

100

4

100

PRN Code repetition (ms)

20

100

4

100

Spectral line spacing (Hz)

50

10

250

10

Data fraction of power (%)

50

50

Data symbol duration (ms)

20

4

Data rate (sps)

50

250

Data rate (bps)

25

125

Interleaver

Block 61 × 8

Block 30 × 8

Error correction Error detection

Convolutional codes r = 1/2, k = 7 CRC-24

Convolutional codes r = 1/2, k = 7 CRC-24

Keying

Binary

Binary

Message

I/NAV 30 s subframes, divided into 2 s pages (even + odd parts). Each page part: 10 sync + 2∗ (114 bits+ 6 tail bits)

Min. power (at 5 el.) (dBW)

F/NAV 50 s subframes Divided into 10 s pages. Each page made of 12 sync + 2∗ (238 bits + 6 tail bits) −158.25

−158.25

−158.25

−158.25

Max. power (dBW)

−153.00

−153.00

−153.00

−153.00

Subcarrier rate

period of the primary code to which it is modulo-2 added. Figure 5.23 illustrates the principle. Receiver designers intending to extend the coherent integration time beyond the duration of one primary code length will need to bear this in mind in order to account for the behavior of the secondary code during the acquisition process, conducting appropriate hypothesis tests to identify the correct secondary code phase. The retained Galileo primary spreading

0004815226.3D 131

sequences were the result of a long optimization process in the Phase C0 of Galileo, around 2003 [39]. Different candidate primary code families were analyzed or traded off in terms of their autocorrelation and crosscorrelation properties, receiver performance during acquisition and tracking, and robustness against interfering narrowband signals. The same optimization efforts were invested on the secondary codes. In this case, however,

13/12/2020 10:19:57 AM

132

5 GALILEO

Np Chips

Period 1

Period 2

Secondary code Generator

Primary code Generator

Chip Rate:Rp

Period 1

Np *Ns Chips

NsChips Np: Primary Code Length Ns: Secondary Code Length

Chip Rate:Rs = Rp/Np

Figure 5.23

Period Ns

XOR Modulo-2- Addition

Principle of the tiered-code construction. G1

Input

q–1

q–1

q–1

q–1

q–1

q–1

Output G2

Figure 5.24

Galileo convolutional coding scheme [5]. Source: Reproduced with permission of European Union.

the driving figure of merit was to achieve low autocorrelation sidelobes. Further details on the Galileo primary and secondary spreading codes can be found in the OS SIS ICD [5].

In the near future, Galileo plans to introduce additional FEC capabilities based on Reed Solomon (RS) codes for some parts of its navigation message. The additional FEC is expected to enhance the time reception and sensitivity performance.

5.7.7 Galileo Forward Error Coding (FEC) and Block Interleaving

5.7.8

In order to provide robust transmission of the data message, Galileo uses Viterbi Forward Error Correcting Coding of rate 1/2 and constraint length 7. The encoder polynomials are identical to those of the GPS L5 CNAV data encoder, but Galileo data components apply in addition an inversion to the output of the G2 polynomial. This ensures that continuous zero inputs do not create a constant symbol output (Figure 5.24). Encoding is applied to full or half pages of the navigation message‚ and all data blocks are treated independently without overlaps with earlier or later blocks. In the next step, a list of predefined tails is applied to provide FEC protection for the complete information content of each navigation page. Finally, interleaving is applied on blocks of eight rows and the number of columns that corresponds to the page size in symbols, as detailed in [5]. This allows the FEC decoder to correct burst errors up to a distance of at least eight symbols.

0004815226.3D 132

Galileo Data Message

Galileo provides users with three different types of public navigation messages through the Galileo navigation signals:

• • •

I/NAV Type: This message type is a legacy of the old Integrity NAVigation message and provides a low latency and high data rate with a short page length navigation message. It carries navigation information on E1B and E5b-I as well as content for the SAR service in E1B only. F/NAV Type: This message type provides a low-data-rate Free NAVigation message and is transmitted on the E5a-I component. It carries navigation content. C/NAV Type: This message type provides a low-latency and near-real-time Commercial NAVigation message and is transmitted on the E6B component.

The content of the navigation message can be roughly divided into pure navigation content (time of transmission, clock correction, ephemeris, etc.), which is mostly repetitive, and other non-repetitive low-latency message

13/12/2020 10:19:57 AM

5.7 Galileo Signal Plan

elements. All these low-latency data components, regardless of their type, are provided by satellites that are directly in contact with the Galileo ground segment‚ and the data content can vary from one satellite to another. The OS SIS ICD [5], its annexes‚ and all its associated support documents provide all the details on the three types of messages above. This section will thus focus on the aspects that are relevant for receiver manufacturers and users, stressing the differences from other systems and its specificities. 5.7.8.1 Relevant Aspects of I/NAV Message

The I/NAV message provides users with navigation content to support users in PVT determination. Apart from other details that are less relevant for the present discussion, the I/NAV fields contain the following information:

•• • ••

GST through a WN and Time of Week (TOW) Ephemeris and clock correction for the transmitting satellite Ionosphere model parameters and bias group delay for single-frequency users Data validity and signal health flags Almanac and other supplementary information

The definitions used by Galileo for the representation of ephemeris, clock corrections, GST-UTC, almanacs, and usage algorithms are based on GPS legacy formats but filled up with Galileo content. For the ionosphere correction message, however, Galileo uses an adapted version of the NeQuick model. Details on the performance can be found in Section 5.8. In addition to the navigation content, the I/NAV message does also include in E1B a return link channel to support the SAR service [25]. This channel is near real time and provides Galileo-equipped SAR beacons with a short acknowledgment that the distress signal was correctly received. The I/NAV channel does also contain other low-latency channels. A particular feature of the I/NAV message is that it is defined to be flexible to modify the nominal order of the pages and also has the capability to replace nominal transmissions by low-latency short message pages which, in the extreme case, might only be transmitted a single time. This capability is on a per-second basis [5], and receivers are required to be designed for these events. The I/NAV message is structured in pages, which represent the smallest unit of interpretable data. A full I/NAV page itself consists of two consecutive data blocks of 1 s duration each known as the “odd” and “even” words. Every word starts with the I/NAV synchronization symbols followed by a block-encoded data field. A full I/NAV page thus requires 2 s to be transmitted and provides an effective capacity of 245 bits, excluding synchronization and tail symbols.

0004815226.3D 133

133

5.7.8.2 Relevant Aspects of F/NAV Message

The F/NAV message is compatible with the I/NAV message and provides users with the same navigation content listed in the previous section in order to support the PVT determination. However, certain parameters such as the clock correction are specific for every message type, and thus can be potentially different. Having said this, it is expected that the F/NAV and I/NAV clock corrections will be very similar in most occasions‚ but this is not guaranteed in the most general case. This is the consequence of the multi-frequency nature of Galileo and the fact that the I/NAV and F/ NAV messages are optimized for different pairs of frequencies: while the I/NAV message, especially its clock correction, is estimated based on the frequency pair formed by E1B and E5b, the F/NAV parameters are optimized based on the reception of E1B and E5a. Consequently, the ephemeris and clock corrections transmitted by F/NAV and I/ NAV are, strictly speaking, only valid for those receivers tracking the respective frequency pairs. For the case of single-frequency receivers in particular, the bias group delay correction of the respective message type also needs to be applied to correct the clock and ephemeris parameters. Figure 5.25 illustrates the principle. Similar to the I/NAV message, the F/NAV message streams are also structured in pages. Every F/NAV page contains a predefined sequence of synchronization symbols followed by the rate-1/2 convolutional-encoded and CRCprotected block of information. It lasts 10 s and provides 238 bits of effective information, excluding synchronization and tail symbols. 5.7.8.3 Relevant Aspects of C/NAV Message

At the time of this writing, C/NAV applications are under development‚ and no content has yet been published. Moreover, neither the C/NAV message nor the I/NAV or F/NAV message types yet support PVT using E6 measurements or triple-carrier measurements. This type of content could be envisaged to be provided in the C/NAV message or through external sources and communication channels. The C/NAV data stream is also structured in pages, and similar to the F/NAV, each C/NAV page consists of predefined synchronization sequence of symbols followed by the rate-1/2 convolutional-encoded and CRC-protected block of information. 5.7.8.4 Data Message Planning and Uplink

Data message planning targets the objective of disseminating the PVT information from each satellite within a welldefined interval of time while other information contents of less relevance for the PVT determination and with longer validity, such as‚ for example‚ the almanac, are transmitted

13/12/2020 10:19:57 AM

134

5 GALILEO

E5a single frequency: Use F/NAV

E5b single frequency: Use I/NAV

E5a F/NAV

E5b I/NAV

E6 single frequency: Use External Navigation Message

Navigation Signals

E1 single frequency: Use I/NAV, may use F/NAV if available

E6 C/NAV

E1 I/NAV

E1/E5b dual frequency: Use I/NAV

E1/E5a dual frequency: • Can use F/NAV or I/NAV Ephemeris • Nominal performance with F/NAV clock correction • Approximation with I/NAV clock correction

Figure 5.25

Rules of use of Galileo message types for PVT.

FNAV Message

Frame 600s (12480 bits) 1 Frame = 12 Subframes

Subframe 50s (1040 bits) 1 Subframe = 5 pages

Page 10s (208 bits eff.)

Figure 5.26

F/NAV page transmission planning.

within longer intervals of time. Figure 5.26 illustrates the concept for F/NAV. The current version of the OS SIS ICD [5] provides message timelines and structures for the message types addressed above. However, they are only for information and with a number of caveats so as to allow room for possible changes and evolutions in the future. Receivers are explicitly reminded in the OS SIS ICD that flexibility needs to be inherent in any Galileo receiver.

0004815226.3D 134

It is expected that new features will be gradually introduced as the system matures and the acceptance of Galileo increases. These new features could target improvements and/or extensions of the navigation message, making use of the existing degrees of freedom and of the spare room available for, as an example, introducing new page types. Such a change would not impact the PVT quality of the legacy data content‚ but it would require legacy receivers to properly deal with page types not known to them yet. In

13/12/2020 10:19:57 AM

5.8 Galileo Ionospheric Model

a similar way, new data content could be defined outside the currently defined ranges by making use of the existing spare space in identifier value ranges. Another example of flexibility can be directly extracted from the OS SIS ICD [5], where the nominal sequence of pages is described, but it is explicitly indicated that there is no guarantee that the same order will remain in the future. This implies that the current sequence of pages may vary in the future for all active satellites and that, instead of assuming a frozen and static order, receiver designers will need to identify the received pages by their actual page identifier. Another of the far-reaching consequences of this built-in flexibility is that the relative timing between I/NAV pages in E1B and in E5b may change one day. Galileo provides a high level of flexibility in the design of its message but this flexibility is not unlimited, in order to ensure backward compatibility for legacy receivers in the future. Certain features such as the modulation up to symbol level or the definition of existing pages will remain unaltered. Equally unquestionable is the fact that existing message content will continue to be provided even if new capabilities are introduced. As one can expect, the tradeoff between reserving enough headroom for potential and surely unknown future needs and optimizing a system for the well-known needs is anything but easy‚ and the discussion will remain in future generations of Galileo. So far, we have addressed the planning of the message and discussed the specificities and flexibility of the Galileo design. The next step is the generation of the message, its uplink, and dissemination to the users. The navigation message information is continuously generated every 10 min by the Orbitography and Synchronization Processing Facility (OSPF), its validity being a maximum of 100 min. In order to reduce the parameterization and quantization errors, the navigation message is generated in sets of eight batches with a different Issue of Data (IOD) value for each batch. The latest available sets of batches are always uploaded by the mission ULSs and stored on board the satellite as soon as the contact is established. Thus, during the time when a satellite has a continuous link with the ground segment, the message information broadcasted by this satellite will also be updated approximately every 10 minutes, and the user will receive the latest and most up-to-date navigation information. If the connection with the mission uplink is not possible for whatever reason and until the next contact occurs, the satellite transmits the set of batches that were previously uploaded on board and broadcasts each message batch one after the other until the very last one is sent. At that point, if no contact was yet possible, the last batch will be continuously transmitted regardless of its age. It is

0004815226.3D 135

135

important, however, to stress that the mission uplinks are scheduled such as to ensure that the on-board message is not older than 100 min, which allows the system to operate on a RAFS – and thus less demanding – configuration. Having said this, if the ground segment changes the PHM to become the master clock on board the satellite, the time between uplinks could be extended beyond this time. Usually, only the first four out of the eight generated batches are uploaded during the contact with the mission uplink station. However, the TTC stations are also able to upload the navigation messages if required, and then distribute all the generated eight batches during that contact, which allows the satellite to operate longer on stored batches.

5.8

Galileo Ionospheric Model

The Galileo single-frequency correction algorithm [41] is based on the three-dimensional representation of the ionosphere. Compared to other thin-layer models, the ionospheric group delay is obtained through the integration of the electron density along the path between satellite and receiver. The background electron density model used is the NeQuick G, which is an adaptation of the original ITU-R NeQuick ionospheric electron density model [42, 43]. It is based on an empirical climatological representation of the ionosphere, which generates the electron density from empirically derived analytical profiles and depending on the input values: solar parameter (e.g. solar radio flux at 10.7 cm (F10.7), sun spot number, etc.), month, geographic latitude and longitude, height‚ and time. The adaptation for Galileo (NeQuick G) is driven by an effective ionization level Az (a solar-related parameter), calculated with three broadcast ionospheric coefficients ai0, ai1, and ai2. The three coefficients are used in a second-degree polynomial as a function of the modified dip latitude (MODIP) of the receiver, in order to determine Az. The performance of the NeQuick G Model is regularly evaluated [44]. The global daily RMS ionospheric residual error (meters of L1) after correction with Galileo NeQuick G (red) and GPS ICA (blue) from April 2013 until December 2017 is presented in Figure 5.27. The achieved residual error as measured is already reaching expectations for the full operational constellation of Galileo. Similar to other GNSS, the Galileo clock corrections are generated for dual-frequency users, and singlefrequency users will need to use the Broadcast Group Delay BGD(f1, f2) provided through the Galileo navigation message as additional correction. BGD(f1, f2) is defined as follows:

13/12/2020 10:19:58 AM

136

5 GALILEO

5 NeQuick G GPS ICA

4.5 4

RMS (mL1)

3.5 3 2.5 2 1.5 1 0.5

2013.5 2014 2014.5 2015 2015.5 2016 2016.5 2017 2017.5 2018 Time (years)

Figure 5.27 Global daily RMS ionospheric residual error in meters of L1 after correction with Galileo NeQuick G (red) and GPS ICA (blue) from April 2013 to December 2017. Source: © ESA – R. Orus.

BGD f 1 , f 2

TR1 − TR2 = 1− f1 f2 2

5 11

where f1 and f2 are the carrier frequencies of the involved Galileo signals “1” and “2,” while TR1 − TR2 is the delay difference of the signals as contributed by the satellite payload. This formulation allows for easy translation of the dual-frequency clock correction information from the navigation message when using only a single-frequency receiver [5]. BGD accuracy was characterized, for example, during the IOV campaign, and was found as expected around 30 cm. It is noted that BGD does not distinguish between pilot and data components. The ground segment measures BGD on the pilot components of the associated dual-frequency combination. The data components are nearly identical to their pilot counterparts, in spectrum and modulation, and the method of signal generation on board ensures that tracking offsets between a data component and its pilot counterpart remain within a few centimeters, an order of magnitude smaller than the BGD accuracy.

5.9

Galileo Navigation Performance

The navigation performance in general and that of Galileo in particular is intimately related to the ranging performance, and mainly driven by three main sources of degradation:

0004815226.3D 136

• • •

Error contributions from the Galileo system itself, mainly due to the inaccurate modeling of the reference system data provided in the ephemeris and clock corrections of the navigation message for the estimation at the user level of orbits, time synchronization‚ and broadcast group delays between carrier frequencies (this one only relevant for single-frequency users) Environment errors, mainly driven by the contribution of the ionosphere in first place and then the troposphere User receiver errors caused by local interference, multipath, and receiver thermal noise

All of these errors are captured under the so-called User Equivalent Ranging Error (UERE) budget, discussed in Chapter 2, Section 2.8, which accounts for the most important sources of error as a function of the satellite elevation. Indicative RMS values for the Galileo UERE contributions are presented in Table 5.9. These are the error contributions expected to be achieved for the Galileo OS in nominal operations. The values correspond to the case that the satellites are received at medium elevations around 45 and at the maximum operational Age Of Data (AOD). The AOD corresponds to the difference between the moment at which the navigation message was generated by the GMS and the maximum valid prediction interval of the clock and orbit estimation (100 min). Thus, the ranging performance at the AOD will be mainly determined by the deviation of the ODTS estimation from the actual clock and orbit parameters, which are the most critical contents of the navigation message from the ranging performance point of view.

13/12/2020 10:19:58 AM

5.10 Building the Future: Galileo Evolutions

137

Table 5.9 Typical range of elevation-dependent error sources UERE budget [m]

Single-frequency user

Dual-frequency user

Signal in space ranging error (SISE)

0.67

0.67

Residual ionosphere error

6 (5 )–3 (90 )

0.08 (5 )–0.03 (90 )

Residual troposphere error

1.35 (5 )–0.14 (90 )

1.35 (5 )–0.14 (90 )

Thermal noise, interference, multipath

0.35 (5 )–0.23 (90 )

0.46 (5 )–0.13 (90 )

Multipath bias error

0.59

0.19

Satellite BGD error

0.30

0.0

Code-carrier ionospheric divergence error

0.30

0.0

Total (1-sigma error)

6.26 (5 )–3.10 (90 )

1.59 (5 )–0.72 (90 )

Note: The two typical error budgets are based on different environmental assumptions and dynamics that explain the different values in the tables [45]. Source: European GNSS (Galileo) Initial Services—Open Service—Service Definition Document, European Commission, Issue 1.0, December 2016.

Note that the actual positioning accuracy is derived from the total UERE for a specific user and its environment, once the reception geometry is accounted for through, for example, the Dilution of Precision (DOP). For the OS dual-frequency (E1/E5) user, the required ranging accuracy amounts to approximately 130 cm. This value is indeed the threshold figure used to determine the expected availability of the service accuracy. Figures 5.28a and 5.28b depict the expected performance for an OS dual-frequency Galileo-only user in the vertical and horizontal position domain with 99.5% availability worldwide. The results are based on extensive simulations. The OS ranging error of the Galileo satellites is monitored regularly at different locations. The ranging error describes the performance of the system per signal, and does not account for the geometry of the user with respect to the constellation. Figure 5.29 shows the actual average (user location) measured ranging errors for the Galileo operational satellites between June and August 2017. As we can recognize, the measured error budgets are well within the expected performance. For the interpretation of the satellite number (Exx) in the caption and the translation into GSATxx notation, refer to Figure 5.14. One of the most important system contributions to the ranging error is the SISE, which accounts for the clock and orbit errors as seen in the user direction. Given the importance of the on-board clock system on the SISE performance, the quality of the clock and orbit estimations is validated systematically. A particularly valuable moment to perform such measurements is during the IOT following each satellite launch. During these periods, all clocks on board are operated at least for some time and tested so as to gather statistics on the performance of all of them.

0004815226.3D 137

It is worth recalling the improvement in the ranging error along the deployment of Galileo. During IOV, when only four satellites were available and the ground segment was limited to a subset of sensor stations, the achieved SISE was around 1.3 m 67%. In 2014, the SISE performance improved to approximately 1.0 m 67%, while in 2015, following the update of the ground segment, a typical SISE of 0.69 m 67% could be reached. To complement the picture on the actual performance of Galileo, Figure 5.30 shows results of the measured positioning accuracy obtained in Torino in October 2017. The position fixes were achieved through a dual-frequency E1b-E5a receiver. The measured horizontal accuracy shown in this example is well within expectations, exhibiting here less than 5 m 95% (dotted light gray line in Figure 5.30). These position results include the effect of DOP, and thus the actual nominal performance will improve as soon as Galileo becomes fully operational. Public quarterly reports on performance are available under the Galileo Service Centre website [46].

5.10 Building the Future: Galileo Evolutions While the Galileo First Generation approaches its FOC, Europe is already paving the way for its modernization. The first work on Galileo’s future started around 2007 under ESA’s EGEP, and between 2013 and 2017 Galileo conducted phase A activities in the frame of Galileo next generation. Since early 2016, these R&D and preparatory activities have progressively transitioned into the EU Horizon 2020 Framework Programme for Research and Innovation in

13/12/2020 10:19:58 AM

Expected Positioning Performance for Galileo Dual Frequency Open Service (Reference Constellation Geometry) 8

90

75 7

6

45

30 5

Latitude

15 4

0

–15 3 –30

2

–45

Vertical Positioning Accuracy in Meter (95th percentile)

60

–60 1 –75

–90 –180–165–150–135–120–105 –90 –75 –60 –45 –30 –15

0

15

30

45

60

75

90 105 120 135 150 165 180

0

Longitude

Figure 5.28a

Expected vertical positioning error for an OS dual-frequency Galileo-only user with 99.5% availability.

Expected Positioning Performance for Galileo Dual Frequency Open Service (Reference Constellation Geometry) 4

90

75 3.5

3

45

30 2.5

Latitude

15 2

0

–15 1.5 –30 1

–45

Horizontal Positioning Accuracy in Meter (95th percentile)

60

–60 0.5 –75

–90 –180–165–150–135–120–105 –90 –75 –60 –45 –30 –15

0 0

15

30

45

60

75

90 105 120 135 150 165 180

Longitude

Figure 5.28b

0004815226.3D 138

Expected horizontal positioning error for an OS dual-frequency Galileo-only user with 99.5% availability.

13/12/2020 10:19:58 AM

5.10 Building the Future: Galileo Evolutions

SIS Ranging Error in [m]

E01 E02 E03 E04 E05

E07 E08 E09 E11 E12

E19 E22 E24 E26 E30

139

Galileo F/NAV SIS Ranging Error June 2017 - August 2017

3.0

2.0

1.0

0.0 2017/06/01

2017/06/11

2017/06/21

2017/07/01

2017/07/11

2017/07/21

2017/07/31

2017/08/10

2017/08/20

2017/08/30

Figure 5.29 Galileo F/NAV SIS ranging error at average user location.

Galileo F/NAV Dual Frequency Horizontal Position Errors - 01-03/10/2017

10 Horizontal Position Accuracy (50%): 0.91 m

8

Horizontal Position Accuracy (95%): 2.4 m

South - North Error in [m]

6 4 2 0 –2 –4 –6 –8 –10 –10

–5

0 5 West - East Error in [m]

10

Figure 5.30 Horizontal position accuracy at end user level in Torino, October 2017.

Satellite Navigation in accordance with the Delegation Agreement between the EC and the ESA. In 2014, the EC drew the first Galileo Evolutions lines at mission level and put them together in the so-called European GNSS Mission Evolution Roadmap (EGMER). This document dealt with the evolution of the GNSS Mission beyond GALILEO FOC‚ and it also addressed the evolution of EGNOS toward its version V3.

0004815226.3D 139

Later in 2016, EGMER evolved into the Evolutions High Level Document (eHLD). It identifies the preliminary objectives and performance requirements that Galileo targets to fulfill around the horizon of 2030-2040, and addresses both unclassified and classified aspects. The eHLD condenses at mission level the user evolution needs gathered by the EC and the European GSA and the system architectures and technical analyses performed by

13/12/2020 10:20:00 AM

140

5 GALILEO

Figure 5.31

GNSS evolutions R&D examples.

ESA in the previous years, leading to the identification of several increasingly demanding evolution scenarios. These scenarios were the outcome of a cycle of discussions between the EC and the Member States of the European Union, in the frame of the so-called Working Group EGNSS Evolution (WGEE). Three mission evolution scenarios were consolidated between end 2016 and early 2017 in the frame of the Phase A Activities that lead to the System PRR, and will be further studied in a Phase B0/B1 that will later to the System Requirements Review (SRR). After this‚ and based on the feedback at mission and system level, the final evolution scenario will be selected (Figure 5.31).

3 Ávila Rodríguez, J.Á., On Generalized Signal Waveforms for

4

5

6 7

References 1 De Gaudenzi, R., Hoult, N., Batchelor, A., Burden, G., and

Quinlan, M., Galileo Signal Validation Development, John Wiley & Sons Ltd., 2000. 2 Hein, G.W., Godet, J., Issler, J-L., Martin, J-C., LucasRodriguez, R., and Pratt, T., “The Galileo Frequency Structure and Signal Design,” Proc. ION GNSS, Salt Lake City, Utah, USA, September 2001.

0004815226.3D 140

8

Satellite Navigation, Doctoral Thesis, University FAF Munich, 2008, available at https://athene-forschung. unibw.de/doc/86167/86167.pdf. Betz, J.W., Engineering Satellite-Based Navigation and Timing: Global Navigation Satellite Systems, Signals, and Receivers, Wiley-IEEE Press, February 2016. European Union, European GNSS (Galileo) Open Service Signal In Space Interface Control Document (OS SIS ICD) OS SIS ICD, Issue 1.3, December 2016. NAVSTAR GPS Space Segment/User Segment L1C Interface IS-GPS-800, 24 September 2013. Regulation (EU) No 1285/2013 of the European Parliament and of the Council of 11 December 2013 on the implementation and exploitation of European satellite navigation systems and repealing Council Regulation (EC) No 876/2002 and Regulation (EC) No 683/2008 of the European Parliament and of the Council. http://eur-lex.europa.eu/LexUriServ/LexUriServ. do?uri=OJ:L:2013:347:0001:0024:EN:PDF, accessed 15 April 2017. ITU-R Recommendation TF.460-6, “Standard-Frequency and Time-Signal Emissions,” International

13/12/2020 10:20:00 AM

References

9

10

11

12 13 14

15 16

17

18

19

20

21

22

0004815226.3D 141

Telecommunication Union, Radio-communication Bureau, Geneva, February 2002. Píriz, R., García, Á.M., Tobías, G., Fernández, V., Tavella, P., Sesia, I., and Hahn, J., “GNSS interoperability: Offset between reference time scales and timing biases,” Metrologia 45(6), pp. 87–102, 2008. Defraigne, P., Aerts, W., Cerretto, G., Signorile, G., Cantoni, E., Sesia, I., Tavella, P., Cernigliaro, A., Samperi, A., and Sleewaegen, J.M., “Advances on the use of Galileo Signals in Time Metrology: Calibrated Time Transfer and Estimation of UTC and GGTO Using a Combined Commercial GPS-Galileo Receiver,” Proc. 45th PTTI Systems and Applications Meeting, Bellevue, Washington 2013, pp. 256–262. Hahn, J.H. and Powers, E.D., “Implementation of the GPS to Galileo Time Offset (GGTO),” Proc. IEEE International Frequency Control Symposium and Exposition, Vancouver, BC, Canada 2005. Galileo High Level Definition Document (HLD), Version 3.0, September 23rd 2002. Blonski, D., “Galileo IOV and First Results,” Proc. ENC, Vienna, Austria, Apr. 2013. Blonski, D., “Performance Extrapolation to FOC & Outlook to Galileo Early Services,” Proc. ENC 2014, Rotterdam, the Netherlands, April 2014. Langley, R.B., “Dilution of precision,” GPS World 10(5), pp. 52–59, 1999. Pauly, K., “Galileo FOC–Design, Production, Early Operations after 1st Launch, and Project Status,” Proc. IAC14-B2.2.1, 65th International Astronautical Congress (IAC 2014), Toronto, Canada, September 2014. Konrad, A., Fischer, H.-D., Müller, C., Oesterlin, W., “Attitude & Orbit Control System for Galileo IOV,” Proc. 17th IFAC Symp. on Automatic Control in Aerospace, Toulouse, June 2007. Zandbergen, R., Dinwiddy, S., Hahn, J., Breeuwer, E., and Blonski, D., “Galileo Orbit Selection,” Proc. ION GNSS, Long Beach, CA Sep. 2004, pp. 616–623. Navarro-Reyes, D., Notarantonio, A., and Taini, G., “Galileo Constellation: Evaluation of Station Keeping Strategies,” Proc. 21st International Symposium on Space Flight Dynamics, Toulouse, France 2009. Burbidge, G.T.A., “Development of the Navigation Payload for the Galileo In-Orbit Validation (IOV) Phase,” Proc. IGNSS Symposium 2007, Sydney, Australia, Dec. 2007, pp. 1–15. Felbach, D., Heimbuerger, D., Herre, P., and Rastetter, P., “Galileo Payload 10.23 MHz Master Clock Generation with a Clock Monitoring and Control Unit (CMCU),” Proc. IEEE FCS and 17th EFTF, Tampa, FL 4–8 May 2003, pp. 583–586. Felbach, D., Soualle, F., Stopfkuchen L., and Zenzinger, A., “Clock Monitoring and Control Units for Navigation Satellites,” Proc. IEEE FCS, Newport Beach, CA 1–4 June 2010, pp. 474–479.

141

23 Montesano, A., Montesano, C., Caballero, R., Naranjo, M.,

24

25

26

27

28

29

30

31

32

33

34

35 36

Monjas, F., Cuesta, L.E., Zorrilla, P., and Martinez, L., “Galileo System Navigation Antenna for Global Positioning,” Proc. 2nd EuCAP 2007, Edinburgh, November 2007, pp. 1–6. Valle, P., Netti, A., Zolesi, M., Mizzoni, R., Bandinelli, M., and Guidi, R., “Efficient Dual-Band Planar Array Suitable to Galileo,” Proc. 1st EUCAP, Nice, November 2006, pp. 1–7. Cospas-Sarsat: International Satellite System for Search and Rescue. Technical Papers T-001, T-014, T-016...020, and C/S R.012. URL http://www.cospassarsat.org/ Paggi, F., Stojkovic, I., Oskam, D., Breeuwer, E., Gotta, M., and Marinelli, M., “SAR/Galileo IOV Forward Link Test Campaign Results,” Proc. ENC, Rotterdam, the Netherlands, April 2014. Paggi, F., Stojkovic, I., Postinghel, A., Ratto, D., Breeuwer, E., and Gotta, M., “SAR/Galileo IOV Return Link Test Campaign Results,” Proc. ENC, Rotterdam, the Netherlands, April 2014. Hein, G.W., Avila-Rodriguez, J.-A., Ries, L., Lestarquit, L., Issler, J.-L., Godet, J., and Pratt, A.R., “A Candidate for the Galileo L1 OS Optimized Signal,” Proc. ION ITM, Long Beach, California, USA, September 2005. Ries, L., Issler, J.-L., Julien, O., and Macabiau, Ch., “Method of Reception and Receiver For a Radio Navigation Signal Modulated by a CBOC Spread Wave Form,” Patents US8094071, EP2030039A1, January 2012. Julien, O., Macabiau, C., Ries, L., and Issler, J.-L., “1-Bit Processing of Composite BOC (CBOC) Signals and Extension to Time-Multiplexed BOC (TMBOC) Signals,” Proc. ION NTM, San Diego, CA, January 2007, pp. 227–239. De Latour, A., Artaud, G., Ries, L., Legrand, F., and Sihrener, M., “New BPSK, BOC and MBOC Tracking Structures,” Proc. ION ITM, Anaheim, CA, January 2009, pp. 396–405. Winkel, J., “Spreading Codes for a Satellite Navigation System,” Patent number WO/2006/063613, International Application No.: PCT/EP2004/014488, Publication date: 22 June 2006. Avila-Rodriguez, J.-A., Hein, G.W., Wallner, S., Issler, J.-L., Ries, L., Lestarquit, L., de Latour, A., Godet, J., Bastide, F., Pratt, A.R., Owen, J.I.R., Falcone, M., and Burger, T., “The MBOC Modulation: The Final Touch to the Galileo Frequency and Signal Plan,” Proc. ION GNSS, Fort Worth, Texas, USA, September 2006. Rebeyrol, E., Macabiau, C., Lestarquit, L., Ries, L., Issler, JL., Boucheret, M.L., and Bousquet, M., “BOC Power Spectrum Densities,” Proc. ION NTM 2005, Long Beach, California, USA, January 2005. Godet, J., “Technical Annex to Galileo SRD Signal Plans,” STF annex SRD 2001/2003 Draft 1, July 2003. Ries, L., Legrand, L., Lestarquit, L., Vigneau, W., and Issler, J.-L.: “Tracking and Multipath Performance Assessments

13/12/2020 10:20:01 AM

142

5 GALILEO

37

38

39

40

0004815226.3D 142

of BOC Signals using a Bit Level Signal Processing Simulator,” Proc. ION GPS, Portland, OR, USA, 2003, pp. 1996–2010. Soellner, M. and Erhard, Ph., “Comparison of AWGN Tracking Accuracy for Alternative-BOC, Complex- LOC and Complex-BOC Modulation Options in Galileo E5 Band,” Proc. ENC GNSS, Graz, Austria, 2003. Lestarquit, L., Artaud, G., and Issler, J.-L., “AltBOC for Dummies or Everything You Always Wanted to Know About AltBOC,” Proc. ION GNSS 2008, Savannah, GA, 2008, pp. 961–970. Soualle, F., Soellner, M., Wallner, S., Avila-Rodriguez, J.A., Hein, G.W., Barnes, B., Pratt, T., Ries, L., Winkel, J., Lemenager, C., and Erhard, P., “Spreading Code Selection Criteria for the Future GNSS Galileo,” ENC GNSS 2005, Munich, July 2005. Falcone, M., Binda, S., Breeuwer, E., Hahn, J., Spinelli, E., Gonzalez, F., Lopez Risueno, G., Giordano, P., Swinden, R., Galluzzo, G., and Hedquist, A., “Galileo on Its Own: First Position Fix,” Inside GNSS 8(2), March/April 2013, pp. 50–71.

41 European GNSS (Galileo) Open Service–Ionospheric

42

43

44

45

46

Correction Algorithm for Galileo Single Frequency Users, European Commission, September 2016. Hochegger, G., Nava, B., Radicella, S., and Leitinger, R., “A Family of Ionospheric Models for Different Uses,” Proc. Physics and Chemistry of the Earth, Part C: Solar, Terrestrial & Planetary Science 25(4): 307–310. doi:10.1016/ S1464-1917(00)00022-2. Ionospheric Propagation Data and Prediction Methods Required for the Design of Satellite Services and Systems, Rec. ITU-R P. 531-12, ITU, September 2013. Prieto-Cerdeira, R., Orus-Perez, R., Breeuwer, E., LucasRodriguez, R., and Falcone, M., “Performance of the Galileo Single-Frequency Ionospheric Correction During In-Orbit Validation,” GPS World 25(6), 2014, pp. 53–58. European GNSS (Galileo) Initial Services Open Service— Service Definition Document, European Commission, Issue 1.0, December 2016. https://www.gsc-europa.eu/

13/12/2020 10:20:01 AM

143

6 BeiDou Navigation Satellite System Mingquan Lu and Zheng Yao Tsinghua University, China

6.1

Introduction

The BeiDou Navigation Satellite System (BDS) is China’s space-based navigation system, designed to be compatible and interoperable with other global navigation satellite systems (GNSSs) [1–3]. The name “BeiDou” (“北斗” in Chinese) means the Big Dipper, an asterism consisting of seven bright stars in the constellation Ursa Major. As one of the most familiar celestial objects in the northern sky, it served as a useful navigation tool in ancient China and was, therefore, selected to be the name of the Chinese satellite navigation system [4, 5]. Similar to other GNSSs, BDS comprises three segments: the space segment, the ground segment, and the user segment. The space segment is a hybrid constellation consisting of geostationary Earth orbit (GEO) satellites, inclined geosynchronous orbit (IGSO) satellites, and medium Earth orbit (MEO) satellites. The ground segment is a distributed ground control network consisting of one master control station (MSC), several time synchronization stations and uploading stations, as well as many monitoring stations. The user segment includes all BDS user terminals. Because of this unique hybrid constellation structure, BDS is a multifunction system that integrates many services. It not only provides basic radio navigation satellite services (RNSSs), namely, users’ position, velocity, and time (PVT) services, as do other GNSSs, but BDS also provides radio determination satellite services (RDSSs), satellite-based augmentation services (SBASs), and search and rescue (SAR) services [6, 7]. The hybrid constellation and multifunctionality are the main differentiation characteristics of BDS from other GNSSs. China’s BDS program began in the 1990s. In order to overcome various difficulties such as limited funds, insufficient technological resources‚ and lack of construction and management experience in large-scale space-based

information systems, China formulated the following three-step development plan for BDS [2, 3]: Step 1: Start the development of the BDS Experimental System (BDS I, also known as BD-1 in earlier times) in 1994 to achieve regional active positioning PNT capability by 2000. Step 2: Start the development of the BDS Regional System (BDS II, also known as BD-2 in earlier times) in 2004 to achieve regional passive PNT service capability by 2012. Step 3: Steadily push forward the development of the BDS and start the development of the BDS Global System (BDS III) in 2013 to achieve global passive PNT service capability by approximately 2020. The three-step development plan of BDS is illustrated in Figure 6.1 [5, 7]. After more than two decades of steady progress, China has completed the first two steps of the development plan. BDS I was established in 2000 as the first generation of China’s navigation satellite system. With three satellites (2+1 GEO), BDS I adopted a two-way active ranging scheme to provide RDSSs for China and surrounding areas. Since then, China has been operating its own independent navigation satellite system and developed its own satellite navigation industry [2, 6, 7]. After more than a decade of continuous operation, BDS I terminated its services at the end of 2012. The second generation of China’s navigation satellite system, BDS II, with a space segment of 14 operational satellites (5 GEO+5 IGSO+4 MEO), was established and began to provide services for the Asia-Pacific region at the end of 2012. In addition to providing RNSS services, BDS II also inherited the RDSS services from its predecessor, BDS I. The completion of BDS II greatly expanded the applications of satellite navigation in China and further promoted the development of its satellite navigation industry [2, 6, 7].

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c06.3d

143

15/12/2020

11:29:57 PM

144

6 BeiDou Navigation Satellite System

BDS I

BDS II

BDS III

Experimental System 2000 IOC, 2003 FOC

Regional System 2010 IOC, 2012 FOC

Global System 2018 IOC, 2020 FOC

3GEO Regional Coverage RDSS Service First Step

Figure 6.1

5GEO/5IGSO/4 MEO Regional Coverage RDSS/RNSS Service Second Step

6.2

BDS Evolution

6.2.1

The Beginning

Research in China for a satellite navigation system can be traced back to the late 1960s [5, 9]. In January 1969, an exploratory project named 691 was established as a Doppler navigation system analogous to Transit. This effort lasted for about 10 years [9]. In the late 1970s, China continued to search for a suitable solution to provide regional or global services for China. Several regional satellite navigation systems with single satellite, twin satellites, and three to five

144

Third Step

The three-step development plan of BDS.

After the completion of BDS II deployment, China immediately started developing BDS III in 2013. The BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signals B1C, B2a (Beta) was released on 5 September 2017 [8]. The first two BDS III satellites were launched on 5 November 2017. It is expected that BDS III will complete its deployment and provide global services by approximately 2020 [6, 7]. The unique and successful GNSS development path “from regional to global and from active to passive” implemented by the Chinese offers a different approach from Global Positioning System (GPS), GLONASS, and Galileo [3]. This chapter provides a comprehensive and in-depth introduction to BDS. Section 6.2 outlines the evolution of BDS. Section 6.3 introduces the geodesy and time systems employed by BDS. Sections 6.4 and 6.5 describe BDS I and BDS II, respectively. Section 6.6 presents the latest progress of the emerging BDS III. Finally, Section 6.7 offers a brief summary of BDS.

c06.3d

3GEO/3IGSO/24MEO Global Coverage RDSS/RNSS/SBAS Service

satellites were considered. GNSSs with more satellites were also proposed. None of those ideas or proposals, however, materialized. In 1983, Mr. Fangyun Chen from the Chinese Academy of Sciences proposed the idea of a regional positioning and communication system with two GEO satellites, called the Dual-Star Positioning System. At that time, GPS had already achieved great success. However, the Dual-Star system using only two satellites was more attractive to China because it was relatively simple, low cost, and had the capability of both positioning and communication. In 1986, the Dual-Star Positioning System project received support from the Chinese government. In 1987, Chen et al. published a paper in which the system architecture, operating principles and mechanisms, and the expected performance of the Dual-Star Positioning System were discussed in detail [10]. In 1989, preliminary demonstration and verification experiments were carried out by using two on-orbit communication satellites. These experiments successfully validated the technical feasibility of the Dual-Star Positioning System [11]. After eight years of research, demonstration‚ and verification, China started developing the complete Dual-Star Positioning System in 1994. This system was officially named BeiDou One, or BD-1 for short. In October and December 2000, two GEO satellites, BD-1 01 and BD-1 02, were successfully launched into geosynchronous orbit from the Xichang Satellite Launch Center. Shortly afterward, BD-1 was declared to have initial operational capability. In May 2003, a third GEO satellite, BD-1 03, was launched as a spare for the previous two. In December 2003, BD-1 was declared to have full operational capability. At the same time, a large number of different types of BD-1

15/12/2020

11:29:58 PM

6.2 BDS Evolution

terminal products had been successfully developed. After the United States and Russia, China became the third country to own an independently developed satellite navigation system. BD-1 adopted a two-way active ranging scheme with two GEO satellites to provide two-dimensional (2D) position, timing, and short message communication services, known as RDSS. Two signals, one outbound in the S band and one inbound in the L band, are employed for two-way active ranging and message transmission in this system [3, 5, 11]. Since 2003, BD-1 has been applied in a large variety of applications, including mapping, telecommunication, water conservancy, marine fisheries, transportation, forest fire prevention, disaster mitigation and relief, public safety, etc. BD-1 played a critical role in the 2008 Wenchuan earthquake rescue effort and in support of the 2008 Beijing Olympics [1]. Short message communication service is a unique advantage and the most successful application of BD-1. However, BD-1 also has notable disadvantages due to constraints in its technical design and system scale. It only provides a small service coverage area with limited user capacity, low 2-D positioning accuracy, inability to provide velocity measurement, etc. In addition, BD-1 user terminals must include a transmitter, leading to limitations in size, weight, power consumption, and cost [1]. Overall, BD-1 was a successful, practical, and economical navigation satellite system that provided regional PNT for China. Even after BD-1 was decommissioned in December 2012, the RDSS continues to be provided by the newgeneration BDS.

6.2.2

From Active to Passive

After completing the deployment of BD-1, China started the second step of the BDS development plan in 2004. The goal was to build a regional navigation satellite system with the capability of continuous, real-time, passive threedimensional (3D) PVT services for the Asia-Pacific region [2, 4]. This system at the time was named BeiDou Two, or BD-2 for short. In April 2007, the first BD-2 MEO satellite was successfully launched. Meanwhile, many technical experiments involving domestically produced space-borne atomic clocks, precise orbit determination and time synchronization, signal transmission schemes, etc., were conducted. In April 2009 and August 2010, the first BD-2 GEO satellite and the first BD-2 IGSO satellite were launched respectively. With these satellites in different orbits, more critical technologies relating to GEO and IGSO satellite operations were validated. By April 2011, a preliminary constellation with three GEO and three IGSO satellites was built. With

c06.3d

145

145

the release of the BD-2 interface control document (test version in Chinese) in December 2011, BD-2 began its trial operation. After more satellites were successively launched, the construction of the BD-2 space segment with five GEO satellites, five IGSO satellites, and four MEO satellites, was completed in 2012. During the deployment of the BD-2 space segment, the BD-2 ground control segment and various BD-2 and BD-2/GNSS-compatible terminals were also developed. Similar to GPS, GLONASS, and Galileo, BD-2 uses oneway passive ranging (passive trilateration) to determine a user’s position. This system transmits six navigation signals at three frequencies (B1, B2, and B3) in the L band to provide continuous, real-time RNSS [12]. With 14 operational satellites in orbit, users can track at least 4 BD-2 satellites anywhere, anytime in the Asia-Pacific region. The position and time performance of BD-2 in its coverage area is compatible with that of other GNSSs. In addition to providing RNSS, the new system also provides RDSS via its GEO satellites [13]. In December 2012, the China Satellite Navigation Office (CSNO) formally declared that BD-2 had begun to provide PNT services for China and most of the Asia-Pacific region. The official English name of BD-2, the BeiDou Navigation Satellite System, or BDS for short, was also announced. An interface control document was also released [7]. The threestep development plan mentioned above was also officially announced at that time. In December 2013, at a press conference held on the oneyear anniversary of the BDS full operation declaration, CSNO announced that BDS performance fully met its design specifications based on signal monitoring and assessment over the Asia-Pacific region. Two additional documents, BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signal (Version 2.0) and BeiDou Navigation Satellite System Open Service Performance Standard (Version 1.0), were also published [13]. It is noteworthy that during the five-year period since BDS II became operational in 2012, CSNO has only released one ICD for its two open service signals B1I and B2I. The latest BDS II ICD for the two open service signals is version 2.1 [12]. However, the detailed format of its third open service signal, B3I, has already become an open secret. Not only many Chinese domestic companies, but also some international companies have developed triple-frequency BDS II receivers that are capable of utilizing B1I, B2I, and B3I signals. BDS is actually ahead of GPS and Galileo in providing high-performance triple-frequency open civil service. In January 2018, the ICD for the B3I signal was officially released by CSNO [14], making BDS II the first navigation satellite system in the world to provide triple-frequency open service.

15/12/2020

11:29:59 PM

146

6 BeiDou Navigation Satellite System

6.2.3

From Regional to Global

The third step in the BDS development plan is to extend the current regional BDS II system to a global system BDS III [2–5]. The BDS III plan envisions a global constellation of 30 satellites, including 3 GEO, 3 IGSO, and 24 MEO satellites to provide worldwide services by approximately 2020. In addition to retaining RDSS, SBAS and SAR will also be integrated into the system [6]. The most anticipated feature is that, by sharing two frequencies in the L band and adopting advanced signal structures, BDS III will be compatible and interoperable with other GNSSs, especially with GPS and Galileo. This implies that BDS III will be further integrated into the international GNSS family to provide worldwide users with better services by jointly using BDS III and other GNSSs [3, 6]. The research for development of BDS III commenced in 2009. The implementation of BDS III started in 2013. From March 2015 to February 2016, five experimental satellites in various orbits were sequentially launched into space for BDS III. In the following years, various technical validation tasks have been performed with the focus on space-borne atomic clocks, inter-satellite links, and new navigation signals. The successful launch of the five experimental satellites has laid the groundwork for the global deployment of BDS III [6]. At the time of this writing, the third step of the BDS development plan is in the deployment stage. The first draft ICD of BDS III was released in September 2017 [7]. This document for the first time clearly identified the BDS III constellation configuration and some of the new navigation signals. At a minimum, two new open service signals, B1C and B2a, which are compatible and interoperable with other GNSS signals, will be broadcast by the MEO and IGSO satellites of BDS III. Following the release of the draft ICD, the first pair of the BDS III satellites was launched in November 2017. They broadcast the B1C and B2a signals and are also equipped with higher-performance rubidium clocks with a stability of 10−14 and a hydrogen atomic clock with a stability of 10−15. By utilizing these state-of-the-art technologies, the signal-in-space (SIS) accuracy will be better than 0.5 m. The successful launch of the first pair of the BDS III satellites marked the beginning of BDS expansion from regional to global coverage [6]. Most recently, the Joint Statement on Civil Signal Compatibility and Interoperability Between the Global Positioning System (GPS) and the BeiDou Navigation Satellite System (BDS) was signed in December 2017 [15]. Two formal ICDs for B1C and B2a were released in late December 2017 [16, 17]. In addition to the first pair of MEO satellites, three more pairs of MEO satellites have been successfully launched into their scheduled orbits in January, February ‚ and March 2018, respectively.

c06.3d

146

BDS is rapidly expanding from a regional system to a global system. The plan is to deploy 18 MEO satellites and provide initial services by the end of 2018 [1, 3, 5]. By 2020, all 30 planned satellites will join the global constellation to complete BDS III as a multifunctional GNSS system compatible and interoperable with other GNSSs. At the end of this section, we want to clarify that BDS has assumed different Chinese and English names at different times and in the open literature. For example, BD-2, BDS-2, Compass, BeiDou Phase II, BDS II, BeiDou, and Beidou all refer to the current BDS regional system constructed in the second step of the three-step development plan. To ensure consistency, in the remainder of this chapter, BDS I, BDS II, and BDS III will be used to refer to the experimental system, the regional system, and the global system of BDS, respectively.

6.3

Geodesy and Time Systems

6.3.1

The BDS Geodesy System

The Beijing Geodetic Coordinate System 1954 and the National Vertical Datum 1985 were once used as the coordinate system for BDS I [4]. With the development of BDS, these legacy coordinate systems no longer satisfy the needs of a modern navigation satellite system. Currently, the BeiDou Coordinate System (BDCS) is used in BDS II and the emerging BDS III [14, 16, 17]. BDCS is a new term that has appeared in the most recent ICDs for B1C, B2a‚ and B3I. It is based on the China Geodetic Coordinate System 2000 (CGCS2000) [18] that appeared in the previous versions of the ICDs [12]. The definition of BDCS is in accordance with the specifications of the International Earth Rotation and Reference System Service (IERS) and is consistent with CGCS2000. BDCS and CGCS2000 have the same ellipsoid parameters. The definition of BDCS is as follows [14, 16, 17]: 1) Definition of origin, axis and scale The BDCS origin is located at Earth’s center of mass. The Z-Axis is the direction of the IERS Reference Pole (IRP). The X-Axis is the intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-Axis. The Y-Axis, together with Z-Axis and X-Axis, constitute a righthanded orthogonal coordinate system. The length unit is the International System of Units (SI) meter. 2) Definition of the BDCS Ellipsoid The geometric center of the BDCS Ellipsoid coincides with Earth’s center of mass, and the rotation axis of

15/12/2020

11:29:59 PM

6.4 BDS I: The BDS Experimental System

6.4.2 System Configuration and Positioning Principle

Table 6.1 Parameters of the BDCS ellipsoid Parameter

Definition

Semi-major axis

a = 6378137.0 m

Geocentric gravitational constant

μ = 3.986004418 × 10 m / s2

Flattening

f = 1/298.257222101

Earth’s rotation rate

Ω = 7.2921150 × 10−5rad/s

6.4.2.1 The System Configuration of BDS I 14

3

the BDCS Ellipsoid is the Z-Axis. The parameters of the BDCS Ellipsoid are shown in Table 6.1.

6.3.2

The BDS Time System

The time system of BDS is BeiDou Time (BDT) [14, 16, 17]. BDT adopts the International System of Units (SI) second as the base unit and accumulates continuously without leap seconds. The start epoch of BDT is 00:00:00 on January 1, 2006 Coordinated Universal Time (UTC). BDT aligns with UTC via UTC (NTSC), and the deviation of BDT to UTC is maintained within 50 nanoseconds (modulo 1 second). The leap second information is broadcast in the navigation message.

6.4 BDS I: The BDS Experimental System 6.4.1

Overview

The BDS experimental system, BDS I, was the first generation of the BeiDou Navigation Satellite System. Unlike other GNSSs, it was a two-way active positioning system designed to provide regional RDSS service, including two-dimensional position, timing, and short message communication. It also consisted of three segments: the space segment with three GEO satellites (including one in-orbit spare), the control segment with one MSC and several calibration stations, and the user segment with various types of user terminals [1, 4, 5, 11]. It was established in 2000 after the successful launch of two operational GEO satellites. In addition, a spare GEO satellite was launched in 2003. BDS I was declared operational soon afterward. A fourth GEO satellite, the final BDS I satellite, was launched in 2007. The service coverage of BDS I included China and surrounding areas (70 E–140 E, 5 N–55 N). The horizontal positioning accuracy of BDS I was 20 m (with calibration) or 100 m (without calibration) [1]. After 10 years’ continuous operation, this experimental system reached mission end in December 2012.

c06.3d

147

147

The BDS I space segment consisted of two operational and one in-orbit spare GEO satellites, orbiting at 80 E, 140 E, and 110.5 E, respectively. The satellites’ orbit altitudes were about 36,000 km. Each satellite had two outbound and two inbound transponders. While the outbound transponders forwarded the signals transmitted from the MSC to the user terminals, the inbound transponders relayed the signals transmitted from the user terminals to the MSC (Figure 6.2). The control segment of BDS I included one MSC in Beijing and more than 20 calibration stations distributed inside China. The main tasks of the MSC included the following: transmitting the outbound signals and receiving the inbound signals, performing satellite orbit determination and ionosphere correction, calculating users’ location, and exchanging short messages for users. The calibration stations provided the basic measurements for orbit determination, differential position, and user elevation computation from barometric altimeter data. The user segment of BDS I consisted of various types of user terminals. The main functions of the BDS I user terminals included the following: transmitting the inbound signal to send the positioning request to the MSC or a short message to other users and receiving the outbound signal to receive location information from the MSC. These user terminals can be classified into two types: one is the basic terminal to provide position, timing, and short message services for personal, vehicular, and ship users; the other is the command terminal, which can control and manage a group of up to 100 individual basic terminals. Although the RDSS service is free of charge, each BDS I user was registered and obtained a unique subscriber number to use the RDSS service. Hence, the RDSS service belonged to the authorized service category.

6.4.2.2 BDS I Position Method

BDS I relied on a pair of two-way radio links between the MSC and a user terminal through the two different transponders on two GEO satellites. Based on the measured transmission time of each two-way radio link, the total distance from the MSC through one GEO satellite to the user terminal could be determined. Because the distance between the MSC and the GEO satellite is known, the distance between this GEO satellite and the user terminal could be extracted from the total distance. Using each of the two-way radio links with the two different satellites, two distance measurements from the user terminal to the

15/12/2020

11:29:59 PM

148

6 BeiDou Navigation Satellite System

Space Segment

Control Segment Control Center

Calibration System

Networks User Segment

Users Ships

Aircrafts

Individuals Commanders Vehicles

Figure 6.2

Schematic diagram of BDS I.

two satellites were obtained. In this way, the so-called twoway ranging was achieved [1, 10, 11]. By using the two distance measurements between the user terminal and the two satellites, as well as the known positions of the two satellites, the 2-D position of the user terminal was calculated. The detailed position procedure is as follows [4, 19]. By using the known position coordinates of the two GEO satellites as two different sphere centers, and using the measured distances from the satellites to the user terminal as radii, respectively, two spheres can be formed. The user terminal must be on the intersection of the two spheres. Using an elevation map provided by the ground control segment, a non-homogeneous Earthcentered curved surface can be established with the Earth center as the origin and the distance from the Earth center to the user terminal as its radius. The exact position of the user terminal is the intersection of the spherical arc and the non-homogeneous curved surface. The MSC calculated the user terminal’s position following this procedure and sent the position to the user terminal via the outbound signal [1, 10, 11].

6.4.3

Outbound and Inbound Signal

Each BDS I user terminal was a transceiver with the capability of transmitting outbound signals and receiving inbound signals. From the user’s point of view, the BDS I signal included an outbound signal transmitted from the satellite to the user terminal and an inbound signal transmitted from the user terminal to the satellite. According to the ITU frequency allocation for RDSS, the outbound

c06.3d

148

and inbound signals of BDS I used the S band (2483.5–2500 MHz) and the L band (1610–1626.5 MHz), respectively. 6.4.3.1 Outbound Signal

The outbound signal was a direct sequence spread spectrum (DSSS) signal with a carrier frequency of 2491.75 MHz and a bandwidth of 8.16 MHz. This signal adopted offset quadrature phase-shift-keying (OQPSK) modulation with a continuous frame structure. Its minimum power was −157.0 dBW on the ground. The outbound signal model is [19, 20] soutbound t = A d1 t − Δ 2 c1 t − Δ 2 sin ωc t + d2 t c2 t cos ωc t

61

where A is the signal amplitude; d1(t) and d2(t) are the data streams of the I and Q components, respectively; c1(t) is the spreading code of I component, using a Kasami small set sequence with a code length of 255. c2(t) is the spreading code of the Q component, using a Gold code sequence with a code length of 221 − 1. The rate of both spread-spectrum codes is 4.08 Mcps. The I and Q components are in carrier quadrature with each other to constitute an OQPSK signal, with a symbol rate 16 ksps. Δ is the half code chip length [20]. d1(t) is used to transmit position, communication, calibration, and other public information, and d2(t) is used to transmit location and communication information. The outbound signal generation diagram is shown in Figure 6.3. Figure 6.4 shows the data frame structure. Each frame consists of 250 bits with its own frame number. The information bit rate is 8 kbps, and the symbol rate becomes 16 ksps after convolution coding. Therefore, the transmission time of a single frame is 31.25 ms. 1920

15/12/2020

11:29:59 PM

6.4 BDS I: The BDS Experimental System

149

I-Channel Data Frame ···

Frame 1920 Frame 1919

···

Frame K

Frame 1

I Branch

Small Set of Kasami Sequence (L = 255) 8KHz

Carrier

Σ

4.08MHz Gold Sequence (L = 221–1)

Outbound Signal

90°

Delay (Δ/2) Q-Channel Data Frame ···

Frame 1920 Frame 1919

···

Frame K

Q Branch

Frame 1

Figure 6.3 Generation diagram of outbound signal.

A superframe Frame 1

Frame 2

Frame 3

...

Frame k

...

Frame 1920

Frame 1

Frame k Data 142

CRC 16

Frame 2

...

250 bits

I branch

Label 7

Frame No. 11

Q branch

Tail 6

Type 8

Public Broadcase Suppression Frame Frame Frame 12 4 2

ID1 21

ID2 21

Type 8

Frame k–1 Data 220

Tail 6

CRC 16

Label 7

Tail 6

250 bits

Figure 6.4 Frame structure of outbound signal.

frames form a super frame. Sending a super frame took 1 min [21].

6.4.3.2 Inbound Signal

The inbound signal was a DSSS signal with a carrier frequency of 1615.68 MHz and a bandwidth of 8.16 MHz. The transmit power was not less than 10 W. This signal adopted BPSK modulation with a variable burst frame structure. The burst frame consisted of three segments: synchronization header, service segment, and data segment. Each segment was spread with three different pseudorandom noise (PRN) codes with a code rate of 4.08 Mcps. The symbol rate was 8 kbps [20]. The inbound signal model is sinbound t = Ac t d t cos ωc t

62

where A is the signal amplitude, and c(t) and d(t) are the spreading code and the user data stream, respectively.

c06.3d

149

For user data, the synchronization header was a truncated m-sequence with length 12240. The spreading code of the service segment was a truncated sequence from an m-sequence with period 221 − 1, and the length of the truncated sequence was determined by the length of the corresponding service section information. The spreading code of the data segment was a Gold code with register length 21, and the spreading code rate was 4.08 MHz. In the inbound signal, since the segment length was variable, the burst frame length was also variable [20]. The variable frame structure of the inbound signal is shown in Figure 6.5.

6.4.4

Service and Performance

As mentioned earlier, BDS I provided unique RDSS services including rapid positioning, precision timing, and short message communication for users in China and surrounding areas. The BDS-1 service area is illustrated in Figure 6.6 and was determined by the location of its geostationary

15/12/2020

11:30:00 PM

150

6 BeiDou Navigation Satellite System

I-Channel Data Frame 8KHz

16KHz

Tail CRC

Data Segment

Data Symbol after convolution coding

Service Segment

Synchronization Header

Inbound Signal

4.08MHz

c06.3d

150

Gold Sequence

M Sequence

Truncated M Sequence

Figure 6.5

Frame structure of inbound signal.

Figure 6.6

Service coverage of BDS I [4]. Source: Reproduced with permission of Springer Nature.

Carrier

15/12/2020

11:30:00 PM

6.5 BDS II: The BDS Regional System

151

satellites as well as the distribution of the calibration stations. The service performance specification of BDS I is summarized as follows [1, 4, 5]: 1) Positioning accuracy: 20 m (with calibration) or 100 m (without calibration) 2) Timing accuracy: 100 ns (one-way), 20 ns (two-way) 3) Short message: 1680 bits/message (120 Chinese characters / message) 4) User capacity: 54 million times/hour (150 times/second) 5) Service area: China and surrounding areas (70 E–145 E, 5 N–55 N) 6) User dynamic range: User speed less than 1000 km/h

6.5

BDS II: The BDS Regional System

6.5.1

Overview

BDS II was developed starting in 2004. It utilizes the oneway time-of-arrival (TOA) ranging scheme to provide regional RNSS service, including continuous 3-D PVT. This system also consists of three segments: the space segment with 14 operational satellites, the control segment with several MSCs, uploading stations and monitoring stations, and the user segment with various BDS II and BDS II/GNSScompatible receivers. After the first BDS II MEO satellite was launched in April 2007, 15 more satellites were sequentially launched within the next five years. A hybrid constellation of 14 operational satellites was eventually built by 2012. In December 2012, CSNO declared the full operational capability (FOC) for BDS II with coverage for China and the Asia-Pacific region. In addition to RNSS services, BDS II also provides RDSS services inherited from BDS I. BDS II has now been operating continuously for more than five years.

6.5.2

Space Segment

6.5.2.1 Constellation

From April 2007 to October 2012, BDS II launched a total of 16 navigation satellites. Among them are 14 operational satellites (5 GEO + 5 IGSO + 4 MEO) as depicted in Figure 6.7 [3, 5, 13, 14]:

• •

c06.3d

151

Five GEO satellites in equatorial orbit with an altitude of 35,786 km and positioned at 58.75 E, 80 E, 110.5 E, 140 E, and 160 E, respectively. Five IGSO satellites at 35,786 km altitude with an orbit inclination of 55 with respect to the equatorial plane, and distributed in three inclined orbital planes with a right ascension of ascending node difference of 120 . The satellite ground tracks for three of the IGSO satellites

Figure 6.7 BDS-II constellation with 5 GEO + 5 IGSO + 4 MEO satellites [5]. Source: Reproduced with permission of Artech House.

•

coincide with an equatorial-crossing longitude of 118 E. The satellite tracks for the other two IGSO satellites coincide with an equatorial-crossing longitude of 95 E. Four MEO satellites at 21,528 km altitude with an orbit inclination of 55 with respect to the equatorial plane. The satellite revisit period is 13 rotations within 7 days. The phases are selected from the Walker 24/3/1 constellation. The right ascension of ascending node of the satellites in the first orbital plane is 0 . The four MEO satellites are positioned at the seventh, eighth phases of the first orbital plane and the third, fourth phases of the second orbital plane, respectively.

The orbital information for the current BDS II constellation is provided in Table 6.2 [22]. The IGSO, MEO‚ and GEO satellites are labeled as I, M, and G in the table, respectively. The orbital periods of the IGSO and MEO satellites are about one and seven days, respectively; thus the revisit period of the entire constellation is seven days. Figure 6.8 show the ground tracks of BDS satellites over a seven-day period from 25 January 2015 to 31 January 2015 (BDT). Figure 6.9 shows the average number of visible BDS II satellites over a one-week period, showing that seven to nine BDS II satellites are visible in China and the surrounding areas during this period. The above discussion highlights the difference between BDS II and GPS constellation designs: BDS II consists mostly of GEO and IGSO satellites, while GPS has all

15/12/2020

11:30:02 PM

152

6 BeiDou Navigation Satellite System

Table 6.2 Orbital information for the current BDS II constellationa

Satellite

Semi-major axis (km)

Eccentricity

Orbit inclination (deg)

Argument of perigee (deg)

Longitude of ascending node (deg)

True anomaly (deg)

1

I01

42166.2

0.0029

54.5

174.9

209.3

220.3

2

I02

42159.3

0.0021

54.7

187.8

329.6

87.0

3

I03

42158.9

0.0023

56.1

187.7

89.6

326.1

No.

a

4

I04

42167.2

0.0021

54.8

167.1

211.4

201.3

5

I05

42157.1

0.0020

54.9

183.3

329.0

65.5

6

M01

27904.9

0.0026

55.4

182.4

108.1

118.2

7

M02

27907.5

0.0028

55.3

180.0

107.6

167.5

8

M03

27905.9

0.0023

54.9

170.0

227.8

325.7

9

M04

27907.6

0.0015

55.0

190.0

227.4

351.3

10

G01

140.0E deg (orbit altitude = 35,786.0 km)

11

G02

80.0E deg (orbit altitude = 35,786.0 km)

12

G03

110.5E deg (orbit altitude = 35,786.0 km)

13

G04

160.0E deg (orbit altitude = 35,786.0 km)

14

G05

58.E6 deg (orbit altitude = 35,786.0 km)

25 January 2013, 00:00:00 GPST

60°N

30°N

0°N

–30°

–60°S

–30°W

Figure 6.8

c06.3d

152

0°

30°E

60°E

90°E

120°E

150°E

180°

150°W

120°W

Satellite ground tracks for the current BDS II constellation [5]. Source: Reproduced with permission of Artech House.

15/12/2020

11:30:03 PM

6.5 BDS II: The BDS Regional System

153

N Access (95%, 5G+5I+4M) 11 10 60°N 9 8 30°N 7 Latitude

6 0° 5 4 30°S 3 2 60°S 1 0 60°W

30°W

0°

30°E

60°E

90°E

120°E 150°E

180° 150°W

120°W 90°W

60°W

Longitude

Figure 6.9 Number of visible BDS satellites over the ground-track repetition period [data collection period: 2015/01/25 0:00–2015/01/ 31 24:00 (BDT) mask angle of 10 ].

MEO satellites; GPS satellites are distributed more evenly across the Earth than BDS II. The unevenly distributed BDS II constellation, however, provides better coverage for China and the surrounding areas [5, 22]. 6.5.2.2 Satellites

All BDS II satellites utilize the DFH-3A satellite bus [23], which includes the structure, power, thermal, control, tracking and telemetry (the IGSO/MEO satellites also have a built-in data management subsystem), propulsion subsystems, etc. The payload includes navigation and antenna subsystems. The GEO payload has the additional components needed for the provision of RDSS services, time and position data transmission, data uploading and precise ranging, and RNSS services. The MEO payload has components for uploads and precise ranging and RNSS services [1, 5]. Figure 6.10 illustrates the BDS GEO and IGSO/MEO satellites in space [24, 25].

6.5.3

Control Segment

The control segment of BDS II is responsible for the operation and control of the entire system, including precise orbit determination and orbital parameter prediction, satellite clock error measurement and prediction, ionosphere monitoring and forecasting, and integrity monitoring and

c06.3d

153

processing [25]. At the time of this writing, the BDS II control segment consists of 1 MSC, 7 Class-A monitor stations, 22 Class-B monitor stations, and 2 time synchronization/ upload stations [1, 4, 25]. The main control segment tasks are as follows [4, 5]: 1) MSC: Collect observation data of every time synchronization/upload station and monitor station, processing data, generating satellite navigation messages, uploading navigation message parameters to satellites, monitoring satellite payloads, accomplishing task planning and scheduling, implementing system operation control and management, etc. It is located in Beijing. 2) Time synchronization/upload stations: Satellite navigation message parameter upload, data exchange with the MSC, and time synchronization measurement under the unified management of the MSC. To achieve the greatest extent of satellite tracking within the Chinese territory, the two stations are located in Kashgar in western China and Sanya in southern China, respectively. 3) Monitor stations: Monitor the navigation satellites continuously, receive the navigation signals, and then send them to the MSC to provide the observation data for the navigation message generation. Class-A monitor stations are for the satellite orbit determination and the satellite clock error measurement and are therefore distributed within the territory with the largest spatial

15/12/2020

11:30:04 PM

154

6 BeiDou Navigation Satellite System

(a)

(b)

GEO Satellite

MEO Satellite Figure 6.10

BDS II GEO (up) and IGSO/MEO (below) Satellites [1]. Source: Reproduced with permission of Springer Nature.

span. The Class-B monitor stations are for the integrity monitoring of the state for the satellite system and are distributed across the country as evenly as possible. Figure 6.11 shows the configuration of the BDS II control segment [4]. At present, the BDS II control segment is significantly constrained by having all of the stations located within China [4]. As a result, it is a challenge to perform orbit determination with the precision required for the highperformance operation and control of BDS II.

6.5.4

User Segment

The BDS II user segment refers to all the BDS II- and BDS II/GNSS-compatible receivers for RNSS services, as well as BDS II RDSS/RNSS combined terminals for users’ position reports and short message communication [5]. The main function of the BDS II receiver is to receive BDS II navigation signals to calculate the user’s PVT. The BDS II/GNSS can simultaneously receive BDS II and other GNSS navigation signals to calculate the user’s PVT by using pseudoranges from different constellations. The integrated terminal is a special device that integrates both RDSS and RNSS services, providing not only RDSS and RNSS services, but also new services that result from the

c06.3d

154

convergence of these two services, such as the users’ position report.

6.5.5

Signal Characteristics

BDS II broadcasts six signals at B1, B2, and B3 frequencies in the L band, which can provide both open and authorized services. The carrier frequencies of B1, B2, and B3 are 1561.098 MHz, 1207.140 MHz, and 1268.520 MHz, respectively. All three signals use a DSSS/QPSK modulation scheme. Each signal consists of two orthogonal components with BPSK modulation. For example, the B1 signal has an in-phase component B1I and quadrature component B1Q providing public and authorized service, respectively. The main characteristics of the B1, B2, and B3 signals are shown in the Table 6.3. It can be seen from the table that the BDS II signals broadcast by the GEO satellites and IGSO/ MEO satellites have different navigation message rates, 500 bps and 50 bps, respectively. The following discussions of this subsection mainly focus on the B1I, B2I, and B3I signals that provide open services. 6.5.5.1 Signal Structures

B1, B2, and B3 are QPSK signals with I and Q components that are in phase quadrature with each other. The ranging codes and navigation messages are modulated on these

15/12/2020

11:30:04 PM

Figure 6.11 Configuration of the BDS II control segment [4]. Source: Reproduced with permission of Springer Nature.

Table 6.3 Signal characteristics of BDS II Signal type

B1I

B1Q

B2I

B2Q

B3I

B3Q

Service type

Open

Authorized

Open

Authorized

Open

Authorized

Carrier frequency

1561.098 MHz

Bandwidth (1dB)

4.092 MHz

4.092 MHz

4.092 MHz

20.460 MHz

20.460 MHz

20.460 MHz

Multi-access scheme

CDMA

CDMA

CDMA

CDMA

CDMA

CDMA

BPSK

BPSK

BPSK

BPSK

BPSK

BPSK

2046

N/A

2046

N/A

10230

N/A

Code rate

2.046 Mcps

N/A

2.046 Mcps

N/A

20.46 Mcps

N/A

Code class

Truncated Gold

N/A

Truncated Gold

N/A

Truncated Gold

N/A

GEO

500 bps

N/A

500 bps

N/A

500 bps

N/A

IGSO/MEO

Modulation Pseudocode

Message code rate

c06.3d

155

Length

1207.140 MHz

1268.520 MHz

50 bps

N/A

50 bps

N/A

50 bps

N/A

Error-correction code

BCH(15,11,1)

N/A

BCH(15,11,1)

N/A

BCH(15,11,1)

N/A

Secondary coding

Code type

NH

N/A

NH

N/A

NH

N/A

Code rate

1 kbps

N/A

1 kbps

N/A

1 kbps

N/A

Length

20 bits

N/A

20 bits

N/A

20 bits

N/A

Polarization

RHCP

N/A

RHCP

N/A

RHCP

N/A

Minimum received power

−163.0 dBW

N/A

−163.0 dBW

N/A

−163.0 dBW

N/A

Elevation

5o

N/A

5o

N/A

5o

N/A

15/12/2020

11:30:05 PM

156

6 BeiDou Navigation Satellite System

carriers. The nominal carrier frequencies of B1, B2, and B3 are 1561.098, 1207.140, and 1268.520 MHz, respectively. All three signals are right-hand circularly polarized (RHCP). Only the signal details of the I components are released publicly. The minimum user-received signal power level is −163 dBW for the I channel measured at the output of a 0 dB RHCP receiving antenna located near the ground, for a satellite elevation angle above 5 [12, 14]. The signal model for B1, B2 and B3 signals is [12, 14] Sij t = AiI CiIj t DiIj t j

cos 2π f i t + φiIj j

+ AiQ C iQ t DiQ t

j

sin 2π f i t + φiQ

where i refers to B1, B2, or B3, while j is the satellite number; AiI and AiQ, CiI and CiQ, DiI and DiQ, φiI and φiQ, are the amplitudes, ranging code, navigation data, and initial carrier phase for the i-th signal in the I and Q channels, respectively; fi is the corresponding signal carrier frequency. The signal generation block diagrams for GEO and MEO/ IGSO satellites are given in Figure 6.12.

20.46MHz

1268.52MHz

The initial phases of G1 and G2 are G1 01010101010 G2 01010101010

65

The generator of CB1I and CB2I is shown in Figure 6.13 [12].

B1Q Signal

BPSK modulator

CB2ICode generator

Σ

B1 Signal 1561.098MHz

B2Q Signal

BPSK modulator

1207.14MHz

NH encoder

G2 X = 1 + X + X 2 + X 3 + X 4 + X 5 + X 8 + X 9 + X 11 64

CB1ICode generator

1561.098MHz

2.046MHz

B1I and B2I use the same ranging codes (denoted as CB1I and CB2I) with a 2.046 Mcps chip rate and a 2046 chip length [12]. The ranging code for B3I (denote as CB1I) has a chip rate of 10.23 Mcps and a chip length of 10230 [14]. CB1I and CB2I both use a balanced Gold code with the last one chip truncated. The Gold code is generated by Modulo-2 addition of G1 and G2 sequences which are derived from the following 11-bit linear shift registers [12]: G1 X = 1 + X + X 7 + X 8 + X 9 + X 10 + X 11

63

2.046MHz

6.5.5.2 Ranging Codes

CB3ICode generator

Σ

B2 Signal 1207.14MHz

B3Q Signal

BPSK modulator

Σ

B3 Signal 1268.52MHz

BCH encoder

f0

Data generator

Figure 6.12

c06.3d

156

Data information

Note: NH encoder is used only in MEO/IGSO satellite signal generation

Block diagram of GEO and MEO/IGSO satellite signal generation.

15/12/2020

11:30:07 PM

6.5 BDS II: The BDS Regional System

157

G1 sequence 1

Reset control clock

2

3

4

5

6

7

8

9

10

11

Phase selection logic

Set to initial phases

G2 sequence

Ranging code

Shift control clock

1

2

3

4

5

6

7

8

9

10

11

Figure 6.13 The generator of CB1I and CB2I.

The G2 sequence phase is determined by the selection of its shift register taps. Currently, 37 phase assignments are defined for 37 ranging codes, of which the first 5 are for GEO satellites and the remaining 32 are for IGSO/MEO satellites [12]. CB3I is generated by truncating a Gold code which is the result of truncating and XORing two linear sequences G1 and G2, which are derived from two 13-bit linear shift registers [14]: G1 X = 1 + X + X 3 + X 4 + X 13 G2 X = 1 + X + X 5 + X 6 + X 7 + X 9 + X 10 + X 12 + X 13 66 The generator of CB3I is shown in Figure 6.14. The code sequence generated by G1 is truncated with the last one chip, making it into a CA sequence with a period of 8190 chips. The CB sequence with a period of 8191 chips is generated by G2. The CB3I with a period of 10230 chips is generated by means of Modulo-2 addition of CA and CB sequences. The G1 sequence is set to an initial phase at the starting point of each ranging code cycle (1ms) or when the phase of the G1 sequence register is “1111111111100”. The G2 sequence is set to its initial phase at the starting point of each ranging code cycle (1 ms). The initial phase of the The G1 sequence is “1111111111111”. The initial phase of the G2 sequence is formed by shifting different times from status “1111111111111”, and different initial phases

c06.3d

157

correspond to different satellites. The phase assignments of the G2 sequence are given in [14]. Currently, 63 phase assignments are defined for 63 ranging codes. To ensure backward compatibility with existing BDS II receivers, the first 37 phase assignments, corresponding to those defined for B1I and B2I, are preferred for use. Consistent with the previous definition, the first 5 are for GEO satellites and the other 32 are for IGSO/ MEO satellites. Of the 26 new defined phase assignments, the last 5 are for GEO satellites and the remaining 21 are for IGSO/MEO satellites [14]. 6.5.5.3 Navigation Messages

The BDS II system has two types of navigation messages. The B1I, B2I, and B3I signals of MEO/IGSO satellites broadcast a D1 navigation message with a 50 bps information rate and contain basic navigation information only. In addition to basic navigation information, the D2 navigation message is broadcast by GEO satellites with a 500 bps information rate that also contains augmentation service information. The basic navigation information comprises the preamble (Pre), subframe ID (FraID), seconds of week (SOW), fundamental navigation information of the satellite (ephemeris), page number (Pnum), almanac information, time offset information from the other GNSS (GPS, Galileo and GLONASS), user range accuracy index, satellite health flag, ionospheric delay model parameters, satellite clock correction parameters and their age, and equipment group

15/12/2020

11:30:07 PM

158

6 BeiDou Navigation Satellite System

Shift control clock

CA sequence 1

2

Reset control clock

3

4

5

6

7

8

9

10

...

13

Register phase is 1111111111100 (from left to right)

Set to initial phases ( ‘1’ in total)

Ranging code

Set to initial phases (different satellites correspond to different initial phases) 1

Figure 6.14

5

6

7

8

9

10

Navigation Messages of Type D1

The type D1 navigation message is partitioned into superframe, frame, and subframe. Every superframe has 36,000 bits, lasts 12 min, and is composed of 24 frames. Every frame has 1,500 bits, lasts 30 s, and is composed of 5 subframes. Every subframe has 300 bits, lasts 6 s, and is composed of 10 words. Every word has 30 bits, lasts 0.6 s, and consists of navigation message data and parity bits. In the first word of every subframe, the first 15 bits are not encoded, and the following 11 bits are encoded in BCH(15,11,1) for error correction. Therefore, only one group of BCH code and 26 information bits are contained in this word. For all the following 9 words in the subframe, both BCH(15,11,1) encoding for error control and

c06.3d

158

CB sequence

The generator of CB3I.

delay differential, etc. The augmentation service information contains the BDS integrity, and differential and ionospheric grid information [12]. The navigation message encoding involves both error control of Bose–Chaudhuri– Hocquenghem (BCH) code BCH(15,11,1) and interleaving. BCH(15, 11, 1) indicates that the code length is 15 bits with 11 information bits and 1 error correction bit. The generator polynomial is g (X) = X4 + X + 1. The navigation message bits are first grouped sequentially every 11 bits. The serial-parallel conversion is then applied to the sequence, and the BCH(15,11,1) error correction encoding is performed in parallel. Parallel-serial conversion is then performed for every two parallel blocks of BCH codes to form a 30-bit interleaved code [12]. 6.5.5.3.1

11 12 13

interleaving are performed. Each of the 9 words of 30 bits contains two blocks of BCH codes and 22 information bits. The frame structure in format D1 is shown in Figure 6.15 [14]. A secondary code in Neumann–Hoffman (NH) format is modulated onto the ranging code for the Type D1 message. The period of the NH code is selected to be the duration of a navigation message bit and is the same as one period of the ranging code. The duration of one navigation message bit is 20 ms, and the ranging code period is 1 ms, as shown in Figure 6.16. Thus, the NH code (0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0) with length 20 bits, rate 1 kbps, and bit duration 1 ms is adopted. It is modulated onto the ranging code synchronously with navigation message bits [12]. The D1 frame structure and information content are shown in Figure 6.17. The fundamental navigation information of the broadcasting satellite is in subframes 1, 2, and, 3. The information content in subframes 4 and 5 is subcommutated 24 times each via 24 pages. Pages 1–24 of subframe 4 and pages 1–10 of subframe 5 shall be used to broadcast almanac and time offsets from other systems. Pages 11–24 of subframe 5 are reserved [12]. 6.5.5.3.2

The Navigation Messages of Type D2

Type D2 messages are also structured with superframe, frame, and subframe. Every superframe is 180,000 bits long, lasting 6 min. Every superframe lasts 3 s and is composed of 120 frames each with 1,500 bits. Every frame lasts 0.6 s and is composed of 5 subframes, each with 300 bits. Every

15/12/2020

11:30:08 PM

6.5 BDS II: The BDS Regional System

159

Superframe 36000 bits, 12 min Frame 1

Frame 2

Frame n

Frame 24

Frame 1500 bits, 30 sec Subframe 1

Subframe 2

Subframe 3

Subframe 4

Subframe 5

Subframe 300 bits, 6 sec

Word 1

Word 2

Word 10

Word 2~10, 30 bits, 0.6 sec

Word 1, 30 bits, 0.6 sec 26 information bits

4 parity bits

22 information bits

8 parity bits

Figure 6.15 Frame structure of Type D1 navigation message.

NAV message

NH code Ranging code

NAV message

1

0

0

0

1

20 ms Period (1 bit duration of NAV message) NH code

Ranging code

0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 ms

Ranging code period (1 bit duration of NH code)

Figure 6.16 Secondary code in Format D1.

Subframe 1

Subframe 2

Subframe 3 Subframe 4

Subframe 5

Fundamental NAV information of the broadcasting satellite Almanac and time offsets from other systems

Figure 6.17 Frame structure and information content of Type D1 navigation.

subframe lasts 0.06 s and is composed of 10 words, each with 30 bits. Every word is composed of navigation message data and parity bits. The first 15 bits in word 1 of every subframe are not encoded, and the last 11 bits are encoded in

c06.3d

159

BCH(15,11,1) for error correction. For the remaining 9 words of the subframe, both BCH(15,11,1) encoding and interleaving are involved, resulting in 22 information bits and 8 parity bits in each word. See Figure 6.18 for the detailed structures [12].

15/12/2020

11:30:08 PM

160

6 BeiDou Navigation Satellite System

Superframe of 180000 bits, 6 min Frame 1

Frame 2

Frame n

Frame 120

Frame of 1500 bits, 3 sec Subframe 1

Subframe 2

Subframe 3

Subframe 4

Subframe 5

Subframe of 300 bits, 0.6 sec Word 1

Word 2

Word 1, 30 bits, 0.06 sec NAV message data, 26 bits

Figure 6.18

4 Parity bits

Word 10

Word 2~10, 30 bits, 0.06 sec NAV message data, 22 bits

8 Parity bits

Structure of navigation message in Type D2.

Subframe 2

Subframe 3

Subframe 4

Subframe 1 Subframe 5

Basic NAV information of the broadcasting satellite

Figure 6.19

Integrity and differential correction information of BDS

Frame structure and information content of type D2 navigation.

The frame structure and information content are shown in Figure 6.19. Subframe 1 broadcasts basic navigation information and is subcommutated 10 times via 10 pages. Subframes 2–4 are subcommutated 6 times each via 6 pages. Subframe 5 is subcommutated 120 times via 120 pages. See [4] for the detailed bit allocation of each subframe in Type D2 format.

6.5.6

Service and Performance

6.5.6.1 Services Types

BDS provides two types of services, namely‚ RDSS and RNSS, for the Asia-Pacific area. The RNSS service also includes open service and an authorized service. 6.5.6.1.1

RNSS Service

The RNSS service is the basic navigation service providing PVT information. BDS II broadcasts six signals on three carrier frequencies (B1, B2, and B3) to provide users with both public and authorized services. The in-phase components of the B1, B2‚ and B3 signals, B1I, B2I, and B3I, are used

c06.3d

160

Almanac, ionospheric grid points and time offsets from other systems

for the open service, while the quadrature components B1Q, B2Q, and B3Q are used for the authorized service [13]. The open service is available to global users free of charge‚ and the authorized service is available only to specific users. 6.5.6.1.2

RDSS Service

The RDSS service is a unique BDS service inherited from and further improving upon the BDS I RDSS service and provides positioning, precision timing, and short message communication to the users of China and surrounding areas via the GEO satellites. However, since the RNSS service of BDS II can provide passive positioning and timing services with better performance, the focus of the RDSS service at present lies on its short message communication, which facilitates communication and location reports between users. Because the RDSS users must have a unique registered ID, the RDSS service can be seen as an authorized service of BDS II. The RDSS service was introduced in detail in the previous section; this section focuses on the RNSS service.

15/12/2020

11:30:09 PM

6.5 BDS II: The BDS Regional System

6.5.6.2 Service Performance 6.5.6.2.1 Service Area

161

Table 6.4 BDS II OS position/velocity/time accuracy standards

The BDS II open service area is defined as the area where both the horizontal and vertical position accuracies are within 10 m with a probability of 95%. At the current stage, the open service area includes most of the region from 55 S to 55 N, 70 E to 150 E, as shown in Figure 6.20 [13]. In China, the term “BDS-focused service area” often appears in the literature. However, this area has not been officially defined so far and is typically referred to as the BDS RDSS services coverage area, that is, China and surrounding areas (70 E–145 E, 5 N–55 N), where the future SBAS services will be provided [7].

Service accuracy

Standard (95% probability)

Positioning

Horizontal

≤10 m

Vertical

≤10 m

Velocity

≤0.2 m/s

Timing (Multi-SISs)

≤50 ns

Constraints

Calculate the statistical PVT error for any point in the service volume over any 24-h interval.

Table 6.5 BDS OS PDOP availability standards [5]

6.5.6.2.2

Service Accuracy

The open service PVT accuracy standards are described in Table 6.4 [13].

Service availability

6.5.6.2.3

PDOP availability

PDOP Availability

The BDS II Open Service position dilution of precision (PDOP) availability standards within its service volume are shown in Table 6.5. 6.5.6.2.4

EAST 60°

90°

120°

150°

60° Europe Asia

45°

45°

PDOP≤6 Calculate at any point within the service volume over any 24-h interval.

Source: From Lu, M. and Shen, J., “BeiDou Navigation Satellite System (BDS),” in Understanding GPS/GNSS: Principles and Applications (eds. C. H. a. E. D. Kaplan), 3rd Ed., Artech House, pp. 273–312, 2017.

Table 6.6 BDS OS position service availability standards Service availability

Standard

Constraints

Positioning availability

≥0.95

Horizontal positioning accuracy ≤10 m (95% probability); Vertical position accuracy ≤ 10 m (95% probability); Calculate at any point within the coverage area over any 24-h interval

30°

30° Pacific Ocean

15°

15° 0°

Indian Ocean

15°

15° Oceania

30°

30° 45°

45°

60°

60° Antarctica EAST 60°

90°

120°

150°

180°

Figure 6.20 BDS-II service area [5]. Source: Reproduced with permission of Artech House.

161

≥0.98

180°

60°

c06.3d

Constraints

Positioning Service Availability

The BDS OS positioning service availability standards within its coverage area are shown in Table 6.6 [13]. Since December 2012, BDS II has been providing FOC services. The actual test results show that BDS II has good

0°

Standard

geometric coverage for China and the Asia-Pacific region [26]. Within the region from 60 S to 60 N and 65 E to 150 E, with an elevation mask angle of 5 , the number of the visible BDS satellites is greater than seven, and the PDOP value is generally less than 5. The pseudorange and carrier phase measurement accuracies are 33 cm and 2 mm, respectively [26]. The 95% horizontal and vertical accuracies of the pseudorange single point positioning are better than 6 m and 10 m, respectively. Furthermore, the accuracy of the carrier phase differential positioning is better than 1 cm in the case of an ultra-short baseline, and better than 3 cm in the case of a short baseline [22, 26].

15/12/2020

11:30:10 PM

162

6 BeiDou Navigation Satellite System

6.6 BDS III: The Emerging BDS Global System 6.6.1

Overview

BDS III will be a multifunctional global system with a hybrid constellation of 30 satellites [6, 16, 17, 27]. Two new navigation signals, B1C and B2a, will be transmitted from the MEO satellites and IGSO satellites for global open service. In particular, these two new signals will share two frequencies with GPS and Galileo, and some modern navigation signal features, such as BOC modulation, pilot data‚ and orthogonal structure, will be adopted. This implies that BDS III will be highly compatible and interoperable with GPS and Galileo. In fact, compatibility and interoperability with other GNSS are the main goals of the third step in the BDS development plan. In addition to continuing to provide its iconic RDSS service and to expand the regional open service to the global open service by using new navigation signals, the SBAS and SAR services will also be integrated into the BDS III constellation [6]. While the B2I signal originated in BDS II will be replaced by the new B2a signal, the B1I signal will continue to be transmitted by all BDS III satellites (GEO/IGSO/MEO) to provide open service. The newly released B3I signal also will be transmitted by all BDS III satellites. The continued broadcast of B1I and B3I signals not only ensures the smooth transition from BDS II to BDS III, but also maximizes the benefits to receiver manufacturers and customers. As a result, BDS III will transmit at least four signals, B1C, B2a, B1I, and B3I, for global open service. After the new ICDs for B1C and B2a were released in September 2017, the first pair of BDS III MEO satellites was successfully launched in November 2017. Currently, a total of eight MEO satellites have been successfully launched. According to the latest deployment plan at the time of this writing, 18 MEO and 1 GEO satellites will be launched by the end of 2018, while an additional 6 MEO, 3 IGSO, and 2 GEO satellites will be launched from 2019 to 2020. It is expected that BDS III will provide initial service by the end of 2018, and will provide full service worldwide around by approximately 2020 [27].

at 35,786 km altitude with an orbital plane inclination of 55 . The 24 MEO satellites are distributed uniformly for BDS global coverage. The GEO and IGSO satellites provide enhanced coverage for China and the Asia-Pacific region. The BDS III space constellation is shown in Figure 6.21. The term BDS-focused service area has two meanings. One is that for users in the “focused service area” better service availability will be ensured with more visible satellites. The other is that for users in this area, the GEO satellites will provide more diversified services, at least including RDSS, RNSS, SBAS‚ and SAR. The coverage of the BDS III open service is depicted in Figure 6.22. This figure shows the geographical distribution of satellite signal coverage in a revisit period. Spare satellites are not considered. Due to the GEO and IGSO satellites, 10 to 14 BDS III satellites can be observed at the same time in the AsiaPacific region with a probability of 95%. For other regions, the number of visible satellites is 8 to 10, while in some mid-latitude areas, only 6 to 8 BDS satellites are visible simultaneously.

6.6.2

6.6.3

Constellation

BDS III constellation consists of 3 GEO, 3 IGSO, 24 MEO satellites, and possibly some spare satellites [16, 17]. The three GEO satellites are positioned at 80 E, 110.5 E, and 140 E, respectively. The MEO satellites are evenly distributed in three orbital planes at 21,528 km altitude, constituting a classic Walker 24/3/1 constellation. The IGSO satellites are also evenly distributed in three orbital planes

c06.3d

162

Figure 6.21 BDS III constellation [5]. Source: Reproduced with permission of Artech House.

Signal Characteristics

The two new navigation signals, B1C and B2a, will be transmitted by BDS III MEO and IGSO satellites, and the two legacy signals, B1I and B3I, will be transmitted by all BDS III satellites. However, the open service signal B2I will not be retained [6, 14, 16, 17]. The following discussions in this subsection are mainly focused on the B1C and B2a signals.

15/12/2020

11:30:10 PM

6.6 BDS III: The Emerging BDS Global System

163

N Access (95%, 3G+3I+24M) 13 12 60°N

11 10 9

30°N Latitude

8 7

0°

6 5 30°S

4 3 2

60°S

1 0 60°W

30°W

0°

30°E

60°E

90°E

120°E 150°E

180° 150°W

120°W 90°W

60°W

Longitude

Figure 6.22 Simulation of the BDS-III global coverage.

6.6.3.1 Signal Structures 6.6.3.1.1 B1C

sB1C_pilot t =

All BDS and global GNSS users will receive this signal. B1C will become an important symbol of BDS III, similar to the current GPS L1 C/A and the future L1C. Besides the compatibility and the interoperability with the GPS L1C and Galileo E1 OS signals, it is necessary to meet a large range of varied requirements, from location services and other consumer users to high-precision measurement and other professional users. Therefore, an advanced signal structure needed to be developed for a variety of different requirements [28, 29]. The carrier frequency of B1C is 1575.42 MHz, which is the same as the carrier frequency of the GPS L1 C/A and L1C, and the Galileo E1 OS signals. A novel modulation scheme, quadrature multiplexed binary offset carrier (QMBOC) modulation, is adopted [16, 30]. B1C has a data and a pilot component: sB1C t = sB1C_data t + jsB1C_pilot t

67

where the data component sB1C_data t =

1 DB1C_data t CB1C_data t scB1C_data t 2 68

is a sine-based BOC(1,1) subcarrier ScBIC_data t modulated by the navigation message data stream DBIC_data t and the ranging code CBIC_data t , while the pilot component

c06.3d

163

3 C B1C_pilot t scB1C_pilot t 2

69

is a QMBOC subcarrier ScBIC_pilot t modulated by the ranging code CBIC_pilot t . The data to the pilot component signal power ratio is 1:3. QMBOC modulation, first proposed in [30], is a timedomain implementation of multiplexed binary offset carrier modulation (MBOC). It consists of two quadrature phase BOC modulations, BOC(1,1) and BOC(6,1), to avoid cross-correlation between the two components. QMBOC has the same power spectrum as other MBOC implementations such as time-multiplexed BOC (TMBOC), which is used in the GPS L1C signal, and composite BOC (CBOC), which is used in the Galileo E1 OS signal. The QMBOC signal supports both a low-complexity receiving mode and a high-performance receiving mode, and hence offers good compatibility and interoperability with GPS and Galileo signals in the same frequency band. Because the QMBOC signal contains a narrowband component with a larger portion of the power and a wideband component with a smaller power allocation, receivers limited by processing complexity only have to deal with the BOC(1,1) component, while the BOC (6,1) component offers more potential for high-precision ranging performance applications. Since a QMBOC subcarrier consists of two bipolar subcarriers, the entire B1C signal actually contains three bipolar components [16]:

15/12/2020

11:30:11 PM

164

6 BeiDou Navigation Satellite System

1 SB1C t = DB1C_data t C B1C_data t sign sin 2π f SC_B1C_a t 2 SB1C

+

1 C B1C_pilot t sign sin 2π f SC_B1C_b t 11 SB1C

+j

t

data

pilot b

t

29 C B1C_pilot t sign sin 2π f SC_B1C_a t 44 SB1C

pilot a

t

6 10 where fsc_a = 1.023 MHz and fsc_b = 6.138 MHz. Table 6.7 shows the other elements of the B1C signal, as well as the modulation, phase relationship, and power ratio of each component. On BDS III MEO and IGSO satellites, both B1C and B1I signals are broadcast. The central frequencies of these two signals are 14.322 MHz apart. In the payload implementation, a multicarrier constant envelope multiplexing technique [31] is used to combine these two signals, as well as the authorization service signal in the same band, into a composite signal, while sharing a common transmitter chain. This implementation not only reduces the volume and weight of the payload transmitter, but also enables joint processing of these two signals in wideband receivers. 6.6.3.1.2

MHz) are multiplexed into a constant envelope signal before transmission in order to reduce payload and multiplexing loss [32]. Moreover, since BDS III has three different types of satellites in three different types of orbits, some B2 signal components may be used to support different services. Therefore, it is desirable to have a flexible power configuration when multiplexing the B2 components. The asymmetric constant envelope binary offset carrier (ACE-BOC) modulation and multiplexing technique with its low-complexity implementation form [32] meets this design requirement well. Therefore, ACE-BOC marries multi-carrier spread-spectrum modulation with constant envelope multiplexing. It can combine four or fewer signals of arbitrary power ratio in phase quadrature onto two sidebands of a split-spectrum composite signal. Moreover, the composite signals can either be received as two sets of QPSK signals located on two different bands respectively, or as a wideband signal. The current ICD only describes the signal structure of B2a [17]. Therefore, the signal is presented as a QPSK (10) modulation signal, as shown in Table 6.8. The baseband complex envelope of B2a signal model is sB2a t = sB2a_data t + jsB2a_pilot t where 1 DB2a_data t C B2a_data t 2 1 C B2a_pilot t t = 2

sB2a_data t =

6 12

sB2a_pilot

6 13

B2a

The design of the BDS III open service signal in the B2 band also took into consideration interoperability with GPS and Galileo. In order to interoperate with GPS L5 and Galileo E5, BDS III broadcasts broadband signals at two frequencies in the B2 band with center frequencies at 1176.45 MHz and 1207.14 MHz, respectively [17]. Both B2a and B2b signals are composed of two phase quadrature components. Their spreading codes (the rate is 10.23

6 11

DB2a_data(t), CB2a_data(t), and CB2a_pilot(t) are the data and ranging codes for the data and pilot channel‚ respectively. Both sB2a_data(t) and sB2a_pilot(t) are modulated in BPSK mode. The power ratio between the data component and the pilot component is 1:1.

Table 6.7 Modulation characteristics of B1C signal Signal

Carrier (MHz)

Component

B1C

1575.42

SBIC_data t SBIC_pilot_a t SBIC_pilot_b t

Modulation

Symbol Rate (sps)

BOC(1,1) QMBOC (6,1,4/33)

BOC (1,1)

Phase relationship

Power ratio

100

0

0

90

29/44

0

1/11

BOC (6,1)

1/4

Table 6.8 Modulation characteristics of B2a signal Signal

Carrier (MHz)

Component

Modulation

Symbol rate (sps)

B2a

1176.45

B2a_data

QPSK

200

0

1

0

90

1

B2a_pilot

c06.3d

164

Phase (deg)

Power ratio

15/12/2020

11:30:12 PM

6.6 BDS III: The Emerging BDS Global System

First main code cycle (N chips)

Second main code cycle (N chips)

First chip

Second chip

165

NSth main code cycle (N chips)

Ranging code

Overlay code

NSth chip

Complex code Total chips N*NS

Figure 6.23 Timing relationships of the ranging code and overlay code.

6.6.3.2 Ranging Codes

The PRN codes for B1C and B2a have a hierarchical code structure with a modulo-2 addition of a ranging code and an overlay code. The symbol width of the overlay code is the same as the period of the ranging code. The start of each overlay code chip is aligned with the first chip of the ranging code. The timing relationship is shown in Figure 6.23 [16, 17]. 6.6.3.2.1

6.6.3.2.2

B1C

The B1C ranging codes chipping rate is 1.023 Mbps. It is obtained by truncating the Weil code with a length of 10,243 chips. The Weil code sequence with length N is defined as follows: W k; w = L k

L k + w , k = 0, …, N − 1

6 14

where L(k) is a Legendre sequence of length N, and w, which ranges from 1 to 5121, is the phase difference between the two Legendre sequences. A Legendre sequence L(k) (k = 0,1,2, …, N-1) of length N is defined as Lk =

0, 1, 0,

k=0 k 0, intx, k = x 2 modN else

c k; w; p = W k + p − 1 mod10243; w , k = 0, …, 10229 6 16 where p is the truncation point indicating that the truncation starts at the p-th Weil code chip, and its value ranges from 1 to 10,243. Since a B1C signal includes a data component and a pilot component, which use different PRN codes, there are 126

165

B2a

Similar to B1C, B2a also has 126 ranging codes, 63 of which are allocated to the data component, and the rest are allocated to the pilot component. The B2a ranging code chipping rate is 10.23 Mcps‚ and the code length is 10230 chips. A B2a ranging code is obtained by a modulo-2 addition of two 10230-bit expanded Gold codes, g1(x) and g2(x). g1(x) and g2(x) are 13-stage linear feedback shift registers, whose polynomials for the data component are g1 x = 1 + x + x 5 + x 11 + x 13 g2 x = 1 + x 3 + x 5 + x 9 + x 11 + x 12 + x 13

6 17

and for the pilot component are 6 15

where “mod” represents the modulo operation. The B1C ranging code is obtained through a circular truncation of the Weil code:

c06.3d

ranging codes for the BDS III B1C signals, 63 of which are for the data components and the remaining are for the pilot components. The length of a B1C pilot component overlay code is 1800, which is obtained by truncating the Weil code with a length of 3607. The generation method is the same as for the ranging code, and w ranges from 1 to 1803.

g1 x = 1 + x 3 + x 6 + x 7 + x 13 g2 x = 1 + x + x 5 + x 7 + x 8 + x 12 + x 13

6 18

The implementations of the ranging code generators for the B2a data component and B2a pilot component are shown in Figures 6.24 and 6.25, respectively. The polynomials for the two B2a ranging code components of a specific satellite are different, but they have the same initialization vector. The initial state of Register 1 is “1111111111111”, while that of register 2 is different for different satellites and is specified in [17]. Registers 1 and 2 are synchronized at the start of a period. At the end of the 8190th chip of a ranging code period, Register

15/12/2020

11:30:12 PM

166

6 BeiDou Navigation Satellite System

Clock (code rate)

C1,1

C1,2

C1,3

C1,4

C1,5

C1,6

C1,7

C1,8

C1,9

C1,10

C1,11

C1,12

C1,13

C S1,1

C S1,2

C S1,3

C1,4 S 1,4

C1,5 S

C S1,6

C S1,7

C S1,8

C S1,9 1,9

C S1,10

C S1,11

CS1,12 1,12

C S1,13

Register 1

Register 1 reset control Register 1 initial value Output

Register 2 reset control

S2,1

S2,2

S2,3

S2,4

S2,5

S2,6

S2,7

S2,8

S2,9

S2,10

S2,11

S2,12

S2,13

C2,1

C2,2

C2,3

C2,4

C2,5

C2,6

C2,7

C2,8

C2,9

C2,10

C2,11

C2,12

C2,13

Register 2 initial value

Register 2

XOR gate

Figure 6.24

BDS III B2a data component ranging code generator.

Clock(code rate) C1,1

C1,2

C1,3

C1,4

C1,5

C1,6

C1,7

C1,8

C1,9

C1,10

C1,11

C1,12

C1,13

S1,1

S1,2

S1,3

S1,4

S1,5

S1,6

S1,7

S1,8

S1,9

S1,10

S1,11

S1,12

S1,13

Register 1

Register 1 reset control Register 1 initial value Output

Register 2 reset control

S2,1

S2,2

S2,3

S2,4

S2,5

S2,6

S2,7

S2,8

S2,9

S2,10

S2,11

S2,12

S2,13

C2,1

C2,2

C2,3

C2,4

C2,5

C2,6

C2,7

C2,8

C2,9

C2,10

C2,11

C2,12

C2,13

Register 1 initial value

Register 2

XOR gate

Figure 6.25

B2a pilot component ranging code generator.

1 is reset to 1. Repeating this process, a ranging code with a length of 10,230 is obtained. The overlay codes of the B2a data component are the same for all satellites. The code is a fixed five-bit code sequence with value “00010”, whereas the overlay codes, of length 100 for the B2a pilot component, are different, and are obtained by truncating the Weil code to a length of 1021.

c06.3d

166

6.6.3.3 Navigation Messages

The navigation message broadcast by the BDS B1C and B2a signals are the B-CNAV1 and B-CNAV2 messages, respectively. 6.6.3.3.1

B-CNAV1 Data Structure

The B-CNAV1 message is broadcast on the B1C signal and modulates the B1C data component. Each frame contains

15/12/2020

11:30:12 PM

6.7 Summary and Future Prospects

167

After Error correction coding: 1800 symbols 18s Subframe1 72 symbols

Subframe2 1200 symbols Subframe3 528 symbols

BCH(21,6)+ BCH(51,8)

Sixty-four systemLDPC(200,100)

Sixty-four systemLDPC(88,44)

Before Error correcting code: 878 bits MSB

LSB

Subframe1 14 bits

Subframe2 600 bits Subframe3 264 bits

Figure 6.26 Basic frame structure of B-CNAV1.

1800 symbols at a 100 sps rate and lasts 18 s. Each frame has three subframes, with the basic frame structure as shown in Figure 6.26. Before error correction coding, subframe1 uses 14 bits to represent the PRN number and second of hour count (SOH). Subframe2 has 600 bits for system time, navigation message version, ephemeris information, satellite clock correction information, and group delay corrections. Subframe3 has 264 bits, which are divided into several pages for ionospheric delay correction model parameters, Earth Orientation Parameters, BDT-UTC time synchronization information, BDS-GNSS time synchronization information, medium precision ephemeris, simplified almanac, SV health status, satellite integrity status identification‚ and SIS monitoring accuracy indications. Subframe1 has its most significant six bits encoded in BCH(21,6), and the least significant eight bits are encoded in BCH (51,8). Subframe2 and subframe3 are encoded using 64-ary low-density parity check (LDPC)(200, 100) and LDPC(88,44), respectively. After application of the encoding, subframe1, subframe2, and subframe3 have 72, 1200, and 528 symbols. respectively.

6.6.3.3.2

B-CNAV2 Data Structure

The B-CNAV2 message is broadcast on the B2a signal modulated on the B2a data component. Each frame contains 600 symbols at 200 sps rate and lasts 3 s. Each frame has three subframes, with the basic frame structure as shown in Figure 6.27. Each frame begins with a frame synchronization header that occupies 24 symbols and is 0xE24DE8 or 111000 100100110111101000. The MSB is transmitted first.

c06.3d

167

Each frame contains 288 bits prior to error correction coding, including a 6-bit PRN number, a 6-bit information type, an 18-bit data message, and 24 bits of CRC parity check information. All of these data are used in the CRC parity check calculation. After being encoded in 64-ary LDPC (96,48), each frame contains 576 symbols.

6.7

Summary and Future Prospects

The BDS program started as a regional, active positioning system, evolved into a regional passive ranging system, and is being rapidly expanded into a global, multifunctional satellite navigation system. This chapter presents the evolution of China’s satellite navigation system following its original three-step development plan. With the completion of the first and second steps, BDS I and BDS II have been widely used in China and the Asia-Pacific region. Currently, BDS III, the product of the third step of the BDS development plan, is expected to offer global and multifunctional services by approximately 2020. As a member of the world’s GNSS family, BDS has many similarities with other GNSSs. However, BDS also possesses many unique features. Its uniqueness is not only reflected in the constellation structure, the control segment configuration‚ and the user terminals, but also in its signal structures, ranging and positioning methods, various services, and applications. BDS even created a completely different development model from other GNSSs. These differences make BDS a unique and distinctive GNSS. As a summary of this chapter, Table 6.9 presents the launch record of BDS satellites as of March 2018. So far, a total of 31 satellites in three types of orbits have been

15/12/2020

11:30:14 PM

168

6 BeiDou Navigation Satellite System

After Error correction coding: 600 symbols 3s synchronous head(Pre) 24 symbols

Message symbol 576 symbols Sixty-four systemLDPC(96,48)

Before Error correction coding: 288 bits LSB

MSB PRN 6 bits

Figure 6.27

MesType 6 bits

SOW 18 bits

Navigation Message 234 bits

CRC 24 bits

B-CNAV2 basic frame structure.

Table 6.9 Launch record of BDS satellites by March 2018 Satellite

c06.3d

168

Date of launch

Carrier rocket

Orbit

1st experimental satellite

2000.10.31

CZ-3A

GEO

2nd experimental satellite

2000.12.21

CZ-3A

GEO

3rd experimental satellite

2003.05.25

CZ-3A

GEO

4th experimental satellite

2007.02.03

CZ-3A

GEO

1st satellite

2007.04.14

CZ-3A

MEO

2nd satellite

2009.04.15

CZ-3C

GEO

3rd satellite

2010.01.17

CZ-3C

GEO

4th satellite

2010.06.02

CZ-3C

GEO

5th satellite

2010.08.01

CZ-3A

IGSO

6th satellite

2010.11.01

CZ-3C

GEO

7th satellite

2010.12.18

CZ-3A

IGSO

8th satellite

2011.04.10

CZ-3A

IGSO

9th satellite

2011.07.27

CZ-3A

IGSO

10th satellite

2011.12.02

CZ-3A

IGSO

11th satellite

2012.02.25

CZ-3C

GEO

12th and 13th satellites

2012.04.30

CZ-3B

MEO

14th and 15th satellite

2012.09.19

CZ-3B

MEO

16th satellite

2012.10.25

CZ-3C

GEO

17th satellite

2015.03.30

CZ-3C

IGSO

18th and 19th satellite

2015.07.25

CZ-3B

MEO

20th satellite

2015.09.30

CZ-3B

IGSO

21st satellite

2016.02.01

CZ-3C

MEO

22nd satellite

2016.03.30

CZ-3A

IGSO

23rd satellite

2016.06.12

CZ-3C

GEO

24th and 25th satellite

2017.11.05

CZ-3B

MEO

26th and 27th satellite

2018.01.12

CZ-3B

MEO

28th and 29th satellite

2018.02.12

CZ-3B

MEO

30th and 31st satellite

2018.03.30

CZ-3B

MEO

15/12/2020

11:30:15 PM

References

169

Outbound 1615.68 MHz

BDS I

2491.75 MHz Inbound B2I

B3I

B1I

Outbound 1615.68 MHz

BDS II 1207.14 MHz

2491.75 MHz

1268.52 MHz Inbound

B2a

B3I

B1I

B1C

Outbound 1615.68 MHz

BDS III 1176.45 MHz

1268.52 MHz

2491.75 MHz

1561.098 MHz 1575.42 MHz

Inbound

Figure 6.28 Spectrum evolution diagram of BDS signals (RDSS-related signals are enclosed with dotted lines).

successfully launched. As BDS further develops into its full constellation, this list will continue to grow. Finally, Figure 6.28 captures the evolution and future prospects of the BDS open signal spectrum from BDS I, BDS II, to BDS III.

7

8

References 1 Fan, B.Y., Li, Z.H., and Liu, T.X., “Application and

2

3

4

5

6

c06.3d

169

development proposition of Beidou Satellite Navigation System in the rescue of Wenchuan earthquake,” Spacecraft Engineering, vol. 17, no. 4, pp. 6–13, 2008. The State Council Information Office of the People’s Republic of China. China’s BeiDou Navigation Satellite System, 2016. “Development Report of BeiDou Navigation Satellite System (v. 2.2),” China Satellite Navigation Office. Available: http://www.beidou.gov.cn. December 2013. Yang, Y., Tang, J., and Montenbruck, O., “Chinese Navigation Satellite Systems,” in Handbook of Global Navigation Satellite Systems (eds. P.J.G. Teunissen and O. Montenbruck), Switzerland: Springer International Publishing AG, pp. 273–304, 2017. Lu, M. and Shen, J., “BeiDou Navigation Satellite System (BDS),” in Understanding GPS/GNSS: Principles and Applications (eds. C. Hegarty. and E.D. Kaplan), 3rd Ed., Artech House, pp. 273–312, 2017. C. S. N. Office, “Update on BeiDou Navigation Satellite System,” presented at the Twelfth Meeting of the

9

10

11 12

13

14

15

International Committee on Global Navigation Satellite Systems, Kyoto, Japan, December 2–7, 2017. Ran, C.Q., “Status Update on the BeiDou Navigation Satellite System (BDS),” presented at the Tenth Meeting of the International Committee on Global Navigation Satellite Systems (ICG), Boulder, Colorado, United States, November 2015. “BeiDou Navigation Satellite System Signal in Space Interface Control Document for Open Service B1C and B2a Signals (Beta version),” China Satellite Navigation Office. Available: http://www.beidou.gov.cn, September 2017. Yu, H.X. and Cui, J.Y., “Progress on navigation satellite payload in China,” Space Electronic Technologies, no. 1, pp. 19–24, 2002. Chen, F.Y. et al., “The development of satellite position determination and communication system,” Chinese Space Science and Technology, no. 3, pp. 1–8, 1987. Tan, S., The Comprehensive RDSS Global Position and Report System. National Defence Industry Press, 2011. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal in Space Interface Control Document (v. 2.1), 2013. China Satellite Navigation Office: Specification for Public Service Performance of Beidou Navigation Satellite System (v. 1.0), Available: http://www.beidou.gov.cn, 2013. “BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B3I (Version 1.0),” China Satellite Navigation Office. Available: http://www.beidou.gov.cn, February, 2018. Joint Statement on Civil Signal Compatibility and Interoperability Between the Global Positioning System

15/12/2020

11:30:16 PM

170

6 BeiDou Navigation Satellite System

16

17

18

19

20

21

22

23

24

c06.3d

170

(GPS) and the BeiDou Navigation Satellite System (BDS), 2017. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B1C (Version 1.0), 2017. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B2a (Version 1.0), 2017. Yang, Y.X., “Chinese geodetic coordinate system 2000,” Chinese Science Bulletin, Vol. 54, No. 15, pp. 2714– 2721, 2009. Ren, J.T., “Capture Algorithm Research of Baseband Signal in Beidou Receiver,” Master’s Degree, Hefei University of Technology, 2011. Jia, D.W., “Design and Implementation of Baseband Signal Processing of BeiDou System Receiver,” Master’s Degree, Xidian University, 2011. Lv, Y., “Research and Design of Passive BeiDou System Timing Receiver,” National University of Defense Technology, 2009. Hu, Z.G., “BeiDou Navigation Satellite System Performance Assessment Theory and Experimental Verification,” Ph.D. Dissertation, Wuhan University, 2013. China Academy of Space Technology, Satellite Platform of DFH-3, available: http://www.cast.cn/Item/Show.asp? m=1&d=2874, 2015. Fan, B.Y., “Satellite navigation systems and their important roles in aerospace security,” Spacecraft Engineering, Vol. 3, No. 3, pp. 12–19, 2011.

25 Yang, Y.X., “Smart city and BDS,” presented at the The 8th

26

27

28

29

30

31

32

China Smart City Development Technology Symposium, Beijing, China, October, 2013. Yang, Y.X., Li, J.L., Wang, A.B. et al., “Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system,” Science China Earth Sciences, Vol. 57, No. 1, pp. 144–152, 2014. Yang, C., Directions 2018: BeiDou builds, diversifies, expands. Available: http://gpsworld.com/directions-2018beidou-builds-diversifies-expands/, 2017. Yao, Z. and Lu, M., “Design and Implementation of New Generation GNSS Signals,” Publishing House of Electronics Industry, 2016. Yao, Z. and Lu, M., “Optimized modulation for Compass B1-C signal with multiple processing modes,” presented at the ION GNSS 2011, Portland. OR, 2011. Yao, Z., Lu, M., and Feng, Z., “Quadrature multiplexed BOC modulation for interoperable GNSS signals,” Electronics Letters, Vol. 46, No. 17, pp. 1234–1236, 2010. Yao, Z., Guo, F., Ma, J., and Lu, M., “Orthogonality-based generalized multicarrier constant envelope multiplexing for DSSS signals,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 4, pp. 1–14, 2017. Yao, Z., Zhang, J., and Lu, M., “ACE-BOC: Dual-frequency constant envelope multiplexing for satellite navigation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 52, No. 1, pp. 466–485, 2016.

15/12/2020

11:30:16 PM

171

7 IRNSS Vyasaraj Rao Accord Software and Systems, India

7.1

History and Genesis

During the days of Kargil war in 1999, the Indian military was dependent on GPS data in the war zone for positioning and timing applications. With the selective availability (SA) off on-board GPS satellites, accurate positioning was not possible. This and the thought of a GNSS owned by a foreign country, denied regionally at crucial times, motivated the need for an indigenous satellite-based navigation system. Both military- and consumer-grade applications that use navigation and timing information primarily based on GNSSs would be greatly benefited by this regional navigation system. Indian space programs are conceptualized, designed, developed‚ and deployed by the Indian Space Research Organization (ISRO). From a navigation perspective, the satellite-based augmentation system (SBAS) and regional navigation system were set up by ISRO in the last decade. The results of this are GPS Aided Geo Augmented Navigation (GAGAN), an operational system, and the Indian Regional Navigation Satellite System (IRNSS). The latter program was approved by the Indian government in May 2006, with a plan to have the system fully operational by 2016. Recently, IRNSS was renamed as NAVIC (Navigation with Indian Constellation); see Figure 7.1 [1]. NAVIC is an autonomous regional navigation system planned to provide accurate real-time positioning and timing services over India and regions extending to 1500 km (930 mi) around it, referred to as the primary service area [3]. The main objective was to achieve position accuracy of 20 m (2σ) for dual-frequency users in the primary service volume. The extended service area lies between the primary service area and the area enclosed by the rectangle from 30 S to 50 N latitude, 30 E to 130 E longitude as shown in Figure 7.2. NAVIC, like any other GNSS system, is expected to support applications such as the following [4]:

•• •• •• ••

Terrestrial, aerial‚ and marine navigation Disaster management Vehicle tracking and fleet management Integration with mobile phones Precise timing Mapping and geodetic data capture Terrestrial navigation aid for hikers and travelers Visual and voice navigation for drivers

The NAVIC system architecture consists of three components: space, control‚ and user segments. The space segment, as with any other GNSS, consists of navigation satellites. The upkeep and maintenance of the space segment is performed by the control segment. Signals from satellites are acquired, tracked‚ and processed by the receivers to provide navigation solutions for the user segment [5].

7.1.1

Space Segment

The NAVIC space segment consists of seven satellites in its full configuration, with three satellites in geostationary and four in geosynchronous orbits. Currently, seven satellites have been deployed and are in the final stages of testing. In addition, there is a proposal to extend NAVIC to an 11-satellite [7] constellation to improve availability and enhanced navigational accuracy in the primary service volume [8]. 7.1.1.1 Development

The first satellite (IRNSS-1A) was launched on 1 July 2013 on-board India’s Polar Satellite Launch Vehicle (PSLVC22) [9] from the First Launch Pad (FLP) of the Satish Dhawan Space Centre (SDSC), Sriharikota. The ‘XL’ version of PSLV was used, which is the same launch vehicle used in the Chandrayaan-1 (lunar) mission of India. The second IRNSS satellite was launched on 4 April 2014 aboard

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume ,1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

172

7 IRNSS

Figure 7.1 NAVIC satellite distribution [2]. Source: https://www.isro.gov.in/sites/default/files/article-files/node/4470/banner_1.jpg. Reproduced with permission of ISRO.

IRNSS Space Segment GSO at 111.75°E

GSO at 55°E GEO at 32.5°E

GEO at 83°E

GSO at 111.75°E

GSO at 55°E

ILSR

IRIMS

IRCDR

GSO at 131.5°E

IRNSS User IRTTC & Nav uplink

IRNWT

INC

IRNSS Ground Segment

Figure 7.2 NAVIC system architecture. Source: From I.S.R.O. [6].

PSLV-C24 [10]. Both IRNSS-1A and IRNSS-1B (shown in Figure 7.3) were placed in geostationary orbits. The third satellite (IRNSS-1C) was launched in the same year on October 15 aboard PSLV-C26, and was placed in a geosynchronous orbit [11]. This was followed by the successful launch of the fourth satellite (IRNSS-1D) on 28 March 2015 [12]. The fourth satellite was placed in a geosynchronous orbit. The last three satellites (IRNSS 1E, 1F, and 1G) were launched in 2016 to complete the seven-satellite constellation [13–15]. The details are summarized in Table 7.1. Certain on-board features of the NAVIC satellites include two solar panels consisting of ultra-triple junction solar cells that generate approximately 1660 W of power, and Sun and star sensors along with gyroscopes to provide the orientation reference to the satellite. Specially designed

thermal control schemes have been implemented for critical elements like atomic clocks. The propulsion system consists of a liquid apogee motor (LAM) and thrusters [16, 17]. 7.1.1.2 NAVIC Payload Overview

All the seven NAVIC satellites carry a navigation and ranging payload onboard. The navigation payload transmits signals supporting dual use, which is Standard Positioning Service (SPS) for civilians and Restricted Service (RS) for military purposes. In addition, the payload operates in the L5 (1176.42 MHz) and S (2492.028 MHz) bands. Multiple highly accurate rubidium atomic clocks are part of the navigation payload on the satellite. The ranging payload consists of a C-band transponder (uplink: 6700–6725 MHz, right-hand circularly polarized (RHCP); downlink:

7.1 History and Genesis

Figure 7.3 IRNSS 1B satellite in the launch pad [18, 19]. Source: http://www.isro.gov.in/irnss-programme/pslv-c22-irnss-1a-gallery; http://www.isro.gov.in/irnss-programme/pslv-c24-irnss-1b-gallery. Reproduced with permission of ISRO.

Table 7.1 NAVIC satellite launch details Satellite

Launch vehicle

Launch date

Orbit

IRNSS-1A

PSLV-C22

1 July 2013

IRNSS-1B

PSLV-C24

4 April 2014

IRNSS-1C

PSLV-C26

15 October 2014

IRNSS-1D

PSLV-C27

28 March 2015

IRNSS-1E

PSLV-C31

20 January 2016

IRNSS-1F

PSLV-C32

10 March 2016

IRNSS-1G

PSLV-C33

28 April 2016

Geosynchronous (55 E longitude, 29 elevation) Geosynchronous (55 E longitude, 29 elevation) Geostationary (83 E longitude) Geosynchronous (111.75 E longitude, 30.5 elevation) Geosynchronous (111.75 E longitude, 28.1 elevation) Geostationary (32.5 E longitude) Geostationary (131.5 E longitude)

3400–3425 MHz, LHCP), which facilitates accurate determination of the range to the satellite, along with corner cube retro reflectors for laser ranging. Figure 7.4 shows a blown-up view of the NAVIC spacecraft [16].

7.1.2

Ground Segment

The IRNSS Ground Segment is responsible for the maintenance and operation of the constellation. This includes the generation of the navigation parameters and transmission, satellite control, ranging, and integrity monitoring

and time keeping. The ground segment comprises the following [4]:

•• •• •• ••

IRNSS Range and Integrity Monitoring Stations (IRIMSs) ISRO Navigation Centre (INC) IRNSS TTC and Unlinking Station (IRTTC) IRNSS Spacecraft Control Facility (IRSCF) IRNSS Network Timing Centre (IRNWT) IRNSS CDMA Ranging Stations (IRCDRs) Laser Ranging Stations (ILRSs) Data Communication Network (IRDCN)

173

174

7 IRNSS

Propellant Tanks Solar Panel Star Sensors

Solar Panel

Global Horn Dual Helix Antenna Corner Cube Retro Reflector C-band Horn

Figure 7.4

Liquid Apogee Motor

IRNSS spacecraft constituents [9]. Source: Reproduced with permission of ISRO.

Seventeen IRIMS sites will be distributed across the country for orbit determination and ionospheric modeling [3]. Four ranging stations, separated by wide and long baselines, will provide two-way CDMA ranging [20].

7.2

IRNSS Reference System

7.2.1

IRNSS Geodetic Reference

IRNSS uses the WGS-84 coordinate system for the computation of navigation solutions.

7.1.3

User Segment

The User segment mainly consists of the following:

• • •

A single-frequency IRNSS receiver capable of processing SPS signal at L5 or S band frequency A dual-frequency IRNSS receiver capable of receiving both L5 and S band frequencies A multi-constellation GNSS receiver compatible with IRNSS and other GNSS constellations

For illustration, a multi-constellation IRNSS (dual-frequency) + GPS + SBAS developed by Accord Software and Systems Pvt. Ltd., Bangalore, India‚ is as shown in Figure 7.5.

Figure 7.5

IRNSS user receiver.

7.2.2

IRNSS Time Reference

IRNSS system time is represented as the week number (WN) and time of week count (TOWC), similar to other global constellations. Since each navigation data subframe is 12 s long, the TOWC is multiplied by 12 to obtain the time of week (TOW) in seconds. The IRNSS system time starting epoch is 00:00 UT on 22 August 1999 (midnight between August 21 and 22). At the starting epoch, the IRNSS system time was ahead of UTC by 13 s. Subsequently, the UTC corrections to the IRNSS system time were applied commensurate to the GPS system time. The epoch denoted in the navigation messages by TOWC and WN will be measured relative to the leading edge of the first chip of the first code sequence of the first subframe symbol. The transmission timing of the navigation message provided through the TOWC is synchronized to IRNSS system time [6]. IRNSS system time is maintained by INC ground stations. It is determined from a clock ensemble composed of cesium and hydrogen maser atomic standards at the INC ground stations. Similar to UTC, the IRNSS system time is also a weighted mean average time, but with two substantial differences: it will be made available in real time, which is continuous without leap seconds. The IRNSS satellites carry an on-board rubidium atomic frequency standard, which is monitored and controlled by the INC ground station. The deviation between the IRNSS system time and the satellite’s

7.4 Ground Segment Configuration

on-board clock is modeled, which is a quadratic function of time. The parameters of this model are calculated and transmitted as a part of the IRNSS broadcast navigation messages [21].

7.3

IRNSS Satellite Constellation

The primary concern for any satellite constellation design is the availability of satellites in the service volume and the impact of its geometry on the navigation accuracy. The geometry is measured by the parameter, position dilution of precision (PDOP). Since IRNSS is a regional navigation system, it is necessary to guarantee the visibility of all the satellites in the primary service area. The satellite constellation with geostationary and geosynchronous satellites was designed according to the primary requirement of availability and the best possible navigation accuracy. Another design consideration is the line-of-sight observability of all the satellites to the ground station. The constellation design of geostationary and geosynchronous orbits paves the way to provide continuous all time line-of-sight observability to all satellites. This ensures constant ranging and integrity monitoring. A summary of nominal constellation parameters is listed in Table 7.2. The space segment can be broadly categorized on the basis of its contribution as system or subsystem. Systemlevel traits include availability, accuracy, reliability, and integrity. However, the subsystem segment mainly focuses on satellite-specific features such as those depicted in Figure 7.4. On the basis of open source literature on IRNSS, the availability and subsystem parameters are explained with necessary assumptions. Among the various design parameters, availability is a paramount requirement in any GNSS, more so in a regional navigation system. With the announcement of any new constellation, an initial assessment of the signal characteristics, stand-alone availability, and achievable accuracies is of main interest. Table 7.2 Summary of nominal constellation characteristics Total number of satellites

7 (will be extended to 11)

Orbital Altitude (km)

35,000

Number of orbital planes

Geostationary orbit (GEO) and 2 geosynchronous orbit (GSO) planes

Number of satellites per plane

2 satellites each in GSO planes and 3 satellites in GEO plane

Inclination ( )

5 (for GEO satellites) 29 (for GSO satellites)

Availability is defined as the period of time a system is usable, or alternatively, it is the ability of the system to provide solutions over a specified region. IRNSS being a regional system, availability has to be highly optimized from an operational perspective. Availability‚ as illustrated in Figure 7.6, assures visibility to a user from all seven satellites over the Indian subcontinent [22, 23]. In the case of IRNSS, assuming clear sky conditions, satellites in a geostationary orbit will always be visible to users on the Indian subcontinent. An advantage of geostationary satellites is that a larger signal coverage footprint is achieved with a minimum number of satellites. However, one needs to estimate the visibility of the satellites in geosynchronous orbits to assess the overall availability. A detailed statistical reliability analysis for the IRNSS constellation is presented in [22].

7.4

Ground Segment Configuration

An integral component of any ground segment is to continuously track the satellites and estimate the integrity of each signal component (for example, code, carrier‚ and data), discretely in real time. In case of any abnormality, alert is announced. IRIMS facilitates this by performing one-way ranging to satellites employing high-end reference station receivers. It receives data from the IRNSS satellites, and processes and transmits the necessary information to the INC. The objectives of the INC are the following [24]:

• • • •

Compute the primary and secondary navigation parameters that include estimation and prediction of the ephemeris and SV clock corrections Initialize on-board time (clock) and monitor its performance Monitor the broadcast parameters in the range domain (in terms of user equivalent range error or UERE) and position domain (through user position computation at the reference stations) Estimate ionospheric corrections and integrity information.

The SV clock and ephemeris corrections are then transmitted to the IRTTC stations, which receive and command IRNSS telemetry data. These stations are used for uplinking the navigation data to the IRNSS satellites. The IRCDR stations facilitate accurate two-way ranging of IRNSS satellites and transmit data to the INC. The primary function of the SCF is to manage and maintain the satellite constellation. The details of the various elements of the IRNSS ground segment are shown in Figure 7.7.

175

Number of IRNSS Satellites Visible 80 60

Latitude (Deg.)

40 20 0 –20 –40 –60 –80 –40

–20

0

20

40

80

60

100

120

140

160

180

Longitude (Deg.)

0

1

2

3

4

5

6

7

No. of satellites

Figure 7.6

IRNSS satellite availability over Indian subcontinent.

The constituent elements of the IRNSS ground segment are: ISRO Navigation Centre (INC) at Byalalu, is the nerve center of the IRNSS Ground Segment. INC primarily generates navigation parameters 200 nm

IRNSS Range and Integrity Monitoring Stations (IRIMS) perform continuous one way ranging of the IRNSS satellites and are also used for integrity determination of the IRNSS constellation.

Gaggal Dehradun

IRNSS CDMA Ranging Stations (IRCDR) carry out precise two way ranging of IRNSS satellites. Lucknow

IRNSS Network Timing Centre (IRNWT) at Byalalu generates, maintains and distributes IRNSS Network Time.

Jodhpur Shillong Udaipur Bhopal

Spacecraft Control Facility (SCF) controls the space segment through Telemetry Tracking & Command networks. In addition to the regular TT&C operations, IRSCF also uplinks the navigation parameters generated by the INC.

Kolkata

Pune

Goa Byalalu

IRNSS Data Communication Network (IRDCN) provides the required digital communication backbone to IRNSS network.

Bangalore

Hassan

PortBlair

Kavaratti Mahendragiri

International Laser Ranging Stations (ILRS) is being used periodically to calibrate the IRNSS orbit determined by the other techniques.

Figure 7.7 of ISRO.

IRNSS Ground Segment distribution and definitions of each functional component [9]. Source: Reproduced with permission

7.5 IRNSS Signal Configuration

The estimation of satellite orbit and clock parameters are done using high-accuracy measurements from the IRIMS stations after removing the atmospheric errors, possible outliers, cycle slips, and carrier phase ambiguity. One of the IRIMSs is driven by IRNWT, which serves as the reference time for precise orbit and clock estimation [17, 25]. A batch filter processes three-day measurements to ensure the stability of the orbital arc. Prior to the generation of navigation parameters, orbits as determined employing twoway ranging measurements are used for validation.

7.5

IRNSS Signal Configuration

IRNSS signal consists of an SPS signal and RS signal in two frequency bands, namely, L5 and S. The frequency band in L5 was chosen from the allocated spectrum (post frequency filing) for Radio Navigation Satellite Services (RNSSs). The signal configuration of both SPS and RS signals consists of the following:

•• •

Navigation data stream Pseudorandom noise (PRN) code Carrier signals in the L5 and S bands

subframe symbols. This is called Forward error correction (FEC) encoding. The FEC-encoded subframe symbols are then interleaved using a block interleaver before appending with 16 bits of SYNC CODE (0xEB90). The synchronization code is not encoded, which allows the receiver to achieve subframe synchronization. The FEC encoding scheme with interleaving is shown in Figure 7.8 and Table 7.3, respectively. There are also tail bits in each subframe, which are a series of six zero bits allowing the completion of FEC decoding of each subframe in the user receiver. A 24-bit cyclic redundancy check (CRC) parity provides protection against burst errors in navigation data as well as random errors with a probability of undetected error

Table 7.3 FEC encoding and block interleaver configuration Parameter

FEC encoder

Value

Coding rate

1/2

Coding scheme

Convolution

Constraint length

7

Generator polynomial

G1 = (171)o G2 = (133)o

7.5.1

Encoding sequence

Navigation Message

The IRNSS navigation message is structured into four subframes [6]. The navigation data in each subframe consists of 292 bits that are rate ½ convolution encoded to obtain 584

Block interleaver

Interleaver size

584

Interleaver dimensions (n columns × m rows)

73 × 8

IRNSS Navigation data (292 Bits)

FEC Encoder G1 Input

q–1

q–1

q–1

q–1

q–1

q–1

Output G2 584 symbols

Block Interleaver

0xEB90

G1 then G2

Interleaved data (584 symbols)

SYNC CODE

Figure 7.8 IRNSS navigation data generation methodology. Source: From I. S. R. O. [6].

177

7 IRNSS

≤ 2−24 = 5.96 e−8 for all channel bit error probabilities ≤ 0.5 [6]. The generator polynomial used for the CRC computation in each subframe given as 24

gi X i

gX = i−0

gi = 1 for i = 0, 1, 3, 4, 5, 6, 7, 10, 11, 14, 17, 18, 23, 24 and 0 otherwise; Xi is the bit stream for which the CRC need to be computed. 7.5.1.1 Frame Structure

The IRNSS master frame is 2400 symbols long and made up of four subframes. Each subframe is 600 symbols long, as explained earlier. Subframes 1 and 2 transmit fixed primary navigation parameters. Subframes 3 and 4 transmit secondary navigation parameters in the form of messages. The master frame structure is shown in Figure 7.9. All subframes transmit TLM, TOWC, alert, AutoNav, subframe ID, spare bit, navigation data, CRC, and tail bits. Subframes 3 and 4 also transmit message ID and PRN ID. Figure 7.9 also shows the subframe structure for the IRNSS navigation data. The most significant bit/byte is transmitted first [6]. The primary navigation parameters consisting of the satellite ephemeris, clock information, signal health status, group delay, and user range accuracy (URA) are transmitted in the first two subframes and are repeated once every 48 s. The secondary navigation parameters, which include

satellite almanac, ionospheric grid parameters, ionospheric delay correction coefficients, UTC and GNSS time offsets, differential corrections, Earth orientation parameters, and text messages, are transmitted in subframes three and four. The contents of subframes 1 and 2 are fixed to transmit the primary navigation parameters.

• •

Subframe 1: Satellite ephemeris and clock parameters (Broadcast interval = as needed but repeats once every 48 s). Subframe 2: Satellite ephemeris (Broadcast interval = as needed but repeats once every 48 s).

The contents of the secondary navigation parameters are transmitted as message types with specific broadcast intervals. The following are the different message types that are defined to be transmitted in subframes 3 and 4:

• • • • •

Message Type 0: Null message, which is broadcast when there is no other message waiting for broadcast (Broadcast interval = as needed). Message Type 5: Ionospheric grid parameters for one region ID (Broadcast interval = 5 min). Message Type 7: Almanac parameters for one satellite (Broadcast interval = 60 min). Message Type 9: IRNSS time correction parameters with respect to UTC and GPS (Broadcast interval = 20 min). Message Type 11: Earth orientation parameters and ionospheric coefficients for Klobuchar model (Broadcast interval = 10 min).

600 Symbols SUBFRAME DATA-FEC encoded (584 Symbols) SYNC CODE 16 bits

48 s

178

Navigation data (292 Bits) TLM

TOWC

ALERT

AUTONAV

SUBFRAME SPARE ID

Subframe One

• Primary navigation parameters

Subframe Two

• Primary navigation parameters

Subframe Three

• Secondary navigation parameters

Subframe Four

• Secondary navigation parameters

DATA

CRC

TAIL

600 Symbols SUBFRAME DATA-FEC encoded (584 Symbols) SYNC CODE 16 bits

Figure 7.9

Navigation data (292 Bits) TLM TOWC

ALERT

AUTONAV

SUBFRAME SPARE MESSAGE ID ID

IRNSS navigation data subframe structuring details.

DATA

CRC

TAIL

7.5 IRNSS Signal Configuration

• • •

Figure 7.10 shows the block diagram of the SPS code generator. Polynomials G1 and G2 are the same as the GPS C/A code generator. The G1 and G2 generators are realized by using 10-bit maximum length feedback shift registers (MLFSRs). Each satellite is assigned to a different initial G2 register state to generate a unique PRN code using different chip delays as shown in Table 7.4 [8].

Message Type 14: Differential correction parameters (Broadcast interval = as needed). Message Type 18: Text messages (Broadcast interval = as needed). Disaster management service could be initiated with the assistance of these messages. Message Type 26: IRNSS time correction parameters with respect to UTC and other GNSS (Broadcast interval = 20 min).

7.5.3 7.5.2

PRN Codes

The IRNSS system provides two types of services, namely, SPS and RS. SPS is primarily meant for civilian and commercial applications and is available to all users. The IRNSS signal-in-space (SIS) Interface Control Document (ICD) for the SPS signal was released in the official ISRO website http://irnss.isro.gov.in in October 2014. The carrier frequencies and bandwidth of transmission for the SPS and RS signals are shown in Table 7.5. The modulation scheme employed for the SPS signal is binary phase shift keying (BPSK (1)) on both frequency bands and binary

IRNSS uses Gold codes for the SPS signal that are generated using linear feedback shift registers (LFSRs). The time period of the PRN sequence generated for the SPS signal is 1 ms with a chipping rate 1.023 Mcps. The two generator polynomials for the G1 and G2 shift registers are given by G1 X10 + X3 + X1 and G2 X10 + X9 + X8 + X6 + X3 + X2 + 1

1 1.023 Mcps Clock

3

4

5

6

7

8

9

10

Set initial bits

SPS PRN code

1

Figure 7.10

2

Composite Signal Generation

2

3

4

5

6

7

8

9

10

SPS code generator mechanism. Source: From I. S. R. O. [6].

Table 7.4 Code phase assignment for SPS signals L5-SPS

S-SPS

PRN ID

Satellite

Initial condition for G2 register

First 10 chips in octal2

Initial condition for G2 register

First 10 chips in octal2

1

IRNSS-1A

1110100111

130

0011101111

1420

2

IRNSS-1B

0000100110

1731

0101111101

1202

3

IRNSS-1C

1000110100

0713

1000110001

0716

4

IRNSS-1D

0101110010

1215

0010101011

1524

5

IRNSS-1E

1110110000

0117

1010010001

0556

6

IRNSS-1F

0001101011

1624

0100101100

1323

7

IRNSS-1G

0000010100

1753

0010001110

1561

179

180

7 IRNSS

Table 7.5 IRNSS services and description of various signal components Service type

Code (Mcps)

Frequency band

Carrier(MHz)

Bandwidth(MHz)

Modulation

SPS

1.023

L5

1176.45

24

BPSK

S

2492.028

16.5

BPSK

L5

1176.45

24

BOC (5,2)

S

2492.028

16.5

BOC (5,2)

RS

2.046

offset carrier (BOC (5, 2)) for RS signals. The IRNSS RS signal consists of a data channel and a pilot channel. The composite IRNSS signal is then generated using interplex modulation technique by adding a fourth signal in order to maintain a constant envelope at the output of the power amplifier [6]. The SPS data signal ssps(t) is represented as [6] ∞

ssps t = i = −∞

The RS BOC data signal srs_d is represented as ∞

srs_d t = i = −∞

crs_d i Lrs_d

drs_d i CDrs_d rect T c,rs_d t − iT c,rs_d scrs_d t, 0 73 In Eq. (7.4) scx represents the subcarrier signal‚ and it is represented as scx t, φ = sgn sin 2π f sc,x t + φ

csps i Lsps dsps i CDsps rect T c,sps t − iT c,sps

The IRNSS RS data and pilot channels use sinBOC, and so the subcarrier phase φ is 0. The composite signal s(t) along with the interplex signal I(t) is then represented as

71 The RS BOC pilot signal srs_p is represented as

st =

1 3

2 ssps t + srs t

+ j 2 srsd t − I t 75

∞

srs_p t = i = −∞

crs_p i Lrs_p rect T c,rs_p t − iT c,rs_p scrs_p t, 0 72

In Eq. (7.5), I(t) is added to maintain the constant envelope of the composite signal. Figure 7.11 shows the block diagram of the IRNSS composite signal generation.

ssps(t)

dsps (Rd_sps)

Csps (Rc_sps) srs_p(t) crs_p

sc(t) srs_d(t)

drs_p(Rd_rs)

Crs_d (Rc_rs)

Figure 7.11

74

sc(t) (Rsc)

Figure 7.11 IRNSS composite signal generation.

Constant Envelope Mux

s(t)

7.7 Ionospheric Model and Representation

The symbol definitions are as follows: cx(i) dx(i) fsc “ [i]x CDx Lx rectx Tc,x Rd,sps Rd,rs Rc,sps Rc,sps Rsc

7.6

i-th chip of the spreading code i-th bit of the navigation data Subcarrier frequency ‘i’ modulo x Integer part of x Number of chips per navigation data Length of spreading code in chips Rectangular pulse function with duration “x” Spreading code chip duration SPS data rate = 50 symbols per second RS data rate = 50 symbols per second SPS code chip rate = 1.023 Mcps RS code chip rate = 2.046 Mcps Subcarrier frequency = 5.115 Mcps

IRNSS Performance Specifications

The following section lists the performance parameters of IRNSS [6].

• • • • •

Signal phase noise: A second-order phase lock loop with 10 Hz bandwidth is guaranteed to be able to track the unmodulated carrier with an accuracy of 0.1 radians (RMS). Correlation loss: Correlation loss is defined as the difference between the transmitted power received in the specified signal bandwidth and the signal power recovered in the ideal receiver of the same bandwidth, which perfectly correlates using an exact replica of the waveform within an ideal band-pass filter with linear phase. For IRNSS signals, the value is 0.6 dB. Spurious characteristics: For IRNSS signals, −50 dB is the in -band spurious level. Received signal power levels: It is assured that a minimum of −159 dBW is guaranteed on ground for L5 and −162.3 dBW for the S band signal, with user elevation above 5 . Polarization characteristics: As with any other GNSS constellation, IRNSS signals are also RHCP.

7.6.1

Channel Group Delay

Channel group delay is defined as a time difference between transmitted RF signal (measured at the phase center of the transmitting antenna) and the signal at the output of the on-board frequency source. There are three different delay parameters [6, 21]:

•

•

Fixed/bias group delay: This is a bias term that is included in the clock correction parameters transmitted

•

in the navigation data, and is thus accounted for during the user computation of system time. Differential group delay: Each IRNSS navigation signal generator payload consists of a main path for the default operation and a redundant path to operate during occurrence of any failure in the main path. The hardware is different for each path in terms of the data generator, modulator, up-converter, traveling wave tube amplifier (TWTA), cable, and integration components. This is the delay difference between two navigation signals on the two RF paths. It consists of random plus bias components. The mean differential is defined as the bias component and can be either positive or negative. For a given navigation payload redundancy configuration, the absolute value of the mean differential delay shall not exceed a few nanoseconds (ns), that is, on the order of 15 to 30 ns [21]. The random variations about the mean will be in the range of 3 ns (2σ). In order to correct the bias component of the group delay, the TGD parameter is broadcast to the user in the navigation message [16]. Group delay uncertainty in bias and differential value: The group delay uncertainty shows the variability in the path delay due to operational environment uncertainty and other factors. The effective uncertainty of the group delay will be in the range of 3 ns (2σ).

7.7 Ionospheric Model and Representation The ionospheric effect on signal propagation is the largest error source for single-frequency IRNSS users. To help single-frequency users achieve relatively better accuracy performance, IRNSS has adopted a grid-based model for ionospheric delay estimation, thereby providing comparable user position accuracies as dual-frequency receivers. A 5 × 5 grid was formulated over the Indian region 350 km above Earth’s surface as shown in Figure 7.12. The ionospheric correction parameters are broadcast as a part of the navigation data (Message Type 5) at 5 min intervals. The correction parameters include the vertical delay estimates at specified ionospheric grid points (IGPs), and are applicable to a signal on L5 for the single-frequency users. There are 90 IGPs defined in total, which cannot be transmitted in a single message. Hence, the entire grid is divided into six regions and each message type broadcasts ionospheric correction parameters for a particular region. The grid parameters include the following:

••

Region ID Grid Ionosphere Vertical Delay (GIVD)

181

7 IRNSS

45 40 35 30

Latitude (deg.)

182

25 20 15 10 5 0 –5 55

60

65

70

75

80 85 Longitude (deg.)

90

95

100

105

110

Figure 7.12 Ionospheric grid for IRNSS system [6]. Source: https://www.isro.gov.in/sites/default/files/irnss_sps_icd_version1.1-2017.pdf.

• • •

Grid Ionosphere Vertical Error Indicator (GIVEI): 99.9% accuracy of the GIVD Regions Masked (10 bits): The total number of regions for which the corrections are provided Issue of Data Ionosphere (IODI): This indicates the change in the region masked and ranges from 0 to 7

In addition to this, ionospheric error for single-frequency L5 users for the entire IRNSS service volume is broadcast as a set of eight coefficients, which is valid over a day. For dual-frequency receivers, the carrier frequency diversity between L5 and S signals is used to correct for the group delay due to first-order ionospheric effects [6]. The correction to pseudorange is ρ, which is a function of the L5derived pseudorange (ρL5), S-derived pseudorange (ρS), carrier frequencies of L5 (fL5), and S (fS5), and can expressed as ρ = ρL5 −

f 2s f 2L5 ρS

1−

f 2s f 2L5

7.8

IRNSS Receiver Architecture

7.8.1

Antenna

75

One of the major challenges in designing a multi-frequency and multi-constellation receiver‚ including IRNSS‚ is the

receiver antenna design. The incoming signal being RHCP, the first element should be compliant with it and a beamwidth (signal capture range) adequate to source satellites from zenith to 5 elevation. Typically, two antenna topologies are used in practice: passive and active. The passive antenna requires that the processing section be very close to the physical antenna. An example is a handheld GNSS receiver. In practice, many applications require the receiver unit to be at a certain distance from the antenna. The cable inter-connecting antenna to the receiver introduces attenuation to the signal. To compensate for this, a low noise amplifier (LNA) of appropriate gain is used closest to the antenna. The power feed to the LNA is typically from the receiver, which makes the configuration active. To protect the receivers from undesired interference, most antennas have a band-pass filter (BPF) following the LNA. This component allows the intended signal and attenuates interfering components outside the desired band, ensuring that subsequent stages operate linearly. Finally, the satellites are spatially distributed and are at different elevations with respect to the user antenna. Typically, an antenna has maximum attenuation for the horizon satellites to suppress ground reflected multipath, which is often high for lowelevation satellites. Unlike other GNSS constellations where around eight satellites are typically guaranteed above 25 elevation, for

7.8 IRNSS Receiver Architecture

• 1176 ± 12 MHz

GPS-IRNSS Wideband Antenna

Frequency Range

• 1575 ± 12 MHz • 2492 ± 8.5 MHz

VSWR

• < 1.5:1

Polarization

• RHCP

Passive Gain @ Zenith

• > 2 dBiC@ L1 & L5 band • > 3 dBiC@ S band

Gain @ 15° Elevation

• > –3 dBi@ L1 & L5 band • > –2 dBi@ S band

LNA Gain Noise Figure

• 20 ± 3 dB @ L1 & L5 band • 17 ± 3 dB @ S band • < 2.0 dB

Figure 7.13 Integrated GPS-IRNSS wide-band antenna.

IRNSS the elevation mask should go all the way until 15 . This ensures that in the desired service volume, all the seven satellites are available and good PDOP is guaranteed. Also, given the wide separation between the L5 and S bands, realization of a compact antenna is a challenge. Alternatively, two antennas – one covering L5 to L1 and the second covering only the S band – can be combined and used. This would call for additional real estate on the platforms and might pose a challenge for retrofit applications. Figure 7.13 is an example of an integrated IRNSS and GPS antenna developed by Thiagarajar Telekom Solutions Limited (TTSL), Madurai [26].

7.8.2

Receiver

The IRNSS receiver architecture is similar to any multifrequency GNSS receiver that is capable of acquiring and tracking multi-frequency GNSS signals. A typical IRNSS/GPS/SBAS receiver developed by Accord Software and Systems Pvt. Ltd. (shown in Figure 7.5) is configurable to operate in various modes: 1) Single-frequency IRNSS: IRNSS-L5 or S 2) Dual-frequency IRNSS: IRNSS-L5 and S 3) Dual-frequency Hybrid: Dual-frequency IRNSS and GPS-L1

7.8.3

IRNSS System Performance

7.8.3.1 Single-Frequency IRNSS-L5 or IRNSS-S

The first mode of operation presented is the singlefrequency IRNSS mode, where the receiver uses only the

measurements from the IRNSS-L5 signal. The IRNSS grid-based ionospheric model is used to compensate for the ionospheric errors. Figure 7.14 shows the 3D position error plot (raw measurements were used for position estimation, without any smoothing) from the IRNSS receiver in single-frequency IRNSS-L5/S modes, respectively. The test was performed at the Accord Software and Systems Pvt. Ltd. head office in Bangalore, India with a static user antenna on 26 October 2017. 7.8.3.2 Dual-Frequency IRNSS

The second mode of operation is dual-frequency IRNSS, where the receiver employs measurements from both L5 and S signals. The errors due to the ionosphere can be eliminated using the frequency diversity of the two signals without any dependence on grid or ionospheric coefficients from navigation data. Unlike the model-based approach, which requires time to collect ionosphere data and then apply corrections, it is instantaneous in dual-frequency mode. Figure 7.15 shows the 3D position error plots from the IRNSS receiver in dual-frequency IRNSS mode. 7.8.3.3 Dual-Frequency Hybrid

The final mode of operation is to use a combined dualfrequency IRNSS with GPS-L1 and SBAS. Figure 7.15 shows the 3D position error plots from the IRNSS receiver in dual-frequency IRNSS mode. The performance is better with the additional GPS measurements, which improves the geometry. Overall, the IRNSS system accuracy is well within the desired limits of 20 m (2-sigma) even in standalone mode of operation.

183

7 IRNSS

RSS Error 18

3Drms(IRNSS-L5) – 2.6 m 3Drms(IRNSS-S) – 5.1 m

16 14

RSS Error(m)

12 10 8 6 4 2

3.5 01:13

3.52 01:46

3.54 02:20

3.56 02:53

3.58 03:27

5 3.6 × 10 04:00

TOWC(s) UTC (HH:MM)

Figure 7.14 3D Position error of Accord’s IRNSS receiver in L5-only and S-only mode using IRNSS grid-based model for ionospheric error compensation.

RSS Error 11

3Drms(HYBRID) – 1.5 m 3Drms(IRNSS-DUAL) – 4.6 m

10 9 8 RSS Error(m)

184

7 6 5 4 3 2 1 3.5 01:13

3.52 01:46

3.54 02:20

3.56 02:53

3.58 03:27

3.6 × 105 04:00

TOWC(s) UTC (HH:MM)

Figure 7.15 3D- Position error of Accord’s IRNSS receiver in dual-frequency IRNSS mode and dual-frequency IRNSS+GPS-L1 mode using IRNSS grid-based model for ionospheric error computation.

References

7.9

Conclusion

With IRNSS, India will have the distinct advantage of having its own navigation constellation, which would be crucial during militarily disturbed conditions. This constellation is the first of its kind with complete regional positioning and satellites always visible in the primary service volume, and will provide several research possibilities in the receiver algorithm design. Regionally, the IRNSS receiver could be integrated with other constellation receivers and used in end applications, with IRNSS primarily used in the basic service volume.

11 ISRO “Brochure of PSLC-C26/IRNSS-1C,” 2014. [Online].

12

13

14

15

References 1 Nair, G.M., “Satellites for Navigation,” Press Information

16

Bureau of the Government of India, Bangalore, 2006. 2 I. S. R. Organization, “Indian Regional Navigation Satellite

System Signal In Space ICD For SPS,” Bangalore, 2014.

17

3 ISRO, “IRNSS-programme Towards-Self-Reliance-

4

5

6

7

8

9

10

Navigation-IRNSS,” [Online]. Available: https://web. archive.org/web/20160310163951/http://www.isro.gov.in/ irnss-programme/towards-self-reliance-navigation-irnss. [Accessed 5 2017]. ISRO “IRNSS—Indian Regional Navigation Satellite System,” 28 April 2016. [Online]. Available: http://www. isac.gov.in/navigation/irnss.jsp. [Accessed November 2016]. Gowrisankar D. and Kibe S.V.“India’s Satellite Navigation Programme,” 10 December 2008. [Online]. Available: http://www.space.mict.go.th/activity/doc/aprsaf15_17. pdf. [Accessed November 2016]. I. S. R. O. ISRO Satellite Centre “Indian Regional Navigation Satellite System Signal In Space ICD for Standar Positioning Service,” Indian Space Research Organization Bangalore India 2017. The Indian Express, “Navigation Satellite Clocks Ticking, System To Be Expanded: ISRO,” 10 6 2017. [Online]. Available: http://indianexpress.com/article/technology/ science/navigation-satellite-clocks-ticking-system-to-beexpanded-says-isro-4697621/. I. S. R. Organization, “Indian Regional Navigation Satellite System (IRNSS) : NavIC,” 2016. [Online]. Available: http:// www.isro.gov.in/irnss-programme. [Accessed 2016]. ISRO “Brochure of PSLV-C22/IRNSS-1A,” 2013. [Online]. Available: http://www.isro.gov.in/sites/default/files/pdf/ pslv-brochures/PSLVC22.pdf. [Accessed October 2016]. ISRO “Brochure of PSLV-C24/IRNSS-1B,” 2014. [Online]. Available: http://www.isro.gov.in/sites/default/files/pslvc24-brochure.pdf. [Accessed October 2016].

18

19

20 21

22

23 24

25

26

Available: http://www.isro.gov.in/sites/default/files/pdf/ pslv-brochures/PSLV-C26%20IRNSS-1C%20Mission.pdf. [Accessed October 2016]. ISRO “Brochure of PSLV-C27/IRNSS-1D,” 2015. [Online]. Available: www.isro.gov.in/irnss-programme/pslv-c27irnss-1d-brochure. [Accessed October 2016]. ISRO “Brochure of PSLV-C31/IRNSS-1E,” 2016. [Online]. Available: www.isro.gov.in/irnss-programme/pslv-c31irnss-1e-brochure. [Accessed October 2016]. ISRO “Brochure of PSLV-C32/IRNSS-1F,” 2016. [Online]. Available: http://www.isro.gov.in/sites/default/files/ pslv_c32_final.pdf. [Accessed October 2016]. ISRO “Brochure of PSLV-C33/IRNSS-1G,” 2016. [Online]. Available: www.isro.gov.in/irnss-programme/pslv-c33irnss-1g-brochure. [Accessed October 2016]. e. Directory “IRNSS (Indian Regional Navigational Satellite System),” [Online]. Available: https://directory. eoportal.org/web/eoportal/satellite-missions/i/irnss. Ganeshan, A.S., Ratnakara, S.C., Srinivasan, N., Raja Ram, B., Tirmal, N., and Anbalagan, K., “Successful Proof-ofConcept Demnostration First Position Fix with IRNSS,” Inside GNSS, pp. 49-52, July/August 2015. ISRO, “PSLV-C22/IRNSS-1A Gallery,” 2014. [Online]. Available: http://www.isro.gov.in/sites/default/files/ galleries/PSLV-%20C22%20Gallery/sat3.jpg. ISRO, “PSLV-C24/IRNSS-1B Gallery,” [Online]. Available: http://www.isro.gov.in/sites/default/files/PSLV-C24% 20Gallery/pslv-c24-13.jpg. Ganeshan, A.S., “Overview of GNSS and Indian navigation program,” ISRO Satellite Centre, Bangalore, 2012. Majithiya, P., Khatri, K., and Hota, J., “Indian Regional Navigation Satellite System - Correction Paramers and Timing Group Delays,” Inside GNSS, pp. 40–46, January/ February 2011. Guru Rao, V., Lachapelle, G., and Bellad, S.V, “Analysis of IRNSS over Indian Subcontinent,” in ION ITM 2011, San Diego, CA, 2011. Guru Rao, V., “Proposed LOS Fast TTFF Signal Design for IRNSS,” PhD thesis, University of Calgary, Calgary, 2012. Saikiran, B. and Vikram, V., “IRNSS architecture and applications,” KIET International Journal of Communications & Electronics, Vol. 1, No. 3, 2013. Kumar, H., “IRNSS: India’s own Navigation System,” 28 March 2015. [Online]. Available: https://www.quora. com/profile/Kumar-Harshit-1/Posts/IRNSS-Indias-ownNavigation-System. [Accessed November 2016]. Thiagarajar Telecom Solutions Limited (TTSL) “IRNSS & GPS Navigational Antenna,” Madurai, 2015.

185

187

8 Quasi-Zenith Satellite System Satoshi Kogure1, Yasuhiko Kawazu1, and Takeyasu Sakai2 1 2

National Space Policy Secretariat, Japan National Institute of Maritime, Port and Aviation Technology, Japan

The Quasi-Zenith Satellite System (QZSS) is a regional, space-based positioning, navigation, timing (PNT) system developed by the Japanese government. The main purpose of the system is to enhance PNT capability and performance even in severe environments by using satellite orbit characteristics which can provide PNT signal transmission from high elevation angles. This chapter describes QZSS in a summary form. Section 8.1 outlines the history and background of the QZSS program and why QZSS is needed in Japan. Section 8.2 describes the current management structure of QZSS. Section 8.3 introduces the geodetic and time reference systems employed by QZSS and their alignments with international standards. Section 8.4 discusses the services provided by QZSS, including comprehensive services that not only provide PNT and augmentation, but also short messaging services with content related to non-PNT services relevant to the main satellite positioning focus of this book. Sections 8.5, 8.6, and 8.7 summarize the key characteristics of the QZSS constellation and space segment, ground segment, and signals, respectively. Finally, Section 8.8 is a brief summary of this chapter.

8.1 History and Background of QZSS Development 8.1.1

Background

In the earlier stage of GPS utilization before many GPS satellites had been deployed in orbit, Japan was one of the leading countries in GPS utilization. In the scientific fields, the Japanese University Consortium for GPS Research (JUNCO) was established and started nationwide crustal deformation observations and research using dualfrequency GPS geodetic receivers in 1987, followed by establishing the Japanese national Continuously Operating

Reference Station (CORS) network and GPS Earth Observation Network (GEONET) in 1996. In the civil commercial market, the world’s first GPS-based car navigation product was released to the market in 1990. Through the progress in both scientific research and practical utilization, the excellent benefits of GPS have been recognized, where users can obtain uniform service globally on a 24/7 basis, regardless of weather, and access a wide variety of applications, but with some drawbacks, such as a strong dependency on the environment surrounding the users. Japan has four major islands and several thousand small islands. Approximately 70% of the territory is mountainous terrain. However, most of the 120 million Japanese people live in cities located in narrow coastal flat lands. These geographical characteristics lead to challenging conditions for satellite navigation. Dense, closely spaced buildings and narrow streets in urban areas block direct signals from satellites, causing non-line-of-sight (NLOS) and multipath-dominated signals, which lead to degraded users’ PNT performance. The figure-eight satellite orbit was a concept based on the inclined geosynchronous orbit (IGSO) satellite applications for mid-latitude regions, which was proposed by the Communications Research Laboratory (CRL, currently the National Institute of Information and Communications Technology (NICT)) [1]. In the late 1990s to early 2000s, some Japanese industries planned to use the concept for mobile communication systems, a GPS augmentation service platform, as well as regional positioning system investigation [2]. The National Space Development Agency (NASDA: currently Japan Aerospace Exploration Agency (JAXA)) applied the combined geosynchronous orbit (GSO) and IGSO satellite constellations to their regional satellite navigation system study. The original QZSS program was launched as a result of a public private partnership project integrating commercial mobile

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

188

8 Quasi-Zenith Satellite System

communications, broadcast satellite services, and Japanese-government-funded R&D programs on satellite navigation technologies in 2003. The Advanced Satellite Business Corporation (ASBC) was established to study their business plan and was funded by 59 companies including Mitsubishi Electric Corporation, Hitachi Ltd, ITOCHU Corporation, NEC Toshiba Space System, Mitsubishi Corporation, and Toyota Motor Corporation in 2002 prior to launching the public private partnership project. In 2006, after the ASBC decided to cancel the public private partnership project and to withdraw their participation from the program, the project was reduced to a technical demonstration with one test satellite. JAXA took the role of the integrator for the entire system construction and technical validation after the launch of the test satellite in collaboration with other Japanese research institutes, including NICT; Electronic Navigation Research Institute (ENRI), which is currently the National Institute of Maritime, Port and Aviation Technology (MPAT)); Geospatial Information Authority in Japan (GSI); National Institute of Advanced Industrial Science and Technology (AIST); and Satellite Positioning Applications Center (SPAC). NICT developed onboard test equipment for Two-Way Satellite Time and Frequency Transfer (TWSTFT) [3] as well as an active hydrogen maser clock [4]. Due to a logistical limitation, the hydrogen maser clock was not implemented in space. ENRI [5] and GSI [6] developed ground test systems to generate augmentation messages and conducted their validations. AIST was involved in verifying the proof-ofconcept study for time synchronization between an onboard crystal oscillator and an atomic clock on the ground. SPAC conducted an application demonstration for Japanese industries using their augmentation system platform [7]. The first QZSS satellite was launched on 11 September 2010. The nickname “Michibiki,” which means “guiding light,” was selected after an open call by the public. The technical verification and application demonstrations were conducted successfully by the JAXA [8] and other research institutes. Because of the successful results, the Japanese government announced on 30 September 2011 that it would establish a four-satellite QZSS constellation as a national infrastructure by the late 2010s, as well as set the future goal of a seven-satellite constellation by around 2023 to maintain an independent PNT capability. The second, third, and fourth QZSS satellites were launched successfully in 2017 on June 1, August 19, and October 10, respectively. Each satellite in-orbit test (IOT) has been conducted. Signal transmission testing and precise orbit determination (POD) software tuning have been performed subsequently. Operational service provisions began on November 1, 2018.

8.2

QZSS Management Structure

The Cabinet Office plays the lead role of coordination and enabling collaborative work across multiple ministries within the Japanese government. The establishment of space policy, strategy, and implementation plan requires discussions and coordination across multiple ministries. Therefore, the National Space Policy Secretariat (NSPS) under the Cabinet Office was established in 2016 after merging the Secretariat of the Strategic Headquarters for Space Policy under the Cabinet Secretariat and the Office of National Space Policy under the Cabinet Office. The deployment, operation of QZSS, and service provision are major tasks of NSPS. Figure 8.1 depicts the current QZSS management organization structure. NSPS manages the QZSS program including the planned future expansion to a seven-satellite constellation. The Civil Aviation Bureau of Japan (JCAB) is currently operating the MTSAT Space-based Augmentation System (MSAS). JCAB is also involved in joint projects with QZSS, and QZSS will be utilized as a MSAS platform in 2020 after the MTSAT-2 operation is terminated. The framework for the QZSS service provision is through a private financial initiative (PFI) from 2018 to 2033. The QZSS Service Incorporation (QSS) was established to implement the ground control segment and service provision for 15 years. It was awarded the contract with NSPS as the QZSS operator, as well as service provider in 2013.

8.3 QZSS Geodetic and Time Reference Systems For QZSS, interoperability with GPS and other GNSSs is an important feature. Its geodetic and time references are aligned with international standards, that is, the International Terrestrial Reference Frame (ITRF) and Universal Time (UTC), respectively. Section 8.3.1 describes the geodetic reference system used by QZSS, while Section 8.3.2 addresses the time reference system.

8.3.1

QZSS Geodetic Reference System

The coordinate system used by QZSS is defined in IS-QZSSPNT [9]. Its coordinate origin is located at Earth’s center of mass, and its coordinate axes are the same as those of the International Terrestrial Reference System (ITRS). It is maintained with centimeter-level accuracy with respect to the ITRF08.

8.3.2

QZSS Time Reference System

QZSS reference time (QZSSRT) is defined according to the ensemble clock generated by four ground reference

8.4 QZSS Services

Figure 8.1 QZSS management structure.

hydrogen maser clocks located in four monitoring stations. In order to maintain interoperability with GPS, QZSS uses the same time scale, origin, and other definitions related to the time system as that of the US GPS. Thus, the epoch is midnight UT on 6 January 1980, with no adjustment for leap seconds, and with “roll-overs” occurring every 1024 weeks after the epoch, as with GPS time. The QZSS ground control segment estimates each satellite orbit and clock offset for both QZSS and GPS. GPST is also estimated based on SV clock offsets from QZSSRT and GPS navigation data. This is achieved by treating QZSST as the estimated GPST. Each QZSS SV clock offset is calculated based on this QZSST and then broadcast as clock offset and quadratic term coefficients in the navigation message. In other words, the system time difference between QZSS and GPS is included in the clock offset parameters broadcast from QZSS. Therefore, the GNSS time offset in CNAV and CNAV2 messages for QZSS L2C, L5, and L1C is set to “Zero” value. The current control segment does not have the capability to generate other GNSS time offsets, though CNAV and CNAV2 messages reserve several bits for other satnav systems. QZSS satellites transmit conversion parameters from QZSST to UTC(NICT) as UTC offset parameters. The UTC offset error is maintained within 40 ns (95%).

8.4

QZSS Services

QZSS provides three main types of functional capabilities to users: (1) GPS complementary, (2) GNSS augmentation, and (3) messaging capabilities. Eight services are provided by QZSS, and Table 8.1 lists the QZSS signals and services.

QZSS Performance Standard (PS-QZSS) defines the performance of the entire civil open services related to satellitebased PNT, such as accuracy, availability, continuity, and integrity [10]. These services are described in detail in the following sections.

8.4.1 GPS Complementary Capability (PNT Service) The GPS Complementary function is a fundamental capability of a space-based PNT system that provides a ranging signal with a navigation message. To implement this capability, QZSS provides satellite PNT Service using L1, L2, and L5 band signals. Users can track QZSS signals, measure the range between a QZSS satellite and their receiver antenna phase center, and calculate their position, velocity‚ and time together with other GNSS satellites’ range measurements as well as their navigation messages, especially in combination with GPS satellites. In order to maximize the performance improvement of using QZSS with GPS and make it easier to use them together on user receiving equipment, the highest level of interoperability with GPS signals is adopted for QZSS. Not only are current GPS Block IIF civil navigation signals, L1C/A, L2C, and L5, provided, but also L1C, which will be transmitted from Block III as the fourth civil signal. Some major fundamental specifications of QZSS PNT services in PS-QZSS are summarized in Table 8.2. It should be noted that QZSS does not have stand-alone PNT capability. Thus, the performance standard defines a limited set of performance parameters. The PNT service coverage is defined as the area where at least one QZSS satellite is visible above 10 elevation angle, and users can track QZSS satellite signals with the

189

190

8 Quasi-Zenith Satellite System

Table 8.1 QZSS signals and services Transmitting satellites Signals

Center freq. [MHz]

Services

QZS-1

QZS-2, 4

QZS-3

L1C/A

1575.42

PNT

X

X

X

L1C

PNT

X

X

X

L1S

SLAS

X

X

X

DC-Report

X

X

X

L1Sb

SBAS

X

L2C

1227.60

PNT

X

X

X

L5

1176.45

PNT

X

X

X

X

X

X

X

L5S

PTV

L6D

1278.75

L6E

CLAS

X

PTV

S band

RTN:2002.50 FWD:2192.50

X

Q-ANPI

X X

PNT: Positioning, Navigation, and Timing SLAS: Sub-meter Level Augmentation Service CLAS: Centimeter Level Augmentation Service DC-Report: Report for Disaster and Crisis Management PTV: Positioning Technology Verification Service Q-ANPI: QZSS Safety Confirmation Service

Table 8.2

Fundamental QZSS performance specifications

Characteristics

Technical specifications

SPS value

Constellation service availability

Time ratio of the simultaneous transmission of healthy signals from at least three of four QZSS satellites

≥0.99

Service availability by each SV

Percentage of time when the signal is healthy for IGSO satellites

≥0.95

Same as above, but for GSO satellites

≥0.80

Accuracy

SIS URE

≤2.6 m (95%)

Integrity

Probability of the RF degradation, TOW failure, SIS URE or UTC errors exceeding criteria without timely alert

≤1 × 10−5[/h] (when integrity status flag (ISF) is “0”) ≤ 1 × 10−8[/h] (when ISF is “1”)

Time to alert

Alarm or warning when signal should not be used due to the following causes:

Continuity Time Accuracy

•• ••

8s 8s 5.2 s 30 s

RF error (Switch to non-standard code) TOW error (Switch to non-standard code) SIS URE error (Switch to non-standard code) UTC error (Alert flag in the NAV message)

Probability over any hour of not losing signal availability without 48 h advanced notifications

0.9998

UTC offset error with regard to UTC(NICT)

40 ns (95%)

minimum user receiving power defined in IS-QZSS-PNT for each signal. Figure 8.2 shows the coverage of PNT services from QZSS. The contour lines indicate elevation angles above which at least one satellite is observed.

8.4.2

GNSS Augmentation Services

As described in the previous sections, the unique feature of QZSS is that one of the satellites in the constellation can provide services from high elevation angles over the service

8.4 QZSS Services

coverage area between Japan and Australia along with the satellite ground track. Unlike other satellite-based augmentation systems such as SBAS, which utilizes geosynchronous satellites, this unique property of QZSS can benefit users by providing an error correction data stream that can be received even in an urban canyon. QZSS has provided two operational services within this category from the beginning of its service provision in 2018. One is the Sub-meter Level Augmentation Service (SLAS) for code phase positioning users [11], and the other is the Centimeter Level Augmentation Service (CLAS) for carrier phase positioning users [12]. These two augmentation services are described in the following subsections. Once the MTSAT-2 (Multi-functional Transport Satellite -2) operation is terminated at its end of lifetime in 2020, the MSAS service will continue through QZS-3. SBAS service provided via QZSS will be introduced in Section 8.4.6. 8.4.2.1 SLAS

SLAS provides differential error correction, that is, Pseudo Range Correction (PRC) for pseudorange measurements of L1 C/A signal for each GPS and QZSS satellite. PRC is generated based on 13 Japanese domestic reference stations and transmitted through the QZSS L1S signal. The SLAS service area is shown in Figure 8.2 along with the locations of 13 monitoring stations. The ionosphere above the southwestern area in Japan is typically more active than the northern area because the former area’s geomagnetic latitudes are lower and near the geomagnetic equator. Densely

distributed monitoring stations are required in such areas to satisfy the user PVT accuracy requirement. SLAS provides user position accuracy with better than 1.0 m (95%) in the horizontal direction, and 2.0 m (95%) in the vertical direction within the area surrounded by red lines in Figure 8.3. Note that the user range error due to receiver noise and environment effects, such as multipath error, is less than 0.87 m (95%). User position accuracy less than 2.0 m (95%) in the horizontal direction, and 3.0 m (95%) in the vertical direction are expected in the area surrounded by black lines.

8.4.2.2 CLAS

CLAS provides error corrections for carrier phase positioning with the State Space Representative (SSR) format, which was standardized in RTCM SC104 as RTCM 10403.2 with the proposed Compact SSR format for future updates of the RTCM standard. [13, 14] Each error component, such as the satellite orbit, clock, code and carrier phase bias, ionospheric delay and tropospheric delay, in the SSR description can be transformed into range correction data in the Observation Space Representative (OSR) for calculating range measurements to obtain a single point positioning result. A user can resolve carrier phase ambiguity by double-differencing measurements between the raw measurements at the receiver and the calculated measurement values, similar to RTK processing, to get centimeterlevel accuracy.

90

60

Latitude[deg]

30

0

–30

–60

–90

0

30

60

90

Figure 8.2 QZSS PNT service coverage.

120

150

180 210 Longitude[deg]

240

270

300

330

360

191

192

8 Quasi-Zenith Satellite System

ground control system detects anomalies on a satellite signal, the error corrections for the detected abnormal satellite are set to an invalid value and the invalid satellite is excluded from the mask message in MT4073,1. In addition, correction message quality indicators can be accessed by users to judge if the error correction for the specific satellite could be directly applied or used after weighting with regard to the indicators. Figure 8.4 indicates the CLAS service coverage area. Ionospheric delay and tropospheric delay error corrections are distributed over 12 areas in Japan and updated every 30 s. Considering the limitation on the data transmission rate of L6D (2.0 Kbps) and the number of satellites, error corrections provided by CLAS are limited. The slant TEC for ionospheric delay corrections for 17 satellites from GPS, QZSS and Galileo are available for each of the 12 local areas, while orbit, clock, and code/phase bias corrections are available for the entire service coverage in Japan. CLAS can provide centimeter-level accuracy as defined in PS-QZSS: 6 cm (95%) in the horizontal direction and 12 cm (95%) in the vertical direction for the static mode at a fixed point, and 12 cm (95%) horizontally and 24 cm (95%) vertically for the kinematic mode on a moving platform within Japan and the surrounding terrestrial waters.

50°N

45°N

40°N

35°N

30°N

25°N

20°N

15°N 120°E 125°E 130°E 135°E 140°E 145°E 150°E 155°E

Figure 8.3 stations.

SLAS service coverage and distribution of reference

Approximately 300 CORS observation stations in the GEONET operated by GSI are utilized to generate an SSR error correction message via the QZSS L6D signal in real time. CLAS provides integrity information. When the

8.4.3

Messaging Service

As a national infrastructure, QZSS is expected to support disaster mitigation and relief operations, especially since

Current Service Area 50

Service Area (After CORS are put in place)

Grid distribution 45

Network 1 Network 2 Network 3

40

Network 4 Network 5 35

Network 6 Network 7 Network 8

30

Network 9 Network 10 25

Network 11 Network 12

20 120

125

Figure 8.4

CLAS service coverage.

130

135

140

145

150

155

8.4 QZSS Services

the Japanese government decided to build the system just after the Great East Japan Earthquake in 2011. Two messaging services, DC-Report service [15] and Q-ANPI service, are provided through QZSS. These two messaging services are described briefly in the following subsections. 8.4.3.1 DC-Report Service (Satellite Report for Disaster and Crisis Management)

DC-Report provides short messages related to disaster warnings such as earthquakes, tsunamis, volcanic eruptions, floods, and crisis management information using 212 bits in the L1S message once every 4 s. In the beginning of the service operation, a weather alert issued by the Japan Meteorological Agency (JMA) is relayed, depending on the priority rank of the type of disaster, by means of a dedicated format using Message Type 43 for Japanese domestic users. DC-Report service is available in the same area as the PNT service shown in Figure 8.2. An early warning message for the Asia-Pacific region is being investigated using Message Type 44, which has not been defined yet. 8.4.3.2 Q-ANPI Service

The QZSS Safety Confirmation Service (Q-ANPI) provides data communication service for information on the state of evacuation shelters, number of evacuees in shelters, and evacuee condition during a disaster. This information transmitted from evacuation shelters will be received and acquired at the control station via QZS during a disaster. Q-ANPI provides these data communication services via the QZS-3 satellite in a geostationary orbit (GEO). This service is available on S-band devices that support Q-ANPI. This service can only be used in Japan and surrounding coastal areas.

8.4.4 Positioning Technology Verification (PVT) Service QZSS has two test signals and/or data channels, L5S [16] and L6E [12, 17], for future service validation. Section 8.4.4.1 describes the Dual Frequency Multi-Constellation (DFMC) SBAS experiment through the L5S signal, whereas Section 4.4.2 introduces the Precise Point Positioning (PPP)/ PPP-Ambiguity Resolution (PPP-AR) experiment through the L6E signal, respectively. 8.4.4.1 DFMC SBAS Experiment Through L5S

The DFMC SBAS is the second-generation SBAS, following the current L5 SBAS, transmitted on the L5 frequency. The DFMC SBAS, or the L5 SBAS, is free from ionospheric effects thanks to the dual-frequency operation, and therefore enables vertical guidance service everywhere in the coverage area with reasonable availability. The

standardization for the L5 SBAS is underway by the International Civil Aviation Organization (ICAO). The National Institute of Maritime, Port and Aviation Technology (MPAT) has been conducting the L5 SBAS experiment since August 2017 using the QZSS PTV Service with the L5S signal. This is the first L5 SBAS experiment with a live L5 signal from space. It is expected that this experiment can demonstrate that DFMC SBAS enables vertical navigation everywhere in the coverage area, and achieves reasonable availability, contributing to popularization of the PBN operations. 8.4.4.1.1

Configuration of the Experiments

Figure 8.5 shows the configuration for this experiment. The prototype DFMC SBAS [18] developed by the ENRI of MPAT has been used for the experiment. The prototype receives GNSS measurements from the GEONET observation network and generates the L5 SBAS message stream in real time. The message is immediately sent to the QZSS master control station (MCS) and transmitted by the QZSS L5S signal. The test involves 13 ground monitoring stations (GMSs) at the same locations as the L1S reference stations, as shown in Figure 8.5. These GMSs output GNSS measurements at 1 Hz. The prototype DFMC SBAS is capable of processing GPS, GLONASS, and Galileo signals. It generates the L5 SBAS message stream compliant with the draft standards of the DFMC SBAS being discussed by the ICAO [19, 20]. 8.4.4.1.2 Static Test Results of the Prototype DFMC SBAS

The static test of the prototype DFMC SBAS was performed for 24 h on 15 December 2016 in GPST. For the test, calculations of position and protection levels were performed at 160 test stations within Japanese territory. Note that, for this static test, GPS and GLONASS with L1 and L2 signals were used due to the limited number of GPS satellites with L5 transmissions. Figures 8.6 shows the result for station Wakayama‚ which is located at the center of Japan. It compares the horizontal position error with and without SBAS corrections, both in dual-frequency operation. The position accuracy is clearly improved by applying SBAS corrections. Figure 8.7 shows the protection levels at the test station. The first hour of the day is excluded since the estimation filter of the prototype system has not yet converged. Horizontal broken lines denote 95% of the protection levels. This result indicates that there is no trend due to any ionospheric activities throughout the day, even at the local time of 14:00

193

8 Quasi-Zenith Satellite System

QZSS #2, #3, and #4

GLONASS GPS

l

Sig

na Si g S L5

al

nk

Si

gn

BeiDou

Measured L5 SBAS OBS ENRI L5 SBAS Message

GEONET

Prototype

GSI (Shinjuku, Tokyo) • Supports DFMC • Provides observation in real time

Figure 8.5

ng

li Up

gi

L5S

Ra n

nal

Galileo

ENRI, MPAT (Chofu, Tokyo)

GEO (QZS-3) + IGSO (QZS-2/4)

QZSS C&C

QZSS MCS (Hitachi-Ota, Ibaraki)

• Operates in real time • Dual-Frequency • Supports GPS, GLONASS, Galileo, and QZSS

• Uplink L5 SBAS message stream for transmission

Configuration of the experiment using QZSS PTV service.

4

4 Eastward error (m)

2

Corrected

None corrected

2 3

0 –2 –4

1

0

4

8

12

16

20

24

0

4

8

12

16

20

24

0

4

8

12

16

20

24

4 2 Northward error (m)

Northward error (m)

0

–1

0 –2 –4 8

–2

4 –3

–4 –3

Vertical error (m)

194

Non-corrected Corrected

0 –4 –8

–2

–1

0

1

2

3

Eastward error (m)

Figure 8.6

GPS time (hour)

Horizontal error (left) and ENU components of position error (right) at Wakayama.

(equivalent to 5:00 GPST), and the results are promising for serving LPV and LPV200 operations. Next, the performance is evaluated at 160 test stations distributed throughout Japan. Figure 8.8 illustrates 95% errors at these test stations. It seems that position errors tend to be worse when moving away from the center; the worst 95% accuracies are 1.2 m and 2.4 m for the horizontal and vertical, respectively. Figure 8.9 shows 95% protection levels at 160 test stations. Protection levels in remote areas are worse than in the

central area because there are fewer augmented satellites, and the associate DOP index increases in remote areas. Figure 8.10 uses triangle charts containing all epochs at all 160 test stations from the south to the north of Japan to describe the relationships between protection level and position error. The results are promising. The actual error never exceeds the associated protection level, thus indicating that there are no MI (Misleading Information) conditions. For LPV200 flight mode with a HAL of 40 m and a VAL of 35 m, the corresponding availability is 99.986%.

8.4 QZSS Services

Finally, ENRI began the L5 SBAS experiment on 23 August 2017 with the L5S signal transmitted by the QZS-2. The message transmitted by the L5S signal is compliant with the ICAO draft standards of DFMC SBAS. The DFMC prototype is now upgraded to process GPS, GLONASS (L1 and L2 only), and Galileo satellites (L1 and L5 only) with L1, L2, and L5 signals. For the real-time experiment with the L5S signal, the prototype usually augments the L1 and L5 signals of GPS and Galileo satellites.

20 95% VPL = 16.93 (m)

Protection Level (m)

16

12 95% HPL = 8.84 (m)

8

4

8.4.4.2 PPP/PPP-AR Experiment Through L6E

Horizontal Protection Level Vertical Protection Level

0

4

8

12

16

20

24

GPS time (hour)

Figure 8.7 Protection levels at Wakayama.

Clearly, the performance of the prototype system meets the requirements of the LPV200 flight mode with enough availability over all of Japan.

8.4.4.1.3

Experiment Using QZSS TV Service

The first satellite with the capability of transmitting the L5S signal, QZS-2, was launched in June 2017. In parallel with the IOT of QZS-2, a communication line between ENRI in Tokyo and the QZSS MCS in Hitachi-Ota, Ibaraki, was set up, and the interface test was conducted. Some interface software connecting the prototype DFMC SBAS with the QZSS TV Service was developed and tested. (a)

(b)

Horizontal positioning error

2.2

0.8

Figure 8.8 Position accuracy at all 160 stations.

95% Horizontal Positioning Error (m)

1.1

0.9

Vertical positioning error 2.4

1.2

1

CLAS on the L6D signal is a domestic service using the Japanese network GEONET. Densely spaced CORS stations with 50 to 60 km baseline separations are required if CLAS has to extend its service coverage to outside Japan. Even if such a condition is met in some countries or regions, CLAS cannot cover the entire QZSS visible area due to the L6 signal bandwidth. To complement its coverage outside of Japan, including the oceans far away from the CORS stations, error corrections for satellite orbit, clock offset, and code/carrier phase bias can be estimated with globally collected observation data and transmitted via the L6E signal as an experimental signal. Users can apply these error correction messages to PPP as well as PPP-AR to obtain decimeter to centimeter position accuracy if the ambiguity can be resolved with the transmitted initial phase bias on L6E. Since local ionospheric and tropospheric errors are not provided through L6E, users have to estimate these values in their computation process. This leads to a longer convergence time, normally 20 to 40 min, to resolve carrier phase

2

1.8

1.6

0.7

1.4

0.6

1.2

95% Vertical Positioning Error (m)

0

195

8 Quasi-Zenith Satellite System

(b)

Horizontal protection level

11.5

22

10.5

10

95% Horizontal Protection Level (m)

23

11

20

19

9.5

18

9

17

Protection levels at all 160 stations.

(a)

(b)

Horizontal stanford chart 105

45

Vertical stanford chart 105

45

Unavailable [0.000%]

40

40 Available [100.000%]

104

30 95% Error 0.86 (m)

103

25 20

102

15 10

95% HPL 9.97 (m)

MI [0.000%]

5

0

10

20

101

104 Available [99.986%]

30 103 25 20 95% VPL 18.97 (m)

15 10

101

5

30

40

100

0

102

MI [0.000%] 100 0

Horizontal Errors (m)

Figure 8.10

Unavailable [0.014%]

35 Vertical Protection Level (m)

35

0

21

95% Error 1.73 (m)

Figure 8.9

Vertical protection level

12

95% Vertical Protection Level (m)

(a)

Horizontal Protection Level (m)

196

10

20

30

40

Vertical Errors (m)

Triangle charts for all 160 stations.

ambiguity or PPP float solutions. The error corrections for QZSS, GPS‚ and GLONASS are available in the beginning of the operation, while for Galileo and BeiDou, error corrections are planned to be added in future updates. During the experimental phase, the Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) [21–23] developed by JAXA is used for generating such error corrections. The message format is defined by a

start-up company, GPAS (Global Positioning Augmentation Service) [17], with the goal of investigating future practical service provision.

8.4.5

Public Regulated Service (PRS)

The service can be utilized by a limited number of users authorized by the Japanese government. PRS provides both

8.5 QZSS Space Segment Configuration

ranging capability and error correction messages with an encrypted spreading code and a different frequency band away from those of GPS civil signals.

8.4.6

SBAS Service

SBAS is the international standard navigation service with a continental service coverage [24–26]. It provides an RNP (required navigation performance) integrity-assured navigation service primarily for civil aviation use by augmenting the GPS constellation. In Japan, the development of its own SBAS, MSAS, was officially decided in 1993. MSAS was originally planned to begin its operation in 2000. After the failure of the launch of the geostationary satellite in 1999, MSAS finally began its operation in 2007 with two geostationary satellites. Since then, MSAS has been in continuous operation up to the present [27–30]. After 10 years of operation, MSAS has recently needed to replace its geostationary satellites. The first satellite for MSAS, MTSAT-1R, launched in 2005 terminated its operation and was decommissioned in December 2015. The other satellite, MTSAT-2, launched in 2006 is still operational, but its operation will terminate by 2020. It is also necessary to update ground facilities built 20 years ago. Recently the Japanese government has decided to replace geostationary satellites for MSAS service as a part of the QZSS regional satellite navigation program. The geostationary satellite of QZSS (QZS-3) has an additional signal called L1Sb for the SBAS service. The ground facilities will be completely replaced by the new system with an increased number of GMSs. The MSAS processors will be co-located with the QZSS MCS in Hitachi-Ota. Note that the QZS-3 L1Sb transmitter for the MSAS service has 24 MHz bandwidth and works with an onboard atomic clock, which is different from the bent-pipe transponder employed by all other SBAS systems. The contents of the SBAS message will be generated by JCAB (Japan Civil Aviation Bureau) facility‚ and the SBAS

JCAB

8.5 QZSS Space Segment Configuration 8.5.1

Constellation

QZSS currently has four satellites in the constellation. Three of them are orbiting in three different orbital planes of IGSO, in a so-called Quasi-Zenith Orbit (QZO), which was designed and optimized to maximize the visibility from Japan and surrounding areas. One satellite is the GSO satellite located at 127 east longitude. The IGSO has a mean altitude of about 36000 km and is inclined around 43 degrees to the equator. The satellite in an IGSO is orbiting around Earth with one sidereal day period, 23 h 56 min. In addition, a slight eccentricity is added so as to allow the satellite to stay for a longer time in the Northern Hemisphere. The apogee is located over north Japan. At the design phase of the four-satellite constellation, the future composition for a seven-satellite constellation had not been specified. The separation of the right ascension of the ascending nodes (RAANs) is not 120 equally distributed among the satellites in order to reserve a future option for four IGSOs of a seven-satellite constellation. The second

CAO

Provision of SBAS service

SBAS Operation

signal will be transmitted to aircraft via the QZSS system (including both the space segment and the ground segment), which is owned by CAO (Cabinet Office of Japan) (see Figure 8.11). The SBAS service area is limited to the Fukuoka FIR (Japanese Flight Information Region) in its initial stage. However, the SBAS signal can be received in the Asia-Pacific region. In addition, a seven-QZSS satellite constellation enables an upgrade of the MSAS service level from NPA (Non-Precision Approach) to APV-I or LPV200. This upgrade will improve navigation performance to a level almost equivalent to PA (Precision Approach) and provide significant benefits for not only aviation users, but also various user communities.

SBAS Equipment

QZSS (GEO)

SBAS Signal

SBAS Signal

GMS Data GMS

Figure 8.11 SBAS configuration after 2020.

GPS

GPS Signal

197

198

8 Quasi-Zenith Satellite System

Table 8.3 QZSS IGSO satellite orbital characteristics Orbit parameter

Value

Semi-major axis

42,165 km (average)

Eccentricity

0.075 ± 0.015

Inclination (deg.)

43 ± 4

Argument of perigee (deg.)

270 ± 2.5

Central longitude of ground track (deg.)

139 ± 5 East

RAAN (Ω)∗

QZS-1: 117 QZS-2: 247 QZS-3: 347

Note: aCalculated at the epoch on 1 September 2025, 00:00:00.

and fourth satellites have additional propellant for potential plane changing maneuvers. Table 8.3 summarizes the orbit parameters for QZSS IGSO satellites.

8.5.2

Satellite Configuration

The first satellite of QZSS, QZS-1, was launched in 2010 as a demonstration satellite developed by JAXA and collaborative institutes as described in Section 8.1. The design life is 10 years for QZS-1. After the launch, the IOT phase, and technical demonstrations, QZS-1 was operated by JAXA for almost 6.5 years. On 28 February 2017, responsibility of the QZS-1 operation and ownership was transferred to the Cabinet Office from JAXA. The Navigation Onboard Computer (NOC) was reprogramed‚ and transmitting messages were updated in accordance with current IS documents established by CAO. Three additional satellites are defined as the Block II series, while the first satellite is Block I. Design lives for the three Block II satellites were extended to 15 years. They were built based on the first satellite design; however, some modifications are made in their designs. The adoption of GaAs solar cells with higher efficiency rather than Si cells for QZS-1 led to a reduction in the number of solar panels from three to two on one side. With other mass reductions such as battery size and simplification of the electrical power and attitude control systems, the dry mass for these three Block II satellites decreased to 1550 kg for QZS-2 and -4 and 1690 kg for QZS-3, from 1800 kg for QZS-1. The difference between QZS-2, 4, and 3 is in the additional payload on QZS-3. It has a 3.2 m dish and S-band communications equipment for Q-ANPI service, and uses mobile communications when ground-based communications breaks down or becomes congested immediately after major natural disasters occur. An additional major change in the third satellite design is that a patch array antenna is adopted as the

main transmission antenna, while other IGSO satellites use a 19-element helical array antenna. Block II satellites are categorized Block II-Q (Q is for QZO) and Block II-G (G is for GSO) depending on the injected orbit. The one more important difference between Block I and II-Q is the change in the attitude control law. The Block I satellite, QZS-1, has two attitude control modes, Yaw Steering (YS) mode and Orbit Normal (ON) mode, in order to point the satellite yaw axis to the center of Earth [31, 32]. The former is applied when the angle between the orbital plane of the satellite and the vector to the Sun, defined as the beta angle, is larger than 20 . When the beta angle is close to the threshold, a switch from YS mode to ON mode or an opposite direction change is planned so as to minimize the required yaw-angle change during attitude transition. This attitude control mode change makes precise orbit estimation difficult and degrades the orbit estimation accuracy. Block II-Q satellites were designed according to their attitude control law, so as to avoid switching two modes except for orbit maintenance maneuvers. When the beta angle is close to zero, a so-called “pseudo yaw steering” is adopted. The yaw rate is controlled at a maximum rate, 0.055 deg/s, so that the yaw angle at noon and midnight are plus or minus 90 [33]. The major characteristics of each category are summarized in Table 8.4, and their photographs are shown in Figure 8.12.

8.6 QZSS Ground Segment Configuration The QZSS ground segment consists of an MCS, tracking stations, and a monitoring stations network. Primary MCS at Hitachi-Ota and secondary MCS at Kobe are separated from each other by more than 500 km to ensure site diversity, so as to provide continuous service even if a huge natural disaster such as mega-typhoon or earthquake occurs. Tracking stations, which communicate with each satellite, have a total of seven antennas in six locations. Unlike other GNSSs, the augmentation function of QZSS requires continuous uplink to the satellites, most of which are located in the southwestern region of Japan, where the antennas can track and communicate with IGSO satellites flying over Australia at their perigee in the orbit. In addition, the monitoring stations network is one of the main contributors to satnav system performance. It is important for obtaining better POD performance to establish a widely distributed monitoring station network with good geometry composed of stations in the network and satellites of QZSS and GPS. In the current configuration, 25 monitoring stations were set up as the monitoring network.

8.7 QZSS Signal Configuration

Table 8.4 QZSS satellite characteristics Block I

Block II-Q

Block II-G

Satellite

QZS-1

QZS-2 and 4

QZS-3

Launch date (UTC)

11 September 2010

QZS-2: 1 June 2017 QZS-4: 9 October 2017

10 August 2017

Orbit

IGSO

IGSO

GSO (E127)

Dry mass (kg)

1800

1550

1690

Design life (years)

10

15

15

Span (m)

25

19

19

Power (W at EOL)

5300

6300

6300

Main antenna type

Helical array

Helical array

Patch array

Attitude control mode

Yaw steering and orbit normal mode during beta angle less than 20

Yaw steering mode except for orbit maintenance maneuver

Orbit normal mode

Signals

L1C/A, L1C, L1S, L2C, L6, L5

L1C/A, L1C, L1S, L2C, L6, L5, L5S, PRS

L1C/A, L1C, L1S, L2C, L6, L5, L5S, L1Sb, PRS, S band

8.7

QZSS Signal Configuration

QZSS has four open PNT signals, four types of augmentation signals including experimental ones, and one authorized signal on four carrier frequencies, in L1, L2, L5, and L6 bands, which are allocated for Radio Navigation Satellite

Service (RNSS) by ITU regulations as shown in Table 8.5. Section 8.7.1 provides a summary of the signal characteristics, and data messages are summarized in Section 8.7.2. The characteristics of the signal for authorized users, denoted as PRS, are not in the public domain and hence are not described in this section.

Figure 8.12 QZSS Block I, GZS-1 (top left) Block II-Q, QZS-2 and 4 (top right) and Block II-G, QZS-3 (bottom).

199

200

8 Quasi-Zenith Satellite System

Table 8.5 Frequency bands used by QZSS Occupied bandwidth (MHz) Frequency band name

Center frequency (MHz)

Block I

Block II

QZSS signals in band

L1

1575.42

24.0

30.69

L1C/A, L1C, L1S, L1Sb

L2

1227.60

24.0

30.69

L2C

L5

1176.45

24.9

24.9

L5, L5S

L6

1278.75

39.0

42.0

L6D, L6E

8.7.1

Signal Descriptions

The detailed information on each QZSS signal is defined in a set of interface specifications documents [9, 11, 12, 16]. Four of six IS-QZSS documents provide PNT and augmentation service as tabulated in Table 8.6. Except for the L6 signal, other signals of QZSS are defined based on the GPS specification and SBAS standard with some modifications due to differences from these system designs and operations. It is especially worth noting that signals for PNT service, L1C/A, L1C, L2C, and L5 have high interoperability with GPS signals. Similar GPS signal RF properties such as center carrier frequency, spreading code modulation scheme, series of PRN code, and message structure are used. A set of PRN codes from 193 to 202 defined by GPS IS documentation is applied to QZSS. Originally the codes for QZSS were assigned in the exact order from 193 when JAXA published the IS-QZSS. However, the current IS-QZSS changed the PRN code allocation within QZSS satellites to two parts: IGSO starting from 193 to 197 and GSO from 199 to 201. 198 and 202 are reserved for nonstandard code use. QZSS L1C has been transmitted since QZS-1 was launched in 2010. However, the Block I satellite, QZS-1, does not transmit TMBOC as GPS plans to do. Instead, it transmits BOC(1,1) for the pilot component of the signal. This is because the hardware design was fixed before the conclusion of the L1C optimization study conducted by the United States and European Union, which agreed to change the L1C signal structure for higher interoperability with the Galileo E1/OS signal in 2006 [34] The phase relationship between L1C/A and L1C for QZS-1 is also different from that for GPS Block III as well as for QZSS Block II. For QZS-1, the L1C/A and L1C data component has a 90 phase lag with the L1C pilot component, while the L1C data component and pilot component have the same phase with L1C/A with a 90 phase lag relative to other QZSS Block II satellites. The signal characteristics for L1Sb via QZS-3, which will be utilized for MSAS service in 2020, are the same as those of L1S.

Table 8.6 The package of interface specifications document for QZSS PNT and augmentation service Service name

IS document

Included QZSS signals

PNT

IS-QZSS-PNT-003

L1C/A, L1C, L2C, L5

SLAS

IS-QZSS-L1S-004

L1S

CLAS

IS-QZSS-L6-002

L6D, L6E

PTV

IS-QZSS-TV-003

L5S

Table 8.7 provides a summary of the characteristics of different QZSS signals.

8.7.2

Data Message Summary

Tables 8.7 and 8.8 summarize each signal’s data message characteristics.

8.7.3

Ionosphere Model

The Klobuchar model is applied to the QZSS PNT service. While the model applied for GPS uses a single set of parameters for the entire Earth, QZSS transmits two sets of parameters for a wide area around Japan defined as the rectangular area in the Figure 8.13. The QZSS control segment uploads new ionospheric parameters at least every 24 h.

8.8

Summary

QZSS is a regional satellite navigation system with four satellites and ground control segments deployed by Japan. The first satellite, QZS-1, was launched in 2010, and three additional Block II satellites were launched in 2017; thus, operational service provision began on 1 November 2018. It provides PNT services that enhance GNSS availability in Eastern Asia and the Western Pacific Rim region. It also offers augmentation services that strengthen GNSS performance as well as a messaging service that improves the national capability to respond to major disasters in Japan.

Table 8.7 Summary of QZSS signal characteristics Signal name

C/A

L1C

L2C

L5

L1S

L6

L5S

Carrier frequency (MHz)

1575.42

1575.42

1227.60

1176.45

1575.42

1278.75

1176.45

Transmit bandwidth, two-sided (MHz)

30.69a/ 24.0b

30.69a/ 24.0b

30.69a/ 24.0b

24.9

30.69a/ 24.0b

42.0a/ 39.0b

24.9

Data and pilot combining

N/A

Code division

Time division

Phase division

N/A

Time division

Phase division

Correlation loss (dB)

0.3a/ 0.6b

0.2a/ 0.6b

0.3a/ 0.6b

0.6

0.6

0.6

0.6

Specified minimum received total power in all components (dBW)

−158.5

−157.0

−158.5a/−160.0b

−154.0a/ −154.9b

−158.5a/ −161.0b

−155.7a/ −156.82b

−157.0

Spreading modulation

BPSKR(1)

BOC(1,1)

BPSK-R(1)

BPSK-R (10)

BPSK-R (1)

BPSK-R(5)

BPSK-R (10)

Spreading code chip rate (Mcps)

1.023

1.023

0.5115

10.23

1.023

2.5575

10.23

Spreading code symbol duration (microseconds)

0.9775

0.9775

0.9775

0.09775

0.9775

0.1955

0.09775

Spreading code type

Gold

Weil-based

L2CM: Short-cycled m- sequencec

L5

Gold

L61b/L62a: Kasami-based

L5

Spreading code duration (ms)

1

10

20

1

1

4

1

Spreading code length (bits)

1,023

10,230

10,230

10,230

1,023

10,230

10,230

Overlay code bit rate (bps)

None

100

None

1000

None

None

None

Overlay code duration (s)

None

None

None

0.01

None

None

None

Overlay code length (bits)

None

None

None

10

None

None

None

Data message bit rate (bps)

50

50

25

50

250

2000

250

Data message symbol rate (sps)

50

100

50

100

500

250

500

Data fraction of power %

100

25

50

50

100

50

50

Pilot component

None

None

Nonea

Data component

Spreading modulation

MBOC (6,1, 4/33)a/ BOC(1,1)b 1.023

BPSK-R(1)

BPSK-R (10)

BPSK-R(5)

BPSK-R (10)

0.5115

10.23

2.5575

10.23

Spreading code symbol duration (microseconds)

0.9775

0.9775

0.09775

0.1955

0.09775

Spreading code type

Weil-based

L2CL: Short-cycled m- sequencec

L5

L61b:Kasamibased

L5

Spreading code duration (ms)

10

1500

1

410

1

Spreading code length (bits)

10,230

76,7250

10,230

1,048,575

10,230

Spreading code chip rate (Mcps)

(Continued)

202

8 Quasi-Zenith Satellite System

Table 8.7 (Continued) Signal name

L1C

L2C

L5

Overlay code bit rate (bps)

100

None

Overlay code length (bits)

1800

Overlay code duration (s) Pilot fraction of power %

C/A

0

L1S

L6

L5S

1000

None

N/A

None

20

None

N/A

18

None

0.02

None

N/A

75

50

50

50

50

0

Notes: a Block II satellites (QZS-2, 3 and 4). b Block I satellite (QZS-1). c Maximal-length sequence. L5S signal is transmitted after Block II satellites. L6 signal after Block II has two data components L1D and L1E, no pilot component.

Table 8.8 Characteristics of QZSS signal data messages Signal name

C/A

L1C

L2C

L5

L1S

L6

L5S

Data message name

LNAV

CNAV2

CNAV

CNAV

L1S

L6D/L6E

L5S

Message structure (fixed/flexible)

Fixed

Flexible

Flexible

Flexible

Flexible

Flexible

Flexible

Message length (bits)

1500

900

300

300

250

2000

250

Message duration (s)

30

18

6

6

1

1

1

Forward error correction

None

BCHa(51,8) for time of day, ½-rate LDPCb for other data

½-rate, constraint length 7

½-rate, constraint length 7

½-rate, constraint length 7

ReedSolomon (255,223)

½-rate, constraint length 7

Error detection

(32,26) Hamming Code

24 bit CRC

24 bit CRC

24 bit CRC

24 bit CRC

256 bit RSC

24 bit CRC

Repetition of clock corrections and ephemeris (s)

30

18

48

24

N/A

N/A

N/A

Maximum broadcast interval for ionospheric model (minutes)

750

Not specified

288

144

N/A

N/A

N/A

Maximum broadcast interval for UTC conversion

750

Not Specified

288

144

N/A

N/A

N/A

Time rollover (weeks)

1024

8192

8192

8192

N/A

N/A

N/A

Leap seconds Included (yes/no)

No

No

No

No

N/A

N/A

N/A

Clock correction and ephemeris validity interval (min)

120

120

120

120

30 s

N/A

Typical message upload rate (uploads/day)

24

24

24

24

Every second

30 s for orbit 5 sec for clock Every second

Notes: a Bose, Chaudhuri, and Hocquenghem. b Low Density Parity Check.

Every second

References

70 North latitude 60° 60 North latitude 50° Japan area⤶

40 30

East longitude 160°⤶

East longitude 110°⤶

50

North latitude 22°

20

East longitude 90°⤶

East longitude 180°⤶

10 0 –10 –20

Wide area⤶ –30 –40 –50 –60 –70 60

South latitude 60° 70

80

90

100

110

120

130

140

150

160

170

180

190

60

210

220

Figure 8.13 Applicable area for QZSS ionospheric model parameters.

It is a new national space asset and highly prioritized in Japanese Space Policy. It will be extended to a seven-satellite constellation around 2023 to realize stand-alone PNT capability to enhance robustness and resiliency while maintaining interoperability and compatibility with other GNSSs. It is expected that the evolution of QZSS can contribute to the stable and sustainable growth of the region.

3 Nakamura, M., Hama, S., Takahashi, Y., Amagai, J. et al.,

4

5

References 1 Tanaka, M., Kimura, K., Kawase, S., and Miura A. et al.,

Application Technique of Figure-8 Satellites System, Technical Report SAT 99(45), 55–62 (Institute of Electronics, Information and Communication Engineers) in Japanese, 1999. 2 Takahashi, H.D., Japanese regional navigation satellite system “The JRANS Concept,” J. Global Position. Syst. 3(1/2), 259–264, 2004.

6

7

Time management system of the QZSS and time comparison experiments, AIAA 2011-8067, 29th AIAA Int. Commun. Satell. Syst. Conf. (ICSSC-2011), pp. 534–538, Nara (AIAA, Reston 2011). Ito, H., Morikawa, T., and Hama, S., Development and performance evaluation of spaceborne hydrogen maser atomic clock in NICT, ION NTM, pp. 452–454, San Diego (ION, Virginia 2007). Sakai, T., Fukushima, S., Takeichi, N., and Ito, K., Augmentation performance of QZSS L1-SAIF signal, Proc. 2007 National Technical Meeting of The Institute of Navigation, pp. 411–421, January 2007. Hatanaka, Y., Kuroishi, Y., Munekane, H., and Wada, A., Development of a GPS augmentation technique, Proc. Int. Symp. GPS/GNSS – Toward New Era Position. Technol., pp. 1097–1103, Tokyo (GPS/GNSS Society Japan, November 2008). Iwata, T., Matsuzawa, T., Machita, K., Kawauchi, T., Ota, S., Fukuhara, Y., Hiroshima, T., Tokita, K., Takahashi, T.,

203

204

8 Quasi-Zenith Satellite System

8

9

10

11

12

13

14

15

16

17

18

Horiuchi, S., and Takahashi, Y., Demonstration experiments of a remote synchronization system of an onboard crystal oscillator using “MICHIBIKI,” Navigation 60(2), 133–142 (2013). Kishimoto, E., Myojin, M., Kogure, S., Noda, H., and Terada, K., QZSS on Orbit Technical Verification Results, ION GNSS, pp. 1206–1211, Portland (ION, Virginia 2011). Quasi-Zenith Satellite System Interface Specification Satellite Positioning, Navigation and Timing Service (IS-QZSS-PNT-003), Cabinet Office, November, 2017, https://qzss.go.jp/en/technical/ps-is-qzss/ps-is-qzss.html Quasi-Zenith Satellite System Performance Standard (PS-QZSS-001), Cabinet Office, November 5, 2018, https://qzss.go.jp/en/technical/ps-is-qzss/ps-is-qzss.html Quasi-Zenith Satellite System Interface Specification Sub-meter Level Augmentation Service (IS-QZSS-L1S-004), Cabinet Office, May 2020, https://qzss.go.jp/en/technical/ ps-is-qzss/ps-is-qzss.html Quasi-Zenith Satellite System Interface Specification Centimeter Level Augmentation Service (IS-QZSS-L6-002), Cabinet Office, December 27, 2019, https://qzss.go.jp/en/ technical/ps-is-qzss/ps-is-qzss.html Miya, M., Fujita, S., Ota, K., Sato, Y., Takiguchi, J., and Hirokawa, R., Centimeter Level Augmentation Service (CLAS) in Japanese Quasi-Zenith Satellite System, its user interface, detailed design and plan, Proc. 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), pp. 1958–1962, September 2015. Hirokawa, R., Sato, Y., Fujita, S., and Miya, M., Design of integrity function on Centimeter Level Augmentation Service (CLAS) in Japanese Quasi-Zenith Satellite System, Proc. 29th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2016), pp. 3258–3263, Portland, Oregon, September 2016. Quasi-Zenith Satellite System Interface Specification DC Report Service (IS-QZSS-DCR-007), Cabinet Office, July 12, 2019, https://qzss.go.jp/en/technical/ps-is-qzss/ps-isqzss.html Quasi-Zenith Satellite System Interface Specification Positioning Technology Verification Service (IS-QZSS-TV003), Cabinet Office, December 27, 2019, https://qzss.go.jp/ en/technical/ps-is-qzss/ps-is-qzss.html Quasi-Zenith Satellite System Correction Data on Centimeter Level Augmentation Service for Experiment Data Format Specification, Global Positioning Augmentation Service Corporation, 1st Ed., Nov 2017 Kitamura, M., Aso, T., Sakai, T., and Hoshinoo, K., Development of prototype dual-frequency multiconstellation SBAS for MSAS, Proc. 30th Int’l Tech. Meeting of the Satellite Division of the Institute of Navigation, Portland, OR, Sept. 2017.

19 SBAS L5 DFMC Interface Control Document (SBAS L5 20

21

22

23

24

25

26 27

28

29

30

31

32

33

34

DFMC ICD), Version 1.3, SBAS IWG, Oct. 2016. DFMC SBAS SARPs Sub Group (DS2), DFMC SBAS SARPs Part B—Proposed Draft Version 0.5, ICAO NSP, DS2/WP/ 3, Montreal, June 2017. Harima, K., Choy, S., and Sato, K., Potential of locally enhanced MADOCA PPP as a positioning infrastructure for the Asia-Pacific, Proc. ION 2017 Pacific PNT Meeting, pp. 698–712, Honolulu, Hawaii, May 2017. Miyoshi, M., Kogure, S., Nakamura, S., Kawate, K., Soga, H., Hirahara, Y., Yasuda, A., and Takasu, T., The orbit and clock estimation result of GPS, GLONASS and QZSS by MADOCA, ISSFD, 2012. Suzuki, T., Kubo, N., and Takasu, T., Evaluation of precise point positioning using MADOCA-LEX via Quasi Zenith Satellite System, ION ITM, pp. 460–470, San Diego (ION, Virginia 2014). International Standards and Recommended Practices, Aeronautical Telecommunications, Annex 10 to the Convention on Int’l Civil Aviation, Vol. I, 6th Ed., ICAO, July 2006. Lawrence, D., Global SBAS status, Proc. 24th Int’l Tech. Meeting of the Satellite Division of the Institute of Navigation, pp. 1574–1602, Portland, OR, Sept. 2011. SBASs: Striving towards seamless satellite navigation, Coordinates, March 2014. Imamura, J., MSAS Program and Overview, Proc. 4th CGSIC IISC Asia Pacific Rim Meeting, 2003 Joint Int’l Conference on GPS/GNSS, Tokyo, Nov. 2003. Manabe, H., MTSAT Satellite-based Augmentation System (MSAS), Proc. 21st Int’l Tech. Meeting of the Satellite Division of the Institute of Navigation, pp. 1032–1059, Savannah, GA, Sept. 2008. Sakai, T. and Tashiro, H., MSAS Status, Proc. 26th Int’l Tech. Meeting of the Satellite Division of the Institute of Navigation, pp. 2343–2360, Nashville, TN, Sept. 2013. Sakai, T., Japanese SBAS Program: Current Status and Dual-Frequency Trial, International Symposium on GNSS, Taiwan, Dec. 2016. Ishijima, Y., Inaba, N., Matsumoto, A., Terada, K. et al., Design and development of the first quasi-zenith satellite attitude and orbit control system, IEEE Aerospace Conference, Big Sky, 2009, pp.1–8, doi:10.1109/ AERO.2009.4839537 Montenbruck, O., Schmid, R., Mercier, F., Steigenberger, P., Noll, C., Fatkulin, R., Kogure, S., and Ganeshan, S., GNSS satellite geometry and attitude models, Adv. Sp. Res. 56(6), 1015–1029, 2015. Cabinet Office, Government of Japan: QZS-2 Satellite Information, SPI-QZS2_C and SPI-QZS4_C, June 28, 2019, https://qzss.go.jp/en/technical/qzssinfo/index.html. Joint Statement on Galileo and GPS Signal Optimization By the European Commission (EC) and the United States (US), Brussels 24 March 2006.

205

9 GNSS Interoperability Thomas A. Stansell, Jr. Stansell Consulting, United States

9.1

Introduction to Interoperability

The International Committee on Global Navigation Satellite Systems (ICG) [1] is headquartered at the United Nations Vienna International Center (VIC) in Austria. Part of its Mission Statement, shown below, is to “encourage coordination among providers of global navigation satellite systems (GNSSs), regional systems, and augmentations in order to ensure greater compatibility, interoperability, and transparency.” Working Group A (WG-A) of the ICG has the charter to study and define GNSS Interoperability, and a 2007 report [2] of WG-A defined Interoperability as follows:

• • • • •

Interoperability refers to the ability of open global and regional satellite navigation and timing services to be used together to provide better capabilities at the user level than would be achieved by relying solely on one service or signal. Interoperability allows navigation with signals from at least four different systems with minimal additional receiver cost or complexity. For many applications, common center frequencies are essential to interoperability, and commonality of other signal characteristics is desirable. Multiple constellations broadcasting interoperable open signals will result in improved observed geometry, increasing end user accuracy everywhere and improving service availability in environments where satellite visibility is often obscured. Geodetic reference frame realization and system time steerage should adhere to existing international standards to the maximum extent that is practical.

Note that WG-A is now known as WG-S, the Working Group on Systems, Signals, and Services [3]. The main objective of Interoperability is illustrated by the often-used cartoon in Figure 9.1. The user has a

handheld receiver in an urban canyon. The receiver can “see” six navigation signals, but only one from each global navigation satellite system: GPS from the United States, GLONASS from Russia, Galileo from the European Union, and BeiDou from China. The GNSS regional systems are QZSS from Japan and NAVIC from India. Because the receiver is handheld, it is important to achieve this result, as stated above, “with minimal additional receiver cost or complexity.” The third bullet under the preceding definition states: “Multiple constellations broadcasting interoperable open signals will result in improved observed geometry, increasing end user accuracy everywhere, and improving service availability in environments where satellite visibility is often obscured.” In addition, interoperability also offers significant value in enabling the use of Advanced RAIM (ARAIM) [4] to maintain aviation integrity while lowering the cost of providing differential correction and integrity messages from Satellite-Based Augmentation Systems (SBASs) [5], as transmitted from geosynchronous satellites and supported by large networks of ground tracking stations, for example, the US Wide Area Augmentation System (WAAS) and the European Geostationary Navigation Overlay Service (EGNOS). Another important beneficiary of interoperability is high-precision GNSS applications, for example, survey, mapping, construction, infrastructure (buildings, bridges, dams, etc.) monitoring, machine control, and precision agriculture. These high-value applications number in the hundreds of thousands and support many billions of dollars of commercial investment as well as aiding research and development activities, for example, volcano monitoring, tracking of tectonic plate drift. The ability to use alternatives to GPS signals provides increased availability, accuracy, productivity, and integrity.

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

206

9 GNSS Interoperability

Galileo

NAVIC

BeiDou

QZSS

GLONASS

Figure 9.1

9.2

GPS

Illustration of interoperability.

Elements of Interoperability

Every GNSS signal is characterized by many parameters, including center frequency, waveform, signal spectrum, number of chips in the spreading code, time duration of the spreading code, number and relative power of the signal components, overlay modulation, data modulation symbol rate, data bit rate, type of message error correction, structure of messages, received signal power, satellite antenna gain pattern, time base, geodesy, and geographic reference frame. Ideal interoperability would be for every GNSS signal to be structured the same. Instead of there being four constellations of 30 satellites each for GPS, GLONASS, Galileo, and BeiDou, each constellation at a different orbit altitude, better interoperability would be achieved if just one of the systems were expanded to 120 satellites having the same signal and orbit characteristics. For example, the ground track of GPS satellites repeats every sidereal day (23 h 56 min 4.1 s), whereas the ground track of GLONASS satellites repeats every 8 sidereal days, the ground track of BeiDou satellites in medium Earth orbit (MEO) repeats every 9 sidereal days, and Galileo ground tracks repeat every 10 sidereal days. Because of the constellation differences, coverage and therefore dilution of precision (DOP) is always changing. Fortunately, with lots of satellites in view, the coverage and the DOP should be consistently excellent. In spite of the constellation differences, a significant advantage of having different system providers is that user

equipment can be designed to detect a system-wide problem in one of the systems and avoid use of those signals until the problem is resolved. With so many differences between signals and orbits, it is valuable to distinguish between “signal-level” and “userlevel” interoperability. If the user equipment, including its internal and post-processing software, is designed to receive and process signals with different characteristics from physically different satellites at different orbit heights and yet give excellent results, the result is “user-level” interoperability. Users normally are not concerned about the source of the signals – only about the results. This is well illustrated in Figure 9.1. Signal-level interoperability affects the difficulty and therefore the cost of combining different signals and, to some extent, the quality of the combined result. The cost difference is primarily of concern for consumer devices. The differences between the Galileo E1 OS and the GPS L1C signals are instructive. Note that many documents and presentations emphasize that these were designed to be interoperable signals [6]. Table 9.1 is a comparison of their characteristics. Except for the most important interoperability parameter of center frequency and the common use of BOC(1,1) modulation, it would be difficult to design two more distinctly different signals than L1C and E1 OS. Signal interoperability clearly was not the most important design objective. In terms of signal-level interoperability, if BeiDou adopts the presumed B1C signal structure of QMBOC [7], it will be almost identical to L1C and thus more signal-level interoperable with GPS than Galileo’s E1 OS signal. Differences in signal parameters that can be accommodated by software are easier and less expensive to implement than differences that require hardware modifications. If signals from different systems are received with one antenna, employ the same radio frequency and/or intermediate frequency (RF/IF) amplifiers and filters, and are converted to digital form by a common analog-to-digital (A/D) converter, all other differences usually can be accommodated by firmware in digital processing chips or by software in subsequent signal processing steps.

9.3 GLONASS Transition Toward More Interoperable CDMA Next, we will begin evaluating the impact of center frequency on interoperability, concentrating on signals in the L1 band, which extends from 1559 to 1610 MHz. The GPS, Galileo, and the expected BeiDou global system signals at L1, as well as the QZSS regional L1 signals, are all

9.3 GLONASS Transition Toward More Interoperable CDMA

Table 9.1 L1C, E1 OS, and B12C signal characteristics Characteristic

GPS L1C

Galileo E1 OS

GPS/Galileo Comment

BeiDou B1C

Center Frequency

1575.42 MHz

1575.42 MHz

Identical

1575.42 MHz

Spreading Code Family

Weil-based

Memory

Different

Weil-based

Spreading Code Length

10,230 Chips

4,092 Chips

Different

10,230 Chips

Spreading Code Duration

10 ms

4 ms

Different

10 ms

Modulation

TMBOC

CBOC

Different

QMBOC

Channels with BOC(6,1)

Pilot

Pilot and Data

Different

Pilot

Channels with BOC(1,1)

Pilot and Data

Pilot and Data

Identical

Pilot and Data

Data Power Percent

25%

50%

Different

25%

Pilot Power Percent

75%

50%

Different

75%

Data Symbol Rate

100 SPS

250 SPS

Different

100 SPS

Data Bit Rate

50 BPS

125 BPS

Different

50 BPS

Error Correction

LDPC

Convolutional

Different

LDPC

Pilot Overlay Code

18 s

100 ms

Different

18 s

Message Frame Length

18 s

720 s

Different

18 s

centered at 1575.42 MHz. To date there are no L1 signals from India’s NAVIC regional system. However, GLONASS L1 signals have 14 different center frequencies from 1598.0625 to 1605.375 MHz spaced apart by 0.5625 MHz. (Some references indicate there are two additional center frequencies at 1605.9375 and 1606.5000 MHz.) The center frequency of each “frequency channel” (F) is (1602 + 0.5625 × F) MHz. The lowest frequency is when F = −7. The highest of the 14 center frequencies is when F = 6. Each center frequency can be duplicated on antipodal (opposite sides of Earth) satellites‚ which is how 14 frequencies can be used for up to 28 satellites [8]. Antipodal satellites can use the same channel number. From the beginning, GLONASS has employed frequency division multiple access (FDMA) to separate and distinguish the individual satellite signals while using identical spreading codes on all common satellite signals. In contrast, GPS and all subsequent navigation satellite systems have transmitted on the identical center frequency, for example, L1 at 1575.42 MHz, while using different code division multiple access (CDMA) codes on each satellite to separate and distinguish the signals. It is significant that GLONASS also is beginning to implement the CDMA method‚ and over time every GLONASS satellite will transmit both FDMA and CDMA signals. The choices made clearly indicate the new CDMA signals are intended to improve interoperability with GPS and the other GNSSs. The Glonass-K satellites have only one CDMA signal, L3OC (meaning an open signal (O) using CDMA (C) at the L3 frequency). The Enhanced

Glonass-K next provides three open CDMA signals at L1, L2, and L3. That satellite uses two phased-array antennas, one to transmit the FDMA signals and the other for the CDMA signals. It is significant that the CDMA antenna is in the preferred location, aligned with the satellite center of mass, while the FDMA antenna is offset [8]. This difference is expected to end with the Glonass-K Evolution (K2) satellites, which will transmit all navigation signals from one antenna aligned with the center of mass. The GLONASS CDMA signals will be transmitted at three center frequencies of L1 at 1600.995, L2 at 1248.060, and L3 at 1202.025 MHz, as shown in Figure 9.2 [9]. The top plot in Figure 9.2 shows the GLONASS L1 and L2 FDMA signals. The lower plot shows the GLONASS CDMA signals. On the left‚ the GLONASS L3 signal is shown in red superimposed over the Galileo E5 signals, which are composed of two components: E5a, which is the large lower lobe that overlays the GPS L5 signal, and E5b, which is higher in frequency than E5a and L5. As shown in the table, the L3 carrier is modulated by a 10.23 MHz spreading code. In the GLONASS L2 band, the second plot shows that the L2 CDMA signals overlap the GLONASS FDMA signals and are modulated by two 1.023 MHz spreading codes, one being a binary phase shift keyed (BPSK) signal and the other which, in addition, is modulated by a 1.023 MHz square wave to form a split band Binary Offset Carrier BOC(1,1) signal. The first “1” in the BOC(1,1) term denotes a 1.023 MHz square wave‚ and the second “1” denotes a spreading code rate of 1.023 MHz.

207

208

9 GNSS Interoperability THE SPECTRUM OF NAVIGATION RADIO SIGNALS OF THE GLONASS SYSTEM

L3/L5

L2

L1

–160 –180 1160

1170

1180

1190

1200

1210

1220 1230

1240

1250 1260 1270

L3/L5

1280 1290

1300

1550 1560

1570

1580

L2

1590

1600 1610 1620

L1

–160 –180 1160

1170

1180

1190

1200

1210

1220 1230

1240

1250 1260 1270

1280 1290

1300

1550 1560

1570

1580

1590

1600 1610 1620

CHARACTERISTICS OF NAVIGATION RADIO SIGNALS OF THE GLONASS SYSTEM WITH CODE DIVISION

Range Carrier frequency, MHz

Signal

L1

1 600,995

L10Cd L10Cp

1 023 4 092

1,023 1,023

BPSK (1) BOC (1,1)

125 pilot signal

L2

1 248.06

L2 CSI L20Cp

1 023 4 092

1,023 1,023

BPSK (1) BOC (1,1)

250 pilot signal

L3

1 202,025

L30Cd L30Cp

10 230 10 230

10.23 10.23

BPSK (10) BPSK (10)

100 pilot

Figure 9.2

Code length, symbols

Clock frequency, MHz Modulation type

Transmission speed CI, bit/s

GLONASS FDMA and CDMA signal plans.

The second plot in Figure 9.2 shows that the GLONASS L1 CDMA signals overlay the GLONASS L1 FDMA signals. The L1 CDMA signals have the same structure as the L2 CDMA signals, namely‚ a BPSK(1) component and a BOC(1,1) component. To the left of the GLONASS L1 plot is a plot of the GPS BOC(1,1) component of the L1C signal, which is centered at 1575.42 MHz. (Note that the GLONASS L2 CDMA plot is not scaled properly. It should have the same width as the L1 CDMA plot.) There are significant differences between the new GLONASS CDMA signals and the traditional FDMA signals. The differences clearly are intended to encourage and enable interoperability with GPS, Galileo, BeiDou, and QZSS. The underlying clocks for GPS and the other systems are based on multiples of a 1.023 MHz common frequency. Like these signals and unlike GLONASS FDMA, the center frequencies of each of the three GLONASS CDMA signals are at multiples of 1.023 MHz, namely L1 at 1565 times 1.023 or 1600.995 MHz, L2 at 1220 times 1.023 or 1248.060 MHz, and L3 at 1175 times 1.023 or 1202.025 MHz. In addition, as shown in Figure 9.2, the code clock frequencies are 1.023 or 10.23 MHz, and the code lengths are 1023, 4092, or 10230 chips.

9.4 Interoperability Impact of Signal Center Frequency One of the very useful aspects of combining signals with a common center frequency is that after each signal is captured by the receiver’s antenna, the time delay through RF/IF filters, amplifiers, and cables is almost identical for each received signal. If the signals are digitized by a single A/D device using only one sampling clock, the time difference between the digitized signals can be assumed to be zero. For accurate navigation and positioning, it is not necessary to calibrate the time delay between signals. For timing receivers, depending on the needed accuracy, calibration from the antenna to the time signal output may be needed, but not the time difference between received signals (other than accounting for the timing difference between system clocks). There are two reasons for the minor exceptions to the “zero difference” assumption. One is the Doppler shift of each signal due to the relative velocity of the satellite and the receiving antenna. Each signal typically will have a different Doppler frequency offset. At 1575.42 MHz‚ the Doppler offset for an Earth-based receiver ranges from about −5 to +5 kHz. Figure 9.3 illustrates this by the width of the lines representing the GPS L1 center frequency and the

9.4 Interoperability Impact of Signal Center Frequency

14 lines representing the GLONASS FDMA center frequencies. Superimposed in Figure 9.3 is the spectrum of the GPS C/A signal, with the first nulls at ±1.023 MHz. The intent is to show that the Doppler shift is a tiny fraction of the spread spectrum bandwidth. The comparison is made because even narrowband receivers must process most of the L1 signal bandwidth. Typical consumer receivers have bandwidths on the order of ±2 MHz or greater. Limitations of the Excel plot do not necessarily show how small the Doppler shift is compared to the spectral width of the C/A signal. Figure 9.4 shows this more clearly. The two lines representing the GPS center frequency are at 1575.42 MHz + 5 kHz and 1575.42 MHz − 5 kHz. Receiver components, especially filters and cables, have a variable time delay as a function of frequency. For almost every application, the time delay difference due to the relatively tiny Doppler shifts can be ignored. There may be a few applications in which even such tiny effects must be measured and calibrated to achieve the utmost precision. The second and more significant reason for small time delay variations between signals is that the antenna itself is not time delay isotropic. Signals arriving at different azimuth and elevation angles suffer small time delay differences. The received carrier phase varies over 360 as a

1570

1575

1580

1585

1590

function of the satellite azimuth relative to the receiving antenna position. For the highest-precision applications, these variations are measured and mapped and corrections are applied when processing the signals. For consumer applications, such small variations are negligible, especially when compared to the much larger sources of error, including multipath and uncorrected ionospheric and tropospheric refraction. As illustrated in Figure 9.3, the center frequency offsets between GLONASS FDMA signals are enormous, especially as compared with Doppler frequency shifts. The frequency offset between GPS L1 and any of the GLONASS FDMA channels ranges from 22.6425 to 29.955 MHz. The frequency offset between individual FDMA channels ranges from 0.5625 to 7.3125 MHz. These differences are large even compared with the span of the C/A signal spectrum. In fact, the spread between GPS and the FDMA channels is so large that most if not all receivers employ different RF/IF hardware, including different filters, for CDMA than for FDMA signals. This violates a main interoperability objective of “allowing navigation with signals from at least four different systems with minimal additional receiver cost or complexity.” To achieve accuracy with an FDMA-only receiver, the filter(s) must be designed to minimize differences in time

1595

1600

1605

1610

GPS and GLONASSL1 Center Frequencies (MHz), Line Width = ± 5 kHz

Figure 9.3 GPS L1 Center frequency and GLONASS center frequencies with ±5 kHz Doppler shifts. The GPS C/A signal spectrum is shown at the GPS L1 center frequency.

1574

1575

1576

Figure 9.4 GPS L1 center frequency with ±5 kHz Doppler shifts and GPS C/A signal spectrum.

1577

209

210

9 GNSS Interoperability

delay from one channel to another. A pre-calibration of these delays should be provided to the processing software, and a built-in test signal to calibrate the differences may be needed. When GLONASS FDMA is used with GPS, Galileo, BeiDou, and/or QZSS, a calibration of the individual FDMA delays can be made with respect to a position solution that is independent of GLONASS measurements. Although filter time delay variations can change over time and with temperature, as long as the calibrations remain valid they can be used to benefit from use of the FDMA signals. Because the additional coverage and accuracy obtained by adding GLONASS to GPS is so valuable, many receivers, from consumer devices to high-precision survey and machine control products are so equipped. Once many more reliable CDMA signals become available from other providers, the question will arise of whether the additional complexity of using FDMA signals will be justified. This is why the emerging GLONASS use of CDMA is so significant. The frequency offset with GPS L1, L2, and L5 will not be eliminated. These differences will be 25.575, 20.46, and 25.575 MHz, respectively. (As factors of 1.023 MHz, the differences are factors of 25, 20, and 25, respectively.) However, having 1.023 MHz as the base for all GLONASS CDMA signals should simplify frequency synthesis in every receiver processing both GLONASS CDMA and other GNSS signals. The frequency differences are large enough to warrant the use of two filters at each band, one for most GNSS CDMA signals and the other for the GLONASS CDMA signals. This requires a larger product size and more cost, but the cumbersome and suboptimal need to individually calibrate the time delay of each FDMA channel will be eliminated. In fact, the calibration can become one additional parameter in the positioning solution. The relative time delay parameter between filters will be very stable, changing only slowly. In many applications‚ that parameter can be combined with the very stable system clock difference parameter. Once a solution is obtained, each one or the combination can be heavily filtered so as not to “waste” even one satellite signal in subsequent positioning solutions. As shown in Figure 9.2, 1.023 MHz is the base not only for the GLONASS CDMA center frequencies but also for the spreading code clocks. The spreading code lengths also are multiples of 1023 chips. Clearly the intent is to be as interoperable as possible with most other GNSS signals even if the center frequencies are not identical.

9.5 Missed Common Third Frequency Opportunity As shown by Figure 1.21 in Chapter 1 of this book [10], many of the existing or planned signals are “orphans,”

meaning they are not provided by any of the other major systems. For example, the GPS and QZSS L2 signals are not provided by GLONASS, Galileo, or BeiDou. The Galileo E5b and BeiDou B2b signals are not present on GPS. Perhaps more important is that they will not be used by FAA-certified avionics. Therefore, there is less incentive for manufacturers to include orphan signals in future receivers if the common signals provided by all major systems are adequate for the supported applications. Only two signal frequencies are supported by all major systems: 1575.42 MHz (L1 for GPS) and 1176.45 MHz (L5 for GPS). These are predicted to become the dominant frequencies in future dual-frequency receivers and applications. At the ION GNSS-2006 conference, Ron Hatch [11] described a three-frequency, geometry-free technique for carrier phase ambiguity resolution. With three common frequencies from multiple satellites, a wide-area differential system could allow receivers to provide approximately 10cm navigation accuracy over an entire continent. This could be the basis for safety-of-life automobile lane keeping services, better performance for precision agriculture, and perhaps consumer-grade survey receivers. With respect to Figure 1.21 in Chapter 1, the best location for a common signal would be on top of the Galileo E6 signal. Ideally Galileo, BeiDou, and GPS should provide signals at this 1278.75 MHz frequency. Sadly, this is a missed opportunity for a major step toward a wide-area, high-accuracy navigation and positioning service.

9.6 Interoperability Impact of Signal Waveform and Spectrum It is often thought that signals with a different waveform and therefore different spectra are inherently less interoperable than those with identical waveforms and spectra. In particular, Figure 9.5 shows the spectrum of the GPS BPSK (1) C/A signal and of the Multiplexed Binary Offset Carrier (MBOC) spectrum of GPS L1C [12–15] as well as Galileo E1 OS, BeiDou B1C, and QZSS L1C signals. The question, therefore, is whether the C/A signal is interoperable with the others. The MBOC signal consists of two components, one being a BOC(1,1) waveform with 90.9% of the signal power and the other a BOC(6,1) waveform with 9.1% of the signal power. Most receivers will track only the BOC(1,1) component, either to minimize cost and/or bandwidth, or in the case of aviation, to minimize complexity. Therefore, we will examine the difference in tracking the C/A signal versus the BOC(1,1) component of MBOC. The most widely used method to track the spreading code of a GNSS signal is the early-minus-late (E-L) correlator. Variations of this also are widely used to reduce the effect

Power Spectral Density (dBW/Hz)

9.6 Interoperability Impact of Signal Waveform and Spectrum

–60 BPSK(1) MBOC

–65

–70

–75

–80 –10

–5

0

5

10

Offset from 1575.42 MHz Center Frequency (MHz)

Figure 9.5 Spectra of C/A and of L1C.

of signal multipath, for example, the narrow correlator, the strobe correlator, the double delta correlator, or the multipath mitigation correlator [16–18]. As explained in [16–18], subtracting a late correlator waveform from an early correlator waveform produces a waveform with three levels, +1, 0, or −1. When the level is +1, a gate is open and the incoming (I channel) signal samples are summed. (The running sum also decays, and so older samples are replaced by newer samples.) When the level is −1, the gate is open but the signal samples are subtracted from the running sum. When the level is 0, the gate is closed and signal samples are ignored. (Ignoring signal samples when there is no transition to track improves the loop signal-to-noise ratio.) Also, as explained in [16–18], the code tracking loop works to center the plus and minus gates on the spreading code transitions, the polarity of the gate being defined by the direction of the signal code transition. The result is that when the average of the running sum is not zero but is either positive or negative, that is the error signal which causes the code tracking loop to center the open gate times on the incoming signal code transitions. When the average of the running sum is zero, the code tracking loop is aligned with the peak of the code autocorrelation function. The process for tracking code transitions of a BPSK(1) or a BOC(1,1) waveform is the same. The only significant difference is that a BOC(1,1) waveform has three times the code transitions per unit time than the BPSK(1), that is, about 500,000 per second for BPSK(1) and 1,500,000 for BOC(1,1). That improves the signal-to-noise ratio in the code tracking loop, but it does not cause one waveform to be less precise than the other except in extremely weak signal conditions. If the receiver RF/IF bandwidth is wide enough, the transient response after a code transition should mostly settle before the next code transition. For the C/A spreading code, the minimum time interval before the next code transition is approximately 1 μs (977.5 ns). For BOC(1,1), the time interval is half that because the 1.023 MHz spreading code

also is modulated by a 1.023 MHz square wave. Therefore, the minimum RF/IF bandwidth for BOC(1,1) should be about twice that of the minimum C/A RF/IF bandwidth. Practically speaking, the bandwidth of a current narrowband C/A receiver may be adequate for BOC(1,1), and a receiver designed for BOC(1,1) certainly has sufficient bandwidth for the C/A signal. From a receiver bandwidth perspective, there is no adverse impact of processing both signals with the same hardware, especially because they have the same center frequency. One characteristic which might seem to affect interoperability between BOC(1,1) and BPSK(1) is the autocorrelation function of each, as illustrated in Figure 9.6. When tracking BOC(1,1), it is important to avoid having the code loop lock to either of the “false” peaks at +0.5 and −0.5 spreading code chips from the main peak. Many papers have been written about how to avoid this trap. If both signals are transmitted from the same satellite, the BPSK(1) autocorrelation function, which has no such ambiguity, can be used to verify the proper alignment of the BOC (1,1) code tracker. The relative “sharpness” of the two autocorrelation functions could imply that one yields better accuracy than the other. This has been a long-term fantasy. When GPS was first designed‚ it was assumed that the P-code would provide about 10 times the pseudorange measurement accuracy of the C/A code because the C/A autocorrelation function is 10 times wider than it is for the P-code. However, as is well known, some of the most precise measurements are made by C/A receivers. There are several reasons for this. One is that receivers using a narrow correlator or a multipath mitigation correlator can use the same earlyminus-late spacing (same gate width) for C/A as for P-code tracking. If both signals are filtered with the same RF/IF

1.2 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –1

–0.5

0 Chips

0.5

1

Figure 9.6 Autocorrelation function of BPSK(1) and BOC(1,1) signals.

211

212

9 GNSS Interoperability

bandwidth, the rounding at the top of either autocorrelation function will be the same, which means that the accuracy of finding code transitions will be the same if the S/N in the code tracking loop is sufficiently positive. To improve the S/N, commercial, scientific, and aviation C/A receivers almost always employ a version of carrier-aided code smoothing, that is, the Hatch filter [19]. This allows the code loop bandwidth to be reduced to 0.01 Hz or less. In most applications, the penalty of needing time for the filter to settle is of little consequence. Therefore, it can be concluded that for most practical purposes the C/A BPSK(1) and the MBOC BOC(1,1) signals are fully interoperable in terms of code tracking accuracy.

9.7 Clocks, Geodesy, and Differential Corrections If you are a scientist and need to squeeze the last millimeter of accuracy and picosecond of time from GNSS measurements, then any difference between system elements is significant. Examples include location of the phase center of the transmitting antenna relative to the satellite’s center of mass, location of the tracking stations used to determine the orbit and clock of each satellite, the geodetic models which predict satellite orbits, the effect of continental drift and polar wander on orbit determination, the short-term and long-term stability of satellite clocks, the wander of each satellite clock relative to a national Universal Time Coordinated (UTC) standard, and how close the national time standard is to the global UTC. In addition, scientists must be concerned with minute aberrations in signal structure, ionospheric and tropospheric refraction effects, variability in receiver antenna characteristics, including phase variations with azimuth and elevation angle, the local multipath environment, the physical stability of structures holding the antennas, and so on. Each one of these and more have been the subject of intense and ongoing study. None of these is of much concern to consumers. Most GNSS receivers are in mobile phones (three billion or more), followed by automobiles. Accuracy is challenged by multipath, signal blockage, poor antenna structures, very limited battery power (which limits sophisticated processing), severely constrained physical space, an environment filled with electronic noise, and so on. A few meters of error apparently is tolerable and has not limited the growth of these markets. In between these quite different applications are professional and commercial uses. The top accuracy requirement is about half a centimeter for survey, machine control, structure monitoring, volcano monitoring, earthquake

monitoring, and so on. Perhaps surprisingly, many precision agriculture applications require accuracy between 1 and 10 cm. Another set of applications requires between half and one meter of accuracy. The most prominent example is data collection for geographic information systems (GISs), such as locating and mapping physical structures. Less accuracy is needed for commercial navigation applications for aircraft, ships, boats, trucks, etc. More accuracy is needed when landing aircraft or navigating large ships in shallow waters. The above paragraphs are meant to show that there are a vast number of GNSS applications, each with its own accuracy and other requirements. Therefore, the need for interoperability of different GNSS signals differs from one application to another. For general navigation‚ it appears interoperability has nearly been achieved. This is because every GNSS provider is striving to improve its accuracy and adhere to international standards. The international standard for time is Coordinated Universal Time, which, in French, is Temps Universel Coordonné. UTC was chosen as a compromise abbreviation. UTC is based on International Atomic Time (TAI) which is computed by the International Bureau of Weights and Measures (BIPM) located near Paris. Interoperability at the level of about 10 ns (approximately 3 m at the speed of light) seems achievable in the near future. Even so, it is recommended that the measured time offset between systems be obtained. Sources include external measurements provided as part of satellite navigation messages or via other communication channels. The most accurate method is for the receiver to calculate time offsets when there are enough satellites visible from each system to include the system time offset as an unknown parameter in the navigation solution. Because the time offset between systems changes so slowly, it can be heavily filtered after the solution has settled. The other standard which all GNSSs are attempting to replicate is known as the International Terrestrial Reference Frame (ITRF) [20]. The difference between the latest GPS reference frame and the latest ITRF is only a few centimeters. All other GNSSs are also approaching this level of agreement. Therefore, for applications which require no more than a few meters of accuracy, it is now – or soon will be – acceptable to combine signals from several GNSSs without concern for time or geodetic interoperability. For applications requiring more accuracy, the answer for many decades has been the use of differential corrections. The basic concept is that one reference station at a defined location, or a network of reference stations at defined locations, tracks the available satellite signals and compute corrections which are supplied to users. There are differential systems with one reference station which operate over a limited distance of between 15 and 50 km from the

9.8 Summary

reference station, and there are other systems with reference stations distributed over broad areas which can serve an entire continent. Over short distances‚ the corrections may be only pseudorange adjustments or, for survey and machine control applications, they also include carrier phase readings. For larger systems, the corrections will include adjustments to each satellite’s orbit parameters as well as pseudorange and/or clock corrections. Some applications permit simple corrections; others may demand a more complex set of corrections. Systems with large coverage areas include the WAAS operated by the US Federal Aviation Administration (FAA) and similar SBASs [5] around the world. There are private systems operated by commercial companies such as OmniSTAR by Trimble, Ltd., StarFire by John Deere, and TerraStar by TerraStar GNSS Ltd. Each of these services employs communication satellites to distribute correction messages. Smaller systems use local radio transmitters and receivers to send correction messages. Importantly, all differential systems eliminate basic interoperability issues of time or geodesy offsets. After differential corrections are applied, the time reference and the orbit coordinates for each satellite are adjusted to agree with common references, as defined by the differential system itself. The only remaining interoperability issues will occur in the user equipment, such as different time delays due to different signal center frequencies. Differential systems are widespread and widely used, even in cell phone networks, and they all but eliminate most concerns about interoperability.

9.8

Summary

Because of the increasing number of GNSSs, with most expected to reach maturation by about 2020, this chapter has focused on whether these systems will work well together. Are they, or will they be, interoperable? The work of the ICG in addressing interoperability was reviewed, including agreement on a definition of interoperability. This was followed by an exploration of the elements of interoperability. Because so many signal parameters differ between systems, it was important to differentiate between “signal-level” interoperability, in which signal parameters should be nearly the same, and “user-level” interoperability, where the differences are accommodated mostly by software in the user equipment and, therefore, are invisible to users. The next section examined the implications of the GLONASS transition from FDMA to the more interoperable CDMA signals. It was shown that combining FDMA signals

imposes an extra costs and the requirement for channel calibration. For example, because GLONASS signals are not centered on 1575.42 and 1176.45 MHz, there may be less combined use of GLONASS in the future than there is today. However, it was noted that the new GLONASS CDMA signals will be more interoperable than the original FDMA signals, despite the difference in GLONASS CDMA center frequencies with most other GNSS CDMA signals. The following section concentrates on the interoperability challenges imposed by combining signals with different center frequencies. A missed opportunity for a common third frequency was then noted. Regretfully, it is unlikely this opportunity will ever be realized. The question of whether differences in a signal waveform or its spectrum would adversely affect interoperability was explored. It appears that waveforms as different as the GPS C/A signal and multiple MBOC signals can be combined with no loss of accuracy. Therefore, they are considered interoperable with the minor caveat of whether some types of Costas (squaring) loop carrier tracking, required for C/A signals, could introduce small offsets between the tracking GPS C/A and MBOC signals on L1. Interoperability of system clocks and of the underlying orbit determination geodesy was reviewed. Except for scientific, survey, and engineering applications requiring the very highest precision, it was judged that these differences are so small – and getting smaller – that they can be ignored for most consumer applications. It also was noted that differential GNSS, which removes all differences in system clocks and geodesy as well as the individual satellite clock and orbit errors, is used for scientific, survey, and engineering as well as most commercial and many consumer applications. In the early to mid-1970s, when GPS and GLONASS were first being designed and developed, no one could imagine the explosion of applications and of the number of users these systems would engender. The impact on safety, freedom to wander, economics of transport, science, and many other aspects of life could not have been predicted. The results have been revolutionary. We are entering a new revolutionary change. The impact cannot be as great as deployment of the first continuous, global, all-weather, four-dimensional navigation and positioning systems. However, as Europe completes Galileo and China completes the global version of BeiDou, perhaps aided by the regional QZSS from Japan and NAVIC from India, the existing capabilities will be improved significantly. The accuracy, availability, and integrity of all applications, especially in challenged environments, will be transformed. Availability and accuracy in urban canyons will be much better. The number of expensive SBAS will

213

214

9 GNSS Interoperability

begin to decline as ARAIM [4] comes into full use. Scientific, survey, engineering, and agricultural applications will improve in accuracy, speed of phase ambiguity resolution, and in availability within challenged environments such as near trees or deep within a pit mine. Integrity for most applications will improve as a much larger number of satellites can be used to cross-check each other as in conventional RAIM or with ARAIM. Interoperability is important in almost every application of GNSS. It largely has been achieved for consumer applications, and it continues to improve for all applications as signal providers strive to increase accuracy, match international time and geodesy standards, and bolster their system integrity. The widespread use of differential corrections can eliminate any remaining interoperability concerns. Interoperability is fueling this important next phase of global satellite navigation and positioning.

12

13

14

References 1 http://www.unoosa.org/oosa/en/ourwork/icg/icg.html 2 http://www.unoosa.org/documents/pdf/icg/activities/

2007/WG-A-2007.pdf 3 http://www.unoosa.org/oosa/en/ourwork/icg/working-

15

groups.html 4 Pullen, S. and Joerger, M., Chapter 23 GNSS Integrity and

5

6 7

8

9 10

11

Receiver Autonomous Integrity Monitoring (RAIM), in Position, Navigation, and Timing Technologies in the 21st Century, (eds. Y.J. Morton et al.), Wiley-IEEE Press, 2020. Walter, T., Chapter 13 SBAS, in Position, Navigation, and Timing Technologies in the 21st Century (eds. Y.J. Morton et al.), Wiley-IEEE Press, 2020. http://www.gps.gov/policy/cooperation/europe/2007/ MBOC-agreement/ Lu, M. and Zheng, Y., Chapter 6 Beidou Navigation Satellite System, in Position, Navigation, and Timing Technologies in the 21st Century (eds. Y.J. Morton et al.), Wiley-IEEE Press, 2020. Karutin, S., Testoedov, N., Tyulin, A., and Bolkunov, A., Chapter 4 GLONASS, in Position, Navigation, and Timing Technologies in the 21st Century (eds. Y. J. Morton et al.), Wiley-IEEE Press, 2020. Karutin, S., Private communication. Parkinson, B.W., Morton, Y.J., van Diggelen, F., and Spilker, J.J., Chapter 1 Introduction, Early History, and Assuring PNT (PTA), in Position, Navigation, and Timing Technologies in the 21st Century (eds. Y. J. Morton et al.), Wiley-IEEE Press, 2020. Hatch, R.R., A new three-frequency, geometry-free, technique for ambiguity resolution, Proceedings of the 19th

16

17

18

19

20

International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), pp. 309–316, Fort Worth, TX, September 2006. Hein, G.W., Avila-Rodriguez, J.-A., Wallner, S., Pratt, A. R., Owen, J., Issler, J.-L., Betz, J.W., Hegarty, C.J., Lenahan, S., Rushanan, J.J., Kraay, A.L., and Stansell, T. A., MBOC: The new optimized spreading modulation recommended for GALILEO L1 OS and GPS L1C, Proceedings of IEEE/ION PLANS 2006, pp. 883–892, San Diego, CA, April 2006. Betz, J., Blanco, M.A., Cahn, C.R., Dafesh, P.A., Hegarty, C. J., Hudnut, K.W., Kasemsri, V., Keegan, R., Kovach, K., Lenahan, L.S., Ma, H.H., Rushanan, J.J., Sklar, D., Stansell, T.A., Wang, C.C., and Yi, S.K., Description of the L1C signal, Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), pp. 2080–2091, Fort Worth, TX, September 2006. Stansell, T., Hudnut, K.W., and Keegan, R.G., GPS L1C: Enhanced performance, receiver design suggestions, and key contributions, Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), pp. 2860–2873, Portland, OR, September 2010. Stansell, T., Hudnut, K.W., and Keegan, R.G., “Future wave: L1C signal performance and receiver design,” GPS World, April 1, 2011. Hatch, R.R., Keegan, R.G., and Stansell, T.A., Leica’s code and phase multipath mitigation techniques, Proceedings of the 1997 National Technical Meeting of The Institute of Navigation, pp. 217–225, Santa Monica, CA, January 1997. Stansell, T.A., Inventor, Leica Geosystems Inc., assignee, Mitigation of multipath effects in global positioning system receivers, U.S. Patent 5,963,582 filed November 21, 1997, and issued October 5, 1999. Stansell, T.A., Knight, J.E., Keegan, R.G., and Cahn, C.R., Inventors, Leica Geosystems Inc., assignee, Mitigation of multipath effects global positioning system receivers, U.S. Patent 6,160,841 filed November 21, 1977, and issued December 12, 2000. Hatch, R., The synergism of GPS code and carrier measurements, International Geodetic Symposium on Satellite Doppler Positioning, 3rd, Las Cruces, NM, February 8–12, 1982, Proceedings. Volume 2 (A84-18251 06-42), pp. 1213–1231, Las Cruces, NM, New Mexico State University, 1983. Rizos, C., Altamimi, Z., and Johnson, G., Chapter 27 Global Geodesy and Reference Frames, in Position, Navigation, and Timing Technologies in the 21st Century (eds. Y. J. Morton et al.), Wiley-IEEE Press, 2020.

215

10 GNSS Signal Quality Monitoring Frank van Graas and Sabrina Ugazio Ohio University, United States

10.1

Introduction

As global navigation satellite system (GNSS) applications become more widespread, the need for service assurances and associated service monitoring continues to grow. In the early days of satellite navigation, the emphasis was on the navigation solution and its accuracy. Once the service approached operational capability, the emphasis shifted to signal monitoring to ensure a guaranteed level of performance. The first GPS Standard Positioning Service (SPS) performance standard was published in 1993, in the same year that GPS initial operational capability (IOC) was declared [1]. The original five-station monitor network was expanded‚ and receiver technology was upgraded to improve satellite signal monitoring, and to reduce the user range error (URE) [2, 3]. Performance standards for other GNSSs that are available include BeiDou [4], and Galileo [5], while others are anticipated to be based on the performance standards being drafted by the International Committee on GNSS (ICG) Working Group on Systems, Signals and Services [6]. The next step in signal monitoring is the development of performance specifications to identify all GNSS parameters that need to be monitored. The first edition of the GPS Civil Monitoring Performance Specification (CMPS) was published in 2005 [7]. In the international community, this activity is pursued under the Joint ICG-IGS (International GNSS Service) International GNSS Monitoring and Assessment (IGMA) Trial Project [8]. The development of monitoring standards and their implementation are an ongoing process for GNSS service providers. Signal Quality Monitoring (SQM) is a subset of all monitoring requirements and primarily covers the transmitted carrier waveform and code performance. Within the SQM subset, there are a number of aspects of the signal that are of interest to the user, ranging from received signal power to potential failure modes and mechanisms. For high-

integrity, safety-of-life applications such as aircraft landing operations, SQM requirements are well developed since their full definition was required for the approval process. This chapter starts with an explanation of the importance of signal quality monitoring, followed by a description of SQM requirements, and an overview of current monitoring systems. Next, SQM algorithms and methods are summarized for six parameters: signal power, cross-correlation, cycle slip, excessive acceleration, code-carrier divergence, and signal deformation.

10.2

The Importance of SQM

Reasons for monitoring signal quality of the GNSS signals broadcast by the satellites can be divided into three categories:

•• •

Service guarantees and user acceptance High-accuracy applications High-integrity, safety-of-life applications

The first category is associated with service providers, and addresses the verification of service guarantees as well as user acceptance of the service. When a navigation signal is made available to the public, documentation of a minimum performance level is needed for the navigation user to design its operational use of the signal. It is noted, however, that many GNSS users rely on advanced signal characteristics that are not documented in the service guarantee, but that the user implicitly trusts. User acceptance can be affected negatively if that trust is breached. High-accuracy applications are in their own category due to the need for a local, regional‚ or global network of ground reference receivers that are used to increase the clock and orbit accuracies of the navigation satellites. In addition, the reference receivers could also be used to mitigate tropospheric and ionospheric propagation delays. High-accuracy

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

216

10 GNSS Signal Quality Monitoring

systems provide corrections to users to improve their position and/or timing performance beyond that provided by a GNSS service. SQM is included to ensure that the accuracy of the user solution is within certain bounds. The third category involves applications that exceed the level of integrity provided by GNSS. These applications were not envisioned in the original GNSS designs, and are not included in current designs due to cost and/or development time considerations. Examples of these systems are the Satellite-Based Augmentation System (SBAS) and the Ground-Based Augmentation System (GBAS), both of which are primarily approved for aviation applications. GBAS and SBAS rely on ground reference receivers to monitor the received satellite signals. User receiver monitoring is also part of this category, where a higher level of integrity is achieved through algorithms implemented in the receiver, such as Receiver Autonomous Integrity Monitoring (RAIM) or Advanced RAIM (ARAIM). Each of the three categories has unique SQM requirements that are summarized in the next section.

10.3

SQM Requirements

Due to the complexity and variety of GNSS applications, no single publication documents a complete set of monitoring requirements. As a starting point, we can consider the GPS Civil Monitoring Performance Specification [9], which derives requirements from multiple US Government documents: the GPS performance standard [10], interface specifications [11–14], the Wide Area Augmentation System (WAAS) performance standard [15], the GPS III System Specification [16], and Interagency Forum for Operational Requirements (IFOR) proposed new operational requirements [17]. Additional requirements are also included from International Civil Aviation Organization (ICAO) Standards And Recommended Practices (SARPS), Annex 10, Attachment D [18]. For other GNSSs, corresponding parameter values can be obtained through a study of their interface specifications and performance standards. The monitoring requirements in the CMPS are divided into three categories:

• • •

System performance monitoring (35 requirements), including, for example, the service volume coverage per satellite and per constellation, and satellite orbital parameters Signal monitoring (136 requirements), including, for example, verification of civil ranging codes, SQM, semicodeless tracking, and navigation message Non-broadcast data (4 requirements), including, for example, Notice Advisory to Navstar Users (NANU) messages and Yuma almanac messages

SQM is a subset of signal monitoring that specifically deals with the assessment of carrier waveform and code performance to ensure that they are within designated limits [19]. The CMPS SQM requirements are summarized in Table 10.1 [9]. Given the summary in Table 10.1, it can be observed that SQM requirements are primarily based on interface specifications; however, requirements related to aircraft precision approach are also included in row 7 and the last three rows of Table 10.1, as they are derived from WAAS and ICAO SARPS standards. The CMPS provides a section with clarifications and algorithms that provides insight into incomplete SQM requirements including verification of absolute power delivered by each satellite and response time, received carrier-to-noise ratio, code-carrier divergence, signal distortion, carrier phase discontinuities‚ and bit inversions. These SQM parameters are summarized in Table 10.2. The signal parameters in Table 10.2 do not have associated monitoring requirements as these depend on the application. To further develop a set of SQM parameters, consider two demanding systems in terms of signal accuracy‚ and integrity; GBAS and SBAS. For a detailed description of these systems, see Chapters 12 and 13 in this volume. Of interest in this chapter are the GBAS/SBAS high-level requirements related to SQM, which are summarized in Table 10.3. For excessive acceleration, code-carrier divergence, and signal deformation‚ the associated missed detection probability is less than or equal to 1 for pseudorange errors smaller than 0.75 m, less than or equal to 10−5 for errors larger than 2.7 m, and less than or equal to 10 − 2 56 Er + 1 92 for pseudorange errors, |Er|, between 0.75 and 2.7 m [20]. For low signal power and cycle slip detection, there are no specific requirements for missed detection probability as they are allocated by the manufacturer of the equipment during the design process. The cross-correlation error can be omitted from the aircraft equipment design [21], but must be considered for the ground reference receiver, although it is not addressed by the SARPS [20]. From Tables 10.1 through 10.3, a complete set of SQM requirements can be developed for each application. Since the requirements do not address the implementation of the monitoring or a specific monitoring architecture, the next section reviews current monitoring systems, followed by a section with example monitor implementations.

10.4

Current Monitoring

The first level of signal monitoring is performed by the service providers. For GPS, the Precise Positioning Service (PPS) signals are monitored at the GPS Master Control

10.4 Current Monitoring

Table 10.1

Summary of CMPS SQM requirements [9]

Paragraph in CMPS

Requirement summary

Source referenced by CMPS

3.2.2.a, b

Received signals: L1 C/A ≥ −158.5 dBW,L2C ≥ -160 dBW

IS-GPS-200 [11]

3.2.2.c, e

Received signals for GPS IIF: L5/I5 ≥ −157.9 dBW,L5/Q5 ≥ −157.9 dBW

IS-GPS-705 [12]

3.2.2.d, f

Received signal for GPS III: L5/I5 ≥ −157 dBW, L5/Q5 ≥ −157 dBW

IS-GPS-705 [12]

3.2.2.g

Received signal L1C ≥ −157 dBW

IS-GPS-800 [13]

3.2.2.h

Received signal in orbit L1C ≥ −182.5 dBW

IS-GPS-800 [13]

3.2.2.i, j, k, l

Report significant drops in C/N0 for L1 C/A, L2C, L5, and L1C

IS-GPS-200 [11], IS-GPS-705 [12], IS-GPS-800 [13]

3.2.2.m, n, o, p

Code-carrier divergence < 6.1 m for 100 < T < 7200 s for L1 C/A, L2C, L5, and L1C

IFOR [17]

3.2.2.q

Average time difference between L1 C/A and L1 P(Y) code transitions < 10 ns (two-sigma)

IS-GPS-200 [11]

3.2.2.r, s, t

Mean group differential delay between codes: L1 P(Y) and L2C < 15 ns, L1 P(Y) and L5 < 30 ns, L1 P(Y) and L1C < 15 ns

IS-GPS-200 [11], IS-GPS-705 [12], IS-GPS-800 [13]

3.2.2.u, v

Stable 90 phase offset (± 100 mrad) between L1 C/A and L1 P(Y) code carriers with C/A lagging P(Y), and between L2C and L2 P(Y) code carriers with L2C lagging L2 P(Y)

IS-GPS-200 [11], WAAS PS [15]

3.2.2.w, x, y, z

Code chip lead/lag variation from a square wave < 0.12 chips for L1 C/A, < 0.02 chips for L2C, < 0.02 chips for L5I and L5Q, < 0.05 chips for L1C

SARPS [18], CMPS Section 5.4.4

3.2.2.aa

Detect and monitor instances when the transient response for each bit transition exceeds the limits defined in SARPS Threat Model B

SARPS [18]

Source: GPS Civil Monitoring Performance Specification, U.S. Department of Transportation, DOT-VNTSC-FAA-09-08, April 30, 2009. Can be found at: https://www.gps.gov/technical/ps/2009-civil-monitoring-performance-specification.pdf. Reproduced with permission of GPS.

Table 10.2

CMPS SQM considerations [9]

Paragraph in CMPS

SQM parameter

Notes

5.4.1

Verification of absolute power

Periodic verification (e.g. yearly)

5.4.2

Received carrier-to-noise

Continuous verification (e.g. every 1.5 s)

5.4.3

Code-carrier divergence and code-carrier divergence failure

Nominal divergence between different code and carrier combinations as well as failure conditions

5.4.4

Signal distortion

Currently only described for GPS L1 C/A code in the SARPS

5.4.5.1

Carrier phase discontinuities

Observed by a receiver as partial cycle, half-cycle or full-cycle slip

5.4.5.2

Bit inversion

A carrier phase discontinuity that results in a half-cycle error in the receiver that causes a parity failure

Source: GPS Civil Monitoring Performance Specification, U.S. Department of Transportation, DOT-VNTSC-FAA-09-08, April 30, 2009. Can be found at: https://www.gps.gov/technical/ps/2009-civil-monitoring-performance-specification.pdf. Reproduced with permission of GPS.

Segment in near real time 24 hours a day [25]. The SPS that includes the C/A code is not monitored continuously, but most errors that affect the SPS also affect the PPS, including satellite clock and orbit parameters. Some aspects of SQM are included, such as periodic verification of absolute power levels [26]. Examples of errors that are not

monitored at the levels required for high-integrity applications are summarized in Table 10.3. High-accuracy applications are monitored with regional or worldwide reference networks, such as the regional Continuously Operating Reference Station (CORS) network, the Jet Propulsion Laboratory (JPL) Global Differential

217

218

10 GNSS Signal Quality Monitoring

Table 10.3 GBAS and SBAS SQM requirements Description

SQM requirement

Reference

Low signal power

Detect signal levels below those specified in Table 10.1 for GPS L1 C/A code

[22]

Cross-correlation

Limit error due to cross-correlation to 0.2 m

[23, 24]

Cycle slip

The satellite signal tracking quality shall be monitored such that the allocated integrity risk due to undetected cycle slips is within the manufacturer’s allocation

[21]

Excessive acceleration

Detect excessive pseudorange acceleration such as a step or other rapid change within 1.5 s

[20]

Code-carrier divergence

Detect excessive code-carrier divergence within 1.5 s

[20]

Signal deformation

Detect fault conditions on the C/A code that deforms correlation peaks used for tracking the pseudorange within 1.5 s

[20]

GPS (GDGPS) service, and an international reference station network coordinated by the IGS. In addition, several commercial correction services are in worldwide operation. As an example, the IGS network, through the Real-Time Service (RTS), provides satellite clock and orbit corrections, Earth rotation parameters, zenith tropospheric path delay estimates as well as global ionosphere maps that can be combined with data from user receivers for Precise Point Positioning (PPP), thus achieving much higher levels of accuracy than that provided by a stand-alone GNSS (see detailed discussions in Chapter 11 of this volume). High-integrity, safety-of-life applications use regional (SBAS) or local (GBAS) reference receivers to monitor all aspects of the received satellite signals. These systems focus on a rapid response to signal malfunctions, generally within a few seconds after the error reaches a potentially hazardous level.

10.5

SQM Algorithms and Methods

This section describes algorithms and methods for monitoring SQM requirements identified in Section 10.3. The monitors described in this section are not necessarily detecting satellite malfunctions. For example, most signal deformation errors are part of normal system operation, although the level of signal deformation may be too high for aircraft landing operations. It would not be appropriate to take that satellite out of service, since the majority of users would not be affected by this error. Another issue is the separation of malfunctions that are unacceptable for certain applications from environmental conditions, such as local interference, which may or may not affect the user. Clearly, if a GBAS ground station is affected by strong interference, it may not be able to generate differential corrections‚ and the aircraft would likely experience the same conditions as it approaches the GBAS ground stations. In this case, the

GBAS ground station should no longer generate corrections for the affected satellite(s). An SBAS reference station, on the other hand, would be removed from the correction generation, as local interference at a reference station would likely not affect the user at a different location.

10.5.1

Low Signal Power

A low received satellite signal power condition can affect satellite acquisition and satellite tracking. Both code and carrier tracking noise increase as the received satellite signal power decreases. The carrier phase measurement noise is given by [27] σϕ =

λ 2π

BW ϕ 10 0 1C

N0

m

10 1

where BWϕ is the carrier loop bandwidth in hertz. The code phase measurement noise is given by [28] σ ρ = chip

0 5 d BW SS m 10 0 1C N 0

10 2

where BWSS is the single-sided code tracking loop bandwidth in hertz, chip is the code phase chip length in meters, and d is the correlator spacing in chips. The carrier and code phase tracking noise are shown in Figure 10.1 for the GPS C/A code with a carrier tracking loop bandwidth of 16 Hz, a correlator spacing of 0.1 chip, and a single-sided code tracking loop bandwidth of 0.0025 Hz, which corresponds to a smoothing time constant of 100 s. From Figure 10.1, both the carrier and code tracking noise increase significantly when C/N0 goes below 40 dB-Hz. For example, the carrier tracking noise standard deviation increases from 1.2 mm to 3.8 mm for a C/N0 decrease from 40 to 30 dB-Hz, while the code tracking noise standard deviation increases from 3.3 cm to 10.4 cm for the same decrease in C/N0.

10.5 SQM Algorithms and Methods

Code BW = 0.0025 Hz

Phase BW = 16 Hz 7

20

6 15

4

cm

mm

5

10

3 2

5

1 0 20

40

60

80

0 20

C/N0 in dB-Hz

40

60

80

C/N0 in dB-Hz

Figure 10.1 Standard deviations of carrier phase tracking noise (left) and code phase tracking noise (right) as a function of C/N0 for a carrier loop bandwidth of 16 Hz and a single-sided code loop bandwidth of 0.0025 Hz.

Low signal power does not directly lead to an integrity concern, but it can affect safety through the loss of signal continuity. Indirect impact on integrity has several mechanisms: 1) Other monitors, such as those used to detect interference, cycle slips, code-carrier divergence, excessive acceleration, ionospheric gradients, and signal deformation, rely on a minimum C/N0 for meeting their probabilities of false and missed detection. 2) Low satellite transmit power could be an indication of other malfunctions onboard the satellite, such as attitude control; therefore, prior failure probabilities assumed for satellite malfunctions are no longer valid. 3) A low C/N0 can result in a large power difference of more than 10 dB with respect to other satellites, which, in turn, can cause cross-correlation depending on the code structure. Also, due to cross-correlation, satellite acquisition could be affected. A separate cross-correlation monitor can be implemented for code structures that are affected by low signal power (see Section 10.5.2) such that the primary purpose of the low-signal-power monitor is to ensure that the C/N0 available to the receiver processing is above a minimum value. For ground reference receivers, the most practical estimate for the received signal power is the C/N0 estimator. Since there is no direct impact on integrity, the C/N0 measurements for each satellite can be averaged to reduce the noise in the estimate: C N0 k =

1 P−1 C N0 k − pΔT Pp=0

10 3

where ΔT is the update rate, and P is the number of C/N0 measurements in the estimate. For example, if the NB/WB estimator from [29] is used, then the standard deviation of the C/N0 estimate does not depend on the value of C/N0, and is approximated by a value of 1 dB for a 1 s update rate. When averaged over 50 s using Eq. (10.3), the standard deviation becomes approximately 0.14 dB. Note that this assumes that the C/N0 measurements are uncorrelated. The threshold for the C/N0 estimator depends on the system design, specifically, whether corrections can be calculated with integrity down to 32 dB-Hz or 25 dB-Hz, especially in the presence of interference. For illustration purposes, assume that the probability of false detection, PFD is set at 10−7, while the probability of missed detection, PMD is set at 10−3, then the minimum detectable drop in C/ N0 is given by kfd + k md σ C

N0

=

2 erf − 1 1 − PFD

+ erf − 1 1 − 2PMD σ C

N0

≈ 1 2 dB

10 4

2 x − t2 e dt, kfd, and kmd are the false detecπ 0 tion and missed detection multipliers, respectively. If the C/ N0 tracking threshold is 32 dB-Hz, then the detection threshold for the averaged C/N0 given by Eq. (10.3), should be set at 32 + 1.2 = 33.2 dB-Hz to guarantee that the averaged C/N0 will not drop below 32 dB-Hz.

where erf x =

10.5.2

Cross-Correlation

Errors due to interaction between ranging codes is a category of error that cannot be monitored by the service provider as it is a function of many parameters, most of which depend on the user location and receiver architecture. Cross-correlation occurs when the correlation function is distorted by energy from a different satellite, either from the same constellation or from a different constellation. The size of the cross-correlation error is a function of several parameters, including the relative received signal strength between two satellites, relative Doppler frequency shift (i.e. fading frequency), relative change in Doppler frequency shift, ranging codes on the two satellites, relative code phase shift, relative phase alignment, relative rate of change of code phase shift, navigation data bits on the two satellites, relative delay between the navigation data bits, smoothing time constant, and correlator type in the receiver [30–32]. The probability of occurrence of cross-correlation is small for stationary users, but the error can reach tens of meters [33], and thus cannot be ignored for high-integrity systems. For differential systems, cross-correlation errors are not common between a reference receiver and the user due

219

10 GNSS Signal Quality Monitoring

to different geometries. Fortunately, if the user is dynamic, then cross-correlation errors tend to be mitigated for the user contribution [24]. Cross-correlation impacts signal acquisition, signal tracking, and C/N0 estimators. Cross-correlation conditions and corresponding monitors have been well characterized for the GPS C/A code, but are of equal concern for GLONASS and other GNSSs [34, 35]. It is noted that any form of energy leakage can distort the correlation function, whether it is from the same frequency, a different frequency, or due to a poor code cross-correlation sequence. Cross-correlation is referred to as self-interference when the impact on the spectrum is evaluated. Because the impact is complicated in terms of the signal parameters and dynamics, care must be taken not to assess the impact too conservatively [36, 37]. A summary of GPS C/A code cross-correlation will be presented, followed by three types of monitors for the cross-correlation error. In 1978, [30] showed that the worst-case correlation sidelobes occur at a 4 kHz Doppler frequency shift offset between two satellites, and that the effect is temporary in nature. At 0 Hz Doppler offsets between satellites, the sidelobe interaction with the main auto correlation peak can last longer. In [30], the emphasis was on the impact of cross-correlation on signal acquisition. In 1992, [33] identified potentially large pseudorange errors on the order of tens of meters during Doppler crossovers (relative Doppler frequency shift between two satellites is close to 0 Hz), and suggested that these errors can be modeled similar to multipath. In 2002, [31] presented bench test results showing meter-level cross-correlation errors that become negligible for precision approach applications after 100 s smoothing with the carrier phase. However, in [31], cross-correlation was not considered in combination with off-nominal power levels due to low-signal-power conditions, or higher than expected power levels due to recent changes in satellite transmit power redistribution [38]. The cross-correlation error is often compared to multipath error, but there are several distinct differences between cross-correlation and multipath errors for the GPS C/A code:

• • •

A cross-correlating signal can be both early and late (multipath always arrives after the direct signal). Cross-correlation errors do not necessarily repeat from day to day if the interfering satellites have relative frequency drifts such that the relative clock offsets change to outside a cross-correlation time window, or if the navigation data bits change. Navigation data bits are not always identical on two interfering satellites and are generally not nearsynchronous.

•

Cross-correlation errors can be twice as large as multipath error for the same relative strength (the crosscorrelation slope of the correlation function can be twice as large as the slope of the autocorrelation function). Multipath errors are only significant for the primary correlation peak (i.e. time shift between direct and multipath signal less than approximately 1.5 code chips), while cross-correlation errors can occur for multiple time offsets between the two codes.

•

The latter two points are illustrated in Figure 10.2, where the cross-correlation error envelope for PRN15 due to PRN24 is shown for relative code chip offsets between 200 and 220 C/A code chips. The receiver correlator spacing, d, is 0.1 chip, and PRN24 is 10 dB stronger than PRN15 (γ = 10 dB).The error is calculated by adding the PRN24 signal to PRN15 with relative delays between 200 and 220 chips, and by evaluating the resulting code tracking error for each relative delay. The blue error envelope is for the in-phase crosscorrelation, whereas the red error envelope is for the out-of-phase cross-correlation. As the carrier phase between PRN15 and PRN24 goes in and out of phase, the cross-correlation error oscillates between the in-phase and out-of-phase error envelopes. Similar to the multipath error envelope, as the relative path delay between the PRN15 and PRN24 codes increases, the error envelope increases linearly and then remains constant when the delay reaches the value of the correlator spacing, or 0.1 chip, relative to the beginning of a chip. If the error would have been due to multipath of equivalent strength, then the error would only have reached the 3 m level instead of the 6 m level reached by cross-correlation. Overall, 62.2% of the relative delay results in zero cross-correlation error, while PRN15 and PRN24 cross correlation for γ = 10.0 dB 10

5 Error in m

220

0

–5

–10 200

205

210

215

220

Relative delay in chips

Figure 10.2 Cross-correlation error for PRN15 due to PRN24, which is 10 dB stronger (γ = 10 dB). Both the in-phase (blue) and out-of-phase (red) error envelopes are shown.

10.5 SQM Algorithms and Methods

36.2% of the delays result in errors oscillating between −3 and +3 m, and for 1.6% of the delays, the error oscillates between −6 and +6 m. The latter corresponds to 16 chip durations out of 1023 chips. The equation for the maximum value of the error envelope is given by [39]

eenvelope

γ − 23 9 20 = chip d 10

10 5

where γ is the relative strength of the cross-correlating satellite in decibels with respect to the affected, weaker satellite. The factor of 23.9 is equal to 20log10(65/1023), which is the ratio of the highest cross-correlation value to the maximum value of the autocorrelation, expressed in decibels. During a Doppler cross-over, the error will oscillate as shown in Figure 10.3. Based on Figure 10.3, cross-correlation errors can be divided into two types: slow fading and fast fading. For both types, the navigation data bit differences between the two satellites will modulate the error due to the 180 phase changes between the two satellites. Both satellites will experience the same navigation data during the last two subframes when the almanac data is transmitted, which lasts for 12 s. Note that several conditions have to line up in order to create the worst-case error given by Eq. (10.5). One, the Doppler offset between the two satellites has to be either zero, or offset by a multiple of 1 kHz [24]; two, the Doppler rate offset has to be within 0.02 Hz/s in order to sustain the error for at least 30 s; three, the relative power difference must be large enough; four, the C/A code chips have to be aligned such that one of the 16 worst-case chip alignments occurs; five, the navigation data has to be identical on both satellites; and six, the navigation data bits must be closely aligned between the two satellites. Clearly, the worst-case error is unlikely to occur, but for high-integrity systems, this error cannot be ignored. It is further noted that for strong cross-correlation errors, the mean error for fast fading is not zero, just like multipath errors, due to the asymmetric shape of the error as a function of the chip delay [40]. At least three different techniques can be used to protect against cross-correlation errors. The first technique, which can be found in GAST-C precision approach applications, uses a screening algorithm that removes satellites from the differential data broadcast that are potentially affected by cross correlation [23]. The screening algorithm starts

with the selection of a bound for the cross-correlation error, and then calculates the thresholds for three parameters: difference in carrier-to-noise ratio, ΔC/N0, difference in Doppler frequency shift, ΔfD, and difference in Doppler rate, Δf D , between two satellites. This calculation is done in advance based on a computer simulation. In operation, the monitor removes satellites from the differential correction broadcast if the screening conditions are violated. The screening conditions that limit the worst-case crosscorrelation error to 0.2 m for 100 s smoothing are shown in Table 10.4 [39]. When any of the 11 conditions in Table 10.4 are met, the weaker satellite will be removed. For example, when it is measured that two satellites have a power difference greater than 10 dB, a Doppler frequency shift difference less than 10 Hz, and the Doppler frequency shift difference is changing more slowly than 2 Hz/s, condition 8 is met, and the error on the weaker satellite can be greater than 0.2 m in Table 10.4 Screening conditions for 100 s smoothing that limit the worst-case cross-correlation error to 0.2 m [39] Item

Condition

1

Δ f D < 0 01 Hz Δf D < 0 01 Hz s

2

ΔC N 0 > 4 dB Δ f D < 0 01 Hz Δf D < 0 02 Hz s

3

ΔC N 0 > 5 dB Δf D < 0 01 Hz Δf D < 0 03 Hz s

4

ΔC N 0 > 6 dB Δf D < 0 01 Hz Δf D < 0 05 Hz s

5

ΔC N 0 > 7 dB Δ f D < 0 01 Hz Δf D < 0 4 Hz s

6

ΔC N 0 > 8 dB Δ f D < 4 Hz Δf D < 0 5 Hz s

7

ΔC N 0 > 9 dB Δ f D < 7 Hz Δf D < 1 Hz s

8

ΔC N 0 > 10 dB Δf D < 10 Hz Δf D < 2 Hz s

9

ΔC N 0 > 14 dB Δf D < 20 Hz Δf D < 5 Hz s

10

(ΔC/N0 > 16 dB) & (ΔfD < 25 Hz)

11

(ΔC/N0 > 20 dB)

Source: Zhu, Z. and van Graas, F., “C/A Code Cross Correlation Error with Carrier Smoothing – the Choice of Time Constant: 30 s vs. 100 s,” Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 464–472. Reproduced with permission of Institute of Navigation.

Time

Figure 10.3 Cross-correlation error shape during a Doppler cross-over.

221

10 GNSS Signal Quality Monitoring

10.5.3

Cycle Slip

Carrier phase cycle slips, or carrier phase discontinuities in general, can affect high-accuracy/high-integrity applications that rely on carrier phase for accuracy or monitoring. For example, real-time high-accuracy systems that are affected by carrier phase anomalies are dynamic surveying, plate tectonics, infrastructure monitoring, dredging, construction, scientific and space applications, such as occultation, formation flight‚ and docking. For real-time highintegrity systems, carrier phase anomalies can result in loss of continuity and loss of correction service coverage [41], as well as loss of integrity if the anomaly affects one or more of the monitors that relies on the carrier phase. The complication with carrier phase anomalies is the source of the problem, which can either be due to the following [42]:

• •

Discontinuities in the carrier phase generated onboard the satellite Environmental conditions that affect the receiver tracking loop such as interference, multipath, signal shadowing, aircraft overflight of the antenna, as well as ionospheric and tropospheric propagation effects

To monitor the discontinuities onboard the satellite, the above two sources need to be separated, which is most effectively accomplished through monitoring at multiple locations, such that environmental errors do not correlate between the two locations [9]. It is noted that actual satellite discontinuities are infrequent, with fewer than four anomalies per day on average for the GPS L1 frequency [42]. Carrier phase discontinuities can be characterized using four models: step, pulse, ramp, and tri-state, as illustrated in Figure 10.4. Examples of each of the four phase discontinuity models for the GPS L1 frequency are shown in Figure 10.5 [42].

Pulse

ϕ in m

Step

ϕ in m

δ

δ > 10 ms Time in s

Time in s Ramp

Tri-State

δ

ϕ in m

the theoretical worst-case cross-correlation. It is noted that only the requisites for the worst-case cross-correlation are met, but in order for this error to materialize, additional conditions must be met, such as alignment of the code, identical navigation data, and navigation data bit alignment. As a result, the screening algorithm is conservative, but effective. The primary drawback of the screening technique is that all satellites must be tracked by the receiver in order to obtain the C/N0, and the Doppler measurements. Two monitors that both detect the actual cross-correlation error are the signal deformation monitor (SDM) and the code-carrier divergence (CCD) monitor [23]. The CCD monitor is described in Section 10.5.5 and the SDM monitor in Section 10.5.6.

ϕ in m

222

δ2

δ1

> 30 ms

> 10 ms

Time in s

Time in s

Figure 10.4 Four models for the characterization of satellite carrier phase discontinuities.

In Figure 10.5 (upper left), a step discontinuity is shown for SVN63 that occurred on 14 September 2016; in the upper right, a pulse discontinuity is shown for SVN45 that also occurred on 14 September 2016; in the lower left, a finite ramp discontinuity is shown for SVN63 that occurred on 8 September 2016; and in the lower right, a tri-state discontinuity is shown for SVN45 that occurred on 14 September 2016. To monitor the phase discontinuities, a high-update rate receiver, for example, 100 Hz, is needed to capture shortduration events, such as the 750 ms duration of the step discontinuity, or the 30 ms portion of the tri-state discontinuity in Figure 10.5. Uncorrelated measurements at 100 Hz can be obtained through the use of a software defined receiver (SDR) or through tracking loop design. A stable receiver reference oscillator is also required to ensure high-quality carrier phase measurements [42]. The carrier phase measurements are de-trended by removing the known dynamics due to satellite motion and satellite frequency offset. Next, a second-order polynomial fit is used through a sliding window 10 s segment of the carrier phase data to remove the remaining receiver oscillator effects. Using nominal, error-free statistics, an overbound Gaussian distribution with standard deviation, σ OB, can be established for each 10 s segment. A step detector can be implemented as follows. Select two successive measurement data sets with a 1 s duration out of the 10 s window. At 100 Hz, each data set will contain 100 samples. Calculate the mean value of each data set, and compare the difference in the mean values to a threshold to detect the presence of a step discontinuity. The test statistic for the difference in the mean values is given by [43]

10.5 SQM Algorithms and Methods

0.020

0.006 0.004

0.015

0.002 0

Phase in m

Phase in m

0.010

–0.002 –0.004

0.005 0

–0.005

–0.006 –0.008 0

0.5

1 Time in s

1.5

–0.010

2

0

0.5

1

1.5

2

1.5

2

Time in s

0.020

0.008 0.006

0.015

0.004 0.002 0.005

Phase in m

Phase in m

0.010

0 –0.005

0 –0.002 –0.004 –0.006

–0.010

–0.008 –0.015 –0.010 –0.020 0

0.5

1

1.5

2

Time in s

–0.012 0

0.5

1 Time in s

Figure 10.5 Examples of observed carrier phase discontinuities for GPS L1 [42]. Source: Reproduced with permission of Institute of Navigation.

μ2 − μ1

T= Sp

1 n1

+

10 6

1 n2

where μ is the mean of a sample set, n is the number of samples in a sample set (n1 = n2 = 100 for this example), and Sp is the pooled sample variance given by Sp =

σ 21

n1 − 1 + n2 − 1 n1 + n2 − 2

σ 22

10 7

where σ is the standard deviation of a sample set. The detection threshold, TD, is calculated based on the false detection probability, PFD: TD =

2erf − 1 1 − PFD σ OB

10 8

where σ OB is the overbound sigma of the de-trended carrier phase measurements averaged over 10 s.

Following the derivation for the low-signal-power monitor (see Eq. (10.4)), the minimum detectable bias for the step discontinuity model is calculated from δstep, min = k fd + kmd σ OB

10 9

Using the same example parameters as those used for the low-signal-power monitor, the minimum detectable step is δstep, min = 8.4 σ OB. A typical value for σ OB is 1 mm, such that the minimum detectable step is 8.4 mm, which corresponds to a phase jump of approximately 16 at the GPS L1 frequency. The location of the step is determined by sliding the observation window by one sample at the time and finding the maximum value of the test statistic, which provides the location of the step with a resolution of 0.01 s. As a final step, detection results from two receiver locations are compared to ensure that the discontinuity is

223

224

10 GNSS Signal Quality Monitoring

caused by the satellite. The distance between the two receivers should be close enough to have a similar view of the satellite in the sky, but far enough to ensure that environmental errors are decorrelated. Decorrelation could be such that errors are not common between the two locations, or that they do not occur within 10 ms of each other. Similar detectors can be designed for the other three discontinuity types. The pulse and tri-state discontinuities can be viewed as two consecutive step anomalies, while the step discontinuity has step values that are equal and opposite. The ramp discontinuity can be modeled as a step discontinuity with a ramp connecting the two levels. With the full characterization of the carrier phase discontinuities, the impact on applications can be evaluated. It is noted that there is currently not much data available on carrier phase anomalies for most GNSSs, with the exception of GPS.

10.5.4

Excessive Acceleration

10 10

where a is the satellite range acceleration error in m/s2, τ is the latency of the correction in seconds, and ΔT is the correction update rate in seconds. Based on Eq. (10.10) and the maximum allowable range error, δρmax, the maximum acceleration error, amax, is given by amax =

2δρmax τ τ + ΔT

rate(k–2)

k–4

k–3

rate(k)

k–2

k–1

k a(k)

Figure 10.6 processing.

Excessive acceleration monitor measurement

aρ k =

δρ k − 2δρ k − 2 + δρ k − 4 2ΔT 2

10 11

For example, if δρmax= 0.75 m, ΔT = 0.5 s, and τ = 3 s, then amax = 0.14 m/s2. To measure the acceleration of the pseudorange correction, two successive pseudorange rate corrections could be differenced as shown in Figure 10.6. The acceleration estimate at time k is based on the five most recent pseudorange corrections. Two differential pseudorange correction rates are calculated for the two most recent seconds of data. Acceleration is then estimated by differencing the two rates:

10 12

Following the derivation for the low-signal-power monitor (see Eq. (10.4)), the minimum detectable acceleration is given by amin = k fd + k md σ a

For correction systems such as GBAS and SBAS, signal acceleration can cause unacceptable range errors if the level of acceleration, including step changes, causes the linear extrapolation based on the broadcast range rate correction to be invalid. The pseudorange error grows quadratically due to an acceleration error, but part of this growth is mitigated by the range rate correction, such that the resulting error in the corrected pseudorange, δρa, is a function of the age or latency of the differential correction and the differential correction update rate [44]: δρa = 0 5aτ τ + ΔT

2 seconds

10 13

where σ a is the standard deviation of the acceleration noise. Using the same example parameters that are those used for the low-signal-power monitor, the minimum detectable acceleration amin = 8.4 σ a. Furthermore, if amax = 0.14 m/s2, then it follows that the standard deviation of the acceleration noise must be less than 1.7 cm/s2. Consider the case where carrier phase measurements are used to calculate the acceleration. Given a C/N0 of 32 dB-Hz and Eq. (10.1), the noise on the carrier phase is 0.3 cm. If the update rate is 0.5 s, then Eq. (10.12) can be used to calculate the acceleration based on the carrier phase measurements: aϕ k = ϕ k − 2ϕ k − 2 + ϕ k − 4

10 14

and the standard deviation of the acceleration estimate based on the carrier phase is given by σ a,ϕ = σ ϕ

22 +

2

2

= σϕ 6

10 15

For σ ϕ = 0.3 cm, the noise on the acceleration estimate is 0.74 cm/s2, which is well below the required 1.7 cm/s2. Although it seems that the smoothed pseudorange noise standard deviation of 8.2 cm would be too high at 32 dBHz, in practice, it is still acceptable due to the time correlation of the noise induced by the 100 s smoothing time constant, which means that the smoothed pseudorange noise is similar to the carrier phase noise over periods of time of a few seconds. The acceleration monitor also responds to a step error‚ as illustrated in Figure 10.7. The response of the monitor to a step input is equal to the size of the step. For example, if the input steps from 0 to 0.1 m, then the monitor will output an

10.5 SQM Algorithms and Methods

Input Step

k–4

k–3

A

k–2

k–3

k

k+1

k+2

k+3

k

k+1 –A

k+2

k+3

A

Monitor Output

k–4

k–1

k–2

k–1

Figure 10.7 Response of the acceleration monitor to a step input.

acceleration of 0.1 m/s2 followed by an acceleration of −0.1 m/s2. The input acceleration changed once, which results in an output that changes three times as shown in the lower part of Figure 10.7. It is also noted that the monitor responds within the update rate.

10.5.5

Code-Carrier Divergence

The CCD anomaly is primarily of concern to differential applications that make use of carrier-smoothed code to mitigate pseudorange noise and multipath errors. Differential range errors are introduced when the reference receiver and the user receiver implement different filter designs or if the smoothing filters start at different times. In addition to the detection of satellite malfunctions, the CCD monitor is also beneficial for the detection of ionospheric anomalies and cross-correlation. Following [45], a divergence monitor can be designed using a divergence rate estimator followed by a detection test to protect against divergence rates that affect integrity. The divergence rate estimator uses a second-order filter to reduce the pseudorange noise and multipath, and is given by d1 k =

1 τ − ΔT d1 k − 1 + z k − z k − 1 τ τ

d2 k =

τ − ΔT ΔT d2 k − 1 + d1 k τ τ

10 16

where z(k) = ρ(k) − ϕ(k) is the code-minus-carrier measurement, and τ is the filter time constant, nominally set at 30 s. The divergence rate estimate at time k is given by d2(k). The divergence detector threshold is set based on the desired false detection probability, PFD: T ccd =

2erf − 1 1 − PFD σ d = kfd σ d

10 17

where σ d is the overbound standard deviation of the divergence rate estimator test statistic. The test statistic is dominated by nominal ionospheric divergence, such that a practical value of σ d is approximately 4 mm/s [45].

Following the derivation for the low-signal-power monitor (see Eq. (10.4)), the minimum detectable divergence rate is given by dmin = k fd + kmd σ d

10 18

Using the same example parameters as those used for the low-signal-power monitor, the minimum detectable divergence rate dmin = 8.4 σ d = 3.34 cm/s. To evaluate the impact on the user solution, the ground monitor performance is combined with the implementation of the airborne monitor (see [21]).

10.5.6

Signal Deformation

GNSS pseudorange measurements rely on correlation functions, but none of them is ideal due to imperfect signal generation, bandwidth limiting, distortions due to propagation effects, or satellite anomalies. Signal deformation can therefore be characterized as nominal and off-nominal. Nominal, or natural, signal deformation is needed to characterize the contribution of the shape of the signal used for the pseudorange measurements, and to derive detection thresholds based on nominal statistics. An early example of off-nominal, or anomalous, signal deformation occurred in the 1990s on SVN19 before GPS was declared IOC. The anomaly introduced ranging errors up to 8 m for certain differential GPS users, while the satellite was within its specified accuracy [46]. The keys to dealing with off-nominal deformation are a precise definition of the measurement along with a threat model that describes off-nominal deformation. Next, SDMs can be developed to protect against excessive signal deformation for high-accuracy/high-integrity applications. Nominal signal deformation. Until the launch of SVN60 in 2004, nominal GPS signal deformations were considered small, at the 5 cm level, and did not receive much attention [47]. When the nominal deformations started to trip the SDM, detailed investigations were initiated‚ and it was found that the actual size of the deformation is not as important as the relative differences between satellites [48]. The relative error directly

225

10 GNSS Signal Quality Monitoring

Pseudorange Natural Biases for Reference Intervals Only 0.15

0.1

Pseudorange Natural Bias [Meters]

226

0.05

0

–0.05

–0.1

–0.15 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

E-L Correlator Spacing [chips] PRN01, SV63, Block IIF, EI:57, Pdi:400s PRN02, SV61, Block IIR, EI:69, Pdi:210s PRN03, SV33, Block IIA, EI:69, Pdi:400s PRN04, SV34, Block IIA, EI:82, Pdi:390s PRN05, SV50, Block IIR-M, EI:87, Pdi:390s PRN06, SV36, Block IIA, EI:58, Pdi:450s PRN07, SV48, Block IIR-M, EI:88, Pdi:1000s PRN08, SV38, Block IIA, EI:77, Pdi:1000s PRN09, SV39, Block IIA, EI:53, Pdi:600s PRN10, SV40, Block IIA, EI:68, Pdi:480s

PRN11, SV46, Block IIR, EI:57, Pdi:730s PRN12, SV58, Block IIR-M, EI:49, Pdi:300s PRN13, SV43, Block IIR, EI:64, Pdi:440s PRN14, SV41, Block IIR, EI:68, Pdi:1150s PRN15, SV55, Block IIR-M, EI:79, Pdi:1510s

PRN21, SV45, Block IIR, EI:79, Pdi:1560s PRN22, SV47, Block IIR, EI:88, Pdi:1270s PRN23, SV60, Block IIR, EI:75, Pdi:450s PRN24, SV65, Block IIF, EI:53, Pdi:780s PRN25, SV62, Block IIF, EI:44, Pdi:400s

PRN16, SV56, Block IIR, EI:88, Pdi:650s PRN17, SV53, Block IIR-M, EI:69, Pdi:980s PRN18, SV54, Block IIR, EI:76, Pdi:750s PRN19, SV59, Block IIR, EI:71, Pdi:780s PRN20, SV51, Block IIA, EI:41, Pdi:850s

PRN26, SV26, Block IIA, EI:57, Pdi:610s PRN28, SV44, Block IIR, EI:80, Pdi:500s PRN29, SV57, Block IIR-M, EI:64, Pdi:1210s PRN30, SV35, Block IIA, EI:84, Pdi:1290s PRN31, SV52, Block IIR-M, EI:77, Pdi:450s PRN32, SV23, Block IIA, EI:60, Pdi:720s

Figure 10.8 Estimated pseudorange natural biases with respect to 0.1 chip correlator spacing for GPS satellites at highest elevation (El) with the average error removed. Coherent integration times (Pdi) used for each measurement are indicated in the legend, from [49]. Source: Reproduced with permission of Institute of Navigation.

contributes to the differential position error, while the common error primarily affects the clock offset estimate from GPS time, which is not of concern for precision landing applications. An example is shown in Figure 10.8 for the relative C/A code pseudorange natural biases for most satellites of the GPS constellation in 2012 [49]. Natural biases are calculated for high-elevation-angle reference time intervals with the lowest level of multipath during a satellite pass. Due to multipath error, the duration of the reference interval is different for each satellite, resulting in different coherent integration times (Pdi) for each satellite. A correlator spacing of 0.1 chip is taken as the reference

point‚ and relative errors are shown for correlator spacing between 0.01 and 1 chip. For example, consider the 0.1 to 0.2 chip zone, where natural biases are less than 10 cm, with the exception of SVN60, which reaches a peak error of 12 cm. For a user with 0.2 chip correlator spacing and a reference station with 0.1 chip correlator spacing, the differential errors between the satellites is multiplied by the geometric dilution of precision, which could easily result in vertical position errors on the order of 0.1 to 0.3 m. Similar characterization of nominal deformation has also been performed for GLONASS [50] and Galileo [51].

10.5 SQM Algorithms and Methods

GLONASS natural deformations were found to be at the 1 m level for the 0.1 versus 0.2 chip spacing comparison, while Galileo natural deformation was found to be at the 1 to 4 cm level. The latter can likely be credited to the digital signal generation architecture of Galileo satellites [51]. Anomalous signal deformation. To determine the impact of anomalous signal deformation, a threat model was developed following the SVN19 anomaly. The threat model was incorporated into precision approach standards developed by RTCA Inc. and ICAO to standardize conditions for monitor design and performance [21, 52]. The current ICAO threat models for GPS and GLONASS L1 C/A codes can be found in [52] and are summarized in Table 10.5. The second-order system used for Threat Model B has a unit step response of [52]: 0 et =

1 − e − σt

σ cos 2πf d t + sin 2πf d t ωd

t≤0 t≥0 10 19

Threat Models A and B are illustrated in Figure 10.9, where Threat Model A shows the lead or lag of the falling edge of a positive chip, while Threat Model B shows the second-order step response on both the leading and falling edges of the signal. Actual occurrences of GPS anomalous signal deformations after the original SVN19 are analyzed in detail in [53]. In [54], the WAAS SDM performance is evaluated against the ICAO Threat Model and actual anomalous signal deformations. It was found that the current WAAS monitor based on the ICAO Threat Model performs adequately. Nevertheless, the formulation of an anomalous signal deformation threat model is a complicated task, especially for new constellations that use different signal structures, digital signal generation techniques, and new navigation payloads [55]. A possible new, generic threat

Table 10.5

Δ A

B

Figure 10.9 Illustration of anomalous signal deformation Threat Models A and B.

model has been proposed in [55] that will be the topic of future research in this area. SDM. Both WAAS ground reference receivers and GBAS ground stations implement SDM for the detection of GPS signal deformation anomalies [47, 56–58]. This section summarizes the GBAS SDM following [47]. GBAS ground station receivers track each satellite with eight correlators located at the following offsets from the correlation peak in units of C/A code chips: −0.05, −0.025, 0, 0.025, 0.05, 0.075, 0.1, and 0.125, as shown in Figure 10.10. Each of the eight correlator measurements is smoothed using a first-order filter to reduce noise: M k,m,n t =

τ − ΔT ΔT M k,m,n t − ΔT + M k,m,n t τ τ 10 20

where Mk, m, n is correlator measurement k (from −2 to 5) for reference receiver m (from 1 to M) and satellite n (from 1 to N), τ is the filter time constant of 100 s, and ΔT is the update rate of 0.5 s. Three correlation functions widths are possible for the C/A code depending on the location of the first sidelobe relative to the main correlation peak. Therefore, the smoothed correlator measurements are compensated for C/A code type as described in [58].

ICAO SDM threat models for GPS and GLONASS L1 C/A codes, from [52]

Threat model

GPS

GLONASS

A: Falling edge of positive chips lead or lag relative to the correct end-time of that chip by an amount Δ in units of code chips

−0.12 ≤ Δ ≤ 0.12

−0.11 ≤ Δ ≤ 0.11

B: Output of a second-order system with complex conjugate poles at σ ± j2πfd, where σ is the damping factor in 106 nepers/s, and fd is the resonant frequency in 106 cycles/s

Δ=0 4 ≤ fd ≤ 17 0.8 ≤ σ ≤ 8.8

Δ=0 10 ≤ fd ≤ 20 2≤σ≤8

C: Combination of Threat Models A and B

−0.12 ≤ Δ ≤ 0.12 7.3 ≤ fd ≤ 13 0.8 ≤ σ ≤ 8.8

−0.11 ≤ Δ ≤ 0.11 10 ≤ fd ≤ 20 2≤σ≤8

Source: Amendment No. 89 to Annex 10 Part 1 Edition No. 6, International Civil Aviation Organization (ICAO), Montreal, Canada, 14 July 2014. Reproduced with permission of International Civil Aviation Organization.

227

228

10 GNSS Signal Quality Monitoring

evaluated considering the signal deformation threat model, and differences in aircraft receiver measurement architecture compared to the ground receiver measurements that are standardized at 0.1 chip correlator spacing [58].

Correlation value (normalized)

10.6 Challenges and New Developments

–0.05

0

0.05

0.1

Correlator offset C/A code chips

Figure 10.10 GBAS ground reference receiver correlator points [47]. Source: Reproduced with permission of Institute of Navigation.

The received signals are also deformed by the receiver hardware components through the radio frequency components. This distortion can be time-varying due to temperature and component variations. Since this distortion is common for all satellites, the monitor subtracts the average over all satellites from all measurements for one receiver: M k,m,n t = M k,m,n t −

1 N M k,m,i t N i=1

10 21

Following the receiver distortion removal, the compensated correlator measurements are differenced and averaged over all M ground receivers: x k,n t =

1 M M k − 2,m,n t − M k − 3,m,n t Mm=1 10 22

where the index k goes from 1 to 7, one fewer than the 8 correlator points due to the differencing. Each satellite now has a vector with 7 elements, xn, that describes its signal deformation. Under fault-free conditions, the vector xn has covariance matrix, P(λ), where λ is the elevation angle of the satellite. A single detection statistic, dn, is formed for each satellite as follows: dn t = P

− 12

λ xn t

T

P

− 12

λ xn t

10 23

where dn is χ 2-distributed with seven degrees of freedom. The detection threshold is set based on the desired false detection probability, the performance of the monitor is

As GNSS constellations and user equipment continue to develop, performance standards will need to be updated or created, along with monitoring standards for service guarantees, user acceptance, and to support high-accuracy and high-integrity applications. The development of these standards is a necessary, albeit time-consuming, process. To encourage compatibility and interoperability among systems, the ICG Working Group on Systems, Signals and Services is drafting performance standards guidelines [6], while the Joint ICG-IGS IGMA Trial Project is tasked with the demonstration of a global GNSS monitoring and assessment capability [8]. Challenges remain for many aspects of GNSS SQM, including algorithm design and implementation for monitoring and assessment. For example, although crosscorrelation conditions and corresponding monitors have been well characterized for the GPS C/A code, much work remains the be done for GLONASS and other GNSSs [34, 35]. Any form of energy leakage can distort the correlation function, whether it is from the same frequency, a different frequency, or due to a poor code cross-correlation sequence. Detection of cross-correlation errors due to satellites that are not tracked by the receiver remains an active area of research. A second example is the lack of information about carrier phase anomalies for all GNSS signals and frequencies. A third example concerns the SDM threat models, which are only applicable to the GPS and GLONASS L1 C/A codes. The development of a generic signal deformation threat model is needed for code signal structures other than L1 C/A, different signal generation techniques, and new satellite navigation payloads [55].

References 1 Global Positioning System Standard Positioning Service

Signal Specification, GPS Civil Performance Standard, U.S. Department of Defense, November 5, 1993. Can be found at: https://www.gps.gov/technical/ps/1993-SPS-signalspecification.pdf 2 Parkinson, B. W., Stansell, T., Beard, R., and Gromov, K., “A History of satellite navigation,” Navigation, Journal of

References

3

4

5

6

7

8

9

10

11 12 13 14 15 16

The Institute of Navigation, Vol. 42, No. 1, Spring 1995, pp. 109–164. Renfro, B., Munton, D., Mach, R., and Taylor, R., “Around the World for 26 Years—A Brief History of the NGA Monitor Station Network,” Proceedings of the 2012 International Technical Meeting of The Institute of Navigation, Newport Beach, CA, January 2012, pp. 1818–1832. BeiDou Navigation Satellite System Open Service Performance Standard (Version 1.0) China Satellite Navigation Office, December 2013. European GNSS (Galileo) Initial Service—Open Service— Service Definition Document, issue 1.0, European Union, December 2016 (OS SDD V1.0). Can be found at: https:// www.gsc-europa.eu/system/files/galileo_documents/ Galileo-OS-SDD.pdf Lavrakas, J. and Bolkunov, A., “An Update from the Performance Standards Team,” International Committee on GNSS (ICG) Meeting 12, 3–7 December 2017, Kyoto, Japan. Can be found at: http://www.unoosa.org/ documents/pdf/icg/2017/wgs/wgs-9.pdf GPS Civil Monitoring Performance Specification, First Edition, U.S. Department of Transportation, DOT-VNTSCOST-05-01, December 1, 2005. Auerbach, J., “International Cooperation on GNSS: A Provider Perspective on the ICG,” International GNSS (IGNSS) Conference, 7–9 February 2018, Sydney, Australia. Can be found at: https://www.gps.gov/multimedia/ presentations/2018/02/IGNSS-australia/auerbach.pdf GPS Civil Monitoring Performance Specification, U.S. Department of Transportation, DOT-VNTSC-FAA-09-08, April 30, 2009. Can be found at: https://www.gps.gov/ technical/ps/2009-civil-monitoring-performancespecification.pdf Global Positioning System Standard Positioning Service Signal Specification, GPS Civil Performance Standard, U.S. Department of Defense, fourth edition, September 2008. Can be found at: https://www.gps.gov/technical/ps/2008SPS-performance-standard.pdf IS-GPS-200D, IRN 001, Navstar GPS Space Segment/ Navigation User Interfaces, 7 March 2006. IS-GPS-705, IRN 001, 002, 003, Navstar GPS Space Segment/User Segment L5 Interfaces, 22 September 2005. IS-GPS-800, Navstar GPS Space Segment/User Segment L1C Interfaces, 4 September 2008. ICD-GPS-240, Navstar GPS Control Segment to User Support Community Interfaces, 1 October 2004. Wide Area Augmentation Service Performance Standard, First Edition, October 2008. SS-SYS-800C, GPS III System Specification for the Global Positioning System Wing (GPSW) (FOUO), 14 August 2008.

17 Salvano, D., “IFOR Proposed New Operational

18

19

20

21

22

23

24

25

26

27 28

29

Requirement,” Federal Aviation Administration, 26 July 2004. ICAO SARPs, Annex 10, Attachment D. Information and Material for Guidance in the Application of the GNSS Standards and Recommended Practices (SARPs), 20 November 2008. Hansen A., Van Dyke, K., Miles, C., and Lavrakas, J., “GPS Civil Signal Monitoring—Advancing Toward Implementation,” Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 3363–3372. Proposed Amendments to Annex 10: Ground-Based Augmentation System (GBAS) Provisions, Working Paper 3, Third Meeting of the Navigation Systems Panel (NSP), Montreal, 28 November–9 December 2016. Minimum Operational Performance Standards for GPS Local Area Augmentation System Airborne Equipment, RTCA DO-253D, Washington, DC, 13 July 2017. Specification for Non-Federal Navigation Facilities, Category I, Local Area Augmentation System Ground Facility, US DOT, FAA, Washington, DC, 29 September 2009. Houston, T., Liu, F., and Brenner, M., “Real-Time Detection of Cross-Correlation for a Precision Approach Ground Based Augmentation System,” Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 3012–3025. Zhu, Z. and Van Graas, F., “Implications of C/A Code Cross Correlation on GPS and GBAS,” Proceedings of IEEE/ION PLANS 2014, Monterey, CA, May 2014, pp. 282–293. 2017 Federal Radionavigation Plan, Published by Department of Defense, Department of Homeland Security, and Department of Transportation, DOT-VNTSCOST-R-15-01, 2017. Edgar, C., Goldstein, D.B., and Bentley, P., “Current Constellation GPS Satellite Ground Received Signal Power Measurements,” Proceedings of the 2002 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2002, pp. 948–954. Spilker, J. Jr., Digital Communications by Satellite, PrenticeHall, Inc., 1977. Gill, W., “A Comparison of binary delay-lock tracking-loop implementations,” IEEE Transactions, Vol. AES-2, Issue 4, July 1966, pp. 415–424. Van Dierendonck, A.J., GPS Receivers, in Global Positioning System: Theory and Applications, Vol. 1 (eds. Bradford W. Parkinson and James J. Spilker, Jr.), Washington, DC: American Institute of Aeronautics and Astronautics, 1996, pp. 329–407.

229

230

10 GNSS Signal Quality Monitoring

30 Spilker, J. Jr., “GPS signal structure and performance

31

32

33

34

35

36

37

38

39

40

characteristics,” Navigation, Journal of The Institute of Navigation, Vol. 25, No. 2, Summer 1978, pp. 121–146. Van Dierendonck, A.J., Erlandson, R., McGraw, G., and Coker, R., “Determination of C/A Code Self-Interference Using Cross-Correlation Simulations and Receiver Bench Tests,” Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 630–642. Zhu, Z. and Van Graas, F. “Effects of Cross Correlation on High Performance C/A Code Tracking,” Proceedings of the 2005 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2005, pp. 1053–1061. Van Nee, R.D.J., “GPS Multipath and Satellite Interference,” Proceedings of the 48th Annual Meeting of The Institute of Navigation (1992), Dayton, OH, June 1992, pp. 167–178. Balaei, A.T. and Akos, D.M., “Cross correlation impacts and observations for GNSS receivers,” Navigation, Journal of the Institute of Navigation, Vol. 58, No. 4, Winter 2011, pp. 323–333. Margaria, D., Savasta, S., Dovis, F., and Motella, B., “Code Cross-Correlation Impact on the Interference Vulnerability of Galileo E1 OS and GPS L1C Signals,” Proceedings of the 2010 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2010, pp. 941–951. Van Dierendonck, A.J., Kalyanaraman, S., Hegarty, C. J., and Shallberg, K., “A More Accurate Evaluation of GPS C/A Code Self-Interference Considering Critical Satellites,” Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 671–680. Hegarty, C. J., “A Simple Model for C/A-Code SelfInterference,” Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 3484–3494. Thoelert, S., Hauschild, A., Steigenberger, P., and Langley, R.B., “GPS IIR-M L1 Transmit Power Redistribution: Analysis of GNSS Receiver and High-Gain Antenna Data,” Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 1589–1602. Zhu, Z. and van Graas, F., “C/A Code Cross Correlation Error with Carrier Smoothing—the Choice of Time Constant: 30 s vs. 100 s,” Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 464–472. Kelly, J.M., Braasch M.S., and DiBenedetto M.F., “Characterization of the effects of high multipath phase rates in GPS,” GPS Solutions, Vol. 7, No. 1, pp. 5–15, 2003.

41 Vary, N., “DR#110: PRN4 Carrier Phase Anomalies Cause

42

43 44

45

46

47

48

49

50

WAAS SV Alerts,” WAAS Technical Memorandum, Federal Aviation Administration WJHTC, Atlantic City International Airport, NJ, 17 October 2012. WAAS Discrepancy Reports can be found at: http://www.nstb.tc. faa.gov/DisplayDiscrepancyReport.htm Kashyap, R., Ugazio, S., and Van Graas, F., “Characterization of GPS Satellite Anomalies for SVN 63 (PRN 1) Using a Dish Antenna,” Proceedings of the ION 2017 Pacific PNT Meeting, Honolulu, Hawaii, May 2017, pp. 167–182. Shao, J., Mathematical Statistics, 2nd Ed., Springer Science and Business Media, LLC, 2003. Brenner, M. and Liu, F., “Ranging Source Fault Detection Performance for Category III GBAS,” Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, September 2010, pp. 2618–2632. Simili, D.V. and Pervan, B., “Code-Carrier Divergence Monitoring for the GPS Local Area Augmentation System,” Proceedings of IEEE/ION PLANS 2006, San Diego, CA, April 2006, pp. 483–493. Edgar, C., Czopek, F., and Barker, B., “A Co-operative Anomaly Resolution on PRN-19,” Proceedings of the 12th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1999), Nashville, TN, September 1999, pp. 2269–2268. Brenner, M., Liu, F., Class, K., Reuter, R., and Enge, P., “Natural Signal Deformations Observed in New Satellites and their Impact on GBAS,” Proceedings of the 22nd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009, pp. 1100–1111. Gunawardena, S. and van Graas, F., “High Fidelity Chip Shape Analysis of GNSS Signals using a Wideband Software Receiver,” Proceedings of the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 874–883. Gunawardena, S. and van Graas, F., “An Empirical Model for Computing GPS SPS Pseudorange Natural Biases Based on High Fidelity Measurements from a Software Receiver,” Proceedings of the 26th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1341–1358. Wireman, M., Gunawardena, S., and Carroll, M., “HighFidelity Signal Deformation Analysis of the Live Sky GLONASS Constellation using Chip Shape Processing,” Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 521–535.

References

51 Gunawardena, S., Carroll, M., Raquet, J., and van Graas, F.,

55 Julien, O., Selmi, I., Pagot, J.-B., Samson, J., and Fernandez,

“High-Fidelity Signal Deformation Analysis of Live Sky Galileo E1 Signals using a ChipShape Software GNSS Receiver,” Proceedings of the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, September 2015, pp. 3325–3334. 52 Amendment No. 89 to Annex 10 Part 1 Edition No. 6, International Civil Aviation Organization (ICAO), Montreal, CA, 14 July 2014. 53 Shallberg, K.W., Ericson, S.D., Phelts, E., Walter, T., Kovach, K., and Altshuler, E., “Catalog and Description of GPS and WAAS L1 C/A Signal Deformation Events,” Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 508–520. 54 Phelts, R.E., Shallberg, K., Walter, T., and Enge, P., “WAAS Signal Deformation Monitor Performance: Beyond the ICAO Threat Model,” Proceedings of the ION 2017 Pacific PNT Meeting, Honolulu, Hawaii, May 2017, pp. 713–724.

F. A., “Extension of EWF Threat Model and Associated SQM,” Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 492–507. 56 Phelts, R.E., Walter, T., and Enge, P., “Toward Real-Time SQM for WAAS: Improved Detection Techniques,” Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/ GNSS 2003), Portland, OR, September 2003, pp. 2739–2749. 57 Phelts, R.E., Altshuler, E., Walter, T., and Enge, P., “Validating Nominal Bias Error Limits Using 4 years of WAAS Signal Quality Monitoring Data,” Proceedings of the ION 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 2015, pp. 956–963. 58 Liu, F., Brenner, M., and Tang, C.Y., “Signal Deformation Monitoring Scheme Implemented in a Prototype Local Area Augmentation System Ground Installation,” Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), Fort Worth, TX, September 2006, pp. 367–380.

231

233

11 GNSS Orbit Determination and Time Synchronization Oliver Montenbruck and Peter Steigenberger German Aerospace Center, Germany

All navigation satellite systems in use today build on the measurement of pseudodistances to compute a user position. These reflect the time difference between signal transmission at the satellite and signal reception at the user, but are based on two clocks that are imperfectly synchronized to each other or to a global system time scale. Accordingly, both the satellite position and the satellite clock offset must be accurately known to compute a user position in a global or regional navigation satellite system (GNSS/RNSS). This chapter discusses the generation of precise orbit and clock information using ground- or space-based observations. Evidently, orbit determination and time synchronization (ODTS) is an integral part of the control system of any GNSS/RNSS provider, where the motion of the satellites and the variation of their clock must be continuously observed, predicted‚ and distributed to the user as part of the navigation message. Similarly, a variety of scientific institutions, such as the International GNSS Service (IGS; [1]), routinely determine precise GNSS satellite orbits and clock offsets. These GNSS products provide the basis for precise point positioning (PPP) applications in engineering, surveying, and geodesy. As a by-product, the precise orbit determination (POD) process delivers information on Earth rotation and the terrestrial reference frame, as well as the state of Earth’s atmosphere. While precise GNSS products have typically shown latencies of days or weeks, an increasing interest in real-time applications has resulted in various real-time correction services that generate and distribute orbit and clock information to their users in a nearinstantaneous manner. Both orbit and clock determination require a suitable tracking network offering an ideally global and continuous coverage (Figure 11.1). This may range from a dozen of highly secure sensor stations in the GNSS control segment to networks with hundreds of stations supporting geodetic and high-performance real-time applications. Ideally, those networks support tracking of more than one constellation

at a time and can thus be used for multi-GNSS applications. For increased autonomy and to cope with territorial constraints in the choice of control segment locations, various GNSSs make use of additional inter-satellite links (ISLs; [2, 3]) to obtain ranging measurements between individual satellites. Finally, satellite laser ranging (SLR; [4]) measurements may be used to augment the radiometric tracking or to validate the POD performance. Despite the great variety in tools and processes utilized today for generation of precise orbit and clock information, the individual systems build on a largely common set of core concepts and models that are presented in this chapter. Other than initial orbit determination methods [5] that seek to find the orbital elements of an unknown space object from a minimum set of observations, the orbit determination of GNSS satellites is essentially an estimation problem. Approximate information on the orbital motion is typically available‚ and the key goal of the ODTS process is thus to improve knowledge of the a priori orbit (and clock) based on new observations. This requires a proper understanding of the measurement process and an observation model that describes the measurements as a function of the transmitter and receiver location as well as other parameters of interest. The models used for ODTS must be consistent with the models employed subsequently by users of the orbit and clock products and vary in complexity depending on the application. For state-of-the-art precise orbit and clock determination, the measurements models agree with those of PPP users aiming at millimeter- to centimeter-level positioning [6]. An overview of these models is given in Section 11.1. A second building block is provided by dynamical models for the orbital motion of the GNSS satellite that are discussed in Section 11.2. Such models are obviously needed to predict the satellite position ahead of time when disseminating broadcast ephemeris data to the navigation user. However, they also form an integral part of the orbit

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

234

11 GNSS Orbit Determination and Time Synchronization

Figure 11.1 Orbit and clock determination of global navigation satellite systems is mainly based on one-way GNSS measurements (red) from a global station network connected to stable atomic clocks as a primary time reference. Complementary observation techniques may include inter-satellite links (blue) or ground-based satellite laser ranging (green). Composite based on images of NASA (Earth, SLR station), ESA/Pierre Carril (GNSS Satellites) and the authors (GNSS stations).

determination process, where they are used to describe the satellite positions at all observation epochs with a minimum set of independent parameters. Even though GNSS satellite positions can also be recovered on an epochper-epoch basis using a “reverse PPP,” dynamic orbit determination is generally more robust and accurate. The use of purely kinematic orbit determination methods is therefore limited to characterizing the GNSS satellite motion during selected phases with improperly known behavior [7]. Estimation methods constitute the third building block of the ODTS process. They are used to obtain optimal corrections of an a priori model and state parameters from the difference between observed and modeled measurements. A variety of different techniques have been developed for this purpose that can largely be divided into batch and sequential estimation methods, and are employed in offline and real-time applications, respectively. Key aspects of these methods in the context of orbit and clock determination are presented in Section 11.3. Finally, Section 11.4 provides an overview of representative ODTS systems and the various types of GNSS orbit and clock products made available to users in postprocessing or real time. It also discusses strategies for validating the precision and accuracy of these products as a contribution to GNSS performance monitoring and product quality control.

11.1

Observation Models

11.1.1

Pseudorange and Carrier Phase

The ODTS process of GNSS satellites is usually based on dual-frequency pseudorange and carrier-phase observations of ground-based tracking stations. Even though three or even four frequencies are nowadays supported by various new-generation and modernized GNSSs, processing techniques that make joint use of more than two frequencies are only gradually evolving. The basic pseudorange observation equation for observations of satellite S by receiver R reads as PSR = ρSR + c

Δt R − Δt S + bR,P + bS,P + Δρion + δρx,P 11 1

with the geometric distance between receiver and satellite ρSR , receiver and satellite clock corrections ΔtR and ΔtS, receiver and satellite code biases bR,P and bS,P, the firstorder ionospheric delay Δρion, and the vacuum speed of light c. δρx,P summarizes station displacements, antenna eccentricities, receiver and satellite antenna phase center offsets and variations, tropospheric and higher-order ionospheric delays, and relativistic effects that will be discussed below, as well as measurement errors. Major differences between the pseudorange and carrierphase observation equations are the sign of the ionospheric

11.1 Observation Models

correction as well as the presence of an integer ambiguity term nSR and the phase wind-up correction δnSR : LSR = ρSR + c

Δt R − Δt S + bR,L + bS,L

− Δρion + λ

nSR + δnSR + δρx,L

11 2

with the receiver and satellite phase biases bR,L and bS,L and the wavelength λ. For GLONASS, additional interfrequency biases (IFBs) have to be considered due to the different transmission frequencies of the frequency-division multiple-access (FDMA) approach used by GLONASS [8, 9]. If observations of different GNSSs are processed simultaneously, additional inter-system biases (ISBs) have to be taken into account [10]. State-of-the-art GNSS receivers provide a pseudorange measurement precision of about 10 cm. The carrier-phase measurement noise is typically around 1–2 mm. Linear combinations of pseudorange and/or phase observations of different frequencies i and j can reduce or eliminate certain parts of the observation equation. The basic form of dual-frequency pseudorange (PC) and carrierphase linear combinations (LC) is given by PCi,j = κi Pi + κ j P j ,

LCi,j = κ i Li + κ j L j 11 3

The most important linear combination is the “ionosphere-free” linear combination, which eliminates the dominating contributions of the ionospheric path delay Δρion and is further discussed later in this section. The Melbourne–Wübbena linear combination is another important combination, which is formed from pseudorange and carrier-phase observations [11, 12] on two frequencies. It is both geometry- and ionosphere-free and is particularly well suited for ambiguity resolution even on very long baselines. By forming differences between observations of different stations and/or satellites, dedicated terms of Eqs. (11.1) and (11.2) can be eliminated: single differences between two stations remove the satellite clock correction and the satellite biases, single differences between two satellites remove the receiver clock correction and the receiver biases. Double differences between two stations and two satellites remove both the clock offsets and biases for receivers and satellites. Among other factors, this is of interest to avoid a large number of estimation parameters when determining only precise satellite orbits (but no clock offsets) from pseudorange and carrier-phase observations. Finally, triple differences between subsequent observation epochs eliminate the ambiguity term if no cycle slip occurs and can therefore be used for cycle slip detection.

11.1.2

Inter-Satellite Links

Next to pseudorange and carrier-phase observations from a terrestrial network, ISLs can be used to measure distances between pairs of GNSS satellites for ODTS purposes [13]. ISLs may operate in the microwave or optical frequency range and mostly provide “dual one-way” measurements, in which each of the two spacecraft measures the transmit time of a signal emitted by the other spacecraft. Even though the two measurements are obtained consecutively rather than concurrently in present ISL implementations and concepts, they can be corrected to refer to a common epoch using a coarse a priori orbit and clock information [3]. As GNSS satellites are operated well above the atmosphere, the respective delays are not relevant for ISLs. The simplified observation equation for satellites S1 and S2 thus reads as I SS21 + I SS12 = 2 ρSS21 + c btS1 + brS1 + c btS2 + brS2 + ΔρSS21 + ΔρSS12

11 4

with the receive and transmit biases br and bt and correction terms for phase center offsets and relativistic effects Δρ. Optical ISL measurements of the latest GLONASS-M satellites have a precision of about 3 cm [14, 15] whereas BeiDou uses Ka-band ISLs with a precision of 8 cm [3]. ISLs are frequently suggested as a means for autonomous orbit determination of GNSS constellations [2, 16, 17], but are only able to determine the inner geometry of the satellites with respect to each other. Therefore, at least one ground-based monitor station is necessary to provide a link to the Earth-fixed reference frame. However, as ISLs can also be used for communication purposes, the size of the expensive ground network can be significantly reduced.

11.1.3

Satellite Laser Ranging

Except for GPS, all modern GNSS satellites are equipped with a laser retroreflector array. This enables SLR from dedicated observatories such as the stations of the International Laser Ranging Service (ILRS; [18]). SLR is a two-way ranging technique that measures the travel time of short laser pulses [19]. It can be used for validation of GNSS orbits determined from microwave observations [20] or provide additional observations for a combined adjustment [21]. The SLR observation equation for telescope T observing satellite S reads as Δt ST =

2 S 1 ρ + Δρatm + Δρrel + Δρsys c T c

11 5

with the measured turn-around light travel time Δt ST, geometric distance between telescope and satellite at the time

235

236

11 GNSS Orbit Determination and Time Synchronization

of reflection at the satellite ρST , atmospheric delay Δρatm, relativistic correction Δρrel, and signal delays in the laser system Δρsys. Within the ILRS, individual SLR range measurements are averaged over a time interval of nominally 5 min for GNSS satellites. These resulting normal points reduce the amount of data and the individual noise level. They exhibit a precision of one to a few millimeters‚ whereas the accuracy is at the 1 cm level for GNSS satellites.

11.1.4

Reference Systems and Frames

Reference systems and their realizations, the reference frames, provide the metrological basis for modeling GNSS observations. Satellite orbits are usually modeled in an inertial reference frame‚ whereas the coordinates of the tracking stations are referred to an Earth-fixed Earth-centered reference frame. The transformation between these frames will be discussed in the following subsection. The International Celestial Reference System (ICRS) is an inertial system whose origin is the barycenter of the solar system. The International Celestial Reference Frame (currently ICRF3; [22]) is the realization of the ICRS by Very Long Baseline Interferometry (VLBI; [23]) observations of extraterrestrial radio sources (quasars). The orientation of the ICRF is realized by a subset of so-called defining sources. For GNSS applications, a Geocentric Celestial Reference Frame (GCRF) is usually employed that has the same orientation as the ICRF, but refers to a different origin. The International Terrestrial Reference System (ITRS) is geocentric, its scale is defined by the SI meter, and its orientation by the 1984 reference meridian of the Bureau International de l’Heure (BIH) [24]. The latest realization of the ITRS is the International Terrestrial Reference Frame 2014 (ITRF2014; [25]). GNSS providers use their own terrestrial reference systems and frames for their broadcast ephemeris products [26]. Currently employed versions include the World Geodetic System 1984 (WGS84) for GPS, PZ90.11 for GLONASS, the Galileo Terrestrial Reference Frame (GTRF), and the BeiDou Coordinate System (BDCS) for BeiDou. All these frames are aligned to the ITRF at the decimeter level or better. This constitutes a negligible contribution of the broadcast ephemeris error budget and facilitates mixed-constellation positioning in GNSS receivers with no need to consider reference frame transformations between individual systems. For the generation of precise multi-GNSS products within the IGS, orbits of all constellations are generated in a common IGS-specific reference frame (currently IGS14; [27]), derived from the ITRF.

11.1.5

Earth’s Rotation

Like a gyroscope subject to external torques, Earth rotates about an axis that is not constant but varies slowly over time. Tidal friction, deformations of Earth, and mass distributions of the ocean and atmosphere furthermore complicate modeling and prediction of Earth’s changing orientation in space [28]. The transformation between the ICRF and the ITRF is described by the precession and nutation angles, Earth rotation angle (which relates to Universal Time 1, UT1), and the location of Earth’s rotation axis relative to the figure of Earth (pole coordinates). Nutation and precession are primarily caused by tidal torques of the Sun and Moon. Whereas precession has a main period of 25 850 years, the dominant term of nutation has a period of 18.6 years. In addition, nutation involves numerous smaller terms with periods down to a few days. The latest precession-nutation model of the International Astronomical Union (IAU2006/2000A) is described in [24]. Celestial pole offsets (CPOs) represent corrections to the precession-nutation model to account for unmodeled effects, for example, free core nutation. Earth Orientation Parameters (EOPs) comprise the CPOs, ΔUT1 = UT1–UTC, and the pole coordinates. Whereas GNSS observations are sensitive to polar motion, they are unable to measure CPOs and ΔUT1 due to correlations with the orbital elements [29]. Only CPO rates and changes in ΔUT1 (length of day, LOD) are observable with GNSS, whereas CPOs and ΔUT1 themselves can only be measured by VLBI. Combined EOP products as well as EOP predictions are provided by the International Earth Rotation and Reference Systems Service (IERS), for example, Bulletin A [30] and the C04 series [31]. As these series only include daily estimates, sub-daily variations have to be modeled according to [24]. As an example, pole coordinates and LOD estimated from GNSS observations are shown in Figure 11.2.

11.1.6

Spacecraft Attitude

Modeling of the antenna phase center location relative to the spacecraft center of mass as well as modeling of the phase wind-up effect within the ODTS process require proper knowledge of the satellite’s orientation in space. Since measured attitude information is rarely available for this purpose, models of the nominal orientations are widely employed as an alternative. The attitude of a GNSS satellite has to fulfill two basic conditions: the transmit antenna has to point toward the center of Earth to maximize the signal power received by users around the globe, and the solar panels have to be oriented toward the Sun to maximize the available electrical power. To jointly fulfill

11.1 Observation Models 2.5

0.6

2 LOD [ms/d]

Y−Pole [as]

0.5 0.4 0.3 0.2 0.1

1.5 1 0.5 0

−0.1

0

0.1 0.2 X−Pole [as]

0.3

−0.5 2013

2014

2015

2016

2017

2018

Figure 11.2 Pole coordinates (left) and length of day (right) derived from GNSS observations. Whereas polar motion is dominated by the Chandler wobble with a period of about 430 days, annual, semi-annual, four-weekly, and fortnightly variations are visible for length of day (LOD).

these conditions, the satellite has to rotate around its Earthpointing (yaw) body axis to keep the solar panel axis perpendicular to the Sun–spacecraft–Earth plane‚ and the solar panels have to rotate around their axis to face the Sun. This nominal yaw steering is employed by most GNSS satellites [32] and can be used to compute the orientation of the spacecraft body axes for a known position of the Sun and satellite relative to Earth. Exceptions to the nominal yaw-steering apply only for specific periods of the year, that is, the eclipse season, when the elevation of the Sun above the orbital plane is close to zero. Near orbit noon and midnight, the Sun and Earth direction are almost collinear in this period‚ and large yaw slews need to be performed in a very short time to maintain the nominal yaw-steering attitude. The resulting yaw rates can exceed the maximum yaw rates supported by the satellite, and a different yaw-steering strategy thus needs to be used. As the attitude control system design and the preferred strategies for yaw angle control in this time period differ widely, dedicated attitude models have been developed for individual constellations and types of satellites (see, e.g. [33] for GLONASS-M). In some cases, relevant models have also been disclosed by the system providers [34, 35], which greatly benefits precise orbit and clock determination within the scientific community.

11.1.7

Station Location

Station positions are either fixed or estimated in the ODTS process. In both cases, a priori station coordinates are needed that account for long-term motion due to plate tectonics, nonlinear motions, and periodic variations. The linear model for station positions consists of a threedimensional set of Cartesian coordinates at a dedicated reference epoch and a velocity vector. As post-seismic deformations cannot be modeled accurately with this simple

model, additional logarithmic and exponential terms can be used to model the nonlinear motion of stations affected by earthquakes [25]. In addition to these long-term motions, the station location is affected by a variety of geophysical processes with annual to sub-daily periods as well as aperiodic effects. State-of-the-art correction models for these are given in the conventions of the IERS [24]. Solid Earth tides are caused by third-body accelerations of Sun and Moon acting on Earth’s surface resulting in deformations of up to 40 cm. The variations in water mass due to ocean tides cause a varying force acting on Earth’s surface resulting in deformations that are most pronounced for coastal regions. This ocean tide loading can reach up to 10 cm in the height component. The amplitude and phase of these periodic variations obtained from different ocean tide models can be computed by the ocean tide loading provider of Chalmers University of Technology [36]. Non-tidal ocean loading is caused by variations in water mass due to, for example, storms, and may result in station position changes with a magnitude of up to 1.5 cm [37]. Changes of Earth’s rotation axis with respect to the surface of Earth are the origin of the pole tide with an amplitude of up to 2.5 cm in the radial direction. The centrifugal force of polar motion has also an impact on the oceans. This ocean pole tide causes deformations of up to 2 mm. Atmospheric tidal loading is caused by daily variations in atmospheric temperature. These cause pressure variations at primarily diurnal and semi-diurnal time scales with a maximum effect of 1.5 mm. Non-periodic variations in the atmospheric masses induce atmospheric pressure loading that is most pronounced for continental sites and can reach up to 2 cm [38]. Correction models for solid Earth tides, ocean tidal loading, and pole tide are applied in the ODTS process resulting in station coordinates, orbit, and clock products free of the

237

238

11 GNSS Orbit Determination and Time Synchronization

periodic part of these effects. As the permanent deformation due to tides is also removed from the station coordinates, these are given in a so-called tide-free system. Users of these products have to apply the same corrections in their own analysis in order to be consistent. However, non-tidal ocean loading and atmospheric pressure loading are usually not considered in the ODTS nowadays‚ and the signatures of these effects remain in the estimated parameters although their amplitude might be damped [39].

11.1.8

Antenna Models

The position of the GNSS satellites is usually referred to the center of mass (CoM) of the spacecraft‚ whereas the position of a ground station refers to a fixed marker. However, GNSS observations correspond to the actual phase centers of the transmit and receive antennas. The antenna phase center offset (PCO) represents the vector between the CoM and the mean antenna phase center for the transmit antennas. For the receiver antennas, a mechanically welldefined antenna reference point (ARP) is used instead of the CoM. The offset vector between the ground marker and the receiver ARP is described by the antenna eccentricity, which usually consists of only a height component. Deviations from a spherical wavefront are modeled by azimuth- and zenith-/nadir-angle-dependent antenna phase center variations (PCVs). PCOs and PCVs are either obtained by calibrations on ground [40] or estimated as additional parameters in global GNSS solutions [41]. Frequency-specific satellite and receiver antenna PCOs and PCVs are provided by the IGS in the antenna exchange format (ANTEX). The latest model consistent with ITRF2014 is called igs14.atx [27]. Also, direction-dependent group delay variations (GDVs) have to be considered for pseudorange observations. These are particularly pronounced for the BeiDou-2 transmit antennas [42], but are also significant for GPS transmit antennas and various receive antennas [43, 44].

11.1.9

Atmospheric Delays

GNSS signals are delayed by the atmosphere on their way from the satellite to the receiver. In view of their different properties, contributions due to the ionosphere and the neutral atmosphere are distinguished in the observation modeling. The ionosphere extends over a height range of about 50–1000 km and consists of a plasma of free ions and electrons. The neutral atmosphere, in contrast, which includes the troposphere in the lowermost regions (0–10 km height) and the subsequent stratosphere, is free of charged particles. The ionosphere represents a dispersive medium, in which the range delays vary roughly with the inverse

square of the signal frequency. Code- and phase-based measurements of signals passing through the ionosphere experience changes of roughly the same size but opposite sign, and the total delay is proportional to the integral of the electron density along the signal path [45]. The dispersive character of the ionosphere can be utilized to eliminate the firstorder ionospheric delay by forming an “ionosphere-free” linear combination of dual-frequency observations, which is given by LCi,j =

1 f 2i − f 2j

f 2i Li − f 2j L j

11 6

for carrier-phase measurements Li and Lj and a corresponding expression for the respective pseudoranges. The firstorder term of the ionospheric delay has an order of magnitude of up to 30 m in the zenith direction. Higher-order ionospheric terms can reach up to 2 cm. Correction models for these effects are given in [46]. The tropospheric delay [47] does not depend on signal frequency and is, furthermore, identical for code and phase measurements. It can be separated into a hydrostatic and a wet part. The hydrostatic part depends primarily on the air pressure and is typically 2.3 m in the zenith direction at sea level. The wet part depends on the humidity and varies between 0 and 40 cm in the zenith direction. [48] gives a simple model to compute the tropospheric delay from temperature, atmospheric pressure, and water vapor pressure. Input data for this model can be obtained from meteorological measurements, the empirical Global Pressure and Temperature (GPT) model [49–51], or numerical weather prediction (NWP) models. Figure 11.3 shows the zenith hydrostatic delay for a GNSS station in Tsukuba (Japan) obtained from a NWP. As the wet delay is difficult to model due to rapid variations, zenith wet delays (ZWDs) are usually estimated in precise applications. In addition to shortterm variations of up to 20 cm, the estimated ZWD for Tsukuba shows a pronounced seasonal variation with a minimum in the dry winter and a maximum in the humid summer. The estimated or modeled delays refer to the zenith direction‚ but observations are obtained at different elevation angles. A mapping function describes the relation between the delay in zenith direction and for a dedicated zenith distance z. Slightly different mapping functions fh(z) and fw(z) are used for the hydrostatic and wet delay. Commonly used mapping functions include the empirical Global Mapping Function (GMF; [52]) and different versions of the Vienna Mapping Function (VMF; [51, 53]) based on NWP data. Asymmetries in the tropospheric delay depending on the azimuth A can be considered by modeling or estimating troposphere gradients [54]. The total tropospheric delay composed of hydrostatic, wet, and gradient delay reads as

11.2 Orbital Dynamics

Jan

Apr

Jul

Oct

N/S gradient [mm]

230

225

2

40 Zenith Wet Delay [cm]

Zenith Hydr. Delay [cm]

235

30 20 10 0

Jan

Apr

Jul

Oct

1 0 −1 −2

Jan

Apr

Jul

Oct

Figure 11.3 Tropospheric parameters for the IGS station TSKB in Tsukuba, Japan: (left) zenith hydrostatic delays from a numerical weather model; (middle) zenith wet delays (ZWDs) estimated from GNSS observations; (right) north/south troposphere gradients estimated from GNSS observations; the solid line represents an annual and semi-annual fit.

Δρtrp z, A = f h z + fg z

Δρh + f w z

Δρw

Δρn cos A + f g z

Δρe sin A 11 7

with the gradient mapping function fg(z) [55], the north/ south gradient Δρn, and the east/west gradient Δρe. Daily north/south gradient estimates of a station with a pronounced annual variation are shown in the right subplot of Figure 11.3.

offset in the clock’s proper time scale. The average part is compensated by shifting the transmit frequency by a constant offset of, for example, −4.4647 10−10 Hz for GPS [57]. As GNSS orbits are not perfectly circular, a periodic term also arises. This effect depends on the eccentricity, the semi-major axis, and the eccentric anomaly of the satellite. It can reach up to 14 m for GPS satellites.

11.2 11.1.10

Phase Wind-Up

GNSS phase observations are based on right-hand circularly polarized electromagnetic waves. As a result of the circular polarization, the carrier-phase of the received signal changes by one wavelength per full rotation of the receive and transmit antenna with respect to each other. For a static reference station antenna, orientation changes originate from rotations of the satellite around its yaw axis to maintain the nominal attitude as well as changes of the line of sight due to the relative motion of the satellite with respect to the receiver. For common satellites, phase windup effects are typically limited to one wavelength and affect mainly the satellite clock offset. Differential phase wind-up effects between two stations can reach up to several centimeters for intercontinental baselines [56].

11.1.11

Orbital Dynamics

Relativistic Signal Propagation Effects

The gravity field of Earth affects the propagation time of GNSS signals traveling from the satellite to the receiver. This general-relativistic effect is called the Shapiro effect and causes a propagation delay of up to 2 cm. As clocks onboard GNSS satellites have different height and velocity with respect to the receiver clock, additional relativistic corrections have to be considered to express the observed clock

A satellite orbiting Earth is subject to the gravitational attraction of Earth as well as a variety of other perturbations. The total acceleration a acting on the satellite can be described through suitable physical models and depends •

on the satellite’s position r, its velocity r = v, and time t. From a mathematical point of view, the propagation of a satellite orbit thus represents an initial value problem, which is solved by numerical integration of the second••

•

order differential equation r = a r, r , t for given initial values. As a rule of thumb, dynamical models for GNSS satellites aim to describe the acceleration at a level of better than 0.1 nm/s2, which is roughly twelve orders of magnitude smaller than the acceleration experienced by a body on the surface of the Earth. While this accuracy is well within reach of current models for the gravitational forces, the description of non-gravitational surface forces often suffers from the lacking knowledge of relevant spacecraft properties. To bridge this gap, empirical models may be employed, in which the parameters of a generic model are adjusted to the observations. Within this section, the most important constituents of the dynamical model for orbit prediction and determination of GNSS satellites are described along with an overview of relevant numerical integration techniques.

239

240

11 GNSS Orbit Determination and Time Synchronization

11.2.1

Gravitational Forces

11.2.1.1

a3rd-body = GM

Earth’s Gravity

Earth’s gravitational attraction is mainly directed toward the center of Earth‚ and the acceleration varies between 0.6 m/s2 at the altitude of a GPS satellite and 0.2 m/s2 at a geosynchronous altitude. In view of Earth’s extended size and slightly irregular mass distribution, a spherical harmonics expansion is used to describe the geopotential U =

GM r

∞

n

Rn Pn,m sin ϕ rn n=0m=0

11 8

Cn,m cos mλ + Sn,m sin mλ at geocentric distance r, latitude ϕ, and longitude λ, and the associated acceleration is given by the gradient agrav = ∇U . Here GM denotes Earth’s gravitational coefficient (i.e. the product of the gravitational constant and Earth’s mass), while Cn,m and Sn,m are the model-specific normalized gravity field coefficients. Various forms of recurrence relations are available in the literature to evaluate the trigonometric functions and the normalized associated Legendre polynomials Pn,m in a numerically stable manner. Among these, the recurrence relations of Cunningham [58] are particularly well suited when working with Cartesian rather than spherical coordinates. Since contributions of individual gravity field terms to the acceleration decrease with the (n + 2)-nd power of the distance, only a small set of low degree and order coefficients need to be considered in the orbit modeling of representative GNSS satellites. Within the IGS, a 12 × 12 subset of recent GRACE+GOCE(+SLR) gravity field models (e.g., GGM05; [59]) is presently applied by most analysis centers. Beyond the static gravity field, various forms of temporal gravity field variations are taken into account for best accuracy. These include secular changes in the low-order zonal (C2,0, C3,0, C4,0) coefficients and changes in C2,1, S2,1 related to polar motion but also tidal variations of the geopotential caused by solid Earth tides, ocean tides, solid Earth pole tides, and oceanic pole tides. Details of the respective models are described in [24] and references therein.

11.2.1.2

Third-Body Attraction

Next to the dominating gravitational attraction of Earth, the motion of a GNSS satellite is also subject to the perturbing gravitational acceleration of the Sun, Moon, and planets. In view of the much larger distance of these bodies, this acceleration can be adequately described by a pointmass model. Given a body with gravitational coefficient GM at geocentric position s , the perturbing acceleration is given by the difference

s−r s−r

3

−

s s

11 9

3

of the gravitational accelerations exerted by the body on the satellite and Earth itself. Representative values of the third-body perturbation amount to 1.5 μm/s2 and 3 μm/s2 for the Sun and Moon, respectively, while the tidal acceleration due to the dominating planets Venus (0.2 nm/s2 at inferior conjunction) and Jupiter (0.02 nm/s2 at opposition) is at least four to five orders of magnitude smaller. For evaluation of Eq. (11.9), the coordinates of the perturbing body must be known with adequate precision. Must commonly, precomputed solar system ephemerides such as the Development/Lunar Ephemerides (DE/LE; [60, 61]) of the Jet Propulsion Laboratory (JPL) are employed for this purpose. Trajectories of the individual bodies in these ephemerides are represented as Chebyshev polynomials, which enables a fast computation of lunisolar and planetary coordinates at moderate storage requirements.

11.2.1.3

Post-Newtonian Dynamics

Even though Newton’s law of gravity provides an excellent description of the gravitational forces acting on a satellite, the high measurement accuracy available in GNSS today requires a careful consideration of relativistic effects in the equation of motion. Differences between a relativistic and a Newtonian formulation scale roughly with the squared ratio of the satellite’s velocity and the speed of light, that is, (v/c)2 ≈ 10−10. Despite ongoing efforts to describe GNSS orbits and measurements in a fully relativistic framework [62, 63], it is common practice to rather apply a post-Newtonian correction of the acceleration in the equation of motion [24]. For near-circular orbits, the leading Schwarzschild term arel =

GM c2 r 3 +4 r v v

4

GM − v2 r r GM r = const r 2 ≈

r v2 3 r c2

11 10

causes a small reduction of Earth’s central gravitational attraction and an associated change in the relation of orbital period and orbital radius (i.e. Kepler’s third law). When considering the relativistic correction (Eq. (11.10)) within the orbit determination process, the resulting orbital radius is lowered by about 4.5 mm compared to the Newtonian formulation irrespective of the altitude.

11.2 Orbital Dynamics

11.2.2

Non-Gravitational Forces

11.2.2.1

Solar Radiation Pressure

Electromagnetic radiation carries a momentum that is proportional to the transmitted energy. When radiation is absorbed or reflected by a surface, this momentum is transferred to the respective body and causes a subtle radiation pressure [64]. Solar radiation pressure (SRP) is the dominating source of non-gravitational perturbations for GNSS satellites, since the Sun is the most intense source of electromagnetic radiation and since the satellites are equipped with large solar panels for energy production. At the mean Earth–Sun distance of about 150 × 106 km, the solar irradiance amounts to Φ = 1361 W/m2 [65], which results in a pressure of P = 4.5 × 10−6 N/m2 upon complete absorption. An additional momentum transfer occurs, when radiation is reflected or re-transmitted from the surface. Denoting the fractions of absorbed, diffusely, and specularly reflected photons by α, δ, and ρ, the total force experienced by a surface element ΔA is given by ΔF = −

Φ ΔA cos θ c

α+δ e +

2 δen + 2ρ cos θ en 3 11 11

[64], where en is the surface unit normal vector and e is the Sun direction unit vector, while θ = arccos e en denotes the angle enclosed by these vectors; see Figure 11.4. Equation (11.11) provides the basis for computing the total SRP acceleration for a given orientation and size of individual surface elements as well as their optical properties. The most sophisticated SRP models are based on computer-aided design (CAD) models of the satellite and make use of ray tracing techniques to describe the illumination conditions for different incidence angles. In this way, mutual shading of structural elements as well as multiple reflections can be taken into account even for complex spacecraft structures. Early results of ray tracing for SRP modeling of GLONASS and GPS Block IIR satellites have been reported in [66–68], while more recent applications to BeiDou-2 satellites are described in [69, 70].

Incident photons

Incident photons e⨀

en

Reflected photons

To reduce the overall complexity of SRP modeling, boxwing models may be applied instead of a detailed CAD model. Here, the spacecraft structure is approximated by a box-shaped satellite body made up of six rectangular plates and two additional plates representing the solar panels. Optical parameters of the individual plate can be inferred from the material properties or adjusted in the orbit determination process [71]. Box-wing models are currently employed for the Galileo and QZSS satellites [72–74] using either adjusted model parameters or spacecraft metadata released by the system providers [35, 34]. Depending on the size and mass, the SRP acceleration amounts to 50–150 nm/s2 and thus constitutes the biggest source of orbital perturbations for GNSS satellites after the tidal accelerations of the Sun and Moon. Besides the dimensions and surface properties, the attitude and solar panel orientation must be known with good confidence to fully benefit from analytical SRP models. During normal operations, the solar panels can typically be assumed to be Sun pointing, and the satellite body follows a yaw-steering orientation [32]. Deviations from this nominal attitude that may occur near noon, and midnight turns will affect the net acceleration due to radiation pressure and have to be taken into account in the SRP modeling.

11.2.2.2

Thermal Emission

Solar radiation that is absorbed by the spacecraft will result in heating and ultimately be radiated back into space in the form of thermal emission. In particular, this applies for most of the electrical energy generated by the solar panels, which is converted to heat in the onboard equipment. Thermal radiators mounted on the shaded side of the spacecraft are commonly used to emit the excess heat produced inside the spacecraft body and may result in a net force acting on the satellite. Likewise‚ temperature differences between the front and backside of the solar panels contribute to accelerations along the Sun direction. A detailed thermal modeling and knowledge of the spacecraft design are required to properly describe the thermal emission and resulting

Reflected photons

Incident photons

θ ΔA

ΔA ΔF

ΔA ΔF

ΔF

Figure 11.4 Depending on the surface properties, solar radiation pressure generates a force opposite to the Sun’s direction (absorption; left), perpendicular to the surface (specular reflection; center), or a linear combination thereof (diffuse reflection; right).

241

242

11 GNSS Orbit Determination and Time Synchronization

acceleration [68, 75], which is mostly impractical for orbit determination. As a workaround, optical properties of boxwing models may be adjusted to best represent the sum of SRP and thermal emission, or additional empirical accelerations may be taken into account and inferred from observations. 11.2.2.3

Earth Albedo and Infrared Radiation

Besides the direct illumination by the Sun, reflected sunlight from Earth as well as infrared radiation from Earth constitute a second source of radiation pressure. Since the reflectivity (or “albedo”) varies notably across Earth, cloud coverage maps are required for a detailed modeling of Earth radiation pressure (ERP). The total ERP acceleration is obtained by summing contributions from individual grid points over the visible portion of Earth [76]. For each grid point, the irradiance is evaluated based on the local albedo and infrared emissivity as well as the Sun–satellite geometry, and the contribution to the ERP acceleration is evaluated in analogy with Eq. (11.11). The impact of ERP on the orbit modeling of GPS satellites has been assessed in [77] based on Earth albedo and emissivity data from the Clouds and Earth’s Radiant Energy System (CERES; [78]). ERP results in a predominantly radial acceleration that counteracts the gravitational attraction of Earth and causes a 1.5 cm reduction of the orbital radius for GPS Block IIA satellites when considered in the orbit determination process. 11.2.2.4

Antenna Thrust

Aside from reflected Sun light or thermal emission, the transmission of radio signals contributes to a recoil acceleration [64] that is always directed away from Earth. The impact of this “radiation rocket” effect on orbit determination of GPS and GLONASS satellites has early on been discussed in [79], but its proper consideration has long suffered from limited public availability of transmit power information for most GNSS satellites. More recently, such values have been derived in [80] from measurements of received signal power using a calibrated high-gain antenna. Transmit powers vary substantially across the various spacecraft types and range from about 50 W for early generations of GPS and GLONASS satellites to roughly ten times this value for some of the most powerful GNSS satellites at a geosynchronous altitude [34]. Depending on the spacecraft mass and orbit, consideration of antenna thrust in the orbit determination process results in a lowering of the orbital radius by up to 3 cm [80]. 11.2.2.5

Empirical Accelerations

The limited availability of GNSS spacecraft design information for orbit modeling purposes has triggered the use of

purely empirical acceleration as a substitute or complement for a priori models of the non-gravitational forces. Among these, the Extended CODE Orbit Model (ECOM; [81, 82]) and its successor ECOM-2 [83] proposed by the Center for Orbit Determination in Europe (CODE) have gained widespread attention and are routinely applied for POD of all GNSSs in the scientific community. The ECOM models describe the acceleration aD aY

aemp =

=

aB

B0 Ds,n Y s,n

+ n

D0 Y0

Dc,n Y c,n

+ n

sin nu

cos nu

Bc,n 11 12

Bs,n

due to SRP and other contributions through constant and harmonic terms in a DYB-frame aligned with the Sun direction (D), the solar panel axis (Y), and the orthogonal Bdirection. The argument u measures the orbital longitude relative to the ascending node of the orbit on the equator (ECOM) or the projection of the Sun’s direction on the orbital plane (ECOM-2). The individual model coefficients (or a well-observable subset thereof ) are adjusted within the orbit determination process. While a five-parameter model considering only D0, Y0, B0, and the harmonics Bc,1 and Bs,1 has proved to be well suited for use with GPS and GLONASS satellites, higher harmonics were introduced in ECOM-2 to best match the conditions of stretched satellite bodies such as those of Galileo and QZSS [83]. In order to compensate remaining modeling deficiencies, additional empirical accelerations in the radial, alongtrack, and cross-track directions may be estimated in the orbit determination process. These are typically modeled as piecewise constant or piecewise linear parameters. Alternatively, pseudo-stochastic pulses can be estimated that represent instantaneous velocity increments at a limited set of epochs within the observation arc [81].

11.2.2.6

Maneuvers

To maintain a desired constellation geometry under the action of secular perturbing forces or to move satellites to a new orbital slot, GNSS satellites need to conduct orbit correction maneuvers at semi-regular intervals. The maneuver frequency varies with constellation and orbit type and ranges from a few maneuvers over the mission lifetime (Galileo) to semi-annual maneuvers of QZSS and BeiDou satellites in inclined geosynchronous orbits, or even monthly maneuvers of geostationary navigation satellites. In most cases‚ maneuvers can be described through a constant acceleration vector in a reference frame aligned with

11.3 Parameter Adjustment

the radial, along-track, and cross-track direction, or, alternatively, an impulsive velocity increment. Even though GNSS satellites are commonly flagged as “unhealthy” in the vicinity of a maneuver and the outage may be announced ahead of time, the planned time and parameters of a maneuver are only available to the control center and system providers themselves. Incorporation of maneuvers into the orbit determination by external institutions is hampered by the lack of a priori information and commonly results in a lack of ephemeris products for the maneuvering satellite over a full day. Various strategies have therefore been developed by individual analysis centers to infer the occurrence of a maneuver and approximate maneuver times from observations for subsequent consideration and adjustment of the maneuver in the subsequent orbit determination process [84, 85].

11.2.3

Numerical Integration

A wide range of numerical integration methods is available to compute a satellite orbit based on the equation of motion and known initial conditions [5, 86, 87]. Since GNSS orbits are typically near circular, a step-size control is not normally required‚ and a fixed step size can be chosen in accordance with the accuracy requirements. The choice of specific methods depends largely on the application and also on the employed estimation strategy. Multi-step methods maintain a table of derivative values at past epochs based on which the solution at the next step can be predicted. This offers high accuracy at a minimum of

acceleration computations and results in high efficiency. On the other hand, much effort is required in the startup phase, which may become impractical if the integrator needs to be restarted frequently. Such restarts are required at orbital maneuvers, but also other events that mark a discontinuity in the higher derivatives of the equation of motion (e.g. shadow transits [88]). Likewise, multi-step methods appear unsuitable for sequential estimation and orbit determination schemes. Here, the initial conditions for the trajectory propagation change at each measurement. To cope with the need for frequent integrator restarts, single-step methods such as the diverse class of Runge–Kutta methods are preferable in these applications.

11.3

Parameter Adjustment

The dynamical and observation models discussed in the previous sections provide the basis for describing the measurements through a limited set of initial conditions and model parameters. Starting from an initial guess or past estimate, refined values of these parameters may then be obtained in a differential correction process [89]. Despite a variety of different estimation techniques and a smooth transition between the extremes, two fundamental classes may be distinguished (Figure 11.5). In the batch leastsquares process‚ all observations are available prior to the start of the adjustment process and used concurrently to derive a set of parameters which minimizes the difference between modeled and measured values over the entire data

Adjusted Orbit

Least Squares Estimation Measurements zi

Reference Orbit xˆ Correction x0 Initial State Extended Kalman Filter

Measurements zi Measurement + xi Update xi– Propagated Orbit (Time Update)

x0 Initial State

Figure 11.5 Schematic view of orbit determination based on least-squares estimation (top) and extended Kalman filtering (bottom).

243

244

11 GNSS Orbit Determination and Time Synchronization

arc. Least-squares estimation is widely used for orbit and clock determination in IGS analysis centers but also forms the basis of the ODTS process in various GNSS control centers. Sequential estimation schemes, in contrast, enable an “on-the-fly” refinement of the estimated parameters as new observations become available. By their nature, sequential estimation is the method of choice in real-time applications. Examples include the Kalman filter of the GPS mission control center [90] or the filters used for generating real-time orbit and clock estimates in PPP correction services [91–93].

11.3.1

Least-Squares Estimation

Given a set of observations z and a model function h x that depends on a set of parameters x, least-squares estimation aims to find the value that minimizes the weighted norm z − h x Pzz− 1 of the difference between the observations and the model. Within the ODTS process, z typically comprises the pseudorange and carrier-phase measurements collected by the monitoring stations, while x combines the initial conditions of the orbit, satellite and clock offsets, phase ambiguities, and tropospheric zenith delays as well as other unknown parameters of interest. When linearizing the loss function about an approximate value x 0, the leastsquares solution is described by the normal equation H WH x − x 0 = H W z − h x 0 ,

11 13

where H = dh dx denotes the design matrix and where the weighting matrix W = Pz−z1 is set equal to the inverse of the measurement covariance. For zero-mean measurement errors, Eq. (11.13) yields an unbiased estimate x of the true

In the same way, normal equations resulting from multiple data batches i may be combined, to find the least-squares solution −1

i

a a

denote the a priori value of x and its covariance. The corresponding minimum is obtained for x = x 0 + H WH + P x−a x1a + Px−a x1a x − x a

−1

N AA N BA

11 14

11 15

N AB N BB

x A − x A,0 x B − x B,0

=

dA dB

11 16

the solution for x A can formally be expressed as −1 dA − N AB x B − x B,0 x A − x A,0 = N AA

11 17

When substituted into the normal equations, the solution −1 −1 − N BA N AA N AB x B − x B,0 = N BB

−1

−1 dA − N BA N AA dA

11 18 is obtained for the second set of parameters. By eliminating parameters A, the dimension of the normal equations has been reduced from dim x A + dim x B to dim x B at the expense of requiring an inversion of the information matrix N AA This can be accomplished with moderate effort, though, if N AA is a sparse or, ideally, diagonal matrix.

11.3.2 H W z − h x0

di i

with N i = H i W i H i and d = H i W i zi − hi x 0 that corresponds to the joint processing of all data in a common estimation. This “normal equations stacking” offers a convenient way to obtain long-arc parameter estimates in GNSS orbit determination without requiring a continuous orbit modeling over extended periods. By way of example, the results of daily solutions may be combined to estimate site displacements, EOPs, or GNSS transmit antenna offsets over a multi-year time frame. Given the large number of satellites, stations, and epochs concurrently processed in a least-squares ODTS, the normal equations quickly attain a dimension that renders a direct solution (or inversion of the full information matrix) cumbersome, if not impossible. On the other hand, large parts of the information matrix are only sparsely populated. Among others, this is due to the fact that pseudorange and carrier-phase observations at a given epoch do not depend on clock offsets at any other epoch. By suitable arrangement of clock offsets in the estimation vector, the normal equations can therefore be arranged into blocks of diagonal and fully populated matrices. This block structure can then be used to pre-eliminate certain parameters and effectively reduce the size of the final normal equations. Considering, for example, a set of estimation parameters A and B and the associated normal equations

−1

solution with covariance P xx = H WH . The solution of the normal equation and, optionally, the covariance matrix can be obtained through a Cholesky decomposition [94] of the information matrix H WH. Alternatively, various other factorization techniques are available to solve the normal equations in a numerically stable manner. Among others, these include the square root information filter (SRIF; [95]) formulation that has been adopted for the GipsyX GNSS processing and orbit determination software of the JPL [96, 97]. A priori information can be incorporated into the leastsquares estimation by considering the modified loss function z − h x Pzz− 1 + x − x a Px− 1x , where x a and P x−a x1a

Ni

x = x0 +

Sequential Estimation

Other than least-squares estimation, which only provides a solution for the parameters of interest after processing all

11.3 Parameter Adjustment

observations in the entire data arc, sequential estimation schemes provide a new solution after processing of each individual observation (or a small batch of observations). In the most widely applied sequential estimation scheme, the extended Kalman filter (EKF), an estimate of the filter state x i and its covariance P i are maintained, which are recursively updated at each observation epoch ti [89, 98]. This update is performed in two basic steps. In the first part, the time update step, a dynamical model is used to predict the evolution of the state parameters and their covariance from one epoch to the next. Within the subsequent measurement update, the predicted state is “blended” with the observations to obtain an optimal estimate of the current state, taking into account both past and new information. The latter step is essentially equivalent to least-squares estimation using the predicted filter state as a priori information and processing just the observations at the new epoch. However, it does not require solution of the normal equations but makes use of an explicit relation to compute the updated state. Using superscripts − and + to denote values before and after processing of the new observations, the EKF time update equations may be summarized as x i− = x t i ; x t i − 1 = x i+− 1

11 19

P i− = Φi P i+− 1 ΦTi + Qi

while the measurement update equations are given by K i = Pi− H i W i− 1 + H i P i− H i x i+ = x i− + K i zi − hi x i−

−1

11 20

P i+ = 1 − K i H i Pi− The factor K is known as the Kalman gain and maps the difference between observed and modeled measurements to a correction of the estimated state. Φi = dx i dx i − 1 denotes the state transition matrix, that is, the partial derivatives of the propagated state x i− with respect to the initial conditions x i+− 1 . The process noise Q that is added to the propagated covariance accounts for an increase in the state uncertainty over the propagation arc due to deficiencies in the dynamical model. Depending on the parameter of interest, different process noise models (white noise, correlated noise) may be applied. Large amounts of process noise will give the filter a “fading memory” and reduce the impact of past observations on the current estimate, while low process noise will make the filter less receptive to new observations and may result in filter divergence. Proper choice of the size and type of process noise is thus part of the “art” of Kalman filter tuning and is often a matter of experience with the specific nature of the problem at hand. While Eq. (11.20) provides a mathematically correct formulation of the filter update step, it is sensitive to

round-off errors and should therefore be avoided in practice. Alternative formulations such as the Joseph update equation P i+ = 1 − K i H i Pi− 1 − K i H i

+ K i W i− 1 K i , 11 21

or factorization methods that directly update a unit triangular matrix U and a diagonal matrix D of a UDU decomposition of the covariance matrix are therefore recommended to ensure numerical stability of the Kalman filter implementation [95]. When applied to orbit and clock estimation of GNSS satellites, the instantaneous satellite position and velocity as well as the instantaneous satellite and station clock offsets constitute individual elements of the filter state that are propagated between epochs and subsequently updated with the new measurements. Compared to a batch least-squares estimator, the filter provides sequential estimates of the “current” clock parameters rather than simultaneously solving for clock parameters at all individual observation epochs. This allows for a dramatic reduction in the size of the estimation parameter vector and greatly facilitates the filter implementation. On the other hand, the filter’s estimate is only based on past observations‚ and a forward-backward filter/smoother is needed to achieve results compatible with the least-squares process when using the Kalman filter in offline processing. The Kalman filter concept also offers an attractive way to handle estimation parameters that cannot be described by a rigorous dynamical model but rather represent a random process. In many cases, the respective states (or their deviation from the model) can be described by a first-order Gauss–Markov process [98]. The corresponding state parameters exhibit an exponential autocorrelation with time scale τ and a steady-state standard deviation σ [89, 95]. In the time update step of the Kalman filter, the exponentially correlated random variables (ECRVs) are described as xi = exp (−(ti − ti − 1)/τ) xi − 1, and their covariance is incremented by a process noise Q = σ 2 (1 − exp (−2 (ti − ti − 1)/τ)). Among others, ECRV states are useful to describe empirical accelerations in the force model or atmospheric delays in the observation model.

11.3.3

Ambiguity Resolution

As discussed in Section 11.1, GNSS receivers provide both pseudorange and carrier-phase observations. In view of their low measurement noise, use of carrier-phase observations is indispensable for high-precision orbit and clock determination. The carrier-phase ambiguity is an unknown quantity, but is constant during continuous tracking of a GNSS satellite by a station. In the ODTS process, a distinct ambiguity parameter must thus be estimated for each individual tracking arc and satellite-station pair.

245

246

11 GNSS Orbit Determination and Time Synchronization

For further improvement of the accuracy, use can be made of the fact that ambiguities can be partitioned into an integer multiple of the signal wavelength as well as a receiver-dependent fractional part (that is common to all tracked satellites) and a satellite-dependent fractional part (that is common to all receivers in the network). When forming between-satellite and between-receiver double differences, the fractional parts vanish‚ and the resulting double-difference ambiguity is of integer nature. Knowledge of this integer value effectively converts the ambiguous double-difference carrier phases into highly precise doubledifference pseudoranges and results in a notably improved stiffness of the observed satellite-station geometry. Mathematically, the combined adjustment of integervalued ambiguities along with float-valued other parameters represents a “mixed-integer” least-squares problem‚ and various sophisticated techniques have been developed to solve it in an optimal and robust manner [99]. However, due to the large number of ambiguity parameters, simpler strategies are employed in common ODTS software packages that build on a so-called wide-lane/narrow-lane ambiguity concept for use with dual-frequency observations [100]. In a first step, the wide-lane ambiguity, that is, the difference n1 − n2 between ambiguities on the first and second frequencies is determined. It can be obtained through integer rounding from double differences of the Melbourne–Wübbena combination over a sufficiently long data arc. In a second step, a float-valued estimate of the n1 ambiguity can then be computed and fixed to an integer value based on the ionosphere-free carrier-phase ambiguity obtained in the initial ODTS process and the knowledge of the wide-lane ambiguity [101]. Ambiguity fixing for undifferenced data is also possible if fractional wide-lane delays are estimated [102]. When constraining double-difference ambiguities for a globally distributed set of stations and satellites to integer values, representative performance improvements by a factor of two have been achieved by IGS analysis centers in the orbit and clock product generation [103].

11.4

Systems and Products

The models and techniques presented in the previous sections provide a common algorithmic basis for all GNSS orbit and clock determination systems. Over time, a multitude of ODTS tools and systems has evolved, which all make use of these basic concepts, but differ in specific aspects in response to application needs or simply inherited preferences. Within this section, we present a selection of ODTS systems along with their overall architecture and operation. Complementary to this, different classes of orbit

and clock products are compared, and basic strategies for quality control and validation are discussed.

11.4.1

Architecture and Tools

To illustrate the overall architecture of the ODTS process, flowcharts for two representative implementations are shown in Figure 11.6. They describe orbit and clock determination in the GPS Control Segment as well as generation of precise orbit and clock products within the IGS and its analysis centers. 11.4.1.1

GPS Control Segment

The left part of Figure 11.6 describes the (near-)real-time orbit and clock determination process employed in the master control station (MCS) of the United States’ Global Positioning System [90, 104]. It is based on a Kalman filter and processes observations in a sequential manner. The MCS continuously receives raw observations on the L1 and L2 frequency from the five GPS monitoring stations. In a first processing step, ionosphere-free combinations are formed‚ and various initial corrections are applied. Furthermore, the pseudorange observations are smoothed with accumulated delta range (i.e. carrier phase) observations to obtain low-noise normal points at a 15 min sampling. These measurements are then processed in the Kalman filter, which computes a state correction relative to a precomputed reference trajectory at the same update interval. These epoch states are then used to predict the future orbit and clock evolution and to adjust the broadcast ephemeris parameters for the subsequent upload to the satellite. In parallel to the actual ODTS process, a performance monitor is operated, which continuously compares epoch states and broadcast ephemerides, and evaluates observed range residuals, that is, the difference between observed pseudoranges and values modeled from the navigation message. The reference ephemeris that serves as the basis of the differential correction process in the MCS Kalman filter is generated in a separate process. The orbital dynamics model comprises an 8×8 gravity model, luni-solar perturbations, solid Earth tides, and an a priori SRP model, while the evolution of clock states is described through secondorder polynomials in time. EOPs that are required for the transformation of satellite positions into the Earth-fixed reference frame are provided to MCS by the National Geospatial-Intelligence Agency (NGA) on a weekly basis and treated as fixed parameters. Within the filter, corrections of the inertial satellite positions and velocities relative to the reference trajectory as well as two radiation pressure parameters are estimated along with the clock offset, drift, and, optionally, rate of satellite and monitoring station clocks.

11.4 Systems and Products

Raw Observations

Raw Observations

A priori orbits, clocks and EOPs Preprocessing

Reference Ephemeris

Corrector & Smoother

Cleaned Observations Iteration loop

Smoothed Observations Ephemeris & Clock Estimation

Measurement model & partials Trajectory propagation & partials Observation loop Normal equation

Epoch loop Epoch States Upload Navigation Data Generator Performance Monitor

Navigation Message

Solution of normal equation Estimated parameters

Ambiguity fixing

Trajectory propagation

Residuals & Screening

Products

Figure 11.6 Flowchart of the orbit and clock determination process for the legacy operational control system of GPS (left) and a representative IGS analysis center (right).

Since only clock differences but no absolute clock offsets can be observed from pseudorange observations, a single monitoring station was originally selected as a master clock to which all other satellite and station clocks were referred. Later, a “composite clock” concept [105] was implemented that realizes GPS time as a weighted average of all clocks in the space and ground segment to improve the overall accuracy. Still, the exclusive use of one-way (pseudorange and carrier phase) observations implies a tight integration of the satellite clock offset and system time determination with the determination of the satellite orbits in the GPS control system. Despite a different overall architecture, the same applies as well for other constellations such as GLONASS and Galileo. As an exception, BeiDou uses a two-way satellite time and frequency transfer (TWSTFT) technique to synchronize the space and ground clocks [106]. The resulting clock offsets are later combined with independent orbit determination results to generate the broadcast navigation message in this navigation system. 11.4.1.2 IGS Precise Orbit and Clock Product Generation

Complementary to the MCS Kalman filter, the right-hand part of Figure 11.6 illustrates the typical data flow of a least-squares orbit and clock determination process as

employed by IGS analysis centers. Examples of software packages using this or similar concepts include the Bernese GNSS Software [101] maintained by the Astronomical Institute of the University of Bern, the GAMIT-GLOBK software of the Massachusetts Institute of Technology [107], JPL’s GipsyX [97], the NAvigation Package for Earth Orbiting Satellites (NAPEOS; [108]) of the European Space Agency, and the Position and Navigation Data Analysis (PANDA; [109]) software of Wuhan University, China. The IGS processing is typically based on daily files of GNSS observation data collected by a global station network with a representative sampling interval of 30 s. Out of the large number of IGS stations‚ only a subset of typically 80–300 stations is processed, which is selected based on data quality, geographic distribution, availability of high-performance atomic clocks, and co-location with other geodetic measurement techniques. As part of the preprocessing, code and phase observations of the selected stations undergo a screening, which may be purely data driven or employ a priori information on satellite orbits and stations coordinates. Furthermore, cycle slips in the carrierphase observations are identified and – if possible – repaired. In addition, the measurements may also be sorted into passes of continuous tracking and constant carrierphase ambiguity.

247

248

11 GNSS Orbit Determination and Time Synchronization

Starting from a priori state vectors, which commonly result from a previous prediction, the trajectories of all GNSS satellite are propagated to the individual observation epochs. Along with this, the variational equations are integrated to obtain the state vector partials with respect to the a priori state as well as the partials with respect to force model parameters. Based on the measurement model for pseudorange and carrier-phase observations, normal equations can then be formed and solved for the parameters of interest. Among others, float-valued estimates of the individual carrier-phase ambiguities are obtained, which may further be fixed to integer values as part of a dedicated ambiguity resolution step. After correcting the initial values of all state, force, and measurement model parameters, subsequent iterations may be used for further refinement to cope with the nonlinearity of the employed models. 11.4.1.3

Estimation Parameters

Aside from the choice of estimation techniques and process flows, the orbit and clock determination in near-real time differs from its post-processing counterpart by the way in which certain parameter groups are estimated or modeled. Representative choices for ODTS in the control segment of a GNSS provider and high-precision ODTS in space geodesy are summarized in Table 11.1. Within the near-real-time ODTS, satellite orbits and clock offsets as well as station clock offsets must be estimated from a limited amount of observation data. To cope with the resulting lack of observability, the ODTS process relies on a priori data and models. Post-processed solutions can be based on a much larger station network and extended data arcs. This enables estimation of a larger set of parameters (such as station coordinates, Earth rotation parameters, and tropospheric delays) from the observations, and also supports the resolution and fixing

of carrier-phase ambiguities for increased accuracy. In both cases, constraints may need to be applied to handle correlations among certain parameters. Most obviously, this applies to satellite and station clocks, which require a common datum (such as a master clock). Likewise, constraints are needed in the joint estimation of station coordinates and Earth rotation parameters. Here, a no-net-rotation condition with respect to a priori station coordinates may be applied to break the correlation of the two parameter sets [110].

11.4.2

Validation

Along with the generation of orbit and clock products for GNSS satellites comes the obvious need to assess the accuracy of these products and to validate their conformance with specified or desired performance values. Given the lack of a truth standard against which a GNSS ephemeris product can be compared, a variety of techniques have been devised to assess the precision, that is, the repeatability, and partly accuracy, of orbit and clock products. These include ephemeris overlaps, inter-comparisons of different solutions, or point positioning analyses. Additional tests may be used to provide specific information on either orbit quality (SLR) or clock quality (TWSTFT; clock fits). The most important techniques are briefly described. 11.4.2.1

Ephemeris Comparison

Comparison of orbit positions computed by different analysis centers in terms of bias and standard deviation (STD) allows evaluation of the consistency of these solutions. However, care must be taken when interpreting the results of such comparisons. As only the consistency of two solutions is assessed, good results can be obtained if two analysis centers consistently use the same bad model.

Table 11.1 Typical ODTS parameters in the control center and scientific post-processing applications Parameter

Control Segment

Post-Processing

Satellite orbits

Estimated

Estimated

Satellite clocks

Estimated

Estimated or eliminated by double differencing

Solar radiation pressure

Estimated

Estimated

Station coordinates

Fixed or heavily constrained

Estimated

Receiver clocks

Estimated

Estimated or eliminated by double differencing

Ambiguities

None or float

Fixed to integers

Differential code biases

—

Estimated or corrected a priori

Troposphere zenith delays

Modeled

Estimated at 1- or 2-h intervals

Troposphere gradients

Neglected

Estimated at daily or shorter intervals

Earth rotation parameters

Fixed

Polar motion, polar motion rates, and LOD estimated at daily intervals

11.4 Systems and Products

40 2016

2017

Radial [cm]

20

0

−20

−40 Jan

Apr

Jul

Oct

Jan

Apr

Jul

Oct

Jan

Figure 11.7 Radial orbit differences between the Center for Orbit Determination in Europe (CODE) and Deutsches GeoForschungsZentrum (GFZ) orbits of Galileo satellite E102. The change in October 2016 is related to the adoption of ECOM-2 by GFZ.

Figure 11.7 illustrates the radial orbit differences of two analysis centers (CODE and GFZ) for a selected Galileo satellite. Until October 2016, CODE and GFZ used different SRP models, resulting in an STD of 9 cm. After GFZ adopted the SRP model of [83] already used by CODE before, the STD decreases to 4 cm with a further decrease down to 2 cm in August 2017 when CODE implemented albedo and antenna thrust. A common quantity to evaluate the stand-alone performance of a GNSS is the signal-in-space ranging error (SISRE). The broadcast orbits, clocks, and group delays transmitted via the navigation message are compared with a precise reference product of superior accuracy‚ and a global average is formed. The SISRE is computed as SISRE = RMS w1 δR − δT

2

+ w22 δ2A + δ2C 11 22

where δR, δA, and δC denote the epoch-wise differences of broadcast and precise ephemerides in the radial, alongtrack, and cross-track directions, while δT denotes the corresponding clock difference. Furthermore, w1 and w2 are weighting factors depending on the orbit height that account for the average contribution of individual orbit errors to the line-of-sight range [111].

Orbit 1

Day n

11.4.2.2

Orbit and Clock Overlaps

Another method of evaluating the internal consistency of GNSS orbit and clock products is overlap comparisons. For multi-day solutions, the 3D orbit RMS or the clock RMS or STD of overlapping sub-intervals can be computed. Figure 11.8 illustrates this differencing for the second day of a two-day arc with the first day of the consecutive two-day arc. For consecutive one-day solutions, orbit predictions can be used or so-called day boundary discontinuities can be computed, that is, the 3D difference between the orbit positions at midnight. 11.4.2.3

Point Positioning

PPP [112] is an absolute positioning technique utilizing dual-frequency pseudorange and carrier-phase measurements as well as precise satellite orbit and clock products. By applying the correction models discussed in Section 11.1 and estimating auxiliary parameters like receiver clocks, troposphere parameters, and ambiguities, positioning accuracies at the several-millimeter level can be achieved. With dedicated orbit and clock products, even integer ambiguity resolution is possible [113]. As the orbit and clock accuracy directly affects the positioning performance, PPP can also be used to evaluate the quality of these products. Formal errors, the convergence time, or the scatter

RMS

Orbit 2

Day n+1

Day n+2

Figure 11.8 Computation of orbit overlap statistics for two orbits with an overlap period of 1 day.

249

11 GNSS Orbit Determination and Time Synchronization

of kinematic coordinate estimates of a static station or multiple static solutions with respect to a reference solution (e.g. the IGS combined reference frame product) are typically used as quality indicators. The same quantities can also be used to assess the broadcast orbit and clock products in a single point positioning with single- or dual-frequency pseudorange observations. 11.4.2.4

Satellite Laser Ranging

As already mentioned in Section 11.1, the optical SLR technique can be used as a validation tool for satellite orbits obtained from microwave observations. SLR residuals represent the differences between the SLR range measurements and the ranges computed from positions of the SLR station and the satellite orbit obtained from GNSS observations. SLR residuals are especially suited to revealing systematic errors in GNSS orbits, for example, due to SRP mis-modeling [114, 115]. As an example, Figure 11.9 shows the SLR residuals for the CODE orbits of Galileo E102. Until 2014, pronounced systematic errors due to an inappropriate SRP model were visible. These errors vanished in 2015, when CODE switched to the more sophisticated ECOM-2 model [83]. However, a systematic bias of about 5 cm remained. This bias became significantly smaller in mid-2017, when albedo and antenna thrust were considered. The biannual short periods with increased SLR residuals are related to eclipses of the satellite.

11.4.3

Orbit and Clock Products

11.4.3.1

Cartesian – are presently employed by the different GNSS providers to describe the evolution of the satellite orbit over time. The Keplerian orbit model enables an analytical computation of the satellite position at any time within a predefined validity period based on a set of orbital elements and complementary perturbation terms. It has been adopted by GPS, BeiDou, Galileo, IRNSS/NavIC, and QZSS and involves a total of 15–17 parameters. The GLONASS navigation message, in contrast, provides the satellite’s state vector (i.e. position and velocity) as well as a vector of luni-solar perturbational accelerations at a reference epoch. Based on these data‚ the user receiver can then obtain the satellite position in the vicinity of the reference epoch through numerical integration. Complementary to the orbit model, low-order polynomials (with two to three parameters) are used by all constellations to describe the evolution of the clock offset over time. The accuracy of broadcast ephemerides depends on a variety of factors, in particular‚ the length of the prediction arc and the fit interval used in their generation, but also the stability of the onboard clock. It is commonly assessed in terms of SISRE, that is, the combined contribution of the orbit and clock errors to the modeled pseudorange (see Section 11.4.2.1). Representative SISRE values for the currently operational constellations range from about 0.2–2 m (RMS) [111, 116–118], which is generally adequate for positioning at the 1–10 m level. So far, broadcast ephemerides provide the only source of satellite orbit and clock information that is ubiquitously available in real-time for all constellations.

Broadcast Ephemerides

Orbit and clock information generated in the GNSS control centers is disseminated to the users in the form of broadcast ephemerides. These represent predictions of the latest ODTS results and comprise a small number of parameters based on which the users can compute approximate positions of the GNSS satellites as well as the expected clock offsets. Two basic parameterizations – Keplerian and

11.4.3.2

Precise Orbit and Clock Products

GPS orbit and clock solutions have been provided by the IGS for more than 20 years and have become a benchmark for high-precision applications in science and engineering [119]. Traditionally, three categories of products are distinguished that differ by their latency, update rate, and accuracy. With a precision at the one- to few-centimeter level (in

20 2014 SLR Residuals [cm]

250

2015

2016

2017

10 0 −10 −20 −30 Jul

Figure 11.9

Oct

Jan

Apr

Jul

Oct

Jan

Apr

Jul

Oct

Jan

Apr

Satellite laser ranging residuals for the CODE orbits of Galileo E102.

Jul

Oct

Jan

Apr

Jul

Oct

Jan

11.4 Systems and Products

terms of orbit, clock, and range modeling errors), the “final products” offer the highest performance level but are only made available after about two weeks. “Rapid products” in contrast are made available the next day and exhibit an only slightly lower precision. “Ultra-rapid” products, finally, are issued four times a day with a latency of 3 h after the end of the data arc. The observed part of the ultra-rapid products is complemented by a one-day prediction, which still provides a 5 cm orbit accuracy but may exhibit clock errors at the 0.5 m level similar to broadcast ephemerides. All three GPS products result from a combination process that computes a weighted average of solutions contributed by individual IGS analysis centers (ACs) to ensure high quality and robustness at all times [120]. Making use of monitoring stations with high-performance atomic clocks and interfaces to national timing laboratories in the clock combination process, a common ensemble time (IGS Time, IGST) is realized that is closely aligned with and traceable to the GPS and UTC time scales. Complementary to GPS, a combined GLONASS final orbit product with 3 cm precision is provided by the IGS. The evolution of the weighted RMS of the individual ACs with respect to the combined orbits is illustrated in Figure 11.10. However, no combined GLONASS clock product is presently provided due to systematic, satellite-, and product-specific clock biases in the solutions of individual ACs [121]. These biases are related to the use of an FDMA modulation scheme in GLONASS along with frequency-channel-dependent code biases in the receivers that vary notably between different receiver types. To cope with this problem, weakly constrained bias parameters are commonly estimated in the orbit and clock determination process. The individual clock products only offer a limited (decimeter- to meter-level) accuracy for pseudorange-based

positioning, but can still be used for centimeter-level PPP based on carrier-phase observations. Aside from the legacy constellations GPS and GLONASS, the IGS has started to provide orbit and clock products for Galileo, BeiDou, and QZSS within the frame of its MultiGNSS pilot project (MGEX; [122]). As of early 2020, three MGEX ACs provide multi-GNSS products covering all five constellations‚ and another three cover a subset thereof. With orbit and clock errors of about 4 cm (RMS contribution to the modeled pseudorange), the MGEX products for Galileo currently exhibit the best performance among the new constellations. Among others, the orbit and clock determination of Galileo benefits from the public release of satellite metadata such as radiation pressure models and antenna characteristics, which greatly facilitate a realistic modeling of Galileo orbits and observations. Compared to Galileo, a roughly three times lower performance is presently achieved for BeiDou satellites in medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO), but substantially larger uncertainties apply for the orbit determination of BeiDou satellites in geostationary orbit (GEO). In view of the near-static viewing geometry, some orbital elements are barely observable with pseudorange and carrier-phase observations from groundbased stations for these satellites, and the resulting solutions are very sensitive to all forms of measurement and modeling errors. Complementary use of SLR [123] and observations from spaceborne GNSS receivers in LEO [124] have been suggested to cope with this problem, but are difficult to realize in practice. QZS-1, the first satellite of the Japanese Quasi-Zenith Satellite System‚ has been included in MGEX orbit and clock products for many years, but only moderate accuracies have been achieved so far. SLR residuals and the consistency of

100 BKG

WRMS [mm]

80

COD

EMX

ESX

GFZ

GRG

IAC

60 40 20 0 2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

Figure 11.10 Weighted RMS of analysis center contributions with respect to the IGS combined final orbits for GLONASS. BKG: Bundesamt für Kartographie und Geodäsie (Germany); COD: Center for Orbit Determination in Europe (Switzerland); EMX: National Resources Canada; ESX: European Space Agency (Germany); GFZ: Deutsches GeoForschungsZentrum (Germany); GRG: Centre National d’Etudes Spatiales, Collecte Localisation Satellites, Groupe de Recherche de Géodésie Spatiale (France); IAC: Information and Analysis Center (Russia).

251

252

11 GNSS Orbit Determination and Time Synchronization

different solutions indicate orbit errors at the 0.5 m level [122] in MGEX products of QZS-1 up to 2016. More recently, incorporation of enhanced radiation pressure models has reduced SLR residuals to less than 1 dm [73, 74]. On the other hand, new challenges are posed by the latest addition of a GEO satellite into the QZSS constellations. All IGS ACs make use of common exchange formats for the distribution of GNSS orbit and clock information. These include the “Special Format 3” (SP3) format for satellite orbit and clock information [125] as well as the complementary “Clock RINEX” format [126] for clock solutions of satellites and monitoring stations. Since GNSS satellite orbits are sufficiently smooth to allow interpolation across extended periods of time, sampling intervals of 5–15 min are commonly adopted for the respective SP3 files. On the other hand, a much higher temporal resolution is required for clock offset information‚ and most ACs nowadays support sampling intervals down to 30 s in their Clock RINEX products. For specific applications, dedicated highrate clock products are, furthermore, made available by the CODE analysis center [127]. 11.4.3.3

Real-Time Products

As a complement to regional, differential correction services, various commercial providers have established dedicated services to support global PPP in real time. These are based on a precise GNSS orbit and clock determination performed by the service provider from a sufficiently dense network of worldwide monitoring stations. The ODTS process is similar to the one performed inside a GNSS control center, but typically designed to support higher accuracy and multiple constellations. To reduce the required communication bandwidth, the precise orbit and clock information obtained in this process is usually expressed as a correction relative to the GNSS-specific broadcast ephemeris valid at the same instant of time. Once generated, the corrections can be disseminated through geostationary communication satellites to users with suitably equipped GNSS receivers. Using frequencies close to the L1/E1-band for transmission of the correction data, combined antennas for GNSS and correction data reception can be used‚ and modems for decoding the correction can be integrated right into the user equipment. Examples of real-time correction services include Fugro’s OmniSTAR, Trimble’s RTX service, NavCom’s StarFire system, and the TERRASTAR service of Veripos [92, 128–130]. In addition, NASA’s JPL has established the Global Differential GPS system and provides real-time correction data and orbit/clock products to interested customers [91] on a commercial basis. A free access to real-time orbit and clock corrections is offered by the IGS Real-Time Service (RTS) [131, 132]. It comprises GPS real-time products from eight ACs and three

streams with combined solutions for improved accuracy and reliability. In addition, some streams include correction data for GLONASS, Galileo, and/or BeiDou. Standard deviations of the GPS real-time orbits and clocks are at the 3 cm (0.1 ns) level, which enables decimeter-level point positioning in real time. Given the increasing public demand for accurate positioning, various GNSS providers are now considering the provision of real-time correction data as part of the transmitted GNSS signals. This is particularly convenient for the respective users since no additional hardware other than a surveying-grade GNSS receiver and antenna are required. Examples of such services include the QZSS Centimeter-Level Augmentation Service (CLAS; [133]) and the planned High-Accuracy Service (HAS) of Galileo. While the QZSS service area is naturally confined to Japan and surrounding territories, Galileo aims to enable decimeter-level PPP on a global scale [134]. To harmonize the exchange of orbit and clock corrections as well as auxiliary data for real-time PPP across different vendors and service providers, the State Space Representation (SSR) concept has been developed [135]. An associated set of messages is also incorporated into the latest version of the standard for Differential GNSS Services of the Radio Technical Commission for Maritime Services (RTCM; [136]). RTCM-SSR messages are used in the IGS RTS, and an advanced set of highly compact SSR messages has been defined for the QZSS CLAS.

References 1 J.M. Dow, R.E. Neilan, and C. Rizos, “The International

2

3

4

5 6

GNSS Service in a changing landscape of Global Navigation Satellite Systems,” Journal of Geodesy, vol. 83, no. 3-4, pp. 191–198, 2009, doi:10.1007/s00190-008-0300-3. S.C. Fisher and K. Ghassemi, “GPS IIF – The Next Generation,” Proc. IEEE, vol. 87, no. 1, pp. 24–47, 1999, doi:10.1109/5.736340. D. Yang, J. Yang, G. Li, Y. Zhou, and C. Tang, “Globalization highlight: Orbit determination using BeiDou inter-satellite ranging measurements,” GPS Solutions, vol. 21, no. 3, pp. 1395–1404, 2017, doi:10.1007/ s10291-017-0626-5. L. Combrinck, “Satellite laser ranging,” in Sciences of Geodesy, vol. 1, pp. 301–338, Springer, 2010, doi:10.1007/ 978-3-642-11741-1_9. G. Beutler, Methods of Celestial Mechanics, vol. I, Springer, 2005, doi:10.1007/b138225. J. Kouba and P. Héroux, “Precise point positioning using IGS orbit and clock products,” GPS Solutions, vol. 5, no. 2, pp. 12–28, 2001, doi:10.1007/pl00012883.

References

7 X. Dai, M. Ge, Y. Lou, C. Shi, J. Wickert, and H. Schuh,

8

9

10

11

12

13

14

15

16

17

18

“Estimating the yaw-attitude of BDS IGSO and MEO satellites,” Journal of Geodesy, vol. 89, no. 10, pp. 1005–1018, 2015, doi:10.1007/s00190-015-0829-x. L. Wanninger, “Carrier-phase inter-frequency biases of GLONASS receivers,” Journal of Geodesy, vol. 86, no. 2, pp. 139–148, 2012, doi:10.1007/s00190-011-0502-y. Y. Chen, Y. Yuan, W. Ding, B. Zhang, and T. Liu, “GLONASS pseudorange inter-channel biases considerations when jointly estimating GPS and GLONASS clock offset,” GPS Solutions, vol. 21, no. 4, pp. 1525–1533, 2017, doi:10.1007/s10291-017-0630-9. D. Odijk, N. Nadarajah, S. Zaminpardaz, and P.J.G. Teunissen, “GPS, Galileo, QZSS and IRNSS differential ISBs: Estimation and application,” GPS Solutions, vol. 21, no. 2, pp. 439–450, 2017, doi:10.1007/s10291-016-0536-y. W.G. Melbourne, “The Case for Ranging in GPS based Geodetic Systems,” in Proc. First International Symposium on Precise Positioning with the Global Positioning System (ed. C. Goad), pp. 373–386, U.S. Department of Commerce, Rockville, Maryland, 1985. G. Wübbena, “Software Developments for Geodetic Positioning with GPS using TI-4100 Code and Carrier Measurements,” in Proc. First International Symposium on Precise Positioning with the Global Positioning System (ed. C. Goad), pp. 403–412, U.S. Department of Commerce, Rockville, Maryland, 1985. F. Amarillo Fernández, “Inter-satellite ranging and intersatellite communication links for enhancing GNSS satellite broadcast navigation data,” Advances in Space Research, vol. 47, no. 5, pp. 786–801, 2011, doi:10.1016/j. asr.2010.10.002. A. Chubykin, S. Dmitriev, V. Shargorodskiy, and V. Sumerin, “Intersatellite laser navigating link system,” in WPLTN Technical Workshop “One-way and two-way SLR for GNSS co-located with RF techniques” (WPLTN-2012), St. Petersburg, Russia, 24–28 Sep. 2012, 2012. S. Revnivykh, A. Bolkunov, A. Serdyukov, and O. Montenbruck, “GLONASS,” in Springer Handbook of Global Navigation Satellite Systems (ed. P. Teunissen and O. Montenbruck), chap. 8, pp. 219–245, Springer, 2017, doi:10.1007/978-3-319-42928-1_8. R. Wolf, Satellite orbit and ephemeris determination using inter satellite links, PhD thesis, Universität der Bundeswehr München, 2000. H. Wang, Z. Chen, J. Zheng, and H. Chu, “A new algorithm for onboard autonomous orbit determination of navigation satellites,” The Journal of Navigation, vol. 64, no. S1, pp. S162–S179, 2011, doi:10.1017/ S0373463311000397. M. Pearlman, J. Degnan, and J. Bosworth, “The International Laser Ranging Service,” Advances in Space

19

20

21

22

23

24

25

26

27

28 29

30

31

Research, vol. 30, no. 2, pp. 135–143, 2002, doi:10.1016/ S0273-1177(02)00277-6. S. Schillak, “Analysis of the process of the determination of station coordinates by the satellite laser ranging based on results of the Borowiec SLR station in 1993.5–2000.5, Part 1: Performance of the Satellite Laser Ranging,” Artificial Satellites, vol. 39, no. 3, pp. 217–263, 2004. K. Sośnica, D. Thaller, R. Dach, P. Steigenberger, G. Beutler, D. Arnold, and A. Jäggi, “Satellite laser ranging to GPS and GLONASS,” Journal of Geodesy, vol. 89, no. 7, pp. 725–743, 2015, doi:10.1007/s00190-015-0810-8. S. Hackel, P. Steigenberger, U. Hugentobler, M. Uhlemann, and O. Montenbruck, “Galileo orbit determination using combined GNSS and SLR observations,” GPS Solutions, vol. 19, no. 1, pp. 15–25, 2015, doi:10.1007/s10291-013-0361-5. International Astronomical Union, “Resolution B2: on The Third Realization of the International Celestial Reference Frame,” XXX IAU General Assembly, August 2018, https://www.iau.org/static/resolutions/ IAU2018_ResolB2_English.pdf H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” Journal of Geodynamics, vol. 61, pp. 68–80, 2012, doi:10.1016/j.jog.2012.07.007. G. Petit and B. Luzum, “IERS Conventions (2010),” IERS Technical Note 36, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main, 2010. Z. Altamimi, P. Rebischung, L. Métivier, and X. Collilieux, “ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions,” Journal of Geophysical Research: Solid Earth, vol. 121, no. 8, pp. 6109–6131, 2016, doi:10.1002/2016JB013098. C. Boucher and Z. Altamimi, “ITRS, PZ-90 and WGS 84: Current realizations and the related transformation parameters,” Journal of Geodesy, vol. 75, no. 11, pp. 613–619, 2001, doi:10.1007/s001900100208. P. Rebischung and R. Schmid, “IGS14/igs14.atx: A new Framework for the IGS Products,” AGU Fall Meeting Abstracts, G41A-0998, 2016. V. Dehant and P.M. Mathews, Precession, Nutation and Wobble of the Earth, Cambridge University Press, 2015. M. Rothacher, G. Beutler, T. Herring, and R. Weber, “Estimation of nutation using the Global Positioning System,” Journal of Geophysical Research, vol. 104, no. B3, pp. 4835–4859, 1999, doi:10.1029/1998JB900078. B. Luzum and D. Gambis, “Explanatory supplement to IERS Bulletin A and Bulletin B/C04,” IERS, URL ftp:// hpiers.obspm.fr/iers/bul/bulb_new/bulletinb.pdf, 2014. C. Bizouard, S. Lambert, O. Becker, and J.Y. Richard, “Combined solution C04 for Earth Rotation Parameters consistent with International Terrestrial Reference Frame

253

254

11 GNSS Orbit Determination and Time Synchronization

32

33

34

35

36

37

38

39

40

41

42

43

2014,” Observatoire de Paris, URL https://hpiers.obspm. fr/iers/eop/eopc04/C04.guide.pdf, 2017. O. Montenbruck, R. Schmid, F. Mercier, P. Steigenberger, C. Noll, R. Fatkulin, S. Kogure, and A.S. Ganeshan, “GNSS satellite geometry and attitude models,” Advances in Space Research, vol. 56, no. 6, pp. 1015–1029, 2015, doi:10.1016/j.asr.2015.06.019. F. Dilssner, T. Springer, G. Gienger, and J. Dow, “The GLONASS-M satellite yaw-attitude model,” Advances in Space Research, vol. 47, no. 1, pp. 160–171, 2011, doi:10.1016/j.asr.2010.09.007. Cabinet Office, “QZSS Satellite Information website,” http://qzss.go.jp/en/technical/qzssinfo/, last updated 2020/06/05, 2020. GSC, “Galileo Satellite Metadata website,” European Galileo Service Centre, https://www.gsc-europa.eu/ support-to-developers/galileo-satellite-metadata, last updated 2019/04/26, 2019. H.-G. Scherneck, “A parametrized solid Earth tide model and ocean loading effects for global geodetic base-line measurements,” Geophysical Journal International, vol. 106, no. 3, pp. 677–694, 1991, doi:10.1111/j.1365246X.1991.tb06339.x. T. van Dam, X. Collilieux, J. Wuite, Z. Altamimi, and J. Ray, “Nontidal ocean loading: amplitudes and potential effects in GPS height time series,” Journal of Geodesy, vol. 86, no. 11, pp. 1043–1057, 2012, doi:10.1007/s00190012-0564-5. L. Petrov and J.-P. Boy, “Study of the atmospheric pressure loading signal in very long baseline interferometry observations,” Journal of Geophysical Research, vol. 109, B03405, 2004, doi:10.1029/ 2003JB002500. P. Steigenberger, J. Boehm, and V. Tesmer, “Comparison of GMF/GPT with VMF1/ECMWF and implications for atmospheric loading,” Journal of Geodesy, vol. 83, no. 10, pp. 943–951, 2009, doi:10.1007/s00190-009-0311-8. F. Menge, G. Seeber, C. Völksen, G. Wübbena, and M. Schmitz, “Results of Absolute Field Calibration of GPS Antenna PCV,” in Proc. ION GPS-98, Nashville, Tennessee, pp. 31–38, 1998. R. Schmid, P. Steigenberger, G. Gendt, M. Ge, and M. Rothacher, “Generation of a consistent absolute phasecenter correction model for GPS receiver and satellite antennas,” Journal of Geodesy, vol. 81, no. 12, pp. 781–798, 2007, doi:10.1007/s00190-007-0148-y. L. Wanninger and S. Beer, “BeiDou satellite-induced code pseudorange variations: diagnosis and therapy,” GPS Solutions, vol. 19, no. 4, pp. 639–648, 2014, doi:10.1007/ s10291-014-0423-3. L. Wanninger, H. Sumaya, and S. Beer, “Group delay variations of GPS transmitting and receiving antennas,”

44

45

46

47

48

49

50

51

52

53

54

Journal of Geodesy, vol. 91, no. 9, pp. 1099–1116, 2017, doi:10.1007/s00190-017-1012-3. T. Kersten and S. Schön, “GPS code phase variations (CPV) for GNSS receiver antennas and their effect on geodetic parameters and ambiguity resolution,” Journal of Geodesy, vol. 91, no. 6, pp. 579–596, 2016, doi:10.1007/ s00190-016-0984-8. M.M. Alizadeh, D.D. Wijaya, T. Hobiger, R. Weber, and H. Schuh, “Ionospheric effects on microwave signals,” in Atmospheric Effects in Space Geodesy (ed. J. Böhm and H. Schuh), chap. 4, pp. 35–71, Springer, 2013, doi:10.1007/ 978-3-642-36932-2_2. M. Fritsche, R. Dietrich, C. Knöfel, A. Rülke, S. Vey, M. Rothacher, and P. Steigenberger, “Impact of higher-order ionospheric terms on GPS estimates,” Geophysical Research Letters, vol. 32, no. 23, L23311, 2005, doi:10.1029/ 2005GL024342. T. Nilsson, J. Böhm, D. D. Wijaya, A. Tresch, V. Nafisi, and H. Schuh, “Path delays in the neutral atmosphere,” in Atmospheric Effects in Space Geodesy (ed. J. Böhm and H. Schuh), chap. 3, pp. 73–136, Springer, 2013, doi:10.1007/ 978-3-642-36932-2_3. J. Saastamoinen, “Contributions to the theory of atmospheric refraction – Part II. Refraction corrections in satellite geodesy,” Bulletin Geodesique, vol. 107, no. 1, pp. 13–34, 1973, doi:10.1007/BF02522083. J. Boehm, R. Heinkelmann, and H. Schuh, “Short Note: A global model of pressure and temperature for geodetic applications,” Journal of Geodesy, vol. 81, no. 10, pp. 679–683, 2007, doi:10.1007/s00190-007-0135-3. J. Böhm, G. Möller, M. Schindelegger, G. Pain, and R. Weber, “Development of an improved empirical model for slant delays in the troposphere (GPT2w),” GPS Solutions, vol. 19, no. 3, pp. 433–441, 2015, doi:10.1007/ s10291-014-0403-7. D. Landskron and J. Böhm, “VMF3/GPT3: refined discrete and empirical troposphere mapping functions,” Journal of Geodesy, vol. 92, no. 4, pp. 349-360, 2018, doi:10.1007/s00190-017-1066-2. J. Boehm, A. Niell, P. Tregoning, and H. Schuh, “Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data,” Geophysical Research Letters, vol. 33, no. 7, L07304, 2006, doi:10.1029/2005GL025546. J. Boehm, B. Werl, and H. Schuh, “Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data,” Journal of Geophysical Research, vol. 111, no. B2, B02406, 2006, doi:10.1029/2005JB003629. C. Lu, X. Li, Z. Li, R. Heinkelmann, T. Nilsson, G. Dick, M. Ge, and H. Schuh, “GNSS tropospheric gradients with

References

55

56

57 58

59

60

61

62

63

64

65

66

high temporal resolution and their effect on precise positioning,” Journal of Geophysical Research, vol. 121, no. 2, pp. 912–930, 2016, doi:10.1002/2015JD024255. G. Chen and T.A. Herring, “Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data,” Journal of Geophysical Research, vol. 102, no. B9, pp. 20489–20502, 1997, doi:10.1029/97JB01739. J.T. Wu, S.C. Wu, G.A. Hajj, W.I. Bertiger, and S.M. Lichten, “Effects of antenna orientation on GPS carrier phase,” Manuscripta Geodaetica, vol. 18, pp. 91–98, 1993. N. Ashby, “Relativity in the Global Positioning System,” Living Reviews, vol. 6, no. 1, 2003, doi:10.12942/lrr-2003-1. L.E. Cunningham, “On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite,” Celestial Mechanics, vol. 2, no. 2, pp. 207–216, 1970, doi:10.1007/ BF01229495. J. Ries, S. Bettadpur, R. Eanes, Z. Kang, U. Ko, Ch. McCullough, P. Nagel, N. Pie, S. Poole, Th. Richter, H. Save, and B. Tapley, The Development and Evaluation of the Global Gravity Model GGM05, Center for Space Research, The University of Texas at Austin, 2016. doi:10.26153/tsw/1461 W.M. Folkner, J.G. Williams, and D.H. Boggs, The Planetary and Lunar Ephemeris DE421, IOM 343R-08003, Jet Propulsion Laboratory, Pasadena, 2008. J.L. Hilton and C.Y. Hohenkerk, “A comparison of the high accuracy planetary ephemerides DE421, EPM2008, and INPOP08,” in Proc. Journées 2010 “Systèmes de Référence Spatio-Temporels” (JSR2010): New Challenges for Reference Systems and Numerical Standards in Astronomy (ed. N. Capitaine), pp. 77–80, Observatoire de Paris, 2011. P. Delva, U. Kostić, and A. Čadež, “Numerical modeling of a Global Navigation Satellite System in a general relativistic framework,” Advances in Space Research, vol. 47, no. 2, pp. 370–379, 2011, doi:10.1016/j. asr.2010.07.007. U. Kostić, M. Horvat, and A. Gomboc, “Relativistic Positioning System in perturbed spacetime,” Classical and Quantum Gravity, vol. 32, no. 21, p. 215004, 2015, doi:10.1088/0264-9381/32/21/215004. A. Milani, A. M. Nobili, and P. Farinella, Nongravitational Perturbations and Satellite Geodesy, Adam Hilger Ltd., Bristol, United Kingdom, 1987. G. Kopp and J.L. Lean, “A new, lower value of total solar irradiance: Evidence and climate significance,” Geophysical Research Letters, vol. 38, no. 1, L01706, 2011, doi:10.1029/2010GL045777. M. Ziebart and P. Dare, “Analytical solar radiation pressure modelling for GLONASS using a pixel array,” Journal of Geodesy, vol. 75, no. 11, pp. 587–599, 2001, doi:10.1007/s001900000136.

67 M. Ziebart, S. Adhya, A. Sibthorpe, and P. Cross, “GPS

68

69

70

71

72

73

74

75

76

77

78

Block IIR Non-Conservative Force Modeling: Computation and Implications,” in Proc. ION GPS 2003, Portland, Oregon, pp. 2671–2678, 2003. W. Marquis and C. Krier, “Examination of the GPS Block IIR Solar Pressure Model,” in Proc. ION GPS 2000, Salt Lake City, Utah, pp. 407–415, 2000. W. Feng, X. Guo, H. Qiu, J. Zhang, and K. Dong, “A Study of Analytical Solar Radiation Pressure Modeling for BeiDou Navigation Satellites Based on Ray Tracing Method,” in China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II, vol. 304 of Lecture Notes in Electrical Engineering, Springer, pp. 425–435, doi:10.1007/978-3-642-54743-0_35, 2014. B. Tan, Y. Yuan, B. Zhang, H.Z. Hsu, and J. Ou, “A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM,” Scientific Reports, vol. 6, 32967, 2016, doi:10.1038/srep32967. C.J. Rodriguez-Solano, U. Hugentobler, and P. Steigenberger, “Adjustable box-wing model for solar radiation pressure impacting GPS satellites,” Advances in Space Research, vol. 49, no. 7, pp. 1113–1128, 2012, doi:10.1016/j.asr.2012.01.016. O. Montenbruck, P. Steigenberger, and U. Hugentobler, “Enhanced solar radiation pressure modeling for Galileo satellites,” Journal of Geodesy, vol. 89, no. 3, pp. 283–297, 2015, doi:10.1007/s00190-014-0774-0. O. Montenbruck, P. Steigenberger, and F. Darugna, “Semi-analytical solar radiation pressure modeling for QZS-1 orbit-normal and yaw-steering attitude,” Advances in Space Research, vol. 59, no. 8, pp. 2088–2100, 2017, doi:10.1016/j.asr.2017.01.036. Q. Zhao, G. Chen, J. Guo, J. Liu, and X. Liu, “An a priori solar radiation pressure model for the QZSS Michibiki satellite,” Journal of Geodesy, vol. 92, no. 2, pp. 109–121, 2018, doi:10.1007/s00190-017-1048-4. Y. Vigue, B.E. Schutz, and P.A.M. Abusali, “Thermal force modeling for Global Positioning System using the finite element method,” Journal of Spacecraft and Rockets, vol. 31, no. 5, pp. 855–859, 1994, doi:10.2514/3.26523. P.C. Knocke, J.C. Ries, and B.D. Tapley, “Earth Radiation Pressure Effects on Satellites,” in Proc. AIAA/AAS Astrodynamics Conference, pp. 577–587, AIAA, 1988. C.J. Rodriguez-Solano, U. Hugentobler, P. Steigenberger, and S. Lutz, “Impact of Earth radiation pressure on GPS position estimates,” Journal of Geodesy, vol. 86, no. 5, pp. 309–317, 2012, doi:10.1007/s00190-011-0517-4. K.J. Priestley, G.L. Smith, S. Thomas, D. Cooper, R.B. Lee, D. Walikainen, P. Hess, Z.P. Szewczyk, and R. Wilson, “Radiometric performance of the CERES Earth radiation budget climate record sensors on the EOS Aqua and Terra Spacecraft through April 2007,” Journal of Atmospheric

255

256

11 GNSS Orbit Determination and Time Synchronization

79

80

81

82

83

84

85

86 87 88

89 90

91

and Oceanic Technology, vol. 28, no. 1, pp. 3–21, 2011, doi:10.1175/2010JTECHA1521.1. R. Eanes, R. Nerem, P. Abusali, W. Bamford, K. Key, J. Ries, and B. Schutz, “GLONASS Orbit Determination at the Center for Space Research,” in Proceedings of the International GLONASS Experiment (IGEX-98) Workshop, IGS, Jet Propulsion Laboratory, pp. 213–221, 2000. P. Steigenberger, S. Thoelert, and O. Montenbruck, “GNSS satellite transmit power and its impact on orbit determination,” Journal of Geodesy, vol. 92, no. 6, pp. 609–624, 2018, doi:10.1007/s00190-017-1082-2. G. Beutler, E. Brockmann, W. Gurtner, U. Hugentobler, L. Mervart, M. Rothacher, and A. Verdun, “Extended orbit modeling techniques at the CODE processing center of the International GPS Service for Geodynamics (IGS): Theory and Initial Results.” Manuscripta Geodaetica, vol. 19, pp. 367–386, 1994. T.A. Springer, G. Beutler, and M. Rothacher, “A new solar radiation pressure model for GPS satellites,” GPS Solutions, vol. 2, no. 3, pp. 50–62, 1999, doi:10.1007/ PL00012757. D. Arnold, M. Meindl, G. Beutler, R. Dach, S. Schaer, S. Lutz, L. Prange, K. Sośnica, L. Mervart, and A. Jäggi, “CODE’s new solar radiation pressure model for GNSS orbit determination,” Journal of Geodesy, vol. 89, no. 8, pp. 775–791, 2015, doi:10.1007/s00190-015-0814-4. L. Prange, E. Orliac, R. Dach, D. Arnold, G. Beutler, S. Schaer, and A. Jäggi, “CODE’s five-system orbit and clock solution-the challenges of multi-GNSS data analysis,” Journal of Geodesy, vol. 91, no. 4, pp. 345–360, 2017, doi:10.1007/s00190-016-0968-8. G. Huang, Z. Qin, Q. Zhang, L. Wang, X. Yan, L. Fan, and X. Wang, “A real-time robust method to detect BeiDou GEO/IGSO Orbital Maneuvers,” Sensors, vol. 17, no. 12, 2761, 2017, doi:10.3390/s17122761. E. Hairer, S.P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Springer, 1987. O. Montenbruck and E. Gill, Satellite Orbits – Models, Methods and Applications, Springer, 2000. J.B. Lundberg, “Mitigation of satellite orbit errors resulting from the numerical integration across shadow boundaries,” Applied Mathematics and Computation, vol. 112, no. 2–3, pp. 193–211, 2000, doi:10.1016/S00963003(99)00042-9. B. Tapley, B. Schutz, and G.H. Born, Statistical Orbit Determination, Academic Press, 2004. J. Taylor, “The GPS Operational Control System Kalman Filter Description and History,” in Proc. ION GNSS 2010, Portland, Oregon, pp. 2329 – 2366, 2010. Y. Bar-Sever, L. Young, F. Stocklin, P. Heffernan, J. Rush, “The NASA Global Differential GPS System (GDGPS) and the TDRSS Augmentation Service for Satellites (TASS),”

92

93

94 95 96

97

98

99

100

101

102

103 104

105

in Proc. NAVITEC 2004, Noordwijk, Netherlands, pp. 1–8, ESA, 2004. M. Glocker, H. Landau, R. Leandro, and M. Nitschke, “Global Precise Multi-GNSS Positioning with Trimble Centerpoint RTX,” in Proc. NAVITEC 2012, Noordwijk, Netherlands, IEEE, pp. 1–8, doi:10.1109/ NAVITEC.2012.6423060, 2012. D. Laurichesse, L. Cerri, J.P. Berthias, and F. Mercier, “Real Time Precise GPS Constellation and Clocks Estimation by Means of a Kalman Filter,” in Proc. ION GNSS+ 2013, Nashville, Tennessee, pp. 1155–1163, 2013. G.H. Golub and C.F. Van Loan, Matrix computations, John Hopkins University Press, 4th ed., 2013. G.J. Bierman, Factorization Methods for Discrete Sequential Estimation, Courier Dover Publications, 2006. S.M. Lichten, “Estimation and filtering for high-precision GPS positioning applications,” Manuscripta Geodaetica, vol. 15, pp. 159–176, 1990. D. Murphy, N. Amiri, W. Bertiger, S. Desai, B. Haines, D. Kuang, P. Reis, C. Sakumura, A. Sibois, and A. Sibthorpe, “JPL IGS Analysis Center Report 2016,” in International GNSS Service Technical Report 2016 (eds. A. Villiger and R. Dach), IGS Central Bureau and University of Bern, pp. 65–70, doi:10.7892/boris.99278, 2017. R.G. Brown and P.Y. Hwang, Introduction to Random Signals and Applied Kalman Filtering: With MATLAB Exercises and Solutions, Wiley, 1997. P.J.G. Teunissen, “The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation,” Journal of Geodesy, vol. 70, no. 1, pp. 65–82, 1995, doi:10.1007/BF00863419. M. Ge, G. Gendt, G. Dick, and F.P. Zhang, “Improving carrier-phase ambiguity resolution in global GPS network solutions,” Journal of Geodesy, vol. 79, no. 1–3, pp. 103–110, 2005, doi:10.1007/s00190-005-0447-0. R. Dach, S. Lutz, P. Walser, and P. Fridez (eds.), Bernese GNSS Software Version 5.2, Astronomical Institute, University of Bern, Bern, Switzerland, 2015, doi:10.7892/ boris.72297. S. Loyer, F. Perosanz, F. Mercier, H. Capdeville, and J.-C. Marty, “Zero-difference GPS ambiguity resolution at CNESCLS IGS Analysis Center,” Journal of Geodesy, vol. 86, no. 11, pp. 991–1003, 2012, doi:10.1007/s00190-012-0559-2. International GNSS Service, “IGS Technical Report 2003 – 2004,” IGS Central Bureau, 2005. A.J. Dorsey, W.A. Marquis, P.M. Fyfe, E.D. Kaplan, and L. Wiederholt, “GPS system segments,” in Understanding GPS: Principles and Applications (eds. E.D. Kaplan and C.J. Hegarty), chap. 3, pp. 67–112, Artech House, 2006. K.R. Brown Jr, “The Theory of the GPS Composite Clock,” in Proc. ION GPS 91, Albuquerque, New Mexico, pp. 223–241, 1991.

References

106 C. Han, Z. Cai, Y. Lin, L. Liu, S. Xiao, L. Zhu, and X.

107

108

109

110

111

112

113

114

115 116

117

Wang, “Time synchronization and performance of BeiDou satellite clocks in orbit,” International Journal of Navigation and Observation, 371450, 2013, doi:10.1155/ 2013/371450. T.A. Herring, R.W. King, and S.C. McClusky, Introduction to GAMIT/GLOBK, Release 10.3, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, 2008. T.A. Springer, “NAPEOS Mathematical Models and Algorithms,” DOPS-SYS-TN-0100-OPS-GN, ESA/ESOC, Darmstadt, 2009. C. Shi, Q. Zhao, J. Geng, Y. Lou, M. Ge, and J. Liu, “Recent development of PANDA software in GNSS data processing,” in International Conference on Earth Observation Data Processing and Analysis (ICEODPA), vol. 7285, p. 72851S, 2008. P. Rebischung, Z. Altamimi, J. Ray, and B. Garayt, “The IGS contribution to ITRF2014,” Journal of Geodesy, vol. 90, no. 7, pp. 611–630, 2016, doi:10.1007/s00190-0160897-6. O. Montenbruck, P. Steigenberger, and A. Hauschild, “Multi-GNSS Signal-in-Space Range Error Assessment – Methodology and Results,” Advances in Space Research, vol. 61, no. 12, pp. 3020–3038, 2018, doi:10.1016/j. asr.2018.03.041. J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins, and F.H. Webb, “Precise point positioning for the efficient and robust analysis of GPS data from large networks,” Journal of Geophysical Research, vol. 102, no. B3, pp. 5005–5017, 1997, doi:10.1029/96JB03860. D. Laurichesse, F. Mercier, J.-P. Berthias, P. Broca, and L. Cerri, “Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination,” Navigation, vol. 56, no. 2, pp. 135–149, 2009, doi:10.1002/j.2161-4296.2009. tb01750.x. C. Urschl, G. Beutler, W. Gurtner, U. Hugentobler, and S. Schaer, “Contribution of SLR tracking data to GNSS orbit determination,” Advances in Space Research, vol. 39, no. 10, pp. 1515–1523, 2007, doi:10.1016/j.asr.2007.01.038. U. Hugentobler, “Laser ranging to GNSS satellites,” GPS World, vol. 28, no. 5, pp. 42–48, 2017. B.A. Renfro, A. Terry, and N. Boeker, “An Analysis of Global Positioning System (GPS) Standard Positioning System (SPS) Performance for 2016,” TR-SGL-17-06, Applied Research Laboratories, The University of Texas at Austin, 2017. G. Galluzzo, R. Lucas Rodriguez, R. Morgan-Owen, S. Binda, D. Blonski, P. Crosta, F. Gonzalez, J. Molina Garcia, X. Otero, N. Sirikan, M. Spangenberg, E. Spinelli, R. Swinden, and S. Wallner, “Galileo System Status,

118

119

120

121

122

123

124

125

126 127

128

129

Performance Metrics and Results,” in Proc. ION ITM 2018, Reston, Virginia, pp. 790–809, ION, 2018. Y. Wu, X. Liu, W. Liu, J. Ren, Y. Lou, X. Dai, X. Fang, “Long-term behavior and statistical characterization of BeiDou signal-in-space errors,” GPS Solutions, vol. 21, no. 4, pp. 1907–1922, 2017, DOI 10.1007/s10291-017-0663-0. G. Johnston, A. Riddell, and G. Hausler, “The International GNSS Service,” in Springer Handbook of Global Navigation Satellite Systems (eds. P.G. Teunissen and O. Montenbruck), chap. 33, pp. 967–982, Springer, 2017, doi:10.1007/978-3-319-42928-1_33. G. Beutler, J. Kouba, and T. Springer, “Combining the orbits of the IGS Analysis Centers,” Bulletin Geodesique, vol. 69, pp. 200–222, 1995, doi:10.1007/BF00806733. W. Song, W. Yi, Y. Lou, C. Shi, Y. Yao, Y. Liu, Y. Mao, and Y. Xiang, “Impact of GLONASS pseudorange interchannel biases on satellite clock corrections,” GPS Solutions, vol. 18, no. 3, pp. 323–333, 2014, doi:10.1007/ s10291-014-0371-y. O. Montenbruck, P. Steigenberger, L. Prange, Z. Deng, Q. Zhao, F. Perosanz, I. Romero, C. Noll, A. Stürze, G. Weber, R. Schmid, K. MacLeod, and S. Schaer, “The multi-GNSS experiment (MGEX) of the International GNSS Service (IGS) – Achievements, prospects and challenges,” Advances in Space Research, vol. 59, no. 7, pp. 1671–1697, 2017, doi:10.1016/j.asr.2017.01.011. B. Sun, H. Su, Z. Zhang, Y. Kong, and X. Yang, “GNSS GEO Satellites Precise Orbit Determination Based on Carrier Phase and SLR Observations,” in IGS Workshop 2016, Sydney, 2016. Q. Zhao, C. Wang, J. Guo, G. Yang, M. Liao, H. Ma, and J. Liu, “Enhanced orbit determination for BeiDou satellites with FengYun-3C onboard GNSS data,” GPS Solutions, vol. 21, no. 3, pp. 1179–1190, 2017, doi:10.1007/s10291-017-0604-y. B. Remondi, “Extending the National Geodetic Survey Standard for GPS Orbit Formats,” NOAA Technical Report NOS 133 NGS 46, National Geodetic Information Branch, NOAA, Rockville, MD, 1989. B. Ray and W. Gurtner, “RINEX Extensions to Handle Clock Information,” v3.02, 2010. H. Bock, R. Dach, A. Jäggi, and G. Beutler, “High-rate GPS clock corrections from CODE: Support of 1 Hz applications,” Journal of Geodesy, vol. 83, no. 11, pp. 1083– 1094, 2009, doi:10.1007/s00190-009-0326-1. J. Tegedor, D. Lapucha, O. Ørpen, E. Vigen, T. Melgard, and R. Strandli, “The New G4 Service: Multi-constellation Precise Point Positioning Including GPS, GLONASS, Galileo and BeiDou,” in Proc. ION GNSS+ 2015, Tampa, Florida, pp. 1089–1095, 2015. K. Dixon, “StarFire: A Global SBAS for Sub-Decimeter Precise Point Positioning,” in Proc. ION GNSS 2006, Fort Worth, Texas, pp. 2286–2296, 2006.

257

258

11 GNSS Orbit Determination and Time Synchronization

130 K. Sheridan, P. Toor, D. Russell, C. Rocken, and L.

Mervart, “TerraStar-C: A Global GNSS Service for cm Level Precise Point Positioning with Ambiguity Resolution,” in European Navigation Conference, 2015. 131 L. Agrotis, E. Schönemann, W. Enderle, M. Caissy, and A. Rülke, “The IGS Real Time Service,” in Proc. DVW Seminar “GNSS 2017 – Kompetenz für die Zukunft,” 21–22 Feb. 2017, Potsdam (eds. M. Mayer and A. Born), DVW – Gesellschaft für Geodäsie, Geoinformation und Landmanagement e.V., pp. 121–131, 2017. 132 T. Hadas and J. Bosy, “IGS RTS precise orbits and clocks verification and quality degradation over time,” GPS Solutions, vol. 19, no. 1, pp. 93–105, 2015, doi:10.1007/ s10291-014-0369-5. 133 M. Miya, S. Fujita, K. Ota, Y. Sato, J. Takiguchi, and R. Hirokawa, “Centimeter Level Augmentation Service

(CLAS) in Japanese Quasi-Zenith Satellite System, its User Interface, Detailed Design and Plan,” in Proc. ION GNSS+ 2016, Portland, Oregon, pp. 2864–2869, 2016. 134 I. Fernandez-Hernandez, I. Rodríguez, G. Tobías, J. Calle, E. Carbonell, G. Seco-Granados, J. Simón, R. Blasi, “Testing GNSS High Accuracy and Authentication – Galileo’s Commercial Service,” Inside GNSS, vol. 10, no. 1, pp. 37–48, 2015. 135 M. Schmitz, “RTCM State Space Representation Messages, Status and Plans,” in PPP-RTK & Open Standards Symposium, BKG, pp. 1–31, 2012. 136 RTCM, “Radio Technical Commission for Maritime Services (RTCM) Standard 10403.3, Differential GNSS (Global Navigation Satellite Systems) Services,” Version 3.3, 7 Oct. 2016, 2016.

259

12 Ground-Based Augmentation System Boris Pervan Illinois Institute of Technology, United States

12.1

Introduction

The Ground-Based Augmentation System (GBAS) is a local area differential GNSS (DGNSS) architecture designed to provide navigation services for civil aircraft users during precision approach and landing. The GBAS ground component, illustrated in Figure 12.1, is composed of a number of key elements, including multiple spatially separated multipath-limiting antennas, a comprehensive integrity monitoring system, and a VHF transmitter to broadcast differential corrections and integrity information to airborne users. The airborne component uses the differential corrections and integrity information to accurately estimate aircraft position (within about 1 m) and to perform the final quantitative assessment of navigation integrity.

12.2

Motivation for GBAS

Navigation for civil aircraft precision approach and landing has a history spanning many decades in the form of the instrument landing system (ILS). An ILS installation is made up of a VHF localizer (horizontal) beam, a UHF glideslope (vertical) beam, and three marker beacons under the approach path. During the final approach, an aircraft uses the localizer signal to determine its displacement from the runway centerline and the glideslope to measure its deviation from the nominal glidepath (typically 3 ). The marker beacons provide coarse distance checks to the aircraft during the approach. ILS has been an extremely reliable system over the years, with a flawless safety record (no fatalities have been directly attributed to ILS failure). However, there are a number of important practical issues that have motivated the development of GBAS. For example, the ILS system:

• • •

provides very limited capabilities for curved and parallel approaches, is highly sensitive to local terrain and nearby structures (the associated multipath must be eliminated through careful assessment and grooming of the local environment), and each glideslope and localizer can serve only a single runway end – meaning that two installations are needed to fully equip a single runway, and many more for an airport with several runways.

GBAS addresses all of these concerns. Curved and parallel approaches are easily handled; multipath is mitigated by antenna design; and a single GBAS facility can serve all runaway ends at an airport.

12.3

History of GBAS

The earliest concept related to today’s GBAS was the Special Category I (SCAT-I) standard developed in 1993 by RTCA [1]. It defined the requirements under which DGNSS could be used to support the same operations as a Category I ILS. At the same time, the Federal Aviation Administration (FAA) launched an agenda with more ambitious goals. The FAA’s “Pathfinder” Category III Feasibility Program [2] was a joint effort involving government (FAA and NASA), industry (E-Systems and Wilcox), and academia (Ohio University and Stanford University). The program was decisive success, culminating in over 400 successful automatic landings using different variants of DGNSS. On the basis of these successes, in 1995, the FAA launched the Local Area Augmentation System (LAAS) program [3]. Over time, the FAA has phased out the use of the LAAS moniker in favor of its international name, GBAS.

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

0004815231.3D 259

13/12/2020 12:53:42 AM

260

12 Ground-Based Augmentation System

GPS Satellites

Ranging Sources

Status Information

GBAS Ground Facility

Differential Corrections, Integrity Data and Path Definition

GBAS Reference Receivers

Omnidirectional VHF Data Broadcast (VDB) Signal

Figure 12.1

Overview of the GBAS (Source: Federal Aviation Administration (FAA)).

12.4 GBAS Performance Requirements The overall quality and utility of an ILS system is rated according to the specific aircraft operations it can support. These are divided into three tiers as follows [3, 4]:

• • •

Category I (CAT I): If the horizontal visibility on the runway, known as the runway visual range (RVR), is greater than 1800 ft, a CAT I system may deliver the aircraft down to a decision height (DH) of 200 ft. Category II (CAT II): If the RVR is greater than 1200 ft, a CAT II system may deliver an aircraft down to a DH of 100 ft. Category III (CAT III): These systems are generally designed for automatic landing. Some variability in ground system performance is allowed, ranging from 50 ft ≤ DH < 100 ft to no DH at all, depending on the degree of fault tolerance in the aircraft’s avionics.

0004815231.3D 260

GBAS is intended to provide equivalent performance with existing ILS CAT I, II, and III systems. It will also provide a “differentially-corrected positioning service” (DCPS) to support terminal area operations including initial approach, non-precision approach, missed approach, and departure, as well as more complex terminal area procedures. The GBAS service volume is approximately 23 nmi. GBAS precision approach and landing performance requirements are classified in terms of GBAS Approach Service Types (GAST). GAST A and GAST B designate systems whose performance is suitable for “approaches with vertical guidance” (APV-I and APV-II). A GAST C system is designed to support precision approach operations to the lowest Category I minima (i.e. RVR and DH). A GAST D system is designed to support precision approach operations to the lowest Category III minima, when augmented with other airborne equipment – as is the case with CAT III ILSequipped aircraft, which additionally use radar altimeters and inertial systems. The required performance is defined

13/12/2020 12:54:01 AM

12.4 GBAS Performance Requirements

as the navigation system performance as observed at the output of a fault-free airborne subsystem. Faults in the avionics are managed by onboard redundancy; these are outside the scope of the ILS and GBAS systems. GAST A and B are much less stringent services than GAST C (CAT I) and will not be discussed further (because any GAST C system will be capable of providing the same services). Going one step further, it is also true that a GAST D (Cat II/III) system will be able to provide GAST C service. The common requirements between the two systems will be described in in the context of a GAST C (CAT I) implementation. A GAST D system, which, as noted above, presumes additional airborne equipment, will satisfy all these requirements plus additional ones to enable CAT II/III operations. As is the case with other aircraft navigation systems, the requirements are allocated across four fundamental areas: Accuracy is the measure of the navigation system output error under fault-free conditions. It is most often specified in terms of required 95% performance. Integrity is the ability of the system to provide timely warnings when the system should no longer be used for navigation – for example‚ due to the presence of faulty sensor measurements. The metric typically used to quantify integrity is integrity risk, which is the joint probability that a navigation system error or failure is not detected and that it results in position errors exceeding either a horizontal alert limit (HAL) or a vertical alert limit (VAL). The effect of this joint event at the aircraft is called hazardously misleading information (HMI). Integrity risk is therefore the same as the probability of HMI. Continuity is the ability of the navigation system to meet the accuracy and integrity requirements for the duration of the intended operation. It is usually quantified by continuity risk, which is the probability of a detected, but unscheduled, navigation function interruption after the operation has been initiated. Availability is the fraction of time the navigation system is usable – as determined by compliance with accuracy, integrity, and continuity requirements – before the operation is initiated. The GBAS requirements for GAST C/CAT I are listed in Table 12.1 [5, 6]. As noted earlier, GAST D systems also need to meet these requirements. However, to understand the additional requirements for GAST D, some knowledge of GBAS integrity threats and their monitoring for GAST C will be required. We will therefore defer a discussion of GAST D requirements after the prerequisite topics are covered.

0004815231.3D 261

Table 12.1

GBAS GAST C requirements

Accuracy

Horizontal (95%)

16 m

Vertical (95%)

4m

Risk

2 × 10−7 per approach (150 s)

Time to alert

6s

LAL

40 m

VAL

10 m

Continuity

Risk

8 × 10−6 in any 15 s

Availability

Fraction of time

0.99 to 0.99999

Integrity

12.4.1

261

Reference Receivers

To ensure integrity and continuity in the event of a reference receiver failure, GBAS uses multiple reference receivers. At least three receivers are required to provide the desired capability for detection and exclusion of a failure of a single reference receiver. Four (or more) receivers can further help ensure availability (of integrity and continuity) after a detected receiver fault. The use of multiple reference receivers will also improve accuracy and fault-free integrity of the differential correction. This improvement is possible because ground multipath, which is the largest normal source of measurement error in GBAS that is not reduced by differential corrections, may be averaged across the multiple receivers. The antennas feeding each of these receivers are typically separated by 100 m or more to minimize multipath correlation between the receivers.

12.4.2

Multipath-Limiting Antennas

If left unmitigated‚ multipath is a significant error source in the measured code phase (pseudorange) at the GBAS ground receivers. Attenuating the multipath error in airport environments is not always easy. GBAS installations typically use special multipath-limiting antennas (MLAs), careful siting, averaging of differential corrections across antennas, and, if needed, masking troublesome spot regions of the sky (if they are the source of unwanted reflections from nearby structures). However, there is some flexibility allowed in ground system quality, which is measured by the standard deviation of the accuracy of the broadcast corrections, σ pr_gnd. GBAS ground system facility accuracy performance is divided into three separate classes, called Ground Accuracy Designators (GADs) [5]. Figure 12.2 shows the upper bound curves for σ pr_gnd as a function of elevation for the three classes of ground installation: GAD-A, GAD-B, and GAD-C. The curves assume averaging

13/12/2020 12:54:02 AM

262

12 Ground-Based Augmentation System

1 0.9

sigmapr-gnd

GAD-A

0.8

GAD-B

0.7

GAD-C

0.6 0.5 0.4 0.3 0.2 0.1 0

0

20

40 60 elevation (deg)

80

100

Figure 12.2 Standard deviation of broadcast carrier-smoothed correction error (in meters) due to multipath and receiver noise for a GBAS ground installation with three reference receivers.

across three reference receivers, which is a typical number for GBAS. The respective GAD performance for different numbers of reference receivers can be easily computed using the standardized formulas provided in [5–7]. The GBAS ground system will broadcast its GAD to airborne users as well as the values of σ pr_gnd for each satellite. It is anticipated that most ground systems will be GAD-C installations, because this high level of accuracy will be needed to enable GAST D service. An example of a vertically stacked dipole MLA for GAD-C is shown in Figure 12.3 (left image).

12.4.3

Ground Processing

GBAS ground processing has two main purposes: (1) generate differential corrections and other reference data for transmission to aircraft in the local area and (2) detect and remove of anomalies present in the GBAS “signal-inspace” (SIS) that would otherwise result in an unacceptable integrity risk to an aircraft on the final approach. The satellite signals and broadcast reference data collectively define the GBAS SIS. The notion of an SIS is introduced to distribute accountability between the ground and airborne navigation subsystems. The aircraft is responsible for the proper functionality of the airborne equipment (which would generally include the implementation of redundant sensor tracks to provide the means for detection and removal of airborne equipment failures), while the GBAS ground system is responsible for the detection of anomalies in both the received satellite signals and the GBAS reference data broadcast to the aircraft. The ground system functions form the core of the GBAS system, and

0004815231.3D 262

Figure 12.3 (Left) BAE ARL-1900 multipath-limiting antenna for GAD-C; (right) DB Systems three-element VHF Data Broadcast (VDB) antenna.

therefore will be discussed separately, in much greater detail, in Section 12.6.

12.4.4

VHF Data Broadcast

The VHF Data Broadcast (VDB) organizes and encodes the data provided by the GBAS ground processor into a standardized format and transmits it to local area users. The VDB operates in the 108–117.975 MHz frequency band in 25 kHz channels, using a time division multiple access (TDMA) protocol. The messages are encoded by a differential 8-phase shift keying (D8PSK) modulation format and updated and broadcast at 2 Hz. An example VDB broadcast antenna is shown in Figure 12.3 (right image). There are 10 message types (see Table 12.2) [8], three of which are directly relevant to differential positioning – Message Types (MT) 1, 2, and 11 – and one message, MT 4, which provides data describing the local final approach and terminal area procedures. MT 4 is broadcast every 10 s. MT 1 is the core GBAS message; it contains the ranging corrections obtained using 100 s carrier-smoothed pseudoranges, associated correction rates and error standard deviations, as well as orbit ephemeris decorrelation parameters, and so-called b-values, which will be described in Section 12.6. MT 1 is broadcast at a 2 Hz rate. It is intended to support GAST C service. For GAST-D-capable GBAS

13/12/2020 12:54:02 AM

12.5 Error Sources and Faults

Table 12.2 Message type

263

VDB messages and broadcast rates from [8]

Message name

Minimum broadcast rate (Note 5)

Maximum broadcast rate

1

Differential corrections – 100 s smoothed pseudoranges

For each measurement type: All measurement blocks, once per frame (Note 1)

For each measurement type: All measurement blocks, once per slot (Note 1)

2

GBAS-Related Data

Once per 20 consecutive frames

Once per frame

3

Null message

N/A

Once per slot

4

Final Approach Segment (FAS) construction data

All FAS blocks once per 20 consecutive frames (Note 2)

All FAS blocks once per frame (Note 2)

Terminal Area Path (TAP) construction data

(Notes 2 and 3)

(Notes 2 and 3)

5

Ranging source availability

All impacted sources once per 20 consecutive frames

All impacted sources once per 5 consecutive frames

6

Reserved for carrier corrections

—

—

7

Reserved for military

—

—

8

Reserved for test

—

—

11

Differential corrections – 30 s smoothed pseudoranges

For each measurement type: All measurement blocks, once per frame (Note 4)

For each measurement type: All measurement blocks, once per frame (Note 4)

101

GRAS pseudorange corrections – (As defined in the ICAO Amex 10 SARPs)

—

—

Note: The notes referenced in the table are in [8]. A “frame” is ½ s in length. Source: From RTCA DO-246E, GNSS-Based Precision Approach Local Area Augmentation System (LAAS) Signal-in-Space Interface Control Document (ICD), 13 July 2017.

installations, MT 11 is also broadcast at a 2 Hz rate to augment MT 1 by additionally providing corrections for 30 s carrier-smoothed pseudoranges (and associated correction rates and standard deviations). The significance of the two different smoothing time constants will be discussed in Section 12.8. MT 2 contains additional information relevant ionospheric and tropospheric spatial decorrelation and protection level generation. The data is not needed for positioning, but it is critical for integrity assurance. However, the data in MT 2 does not change in response to real-time measurements at the reference station, and therefore it does not need to be broadcast at the same high rate as MTs 1 and 11. Like MT 4, it will typically be broadcast once every 10 s.

12.4.5

Avionics

At the GBAS user end, the avionics processor applies the received differential corrections to the smoothed pseudoranges obtained at the aircraft. The corrected pseudoranges are then used to estimate the aircraft’s position, with a resulting accuracy of about 1 m (1-σ). In addition to generation of these real-time position estimates, which is an obvious practical requirement for the navigation system, the GBAS avionics also has an important role in the integrity

0004815231.3D 263

assurance process. Because it has knowledge of the satellites that are being used in the position estimate, which the ground does not, the position-domain protection levels are also produced by the avionics. In addition, there are some specific SIS monitoring functions, in particular aiding the detection of ionospheric fronts, that are also resident in the avionics. These integrity functions and the protection levels will be discussed in detail in the next section.

12.5

Error Sources and Faults

In basic local area DGPS, a reference GPS receiver is placed at a precisely known location in the near vicinity of the user to calibrate GPS SIS errors. These include nominal satellite orbit and clock errors and nominal ionospheric and tropospheric delays, all of which are highly spatially correlated. DGPS is not effective against native receiver errors like thermal noise and multipath; these are actually increased because multiple receivers are used – two in basic DGPS (reference plus user) and more in GBAS (multiple references plus user). Nevertheless, because the SIS errors are typically much larger, positioning accuracy can be improved significantly, to the sub-meter level, using GBAS.

13/12/2020 12:54:02 AM

264

12 Ground-Based Augmentation System

12.5.1

Nominal Error Sources

σ tropo = σ N h0 f θ

The residual nominal errors are due to multipath, thermal noise, and spatial and temporal decorrelation. A detailed description of these error sources and their modeling can be found in [7]. Multipath and thermal noise error variances at the GBAS ground system can vary depending on the multipath rejection capabilities of the ground system antennas; the three GAD classes are shown in Figure 12.2. It is expected that GAST C and D installations will adhere to the GAD-C standard. The aircraft multipath and thermal noise variances are classified into either of two types, Airborne Accuracy Designator (AAD) A or B; these are shown in Figure 12.4. Aircraft serving GAST D must be equipped with AAD B equipment [9]. Residual tropospheric errors are primarily due to the altitude differences (Δh) between the reference station and aircraft. They are largely removed via modeling using broadcast data in MT 2, which includes the local estimated refractivity index (NR) and tropospheric scale height (h0), as well as the refractivity uncertainty (σ N). The tropospheric correction (TC) applied at the aircraft is TC = N R h0 f θ

1 − e − Δh

h0

≈ N R f θ Δh 12 1

where θ is the satellite elevation angle, and f (θ) is the associated mapping function: f θ = 10 − 6

0 002 + sin 2 θ

12 2

The post-correction tropospheric error is assumed to be zero mean with standard deviation given by

0.6

Sigmapr-air

0.55 0.5

AAD A

0.45

AAD B

0.4 0.35 0.3 0.25 0.2 0.15 0.1

0

20

40 60 Elevation (deg)

80

100

Figure 12.4 Standard deviation of carrier-smoothed pseudorange error (in meters) due to multipath and receiver noise for a GBAS-equipped aircraft.

0004815231.3D 264

1 − e − Δh

h0

≈ σ N f θ Δh 12 3

Residual ionospheric error due to spatial decorrelation cannot be modeled like the troposphere because of the extreme spatial variability of the ionosphere (even under normal conditions). However, the differential ranging error is equally likely to be positive or negative, so it is modeled as zero mean. The standard deviation of the error is proportional to the standard deviation of the vertical ionospheric gradient (σ VIG), and the effective displacement (xeff) between the reference station and the aircraft: σ iono = σ VIG g θ x eff

12 4

where g(θ) is the obliquity factor gθ =

1−

RE cos θ RE + hI

2

12 5

RE is the Earth radius (6378 km), and hI is the assumed ionospheric shell height (350 km). The effective distance is the sum of the physical distance and an additional virtual displacement caused by the “memory” of the airborne smoothing filter of the aircraft traveling through the gradient: x eff = x air + 2vair τ

12 6

where xair is the physical displacement between the current aircraft location and the GBAS reference point indicated in MT 2, vair is the aircraft’s ground speed, and τ is the smoothing filter time constant. The proof of this result is provided in [10]. The parameter σ VIG is broadcast in MT 2. Values of 2 to 4 mm/km are typical, but some margin may be implemented to account for unmodeled effects of horizontal tropospheric variations, as suggested in [11]. Orbit ephemeris errors also decorrelate spatially, but under normal (unfaulted) conditions the resulting satellite position errors are on the order of a few meters, which is far too small to cause appreciable differential error even for aircraft at the outer edges of the GBAS service volume. Finally, as noted earlier, the effect of data link latency is managed by broadcasting the rate of change of the pseudorange correction in MT 1. The result is centimeter-level differential error at the aircraft given nominal range accelerations. It is important to keep in mind, however, that satellite orbit and clock faults can cause much larger differential ranging errors. This will be discussed in some detail in the next sections. The effects of all of the nominal errors are quantified by the fault-free protection levels [5]. For example, the faultfree vertical protection level is

13/12/2020 12:54:02 AM

12.5 Error Sources and Faults

N

S2v,i σ 2i = kffmd σ v

VPLH0 = kffmd

12 7

i=1

where N is the number of satellites usesd in the position estimate, Sv,i is the partial derivative of position error in the vertical direction with respect to the corrected pseudorange error on the ith satellite, σ 2i is an upper bound of the variance of the nominal error (due to all sources) of the corrected pseudorange used at the aircraft for satellite i, and σ v is the standard deviation of the nominal vertical position error. This position error bound is consistent with the integrity risk allocated to the fault-free hypothesis, which is encoded in the integrity multiplier, kffmd, whose value (based on a bounding zero-mean normal distribution) ranges from 5.76 to 5.85 [9], depending on the number of reference receivers being used.

12.5.2

Anomalous Error Sources

The most important potential threats to GBAS integrity are listed in Table 12.3. There are three possible ultimate origins: GPS SIS faults (i.e. the satellites), GBAS ground station faults, and anomalies in the propagation medium. The mean fault rate for most of the SIS faults is assumed to be 10−4/h. This rate is much larger than the satellite fault probability of 10−5/h specified in the GPS Standard Positioning Service Performance Specification (GPS-SPS-PS) [12]. The reason for this Table 12.3

265

is that the definition of fault in the GPS-SPS-PS corresponds only to errors larger than 4.42 × σ URA. The broadcast GPS navigation data provides the information needed to compute σ URA for each satellite, and the smallest σ URA that can currently be encoded is 2.4 m. This means that faults smaller than about 10 m are never accounted for in the specified 10−5/h rate, and that faults much larger than 10 m may not be covered for satellites with larger σ URA. Because operations with VAL = 10 m will be heavily influenced by ranging errors with magnitudes smaller than 10 m (per satellite), the GPS SPS-PS fault definition is not suitable for GBAS. So, to include the probability of occurrence of smaller faults, a fault rate of 10−4/h – an order of magnitude larger than the GPS-SPS-PS rate – is used instead. This specific rate is based on analysis in [13]. The use of 10−5/h for ephemeris faults is justified by the fact that extremely large satellite position errors (1000 m or more) are needed to produce worrisome differential positioning errors. As long as only satellites with σ URA≲ 200 m are used, the GPS-SPS-PS specified rate of 10−5/h can be safely assumed. As discussed in Section 12.5.1, nominal spatial and temporal variations in the ionospheric delays are accounted for in GBAS and do not pose a threat. However, unusual behavior during ionospheric storms may result in large spatial gradients, over 400 mm/km in slant ionospheric delay, which are referred to as ionospheric fronts. Such structures have been observed over continental United States (CONUS) in 2000 and 2003 and are detailed in [14]. It is expected that much higher values are possible in more active regions near the equator. For an approaching aircraft using GBAS, gradients this large could cause vertical

GBAS anomalous error sources and faults [4], and prior probabilities of occurrence

Origin

Fault/anomaly

Threat

Prior probability

SIS

Excessive range acceleration

Rapid accelerations cause large differential errors over latency period

10−4/h

SIS

Erroneous ephemeris data

Large satellite position errors lead to differential positioning errors

10−5/h

SIS

Satellite signal deformation

Inconsistent correlation errors between ground and air receivers causes differential ranging error

10−4/h

SIS

Code-carrier divergence

Ground and air filter mismatches and differences in start times lead to differential ranging error

10−4/h

SIS

Low satellite signal power

Possible ranging error caused by cross-correlation with satellite with stronger signal

10−4/h

Propagation Environment

Ionospheric storm fronts

Large ionospheric gradients cause large differential ranging errors due to spatial decorrelation

10−3 to 1 (state probability)

GBAS Ground System

Reference receiver/ antenna failures

Erroneous measurements from reference receiver lead to errors in broadcast correction

10−5/approach

Source: From Federal Aviation Administration, “Criteria for Approval of Category III Weather Minima for Takeoff, Landing, and Rollout,” Washington DC, Advisory Circular AC 120-28D, July 1999.

0004815231.3D 265

13/12/2020 12:54:02 AM

266

12 Ground-Based Augmentation System

position errors of up to 20 m. More details about the hazardous impact of sharp ionospheric fronts on GBAS navigation are provided in [14]. The prior probability that may be assumed for ionospheric storm fronts is still a matter of some debate. The range provided in the table is bounded on the high end by the most conservative possible assumption and on the lower end by a more realistic value that may be justifiable based on data collected to date. The probability of a ground receiver failure is limited by specification to be no larger than 10−5 per 150 s aircraft approach (equivalent to 2.4×10−4/h). This ensures that at most one reference receiver fault would ever need to be detected to satisfy the 10−7/approach integrity requirement.

12.6

12.6.1

The SIS Receive and Decode (SISRAD) function (A) is executed by the GPS reference receiver and antenna subsystem. Its inputs are the L1 RF Signals from the GPS satellites, conforming to the GPS-SPS-PS [12]. Its outputs are raw code phase (pseudorange) and carrier phase measurements, both at 2 Hz rates, as well as decoded satellite navigation data, which is output immediately after the is decoded. The Signal Quality Receive (SQR) function (B) is also a GPS receiver, but it has the more specific purpose of generating observables to be used in some Signal Quality Monitor (SQM) tests, in particular those that target signal deformation faults. Other SQM tests are designed to detect codecarrier divergence and low satellite signal power events. These latter monitors can work with either SISRAD or SQR outputs. It is also possible to implement the SISRAD and SQR functions in a single receiver. The intent of the SQM functions (E) is to detect and identify anomalies in the received GPS SIS resulting from satellite signal generation or transmission failures – for example, deformation of the L1 code correlation peak. Implementation of SQM at the GBAS ground segment is necessary to ensure interoperability of different types of

GBAS Integrity Monitoring

An example functional flow diagram of GBAS groundbased integrity monitoring is shown in Figure 12.5. The associated function and acronym definitions are provided in Table 12.4. It is evident from the diagram that GBAS integrity monitoring presents a complex and multifaceted challenge. Some of the important details involved are discussed in the following subsections.

GPS SIS

Signal Quality Monitoring

P

Database

A

SISRAD C

B

D

MQM

SQR

Smooth GBAS Messages

E

F

SQM

DQM L

G

VDB Message Formatter & Scheduler

Executive Monitor

M

VDB TX

GBAS Messages

H

Correction O I

J

Average

Q

Figure 12.5

0004815231.3D 266

K

MRCC

σ-Monitor

VDB Monitor

N

VDB RX

LAAS Ground System Maintenance

GBAS ground system functional flow.

13/12/2020 12:54:02 AM

12.6 GBAS Integrity Monitoring

Table 12.4

267

GBAS function definitions and acronyms

A. SISRAD: Signal-in-Space Receive and Decode Function B. SQR: Signal Quality Receiver Function C. MQM: Measurement Quality Monitor Functions D. Smooth: Carrier-Smoothed Code Function E. SQM: Signal Quality Monitor Functions F. DQM: Data Quality Monitor Functions G. EXM: Executive Monitor Functions H. Correction: Correction Generation Function I. Average: Clock Adjustment and Correction Average Functions J. MRCC: Multiple Receiver Consistency Check Functions K. σ-Monitor: Standard Deviation and Mean Monitoring Function L. VDB Message Formatter and Scheduler M. VDB TX: VDB Transmitter N. VDB RX: VDB Receiver O. VDB Monitor: Data Broadcast Parameter Verification Functions P. Database: Approach Path, Antenna Loc., Elev. Mask, VDB Info. Q. LAAS Ground System Maintenance: External Maintenance Function and Data Archive

receivers in the LAAS service volume. This is important because ground and airborne equipment will typically be built by different manufacturers. Detection and isolation of signal anomalies on the ground is needed because ground and airborne receivers may respond differently during such events‚ resulting in differential ranging errors. The impacts and monitoring of signal deformation faults are discussed in detail in Chapter 10, so the subject will not be elaborated on further here. The SQM signal deformation monitor specifications for GBAS are provided in attachment D of [6]. Low satellite signal power (due to an onboard failure) can directly affect the thermal noise contribution to the ranging error standard deviation. The most straightforward monitor simply tests the estimated C/N0 against a predetermined threshold. However, satellites that are broadcasting at anomalously low power levels can present additional problems because of the potential for cross-correlation within the receiver with other satellite PRNs with higher received powers. The effect occurs only when the Doppler difference between the two satellites is an integral multiple of 1 kHz [15, 16]. Therefore, it can be monitored by using predicted Doppler differences together with the estimated C/N0. Code-carrier divergence (CCD) can be caused by ionospheric activity or a satellite fault. The latter is the primary CCD threat, because the ionosphere cannot produce arbitrarily large divergence rates, but it is theoretically possible that satellite failures can. This motivates the need for ground-based CCD monitoring. During active ionospheric

0004815231.3D 267

events, the CCD monitor can also help detect moving storm fronts. However, as will be discussed shortly, there are other means of monitoring against ionospheric fronts. In GBAS, both the reference station and the aircraft employ code-carrier smoothing to mitigate the effects of receiver noise and multipath. For GAST C, a first-order filter with a 100 s time constant is implemented; for GAST D, a separate 30 s filter is also used. In the event of a CCD fault, transient differential ranging errors will result if there are differences in either (1) ground and air filter implementations, or (2) start times of ground and air filters. A typical GBAS CCD ground monitor filters raw code-minus carrier over time to estimate the divergence rate. A detailed description of this type of monitor may be found in [17]. The smoothing function (D) uses the carrier phase measurements to reduce errors on the code phase due to noise and high-frequency multipath. The standard GBAS smoothing filter is pk =

N −1 1 p k − 1 + ϕk − ϕ k − 1 + p k N N

12 8

where k is the time index, Δt is the sample interval (0.5 s for the ground; 0.2 s for air), N is the number of samples used to define the filter gain, τ = N × Δt is the time constant of the smoothing filter (100 s for GASC C and 30 s for GAST D),

13/12/2020 12:54:02 AM

268

12 Ground-Based Augmentation System

p is the raw pseudorange (code phase), p is the smoothed pseudorange, and ϕ is the carrier phase (expressed in the same length units as p). The same filter is prescribed at the ground and aircraft, which helps to significantly limit the potential impact of undetected CCD faults, but some variation in filter startup is permitted. The linear time-invariant (LTI) filter defined above can be implemented directly. Alternatively, a linear time-varying (LTV) version can be used at startup. This filter differs from the LTI filter only during the first 100 s (or 30 s) of operation, when the effective filter time constant increases uniformly in time up to the k = τ/Δt, at which point the gain is held constant and the LTI filter is the result [9]. Using a time-varying gain at start-up significantly speeds up the noise reduction benefits of the filter, but it does increase the differential ranging error somewhat after a CCD fault. These small effects have been carefully considered in the design of and integrity analysis; see, for example, [17].

12.6.2

Measurement Quality Monitoring

The MQM functions (D) are designed to detect anomalous satellite signal generation and propagation behaviors that are potentially observable in the measurements directly. For example, they provide the means for detection of excessive range acceleration faults, including step and impulsive errors. Detection of these faults is necessary for ground/air interoperability because a constant range rate model is used at the aircraft to account for latency in the broadcast corrections. Due to natural delays in the ground processing, data formatting, and transmission, the reference corrections received at the aircraft will typically be delayed about 0.5 s relative to the punctual airborne GPS receiver output. There are two basic ground-based tests that have been put forward to detect these events. The first is the carriersmoothed-code innovations test, which compares the filter-predicted pseudorange, pk − 1 + ϕk − ϕk − 1 , with the actual measurement, pk, relative to a predefined threshold. It is effective as a coarse check against rapid changes in the range rate. The second monitor, known as the excessive acceleration (EA) test, is more important, because it directly estimates the second derivative of the clock error using the last three measurements [18]. Using the estimate, along with the known estimate error statistics, the maximum differential ranging error can be upper-bounded for any specified data latency. The MQM function also includes an ionospheric gradient monitor (IGM) to detect potentially hazardous ionospheric storm fronts. GBAS installations will have multiple spatially separated GPS antennas, primarily intended to detect and

0004815231.3D 268

isolate receiver faults, but also to reduce the ranging error by averaging measurements for a given satellite. However, differential carrier phase measurements across these antennas can also be used to detect the presence of ionospheric fronts. This type of monitor was first introduced in [19] and subsequently investigated in more detail in [20, 21] and [22]. It is a powerful means of detecting ionospheric fronts, but it cannot see fronts that do not reach the GBAS ground antennas; these can still affect an aircraft during parts of its final approach. As noted in the SQM discussion above, the ground CCD monitor also contributes to ionosphere front detection. However, fronts that are nearly static are invisible to it. Because of the limitations of the IGM and CCD ground monitors against ionospheric fronts, GAST D aircraft are also required to take an active role by applying the following four monitors and mitigations [9]:

• • • •

Implement an airborne CCD monitor of the type similar to that on the ground. As the aircraft passes through a gradient‚ it will be visible as CCD, unless that front is moving at nearly the same speed as the aircraft. Generate and use position estimates using 30 s smoothed pseudoranges instead of the standard 100 s smoothed pseudoranges used for GAST C. This decreases τ in Eq. (12.6), thereby making xeff smaller and reducing the effect of gradients (nominal or anomalous) on the differential ranging error. Implement a new detection function, called the Dual Solution Ionospheric Gradient Monitoring (DSIGMA), which computes the difference between the 30 s smoothed and 100 s smoothed position solutions. If the absolute value of the difference between the two is greater than 2 m, the aircraft must fall back to GAST C operations. Perform satellite geometry screening, in which the aircraft will compare the maximum absolute value of any single Sv,i and the sum of the two maximum absolute values of Sv,i (and their lateral equivalents) to separate user-specified thresholds. If either threshold is exceeded, the aircraft must fall back on GAST C operations. The test assumes that the probability of three or more satellite being affected by an ionospheric front is negligibly small. The thresholds are based on the aircraft airworthiness requirements described in Appendix J of [9].

12.6.3

Data Quality Monitoring (DQM)

The DQM functions (F) are implemented to detect anomalies in the decoded GPS satellite navigation data. Of particular importance is the need to provide protection against the possibility of errors in the broadcast ephemerides that

13/12/2020 12:54:02 AM

12.6 GBAS Integrity Monitoring

define the satellite orbits. Satellite ephemeris errors that are in the reference-to-satellite line-of-sight (LOS) direction are implicitly corrected for using DGPS. However, satellite orbit errors orthogonal to the LOS can lead to an effective differential ranging error proportional to the distance between the reference station and the aircraft. Although there may be a variety of potential causes for such anomalies, for example, unscheduled maneuvers, incorrect orbit uploads, and faulted data decoding in the receiver, all ephemeris errors can be categorized into just two basic types, with the first type being further subdivided into three subtypes: Type A: The broadcast ephemeris data is erroneous following a satellite maneuver. Type A1: A nominal station-keeping maneuver occurs, and the satellite is set to unhealthy status by the GPS ground segment during the maneuver, but after the maneuver the satellite is restored to healthy status with an incorrect ephemeris. Nominal GPS maneuvers only occur in the along-track direction (i.e. tangent to the direction of motion of the satellite, either positive or negative). Type A2: A nominal station-keeping maneuver occurs, but the satellite is not set to unhealthy status by the GPS ground segment during the maneuver. GBAS continues using the broadcast (pre-maneuver) ephemeris, but the satellite orbit has since changed. Type A2’: An unscheduled maneuver occurs in any direction. This fault subtype acknowledges the possibility of an operational fault causing the firing of arbitrary thrusters, thereby changing the orbit. Type B: The broadcast ephemeris data is erroneous, but no satellite maneuvers are involved. Both Type A and Type B events can cause differential ranging errors. However, the two failure types differ in both likelihood of occurrence and means of detection. The likelihood of Type B failures is relatively higher than Type A because orbit ephemeris uploads and broadcast ephemeris changeovers are frequent (nominally once per day and once every two hours, respectively, for each satellite), whereas spacecraft maneuvers are rare (not more frequent than once or twice per year). Nevertheless, both fault types have occurred in the past: Type B on 17 June 2012 (SVN 59), Type A1 on 20 July 2004 (SVN 60), and Type A2 on 10 April 2007 (SVN 54). In each of these cases‚ the maximum orbit error ranged from 400 m to many kilometers. No known Type A2’ faults are known to have occurred, and the corresponding prior probability of such faults is expected to be lower. However, the potential for this type of fault must still be accounted for in GAST D designs.

0004815231.3D 269

269

GBAS standards [5, 6] assign the responsibility for detecting orbit ephemeris faults to the ground facility, rather than to the users. However, it is recognized that any monitor implementation, ground or aircraft based, will be imperfect (i.e. smaller ephemeris errors will be difficult to detect) and any undetected orbit error will ultimately cause navigation errors that are dependent on the (time-varying) displacement between the ground and aircraft antennas. Therefore, the impact of possible undetected orbit errors on navigation must ultimately be assessed separately by each individual aircraft within the GBAS service volume. Accordingly, along with the DGPS ranging corrections, the GBAS MT 1 also carries an ephemeris decorrelation parameter that defines the minimum ephemeris gradient error detectable by the ground monitor. The bound on navigation error is consistent with the integrity risk allocated to ephemeris faults, which is also broadcast to users in MT 1 via a missed detection multiplier k mde . The aircraft uses this information to compute vertical and horizontal position error bounds under the hypothesis of an ephemeris failure. The vertical error bound associated with an ephemeris fault on satellite j is N

VEB j = Sv,j x air

j

S2v,i σ 2i ,

+ k mde

12 9

i=1

The resulting bound over all satellites being used is then VEB = max VEB j j

12 10

The horizontal/lateral ephemeris error bounds are analogous. An alert condition will be triggered at the aircraft when the ephemeris position bounds exceed fixed alert limits, VAL (and LAL), defined for the specific aircraft procedure. The capability to generate such alerts is necessary to ensure navigation integrity. However, to maintain continuity‚ it is important that the minimum position error bound be small, which, in turn, means that j must be small, establishing a minimum performance limit for the ephemeris monitor. The decorrelation parameter is defined as a spatial gradient in terms of the minimum detectable satellite position error (MDE), j

= MDE ρ j ,

12 11

where ρj is the distance to the satellite from the reference station. The detection probability associated with MDE must also be consistent with the broadcast value of k mde as well as the assumed prior probability of ephemeris fault (in Table 12.3). As each new ephemeris – with new or updated parameters – is received it must be validated before it is

13/12/2020 12:54:03 AM

270

12 Ground-Based Augmentation System

used. To mitigate Type B threats, the GBAS ground station can store validated prior ephemerides and use them to project forward an independent predictive estimate of the current ephemeris for comparison. The last available validated ephemeris will usually be the previously transmitted one (2 h old). For a new rising satellite‚ however, it will be the last ephemeris received at that particular LGF on the previous pass. The limiting case will be for a pass that is shorter than 2 h, where the difference in broadcast ephemeris times approaches 24 h. Figure 12.6 shows an example of variation of an orbit semimajor axis over adjacent 24 periods for a typical satellite. Forward projection of previously validated ephemeris parameters for monitoring can be done in a variety of ways, the simplest of which, the zero-order hold (ZOH) and first-order hold (FOH), are shown in Figure 12.7. These types of monitors have been described in detail in [23].

Variation in semimajor axis

300 250

Meters

200 150 100 50 0 0

5

10

15

20 25 Days

30

35

40

Figure 12.6 Example change in broadcast semimajor axis at 24-hour intervals.

45

In Type A faults, ephemeris data is erroneous following a satellite maneuver. A Type B monitor like the one described above is not effective against such threats because its predictive capability is compromised by the intervening maneuver. Instead, it is necessary to directly monitor ranging measurements to determine whether they are consistent with the broadcast ephemerides. The most straightforward approach is to monitor the size of the pseudorange correction. GBAS will actively cull any ephemeris errors that have a component in the LOS direction exceeding 328 m, the correction message field in MT 1. However, this test alone is not sufficient because errors orthogonal to the LOS (which are the main risk for GBAS) are not removed. Another proposed monitor compares range rate measurements over time against the ephemeris predictions. The monitor is generally effective, but analytical proof of its integrity sufficiency is difficult, especially for Type A1 and A2’ faults [24]. The most effective monitor against such faults is the GAST D IGM, which is equally capable of detecting gradients that originate from either ionospheric fronts or orbit ephemeris errors. The application of this monitor concept to the detection of orbit ephemeris faults is discussed in detail in [25, 26] and [27]. In addition to integrity screening of the navigation data, the GBAS ground system also broadcasts an Issue of Data (IOD) time tag for each satellite in MT 1. This ensures that the aircraft will know what ephemeris was used on the ground to generate the broadcast corrections. Inconsistencies in the ephemerides used on the ground and in the air can lead directly to effective differential ranging error because the aircraft will not be able to correctly “reconstitute” the ground measurements. For added integrity, the GBAS ground system also broadcasts a 16bit CRC on the ephemeris message used to generate the corrections.

12.6.4 ZOH

Today–2 Today–1 Today

Figure 12.7 concepts.

0004815231.3D 270

FOH

Today–2 Today–1 Today

Zero- and first-order hold parameter prediction

Executive Monitor

The Executive Monitor (EXM) function (G) is a central logic processing algorithm that consolidates detection decisions across different monitors to identify which satellites and which receivers have failed. Given the outputs of the monitors described so far, it is possible to make determinations about failed satellites (including satellites that have experienced propagation anomalies). In the first phase of EXM, satellites are either screened or validated based on the current monitor detection results. The second phase is implemented in conjunction with the Multiple Reference Consistence Check (MRCC), which will be described shortly.

13/12/2020 12:54:03 AM

12.6 GBAS Integrity Monitoring

12.6.5 Correction Generation, Clock Adjustment‚ and Correction Average Functions The correction function (H) is used to reduce the amount of data broadcast. For each satellite on each reference receiver, the computed range to the satellite (rk), based on the known location of the reference antenna and the location of the satellite (as computed using the navigation data), is subtracted from the smoothed measurements to compute the pseudorange correction ck = pk − r k . Since the aircraft also has access to the GPS satellite navigation data, it has enough information to reconstitute the original reference receiver measurement by simply adding back the removed terms. This is not necessary, however, because the correction can be applied directly to the aircraft’s ranging measurements. The clock adjustment and correction average function (I) is implemented to level the receiver clock biases; these biases are different for each of the reference receivers. This function is required for two reasons: (1) to further reduce the amount of unnecessary data broadcast and (2) to facilitate a simpler consistency check of measurements across reference receivers. The clock adjustment sub-function is implemented by subtracting the average of the smoothed corrections across each receiver from those for each individual satellite. Define Sc to be the set of common satellites tracked by all EXMvalidated reference receivers, Nc as the number of elements in Sc, and m and n to be individual receiver and satellite indices, respectively. Then the clock-adjusted smoothed pseudorange corrections is ck n, m = ck n, m −

1 Nc n

ck n, m

12 12

Sc

The correction average sub-function generates candidate broadcast corrections by averaging ck n, m for a given satellite across all reference receivers tracking the satellite. Define Sn as the set of reference receivers with at least two EXM-endorsed values of ck n, m for satellite n. (Two or more measurements are needed for subsequent processing, as described below.) Also, define M(n) to be the number of elements of Sn. The candidate broadcast correction (smoothed, clock-adjusted, and averaged) is then ck n =

1 M n

B-Values and MRCC

The purpose of the “b-value” generation and MRCC functions (J) is primarily to facilitate the computation of integrity protection levels at the aircraft, and secondarily to prescreen reference receiver measurements prior to broadcast of the corrections. The b-values are defined as the difference between ck n as defined in Eq. (12.13) and its equivalent with each individual receiver removed in turn: bk n, m = ck n −

ck n, m

12 13

m Sn

1 M n −1

12 14

ck n, i i i

Sn m

As defined, the b-value gives the best estimate of the error in the broadcast correction under the hypothesis of a single reference receiver failure. For example, if N satellites are being tracked on all M reference receivers, given a fault ∗ f nm∗ on reference receiver m∗on the receiver channel corresponding to satellite n∗, the mean b-values are n∗

∗

E bnm∗ = N − 1 f m∗ E bnm∗ n

12 15

n∗

∗

= − f m∗

12 16

E bnm

m∗

=

N − 1 n∗ f ∗ M−1 m

12 17

E bnm

n∗ m∗

=

1 n∗ f m∗ M−1

12 18

∗

n∗

∗

where f m∗ ≜ f nm∗ MN . For a large fault, it is evident the b-value in Eq. (12.15) will be much larger than the others. The MRCC test exploits this fact to detect large faults and then returns the result to the EXM for a second phase of fault identification and screening. However, it is possible that faults of intermediate size will be left undetected by MRCC/EXM and be passed along to the aircraft in the broadcast corrections. To ensure integrity, the ground broadcasts the b-values to the aircraft so that it can compute position-domain protection levels under the hypothesis (H1) of a failure on reference receiver m [9]: N

VPLH1 m =

Averaging across multiple independent receivers reduces the variance of the multipath error in the broadcast correction for satellite n by a factor of 1/M(n).

0004815231.3D 271

12.6.6

271

N

Sv,n b n, m n=1

S2v,n σ 2n

+ kmd n=1

12 19 The upper bound protection level over all reference receivers is

13/12/2020 12:54:03 AM

272

12 Ground-Based Augmentation System

VPLH1 = max VPLH1 m m

12 20

This position error bound is consistent with the integrity risk allocated to the H1 hypothesis, which is encoded in the integrity multiplier bound, kmd, whose value is approximately 2.8 (the exact value differs very slightly depending on the number of reference receivers being used) [9].

12.6.7

Sigma Monitor

The GBAS ground system will broadcast the values for σ pr_gnd each to use for each satellite. These will be used as inputs to position error bounds in Eqs. (12.7), (12.9), (12.10), (12.19), and (12.20). Therefore, it is critical that the ground system be capable of detecting any changes – in particular, increases – in σ pr_gnd over time. Monitoring changes in variance can be done in a number of ways, including direct estimation and cumulative sum (CUSUM) monitoring. These methods are described in some detail in [28] and [29]. It is important to understand that detection of variance changes takes some time, and cannot be expected to meet GAST C or D time to alert requirements. However, if the probability of undetected variance change is treated as a state probability (related to an attribute of the ground station), rather than as fault event to be detected within a specified time to alert, it is possible to build a coherent integrity case. A rigorous approach to do this is provided in [29].

12.7

GBAS Integrity Analysis: GAST C

requirements. For all these faults, we must ensure that the probability of the aircraft position error exceeding the VPL (or LPL) is no larger than the ratio of the GBAS ground system manufacturer’s integrity risk allocation for the fault and its prior probability of occurrence (10−4/h for all remaining faults in Table 12.3). As will become evident in the remainder of this section, this is not an easy task, even for the simplest monitors. For a given SIS monitor and a fault fj on satellite j, we can express the test statistic qj ≥ 0 as a positive random variable with a known cumulative distribution function Fq(x; fj). For a given continuity allocation to the monitor’s fault-free detection probability, Pffd, the detection threshold is L = F q− 1 Pffd ; 0 The probability of a Loss of Integrity (LOI) is then defined as P LOI f VPL t −∞ , T A − τg

t

f

0, T A

t

qj t 12 21

j

where ev is the vertical position estimate error, TA is the required time to alert, τg is the latency in the transmission of information to the aircraft, and t is the time since fault onset. For GAST C, TA = 6 s, and τg will typically be less than 1 s and can never exceed TA (because the continuity of the navigation function will be terminated at that point). Only vertical errors are considered in Eq. (12.21), but the same analysis can be applied to the lateral case. Noting that VPLH0 ≤ VPL, we can write the following upper bound on Eq. (12.21): P LOI f

The largest of the position error bounds in Eqs. (12.7), (12.9), (12.10), (12.19), and (12.20) (and their lateral counterparts) is the overall VPL (and LPL). It is compared to the VAL (and LAL) to ensure that integrity requirements are met under normal error conditions, and under the hypotheses of orbit ephemeris and reference receiver faults. Implicit in this statement is that GBAS ground system manufacturers demonstrate that

j

j

ev t > VPLH0 t

VPLH0

P

P

ev > VPLH0

f

j

=P

Sv,j f

j

+ εv > k ffmd σ v , 12 27

where εv is the nominal (fault-free) contribution to the vertical position estimate error, which can be upperbounded using a normal distribution with standard deviation σ v using the techniques described in [30] and [31]. Let Q(x) be the right tail probability of the standard normal distribution (i.e. the complement of its cumulative distribution function). Then, we have

P

ev > VPLH0

f

j

= Q kffmd −

Sv,j f

P LOI f

j

σj

12 31

= 1 − F q L; f

j

12 32

j

σj 12 33

j

In general, a space segment fault event fj on satellite j will cause different transient responses in the differential position error ev and the monitor test statistic qj. The LOI probability in Eq. (12.33) will be a function of both of these fault response functions, the magnitude of the fault itself, the elapsed time since fault onset (t), as well as the ground and airborne receiver tracking start times (t0g) and (t0a). For every type of SIS fault, it is necessary to find the specific conditions that maximize the LOI probability and to determine whether the result exceeds the integrity risk allocation for the failure mode.

12.7.1

Example GAST C SIS Integrity Case

Figure 12.8 shows example results of this analysis for a CCD monitor of the type described in [17]. The plot shows the LOI probability as a function of the fault magnitude, which,

CCD LTI/LTV P(LOI)

10–4 P(LOI|fault)

so that we can write

10–6

10–8

σ v,j f j = Q kffmd − σv σ j 12 30

The upper bound probability occurs when σ v, j/σ v 1. Therefore, it is convenient to conservatively use the following satellite-geometry-free expression

0004815231.3D 273

j

= Q k ffmd − f

10–2

12 29

j

f

σv

σ v,j ≜ Sv, j σ j

f

j

1 − F q L; f

j

Now define

ev > VPLH0

= Q k ffmd −

Substituting Eqs. (12.31) and (12.32) into Eq. (12.24) yields

12 28

P

j

Now we turn our attention to the second term on the right-hand side of Eq. (12.24), which can be directly expressed as follows: P q tq < L f

so that the monitor detection probability (the second term on the right side of Eq. (12.24)) is evaluated TA − τg later than the position error bounding probability (first term on the right-hand side of Eq. (12.24)). The basis for this choice is that it allows the monitor TA − τg extra time (relative to the position error) for the test statistic to grow beyond the threshold. Consider now the two terms on the right-hand side of inequality (12.24) separately. For brevity in notation in the following few steps, the time variables will be temporarily omitted. They will be included again in the final result. Given a failure on satellite j with a fault vector fj not close to zero, the first term is closely approximated by

f

273

10–10 –4 10

10–3

10–2

10–1

100

d (m/s)

Figure 12.8 Worst-case P(LOI| fj) for any value of t, t0g, and t0a, versus magnitude of divergence rate fault d: GAST C case.

13/12/2020 12:54:03 AM

12 Ground-Based Augmentation System

in this example, is the divergence rate d. To obtain worstcase results, it was assumed that the aircraft uses an LTV smoothing filter and the ground uses an LTI filter. The LOI probability is a function of four variables: t, t0g, t0a, and d. For each value of d on the figure, the values of t, t0g, and t0a were found to maximize the probability of LOI. The dotted horizontal line was located at 10−4, a typical monitor integrity risk allocation. As long as long all points on the curve are below the allocation, integrity is assured.

Example GAST D Integrity Requirement: |Er| vs. Pmd

100 10–1

Malfunction requirement (with example 10–5 prior)

10–2 P(MD∣fault)

274

10–3 10–4 10–5

12.8 GAST D Requirements and Integrity Case

10–7

As noted in Section 12.4, there are additional requirements for GAST D operations. These are defined in terms of Er , which is the differential ranging error on the 30 s smoothed corrected pseudorange at the landing threshold point (LTP) (of any runway for which the ground system supports GAST D). The first requirement, termed the “limit case” requirement, specifies the minimum required probability of missed detection of a ranging source fault as a function of Er . The requirement is given in Table 12.5. An additional requirement, known as the “malfunction case” requirement, applies to all faults that have a prior probability of occurrence greater than 1×10−9. It stipulates that the probability of an undetected fault leading to a differential ranging error greater than 1.8 m must not exceed 1×10−9. The time to alert for the GAST D ground system to detect an out-of-tolerance condition is 1.5 s [31]. Details concerning the origin of these requirements may be found in [32] and [33]. An example visual illustration of the requirements is shown in Figure 12.9 for the case where the prior probability of the fault is 10−5. A hypothetical, compliant performance curve is also shown. There are also additional requirements for ionospheric front monitoring for GAST D. For the most part, these were already discussed in Section 12.6 – namely, 30 s smoothed pseudoranges, airborne CCD and DSIGMA monitors, and geometry screening at the aircraft. The ground system manufacturer is responsible for ensuring that through the

Table 12.5

GBAS GAST D limit case integrity requirements [34].

Probability of missed detection

Pseudorange error (meters)

Pmd_limit ≤ 1

0≤

Pmd

limit

≤ 10

Pmd_limit ≤ 10

0004815231.3D 274

− 2 56 × E r + 1 92 −5

0.75 ≤ 2.7 ≤

≤ 0.75

Er

Er Er

Example GAST D compliant monitor

10–6

≤ 2.7 ≤∞

0

0.5

1

Limit case requirement

1.5

2

2.5

3

3.5

4

|Er| (m)

Figure 12.9 Example GAST D SIS integrity requirement and hypothetical compliant performance curve.

combined use of all air and ground monitors, the probability of an undetected ionospheric front leading to a differential ranging error greater than 2.75 m must not exceed 1×10−9 at the LTP for any approach supporting GAST D [32, 34]. The total probability of an undetected ionospheric front gradient includes both the prior probability of the front (if applicable) and the probability of not detecting it.

12.9

Current State and Future of GBAS

To date, GBAS systems have been installed at 30 airports in the United States, Europe, Australia, India, Brazil, and Russia. Honeywell International’s SLS-4000 SmartPath GBAS ground system has been certified by the FAA for Category I (GAST C) precision approach operations, and RockwellCollins’s Multi-Mode Receiver (MMR) and Honeywell International’s Integrated Navigation Receiver (INR) are approved GBAS avionics packages. GBAS avionics are available as standard or optional equipment on all Boeing and Airbus aircraft. Current air carriers using GBAS include United Airlines, Delta Airlines, British Airways, Emirates Airlines, Lufthansa, Cathay Pacific, Qantas, TUI, Swiss Air, Air Berlin, and various Russian airlines [35]. In October 2016, The International Civil Aviation Organization (ICAO) issued an update (Amendment 90) to [6] to officially codify GAST D standards, including those cited in the source documents [34, 36], and [37]. Validated standards for dual-frequency equipment and multiple core constellations are planned for the 2022–2023 timeframe [38].

13/12/2020 12:54:03 AM

References

References 1 RTCA SC-159, “Minimum Aviation System Performance

2

3

4

5

6

7

8

9

10

11

0004815231.3D 275

Standards for DGNSS Instrument Approach System: Special Category I – SCAT I,” Washington, DC, RTCA/DO 217, August 1993. Braff, R., O’Donnell, P., Wullschleger, V., Velez, R., Mackin, C., Swider, R., Enge, P., van Graas, F., and Kaufmann, D., “FAA’s CAT III Feasibility Program: Status and Accomplishments,” in Proc. 8th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GPS 1995), Palm Springs, CA, September 1995, pp. 773–780. Braff, R., “Description of the FAA’s Local Area Augmentation System (LAAS),” in Navigation, Journal of The Institute of Navigation, Vol. 44, No. 4, 1997–1998, pp. 411–424. Federal Aviation Administration, “Criteria for Approval of Category III Weather Minima for Takeoff, Landing, and Rollout,” Washington DC, Advisory Circular AC 120-28D, July 1999. RTCA SC-159, “Minimum Aviation System Performance Standards for the Local Area Augmentation System (LAAS),” Washington, DC, RTCA/DO 245A, Dec. 2004. International Civil Aviation Organization (ICAO), “Annex 10 to the Convention on International Civil Aviation: Aeronautical Telecommunications—Vol. 1 Radionavigation Aids (with Amendment 89),” 6th Ed., 2006. McGraw, G., Murphy, T., Brenner, M., Pullen, S., and Van Dierendonck, A.J., “Development of the LAAS Accuracy Models,” in Proc. 13th Int. Tech. Meeting Sat. Div. in Proc. of the 12th Int. Tech. Meeting of the Sat. Div. Institute of Navigation (ION GPS 2000), 19–22 September 2000, Salt Lake City, UT. RTCA DO-246E, GNSS-Based Precision Approach Local Area Augmentation System (LAAS) Signal-in-Space Interface Control Document (ICD), July 13, 2017. RTCA SC-159, “Minimum Operational Performance Standers for GPS Local Area Augmentation System Airborne Equipment,” Washington, DC, RTCA DO 253D, July 2017. Christie, J., Ko, P.-Y., Pervan, B., Enge, P., Powell, J.D., and Parkinson, B., “Analytical and Experimental Observations of Ionospheric and Tropospheric Decorrelation Effects for Differential Satellite Navigation during Precision Approach,” in Proc. 11th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp. 739–747. Skidmore, T. and van Graas, F., “An Investigation of Tropospheric Errors on Differential GNSS Accuracy and Integrity,” in Proc. 17th Int. Tech. Meeting Sat. Div. Institute

12

13

14

15

16

17

18

19

20

21

22

23

275

of Navigation, (ION GNSS 2004), Long Beach, CA, September 2004, pp. 2752–2760. Department of Defense, “GPS Standard Positioning Service Performance Standard,” 4th Ed., Washington DC, September 2008. Braff, R. and Shively, C., “Derivation of ranging source integrity requirements for the Local Area Augmentation System (LAAS),” in Navigation, Journal of The Institute of Navigation, Vol. 47, No. 4, 2000–2001, pp. 279–288. Pullen, S., Park, Y.-S., and Enge, P., “Impact and mitigation of ionospheric anomalies on ground-based augmentation of GNSS,” in Radio Science, Vol. 44, Issue 1, February 2009. Zhu, Z. and van Graas, F., “Implications of C/A Code Cross Correlation on GPS and GBAS,” Proc IEEE/ION Position, Location, and Navigation Symposium (PLANS 2014), Monterey, CA, May 2014, pp. 282–293. Zhu, Z. and van Graas, F., “Operational Considerations for C/A Code Tracking Errors Due to Cross Correlation,” in Proc. 18th Int. Tech. Meeting Sat. Div. Institute of Navigation, (ION GNSS 2005), Long Beach, CA, September 2005, pp. 1255–1262. Simili, D. and Pervan, B., “Code-Carrier Divergence Monitoring for the GPS Local Area Augmentation System,” Proc. IEEE/ION Position, Location, and Navigation Symposium (PLANS 2006), San Diego, CA, April 24–27, 2006. Rife, J., Pullen, S., and Enge, P. , “Evaluating Fault-Mode Protection Levels at the Aircraft in Category III LAAS,” Proc. 63rd Annual Meeting Institute of Navigation (2007), Cambridge, MA, April 2007, pp. 356–371. Khanafseh, S., Yang, F., Pervan, B., Pullen, S., and Warburton, J., “Carrier phase ionospheric gradient ground monitor for GBAS with experimental validation,” in Proc. of the 23rd Int. Tech. Meeting of the Sat. Div. Institute of Navigation, (ION GNSS 2010), Portland, OR, September 2010. Khanafseh S., Pullen, S., and Warburton, J., “Carrier phase ionospheric gradient ground monitor for GBAS with experimental validation,” Navigation, Journal of The Institute of Navigation, Vol. 59, No. 1, Spring 2012, pp. 51–60. Jing, J., Khanafseh, S., Chan, F.-C., Langel, S., and Pervan, B., “Carrier phase null space monitor for ionospheric gradient detection,” in IEEE Transactions on Aerospace and Electronic Systems, Vol. 50, No. 4, October 2014. Reuter, R., Weed, D., and Brenner, M., “Ionosphere Gradient Detection for Cat III GBAS,” in Proc. 25th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 2175–2183. Pervan, B. and Gratton, L., “Orbit ephemeris monitors for local area differential GPS,” in IEEE Transactions on Aerospace and Electronic Systems, Vol. 41, No.2, April 2005.

13/12/2020 12:54:03 AM

276

12 Ground-Based Augmentation System

24 Tang, H., Pullen, S., Enge, P., Gratton, L., Pervan, B.,

25

26

27

28

29

30

31

0004815231.3D 276

Brenner, M., Scheitlin, J., and Kline, P., “Ephemeris Type A Fault Analysis and Mitigation for LAAS,” in Proc. of IEEE/ION Position, Location, and Navigation Symposium (PLANS 2010), Indian Wells, CA, May 2010, pp. 654-666. Khanafseh, S., Patel, J., and Pervan, B., “Spatial Gradient Monitor for GBAS Using Long Baseline Antennas,” in Proc. 30th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GNSS+ 2017), Portland, OR, September 2017. Jing, J., Khanafseh, S., Langel, S., Chan, F.-C., and Pervan, B., “Optimal antenna topologies for spatial gradient detection in differential GNSS,” in Radio Science, Vol. 50, Issue 7, July 2015. Pervan, B. and Chan, F.-C., “Detecting global positioning satellite orbit errors using short-baseline carrier phase measurements,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, January–February 2003. Pullen, S., Lee, J., Xie, G., and Enge, P., “CUSUM-Based Real-Time Risk Metrics for Augmented GPS and GNSS,” in Proc. 16th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 2275–2287. Khanafseh, S., Langel, S., Chan, F.-C., Joerger, M., and Pervan, B., “Monitoring Measurement Noise Variance for High Integrity Applications,” in Proc. 2012 Int. Tech. Meeting Institute of Navigation, Newport Beach, CA, January 2012, pp. 1157–1163. DeCleene, B., “Defining Pseudorange Integrity— Overbounding,”Proc. 13th Int. Tech. Meeting Sat. Div. Institute of Navigation (ION GPS 2000), Salt Lake City, UT, Sep. 2000, pp. 1916–1924. Rife, J., Pullen, S., Enge, P., and Pervan, B., “Paired overbounding for nonideal LAAS and WAAS error

32

33

34

35

36

37

38

distributions,” in IEEE Transactions on Aerospace and Electronic Systems, Vol. 42, No.4, October 2006. Shively, C., “Treatment of Faulted Navigation Sensor Error when Assessing Risk of Unsafe Landing for CAT IIIB LAAS,” in Proc. 19th Int. Tech. Meeting Sat. Div. Institute of Navigation, (ION GNSS 2006), Fort Worth, TX, September 2006, pp. 477–491. Shively, C., “Comparison of Alternative Methods for Deriving Ground Monitor Requirements for CAT IIIB LAAS,” Proc. 2007 Nat. Tech. Meeting of The Institute of Navigation, San Diego, CA, January 2007, pp. 267–284. Burns, J., Clark, B., Cassell, R., Shively, C., Murphy, T., and Harris, M., “Conceptual Framework for the Proposal for GBAS to Support CAT III Operations,” Montreal, Canada, Navigation Systems Panel (NSP) WGW Report— Attachment H, November 2009. Federal Aviation Administration, “GBAS—Quick Facts,” TC16-004, available for download at https://www.faa.gov/ about/office_org/headquarters_offices/ato/service_units/ techops/navservices/gnss/laas/. ICAO IGM Ad-hoc Working Group, “Proposed Modification for GAST D Anomalous Ionosphere Gradient Requirements,” NSP CSG Meeting, Flimsy 9, 17–20 February 2015. ICAO IGM Ad-hoc Working Group, “IGM Ad-Hoc Requirement Validation,” NSP GBAS Working Group Meeting, Seattle, WA, GWGs/1-WP/2, 12 August 2016. Wichgers, J. and Harris, M., “GPS/LAAS Development Status: Working Group 4 (WG-4) Report to RTCA SC-159 Working Group of the Whole,” RTCA, Washington DC, October 27, 2017.

13/12/2020 12:54:03 AM

277

13 Satellite-Based Augmentation Systems (SBASs) Todd Walter Stanford University, United States

The concept of an SBAS has its roots in the 1980s. The GPS constellation was not yet complete, but people immediately began to consider how it could be used for aviation. The main problem was that since GPS was not designed as a safety-of-life system, it occasionally provides misleading information. A network of monitoring stations was envisioned to send flags to the user when a satellite’s ranging information was not correct. Then it was realized that this network could differentially correct the errors, leading to better accuracy and availability. Finally, the idea of broadcasting the corrections and flags from a geostationary satellite was incorporated. The signal from this satellite would be similar to the GPS satellites and be able to provide ranging as well as data. These three ideas together are what make up an SBAS.

13.1

Introduction to SBAS

An SBAS is a system designed to improve global navigation satellite system (GNSS) service such that the augmented service meets the strict requirements of air navigation. In particular, the service must be accurate, safe, and sufficiently available to guide aircraft in close proximity to each other or to other obstacles. Stand-alone (or unaugmented) satellite navigation does not meet all of these aviation requirements. Specifically, the reliability of the signals is not assured. Large positioning errors could be presented to the pilot without suitable warning. An SBAS monitors the core constellation signals using a network of ground monitoring equipment and broadcasts information about the status of their performance via a satellite communication link. An SBAS has a strict upper limit on the length of time that erroneous information could be presented to the pilot. The Time-To-Alert (TTA) for an SBAS is 6 s in order to support operations where the aircraft is near to the ground.

Each SBAS also evaluates the effects of the ionosphere on the ranging signals. Differential corrections and confidence bounds are produced to improve the nominal positioning accuracy and alert the user when the ionosphere may be creating unacceptably large errors. SBAS has been used for many years to guide aircraft both at high altitude and down to within 200 feet of the ground. Examples of SBASs are the Wide-Area Augmentation System (WAAS) covering North America [1] and the European Geostationary Navigation Overlay Service (EGNOS) covering Europe [2].

13.1.1

Principles and Use in Civil Aviation

An SBAS is designed to replace a large number of distributed navigational aids with a single integrated system. An SBAS is capable of providing guidance for all phases of flight including takeoff, ascent, en route, terminal area, and approach. It was conceived to supplant non-directional beacons (NDBs), distance measuring equipment (DME), tactical air navigation systems (TACANs), VHF Omni Range systems (VORs), and Category I instrument landing systems (ILSs) [3]. There are, or were, over a thousand of each type of navigational aid (navaid) in use in US air space when the decision was made to implement WAAS. The Federal Aviation Administration’s (FAA’s) goal was to replace the thousands of pieces of equipment and their associated maintenance cost with a single much more easily maintained system. Over time, the need to back up GNSS-based navigation became better understood‚ and the reduction of traditional navigational aids has been much more gradual than initially planned. Nevertheless, WAAS has fulfilled its goal of providing seamless guidance throughout US airspace. The advantages of satellite-based navigation are clear; GNSS provides global coverage‚ and its signals come down from space, covering almost all areas where aircraft are most likely to operate. Unlike terrestrial navigation aids,

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c13.3d

277

15/12/2020 5:21:08 PM

278

13 Satellite-Based Augmentation Systems (SBASs)

the signals are rarely limited by terrain in any open sky environment. GNSS provides all-weather service. It provides three-dimensional guidance (including altitude) whose accuracy does not rapidly degrade as the user moves away from reference locations. Aircraft can fly any threedimensional path that they desire and are not constrained to particular routes extending from one navaid to another. Any airport can be supplied with a precision approach (PA) capability without the need for specific guidance equipment to be installed at that airport. The avionics are simplified, as a single SBAS box can supply navigation at all locations rather than needing different boxes for different navigational aids that have to be handed off from one frequency to another. Finally, the accuracy of GNSS is much higher than that of traditional navaids. The uncertainty of position is reduced so that more aircraft can be placed closer together without increasing the risk of collision. Navigation systems designed for use in aviation are judged by four important criteria: accuracy, integrity, continuity, and availability. Accuracy is perhaps the most obvious of these required attributes. It is a statistical measure of how close the indicated position is to the true position. Integrity consists of two key aspects: an upper bound on the position error at any given time and a maximum time required to alert the user if that upper bound cannot be assured to the required level of confidence. Both aspects must be met at all times to claim that the system meets the required integrity. It is this requirement in particular that motivated the development of the different augmentation systems. It is this requirement that is held above all others when making system design choices. Continuity and availability measure the

system’s ability to provide a predictable and consistent level of service. The requirements on these latter two criteria also create a challenge, as it can be difficult to maintain service in the face of potential integrity threats. For a much more detailed description of these parameters, please see Chapter 23 on GNSS integrity.

13.1.2

SBAS Architecture Overview

The SBAS ground segment consists of four elements as shown in Figure 13.1. It has a network of reference stations to observe GNSS performance, a communication network to transfer data to and from the other elements, a master station to aggregate the data and decide what information to send to the users, and an uplink station to send the data to a communication satellite so that it can be relayed to the user. The reference stations are the eyes and ears of an SBAS. Each reference station has multiple (either two or three depending on the system) GNSS receivers that are capable of precisely measuring the code and carrier on two frequencies. Currently, GPS is the only constellation monitored by operational SBASs, and measurements are made on the GPS L1 and L2 frequencies. However, SBASs are evolving to incorporate other constellations (Galileo, GLONASS, and BeiDou) as well as new signals on different frequencies (e.g. GPS L5 and Galileo E5a). Two different frequencies are used so that the system can measure the effects of ionospheric delay. The redundancy of receivers is to identify and isolate individual receiver faults or excessive multipath effects. The reference stations have atomic clocks and

GPS Satellites

I

o

n

Atmospheric Effects

Reference Station

Figure 13.1

c13.3d

278

Master Station

o

s

p h e r

i c E f

GEO Satellite f e c t s

Ground Uplink Station

SBAS architecture.

15/12/2020 5:22:22 PM

13.1 Introduction to SBAS

precisely surveyed antennas to improve the overall measurement consistency and aid in detecting and isolating errors. The raw measurements from all of the reference stations are sent once per second to the master stations. The master stations are the brains of the SBAS. They take in the raw measurements, process them to reduce the effects of noise, and make estimates of the errors that are affecting the signals. The master stations generate corrections to reduce the errors to the user. The corrections improve the accuracy compared to stand-alone ranging signals. Most importantly, each master station estimates how much the corrections may be in error and sends confidence bounds on these corrections to the user. This information is packaged into individual messages and then transmitted to the user. The avionics are then able to use these bounds to determine if the corrected position solution may be used for its intended operation. The master station also determines if there is any unsafe information being used by the SBAS receiver and can immediately send an alert to the user if needed. The communication network carries the data to and from the master station. It needs to be redundant and reliable. The information is time critical, so it cannot get lost or delayed. Consequently, it has very tight requirements in terms of latency (no more than 50 ms in the case of WAAS) and reliability. WAAS requires that more than 99.9% of messages reach their intended destination on time along each channel and that the two parallel channels achieve at least 99.999% reliability. Ground uplink stations and communication satellites (currently all geostationary satellites) take the information on its final leg to the user. The signal from the geostationary Earth orbit (GEO) satellites is very similar in structure to the GPS L1 C/A signal. The primary difference is that the data rate has been increased to 250 bits per second. The information is encoded into 1-s-long, 250-bit messages that each contain a portion of the information required by the user. The user must aggregate information from many messages over time in order to obtain the full set of corrections and integrity bounds.

13.1.3

WAAS Architecture Overview

The previous section described a generic SBAS architecture. This section presents the specific structure and nomenclature used by WAAS, as illustrated in Figure 13.2. WAAS has a network of 38 WAAS reference stations (WRSs) spanning most of North America, each containing three parallel threads of equipment. These WAAS reference elements (WREs) each consist of a GPS antenna, a GPS receiver, a cesium clock, and a computer to format the data and send it to the WAAS master stations (WMSs). Each of the three

c13.3d

279

279

WMSs has a Corrections and Verification (C&V) processor that consists of two parts: a Corrections Processor (CP) and a Safety Processor (SP). The CP performs an initial screening of the data to identify and remove outliers. The resulting output is fed into filters that estimate the receiver and satellite inter-frequency biases (IFBs) [4], the WRE clock offsets, the satellite orbital locations, and the satellite clock offsets [5]. These are then passed along to the SP for evaluation. The SP is responsible for ensuring the safety of the WAAS output. It will decide what information will be sent to the user and to what level such information can be trusted. The SP performs its own independent data screening on the input WRE data. Its Code Noise and MultiPath (CNMP) monitor [6] performs data screening, carrier smoothing, and produces a confidence bound for the remaining uncertainty on the smoothed pseudorange values. The user differential range error (UDRE) monitor takes in the smoothed ionosphere-free pseudoranges and bounds from the CNMP monitor and uses them to determine a confidence bound on the satellite clock and orbital correction errors from the CP [7]. The code-carrier coherence (CCC) monitor [8] and the signal quality monitor (SQM) [9] use inputs from the CNMP monitor to determine whether or not the UDRE bound is also sufficiently large to protect against potential code-carrier divergence and/or signal deformations, respectively. The grid ionospheric vertical error (GIVE) monitor [10, 11] takes in the smoothed ionospheric delay estimates and bounds from the CNMP monitor as well as the IFB estimates from the CP to estimate the ionospheric delays and confidence bounds for a set of ionospheric grid points (IGPs) defined to exist 350 km above the WAAS service area [12]. The user is able to interpolate between these IGPs to determine an ionospheric delay correction and corresponding confidence bound for each of their satellite measurements. The range domain monitor (RDM) then evaluates all of the corrections and confidence bounds. The RDM uses smoothed L1 measurements and bounds from the CNMP monitor to determine whether corrections and bounds from the prior monitors combine as expected to bound the fully corrected single-frequency measurements. If there is a problem, the RDM may increase the corresponding UDRE and GIVE values‚ or it may flag the satellite as unsafe to use. All of this information is then passed to the user position monitor (UPM) [13], which evaluates whether all the corrected position errors at each WRE are properly bounded. Like the RDM, it too has the ability to increase the broadcast bounds or set a satellite as unusable. Finally, the corrections, UDREs, and GIVEs are broadcast to the user in a sequence of messages [12, 14]. In order to understand the functioning of these monitors,

15/12/2020 5:22:22 PM

280

13 Satellite-Based Augmentation Systems (SBASs)

GPS GEO

USER Receiver

Receiver

Receiver

Clock

Clock

Clock

WRE A

WRE B

WRE C

Corrections Processor (CP) Process & Screen Data

WRS 1 CNMP

Interfrequncy Bias Filter

GIVE Monitor

UDRE Monitor

Orbit Estimator

RDM

Clock Estimator

UPM

Message Process

Safety Processor (SP)

Receiver Clock

WMS 1

CNMP

Interfrequncy Bias Filter

GIVE Monitor

UDRE Monitor

Orbit Estimator

RDM

Receiver

Receiver

Receiver

Clock

Clock

Clock

Safety Processor (SP)

WRE B

WRE C

WMS 3

WRE A

Signal Generator

GUS

Corrections Processor (CP) Process & Screen Data

Control Loop

Clock Estimator

UPM

Message Process

Receiver Clock

Control Loop

Signal Generator

GUS

WRS 38 Figure 13.2

WAAS system architecture.

it is necessary to understand the threats that they address. Section 13.2 describes these threats. The monitors are then described in greater detail in Section 13.3.

13.2 Error Sources and Threats to SBAS Service There are many error sources that may affect GNSS ranging. The rows of Table 13.1 [15] provide a list of the eight major error sources evaluated by all augmentation systems. Each error source is capable of degrading the ranging accuracy. All of the error sources have some nominal or unfaulted level of error as described in the second column of Table 13.1. For WAAS, these typically lead to nominal horizontal positioning errors of less than 0.75 m 95% of the time (and vertical errors below 1.2 m 95%) [16]. Most of these error sources also have fault modes where

c13.3d

280

anomalous behavior may lead to larger and unexpected errors. If the fault only affects one satellite ranging measurement‚ it is referred to as a narrow fault. If the same underlying cause can affect multiple (or even all) ranging sources, then it is referred to as a wide fault. The last two columns of Table 13.1 briefly describe some sources of such fault types. If a fault type is sufficiently unlikely or only has a negligible effect on SBAS, it is identified as N/A (Not Applicable) in the table. Threat models describe the anticipated events that a system must protect the user against and conditions under which it must provide reliably safe confidence bounds. Each threat model describes the specific nature of the threat, its magnitude, and its likelihood. It also describes the nominal error magnitudes that may be expected under unfaulted conditions. Together, the various threat models must be comprehensive in describing all reasonable conditions under which the system might have difficulty protecting the user. Ultimately the threat models form a major part

15/12/2020 5:22:22 PM

13.2 Error Sources and Threats to SBAS Service

Table 13.1

GNSS error sources Nominal

Narrow fault

Wide fault

1-Clock and Ephemeris

Orbit/clock estimation and prediction inaccuracy

Includes clock runoffs or jumps, bad ephemeris, and unflagged maneuvers

Includes errors in operating the constellation including the possibility of erroneous broadcast data

2-Signal Deformation

Nominal differences in signals due to RF components and waveform distortion

Failures in satellite payload signal generation components

N/A

3-Code-Carrier Incoherence

Incoherence in generated code and carrier signals

Failures in satellite payload signal generation components

N/A

4-Inter-Frequency Bias

Delay differences in satellite payload signal paths at different frequencies

Failures in satellite payload signal generation components

Errors in off-line determination or dissemination

5-Satellite Antenna Bias

Look-angle-dependent biases caused at satellite antennas

Failures in satellite antenna components

N/A

6-Ionosphere

Incorrectly modeled ionospheric delay

Large ionospheric deviations due to disturbed ionosphere

Multiple large ionospheric deviations due to disturbed ionosphere

7-Troposphere

Incorrectly modeled tropospheric delay

N/A

N/A

8-Receiver Noise and Multipath

Nominal noise and multipath errors

Receiver fault or a single strong multipath reflection

Receiver fault or environment with multiple strong multipath reflections

of the basis for determining if the system design meets its integrity requirement. Each individual threat must be fully mitigated to within its allocation. Only when it can be shown that all threats have been sufficiently addressed can the system be deemed safe. SBAS was originally developed to address threats affecting satellite ranging. However, an SBAS also runs the risk of introducing new threats in the absence of any ranging fault. Included in the set of threat models must be the possibility of erroneous corrections introduced by the SBAS. Some of these threats are universal to any design‚ while others are specific to the implementation. The following paragraphs provide an overview of many of the SBAS threats, although the full details depend on implementation and must be decided by the service provider.

13.2.1

SV Clock/Ephemeris Estimation Errors

GPS and the other core constellations broadcast orbit and clock information to predict the satellite location and clock value at the time the signals are broadcast. These broadcast parameters contain some level of nominal error even when there are no faults in the core constellation [17–19]. The clock error magnitude is strongly dependent on clock type and age of data [20]. GPS satellites with cesium clocks generally see larger error values than those that have rubidium oscillators [20, 21]. The errors are also smaller when the

c13.3d

281

281

GPS satellite has recently been uploaded with new ephemeris parameters. The better-performing clocks have their errors bounded by 0.75 m 95% right after an upload (and below 1.5 m 95% when the upload data is 24 h old). The nominal cesium clock error is usually below 1.5 m 95% right after upload (and below 3 m 95% after 24 h). GLONASS satellites all use cesium clocks‚ and their error is closer to 5 m 95% (age of data information is not available through its broadcast) [22]. The nominal orbital errors are typically on par with the clock errors. These errors are best expressed in terms of radial, cross-track, and along-track errors, as errors in this coordinate frame exhibit the greatest stability. Figure 13.3 shows histograms of these orbital errors, along with the clock errors and Instantaneous User Ranging Error (IURE), for both the GPS [20] and GLONASS [22] satellites. These histograms contain data collected from all healthy satellites from 1 January 2013 through 31 December 2016. Note that the error scale is twice as large for the GLONASS data. The radial error is the smallest component, the along-track is the largest, and the cross-track falls in between. For GPS the errors are approximately 0.45 m, 2.25 m, and 1.25 m 95%, respectively. For GLONASS the errors are approximately 1 m, 6.5 m, and 5 m 95%, respectively. The radial error is closely aligned with the lines of sight to the user, and therefore nearly all of it directly affects the IURE. The along-track and cross-track are nearly

15/12/2020 5:22:23 PM

282

13 Satellite-Based Augmentation Systems (SBASs)

10–1 Radial Along-Track Cross-Track Clock IURE

Probability of Occurance

10–2

10–3

10–4

10–5

10–6

10–7 –15

–10

–5

0 Error (m)

5

10

15

10–1 Radial Along-Track Cross-Track Clock IURE

Probability of Occurance

10–2

10–3

10–4

10–5

10–6

10–7 –35

Figure 13.3

–20

–10

0 Error (m)

10

282

30

Radial, along-track, cross-track, clock, and projected error distributions of the GPS (top) and GLONASS (bottom) satellites.

perpendicular to these lines of sight, so only about 15% of these errors affect the IURE. The resulting uncorrected, nominal clock and ephemeris IURE errors are about 1.8 m and 5.1 m 95% for GPS and GLONASS, respectively. WAAS only corrects the GPS constellation. After applying its differential corrections, WAAS reduces the nominal clock and ephemeris IURE errors to about 0.33 m 95% for satellites that are well observed by the reference network.

c13.3d

20

Beyond the nominal conditions, the broadcast satellite clock and ephemeris information sometimes contain significant errors in the event of a satellite fault or erroneous upload. Such faults may create jumps, ramps, or higherorder errors in the satellite clock, ephemeris, or both [23–28]. Such faults may be created by changes in state of the satellite orbit or clock, or simply due to the broadcasting of erroneous information. GPS has experienced five such faults since 2008 [29]. One event was a 20 m clock step,

15/12/2020 5:22:23 PM

13.2 Error Sources and Threats to SBAS Service

two events were clock runoffs where the clock gained errors of order one meter per minute for roughly an hour, and two events were broadcasts of incorrect orbital estimates that led to errors of order 10 m in the first case and over 400 m in the second. A much greater number of faults have been observed on GLONASS in the same time period. When the GPS errors occurred in view of WAAS, it was able to correct the error in the case of smaller faults and otherwise to flag the error to the user when it was too large to differentially correct. Either the user or the SBAS may also experience incorrectly decoded ephemeris information. Therefore, both must take steps to ensure the received parameters are correct. The ephemeris must be decoded more than once and a bitwise verification performed to ensure it was correctly received. Further, the computed ephemeris position is compared against the almanac position to ensure that the receiver is correctly tracking the intended satellite. Although GPS has never broadcast faulty clock and orbital data for multiple satellites at the same time, such wide faults are viewed as a possibility. Such events have been observed on GLONASS [22, 30]. SBAS systems undergo thorough evaluation in order to ensure that their risk of broadcasting erroneously characterized clock and/or ephemeris corrections is well below 10−7 per hour.

13.2.2

Signal Deformations

The ranging measurement depends on correlating the incoming signal with an internally generated replica of the expected code. If the incoming signal is distorted (i.e. different from expectation), it can lead to timing/ranging errors. If these distortions differ from one satellite to another, positioning errors will result. The International Civil Aviation Organization (ICAO) [31] has adopted a threat model to describe the possible signal distortions that may occur on the GPS L1 CA code. The threat model creates a representative set of faulted signals. These faults contain digital and analog components. The digital component is a measure of the positive chip length compared to the negative chip length. Ideally, these would be equal, and the zero crossing as the signal transitions from one to the other would occur exactly where expected. In reality, the zero crossing in one direction will be slightly delayed or advanced relative to the crossing in the opposite direction. The GPS specification states that this difference should be no greater than 10 ns nominally [32]. The ICAO fault model includes cases that go to 120 ns [31]. The analog model accounts for effects of finite bandwidth and filtering. Rather than producing a perfect square wave, the chips are rounded with some overshoot and ringing following each transition. The right side of Figure 13.4 shows

c13.3d

283

283

nominal signals in red for multiple GPS satellites where these effects can clearly be seen. These distortions will lead to biases that depend on the correlator spacing and bandwidth of the observing receivers. The left side of Figure 13.4 shows an example of the magnitude of these errors as the receiver correlator spacing is changed. For this figure, it was assumed that a reference receiver was used with a 1-chip correlator spacing‚ and therefore all of these errors would cancel if the user receiver was identically configured. The errors grow, and can exceed half a meter for users with very different spacings. Such biases would not be observable in the ranging measurements from a network of identically configured receivers [33–35]. Some sudden changes to the signal structure have been observed on GPS, but all such events have had only a small impact on the pseudorange errors and did not necessitate tripping the WAAS SQM monitor [36]. Threat models for other satellite signals are still under development‚ although it has been proposed that the GPS L1 threat model is also applicable to the GPS L5 signal.

13.2.3

Code-Carrier Incoherency

The satellite is expected to maintain coherency between the broadcast code and carrier. This potential fault mode describes a threat that originates on the satellite and is unrelated to differences in the code and carrier caused by the ionosphere. This satellite-based threat is modeled as either a step or a rate of change between the code and carrier broadcast from the satellite. The nominal error is too small to adequately measure as it is obscured by the effects of the ionosphere and multipath. It is nominally modeled as having zero effect. Similarly, no fault has ever been observed on the GPS L1 signals. However‚ nominal errors have been observed on WAAS geostationary signals and on the GPS L5 signal [37, 38]. This threat harms users because the SBAS ground segment and the users each employ carrier smoothing to reduce multipath, but with very different time scales. Any noticeable code and carrier incoherence would lead to unaccounted errors for the user.

13.2.4

Inter-Frequency Bias Estimation Errors

For the current L1-only SBAS service, the correction algorithms need to know the hardware differential delay between the L1 and L2 frequencies in order to convert their dual-frequency measurements into single-frequency corrections. These hardware delays are referred to as timing group delay (TGD) for the bias on the satellite and IFBs for the biases in the reference station receivers/antennas. These values are typically estimated in tandem with the ionospheric delay estimation [4].

15/12/2020 5:22:24 PM

284

13 Satellite-Based Augmentation Systems (SBASs)

L1: Normalized Step Response [μsec]

1.4

GPS-L1 Normalized Step Response vs Time [μsec] Ideal Actual (Multi-SVN)

Spread of Analog Distortions

1.2

Spread of Digital Distortions

1 0.8 0.6 Analog Distortions 0.2 0

0

0.2

0.4

0.6

0.8

Time [μsec]

Digital Distortions

L1-GPS - Mean Removed - 1 chip

1 0.8 0.6

Reference Correlator Spacing Early-minus-late (1-chip)

Error [m]

0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1

0

0.2

0.4

0.6

0.8

1

1.2

User Correlator Spacing [Chips]

Figure 13.4

Nominal signal distortions (top) and their potential ranging errors (bottom).

Although these values are nominally constant, there are some conditions under which they may change their value over time. One concern is component switching. If a new receiver or antenna is used to replace an old one, or if different components or paths are made active on a satellite, then there may be a change in the relative delay between the two frequencies. Another means is through thermal variation either at the reference station or on the satellite as it goes through its eclipse season. Finally, component aging may also induce a slow variation in these values. The estimate of these values will contain some small

c13.3d

284

nominal error (typically a few centimeters), and occasionally one or more of them will contain a larger error (up to a few meters). Inter-frequency bias errors will be very similar to clock errors in that there is no spatial variation in their effect on the user. The difference is that their effect is specific to the frequency combination employed by the user. The satellite clock is in reference to a specific combination. Currently for GPS, the broadcast clock is in reference to the L1P/L2P ionosphere-free code combination. The L1-only clock is offset from this reference by the TGD. The future

15/12/2020 5:22:24 PM

13.2 Error Sources and Threats to SBAS Service

L1/L5 ionosphere combination will be offset by a combination of TGD and an inter-signal correction or ISC. Any errors in these values will appear as a clock difference to the user.

13.2.5

Antenna Bias and Survey Errors

Look-angle-dependent biases in the code phase on both frequencies are present on the reference station and GPS satellite antennas [39, 40]. These biases may be several tens of centimeters. In the case of at least one reference station antenna, they did not become smaller at a higher elevation angle. These biases are observable in an anechoic chamber, but are more difficult to characterize in operation. They may result from intrinsic antenna design as well as manufacturing variation. So far, no significant change in these patterns has been reported for an operational GPS satellite, but there is a concern that multi-element antennas could suffer from a fault that would create a significant degradation in performance. GPS Space Vehicle Number (SVN) 49 was launched with an incorrect antenna connection that resulted in meter level antenna variations on the L1 signal [41]. However, this satellite was never set healthy as a result of this fault. Errors in the surveyed coordinates of the reference station antenna code and/or carrier phase center can affect users in a similar manner as antenna biases. However, survey errors tend to be much smaller in magnitude and affect all frequencies identically. Survey values must be carefully checked before being applied. Further, position estimates for the reference stations are continuously evaluated to detect any unexpected changes. Fault sources could include slow motion due to continental drift or due to subsidence due to ground water pumping. Further rapid changes could be observed during earthquakes.

13.2.6 Ionosphere and Ionospheric Estimation Errors The propagation delays caused by the ionosphere may significantly limit the ability of an SBAS to provide its higheraccuracy services, especially in the equatorial and auroral regions. Propagation delays are caused by the presence of free electrons in the upper atmosphere along the propagation path of the signal. SBAS performance can be affected by the ionosphere through (1) rapid changes in electron density that cause estimates of range delays to be less accurate, (2) spatial gradients in electron density that cannot be resolved by the 5 by 5 ionospheric grid, (3) amplitude scintillation fading, that, in the worst case, can result in the intermittent loss of the signal, and (4) phase scintillation effects that can cause signal outages on semi-codeless receivers operating on the GPS L2 frequency. All of these ionospheric effects

c13.3d

285

285

are related to geography, season, and time of day, as well as solar activity level and geomagnetic activity [42]. Most of the time, mid-latitude ionosphere is easily estimated and bounded using a simple local planar fit. However, periods of disturbance occasionally occur where simple confidence bounds fall significantly short of bounding the true error [10]. Additionally, in other regions of the world, particularly in equatorial regions, the ionosphere frequently cannot be adequately described by this simple model [43]. Some ionospheric disturbances can occur over very short baselines‚ causing them to be difficult to describe even with higher-order models. Gradients larger than 3 m of vertical delay over a 10 km baseline have been observed, even at mid-latitude [44, 45]. Further, because the ionosphere is not a static medium‚ there may be large temporal gradients in addition to spatial gradients. Rates of change as large as four vertical meters per minute have been observed at mid-latitudes [44]. GPS broadcasts a simple global model of the ionosphere that typically cuts the error in half. However, on some days, the errors will be significantly larger and the simple model does not have the spatial or temporal resolution to capture the true variability. An SBAS sends estimated ionospheric delay values on a 5 by 5 grid that is updated every 5 min [12]. Even this model has days where it cannot capture the true ionospheric variation.

13.2.7

Tropospheric Errors

Tropospheric errors are typically small compared to ionospheric errors or satellite faults. Historical observations were used to formulate a model and analyze deviations from that model [46]. The tropospheric delays are about 2.4 m for a satellite directly overhead, to about 25 m at 5 above the horizon. A very conservative bound was applied to the distribution of the deviations about this model. They are bounded by a 1-σ value of 0.12 m at zenith and 1.23 m at 5 . The model and bound are described in the Minimum Operational Performance Standards (MOPS) [12]. These errors may affect the user both directly through their local troposphere and indirectly through errors at the reference stations that may propagate into satellite clock and ephemeris estimates. Both sides reduce the direct effect using the specified formulas.

13.2.8

Multipath and Thermal Noise

Multipath is the most significant measurement error source. It limits the ability to estimate the satellite and ionospheric errors. It depends upon the environment surrounding the antenna and the satellite trajectories. While many receiver tracking techniques can limit multipath’s magnitude, at the reference stations its period can be tens

15/12/2020 5:22:25 PM

286

13 Satellite-Based Augmentation Systems (SBASs)

of minutes or greater [6, 47]. Fortunately, both SBAS reference receivers and aircraft receivers operate in clear sky environments. Severe multipath can be avoided though careful placement of the antennas. The effects of multipath can be further reduced through the application of a narrow correlator spacing. More advanced techniques are generally avoided due to their uncertain performance under signal deformation threats. Carrier smoothing is employed to further reduce the effects. At the aircraft, after applying a 100 s smoothing filter, the 1-σ residual multipath error is expected to be below 0.13 m at zenith and below 0.45 m at 5 .

13.3

SBAS Integrity Monitoring

Monitors are algorithms that determine the potential impact of the previously described threats. The monitors estimate the magnitude of the remaining error that may affect the user after they apply corrections. This magnitude is then broadcast to the user so that they may both properly weight the relative contributions of the satellites and determine an overall confidence bound on their position estimate. The monitors also may alert the users that one or more satellites are unsafe to use as they either have an error too large to correct or the uncertainty surrounding the error magnitude is too large. The SBAS integrity parameters sent to the users are the UDREs to bound the ranging errors to a specific satellite and the GIVEs to bound the estimated errors in the SBAS ionospheric delay model. This chapter will use the existing WAAS L1 design to describe the different SBAS monitors. As other SBASs have to mitigate the same threats, their designs will include a similar set of monitors; however‚ the details vary from system to system. WAAS has been operational since 2003 and has been designed to mitigate all of the threats identified for an L1-only user [48]. Figure 13.5 shows a high-level overview of the major integrity monitors. The CNMP algorithms process the receiver measurements from each of three receivers at the 38 WRSs. It provides smoothed measurements and confidence bounds to the remaining monitors The UDRE is initially set by the UDRE monitor, which evaluates the accuracy of the clock and ephemeris corrections and residual threats for each satellite in view. The CCC monitor then evaluates if that threat can be protected by the same UDRE or if it needs to be increased. Next, the SQM evaluates if the risk of unobservable signal deformation can also be bounded by the UDRE resulting from the previous two monitors. While nominal errors of all types need to be bounded simultaneously, it is unlikely that more

c13.3d

286

Raw Code & Carrier from WRSs CNMP

Code Noise & Multipath error bounding

UDRE

SQM

CCC

UDRE Maximum bound on clock/ephemeris error, CCC error, and signal deformation error

RDM UDRE & GIVE

User Position Monitor: bound on combined errors across all ranges

UPM

GIVE GIVE

Bound on ionospheric error

Range Domain Monitor: bound on combined range error including IFB UDREs & GIVEs to user

Figure 13.5 A high-level schematic of the major integrity monitors of the current WAAS system.

than one fault type (clock/ephemeris, CCC, or SQM) will be initiated within the same 6 s window. Therefore, the portion of the UDRE covering unobserved faults can be the maximum of the portion needed individually by any of the monitors. Because the clock and ephemeris threat creates errors that may be spatially varying, it generally has greater uncertainty than other satellite threats for the L1only user. Most often, the UDRE monitor determines the minimum UDRE that can be safely broadcast and only occasionally is it increased or flagged by later monitors. In parallel, the GIVE monitor determines the ionospheric corrections and the confidence bound that must be applied to each IGP. These ionospheric corrections and GIVEs are then combined with the satellite corrections and the UDREs to determine if the total L1 correction on each line of sight between the reference stations and the satellites is properly bounded by the combination of the UDRE and GIVE terms (Section 13.4.5 has more details on how they are combined). This comparison is made by the RDM, which ensures that the individual corrections safely combine. The primary threat addressed by this monitor is related to IFBs. Finally, all of the corrections applied to each reference station result in a net WAAS positioning error that is checked against the known survey coordinates of the reference receiver’s antenna in the UPM. If either the RDM or UPM observe faults or lack the observability to validate the input UDREs and GIVEs, it will be increased or flagged unsafe by these monitors.

13.3.1

CNMP

The aims of the CNMP algorithms are to estimate and correct for observed code noise and multipath errors and then to provide a confidence estimate for residual error in smoothed L1 and L2 pseudorange measurements. To

15/12/2020 5:22:25 PM

13.3 SBAS Integrity Monitoring

perform this function, CNMP must check for cycle slips, data gaps, and other anomalous signal tracking conditions. Inconsistent measurements are identified and removed or deweighted. The surviving measurements are then used for carrier smoothing. Having three parallel threads at each reference station allows voting to remove large artifacts that affect each thread differently. Measurements also have to be consistent over time in order to initialize the carrier smoothing of the code. The CNMP algorithms produce smoothed ionosphere-free pseudoranges for use by the UDRE monitor, smoothed ionospheric estimates for use by the GIVE monitor, and smoothed L1-only measurements for use by the RDM and UPM [6, 47]. In addition, the instantaneous discrepancies between the smoothed code and raw code are provided to the CCC monitor for evaluation. In addition, the CNMP algorithms produce upper bounds on the possible remaining error affecting each of these outputs. The error curve is a function of the number of screened measurements that have been used by each smoothing filter. If there are too many missing or inconsistent measurements, the filter is restarted. At initialization, the multipath error is assumed to be large (up to 10 m 99.9% of the time on each L1 and L2). For GPS satellites, it is further assumed to initially follow a sinusoid with a 10 min period that decorrelates over time [6]. Figure 13.6 shows the bounding 1-σ confidence values for GPS (on the left) and GEO (on the right) satellites. The curves in this figure assume that the measurements were collected at 1 Hz and that all survive the screening process. If instead some measurements are removed, the curve will hold at the previous value until a new valid measurement is obtained. The curve will be reset if 6 s elapse without any valid

measurements. GPS satellites that restart while above a 30 elevation angle use the lower red line since the multipath will be much smaller for the higher elevation. For GEO satellites, the initial period is assumed to be 24 h. Earlier narrow bandwidth GEOs were further assumed to have initial multipath errors of 30 m 99.9%. Later wide-band GEOs could utilize narrow correlators and therefore assume a smaller 10 m initial multipath value as shown in the lower red curve.

13.3.2

UDRE

The orbit determination algorithms in the CP estimate the satellites’ clock and orbital states, along with the WRS clock states, as part of a large extended Kalman filter [5]. This filter has been found to be very accurate. However, due to its complexity, its potential fault modes have not been exhaustively analyzed. Instead, it is treated as an untrusted component, despite its excellent track record of service. The much simpler UDRE monitor, which is part of the SP, determines the error bounds on these satellite corrections. The UDRE monitor applies the corrections to the ionosphere-free pseudorange measurements from each WRS and compares each residual difference against a respective threshold. These threshold values are a function of the CNMP confidence values and the expected filter error. If the threshold is exceeded by two WREs at any given WRS, the satellite is set to be unusable. Otherwise, the magnitude of the residual errors is compared against one of the 14 possible broadcast UDRE values. The UDRE monitor determines the probability of latent fault versus these discrete UDRE values [7]. The smallest UDRE value that meets the required probability of fault is selected for

10

3.5 Above 30° Start Below 30° Start

3

9 Original Curve (A = 30 m) Reduced Curve (A = 10 m)

8 7 CNMP (m)

2.5 σCNMP (m)

287

2 1.5

6 5 4 3

1

2 0.5 0

1 0

0.5

1

3 2 2.5 1.5 Smoothing Time (hours)

3.5

4

0

0

10

20

30

40

50

60

70

80

Time Since Reset (hours)

Figure 13.6 One-sigma CNMP error bounding curves for GPS (left) and GEOs (right).

c13.3d

287

15/12/2020 5:22:26 PM

13 Satellite-Based Augmentation Systems (SBASs)

broadcast. If there are insufficient measurements or if none of the numerical UDRE values meet the requirement, the satellite is flagged as unusable. The UDRE monitor also evaluates prior broadcast correction and UDRE values to evaluate whether they remain safe for use. If a change makes old information unsafe to continue using, the UDRE monitor will trigger an alert to warn all SBAS users to immediately discontinue use of that satellite. The UDRE monitor is also responsible for generating a covariance matrix that describes its ability to bound the clock and ephemeris error. This four-by-four matrix describes the correlated errors affecting the satellite clock and its three-dimensional positioning errors. This matrix is normalized such that the resulting minimum value projected along any line of sight is one. Typically, this line of sight corresponds to one between the satellite and the weighted centroid of WRSs able to observe the satellite. The projected normalized matrix value is larger than one for lines of sight that are farther from the observing network. These parameters are broadcast in a message whose identifying number is 28 and are referred to as Message Type 28 (MT28) parameters [49]. These parameters are used to multiply the UDRE so that the error bound is smallest where observability is the best, and it appropriately increases the uncertainty at the edges of coverage where unobserved errors may lurk. Correctly formulating the MT28 parameters is an important part of the UDRE monitor‚ and they factor heavily into determining the minimum safe broadcast UDRE values [50].

42

10/28/2003, 20:35:00UT

13.3.3

GIVE

Unlike the UDRE monitor, the GIVE monitor determines both the corrections and the confidence values. SBASs broadcast corrections on a 5 by 5 grid of points set at a fixed 350 km height above the surface of Earth [12, 14]. Users interpolate the expected delay on their specific line of sight by interpolating the correction values at the surrounding IGPs. The GIVE monitor estimates the amount of vertical ionospheric delay occurring at each grid point. WAAS uses a simple linear model of ionospheric behavior. It assumes that in the immediate area around each IGP, the ionosphere can be modeled by three deterministic parameters: the vertical delay at the IGP plus the vertical ionospheric gradients in the east and north directions. It further assumes that the underlying ionospheric model has a stochastic component. Initially this component was treated as being independent of location (i.e. two co-located measurements had the same correlation as two widely spaced measurements) [10]. A later update to the monitor introduced spatial correlation to this stochastic component. This later technique is called kriging, and it allowed the GIVE monitor to more accurately model non-planar behavior about each IGP [11, 51]. The magnitudes of the gradients and of the stochastic components can vary greatly with time of day, season, location, and solar and geomagnetic activity. It has further been observed that sometimes the assumed model could not properly capture all of the variability of the ionosphere [52]. Figure 13.7 shows a dense sampling of the ionosphere

10/29/2003, 20:31:00UT 42

41

41

40

40

20 18 16 14

39

39

38

38

37

37

36

36

35

35

12 10 8 6 4

34 34 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80

Figure 13.7

c13.3d

288

Vertical lonospheric Delay in m

288

2 0

Vertical ionospheric delay measurements for quiet (left) and disturbed (right) days.

15/12/2020 5:22:26 PM

13.3 SBAS Integrity Monitoring

on two successive days (much denser than actual WAAS sampling). Each circle represents the intersection of a line of sight with the assumed ionosphere at 350 km altitude. The line extending from the center of each circle points back to the receiver location. Longer lines correspond to lower elevation satellites. On the left is a typical quiet day where nearly every measurement consistently identifies about 8 m of vertical delay regardless of location or elevation angle. On the right is 24 h later on a severely disturbed day where the vertical delay values range from nearly zero to over 20 m. These variations occur in close proximity to each other; well within 5 of latitude and longitude. Figure 13.8 shows the vertical stochastic ionospheric error component as a function of the distance between any two measurements. The different colors show the containment at different probability levels. The 95% and 99.9% bounds are converted to one-sigma expectations by dividing those values by 1.96 and 3.29, respectively. If the random component were perfectly Gaussian, the three curves would lie on top of each other. The separation of the lines indicates that a small fraction of the data is more likely to have large errors than would be expected from a Gaussian distribution. The left side of Figure 13.8 corresponds to a nominal or quiet day. The lines are closer together. Note that even for zero separation there is 0.2 m of expected difference. This “nugget” is due to the fact that co-located vertical measurements of the ionosphere actually sample differing lines of sight. That is, the simple two-dimensional model of the ionosphere fails to account for ionospheric variability in three dimensions. On most days, this effect is small and easily absorbed into the GIVE.

The right side of Figure 13.8 shows the behavior of the vertical ionosphere on a disturbed day. On this day, the nugget value was greater than 3 m (it was even worse on the day shown on the right for Figure 13.7). Even closely spaced observations using the grid model would have significant discrepancies. The WAAS GIVE algorithm uses the chi-square value of the measurements with respect to the nominal model to determine the current state of the ionosphere. If the measurements match the model, a quiet ionosphere may be assumed. If there are significant discrepancies, the assumed stochastic level must be appropriately increased along with the corresponding GIVE. This chisquare evaluation serves as the basis for the WAAS “storm detectors” [10, 53, 54]. These detectors operate on a per-IGP level for smaller disturbances and at a system level for larger ones. When storms are detected, the GIVEs are set to a maximum numerical value for a period of time. These values are too large to support the most demanding vertical operations, but are sufficiently small to always support horizontal guidance. Fortunately, the ionosphere over North America is nearly always well behaved. Less than 0.5% availability of vertical guidance is lost due to disturbed ionospheric conditions. The GIVE monitor contains another component to protect against the concern that the ionosphere may be in a disturbed state, but the measurements are not sufficiently sampling this behavior. This so-called “undersampled” threat is primarily a concern near the edges of coverage, where the sampling density becomes low. It has been observed that sometimes the disturbances are not sampled or are only barely sampled by the WRS measurements [55, 56]. To counteract this threat, three actions are taken:

Vertical lonosphere Containment σ, 1st Order Correlation (CONUS, 2nd July 2000) 2

1.4

7 σ Bound (m)

σ Bound (m)

8

1 0.8

σ (68) σ (95%) σ (99.9%)

9

1.6

1.2

Vertical lonosphere Containment σ, 1st Order Correlation, (CONUS 15nd July 2000)

10

σ (68) σ (95%) σ (99.9%)

1.8

289

6 5 4

0.6

3

0.4

2

0.2

1 0

0 0

500

1000 1500 Distance (km)

2000

2500

0

500

1000 1500 Distance (km)

2000

2500

Figure 13.8 One-sigma ionospheric error bounding curves for quiet (left) and disturbed (right) ionosphere.

c13.3d

289

15/12/2020 5:22:28 PM

290

13 Satellite-Based Augmentation Systems (SBASs)

(1) the assumed level of stochastic error is always increased relative to the expected value; (2) storm detectors remain in their tripped state for a period of time after the ionosphere appears to return to its quiet state; and (3) a specific undersampled threat term is added to the GIVE that is a function of the sampling density. This last term significantly increases the GIVE at the edges of coverage.

13.3.4

CCC and SQM

For each satellite corrected by WAAS, the CCC monitor averages the instantaneous raw pseudorange error across all measurements to that satellite. Individual multipath errors are reduced, especially when many receivers view the satellite as is the case for satellites with low UDRE values. If the satellite were to create a divergence between the code and the carrier, it would bias this test metric and, when sufficiently large, cause the monitor to trip and alert the user to the error [8]. Any incoherence between the code and the carrier would create a bias between the satellite clock correction (based on long-term smoothing) and the user measurement (based on a 100 s smoothing filter). The monitor metric has greater sensitivity against this threat and can detect such a fault well below the error bounds implied by the broadcast UDRE. This monitor has not ever tripped over the lifetime of WAAS, nor has it needed to. Nevertheless, it protects against the possibility of future events. The WAAS reference receivers provided measurements at nine different correlator spacings. The SQM algorithms evaluate the symmetry and consistency of the chip shapes broadcast by the different satellites [9]. These algorithms are used to evaluate performance off-line in order to ensure there are no latent harmful deformations. The real-time implementation uses four metric values to evaluate the differences among the satellites. A common mode shape distortion would lead to identical pseudorange errors on all satellites. Such an error mode would only affect the user clock estimate and not lead to a position error. Therefore, the monitor determines and removes a common mode shape‚ and the metrics are only affected by differences from one satellite to another. When any one of the metrics exceeds its threshold, the satellite is flagged as unusable. This flag persists for 12 h after the metric returns below the threshold. The magnitude of the threshold is a function of the UDRE determined by the prior monitors.

values that may not be detected at the UDRE or GIVE monitor. It uses the broadcast TGD values from the GPS satellites. The RDM also does not use the CP-estimated WRS clock biases. Instead it determines its own estimates of the WRS clock biases using the corrected pseudorange residuals based on the surveyed location of the WRS antennas. The IFB is common across all measurements to each specific WRE and therefore is incorporated into this clock estimate. The RDM evaluates the quality of its measurements, and if they cannot support the input UDRE, it will increase this value to one that is supported by the measurement quality. If it sees an error that exceeds its threshold, it will raise an alert that the satellite should not be used. It will also signal the CP that it needs to reset the TGD and IFB estimates for the affected satellites and WRSs. The UPM examines the corrections and checks if correlated errors exist that create a larger position error than expected. Recently, a new UPM algorithm was developed that guarantees user protection against the correlated error threat [13]. It performs a chi-square check on the sum of the square of the normalized corrected residuals at each WRS. A mathematical proof shows that users will be protected as long as this chi-square metric is below a specified residual. This new chi-square UPM was fielded in 2017. At the moment, no integrity credit is taken for this monitor. However, in the future, the UDRE and/or GIVE values may be lowered, to exploit the protection now provided by this monitor.

13.4 SBAS Message, GEO Signal Definition and Processing Messages sent to the user are defined in a document called the SBAS MOPS [12]. It is a large document written by committee to describe a complicated system. It has evolved slowly over time, and some of the nomenclature and writing reflects a history of ideas and approaches. As such, it can be an intimidating and difficult document for the uninitiated. This section is intended to provide an overview to assist the reader in understanding how the different message types connect together to form a differential GPS correction. The corrections are broken into two categories: clock-ephemeris corrections and ionospheric corrections.

13.4.1 13.3.5

RDM and UPM

The RDM evaluates the performance of the satellite and ionospheric corrections together on each observed line of sight. It does not use the internal IFB and TGD estimates from the CP and therefore is able to detect errors in these

c13.3d

290

Message Format

Messages are sent once per second and contain 212 bits of correction data comprising 8 additional bits of acquisition and synchronization data, 6 bits to identify the message type and 24 bits designated for parity, for a total of 250 bits. This format is shown in Figure 13.9. The parity bits protect

15/12/2020 5:22:28 PM

13.4 SBAS Message, GEO Signal Definition and Processing

291

DIRECTION OF DATA FLOW FROM SATELLITE; MOST SIGNIFICANT BIT (MSB) TRANSMITTED FIRST 250 BITS - 1 SECOND 24-BITS PARITY

212-BIT DATA FIELD

6-BIT MESSAGE TYPE IDENTIFIER (0-63) 8-BIT PREAMBLE OF 24 BITS TOTAL IN 3 CONTIGUOUS BLOCKS

Figure 13.9 SBAS message structure.

Table 13.2 SBAS message types and update intervals Message Type

Messages Contents

Update Period (s)

0

Do not use this GEO for safety of life (it is only for testing)

6

1

PRN Mask assignments, set up to 51 of 210 bits

120

2–5

Fast corrections (satellite clock error)

6–60

6

Integrity information (UDREI)

6

7

Fast correction degradation factors

120

9

GEO navigation message (X, Y, Z, time, etc.)

120

10

Degradation parameters

120

12

WAAS network time/UTC offset parameters

300

17

GEO satellite almanacs

300

18

Ionospheric grid point masks

300

24

Mixed fast/long-term satellite error corrections

6–60

25

Long-term satellite error corrections

120

26

Ionospheric delay corrections

300

27

WAAS service message

300

28

Clock/ephemeris covariance matrix

120

63

Null message

—

against the use of corrupted data. The information from multiple messages must be stored and combined to form the corrections and confidence bounds for all of the satellites [14]. The different message types are listed in Table 13.2 along with their nominal update rates. Some information, such as satellite clock corrections and the associated UDREs, are updated very frequently (every 6 s). Other information, such as the ionospheric corrections, can be transmitted much less frequently (every 5 min). For precise vertical operations, the user must stop using data from messages that were received earlier than two update periods. This restriction prevents users from applying outdated information, but allows them to operate even when they are missing the most recent copy of any given message. For the less precise lateral-only operations,

c13.3d

291

the user may continue to use older information until three update periods have passed. This allows them to operate even when they have missed the two most recent copies of any given message.

13.4.2 Clock and Ephemeris Corrections and Bounds The satellite clock and ephemeris errors are corrected and bounded by information in Message Types (MT) 1–7, 9, 10, 17, 24, 25, 27, and 28. The corrections are split into two types: fast corrections, which are scalar values that affect all users identically; and long-term corrections, which are in the form of a four-dimensional vector (delta position and clock) that affect users differently depending on their

15/12/2020 5:22:28 PM

292

13 Satellite-Based Augmentation Systems (SBASs)

location. Most of the common errors, particularly most of the satellite clock errors, are removed by the fast correction. The long-term correction primarily removes the satellite ephemeris errors. Any discontinuities between one set of ephemeris parameters broadcast from a GPS satellite and the next set are incorporated into the long-term corrections. This is done for two reasons: to keep the fast corrections continuous, and to match specific ephemeris parameters, since only the long-term corrections are specifically linked to the issue of data from the GPS satellites. Any discontinuities in the broadcast GPS clock terms between one ephemeris and the next are absorbed into the long-term clock correction. Message Type 1 contains what is called the satellite mask. It identifies for which satellites the SBAS will broadcast corrections. This saves the SBAS from having to broadcast a PRN value along with the correction. Instead, the first satellites listed in the mask are corrected in MT2, the next set in MT3, and so on. Message Types 2–5 and 24 contain fast corrections. The pseudorange correction contained is specific to the time of reception. Users update these corrections over time by applying a range rate correction term formed from recent corrections. The range rate correction is determined by differencing the most recent fast clock correction from a prior one, and dividing this difference by the difference between the times of arrival of two messages. The range rate correction is then multiplied by the time since receiving the most recent fast correction and added to the correction value in that fast correction. This extrapolated fast correction is added to the user’s pseudorange measurement. Message Types 2–5 are each capable of providing up to 13 fast corrections and associated UDRE values. Message Types 24 and 25 contain long-term corrections, that is, x, y, z, and clock corrections in an Earth Centered Earth Fixed (ECEF) frame. The rates of change of these values are also included in the message. The correction vector is added to the satellite position and clock vector calculated from the navigation message broadcast by each GPS satellite. The corrections effectively move the estimated satellite position and clock values from those broadcast by the GPS satellite to the values estimated by the SBAS. Message Type 9 contains the full ephemeris information from each geostationary satellite for itself. This message provides the full x, y, z, and clock states for the GEO. The message contains three-dimensional position, velocity, and acceleration states in the ECEF frame as well as clock and clock rate states. Message Type 17 contains almanac data for up to three GEOs. These messages contain only approximate three-dimensional position and velocity estimates for each GEO.

c13.3d

292

Message Types 2–5, 6, and 24 also contain UDREs. The UDREs are quantized into 1 of 16 states. Each one is broadcast as a 4-bit number called a UDRE Index (UDREI). UDREIs run from 0 to 15. The values 0 to 13 correspond to numerical values with smaller indices corresponding to smaller UDRE values. A UDREI of 14 indicates that the satellite is “Not Monitored” (NM), and a value of 15 indicates that the satellite has been set to “Do Not Use” (DNU). NM indicates that the satellite is either out of view or so poorly viewed that the SBAS cannot verify its current level of performance. DNU indicates that the satellite is in view, but that it may have some problem such that it should not be used. In practice, both of these designations mean that the aircraft may not use the satellite as part of any SBAScorrected position solution.

13.4.3

Ionospheric Corrections

The ionospheric corrections and integrity bound information are broadcast in Message Types 18 and 26. Message Type 18 defines a “mask” of activated IGPs. This mask allows the user to determine the latitude and longitude of the corrections and confidences in the Type 26 messages. As shown in Figure 13.10, Earth is divided into 10 regions‚ and a separate MT18 is sent for each region which may contain up to 201 possible IGPs. An MT18 is only sent for regions where the SBAS chooses to broadcast corrections. WAAS, for example, only broadcasts masks for regions 0, 1, 2, 3, and 9. The application of ionospheric corrections requires the user to interpolate corrections for their measurements from a predefined grid of vertical delay values. The user must determine which grid points to use for interpolation and then apply the proper weights to each one to form their vertical delay estimate and confidence. This vertical delay estimate at the user’s ionospheric pierce point (IPP) is then scaled by the obliquity factor to convert it to a slant range correction. As depicted in Figure 13.10, Earth can be divided into four interpolation regions: 1) 2) 3) 4)

|Latitude| ≤ 60 60 < |Latitude| ≤ 75 75 < |Latitude| ≤ 85 85 < |Latitude|

The first region uses rectangular grids with equal spacings in latitude and longitude. The second region uses cells that are 5 in latitude and 10 in longitude. In Region 3, the cell sizes are 10 in latitude and 30 in longitude. Region 4 is a circular region‚ and the interpolation has slightly different form. In all regions‚ the user’s IPP must be surrounded

15/12/2020 5:22:28 PM

13.4 SBAS Message, GEO Signal Definition and Processing W140

W180

W100

W60

W20

N85

0

E20

E60

E100

293

E140

9

N75

N60 N55

0

0

1

2

3

4

5

6

7

8

S55 S60

S75

10

S85

Figure 13.10

SBAS ionospheric grid point locations.

by active grid points with valid data. The user first seeks to use the four active surrounding IGPs defined in the mask to create a rectangle that can be used to interpolate to the location of the IPP. If there is no surrounding rectangle, the user then checks for a surrounding triangular region. If this too is unavailable, the user cannot form a differential ionospheric correction. The selection criteria for choosing surrounding grid points are given in Section 13.4.4.10.2 of [12]. Message Type 26 also contains GIVEs. The GIVEs are quantized into one of 16 states. Each one is broadcast as a 4-bit number called a GIVE Index (GIVEI) that runs from 0 to 15. Values 0 to 14 correspond to numerical values. A GIVEI of 15 indicates that the satellite is not monitored. As with the satellites, NM indicates that the IGP is so poorly viewed that the SBAS cannot verify its current level of performance.

13.4.4

Issue of Data (IOD)

Information must be coordinated across different messages and with the information broadcast from the GPS satellites. It is necessary to have a way to identify which different

c13.3d

293

sources of data may be used in combination. Issue numbers, termed IOD, are used to match different messages each containing only some of the required information. When IODs are the same across two different messages, the user knows that those two parts work together. When the IODs do not agree, the user knows that they are attempting to combine incompatible data and that they may be missing crucial pieces of information. The use of IODs maintains the high level of integrity mandated by the system. Specific examples will be given in the paragraphs below. There are five defined types of IOD. On the unaugmented GPS system there are IODs to coordinate clock (IODC) and ephemeris (IODE) information [32]. Each satellite has its own individual values. The IODE represents the eight least significant bits of the ten-bit IODC. The ephemeris data is split into three subframes of data. The three subframes must all have the same matching IODE to be combined together to obtain the full ephemeris data set. The IODE also enables the WAAS service provider to uniquely identify which ephemeris information is being corrected. The user must ensure that the IODE in the MT25 WAAS

15/12/2020 5:22:28 PM

294

13 Satellite-Based Augmentation Systems (SBASs)

correction matches the value in the GPS ephemeris data set used for that satellite. Within the MOPS messages there is an IODP that allows the user to uniquely match the PRN number of the satellite identified in the mask (MT1) to the location of the corrections and bounds in the messages 2–5, and 24 and 25. That is, the IODPs in MTs 2–5, and 24 and 25 must match the IODP in MT1. There is also an IODF that allows the integrity information in Message Type 6 to be traced back to a specific fast correction. The IODF also serves another purpose: it increments by one from one fast correction to the next, modulo 3. Thus, users can detect when they have missed a message because when that happens, the IODFs will not be sequential for the received messages. By determining that they are missing information, users can then take the prescribed steps to ensure that their integrity bound sufficiently covers the increased uncertainty. The IODI allows latitude and longitude to be mapped onto the ionospheric correction information. It coordinates the information in the MT18 messages with the data in the MT26 messages. That is, the IODI must match across all MT18 and MT26 messages that are used together. If the information were not divided in this manner, it would be impossible to fit the data into the 250 bps bandwidth. Further, the user could not recombine the information with sufficient integrity without the use of the IODI or a similar matching mechanism.

the tropospheric error comprises a vertical one-sigma error bound of 0.12 m that is multiplied by a mapping function to convert from vertical to slant as specified in [12]. The last term describes the airborne noise and multipath and is a fixed function of the elevation angle. The pseudorange variance for each satellite, σ i, is inverted and placed on the diagonal elements of the weighting matrix, W, and is combined with the geometry matrix, G, to form the covariance of the position estimate. P = GT W G

Protection Levels

VPLSBAS = 5 33

13 1

The first three terms are more fully described in Appendix A of [12], while the last term is described in Appendix J. The first term, σ flt, covers the fast and long-term satellite corrections. It is the product of the σ UDRE with the multiplier from MT28 plus additional terms to account for the error growth since receiving the fast corrections and to account for any lost or missing messages. The second term, σ UIRE, is the interpolated GIVE values at the user’s pierce point location multiplied by the obliquity factor to convert the value form vertical to slant. The third term bounding

c13.3d

294

13 3

p3,3

where p3,3, is the third diagonal element of P. The Horizontal Protection Level (HPL) is given by p1,1 + p2,2 + 2

p1,1 − p2,2 2

2

+ p21,2 13 4

The SBAS protection level equations are based upon the observation that the error sources are approximately Gaussian and that an inflated Gaussian model can be used to conservatively describe the positioning errors [57, 58]. Therefore, four error terms were developed to describe satellite clock and ephemeris errors, ionospheric delay errors, tropospheric delay errors, and airborne receiver and multipath errors. The conservative variances of these terms were combined to form a conservative variance for the individual pseudorange error: σ 2i = σ 2flt,i + σ 2UIRE,i + σ 2tropo,i + σ 2air,i

13 2

When the G matrix is expressed in the local East-NorthUp (ENU) reference frame, the third diagonal element of the position covariance matrix represents the conservative estimate of the error variance in the vertical direction. Since the Vertical Protection Level (VPL) is intended to bound 99.99999% of errors, we need to multiply the one-sigma overbound by an appropriate factor. Using Gaussian statistics, 68% of the error is bounded within one-sigma, and 99.99999% of the errors will be within 5.33-sigma. Thus, the VPL for SBAS is given by

HPLSBAS = K H

13.4.5

−1

where KH is set to 6.0 for PA mode and to 6.18 for non-precision approach (NPA) mode. These differences were initially derived from different integrity allocations and exposure times. In the PA mode, the maximum allowable risk is 10−7/approach (where an approach is considered to last 150 s) and is split with 98% allocated to vertical and 2% allocated to horizontal. In the NPA mode, the HPL gets 100% of the allocation‚ which is 10−7/hour. The VPL allocation of 9.8 × 10−8 corresponds to a 5.33σ Gaussian error. The PA HPL allocation of 2 × 10−9 corresponds to a 6σ Gaussian error. For the PA mode, the HPL protects against a one-dimensional cross-track error. For the NPA mode, the HPL protects against a twodimensional horizontal error. The NPA HPL allocation is defined as per hour; therefore‚ it contains twenty-four 150 s exposure periods. The corresponding allocation of (10−7)/24 = 4.17 × 10−9 corresponds to a 6.21σ twodimensional Gaussian error. The reason behind the discrepancy between 6.18 and 6.21 is not known. The discrepancy is not important as it leads to less than a 0.5% difference in the required bounding sigmas. These protection levels provide real-time upper bounds on the possible

15/12/2020 5:22:29 PM

13.5 SBAS Implementations

magnitudes of the position errors. They are compared against the Vertical and Horizontal Alert Limits (VALs and HALs) to determine the availability of an operation. For example, a VAL of 50 m and an HAL of 40 m supports a PA operation called LPV [59] that can guide the aircraft to within 250 feet above the ground. That is, as long as the VPL is below 50 m and the HPL is below 40 m, an aircraft may use SBAS to navigate down to 250 feet above ground level. After that point, the pilot must be able to see the runway well enough to land visually, or abort the landing.

295

WRSs IGPs

80° N 70° N 60° N N

60°

13.5.1

SBAS Implementations WAAS

WAAS consists of 20 WRSs in the Conterminous United States (CONUS), in addition to 7 in Alaska, 1 in Hawaii, 1 in Puerto Rico, 4 in Canada, and 5 in Mexico for a network of 38 WRSs in all [1]. The WRS locations are shown as red circles in Figure 13.11. WAAS also has three WMSs and three geostationary satellites (GEOs), whose footprints are shown in Figure 13.12. The current GEOs are the SES-15 satellite at 129 W (labeled S15 and using PRN 133), the Telesat ANIK F1R satellite at 107 W (labeled CRE and using PRN 138), and the EUTELSAT 117 West B at 117 W (labeled SM9 and using PRN 131). Each GEO has two independent ground uplink stations (GUSs). WAAS was commissioned for service in July 2003 and has undergone many changes with many improvements to its service since that time [60]. As can be seen in the left side of Figure 13.13, availability of the LPV service is very high for most of North America. In general, this performance meets the goals for the system. The right side of Figure 13.13 shows the NPA availability for an operation called Required Navigation Performance (RNP) with a 0.3 nautical mile HAL.

13.5.2

EGNOS

EGNOS consists of 29 Ranging and Integrity Monitoring Stations (RIMSs) in Europe, in addition to 1 in Turkey, 6 in Africa, 1 in North America, 1 in Israel, and 1 in South America for a total of 39 [61]. The station locations are shown as green squares in Figure 13.14 (except for Kourou [French Guiana] and Hartebeesthoek [South Africa]). There are four Master Control Centers (MCCs) and three operational GEOs. The operational GEOs are the Inmarsat-4 F2 satellite at 63.9 E, the Astra-5B satellite at 31.5 E, and the SES 5 satellite at 5 E. Their PRNs are 122, 123, and 136 respectively and they are shown in Figure 13.15. EGNOS was declared operational in October 2009, and was certified

c13.3d

295

70° W

W 160° W

Figure 13.11

80° W

WRS and IGP locations for WAAS.

80 60 40 20 Latitude

13.5

0

S15 133

–20

SM9 131

CRE 138

–40 –60 –80 –200

–150

–100

–50

0

Longitude

Figure 13.12

GEO footprints for WAAS.

for safety-of-life service in March 2011. EGNOS uses MT27 to restrict the use of their satellite corrections to within the red boundary box also shown in Figure 13.15. For a variety of reasons‚ EGNOS has chosen to implement its GEO satellites without a ranging capability. EGNOS also currently implements Message Type 27 (MT27) rather than Message Type 28 (MT28) [49] as do WAAS and Multifunction Satellite Augmentation Service (MSAS). MT27 restricts the use of low UDRE values to a box centered on the European region. Its borders can be seen in Figures 13.15 and 13.16 (right). Currently MT27 impacts only LPV service

15/12/2020 5:22:29 PM

296

13 Satellite-Based Augmentation Systems (SBASs) WAAS LPV Coverage Contours 12/18/17 Week 1980 Day 1

WAAS RNP 0.3 Coverage contours 12/18/17 Week 1980 Day 1 1

80

1

60

0.9

70

60

0.8

40 0.95

0.6

Latitude

Latitude

0.7

20

50

40 0.9

30

0 0.5

–20 0.4 –40

20

0.3

–60 0.85

10 –160

–140

–120

–100

–80

–60

0.2

–80 E110

0.1 E160

W150

Longitude

Figure 13.13

W100

W50

0

E50

E100

Longitude

WAAS LPV (left) and RNP 0.3 (right) availability. Source: Courtesy FAA [FAATC].

80

RIMS

80° N 70° N

IGPs 60

N

40

Latitude

20 0 –20 –40 –60 50°

W

40° E 30° W 20° W

Figure 13.14

30° E 10° W

0°

10° E

20° E

RIMS and IGP locations for EGNOS.

to the north, but it is a limiting factor for NPA service. Availability of LPV service is very high for most of Europe.

13.5.3

MSAS

MSAS is in its initial operating phase. It consists of six ground monitoring stations (GMSs) on the Japanese islands. The station locations are shown as magenta diamonds in Figure 13.17. There are two Master Control Stations (MCSs) and one Multi-function Transport Satellite

c13.3d

296

–80 –80

–60

–40

–20

0

20

40

60

80

100

Longitude

Figure 13.15

GEO footprints for EGNOS.

(MTSAT) geostationary satellites at 145 E broadcasting on two different PRNs. MSAS was commissioned for service in September 2007 [63]. Due to the limited network size, the GEO UDREs for MSAS are set to 50 m and therefore do not benefit vertical guidance. Further, the limited ionospheric observations offer little availability of LPV. As a result, vertically guided operations have not yet been authorized based upon MSAS. The Japanese Civil Aviation Bureau (JCAB) has studied performance improvements that could allow it to provide

15/12/2020 5:22:31 PM

13.5 SBAS Implementations

55

≥99.9 ≥99 ≥98 ≥95 ≥90 ≥80 ≥70 85 % > 90 % > 95 % > 99 % > 99 .5% > 50 % Availability with VAL = 50, HAL = 40, Coverage(99%) = 10.98%

> 99 9%

Existing L1-only LPV coverage

15/12/2020 5:22:41 PM

13.6 Future Evolutions (Dual-Frequency, Multi-Constellation)

301

Availability as a function of user location 80 60 40

Latitude (deg)

20 0 –20 –40 –60 –80 –150

–100

–50

0

50

100

150

Longitude (deg)

< 50 %

Figure 13.23

> 75 % > 85 % > 90 % > 95 % > 99 % > 99 .5% > 50 % Availability with VAL = 50, HAL = 40, Coverage(99%) = 31.53%

DF LPV coverage for existing systems.

dynamic range of the corrections. Therefore, the user needs to add another clock state to be estimated for each additional constellation from which they use ranging measurements. This estimated clock state will absorb both the differences in the constellation time base, and also those due to the different signal structure employed by the new constellation. Figure 13.22 shows the LPV coverage provided by the currently operating systems. As can be seen, coverage is limited to the four regions: North America, Europe, Japan, and India. Figure 13.23 shows the coverage if those four systems all implemented dual frequency. This modeling further assumes that EGNOS switches from using MT27 to using MT28. Dual frequency eliminates the reliance on the ionospheric grid and large associated uncertainty at the edges of each system. Now coverage expands well beyond the original borders. The current systems only provide LPV service to approximately 11% of Earth’s surface. Switching to dual frequency nearly triples the area covered to now over 31%. Adding another constellation to the set of corrections nearly doubles the area covered to 59%. Figure 13.24 shows

c13.3d

301

> 99 9%

this result when these same four systems provide DFMC service correcting both GPS and Galileo. These results are calculated using Stanford University’s MATLAB Algorithm Availability Simulation Toolset (MAAST) [72]. MAAST uses the locations of the reference stations and satellites (obtained from the constellation almanacs) and replicates the UDRE and GIVE algorithms for each of the different systems. It is able to then estimate the resulting VPL and HPL at each time step and user location to compute the expected availability. MAAST provides the ability to evaluate DFMC algorithms long before any DFMC-capable receivers are fielded or satellites are launched. It is used extensively by WAAS to determine which algorithm candidates are most promising. It allows SBAS providers to estimate the expected levels of service for future evolutions as can be seen in Figures 13.23 to 13.25. Figure 13.25 shows the resulting LPV availability if the remaining planned SBASs are also implemented with DFMC service. The most significant expansion is now over Africa. This is because all of the planned services, with the exception of ASECNA, are in the Northern Hemisphere and tend to overlap. In order to expand further, more

15/12/2020 5:22:42 PM

Availability as a function of user location 80 60

Latitude (deg)

40 20 0 –20 –40 –60 –80 –150

–100

–50

0

50

100

150

Longitude (deg)

< 50 %

> 50 %

> 75 %

> 85 %

> 90 %

> 95 %

> 99 %

> 99 .5% > 99 9%

Availability with VAL = 50, HAL = 40, Coverage(99%) = 59%

Figure 13.24

DFMC LPV coverage for existing systems.

Availability as a function of user location 80 60 40

Latitude (deg)

20 0 –20 –40 –60 –80 –150

–100

–50

0

50

100

150

Longitude (deg)

< 50 %

> 50 %

> 75 %

> 85 %

> 90 %

> 95 %

> 99 %

> 99 .5%

> 99 9%

Availability with VAL = 50, HAL = 40, Coverage(99%) = 62.44%

Figure 13.25

c13.3d

302

DFMC LPV coverage for all systems.

15/12/2020 5:22:44 PM

References

development is required over South America and Australia. These regions have expressed interest and may well field their own SBAS services in the future.

References

9 Phelts, R.E., Walter, T., and Enge, P., “Toward Real- Time

10

1 Lawrence, D., Bunce, D., Mathur, N.G., and Sigler, C.E.,

2

3

4

5

6

7

8

c13.3d

303

“Wide Area Augmentation System (WAAS)—Program Status,” Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 892–899. de Blas, F.J. and Sanchez, M.A., “The EGNOS Services Provision within the Single European Sky—The Start of the Safety-of-Life Service,” Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, September 2010, pp. 1984–1993. Holland, F., Rucker R., and Horowitz, B., “Structure of the Airspace,” in IEEE Transactions on Communications, vol. 21, no. 5, pp. 382–398, May 1973. doi: 10.1109/ TCOM.1973.1091698 Komjathy, A., Wilson, B.D., Runge, T.F., Boulat, B.M., Mannucci, A.J., Sparks, L., and Reyes, M.J., “A New Ionospheric Model for Wide Area Differential GPS: The Multiple Shell Approach,” Proceedings of the 2002 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2002, pp. 460–466. Bertiger, W.I., Bar-Sever, Y.E., Haines, B.J., Iijima, B.A., Lichten, S.M., Lindqwister, U.J., Mannucci, A.J., Muellerschoen, R.J., Munson, T.N., Moore, A.W., Romans, L.J., Wilson, B.D., Wu, S.C., Yunck, T.P., Piesinger, G., and Whitehead, M., “A Real-Time Wide Area Differential GPS System,” NAVIGATION, Journal of The Institute of Navigation, Vol. 44, No. 4, 1997–1998, pp. 433–448. Shallberg, K., Shloss, P., Altshuler, E., and Tahmazyan, L., “WAAS Measurement Processing, Reducing the Effects of Multipath,” in Proceeding of ION GPS-2001, Salt Lake City, UT, September 2001. Wu, T. and Peck, S., “An Analysis of Satellite Integrity Monitoring Improvement for WAAS,” Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 756–765. Shloss, P., Phelts, R.E., Walter, T., and Enge, P., “A Simple Method of Signal Quality Monitoring for WAAS LNAV/ VNAV,” Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 800–808.

303

11

12

13

14

15

16 17

18

19

20

21

SQM for WAAS: Improved Detection Techniques,” Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS/ GNSS-2003, September 2003. Walter, T. et al. “Robust Detection of Ionospheric Irregularities,” in Navigation, Journal of the Institute of Navigation, Vol. 48, No. 2, Summer 2001. Sparks, L., Blanch, J., and Pandya, N., “Estimating Ionospheric Delay Using Kriging: 1. Methodology,” Radio Science, 46, 2011, doi:10.1029/2011RS004667. RTCA, DO-229E, “Minimum Operational Performance Standards for Global Positioning System/Satellite-Based Augmentation System Airborne Equipment (SBAS MOPS),” prepared by RTCA SC-159, December, 2016. Walter, T. and Blanch, J., “Improved User Position Monitor for WAAS,” Published in Navigation, Vol. 64, No. 1, Spring 2017, pp. 165–175, DOI 10.1002/navi.180. Walter, T., “WAAS MOPS: Practical Examples,” Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1999, pp. 283–293. E.U. U.S. Bilateral Working Group C, “Interim Report of ARAIM Technical Subgroup,” available at https://www. gps.gov/policy/cooperation/europe/2013/workinggroup-c/ William J. Hughes FAA Technical Center, http://www. nstb.tc.faa.gov Jefferson, D.C. and Bar-Sever, Y.E., “Accuracy and Consistency of GPS Broadcast Ephemeris Data,” in Proceeding of ION GPS-2000, Salt Lake City, UT, September 2000. Creel, T., Dorsey, A.J., Mendicki, P.J., Little, J., Mach, R.G., and Renfro, B.A., “Summary of Accuracy Improvements from the GPS Legacy Accuracy Improvement Initiative (L-AII),” Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 2481–2498. Heng, L., Gao, G. X., Walter, T., Enge, P., “Statistical Characterization of GPS Signal-In-Space Errors,” Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 312–319. Walter, T., Gunning, K., Phelts, R.E., and Blanch, J., “Validation of the Unfaulted Error Bounds for ARAIM.” Presented May 2017 at the Institute of Navigation (ION) Positioning, Navigation and Timing Conference, Honolulu, Hawaii. Senior, K.L., Ray, J.R., and Beard, R.L. “Characterization of Periodic Variations in the GPS Satellite Clocks,” GPS

15/12/2020 5:22:46 PM

304

13 Satellite-Based Augmentation Systems (SBASs)

22

23

24

25

26

27

28

29

30

31

32

c13.3d

304

Solutions, Vol. 12, Issue 3, pp. 211–225, July 2008, doi 10.1007/s10291-008-0089-9 Gunning, K., Walter, T., and Enge, P., “Characterization of GLONASS Broadcast Clock and Ephemeris: Nominal Performance and Fault Trends for ARAIM,” Presented January 2017 at the Institute of Navigation (ION) International Technical Meeting, Monterey, California. Shank, C.M. and Lavrakas, J., “GPS Integrity: An MCS Perspective,” in Proceeding of ION GPS-1993, Salt Lake City, UT, September 1993. Hansen, A., Walter, T., Lawrence, D., and Enge, P., “GPS Satellite Clock Event of SV#27 and Its Impact on Augmented Navigation Systems,” in Proceedings of ION GPS-98, Nashville, TN, September 1998. Rivers, M.H., “2 SOPS Anomaly Resolution on an Aging Constellation,” Proceedings of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000), Salt Lake City, UT, September 2000, pp. 2547–2550. Gratton, L., Pramanik, R., Tang, H., and Pervan, B., “Ephemeris Failure Rate Analysis and its Impact on Category I LAAS Integrity,” Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 386–394. Heng, L., Gao, G.X., Walter, T., Enge, P., “GPS Signal-inSpace Anomalies in the Last Decade: Data Mining of 400,000,000 GPS Navigation Messages,” Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, September 2010, pp. 3115–3122. Walter, T., Blanch, J., Joerger, M., and Pervan, B., “Determination of Fault Probabilities for ARAIM,” Proceedings of IEEE/ION PLANS 2016, Savannah, GA, April 2016, pp. 451–461. Walter, T. and Blanch, J., “Characterization of GNSS Clock and Ephemeris Errors to Support ARAIM,” Proceedings of the ION 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 2015, pp. 920–931. Heng, L., Gao, G. X., Walter, T., and Enge, P., “GLONASS Signal-in-Space Anomalies Since 2009,” Proceedings of the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 833–842. International Civil Aviation Organization (ICAO), “International Standards and Recommended Practices, Annex 10 to the Convention on International Civil Aviation, Volume I Radio Navigation Aids,” 7th Edition, July 2018. GPS “Interface Specification IS-GPS-200,” IRN-IS-200H005 May 2017 available at: https://www.gps.gov/ technical/icwg/

33 Phelts, R.E., Walter, T., and Enge, P., “Characterizing

34

35

36

37

38

39

40

41

42

43

Nominal Analog Signal Deformation on GNSS Signals,” Proceedings of the 22nd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009, pp. 1343–1350. Wong, G., Phelts, R.E., Walter, T., and Enge, P., “Bounding Errors Caused by Nominal GNSS Signal Deformations,” Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011. Hsu, P.H., Chiu, T., Golubev, Y., and Phelts, R.E. “Test Results for the WAAS Signal Quality Monitor,” Proceedings of IEEE/ION PLANS 2008, Monterey, CA, May 2008, pp. 263–270. Shallberg, K.W., Ericson, S.D., Phelts, E., Walter, T., Kovach, K., and Altshuler, E., “Catalog and Description of GPS and WAAS L1 C/A Signal Deformation Events,” Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 508–520. Gordon, S., Sherrell, C., and Potter, B.J., “WAAS Offline Monitoring,” Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, September 2010, pp. 2021–2030. Montenbruck, O., Hauschild, A., Steigenberger, P., and Langley, R. B., “Three’s the Challenge,” GPS World, July, 2010. Shallberg, K. and Grabowski, J., “Considerations for Characterizing Antenna Induced Range Errors,” Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 809–815. Haines, B., Bar-Sever, Y., Bertiger, W., Byun, S., Desai S., and Hajj, G., “GPS Antenna Phase Center Variations: New Perspectives From the GRACE Mission,” Dynamic Planet 2005, Cairns, Australia. Ericson, S. D., Shallberg, K. W., and Edgar, C. E., “Characterization and Simulation of SVN49 (PRN01) Elevation Dependent Measurement Biases,” Proceedings of the 2010 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2010, pp. 963–974. SBAS Ionospheric Working Group, “Ionospheric Research Issues for SBAS— – A White Paper,” February 2003, available at: http://web.stanford.edu/group/scpnt/gpslab/ website_files/sbas-ion_wg/sbas_iono_white_feb2003.pdf Rajagopal, S., Walter, T., Datta-Barua, S., Blanch, J., and Sakai, T., “Correlation Structure of the Equatorial Ionosphere,” Proceedings of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2004, pp. 542–550.

15/12/2020 5:22:46 PM

References

44 Datta-Barua, S., Walter, T., Pullen, S., Luo, M., and Enge,

55 Walter, T., Rajagopal, S., Datta-Barua, S., and Blanch, J. A,

P., “Using WAAS Ionospheric Data to Estimate LAAS Short Baseline Gradients,” in Proceeding of ION NTM, San Diego, CA, January, 2002. Datta-Barua, S., Lee, J., Pullen, S., Luo, M., Ene, A., Qiu, D., Zhang G., and Enge, P., “Ionospheric Threat Parameterization for Local Area GPS-Based Aircraft Landing Systems,” AIAA Journal of Aircraft, Vol. 47, No. 4, Jul. y 2010, pp. 1141–1151. Collins, J. P. and Langley, R. B., “The Residual Tropospheric Propagation Delay: How Bad Can It Get?,” in Proceedings of ION GPS-98, Nashville, TN, September 1998. Shallberg, K. and Sheng, F., “WAAS Measurement Processing; Current Design and Potential Improvements,” Proceedings of IEEE/ION PLANS 2008, Monterey, CA, May 2008, pp. 253–262. Walter, T., Enge, P., and DeCleene, B., “Integrity Lessons from the WAAS Integrity Performance Panel (WIPP),” Proceedings of the 2003 National Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2003, pp. 183–194. Walter, T., Hansen, A., and Enge, P., “Message Type 28,” Proceedings of the 2001 National Technical Meeting of The Institute of Navigation, Long Beach, CA, January 2001, pp. 522–532. Blanch, J., Walter, T., Enge, P., Stern, A., and Altshuler, E., “Evaluation of a Covariance-based Clock and Ephemeris Error Bounding Algorithm for SBAS,” Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 3270–3276. Sparks, L., J. Blanch, J., and N. Pandya, N., “Estimating Ionospheric Delay Using Kriging: 2. Impact on SatelliteBased Augmentation System Availability,” Radio Science., 46, 2011, doi:10.1029/2011RS004781. Komjathy, A., Sparks, L., Mannucci, A. J., and Coster, A., “The Ionospheric Impact of the October 2003 Storm Event on WAAS,” Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), Long Beach, CA, September 2004, pp. 1298–1307. Sparks, L., A. Komjathy, A., A.J. Mannucci, A.J., E. Altshuler, E., T. Walter, T., J. Blanch, J., M. Bakry El- Arini, M., and R. Lejeune, R., “Extreme Ionospheric Storms and Their Impact on WAAS,” Proceedings of the Ionospheric Effects Symposium 2005, Alexandria VA, 2005. Sparks, L. and Altshuler, E., “Improving WAAS Availability Along the Coast of California,” Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 3299–3311.

“Protecting Against Unsampled Ionospheric Threats,” Presented October 2004 at the Beacon Satellite Symposium, Trieste, Italy. Paredes, E., Pandya, N., Sparks, L., and Komjathy, A., “Reconstructing the WAAS Undersampled Ionospheric Gradient Threat Model for the WAAS Expansion into Mexico,” Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September 2008, pp. 1938–1947. Walter, T., Enge, P., and Hansen, A., “A Proposed Integrity Equation for WAAS MOPS,” Proceedings of the 10th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1997), Kansas City, MO, September 1997, pp. 475–484. DeCleene, B., “Defining Pseudorange Integrity— Overbounding,” Proceedings of the 13th International Technical Meeting of the Satellite Division of the Institute of NavigationThe Institute of Navigation (ION GPS 2000), Salt Lake City, UT, September 2000, pp. 1916–1924. Cabler, H. and DeCleene, B., “LPV: New, Improved WAAS Instrument Approach,” Proceedings of the 15th International Technical Meeting of the Satellite Division of the Institute of NavigationThe Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 1013–1021. Walter, T., Shallberg, K., Altshuler, E., Wanner, W., Harris, C., and Stimmler, R., “WAAS at 15,” Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, Reston, VA, January 2018. Gobal Navigation Satellite Systems Agency, “EGNOS Safety of Life (SoL) Service Definition Document 3.1,” September, 2016 available at: https://egnos-user-support. essp-sas.eu/new_egnos_ops/sites/default/files/library/ official_docs/egnos_sol_sdd_in_force.pdf European Satellite Services Provider, https://egnos-usersupport.essp-sas.eu/new_egnos_ops/index.php Sakai, T. and Tashiro, H., “MSAS Status,” Proceedings of the 26th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2343–2360. Airports Authority of India, http://gagan.aai.aero/gagan/ http://www.sdcm.ru/index_eng.html Langley, R. B., “Innovation: GLONASS — Past, Present and Future,” GPS World November 1, 2017, http:// gpsworld.com/innovation-glonass-past-present-andfuture/ China Satellite Navigation Office, “Update on BeiDou Navigation Satellite System,” Presented at Twelfth Meeting of the International Committee on Global Navigation Satellite Systems (ICG), Kyoto, Japan, 3–7 December 2017,

45

46

47

48

49

50

51

52

53

54

c13.3d

305

56

57

58

59

60

61

62 63

64 65 66

67

305

15/12/2020 5:22:46 PM

306

13 Satellite-Based Augmentation Systems (SBASs)

http://www.unoosa.org/documents/pdf/icg/2017/ 05_icg12.pdf 68 Agency for Aerial Navigation Safety in Africa and Madagascar, https://www.asecna.aero/index.php/en/ 69 Lapie, J., “SBAS-ASECNA Programme Update” Presented at the EGNOS Service Provision Workshop in Warsaw, Poland on 27–28 September 2016, available at: https:// egnos-user-support.essp-sas.eu/new_egnos_ops/sites/ default/files/workshop2016/08.%20ASECNA%20-% 20SBAS-ASECNA%20Programme%20Update.pdf 70 Walter, T., Blanch, J., Phelts, R. E., and Enge, P, “Evolving WAAS to Serve L1/L5 Users,” Proceedings of the 24th International Technical Meeting of The Satellite Division

c13.3d

306

of the Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 2495–2504. 71 Datta-Barua, S., Walter, T., Blanch, J., and Enge, P., “Bounding Higher Order Ionosphere Errors for the Dual Frequency GPS User,” Proceedings of the 19th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2006), Fort Worth, TX, September 2006, pp. 1377–1392. 72 Jan, S.S., Chan, W., Walter, T., and Enge, P., “Matlab Simulation Toolset for SBAS Availability Analysis,” Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), Salt Lake City, UT, September 2001, pp. 2366–2375.

15/12/2020 5:22:46 PM

307

Part B Satellite Navigation Technologies

309

14 Fundamentals and Overview of GNSS Receivers Sanjeev Gunawardena1 and Y.T. Jade Morton2 1 2

Air Force Institute of Technology, United States University of Colorado Boulder, United States

The technology evolution of satellite navigation and timing receivers over the past five decades since the first GPS sets were developed is truly remarkable. Compared to the handful of early GPS receiver types classified as either military or civilian, with form factors comprising stationary reference, geodetic, aviation‚ or portable, today’s receivers span a large set of market segments and innumerable applications. For example, emerging reference station receivers used for global navigation satellite system (GNSS) constellation monitoring are capable of directly sampling the entire 1–2 GHz L-band radio frequency (RF) spectrum and perform GNSS signal monitoring as well as interference detection and characterization in real time. High-accuracy users are served by both real-time kinematic (RTK) receivers that provide millimeter-level carrier-phase-based relative positioning as well as precise point positioning (PPP) technology that can provide unprecedented sub-centimeter-level stand-alone absolute positioning. On the mass-market end of this product spectrum, current generation cellphones have integrated the entire position, navigation, and timing (PNT) functionality‚ including an all-GNSS constellation receiver into a single CMOS chip that is less than 3×3 mm in size, consumes tens of milliwatts, and costs a few dollars (e.g. [1]). In terms of time to first fix (TTFF), sensitivity, and in some cases accuracy, these cellphone GNSS receivers significantly outperform aviation-grade GPS sets from the previous decade that cost thousands of dollars. As a final example, the GNSS receivers used in low-cost asset tracking devices sample and store a 1–2 ms “snapshot” of the L1 band at the smallest possible bandwidth once every few hours to flash memory. Once retrieved, these coarsely time-tagged samples are post-processed at a server to pinpoint location to within a few meters anywhere on Earth. From the extreme high end to the extreme low end, at their core, all GNSS receivers share a common set

of functions to provide range measurements to visible radio navigation satellites. This chapter provides an overview of the fundamentals of receiver technology, its development history, and current trends. All radio receivers extract raw modulated information through a process known as detection. Figure 14.1 shows the so-called eye pattern or eye diagram of a received binary phase-shift keying (BPSK) signal just prior to detection. In this case, the diagram shows the synchronized superposition of repeated GPS L5Q chip transitions. For a communication receiver, the detection process recovers symbols, which for BPSK involves evaluating whether the signal value is positive or negative at a consistent point in time where transients have settled. It is clear from the figure that although there is significant variation in the signal in both time and amplitude due to noise and distortion, ample margin exists to perform error-free detection, as seen by the open “data eye.” Receivers that perform PNT using radio signals differ fundamentally from other digital receivers; the data communications example just described is a case in point. While it is true that most PNT receivers need to demodulate data that contains essential parameters needed for positioning and coarse time synchronization, the primary information detected by the receiver is precise timing. Timing is performed by estimating the average zero-crossing point of one or more phase transitions. As shown in Figure 14.1, the true phase transition zero-crossing times are unique, as opposed to a range of times for symbol detection, and its detection affords no margin. In practice, the receiver’s timing estimate is never error free. All physical processes that cause phase transition jitter and waveform deformation such as thermal noise, multipath, interference, atmospheric effects, and transmitter/receiver reference oscillator frequency drift and phase noise will cause timing, and

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

14 Fundamentals and Overview of GNSS Receivers

PNT Receiver: Determine the time of transition

Communication Receiver: Determine the sign of the wavefrom

2.0 Normalized Amplitude (Q5)

310

1.5 1.0 0.5 0.0 –0.5 –1.0 –1.5 –2.0 –2.5 0.00

0.05

0.10 0.15 Time (microseconds)

0.20

Figure 14.1 Phase transition eye diagram for a BPSK-modulated signal containing noise, phase jitter‚ and distortion (live sky GPS L5Q chip transitions) [2].

Radio wave free space propagation model (Friss free space equation):

Pr =

Pt Gt Gr

λ2

Lt

( 4πr )2

Effective Isotropic Radiated Power (EIRP) Free Space Path Loss (FSPL) GPS L1 CA signal transmission power: Pt = 25W = 14 dBW Satellite transmission antenna gain: Gt = 13dB; transmitter loss Lt ~ 2dB Receiver antenna gain Gr = 0 EIRP = 10log10(Pt) + 10log10(Gt) + 10log10(Gr) – 10log10(Lt) = 25dB Satellite-receiver range r = 21,000km; GPS L1 wavelength λ = 19cm FSPL = –32 – 20log10(r) – 20log10( f ) = –183 dB Receiver power (dB) = EIRP + FSPL = 25 – 183 = –158 dB

Figure 14.2 GPS-SPS link budget.

consequently ranging, errors. A well-designed PNT receiver strives to minimize these errors while conforming to the size, weight, power consumption‚ and cost (SWAP-c) constraints stipulated by its application and market segment. Arguably, as challenging as PNT receivers are to design and implement compared to digital communications, it is more so for satellite navigation. As shown in Figure 14.2, the power induced by a GPS standard positioning service (SPS) signal-in-space (SIS) on a receive antenna on the surface of Earth is about 10−16 W (−160 dBW). This unimaginably small value is representative of all received GNSS signals to within a few decibels (dB). Free electrons within all matter at temperatures T(K) above absolute zero experience random Brownian motion, which gives rise to thermal noise. In theory, this noise has a constant spectral density from DC to infinity. Hence, thermal noise power is bandwidth dependent and defined as Pn=kTB, where k =1.38

× 10−23 J/K is the Boltzmann constant, and B is the bandwidth in hertz. For the 24 MHz transmitted bandwidth of the legacy GPS L1 signal, where all of the GPS-SPS signal power is contained, the thermal noise power at room temperature (T=293 K) is 10−13 W (−130 dBW). This results in a signal-to-noise ratio (SNR) on the order of −30 dB at the antenna. In other words, in a 24 MHz bandwidth, the received GPS-SPS signal is 1000 times less powerful than thermal noise! A GNSS receiver performs the challenging precise timing estimation process described above on a signal that it cannot directly observe above the noise floor. Moreover, provided there is no in-band interference, most low-cost GNSS receivers perform this feat to produce meterlevel positioning accuracy (3 ns timing accuracy) by sampling this received signal at only one bit (i.e. only the sign of the received signal is considered)! This chapter provides the foundation to understand how this seemingly magical task is accomplished using modern front-end design techniques and digital signal processing. The organization of this chapter is the following. Section 14.1 will provide an overview of the anatomy of a GNSS receiver. The functionalities and interrelationships among the various components are described. Section 14.2 discusses signal generation and transmission. Signal models at the satellite transmission and receiver antennas are presented. Section 14.3 focuses on RF front-end (RFFE) functionalities, components, performance metrics, and architecture. The signal model at the RFFE is covered in the subsequent section, Section 14.4. A central operation in a GNSS receiver is correlation regardless of the application or specific implementations of a receiver. We devote Section 14.5 to the correlation operation output model and correlation at hardware and software levels. Section 14.6 provides a quick overview of a receiver channel control state machine without dwelling on the details of the state machine implementations as they are covered in Chapters 15, 17, and 18. Section 14.7 discusses the generation and relationship among the various timing bases in a GNSS receiver. The future outlook of GNSS receiver trends are presented in Section 14.8.

14.1

Anatomy of a GNSS Receiver

Irrespective of the receiver type, the functionality of all GNSS receivers can be broken down into three major blocks: RFFE, baseband processor (BBP), and system processor (SP). In the literature, the term “baseband processor” may be used to refer to the combination of both the BBP and SP defined here. The general anatomy of a GNSS receiver is shown in Figure 14.3.

14.1 Anatomy of a GNSS Receiver

Baseband Processor (BBP)

Antenna

RF Front End (RFFE)

Signal conditioning Reference oscillator

Frequency translation

Dynamic range management, quantizer optimization

Bandwidth selection

Sampling, digitization

Digital stream

Sample Processor (SMP) Situational awareness processor

Acquisition engine

Sample conditioner

Correlation engine

Counters, timers, pulse generators

Phase-locked frequency synthesis

Hardware-software interface

• PPS • PVT • Status

System Processor (SP) User interface

Receiver intelligence

PVT solution

Channel management

Nonvolatile memory

Initialization

• • • •

Acquisition commands State updates Resource management TOR adjustments

Acquisition management Ctrl. state machines (CSM)

Power supply • Low-power oscillator • Realtime clock • Battery

Reduced Data Processor (RDP)

• • • •

ADR, TOT, I/Q, C/N0 Acquisition results Nav data bit streams Situational awareness indicators

Error correction

Tracking loops Data decoding

Interference/spoofing detection/mitigation

Figure 14.3 Simplified block diagram of a modern GNSS receiver.

The RFFE converts the signals induced at one or more antennas into digitized sample streams. Depending on the application and market segment, data rates for these streams may be as low as 0.4 Mbytes/s (e.g. L1 band sampled at 3.5 MSPS and 1-bit sampling in an asset tracking device) to greater than 3 GB/s (e.g. L1 and L2 bands sampled at 60 MSPS and 16 bits across seven elements in an anti-jam military GPS receiver). The BBP performs digital signal processing to acquire and track GNSS signals present in the digitized sample streams to produce raw GNSS observables for each visible satellite. These observables include time of transmission (TOT), accumulated Doppler Range (ADR), signal quality metrics such as carrier-to-noise density ratio (C/N0), in-phase and quadrature prompt correlator output (I/Q), and raw symbols of a GNSS signal’s broadcast navigation message (which are subsequently decoded). In addition, modern receivers typically perform varying degrees of situational awareness processing to monitor in-band interference such that a level of confidence can be assigned to these raw observables. Some advanced receivers have the ability to identify spoofing signals. Depending on the application, situational awareness outputs may be as rudimentary as the automatic gain control (AGC) voltage used to adjust front-end amplification or as sophisticated as spectrogram, histogram, and sample statistics for all streams evaluated at full sample precision.

The BBP also contains a counter that is driven by a digital clock signal that is phase-locked to the receiver’s reference oscillator. This counter is the basis for the receiver’s clock and is used to generate time-of-reception (TOR) epochs. Raw observables for all satellites in view that lead to range measurements are computed with respect to TOR epochs. Since the receiver clock is based on its reference oscillator, it drifts with respect to GNSS system times. Although possible, the frequency bias, drift, and drift rate of the reference oscillator are typically not adjusted to align with GNSS system time because dynamic adjustment of the oscillator can lead to instabilities. Instead, these parameters are estimated and used to drive a separate adjustable-rate counter that compensates for the reference oscillator errors. This forms the basis for GNSS disciplined oscillators. It is possible to partition all baseband processing into two categories: sample processor (SMP) and reduced-data processor (RDP). The SMP performs high-rate but simple and algorithmically regular operations which largely comprise multiply-accumulate operations performed at the sample rate. The SMP may also contain configurable timers and pulse/event generators that determine sample processing intervals, as well as output precise timing pulses that are synchronized down to the nanosecond level with respect to GNSS system times (timing accuracy and precision are dependent on the application and market segment). The

311

312

14 Fundamentals and Overview of GNSS Receivers

RDP performs low-rate but algorithmically complex operations. Some representative software functions running within the RDP are illustrated in Figure 14.3. Bidirectional communications occur between the SMP and RDP at regular timed intervals corresponding to a kilohertz rate. This rate is easily handled by all modern microprocessors. Since these SMP/RDP transactions are time critical, the RDP runs either bare-metal code (i.e. no operating system) or a real-time operating system. The operations within the BBP are inherently parallel and largely independent of each other at the signal processing level. Some coupling occurs, for example‚ in code-carrier aiding, inter-frequency aiding (see Chapter 15), inter-satellite aiding (referred to as vector tracking, described in Chapter 16), and multi-element processing. However, this coupling is typically implemented at higher levels of abstraction. Modern multi-band and multi-constellation receivers are capable of tracking hundreds of GNSS signals simultaneously. To facilitate this highly complex command and control structure – which also needs to be dynamically scalable and adaptive depending on the number of satellites in view, environmental conditions‚ and operating modes – the control architecture is typically layered (i.e. hierarchical). Control at the individual signal acquisition and tracking layers is performed using simple configurable finite state machines (FSMs) whose state transitions are based on signal condition indicators such as code lock, phase lock, C/N0, and code-carrier divergence (CCD). These FSMs operate independently but are typically managed at a high level by the SP. The SP takes the raw signal observables produced by the BBP and transforms them to the standard GNSS receiver measurements. These measurements include pseudorange (PR), ADR, carrier phase (CP), carrier Doppler, and C/N0. All modern GNSS receivers also compute position, velocity, and time (PVT) at configurable rates (1 to 100 Hz depending on the receiver type). The SP encodes these in one or more industry-standard data formats for distribution. These formats include Receiver Independent Exchange Format (RINEX) [3], the National Marine Electronics Association (NMEA) format [4], the Radio Technical Commission for Maritime Services (RTCM) format [5], and vendor-specific proprietary binary formats. The SP also performs all high-level functions that include receiver initialization, channel management, and user interface functions. Unlike the BBP, the operations within the SP are generally not time critical. In modern GNSS receivers, the SP is often an embedded computer running an advanced non-real-time operating system. It may also support modern data interfaces (wired USB and Ethernet, or wireless/cellular connectivity) and an advanced graphical user interface with

touchscreen support. While too numerous to mention, representative software processes running within the SP are illustrated in Figure 14.3. Although not shown in Figure 14.3, modern receivers (or the navigation system to which they are interfaced) may also support aiding from external sensors such as inertial measurement units (IMUs), magnetometers, inclinometers, barometers, wheel sensors, RADAR, LiDAR, infra-red (IR), and electro-optical (EO) sensors. This external aiding to GNSS can occur at three levels: loose coupling (position level), tight coupling (measurement level), or ultra-tight coupling (sampled signal processing level). GNSS aiding using various non-GNSS sensors is described in Chapters 43–51 in Volume II, Part E. As shown in Figure 14.3, a stand-alone GNSS receiver contains battery-powered low-power circuitry to keep track of absolute time while it is turned off. A real-time clock (RTC) driven by a low-power crystal oscillator accomplishes this task. In some cases, this crystal may be the same as the reference oscillator. Knowledge of absolute time, along with the last known location and previously decoded almanac/ephemeris data stored in the receiver’s nonvolatile memory, allows it to estimate satellites in view and their Doppler offsets, thereby significantly reducing the TTFF: the time needed to acquire satellites and produce the initial PVT solution. In the case of modern military receivers such as M-Code, or subscription-based services such as the Galileo Public Regulated Service (PRS), the receiver must acquire the cryptographically generated spreading code that may never repeat. In this case, the initial time uncertainty has a significant impact on the acquisition search space and consequently the computational resources consumed by the acquisition engine as well as power consumption. The TTFF can be dramatically reduced when absolute time, the satellites in view, their Doppler frequencies, and ephemerides are sent to the receiver from a nearby reference station via a communications link. This describes the basis of Assisted GNSS (A-GNSS) technology, covered in Chapter 17 of this book. In some respects, the reference oscillator can be considered the single most important component that affects GNSS receiver performance. Although the PVT solution estimates the deterministic components of the reference oscillator’s frequency error (i.e. short-term bias, drift, and drift rate), the stochastic component cannot be estimated and hence represents additional dynamics that must be tracked (i.e. in addition to satellite motion, user motion, satellite clock motion, and any ionospheric scintillation and multipath). The bandwidth of the carrier tracking loops must be increased to accommodate this close-in phase noise of the reference oscillator. This in turn increases the variance of the range measurements. The reference

14.2 Signal Generation and Transmission

oscillator is also the only “moving part” in the receiver since it is based on the resonance of a quartz crystal or microelectromechanical systems (MEMS) structure. In addition to microphonics, which are small phase variations that may occur within the RFFE due to external forces (particularly if the RFFE comprises large discrete components), these forces couple through the resonating element leading to shock and vibration sensitivity [6]. Similarly, thermal expansion of the crystal as well as analog components in the RFFE due to changing ambient temperature, unless appropriately compensated or isolated, causes temperature sensitivity. The frequency synthesizer in the RFFE multiplies the oscillator phase noise and dynamics by the ratio of the synthesizer output frequency to the oscillator fundamental frequency, thus placing a significant short-term stability requirement on the reference oscillator. Oscillator short-term stability limits the coherent integration time, which is proportional to the processing gain. Hence, the quality of the reference oscillator directly impacts the receiver’s attainable sensitivity (i.e. the minimum observable signal levels) as well as the rate at which it can output statistically independent measurements. Oscillator effects are covered in detail in Chapter 47. The receiver intelligence process within the SP shown in Figure 14.3 performs functions such as determining what satellites are in view, how best to mitigate any in-band interference (as observed by the situational awareness indicators), dynamically adapting to varying operating conditions, determining the best set of range measurements to use for the PVT solution based on optimum satellite geometry and estimated range error metrics indicated by C/N0 (for signal blockage) and CCD fluctuations (for multipath and ionospheric effects), and many such highly complex decisions. Typically, these high-level functions occur at a lower rate such as 1 Hz or less. To a large degree, the level of sophistication and engineering embedded within the receiver intelligence block, as well as the other low-level control functions determines the receiver’s performance in the real world, as expressed by established figures of merit. These include measurement accuracy, update rate, TTFF, sensitivity, dynamics handling capability, multipath mitigation performance, interference detection and mitigation capability, receiver autonomous integrity monitoring, and fault detection and exclusion (see Chapter 23). In other words, for a given market segment and its associated SWAP-c constraints, the receiver’s hardware and available signal processing capabilities can only do so much. The rest, and quite often the attributes that distinguish it in the marketplace, lies within the hundreds of thousands of personhours and centuries of combined experience baked into its sophisticated software/firmware.

14.2 Signal Generation and Transmission 14.2.1

Signal at the Satellite Transmit Antenna

The general form of a GNSS signal sTX emanating from the transmit antenna of a satellite vehicle (SV) at time t with nominal frequency fTX can be modeled as sTX t = hSV t ∗ +

2PTX,I cos ωSV t + ϕI t

2PTX,Q sin ωSV t + ϕQ t

14 1

where ωSV = 2π f TX + δf SV t

14 2

is the radial frequency, δfSV(t) is the random frequency variation due to the small but significant drift of the satellite’s signal generation payload reference oscillator, and ϕ represents the instantaneous phase relative to time t. Equation (14.1) describes a real signal whose in-phase and quadrature carrier components have been phase-modulated with functions ϕI(t) and ϕQ(t), respectively. This is referred to as phase quadrature modulation. A real signal is defined as one that can be transmitted using a single port or channel. hSV(t) represents the time-domain impulse response of the satellite’s signal generation and transmission hardware. The convolution of hSV(t) with the ideal signal (denoted by the ∗ operator) models the fact that the transmitted signal is band-limited for transmission efficiency as well as to conform to International Telecommunications Union (ITU) regulations. It is important to note that hSV(t) introduces a time delay from the generation of the signal at the payload to when it is radiated by the antenna. This delay, also referred to as equipment group delay, is included in the clock correction parameters relayed to the user via the navigation message [7]. Also note that hSV(t) in (14.1) represents a simplified model. In reality, this function has dependencies on the nadir angle and azimuth (stemming from the transmit antenna gain and phase pattern), and may change due to satellite aging – all of which can impact high-accuracy users. The detailed study of hSV (t) falls under SV signal quality monitoring (SQM), which is covered in Chapter 10. Since the transmitted in-phase and quadrature signal powers PTX,I and PTX,Q in (14.1) are constant over time, the in-phase and quadrature components of sTX(t) will each have a constant envelope. In other words, the amplitude of the signal conveys no information. This is an important design constraint for GNSS signals as it allows the use of efficient power amplifiers in the signal generation and transmission payload. However, modern GNSSs have requirements to modulate multiple signal components at different power levels onto the same carrier. These include

313

314

14 Fundamentals and Overview of GNSS Receivers

pilot and data components across multiple services (e.g. civilian, military, and commercial). Hence, the only way to deliver multiple signal components with a single amplifier and antenna while maintaining a constant envelope for sTX(t) is to embed all signal information into the phase modulation terms ϕI(t) and ϕQ(t). Techniques to achieve this include majority vote, Interplex [8], Coherent Adaptive Subcarrier Modulation (CASM) [9, 10], and PhaseOptimized Constant Envelope Transmission (POCET) [11]. However, to a receiver that is performing correlation for a specific pair of quadrature-modulated signal components, provided that the other signal components have low cross-correlation and are sufficiently separated in spectrum, sTX(t) appears as though ϕI(t) and ϕQ(t) are only modulated by the said pair. The remainder of this description assumes a single pair of quadrature-modulated signal components, otherwise known as quadrature phase shift keying (QPSK). For a GNSS signal with two components modulated in phase quadrature, the phase terms ϕI and ϕQ are given by ϕI t = πW I t ϕQ t = πW Q t

14 3

where WI and WQ are binary sequences with alphabet {0, 1} that are ideally uncorrelated. That is, for all possible delays τ: RW I ,W Q τ =

+∞ −∞

W I t W Q t − τ dt = 0

14 4

where W is sequence W transformed to {+1, −1} sign representation given by W = 1 − 2W

14 5

W is the modulo-2 sum (i.e. XOR operation, denoted by ⨁) of two digital sequences C and D: W I t = DI f D , t ⨁CI f C , t

14 6

W Q t = DQ f D , t ⨁CQ f C , t D is a slow-rate digital sequence with rate fd symbols/s that is used to convey data and/or coarse timing information. C is a fast-rate sequence with rate fC symbols/s that achieves direct-sequence spectral spreading and shaping. Equation (14.6) denotes fC and fd to be the same on both in-phase and quadrature components. This is to simplify the notation‚ and in general they may be different for each component. The transitions of C and D are digitally synchronized to occur at precisely the same time, and these transitions are also synchronized to the carrier cycles:

f TX = α f C = β f D

14 7

where α and β are integers. For example, for the GPS C/A code modulation on the GPS Link-1 (L1) frequency, fTX = 1575.42 MHz, fC = 1.023 × 106 symbols/sec, fd = 50 symbols/s, α = 1540, and β = 31,508,400. For BPSK modulation with rectangular spreading symbols, denoted by BPSK − R(n), C represents the primary pseudorandom spreading sequence at a chipping rate of n×1.023×106 chips/s. The normalized autocorrelation of this spreading sequence is given by

RC ,C τ =

1− τ ,τ ≤ 1 0, τ > 1

14 8

For binary offset carrier modulation with BOC(m, n) notation, C represents the modulo-2 sum of the primary spreading sequence with a 50% duty cycle square wave at the frequency m × 1.023 MHz, which is known as the subcarrier. The subcarrier spreads power away from the center of the band‚ and in conjunction with the spreading sequence is used to spectrally separate multiple signal components to achieve both inter-signal-component and intersystem interoperability. The binary assumption for C holds true for the majority of GNSS signals. Notable exceptions include the Galileo E5 Alt-BOC and E1 CBOC modulations. Further details of GNSS signal modulation techniques can be found in Chapter 2. D comprises data symbols and/or secondary codes, depending on the particular GNSS signal structure. In the context of data modulation, the term symbol refers to the actual binary sequence that is modulated onto the carrier. One or more symbols may be used to represent a single information-carrying bit, and depends on the type of error correction coding that is applied to the navigation data message. Secondary codes (also referred to as overlay codes) are used to effectively lengthen the periodicity of the primary spreading code, thereby improving its cross-correlation properties while not significantly increasing the signal acquisition burden for the receiver. These deterministic secondary codes are also used for coarse timing alignment. In general, the secondary codes have a known timing relationship with the data symbols. Hence, aligning with the known secondary code, for example‚ on a pilot signal component, avoids the bit synchronization process that is required in legacy GPS and GLONASS receivers. A pilot signal is one that contains no data modulation. These are designed primary for signal tracking and impose no restrictions on how long the signal can be coherently integrated for at the receiver.

14.2 Signal Generation and Transmission

14.2.2

Signal at the Receiver Antenna

The signal rAnt incident at the antenna of a GNSS receiver with Γ visible SVs, each broadcasting its version of signal sTX can be modeled as Γ

r Ant t =

sRX,i t + X t + nAnt t

14 9

i=1

where sRX,i is the signal received from the ith satellite given by sRX t = henv t ∗ hSV t ∗

PRX,I cos ωRX t + πW I t − τRX + ϕRX

+

PRX,Q sin ωRX t + πW Q t − τRX + ϕRX 14 10

and ωRX t = 2π f TX + δf SV t + f d t

14 11

PRX,I and PRX,Q represent the received signal powers of the in-phase and quadrature components, respectively. As is evident from Figure 14.2, the signal power induced at a receiver antenna is severely attenuated with respect to the transmit power. While this power level is certainly low compared to terrestrial RF systems, it is important to note that this is typical for all GNSS systems and stems from practical limitations on the amount of power that can be transmitted from a navigation satellite, the free space loss that the signal experiences as its transmitted power is spread out over an area that is proportional to 1/4πR2 (where R is the radius of a sphere expanding outward from the phase center of the antenna), and the reception of that signal on Earth by a small aperture antenna. Hence, all GNSS signal structures must incorporate large processing gains to increase the SNR through receiver signal processing. In a spread-spectrum system, the processing gain is defined as the ratio of the spread bandwidth to the un-spread bandwidth. For example, the processing gain of the GPS L1 C/A code signal, which has a BPSK − R(1) modulation and 50 Hz symbol rate, is 10log10(2.046 × 106/ 100) ≈ 43 dB. For pilot signals that do not have symbol modulation or have symbol modulation that is known to the receiver, the processing gain is theoretically infinite but practically limited by the stability of the receiver’s reference oscillator. fd is the Doppler frequency offset due to line-of-sight (LOS) velocity, v, given by fd = −vfTX/c. The negative sign relating Doppler to the velocity stems from the definition of range. The range of an object (and hence its time derivative velocity) is defined to be positive when it is moving away from an observer. Conversely, the frequency of a signal source is observed to be less than its nominal value when

it is moving away from the observer. For a satellite at medium Earth orbit (MEO), the velocity in the LOS direction for a stationary user on the surface of Earth can vary by as much as ±800 m/s. This is equivalent to a carrier Doppler frequency range of ±4.2 kHz at L1. Doppler also affects the modulations on the received signal by their respective rates. For the GPS L1 C/A code example, code Doppler varies by as much as ±2.73 chips/s due to satellite motion with respect to a stationary observer on the surface of Earth. τRX represents the signal propagation delay as it travels from the SV to the receiver antenna. This delay is made up of signal propagation in free space and delays through the ionosphere and troposphere. For an MEO satellite and user on Earth’s surface, τRX varies between 67 ± 20 ms [12]. ϕRX is the fractional CP due to propagation delays and distortions. Assuming point source antennas and freespace-only propagation, the relationship between τRX and ΦRX is given by τRX = f 1 L + ΦRX 2π , where L is an inteRX

ger. In reality, the received phase deviates from this relationship due to antenna phase windup effects, propagation through the ionosphere, SV and receiver electronics group delay effects, and multipath. X(t) represents any type of interference that may be induced onto rAnt. This may include intentional or unintentional interference. The latter includes harmonics and spurious emissions from nearby transmitters. In the case of the GNSS receiver function that is embedded into a multifunction RF chipset in a mobile device application (e.g. multiple cellular and Wi-Fi standards and bands, Bluetooth), a significant amount of interference is generated and coupled into the GNSS band RFFE within the chipset itself [13]. Even when the GNSS receiver and the other radios are separated, the proximity of the various transceiver antennas to the GNSS antenna within the handset can cause interference on the received signal through processes such as intermodulation (IM) and reciprocal mixing that occur within the RFFE. Types of interference include continuous wave (CW), swept CW, chirp, pulsed, pseudo random noise, and broadband noise. GNSS receivers have widely varying impacts based on the type of interference and how the receiver is designed. Further details will be found in Chapter 24. It should be noted that XAnt does not represent spoofing. The intentions and the corresponding response of the receiver to spoofing are fundamentally different from interference. In (14.9), spoofing would be represented by additional signals sRX whose received parameters closely resemble those of one or more genuine GNSS signals in view. Further details on spoofing can be found in Chapter 25.

315

316

14 Fundamentals and Overview of GNSS Receivers

nAnt is the noise induced at the antenna. Noise contributions to nAnt include the following: (1) ground noise, which is noise from Earth that can be modeled as a blackbody radiator, (2) sky noise, which comprises atmospheric noise, noise from celestial objects, and cosmic noise, and (3) thermal noise induced by the random motion of electrons in the resistive elements within the antenna. Of these, thermal noise is by far the largest contributor to nAnt. All these noise processes can be modeled as additive white Gaussian, but the actual contributions depend on the antenna gain pattern, time of day, space and local weather, and ambient temperature. A simplified model for antenna noise power is given by σ 2n = kT Ant BAnt , where TAnt and BAnt represent the antenna equivalent temperature and bandwidth, respectively. In practice, TAnt is several kelvins higher than ambient temperature to account for ground noise and sky noise. It should also be noted that BAnt is generally larger than the receiver RFFE bandwidth‚ and hence some antenna noise is rejected by the RFFE. henv represents a time-varying transfer function that models environmental effects such as multipath, ionosphere, and troposphere which affect the amplitude, delay, and phase of the received signal. These effects are further described in Chapters 22, 31, and 30, respectively. In general, the primary goal of GNSS receiver signal processing is to estimate τRX, fd, and ϕRX for each visible SV at regular intervals and as accurately as possible in the presence of noise, signal distortion, and potential interference and spoofing. In addition, the SNR or the C/N0 and interference-to-signal ratio (I/S) (when applicable) are used to determine error bounds for these estimates. As described in Chapter 2, these signal parameter estimates are used to compute absolute PVT. In general, henv represents a nuisance parameter caused by multipath, the ionosphere, and other environmental effects. On the other hand, since henv affects PRX, τRX, fd, and ϕRX, and assuming that hTX and the receiver RFFE transfer function hFE (described below) can be modeled, these estimates can be used to characterize the environment. This describes the essence of GNSS-based reflectometry and remote sensing, described in Chapters 19, 30, 33, and 34.

14.3

Receiver RFFE

This section describes the architectures, performance metrics, and some practical aspects of GNSS receiver RFFE. An RFFE performs four primary functions as shown in Figure 14.1: signal conditioning, frequency translation (also referred to as down-conversion), pre-correlation bandwidth selection (or filtering), and sampling and digitization.

Signal conditioning includes amplification and filtering‚ and it is performed throughout the RFFE. An RF amplifier or a filter is typically the first component after the antenna. Additional amplifier and filters may also be placed after the frequency translation stage. The amplification is needed to bring the weak signal and noise (below −100 dBm or on the order of microvolts) from the antenna to a useful level (about −10 dBm or 100 mV). The filters reject out-of-band noise and interferences at various stages of the RFFE. Two important factors to consider in signal conditioning circuitry are noise figure and linearity. They will be discussed later in this section. Frequency translation is the conversion of the RF signal to lower, intermediate-frequency signals. The correlation processing required to obtain observables for the GNSS signals induced at the antenna cannot be performed directly since the frequencies involved are too high. The band of interest must therefore be translated to a value that is close to baseband. Pre-correlation bandwidth selection is needed for tradeoff between the accuracy and efficiency of pseudorange measurements provided by a GNSS receiver. Pseudorange accuracy depends on how well we can estimate the timing of received signal phase transitions. The timing is derived from the code phase discriminator. The sharper the peak of the correlation function and the narrower the early-tolate correlator spacing, the more accurate the pseudorange measurement will be. The time-domain correlation function is made sharper by increasing the pre-correlation bandwidth, which lets in more high-frequency components from the transmitted signal. However, the higher the selected pre-correlation bandwidth, the higher the sample rate, and the number of computations required in downstream digital signal processing and the amount of power consumed are also increased. The selection of precorrelation bandwidth is therefore a trade-off between the pseudorange accuracy requirements of the application, the available computation technology and its power efficiency (characterized in terms of performance per watt), and the overall cost of implementation (because more computations required per unit of time increases the area of the integrated circuit). Sampling and digitization is the process of converting the received analog signal to a discrete time and quantized amplitude representation. As is the case with all modern communication systems, GNSS receivers employ digital signal processing technology. All processing performed in BBP are on the digitized signals. The RFFE design process involves implementing the above functions while introducing as little signal degradation or distortion as possible. The analog processes of amplification, filtering, down-conversion, and sampling

14.3 Receiver RFFE

that occur within the RFFE introduce unavoidable degradation. In the context of a GNSS receiver, this degradation can be classified into the following three different types: 1) Degradation that reduces post-correlation SNR. There are many factors that can lead to reduction in postcorrelation SNR. They include noise figure, nonlinearity, IM distortion, oscillator and frequency synthesizer phase noise, and quantization losses. Post-correlation SNR degradation reduces the sensitivity of the receiver. The predetection integration time can be increased to compensate for the reduction. However, this in turn limits the receiver’s ability to track dynamics, or external velocity aiding is required. Acquisition also needs more search bins, which leads to increased power consumption. Hence, minimizing this degradation is crucial for high-sensitivity and highdynamics receivers. 2) Degradation that distorts the correlation function. The RFFE introduces group delay and group delay variation in the passband, and also internal reflections due to component-induced multipath. These effects are also temperature dependent. The associated degradation is responsible for inter-channel biases between code as well as carrier measurements and produces pseudorange biases as a function of the correlator spacing. Component-induced multipath introduces distortions that then cause correlatorspacing-based biases. 3) Degradation due to spurious dynamics. Ideally, the digitized signal from the RFFE should contain only the dynamics present in each GNSS signal, dynamics due to receiver motion‚ and those due to channel effects (i.e. multipath and ionosphere). However, spurious dynamics are introduced through the processes of downconversion and sampling. Even though these dynamics are largely common mode (affects all received signals identically) and hence eventually revealed in the time component of the PVT solution, they must be tracked as part of the composite-signal dynamics. Spurious dynamics largely arise from the drift as well as the receiver reference oscillator’s sensitivities to the receiver platform and environmental factors such as shock, vibration, and temperature. These dynamics are amplified by the frequency synthesizers that are phase-locked to the reference oscillator. In addition, the sensitivities of the voltage-controlled oscillators (VCOs) to the environmental factors that are present within these synthesizers can introduce further dynamics. Finally, physical flexing of the RFFE due to the environmental factors can modulate the output signal phase. Severe microphonics (shock and vibration) can cause carrier cycle slips or even loss of lock. The stochastic component of these spurious

dynamics needs to be tracked in order to not lose lock or have cycle slips. However, that means increasing the tracking loop bandwidth‚ which in turn increases the noise in the measurements. Phase noise above the tracking loop bandwidth is filtered out – but this phase noise reduces the SNR in the correlation stage. The degradations due to the above reasons and the performance of the RFFE can be described by several metrics, including noise figure, linearity, dynamic range, passband group delay and variation, frequency bias and drift, and phase noise. The following subsections will discuss these metrics in detail.

14.3.1

Noise Figure

The noise factor, F, of a two-port electronic device characterizes the amount of SNR degradation that occurs when a signal flows through it: F=

S N

input

S N

output

14 12

When the noise factor is expressed in dB, it is known as the noise figure (NF): NF = F

dB

= 10 log 10 F

14 13

Since any device above a temperature of 0 K adds thermal noise to a signal, the noise factor of practical devices is always greater than one (F > 1, NF > 0 dB). The noise factor of a device can be measured by injecting a precisely calibrated noise source at its input and measuring the output power. The output power that is above the expected value is attributed to device noise. A passive device has gain G < 1 (G < 0 dB). Since thermal noise exists at both input and output, the noise factor of a passive device is given by F=

st kTB = G − 1 , NF = − G dB × kTB Gs t

14 14

For example, a 3 dB attenuator has a gain of −3 dB and hence an NF of 3 dB. The noise factor Fsys of a system of N cascaded components with gain Gi and noise factor Fi is given by the Friis equation for the noise factor [14]. Assuming that the device ports are ideally matched (i.e. no reflected power): F sys = F 1 +

F2 − 1 F3 − 1 F4 − 1 FN − 1 + + +…+ N G1 G1 G2 G1 G2 G3 i = 1 Gi 14 15

If the first device has a low noise factor and a high gain (i.e. a low-noise amplifier [LNA]), then the contribution to the system noise factor from the remaining components

317

318

14 Fundamentals and Overview of GNSS Receivers

becomes negligible. It is said that the LNA “sets” the noise factor of the system. On the other hand, if the first device is passive, the system noise factor is degraded by the loss of this first device‚ and no amount of low-noise amplification thereafter can help to improve it. In a practical receiver, the first component is always passive and represents the insertion and transmission line losses from the antenna element to the LNA. This can be kept to a minimum by placing the LNA as close to the antenna feed point as possible. For this reason, most GNSS receiver antennas embed the LNA into the antenna housing, and are referred to as active antennas. Direct current (DC) power to the embedded LNA is supplied through the transmission line. GNSS antennas are supplied as passive types only in a few instances. For example, for antennas used in miniaturized portable devices (such as cell phones), the transmission line loss is negligible due to the close proximity of the antenna element to the RF integrated circuit that includes the LNA. Multi-element GNSS antennas used for beam-steering and null-forming are also supplied as passive types. This simplifies measurement of the gain and phase characteristics of elements with respect to a reference element (a process known as antenna manifold calibration) by the antenna electronics manufacturer. The NF of a commercial GNSS antenna is typically around 2.5 dB, and the embedded LNAs have gains above 20 dB. This is sufficient to set the low NF of the active antenna as the receiver’s system NF even with a moderate amount of cable loss between antenna and receiver. As can be seen from (14.15), the system NF starts to degrade significantly when this cable loss approaches the gain of the embedded LNA.

14.3.2

Linearity

A two-port device input and output signals sin and sout can be modeled as sout = A0 + A1 sin + A2 s2in + A3 s3in + … + An snin 14 16 where A0 represents the DC bias‚ and A1 represents the voltage gain of the device. The device is said to be purely linear if and only if Ai = 0, i > 1. In practice, any component that employs semiconductors to achieve its function does not exhibit linear behavior. In fact, as described later, the essential process of frequency mixing exploits second0). The nonlinearity of a device is order behavior (A2 characterized by coefficients A2 through An. When the input is a pure tone of the form sin = a cos (ω0t + ϕ0), also known as the fundamental tone, the nonlinear operations s2in , s3in , …, snin in (14.16) produces output tones with frequencies 2ω0, 3ω0, …, nω0,

respectively. These are known as ith-order harmonics. A purely linear device does not produce any harmonics. In general, harmonics are distant enough in frequency from the desired channel bandwidth that they can be removed through filtering. On the other hand, extracting a particular harmonic is the principle used to implement frequency multipliers. Now consider a two-tone input signal of the form sin = a cos (ω0t + ϕ0) + a cos (ω1t + ϕ1). The second-order term (i.e. the input squaring operation) in (14.16) will produce output tones at 2ω0, 2ω1, ω0 + ω1, and ω0 − ω1, as shown in Figure 14.4. The first two terms are the second-order harmonics. The latter two terms are referred to as second-order inter-modulations or “intermods.” In general, spectral components that are algebraic combinations of the input tones are known as IM products. A purely linear device does not produce any intermods. In general, the second-order intermodulation (IM2) products are also sufficiently separated in frequency from the desired band that they can be easily filtered out. However, if either ω0 or ω1 is the desired signal and the other is an interference source, and if the A2 of the device is sufficiently large, the resulting IM2 will cause some of the desired signal power to be shifted away from the passband. This is known as gain compression‚ which occurs when the input signal amplitude is large and the device becomes nonlinear. For a two-tone input, a nonzero A3 term in (14.16) will produce third-order harmonics at 3ω0 and 3ω1 as well as IM3s at 2ω0 + ω1, 2ω1 + ω0, 2ω0 − ω1, and 2ω1 − ω0 as shown in Figure 14.4. If the frequency difference of the two tones is small, the latter two intermods can fall so close to the desired ω0 and ω1 frequencies that they can be extremely difficult if not impossible to filter out. If either ω0 or ω1 is the desired signal with modulation and the other is an interferer, not only does the interferer degrade the signal reception but it also modulates the desired signal in a manner that is unpredictable to the receiver, and this IM can pass through the RFFE passband, causing further degradation. For example, if the desired signals are the received GNSS signals, where each is at frequency fL + fdi and the interferer is a CW signal at frequency fCW, the intermods will be the frequency-shifted GNSS signals at (2fL − fCW) + 2fdi and (2fCW − fL) − fdi. If fCW is close to

ω0 ω1 ω1-ω0

2ω0–ω1

2ω1-ω0

2ω0 ω1+ω0 2ω

1

ω1+2ω0 2ω1+ω0 3ω0 3ω1

Frequency

Figure 14.4 Second- and third-order harmonics and IM products for a two-tone input.

14.3 Receiver RFFE

fL and A3/A1 is sufficiently high, the result is attenuated GNSS signals at unexpected Doppler frequencies in the passband. In RFFE architectures where the passband starts off wide and is progressively narrowed using one or more frequency conversion stages (as is the case for the superheterodyne receiver architecture described below), the interferer may be a strong adjacent band signal that is well outside the receiver’s intended pre-correlation bandwidth. However, IM3 occurring within the first amplifier stage of the RFFE could place significant interference power directly in the final pre-correlation passband. Higher-order terms of (14.16) produce additional harmonics and intermods. In general, the higher-order terms produce harmonics at higher frequencies, which makes them easier to filter out from the desired passband. Likewise, even-order intermods fall outside the passband. However, some intermods from odd-order terms fall within the passband and have the same detrimental effects as described above for the third-order case. For small signal levels, a practical amplifier produces the amplified version of the input signal according to its voltage gain, and some additional distortion that can be

–1-dB Compression Point, P1

characterized by the higher-order terms of (14.16). However, if the input signal level is steadily increased, at some point the output signal becomes severely distorted as the peak output levels approach the power supply rails. In the frequency domain, this distortion results in the relative reduction of spectral components from the desired signal and a relative increase of spectral components stemming from harmonics and IM. Hence, the coefficients in (14.16) are in general not constant for a given device but rather change as a function of the input level and also the type of signal being amplified. Therefore, it is not convenient to characterize the linearity of practical devices using transfer function coefficients. Instead, we use gain compression and third-order intercept points. Figure 14.5 plots, on a logarithmic scale, the input and output powers of the primary spectral components and the IM3 products when a practical device is presented with a two-tone signal. These spectral components are typically directly measured using a spectral analyzer. Due to the logarithmic scale, the fundamental and IM3 curves in Figure 14.5 have slopes of 1 and 3, respectively. These curves start to flatten out for large input signal levels due

IP3 (dBm)

OIP2 (dBm)

IP2 (dBm)

OIP3 (dBm) 1 dB

POUT (dBm)

Fundamental 1 1 1

2

IMD2

3 1 IMD3 IIP2 (dBm)

IIP3 (dBm)

PIN (dBm)

Figure 14.5 Illustration of P1dB, IP2, and IP3 through the input and output powers of the primary spectral components and the thirdorder intermodulation products for a practical device with a two-tone input signal [15]. Source: Reproduced with permission of Texas Instruments.

319

320

14 Fundamentals and Overview of GNSS Receivers

to gain compression. The point where the fundamental curve diverges by 1dB compared to the slope-1 line is referred to as the 1 dB compression point (P1dB). P1dB may be referenced to the input (IP1dB) or output (OP1dB) and is related by OP1dB = G × IP1dB, where G is the small signal power gain of the device. The greater the separation of the x-axis intercepts of the fundamental and IM3 lines, the greater the linearity of the device. Where these extrapolated slope-1 and slope-3 lines cross is referred to as the third-order intercept point (IP3). IP3 is a virtual measurement since the device can never reach this point due to gain compression. As with P1dB, IP3 may be referenced to the input (IIP3) or the output (OIP3). In general, IP3 for a high-linearity amplifier is at least 15 dB greater than P1dB. Similar to IP3, intercept points for other IM products can be measured by subjecting the device to a twotone test signal and measuring the total power of the expected intermods using a spectrum analyzer. P1dB and IP3 that characterize the dynamic range and linearity of practical devices, as well as the test conditions used to measure them‚ are specified in the device data sheets. These device parameters are useful for evaluating the suitability of devices for the target application as well as to compare and contrast competing solutions. The actual performance of the RFFE subsystem can be modeled using simulation tools as well as measured using test instruments. It is usually adequate to characterize nonlinearity by considering IM3 only. For practical devices operating in the small signal power range for which they are designed, the higher-order coefficients of their transfer characteristic diminish rapidly as a function of order. Devices such as amplifiers and mixers that are designed to be as linear as possible operate this way when the input signal levels are small. For larger input signal levels, output compression or gain compression occurs as the device starts to deviate from nominally linear behavior. Compression can be exploited for useful functions such as limiters that are used to prevent large input signals (such as voltage spikes induced at the antenna from lightning) from potentially damaging sensitive RFFE components such as LNAs. For amplifiers, compression occurs when the output signal starts to approach its power supply voltage. For mixers, input signal interaction with the mixer core starts to modulate the local oscillator (LO) signal rather than the other way around.

14.3.3

expressed in decibels. In a receiver, the dynamic range is typically defined to extend from its IP3 at the high-level end to its sensitivity limit at the low-level end. The highlevel end is a result of signal saturation and distortion effects. An AGC circuit in a receiver RFFE is a mechanism designed to minimize signal saturation and distortion. The sensitivity limit at the low-level end is determined by the receiver thermal noise, NF, spurious signals, harmonics, and phase noise. It can be estimated by measuring the average noise level. A receiver’s dynamic range is mainly determined by the mixers and amplifiers in the system. Other components such as active and passive filters play a secondary role. Other parameters have also been used to define the highest-level signal, such as P1dB. This is because P1dB corresponds to the signal power level above which the linearity of the amplifier begins to degrade. For a mixer, signals with power above P1dB may generate high levels of IM distortion. For passive RF mixers, the P1dB is typically about 5–10 dB below the mixer’s LO power. Passive RF mixers are commonly classified as low-, medium-, or high-level mixers based on the LO power required for their operation. Typically, low-, medium, and high-level mixers have LO power at +7, +10, and +14 dBm, respectively. For example, Mini-Circuits offers mixers with LO powers ranging from +3 dBm through +17 dBm. A mixer with a higher LO power level yields a higher P1dB and a higher receiver dynamic range [16]. Using different parameters to define dynamic range often leads to confusion when comparing the dynamic ranges for electronic components or systems. In modern GNSS receivers designed to operate in the presence of in-band interference, the RFFE is designed to have a high dynamic range, and interference mitigation processing is performed on the digitized sample stream prior to correlation. The digitizer or the analog-to-digital converter (ADC) also has a dynamic range which is related to the number of bits that are used to digitize the analog signal. Consider an N-bit ADC. The minimum value that can be detected is one least significant bit (LSB). The maximum value is 2N−1 times the LSB value. Therefore, the dynamic range of an ADC is 20 log10(2N−1) ≈ 6×N (dB). A 4-bit ADC therefore has a dynamic range of ~24 dB. This preprocessing is most effective when the RFFE is designed to be as linear as possible up to the expected received interference power level – usually specified as a maximum interference-to-signal ratio performance requirement.

Dynamic Range

The dynamic range is an important parameter of an electronic system. It is defined as the ratio of the highest signal level to the lowest signal level a system or component can process in a linear manner. Dynamic range is typically

14.3.4

Frequency Translation and Sampling

Frequency translation, also referred to as down-conversion or mixing, can be accomplished through analog mixing or through intermediate-frequency (IF) sampling (also known

14.3 Receiver RFFE

as bandpass sampling). Figure 14.6 shows the block diagram of a single channel (left) and a dual-channel (right) analog mixing operation. The mixer is a nonlinear device that is effectively a multiplier of the input signal and a reference signal generated by the frequency synthesizer. The multiplication operation effectively translates the input signal frequency into two bands: an upper band centered around fRF + fLO and a lower band centered around fRF − fLO. A low-pass or bandpass filter is applied at the output of the mixer operation to remove the upper band, leaving only the lower band component as the IF signal for subsequent processing. The single channel mixer generates one IF output. The dual-channel mixer employs two mixers, each operating on the equally split RF input with one of the mixers taking a direct LO signal and the other a 90o phase-shifted LO signal. Both mixers’ outputs will further go through low or bandpass filters to remove their corresponding upper bands to yield the IF I and Q channel outputs. Note that although the diagrams indicated that the inputs to the mixers are RF

signals, they could also be an early stage IF output in a multi-stage mixing operation. The IF sampling process is often used to further downconvert the IF signal to baseband signals. It is based on the sampling property of a band-limited analog signal. For a continuous band-limited time-domain signal sa(t) with a frequency-domain representation Sa(f), its time-domain samples sd(t) and frequency-domain function Sd(f) are ∞

δ t − nt s

sd t = sa t n = −∞

Sd f = Sa f ∗

∞

f sδ f − k f s

k = −∞ ∞

= fs

Sa f − k f s

where fs is the sampling frequency, and t s = 1 f s is the sample interval. Figure 14.7 illustrates the samplingprocess-generated spectrum for a band-limited signal

IF signal fIF I channel Mixer M RF signal fRF

IF signal fIF

90° fLo IF signal fIF Q channel

Frequency Synthesizer

fLo

Mixer M

Frequency Synthesizer

Figure 14.6

Single and dual analog mixing operation.

Sa(f)

Sd(f)

f

f -fs

B

B

fs

Output frequency fs/2

fs/2 Direct Transition Mode

Inverse Transition Mode

fs

3fs/2

2fs

14 18

k = −∞

Mixer M

RF signal fRF

14 17

5fs/2

foutput = finput – nfs and foutput
0 9960 σ r 14 33

This ADC produces the set of values {−3, −1, 1, 3}. The 0.9960 scale factor in (14.33) represents the optimum value that minimizes correlation loss. The signal standard deviation estimation σ r is typically derived from the AGC voltage in a low-cost receiver. Modern receivers that are designed to mitigate interference sample rIF[k] using ADCs with a high dynamic range, typically 12 bits with at least 10 effective number of bits (ENOB), yielding 60 dB of digital dynamic range (see discussions in Section 14.3.3). In this case, the analog AGC is only engaged to the extent of maintaining linear operation of the front-end. Utilizing the ADC’s full dynamic range maximizes the options available for applying various signal processing techniques to identify and mitigate interference. These techniques are implemented in the situational awareness processor and sample conditioner blocks shown in Figure 14.3. It is important to note that (14.26) considers noise due to thermal effects only. In practice, additional noise-like effects in the front-end contribute to lowering the SNR. These include spurious emissions and IM products. The digitized complex signal is given by r IF k = hFE k ∗

Γ

hSV ,i k ∗henv,i k ∗sIF,i k

i=1

+ X IF k + nIF k

14 34

where, for the 2-bit sign-magnitude encoded ADC: − 3, − 1, + 1, + 3

r IF k

14 35

Recognizing that in general the front-end transfer function can distort received SV signals by different amounts according to sequence W: Γ

r IF k =

hS,i k ∗sIF,i k

+ hFE k ∗ X IF k + nIF k

i=1

= bandlimited received signals + bandlimited inteference and noise

14 36

where hS,i = hSV ,i ∗henv,i ∗hFE,i

14.5

Correlation Processing

14.5.1

Correlation Outputs

14 37

GNSS signals contained within the sampled stream rIF[k] are below the noise floor and hence are not directly observable. The receiver tracks a desired signal by correlating rIF[k] with a locally generated replica signal sIF k . The correlation output is then used to determine signal

14.5 Correlation Processing

parameters that represent how closely sIF k is aligned relative to the true signal sIF[k] buried within rIF[k]. These somewhat noisy signal parameters are then filtered and used to estimate LOS signal dynamics, and steer the local replica at regular intervals to keep it as closely aligned to the true signal as possible. The receiver also uses the correlation outputs to compute C/N0 and other quality metrics that indicate how well the local replica is aligned to the true signal, as well as to assess statistical error bounds for the measured signal parameters. When criteria for good alignment and confidence are met, the receiver processes the sIF k steering commands into range measurements. It is important to note that during this entire process, at no point is the true signal sIF[k] directly visible to the receiver – it is still buried in noise within rIF[k]. Incidentally, the only way to directly observe GNSS signals above the noise floor from Earth is to utilize a high-gain dish antenna. This section describes the digital signal processing that is performed on front-end sample stream rIF[k] to obtain range measurements and signal quality metrics for GNSS signals that are contained within it. Without loss of generality, suppose the receiver intends to track the in-phase component of the received signal from SVi that is contained within sample stream rIF[k] from (14.34). Then the correlation operation is given by N n + 1 −1

r IF k sIF,i,I,n k , n = 0, 1, 2, …

Corr i,I n = k = Nn

14 38 n represents discrete time epochs where an N-sample block is correlated, and the resulting output returned for signal parameter estimation. The time interval associated with this integrate-and-dump operation is therefore referred to as the pre-detection integration interval Tpdi: T pdi = NT s

14 39

The locally generated replica corresponding to SVi’s in-phase signal component at epoch n is given by sIF,I,n k = CI

f C + α − 1 f d,n , kt s − τn e − j2πf IF,n kts + ϕn 14 40

where τ, f IF = f Offset + f d, and ϕ are the receiver’s estimates of code phase, carrier frequency offset, and CP, respectively. In most legacy GPS receivers, these estimates are constant over Tpdi, which makes the assumption that incomingsignal dynamics are largely constant over this interval. However, for applications such as space receivers where signal dynamics are large or high-sensitivity receivers where Tpdi is on the order of a second, multiple parameter updates may be required to keep the replica adequately aligned to the desired signal. For this ongoing description

it is assumed that the receiver’s given Tpdi interval n is aligned with the transitions of the slow-rate modulation D I in (14.6). In practice, this is only true when the receiver has achieved symbol synchronization. Given the sampled signal model of (14.36), the correlation output of (14.38) (now generalized to either the inphase or quadrature signal component) can be expressed as the sum of four components: (1) Corr SV i: correlation with the desired GNSS signal component, (2) CorrY: crosscorrelation with other modulation components on the same SV carrier signal as well as cross-correlation with other received GNSS signals and/or spoofing signals that may be present in rIF(k), (3) CorrX: correlation with interference signals, and (4) Corrnoise: correlation with noise: Corr i = Corr SV i + Corr Y + Corr X + Corr noise 14 41 Cross-correlation, spoofing, and interference each have different types of effects on the correlation output and how desired signal acquisition and tracking is ultimately affected. These topics are further described in Chapters 10, 24, and 25. Assuming that the receiver’s initial estimates of code phase and carrier frequency are close to those of the desired signal, the correlation output at epoch n for the desired component of GNSS signal from SVi is given by Corr SV i n = An Dn hS,i ∗ R δτn sin πδf n NT s πδf n NT s

cos δϕn + jsin δϕn

= I SV i ,n + jQSV i ,n 14 42

where An is the average received signal level during interval n, and R δτn is the correlation over N samples of the desired signal component’s spreading sequence at an arbitrary phase τRXwith the locally generated copy of that sequence with an estimated rate f C + α − 1 f d and estimated code phase τn : N n + 1 −1

R δτn =

C

f c + α − 1 f d , kt s − τRX C

k = Nn

f c + α − 1 f d,n , kt s − τn

14 43

It should be clear from (14.8) that |R(δτ)| 0 when δτ > 1. Otherwise |R(δτ)| increases linearly with N, as long as the sign of D stays constant during the integration interval. If the sign of D changes at any time during this interval, the increasing correlation magnitude will start to diminish – this is why correlation intervals need to be precisely aligned to the sign changes of D . During the initial signal acquisition and pull-in phase, this information is generally

331

332

14 Fundamentals and Overview of GNSS Receivers

| sincπδfmTpdi |

–δf

–1/Tpdi

1/Tpdi

δf

sin πδf T pdi πδf T pdi magnitude and its null-to-null bandwidth dependence on the pre-detection integration interval Tpdi.

Figure 14.16

Illustration of the sinc function

threads, single instruction, multiple-data (SIMD) vector instructions, bit-wise parallel techniques, general-purpose graphics processing units (GPGPU), and combinations thereof. We use the term “hardware correlation” here to refer to this constant-interval component of the operation rather than the implementation approach. After hardware correlation, the outputs are dumped to software where consecutive hardware correlation outputs can be accumulated to extend the pre-detection time in increments of 1 ms. These software accumulated outputs are referred to as narrowband or coherent correlation. T HW = N HW T s = 0 001 sec

unknown. Alignment to D must be performed using a symbol synchronization technique. It is also important to note that R(δτ) within Corr SV i is band-limited due to convolution with the impulse response hS,i . The sinc function in (14.42) results from the correlation of two sinusoids. Figure 14.16 shows the response as a function of the average frequency error δf over the integration interval between the desired signal and the local replica. The null-to-null bandwidth of this sinc function is inversely proportional to the pre-detection integration interval. As a result, the longer the integration interval, the higher the precision to which the receiver must steer f to follow the dynamics of the desired signal. Equations (14.42) and (14.43) indicate that as long as the local replica is aligned, the correlation power increases by N2: I 2SV i + Q2SV i N 2 . Correlation of the local replica with band-limited noise within the sample stream rIF(k) is given by N n + 1 −1

hFE k ∗nIF k

Corr noise n =

sIF,i,I,n k ,

k = Nn

n = 0, 1, 2, … = I noise,n + jQnoise,n

14 44

The real and imaginary components are uncorrelated: Cov (Inoise, Qnoise) = 0. Unlike the signal power which increases with N2, the noise correlation power increases with N: I 2noise + Q2noise N . Therefore, the SNR is proportional to the pre-detection integration time (also known as the coherent integration time).

14.5.2

Hardware and Software Correlation

In general, since fs is relatively high, initial correlation is performed in hardware. Typically, the hardware integration time is 1 ms. This is performed in the hardware correlation engine (within the SMP) as shown in Figure 14.17. Note that in a full software-based GNSS receiver‚ the 1 ms correlation is performed using highly optimized implementations leveraging multiple CPU cores and/or

14 45

M n + 1 −1

I WB,n , m = 0, 1, 2, …

I NB,m = m = Mn

M n + 1 −1

QWB,n , m = 0, 1, 2, …

QNB,m =

14 46

m = Mn

The coherent correlation outputs are used to detect the carrier frequency and/or phase deviations with respect to the replica carrier (δf n , δ Ø n) as well as correlation envelopes for the Prompt, Early, and Late code replicas. The detected correlation envelopes are further accumulated for K Pdi intervals and dumped. This is known as non-coherent integration and further improves the SNR. These non-coherent P, E, and L outputs are used to compute code phase deviations with respect to the replica code generator (δτn ). Instead of the correlation envelope, some receivers may detect and use correlation power for code tracking: Em = I 2E,m + Q2E,m . Receivers also use various techniques to reduce the total number of hardware accumulators needed for signal tracking. For example, instead of processing separate Early and Late correlator outputs, the E-L function necessary for computing δτn is derived from the replica code generator and applied to a single complex correlator. More detailed discussions of coherent and non-coherent integration gain/limitations and signal tracking techniques are presented in Chapters 18 and 15, respectively.

14.5.3

C/N0 Calculation

C/N0 is an important signal quality metric. There are two commonly used methods to compute C/N0: the power ratio method (PRM) and the variance summing method (VSM) [33–35]. While both methods generate similar estimations for the nominal signal, the PRM is known to show signs of saturation at higher C/N0 levels, while the VSM performance degrades more for signals experiencing rapid powerlevel fluctuations. Reference [36] applied both methods to several sets of data collected using a conventional and a high-gain antenna during quiet and active ionospheric

14.6 Channel Control State Machine

Post-detection (Non-Coherent) Integration

Pre-detection (Coherent) Integration, Tpdi HW Correlators (within SMP)

SW Accumulators (within RDP) L

Accumulate & Dump

rIF(k)

Accumulate & Dump

ˆ

IWB,m QWB,m

ˆ

e –j 2πfIF,nkts + øn Cl′(fc + α–1fˆd,n,kts– τˆ n)

Accumulate & Dump

Wideband Correlators Integration time:Thw = 1 ms * Bandwidth:1/T hw = 1 kHz

NCO Commands and Code Generator Settings

Processing Rates:

Accumulate & Dump

Replica Code

Replica Carrier

>3MHz

Pm, Em, Lm

P, E, L

E

P

INB,m Envelope Detection

QNB,m

Em =

Ip,m Qp,m

2 IE,m

(P), E, L Accumulate & Dump

2 + QE,m

Phase/ Frequency Detection

δτˆi δfˆn,δøˆ n Narrowband Correlators * The bandwidth of the correlator output is Integration time:M*Thw = M ms defined as the peak-to-null (i.e. single Bandwidth*:1/MThw = 1/M kHz sided) bandwidth of it’s sinc function (see Figure 14.16) 1/M kHz

1kHz

1/KM kHz

Figure 14.17 Illustration of how hardware correlators integrate and dump for 1 ms and how software further coherently accumulates multiples of these to dynamically adjust TPdi based on signal conditions (e.g. high-dynamics vs. high-sensitivity modes). Coherently integrated outputs are detected to yield carrier phase/frequency and envelope discrimination. The envelopes are further integrated noncoherently prior to code phase discrimination.

scintillation conditions to illustrate the deficiencies of the two methods. Both methods estimate C/N0 using the correlation outputs. The PRM method first computes the wideband and narrowband power:

where Z2 is the average I and Q correlator output sequence over an accumulation time period Taccu, and σ 2Z is the sequence standard deviation: Z=

M

I 2WB,m + Q2WB,m

PWB = PNB =

m=1 I 2NB +

14 47

Q2NB

σ 2Z =

14 48

The normalized power is given by PNB,k NPk = PWB,k

14 49

1 K NPk Kk=1

14 50

σ 2IQ =

μNP − 1 T WB M − μNP

dB − Hz

14 51

The VSM computes the average carrier power using the following formula: PC =

2

Z − σ 2Z

14 52

K 1 Zk − Z K − 1 k−1

14 54

1 K Z − PC 2 k−1

14 55

The C/N0 is computed based on PC and σ 2IQ : C N 0 = 10 log

Typically, in steady-state tracking, M is set to 20 and K to 50 to yield the update rate of 1 Hz C/N0 calculations. C/N0 is given by C N 0 = 10 log

14 53

The I and Q channel noise power is computed based on the variance of the noise accumulation:

The average normalized power is then obtained over K consecutive normalized power values: μNP =

1 K 2 I + Q2k K k−1 k

14.6

PC 2T accu σ 2IQ

dB − Hz

14 56

Channel Control State Machine

Figure 14.18 depicts the channel control state machine state diagram. The states are shown in the block diagram in the left, while the functionalities of each state are summarized and explained on the right. Detailed discussions on some of

333

334

14 Fundamentals and Overview of GNSS Receivers • • •

Initialization

Re-Acquisition Potential Hit

Verification

Pull-In

Steady-State Tracking N

SP high-level command: ‘acquire PRN(x) and track on channel(y)’ SP provides initial Doppler and time estimate if available SP provides C/N0 estimates if available (initial acq. engine parameters)

• Setup detection thresholds, coherent/non-coherent intervals • Compute delay-Doppler hypotheses (search space) • Return acquired signal parameters and search parameters (e.g. Tpdi) • Verify persistence of signal at detected hypothesis • Setup tracking channel with wide signal pull-in parameters • Converge tracking loop filters to current dynamic state • Monitor and correct ‘false lock’ conditions (carrier/code sidelobes) • Transition from wide FLL to narrow PLL, narrow coherent DLL • Decode navigation message and initialize TOT register Meas. • Update TOT and carrier phase accumulator • Monitor tracking performance • Challenging conditions: low C/N0, rapid fades, sudden dynamics

Stress? Y

• Low C/N0 and high dynamics signal tracking strategies » FLL or FLL-aided-PLL, non-coherent wide-correlator-spacing DLL » External sensor aiding

HOBYT* N

Lost?

• Signal lost, but last-known-good parameters available • Attempt reacquisitionorretiresignal tracking and set channel idle

Y

Reassign Channel

Figure 14.18

* “Hold-On By Your Teeth!” credit: Phillip W. Ward, Navward Consulting

Typical flow diagram for a GNSS receiver signal acquisition and tracking channel control state machine.

the processes depicted in the diagram can be found in other chapters. For example, acquisition is discussed in Chapter 18. Signal tracking loops such as frequency lock loop (FLL), phase lock loop (PLL), and FLL-assisted-PLL are discussed in Chapter 15. Inertial aiding is covered in Chapter 46. Other functions such as bit and frame synchronization, raw symbols extraction from FLL and PLL tracking, preamble location, data decode, parity/CRC checks, forward error correction, and pseudorange calculation are straightforward processes that are well documented [37].

14.7 Correlator and Tracking Channel Timing Several time bases are present within a GNSS receiver. This section describes what these are, how they are generated, and how they interact with each other. Figure 14.19 illustrates the timing circuitry present in a typical low-channel-count GNSS receiver. In this type of receiver, data transfers between the SMP and RDP are carried out using a programmed input/output (PIO) interface. This type of interface performs individual register read/write operations that are mapped to a microprocessor’s I/O address space. Even though the PIO interface is bidirectional, Figure 14.19 shows separate read and write data busses for clarity.

In order to avoid losses due to sign changes, the correlation intervals in a tracking channel (within the SMP) must be aligned to the incoming signal’s data and/or secondary code symbol boundaries. These integration intervals, referred to as SV time epochs, are derived from the replica code generator. Since the range to each satellite is dynamically changing, SV time epochs are not synchronous to receiver time epochs. Since computing a PNT fix is based on the principle of trilateration at a given instant, ranges to each visible satellite must be measured at precisely the same receiver-based time instant. These receiver time epochs are derived from the receiver’s reference oscillator, typically by dividing the sampling clock by an integer value. It is important to note that the reference oscillator is not an accurate timing source compared to GNSS system times. Hence, any precise timing outputs generated by the receiver (such as the pulse per second, PPS, output) is synthesized by compensating for the oscillator’s bias and drift characteristics that become known after observing the PNT solution over time. In most receivers‚ the reference oscillator itself is free running and never adjusted since doing so can impact its characteristics in unpredictable ways. The receiver epoch count represents the receiver time, which can be directly read into software and converted to the required absolute time scale. As shown in Figure 14.19, receiver epochs latch the replica code and carrier states of all channels into holding registers that can be read though the PIO interface. These values represent the highest-resolution components required to

14.7 Correlator and Tracking Channel Timing

Receiver Epoch Logic

Tracking Channel Logic

Latch

Correlator Outputs Accumulators

Integer Cycles

Clear Cycle Counter

Fractional Cycles Overflow

Carrier NCO

Replica Code Replica Carrier

Initialize/Update

Carrier Rate/Phase

Code Phase

Code Rate

Sample Stream Write Bus

PIO Write Divide Value

Sample Clock

Apply Epoch

Initialize/Update

Programmable Divider

Epoch Counter

SV1ms Epoch

Code Generator

Overflow

Code NCO

Rcvr. Epoch Interrupt Epoch Counter

Apply Epoch Generator

Apply Epoch

PIO Read

SV Time

Integer Chips

Fractional Chips

Read Bus

SV Epoch Interrupt

Figure 14.19

Timing circuitry for a GNSS receiver employing a PIO interface.

compute the raw range measurements, which are SV TOT and carrier cycles accumulated since last initialization, respectively. As these values are latched, an interrupt is generated to prompt software to read them as soon as possible (i.e. before the next interrupt). Values are read‚ and a set of raw measures are computed, typically inside an interrupt service routine (ISR). Figure 14.19 shows a programmable counter that may be used to set the receiver epoch interval. This is typically set to the receiver’s measurement update rate. The software-based tracking algorithms that read correlator outputs and produce numerically controlled oscillator (NCO) rate steering commands are processed within the RDP. The embedded microprocessor inside this block is typically clocked by a different (often low-quality) crystal oscillator. In general, there is no timing relationship between software processing cycles and receiver time epochs. When a channel is initialized, write registers configure its primary code PRN, initial code phase, and carrier/code rates. Assuming that the replica code phase and carrier Doppler are approximately aligned, the incoming signal is “pulled in” and tracked by adjusting only the rates of the carrier and code NCOs thereafter. In early GNSS receivers, values written to registers went into immediate effect. These receivers used the same channel to perform acquisition by employing serial search techniques. The acquisition algorithm sets the code phase,

carrier Doppler (and optionally code Doppler scaled from the carrier Doppler) and observes the correlator output for some dwell time. Detecting a relatively large correlator magnitude implies approximate alignment of the incoming-signal parameters. Then, the software immediately transitions to the pull-in and tracking phases. The GP2021 12-channel correlator IC is an example of this immediate-application technique (see the GP2021 datasheet at https://www.digchip.com/datasheets/parts/datasheet/537/GP2021-pdf.php]. When separate acquisition and tracking resources are used, it becomes necessary to initialize code phase for a precisely known reference epoch (which is necessarily the receiver time since no other precise time is available at start-up). This way, when the acquisition resource produces a correlation peak, the corresponding replica code phase that aligns with the incoming signal at a future time can be computed and programmed into the code generator of an available tracking channel. Figure 14.19 shows details of how this is done using an Apply Epoch Generator. This unit is programmed to output a one-shot “command apply” that aligns with a future receiver epoch. This mechanism can also be used to modify the states of the SV Epoch counters through software in order to align them to an SV’s TOT. Alternatively, this counter is not adjusted, but the offset that aligns the count to SV time is recorded and applied in software. Note that the carrier cycle counter is typically cleared after the previous count is latched. Whole cycles are

335

336

14 Fundamentals and Overview of GNSS Receivers

accumulated in software to avoid the need for wide counters in hardware. As mentioned previously, correlation is always performed with respect to SV time. Most receivers perform integration in hardware for 1 ms and dynamically extend the pre-detection integration time in software by coherently summing these hardware correlator outputs (see Figure 14.17). This avoids large numerical values building up in the hardware accumulators, which would otherwise require additional logic resources. This 1 ms hardware accumulation scheme will continue to be applicable to future receivers since the vast majority of GNSS signal structures define spreading code periods, data symbol lengths, and secondary code intervals that are integer divisible by 1 ms. The SV 1 ms epochs are derived from the code generator. In the case of short algorithmically defined spreading code sequences, SV epochs are generated by sensing the internal states in the code generator that are PRN number invariant. For example, the “all 1’s” state of the 10-bit G1 register corresponds to the SV 1 ms epoch for the C/A code family. In other cases, it may be simpler to use a separate code phase counter. This is the only option available for Galileo E1 memory codes. In this case, the code phase counter also serves as the address to the spreading sequence stored in memory. When a 1 ms correlation operation is complete, the accumulator values are transferred to holding registers‚ and the accumulators are immediately cleared for the next interval (known as accumulate and dump). The SV epoch triggers an interrupt that notifies the RDP to read these registers as soon as possible (i.e. before they are overwritten at the next SV epoch). When an SV epoch interrupt occurs, the processor determines which channel triggered the interrupt and reads the corresponding registers. Since SV epochs for different channels can occur at any time, it is possible to receive additional interrupts while the current one is being serviced. Arbitration or interrupt aggregation logic is used to handle these cases depending on the implementation. For example, when the ISR is done reading registers from one channel, it checks an “interrupts flagged” register to check for additional interrupts that may have occurred and proceeds to read data from those channels before returning. In general, this overlapped interrupt issue is manageable for receivers that contain a relatively small number of channels. Modern GNSS receivers may actively use more than a hundred channels (when tracking all visible GNSS and Satellite-based Augmentation System (SBAS) signals at multiple frequencies), with each containing multiple

correlator outputs. In this case, a PIO interface may not be suitable due to the large number of register read/write operations that need to be performed one by one. Moreover, the large number of asynchronous SV epoch interrupts generated may become too complex to manage efficiently. In this case, a burst transfer interface such as direct memory access (DMA) is more appropriate. For DMA, memory segments are allocated and locked by the operating system ahead of time to prevent them from getting cached. The processor is able to read and write to these physical memory addresses at any time. However, the rapid sequential transfer of data to and from these memory regions is managed by the DMA controller without processor involvement. Read and write DMA transfers can occur at the same time in full-duplex mode. Figure 14.20 shows the timing circuitry for a GNSS receiver that employs burst transfers. Here, data between the SMP and RDP are exchanged in rapid full-duplex bursts triggered by receiver 1 ms epochs. The DMA controller within the SMP manages the transfer (bus master), and there is no RDP-CPU involvement in the transfer. In fact, during this time, the RDP may be processing data from the previous epoch and writing to DMA upload memory regions that will get transferred to the SMP at the next epoch. As data transfer continues, a delayed interrupt is issued to inform software that new data are available (typically‚ correlator outputs are transferred first). This 1 ms data exchange between the SMP and RDP using a single interrupt significantly simplifies the hardware/software interaction and also eliminates the need for some hardware resources compared to a PIO-based implementation. For example, all carrier and code replica states in hardware are fully deterministic in software. Hence, TOT and ADR/CP can be calculated in software without the need for replica state counters and registers. (Note: This statement is also true for PIO architectures that apply NCO updates at receiver epochs, as shown in Figure 14.19. However, not all receivers implement this technique, as explained previously.) The method used to transfer correlator outputs represents the most significant change between PIO and DMA approaches. Since it takes some time for the DMA controller to read individual correlator outputs, it is possible to have values that correspond to neighboring SV epochs. This is prevented by registering the correlator output a second time with the SV epoch line. Since SV epochs slide past receiver epochs due to SV motion, it is possible to have none or two correlator dumps within a receiver 1 ms interval. However, the occurrence of these events is infrequent

References

Read Bus

DMA Read DMA Controller

Tracking Channel Logic

Holding Registers Correlator Outputs

DMA Write

Accumulators Rcvr. Epoch Interrupt

Delay

Rcvr 1ms Epoch

Latch Clear

Carrier NCO

Replica Code Replica Carrier

Carrier Rate/Phase

Sample Stream

Write Bus Apply Epoch Divide Value

Sample Clock

Apply Epoch

Code Phase SV 1ms Epoch

Programmable Divider Epoch Counter

Code Generator

Code Rate Overflow

Code NCO

Apply Epoch Generator

Receiver Epoch Logic Figure 14.20

Timing circuitry for a GNSS receiver employing a burst transfer interface.

(approximately every tens of minutes for MEO, depending on Doppler) and can be compensated for in software.

References 1 GPS World Staff, “Dual-band GNSS market moving from

14.8

Conclusions and Future Outlook

GNSS receivers have been extensively covered in the literature. The purpose of this chapter is to provide a historical and forward-looking perspective of GNSS receiver development. Fundamental concepts, practical design analysis, and implementation strategies are presented to offer readers insights which are not covered in the research literature. In-depth mathematical treatment of receiver signal processing such as acquisition and tracking are covered in other chapters of this book (Chapter 15 through 18). Other routine processing such as bit/frame synchronization, navigation data extraction, and range measurements have not evolved much since the early GPS receivers. Readers are referred to references provided in the chapter on these topics. The past decades have seen GNSS receivers evolve to become highly specialized and customized for specific applications. The future trend of GNSS receivers is driven by the continued diverging needs of specialized applications and to ensure efficient sensor integration. Such needs will favor more open architectures and standardization. While custom application-specific integrated circuits (ASICs) have been demonstrated to be the best in terms of performance and low power, softwareprogrammable efficient domain-specific ASICs will most likely be the dominant platform for future GNSS receivers due to their flexibility and the maturing enabling technologies.

2

3

4

5

6

7

8

insignificant to billions in less than 5 years,” https://www. gpsworld.com/dual-band-gnss-market-moving-frominsignificant-to-billions-in-less-than-5-years/, December 6, 2018. York, J., Joplin, A., Bratton, M., and Munton, D., “A detailed analysis of GPS live-sky signals without a dish,” Navigation, J. Inst. Navigation, 61(4), Winter 2014, pp. 311–322. 10.1002/navi.69. IGS RINEX Working Group and Radio Technical Commission for Maritime Services Special Committee 104 (RTCM-SC104), RINEX, the Receiver Independent Exchange Format, Version 3.04,” November 23, 2018. Gakstatter, E., “What exactly is GPS NMEA data?” GPS World Magazine, https://www.gpsworld.com/whatexactly-is-gps-nmea-data/, February 2015. RTCM Special Committee No. 104, RTCM Standard 10403.3, Differential GNSS (Global Navigation Satellite Systems) Services – Version 3, October 7, 2016. Filler, R.L., “The acceleration. Sensitivity of quartz crystal oscillators: A review,” IEEE Trans. Ultrasonics, Ferroelectrics, & Frequency Control, 35(3), 297–305, doi: 10.1109/58.20450, May 1988. Interface Control Working Group, IS-GPS-200, https:// www.gps.gov/technical/icwg/IS-GPS-200K.pdf, Updated June 2019. Zhang, X.M., Zhang, X., Yao, A., and Lu, M., “Implementations of constant envelope multiplexing based on extended interplex and inter-modulation construction method,” Proc. ION ITM, 893–900, Nashville, TN, September 2012.

337

338

14 Fundamentals and Overview of GNSS Receivers

9 Dafesh, P.A., “Coherent adaptive subcarrier modulation 10

11

12

13 14 15 16

17 18

19

20

21 22

23

24

method,” US Patent 6,430,213, 2002. Dafesh, P.A., Nguyen, T.M., and Lazar, S., “Coherent adaptive subcarrier modulation (CASM) for GPS modernization,” Proc. ION NTM, 649–660, San Diego, CA, January 1999. Dafesh, P.A. and Cahn, C.R., “Phase-optimized constantenvelope transmission (POCET) modulation method for GNSS signals,” Proc. ION GNSS, 2860–2866, Savanna, GA, September 2009. Misra, P. and Enge, P., Global Positioning System: Signals, Measurements, and Performance, revised 2nd Ed., GangaJamuna Press, 2006. Van Diggelen, F., A-GPS: “Assisted GPS, GNSS and SBAS,” Artech House, 2009. Frisis, H.T., “Noise figures of radio receivers,” Proc. IRE, 32 (7), 419–422, 1944. Karki, J., “Calculating noise figure and third-order intercept in ADCs,” Analog Applications Journal, 4Q, 2003. Browne, J., “Understanding dynamic range,” Microwave & RF, https://www.mwrf.com/test-and-measurement/ understanding-dynamic-range, February 2011. Tsui, J.B.Y., Fundamentals of Global Positioning System Receivers, Wiley & Sons, 2004. Kou, Y. and Morton, Y., “Oscillator frequency offset impact on software GPS receivers and correction algorithms,” IEEE Trans. Aero. Elec. Sys., 49(4), 2158–2178, 2013. Aigner, R, “SAW and BAW technologies for RF filter applications: A review of the relative strengths and weaknesses,” Proc. 2008 IEEE Ultrasonic Sym., 10.1109/ ULTSYM.2008.0140, 2008. Guerrero, J.M. and Gunawardena, S., “Characterization of timing and pseudorange biases due to GNSS front-end filters by type, temperature, and Doppler frequency,” Proc. 2017 International Technical Meeting of The Institute of Navigation, pp. 418–444, Monterey, California, January 2017, https://doi.org/10.33012/2017.14911. Ahmed, I., Pipelined ADC Architecture Overview, Springer, 2010. Akos, D.M. and Tsui, J.B.Y., “Design and implementation of a direct digitization GPS receiver front end,” IEEE Trans. Microwave Theory Tech., 44(12), 2334–2339, 2002. Psiaki, M.L., Powell, S.P., Jung, H., and Kintner, P.M., “Design and practical implementation of multifrequency RF front ends using direct RF sampling,” IEEE Trans. Microwave Theory Tech., 53(10), 3082– 3089, 2005. York, J., Little, J., and Munton, D., “A direct-sampling digital-downconversion technique for a flexible, low-bias GNSS RF front-end,” Proc. 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation

25

26

27

28

29

30

31

32

33

34

35

36

37

(ION GNSS 2010), pp. 1905–1918, Portland, OR, September 2010. Rajan B., “Introducing RFSoC,” EDN, March 14, 2017. https://www.edn.com/electronics-blogs/out-of-this-worlddesign/4458132/Introducing-RFSoC. Phelts, R.E. and Akos, D.M., “Nominal signal deformations: Limits on GPS range accuracy,” Proc. Int. Sym. GNSS/GPS, Sydney, Australia, 2004. Gunawardena, S. and van Graas, F., “GPS-SPS Inter-PRN pseudorange biases compared for transversal SAW and LC filters using live sky data and ChipShape Software receiver processing,” Proc. 2015 International Technical Meeting of The Institute of Navigation, pp. 393–403, Dana Point, California, January 2015. Pisoni, F. and Mattos, P.G., “Correction of pseudorange errors in Galileo and GLONASS caused by biases in group delay,” Proc. 6th ESA Workshop on Satellite Navigation Technologies (Navtech 2012) & European Workshop on GNSS Signals and Signal Processing, 1–7, Noordwijk, doi: 10.1109/NAVITEC.2012.6423041, 2012. Bastide, F., Akos, D., Macabiau, C., and Roturier, B., “Automatic gain control (AGC) as an interference assessment tool,” Proc. ION GPS/GNSS, 2042–2053, Portland, OR, 2003. Akos, D.M., “Who’s afraid of the spoofer? GPS/GNSS spoofing detection via automatic gain control (AGC),” Navigation, J. Inst. Navigation, 59(4), 281–290, 2012. Hegarty, C.J., “Analytical model for GNSS receiver implementation losses,” Navigation, J. Inst. Navigation, 58(1), 29–44, Spring 2011. Hegarty, C.J., van Dierendonck, A.J., Bobyn, D., Tran, M., Kim, T., and Grabowski, J., “Suppression of pulsed interference through blanking,” Proc. IAIN World, 2000. Sharawi, M.S., Akos, D.M., and Aloi, D.N., “GPS C/N0 estimation in the presence of interference and limited quantization levels,” IEEE Trans. Aero. Elec. Sys., 43(1), 227–237, 2013. Psiaki, M.L., Akos, D.M., and Thor, J., “A comparison of direct RF sampling and down-covert & sampling GNSS receiver architectures,” Proc. ION GPS, 1941–1952, Portland, OR, 2003. Van Dierendonck, A.J., “GPS Receivers,” in Global Positioning System: Theory and Applications (B.W. Parkinson, J.J. Spilker, P. Axelrad, and P. Enge, eds.), Vol. 1, AIAA, 1996. Morton, Y., Xu, D., Bourne, H., Breitsch, B., Taylor, S., van Graas, F., and Pujara, N., “Ionospheric scintillation observations in Singapore using a high gain antenna and SDR,” Proc. Pacific PNT, 866–875, Honolulu, HI, May 2017. ESA Navipedia website, “Data Demodulation and Processing,” 2011. https://gssc.esa.int/navipedia/index. php/Data_Demodulation_and_Processing.

339

15 GNSS Receiver Signal Tracking Y.T. Jade Morton, R. Yang, and B. Breitsch University of Colorado Boulder, United States

There has been extensive research and implementations of various global navigation satellite system (GNSS) receiver signal tracking algorithms. There are also several classic treatments of the fundamentals of GPS/GNSS receivers (e.g. see [1–4]). This chapter intends to provide an integrated overview of the fundamentals of GNSS signal tracking and the latest developments in advanced signal tracking techniques to improve sensitivity, robustness, and accuracy of performance. The chapter will start with the objectives of signal tracking, followed by a conceptual description of a closed-loop tracking system. A brief conventional treatment of code delay lock loop (DLL) is then presented. Carrier tracking is the more challenging and more intensely researched subject. This chapter will summarize the conventional phase lock loop (PLL) design. Tracking of simulated GPS L1 signals will be used to illustrate the concepts presented in the traditional implementations of DLL and PLL techniques. Following the conventional PLL description, we present a state space-based feedback control theory to demonstrate that some of the popular carrier tracking loop implementations are fundamentally equivalent. PLLs using the proportion-integration filter (PIF), Wiener filter (WF), and Kalman filter (KF) implementations are discussed. Optimization strategies of carrier tracking for weak signals and for receivers operating on dynamic platforms are presented‚ and their performance is analyzed. Finally, the latest developments in inter-frequency aiding will be summarized. The code and data used to generate example implementations can be downloaded by readers hosted at the authors’ website [5].

15.1 GNSS Receiver Signal Tracking Loop Objectives The purpose of GNSS signal tracking is to make continuous and accurate estimations of the signal code and carrier

phase, which are then used to obtain the signal time of arrival (TOA) at the receiver. A by-product of the tracking loop is the detection of navigation data bit edges, which is essential for navigation data decoding. The TOA is the signal reception time at the receiver relative to its transmission time at the satellite. The signal reception time is obtained through estimation of the signal code phase or carrier phase. While different GNSS signals may have varying signal structures, the fundamental concept and architecture are similar. Figure 15.1 shows how the signal code phase (bottom block) is related to the signal reception time tr at the receiver (the top block) for the GPS L1 CA signal. The top block in the figure shows a navigation data subframe. The transmission time of the subframe is encoded in the navigation data, referred to as the Z count. A subframe is 6 s long and contains 300 navigation data bits. Each navigation data bit is 20 ms long and contains 20 CA code periods. Each CA code period has 1023 chips. A first approximation for the receiver time at reception, tr (which excludes signal travel and propagation effects), relative to the broadcasted subframe transmission time tb is t r = t b + N − 1 × 20 × 10 − 3 + M − 1 × 10 − 3 + τ 15 1 As shown in the figure, the receiver intercepted the signal at the N-th bit, on the M-th code period within the N-th bit, with a code delay time τ from the start of the code period. While the values of N and M have to be resolved after bit synchronization and navigation data decoding, the code phase τ was estimated during coarse acquisition and will be updated during the tracking process. One of the main objectives of signal tracking is to estimate the fractional code phase delay offset of the receiver reception time relative to the coarse code phase obtained from acquisition. In addition to the code phase, a more accurate range measurement is based on the signal carrier phase. The disadvantage of the carrier phase measurement is its cycle

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

340

15 GNSS Receiver Signal Tracking

tb

tr

A Navigation Data Subframe Bit 1

Bit 2

CA 1

Bit N

Z Count

CA 2

Bit 300

CA M

CA 20

Chip K

Chip Chip 1 2

Chip 1023

τ

Figure 15.1

Illustration of the receiver signal interception time and signal code phase alignment.

ambiguities. Nevertheless, carrier phase measurements are used in all precision positioning applications after applying techniques to resolve the cycle ambiguities (e.g. Chapters 18 and 19 in this book). The carrier phase measurement is also used to “smooth” the noisier code phase measurements (e.g. Chapter 21). A signal’s carrier phase can be approximated as 1 d2 ϕ dϕ t − t0 t − t0 + 2 dt 2 dt + higher order terms

ϕ t = ϕ t0 +

≈ ϕ0 + ω t t − t 0 +

1 a t t − t0 2

2

2

15 2

where ϕ0 is the initial phase at t0, ω(t) is the signal angular carrier frequency, and a(t) is the rate of the angular frequency. GNSS receiver tracking loops estimate the code phase, carrier frequency, and carrier phase by aligning the incoming signal with locally generated reference signals. When a match is made, the reference signal parameters are taken as the estimations for the ones in the input signal. How do we know if the match is not a false alarm, and how much confidence do we have in the match? A convenient and effective measure is the carrier-to-noise power ratio (C/N0) of the tracked signal. A higher C/N0 is an indication that your tracking loop is doing well. To summarize, GPS signal tracking objectives are to estimate the following five quantities: 1) 2) 3) 4) 5)

Code phase Carrier Doppler frequency Carrier phase C/N0 Navigation data bit edge

In this chapter, we will focus on techniques that aim to achieve the first three objectives. While C/N0 (the fourth

objective) is often used as a control parameter in adaptive tracking algorithms, its estimation is a subject of a number of studies‚ and interested readers can refer to [6–8] and Chapter 14 in this book. The fifth objective is a natural product of the techniques that will lead to the first three objectives. Subsequent bit and frame synchronization and navigation data retrieval are straightforward processes and can be readily found online (e.g., see [9]).

15.2 GNSS Signal Tracking: Conceptual Description Figure 15.2 shows the block diagram of a typical closedloop GPS signal tracking system. It consists of a reference generator, correlators, discriminators, and filters. For some receiver implementations, other processes or sources may also provide aiding parameters for the tracking loop. For example, Section 15.3.6 discusses the code tracking loop using Doppler aiding from the carrier tracking loop. Section 15.5.4 focuses on inter-carrier aiding, where estimations from a carrier tracking loop having a nominal signal are used to aid another carrier tracking loop with a weak signal transmitted from the same satellite. In Chapter 16, aiding from other satellite measurements is used in the vector processing architecture. GNSS tracking loops are also often aided by measurements from other sensors. For example, in Chapter 45, aiding using inertial sensors in loose, tight, and ultra-tight integration modes is discussed. In this chapter, we will limit our discussions to stand-alone GNSS receivers. In this section, we will focus on the architecture, as shown in Figure 15.2, without getting into the aiding portion of the scheme.

15.2 GNSS Signal Tracking: Conceptual Description

Figure 15.2 Block diagram of a typical closed-loop GNSS signal tracking process.

Z (τ) Correlators Input baseband signal xb (t)

Discriminators

ε + Nε

Filters εˆ

Reference signal xr (t)

Reference generation

Aiding parameters Other processes or sources

15.2.1

R(δτ) is the code correlation function and δτ = τ − τ:

Correlation

An incoming baseband GNSS signal’s power in xb(t) is well below the noise floor, so its parameters cannot be measured directly. Instead, correlation with a closely matching reference signal is used to bring the signal energy above the noise floor. The result of this correlation can then be used to estimate the discrepancy between the incoming and reference signal, as will be evident from the correlation’s analytical expression. A detailed discussion on correlation operation is presented in Chapter 14. Only a brief summary of the correlation operation in the tracking loop is presented here. Let the input baseband signal for a satellite being tracked be x b t = ADC t + τ e

j ωd t + ϕ0

+ Nx

15 3

where A is the signal amplitude, D is the navigation data, C is the code, ϕ0 is the initial fractional carrier phase, τ is the code phase, and ωd is the carrier Doppler angular frequency in rad/s. Note that only one satellite signal is being considered, while others are lumped into the noise term Nx. When the tracking loop reaches steady state, we can assume that it generates accurate estimations of τ and ωd: ωd ≈ ωd , τ ≈ τ

15 4

These estimations are used to construct a reference signal: xr t = C t + τ e

jωd t

15 5

The correlation between the incoming and reference signals over period T is Z τ = AD

C t+τ C t+τ e

jωd t + jϕ0 − jωd t

e

15 6 Applying the approximations in (15.4) to (15.6): jϕ0 − j ωd − ωd T 2

+ NZ

1 T

C t C t + δτ dt

15 8

T

At the peak of the correlation function, Z 0 = ADTe

jϕ0

+ NZ

15 9

Equation (15.9) shows that the correlation process “wipes off” the code and carrier modulations on the signal when the reference is aligned with the input signal, leaving only the accumulated signal amplitude over the correlation interval. The initial phase of the signal is preserved. Therefore, the correlation operation accumulates the signal energy to allow a matched signal to rise above the noise floor, while all other satellite signals’ energy and noise are non-coherently averaged out. By examining the correlator outputs, we can estimate the amount of “mismatch” between the reference and the input signals’ parameters. This is accomplished by a discriminator, which we will discuss next.

15.2.2

Discriminators

A discriminator is an estimator that provides a measure of one signal parameter while suppressing variations caused by other signal parameters. For example, we can use the following function as a discriminator to estimate the initial phase ϕ0 in (15.9): lϕ = tan −1

Im Z 0 Re Z 0

15 10

dt + N Z

T

Z δτ = ADTR δτ e

R δτ =

15 7

where Im and Re refer to the imaginary and real part, respectively, of Z(0). If there is no noise, the discriminator will produce the initial carrier phase ϕ0. As a discriminator, lϕ is a measure of the carrier phase while suppressing the impact of the signal amplitude and data bit. Different

341

342

15 GNSS Receiver Signal Tracking

discriminators are designed to estimate different signal parameters. Some of the discriminators are constructed using outputs from multiple correlators, while others involve more complicated functions. We will discuss them in more detail in later sections.

15.2.3

Filters

There is always noise in the data. A discriminator cannot produce the true measure of a signal parameter. In order to reduce the impact of noise on the accuracy of the discriminator outputs, we have to apply appropriate filtering. Typically, these are low-pass filters that allow the features associated with the signal parameters to pass while “smoothing” out the noise effects. But sometimes we have to be very careful about the filtering operation because a signal parameter may have features that are difficult to separate from the noise. For example, the receiver platform may experience acceleration and random movement. We do not want to treat the effects of these motions as noise. GNSS receivers have also found wide-ranging applications in remote sensing. Disturbances in the signals due to propagation through the ionosphere, troposphere, foliage, or reflections from Earth’s surface are desirable signatures that allow us to infer the properties of the propagation environments. Designing filters that can preserve the true values of the signal, disturbance signatures, and receiver platform parameters while suppressing unwanted random noise is a challenging part of a tracking loop design. We will discuss filter implementations for code, carrier, and frequency tracking loops for nominal signals in Sections 15.3 and 15.4 and then address optimizations for weak signals and for receivers on dynamic platforms in Section 15.5.

15.2.4

Reference Generation

The output of a good tracking loop filter provides accurate estimations for signal parameters such as carrier phase, code phase, and carrier Doppler. These parameters are used to generate a reference signal. The reference signal is then fed back to the correlator to “wipe off” the code and carrier from subsequent input signals. This process repeats itself continuously as long as the receiver maintains lock of the signal, meaning that the reference signal parameters are within certain bounds of the corresponding input signal parameters.

15.2.5

GNSS Signal Tracking Loop Architecture

While modern GNSS signals have multiple layers of modulations, the fundamental problems of signal tracking can be broken down to two layers of modulations: the carrier and the code. A generic tracking loop architecture is shown in Figure 15.3. The carrier and code tracking loops are parallel and interconnected feedback control loops. Each has its own discriminators that generate appropriate error functions. Each has its own filter implementations to mitigate noise effects while maintaining its signal features. Each also has its own plant which generates the appropriate reference signals. These reference signals are fed back to the correlators to perform subsequent code and carrier wipe-offs. As we will discuss later in this section, the carrier tracking loop requires more frequent updating than the code tracking loop due to its higher frequency.

15.3

GNSS Signal Code Tracking: DLL

The DLL estimates the code phase, which is the delay of the beginning of the code period relative to the time of signal interception. Figure 15.4 shows a generic block diagram

Input baseband signal xb (t) Coarse Doppler from acquisition Initial code phase from acquisition Carrier tracking Carrier wipeoff

Carrier discriminator

δϕ + Nϕ

Carrier loop filter

δϕ

Carrier reference

Code wipeoff Correlators

Code discriminator

δτ + Nτ

Code loop filter

Code tracking

Figure 15.3

A generic GNSS signal tracking loop architecture.

δτ

Code reference

15.3 GNSS Signal Code Tracking: DLL

Input baseband signal

Code phase output ZE ZP ZL

Early, prompt, late correlators

Loop filter

Discriminator

To carrier tracking loop

Early, prompt, late code generators

Acquisition output

Figure 15.4 DLL block diagram.

early, and late code with the input code are also shown in the figure. Following the same reasoning that led us to (15.7) and (15.9), we obtain all three correlators to be a scaled version of the code correlation function with different delays:

of the DLL with three correlators, computed using three references. There are implementation variations using two or more correlators. With multiple correlators, each can be constructed with a reference code that has a fixed delay time relative to the other reference codes. The relative values of these multiple correlators enable the derivation of the delay time.

15.3.1

DLL Correlators

Figure 15.5 explains the concept of using three correlators to achieve an estimate of the code delay τ. The top pulse symbolizes the code associated with the input signal. During acquisition or prior iteration of the tracking process, the input signal code phase is estimated and used to construct the “prompt” reference code CP. Two additional reference codes, the early code CE and the late code CL, are generated by time shifting −d and +d relative to the prompt code. This magnitude of the time shift is called the correlator spacing. A commonly used correlator spacing is half of a chip width: d = Tc/2. Figure 15.5 shows four scenarios: the prompt code is shifted relative to the − Tc − Tc Tc , , 0, and , respecinput signal code by δτ = 2 4 4 tively. The correlation function values for the prompt, Incoming signal

Incoming signal

L

1/2 0

1/2

E –Tc δτ =

–Tc τ

0

Tc 2

0

Z L δτ = αR δτ + d + N L

15 13

α = ADTe

1 1/2

E –Tc δτ =

0

–Tc Tc 4

τ

0

Since R(δτ − d) and R(δτ + d) are R(δτ) time-shifted by −d and +d, respectively, there is a unique relationship between

CP CL

P L 0 δτ = 0

15 14

15 15

Incoming signal

E –Tc

δτ Tc

R δτ = 1 −

CL L

P

jϕ0 − j ωd − ωd T 2

Figure 15.6 shows a simplified version of the GPS L1 CA code correlation function. It ignores the correlation side lobes to focus on the analysis of the relationships between the early, prompt, and late correlators. The main correlation lobe is simply a triangle function, which can be expressed as

CP

1

P

15 12

CE

CL

CL 1

Z P δτ = αR δτ + N P

CE CP

CP

15 11

where

Incoming signal

CE

CE

Z E δτ = αR δτ − d + N E

–Tc τ

E

1

P

1/2 0

L –Tc

0 δτ =

–Tc

τ

Tc 4

Figure 15.5 Conceptual illustration of early, prompt, and late code references for δτ = −Tc/2, −Tc/4, 0, Tc/4.

343

344

15 GNSS Receiver Signal Tracking

R(δ τ – d) = 1 –

| δτ – d | Tc

R(δ τ) 1

lτ =

R ( δ τ) = 1 –

| δτ | Tc

δτ – d 0

–Tc

d δτ

lτ = R δτ − d − R δτ + d

|δτ + d | Tc

Figure 15.6 Early, prompt, and late correlator function relationship.

lτ = the values of the three correlator functions. For the four code delay values shown in Figure 15.5, we can associate the following correlator values with the prompt code delays:

1 3 3 , , 4 4 4

R δτ − d , R δτ , R δτ + d =

1 1 , 1, 2 2

δτ = 0

R δτ − d , R δτ , R δτ + d =

3 3 1 , , 4 4 4

δτ =

1 δτ = − T c 4

1 Tc 4

The above analysis is for the ideal scenario where there is no noise in the input signal. In reality, noise must be taken into consideration, as will be discussed in subsequent sections.

15.3.2

2 δτ Tc

lτ = R δτ − d − R δτ + d +

DLL Discriminators

lτ =

lτ

2 1 δτ + NE − NL Tc α

lτ 0.5 δτ

0

0.5

1

1.5

–0.5 –1

Figure 15.7

Tc

–1.25

–0.75

15 19

15 20

Figure 15.8 illustrates the effect of noise on the discriminator. The noise raises the value of lτ by the amount

1 0.5

1 NE − NL α

Again, let us assume d = Tc/2; within the center linear region,

The above discussion associates the set of early, prompt, and late correlator values with a unique prompt code delay estimation error. The purpose of discriminators is to estimate the code delay based on the computed correlator values. We use a simple coherent discriminator, referred to as the “null tracking discriminator,” to illustrate the process:

–1.5 –1

15 18

Equation (15.18) shows that lτ can be used to estimate the code delay error δτ. However, this discriminator is only valid in the highlighted areas. It is evident that if the correlator spacing is half the chip width, the discriminator will work only if the actual code delay error is within half a chip width. If the correlator spacing is a quarter of a chip width, then the code delay error must be within a quarter of a chip width for the estimator to work. When designing an acquisition algorithm to obtain a rough estimation of the code phase, one must make sure that the code phase bin is sufficiently fine that the coarse estimation is within the accuracy defined by the DLL’s correlator spacing. For receivers operating on high dynamic platforms, the correlator spacing should be no more than the anticipated change in the code phase from one DLL iteration to another. If we take noise into consideration, then

1 δτ = − T c 2

R δτ − d , R δτ , R δτ + d =

15 17

Figure 15.7 depicts lτ as a function of δτ for d = Tc/2 and d = Tc/4. The highlighted areas in the figure show the regions where the discriminator is linearly proportional to the code delay error δτ:

δτ

δτ + d Tc

1 R δτ − d , R δτ , R δτ + d = 0, , 1 2

15 16

Under the noiseless assumption,

R(δτ + d) = 1 – d

1 ZE − ZL α

–0.25 0 0.25 –0.5

d = Tc / 2

Noiseless null tracking discriminator for d = Tc/2 and d = Tc/4.

0.75 d = Tc /4

1.25

δτ Tc

15.3 GNSS Signal Code Tracking: DLL

Lτ

lτ4 =

ZE − ZL ZE + ZL

lτ5 = Re Z E − Re Z L + Im Z E − Im Z L

1

lτ6 =

NE – NL α

δτ

Delay error

ZE − ZL ZP

15 24d × Re Z P × Im Z P

15 24e 15 24f

All these discriminators are linearly related to the code phase error δτ within a limited range of δτ values: lτ = βδτ

Figure 15.8 Null tracking with noise.

(NE − NL)/α. As a result, the zero-crossing point for lτ does not occur at δτ = 0. Instead, it occurs at Nτ =

Tc NE − NL 2α

15 21

This new zero-crossing point represents the amount of delay estimation error using this discriminator when there is noise. Assuming the correlator output noise is zero mean with average power being N0, then Nτ =

Tc 2α

2N 0 =

Tc AT

N0 2

Tc 2

1 1 T C N0

15 23

where C = A /2 is the carrier signal power. Equation (15.23) shows that to reduce the estimation errors, we can do one or more of the following: Decrease the chip width Tc Increase the correlation data length T Increase C/N0

For GPS, its P code width is 1/10 that of the CA code. This is one reason why the P code is the more precise code. Since the code width is fixed for a given signal and C/N0 is determined by the input signal and receiver environment, the only parameter we can control at the receiver signal processing stage is the correlation integration time T. Some popular DLL code discriminators are the following: lτ1 = Z E − Z L lτ2 = Z E 2 − Z L lτ3 = Z E − Z L

15 24a 2

15.3.3 DLL Filter: Transformation from Analog to Digital Domain Let us start with a general, simple noise reduction filter, which is a weighted average of raw discriminator estimations: t

2

•• •

The scale parameter β may be related to the signal amplitude, correlator integration time, correlator spacing, code chip width, noise power, and so on, unless normalized quantities such as lτ5 and lτ6, are used. For the normalized discriminators, β does not depend on the amplitude and correlator spacing, but is implicitly dependent on the integration time because the time determines the noise level. If we want to avoid estimating signal parameters when applying the discriminator, we will need to use the normalized versions. But if we want to have discriminators that reflect changes in signal parameters for adaptive processing, then we will need to use the other forms. Readers interested in more detailed discussions of the discriminators may consult references [10–13].

15 22

The corresponding delay estimation error has zero mean‚ and its standard deviation is στ =

15 25

15 24b 15 24c

yt =

ωn x ξ dξ

15 26

0

where x is the raw estimation, y is the filtered outputs, and ωn is the weight. Since filtering is an operation that can be understood more directly in the frequency domain, we convert (15.26) into its S-domain representation using the Laplace transform [14]: Y s = ωn

X s s

15 27

where X(s) and Y(s) are the Laplace transforms of x(t) and y(t), respectively. From (15.27), the S-domain transfer function for the simple noise reduction filter is F s =

Y s ωn = X s s

15 28

This transfer function can be described by the block diagram shown in Figure 15.9. It is a first-order filter because the transfer function only includes one 1/s term.

345

346

15 GNSS Receiver Signal Tracking

X (s)

1⁄

ωn

a discrete sequence xd[n] at sampling interval ts, then the discrete samples’ frequency domain representation is

Y(s)

s

Xd Ω =

Figure 15.9 S-domain block diagram for the simple weighted averaging filter.

1 ∞ X c ω − kωs ts k = − ∞

15 29

where Ω = ωt s = 2π ωωs , which relates the S-domain freTime-domain

quency ω to the Z-domain frequency Ω. According to Shannon’s theory, if the bandwidth of the CT signal ωc < ωs/2, then the discrete baseband spectrum is a scaled replica of the CT spectrum:

Frequency-domain Laplace Transform

F(s)

Continuous: f (t)

s = σ + jω

Z Transform

Discrete: f [n]

F [z]

z=

Xd Ω =

re jΩ

1) Write the S-domain transfer function Hc(s) in its standard form:

This S-domain representation has to be transformed to the discrete time domain for digital implementation. The discrete counterpart of the S-domain representation is the Z-transform. After obtaining the Z-transform of the filter transfer function, we have to also obtain the discrete difference equation in the time domain for real-time implementation. Figure 15.10 summarizes this process. There are a number of ways to convert a continuous time (CT) filter to a discrete time (DT) filter for digital implementation. Commonly used approaches are the impulse invariance method, the bilinear transformation [15], and the Euler transformation [16]. The impulse invariance method is discussed below, while the bilinear and Euler transformations will be applied to the PLL in Sections 15.4 and 15.5, respectively. The impulse invariance method performs a linear mapping between the continuous and discrete designs. Figure 15.11 illustrates the concept of the impulse invariance method. Consider a CT function xc(t). Its frequency domain representation is Xc(ω). If xc(t) is sampled to form xc (t)

Time Domain

15 30

Based on this impulse invariance principle, we can construct the Z-domain representation of a band-limited filter transfer function by following this procedure.

Figure 15.10 Process flow schematics from continuous time domain filter design to discrete time-domain implementation.

CT

1 1 Ω Xc ω = Xc ts ts ts

N

Hc s =

Ak s − sk k=1

15 31

2) Apply the inverse Laplace transform to Hc(s) to obtain the filter time-domain impulse response hc(t): N

hc t =

A k e sk t

t≥0

k=1

0

15 32

t 2), when provided for by an external provider, or one can treat them as unknown, but time-stable parameters. In the latter case, the redundancy of Eq. (20.29) for a static user, tracking m satellites, with f frequencies, over k epochs, is (m − 5) + (2f − 1)(m − 1)(k − 1), while it will be (f − 2)(m − 1) larger if one corrects for the code biases. Correcting for the multi-frequency estimable code biases also has the advantage that the per satellite-pair extra (f − 2) code user equations will contribute to the speeding up of the convergence. This will not happen to that extent st in case the code biases d,j are treated as unknown constants. In that case‚ the per satellite-pair extra (f − 2) code user equations play a somewhat similar role as the carrier-phase equations and will primarily contribute once a sufficient change in relative receiver-satellite geometry has occurred. The generalization to the multi-frequency case for PPPRTK follows quite naturally that of PPP itself. With the code

Overview of GNSS frequencies (CDMA signals)

System

GPS (G)

Frequency band

L1

L2

L5

GLONASS (R) Galileo (E)

L3 E1

BeiDou (C) QZSS (J)

E6 B1

L1

E5b B3

LEX

E5

B2 L2

L5

IRNSS (I) Freq. (MHz)

E5a

L5 1575.42

1561.098

1278.75

1268.52

1227.60

1207.14

1202.025

1191.795

1176.45

20.9 Multi-GNSS PPP

bias corrections applied, the multi-frequency, ionospherefloat PPP-RTK user equations follow from Eq. (20.25) as st

pstu,j + dt stIF + d,j = ρstu + μ j ιstu,GF st

ϕstu,j + dt stIF + δ,j = ρstu − μ j ιstu,GF + λ j zstru,j

j = 1, 2, … 20 31

Hence, next to the orbits, there are in total 2f − 1 corrections st

st

dt stIF , d,j , δ,j , namely, 1 clock, (f − 2) code biases, and f

The extra two terms in these equations are the inter-system 12 biases, the code ISB d12 u,j and the phase-ISB δu,j . They are absent from the equations when the between-satellite differencing is done with satellites of the same system, that is, when t2 is replaced by t1. In the following, we first consider the dual-frequency case (f = 2) for multi-GNSS PPP and multi-GNSS PPPRTK and then we generalize to the multi-frequency case (f > 2).

phase biases.

20.9.1

20.9

Multi-GNSS PPP

With the ongoing proliferation of navigation satellite systems, the availability of more satellites and signals brings a range of improvements. Precision and reliability in parameter estimation will improve, as will convergence times, position availability‚ and robustness of ambiguity resolution [129–132]. However, with multi-GNSS PPP, new challenges are also introduced. When using pseudorange and carrier-phase data from different GNSSs‚ one has to account for ISBs, which are due to differences in receiver hardware delays between the signals of different constellations [133–135]. Thus‚ instead of our earlier receiver clock offsets (cf. Eq. 20.2), we now have dt u,j = dt u + du,j ,

δt u,j = δt u + δu,j

20 32

with = 1, 2, … being the system indicator. With the tracking of satellites from different systems, our earlier satellite index “s” will be replaced by the satellite index s (s = 1 , …, m ) for the system . Although each system can broadcast signals in different frequency bands, we restrict ourselves here to the frequency bands that combined systems have in common. Hence, the frequency index “j” (j = 1, …, f) will now stand for the j-th overlapping frequency of the systems. This restriction does not, however, affect the generality of our discussion; see [10]. Table 20.6 gives an overview of the current frequencies shared by the navigation satellite systems. The two systems GPS and QZSS, for instance, have the three frequencies L1, L2, and L5 in common, while with the Galileo system, they share the two overlapping frequencies L1 and L5 (E5a). As the receiver hardware delays, du,j and δu,j , are system dependent, they will not get eliminated when betweensatellite differences are taken with satellites from different systems. Hence, for satellite s1 from system = 1 and satellite t2 from system = 2, the between-satellite observation equations will, instead of Eq. (20.3), now read psu,j1 t2 = ρsu1 t2 + μ j ιsu1 t2 − dt s,j1 t2 − d12 u,j s1 t 2 ϕsu,j1 t2 = ρsu1 t2 − μ j ιsu1 t2 − δt s,j1 t2 − δ12 u,j + λ j z u,j

20 33

Dual-Frequency Multi-GNSS PPP

Just like the IF- and GF-components of the satellite hardware delays, dst,1 and dst,2, lack estimability and are therefore lumped with the satellite clock and ionospheric delay, the 12 single-station code ISBs, d12 r,1 and dr,2, also lack estimability and will therefore be lumped in a similar way. Using the 12 12 decomposition d12 r,j = dr,IF + μ j dr,GF (j = 1, 2), we get instead of Eq. (20.6), s1 t 2

dt IF = dt s1 t2 + dsIF1 t2 − d12 r,IF

and

1 t2 1 t2 ιsr,GF = ιsr1 t2 − dsGF − d12 r,GF

20 34 Thus‚ when the ionosphere-free satellite clocks are estimated from a reference network tracking multiple GNSSs, the between-system ionosphere-free satellite clocks will have the ionosphere-free code ISB of one of the reference stations, say, r, included. As a result, with the networks1 t 2 provided satellite clock dt IF , the dual-frequency PPP user equations take the form s1 t 2

1 t2 + d12 psu,j1 t2 + dt IF = ρsu1 t2 + μ j ιsu,GF ru,IF

s1 t 2

1 t2 ϕsu,j1 t2 + dt IF = ρsu1 t2 − μ j ιsu,GF + λ j asu,j1 t2

j = 1, 2 20 35

with the non-integer ambiguities given as 1 t2 = zsu,j1 t2 − asu,j

s1 t 2 s1 t 2 12 12 δs,j1 t2 − δ12 u,j − dIF − dr,IF + μ j dGF − du,GF

λj

20 36 Compare the structure of the above user equations (Eq. (20.35)) with that of the single-system equations (Eq. (20.18)). The phase equations have the same structure, but the code equations do not. The dual-system code user equations have, in the case of between-system differencing, one extra term, namely‚ the ionosphere-free code differential ISB (DISB), d12 ru,IF . This term is absent, and Eq. (20.35) reduces to Eq. (20.18), when t2 is replaced by t1, that is, when the between-satellite differencing is done within the same system. Next to the extra DISB-term, the interpretation of some of the parameters in Eq. (20.35) is also different from their counterparts in Eq. (20.18). The user ionospheric delay

519

520

20 GNSS Precise Point Positioning

has now also the geometry-free component of its receiverISB lumped with it, and a similar change applies to the ambiguities; compare Eq. (20.36) with Eq. (20.23). As the DISB d12 ru,IF is estimable (in contrast to the singlestation ISBs), the user can treat it as an additional unknown parameter that needs to be solved for. There are, however, also situations when the user may assume that the DISB is known a priori. In that case there is no essential difference between the dual-system structure (20.35) and its singlesystem counterpart (20.18). The two combined systems can then be treated as if they constitute a single system. The case of a priori known DISBs is further discussed in Section 20.9.3 If the DISB d12 ru,IF is treated as an unknown but time-stable parameter, then for a dual-system user, tracking m1 system1 satellites and m2 system-2 satellites, with satellite s1 as the chosen pivot-satellite, the dual-frequency equations (Eq. (20.35)) represent a system consisting of 4(m1 − 1 + m2) equations per epoch. For a static user, tracking the satellites over k epochs, assuming a random walk ZTD and time-constant or time-stable ambiguities, the redundancy of the system equals (m1 + m2 − 6) + 3(m1 + m2 − 1) (k − 1). This shows that the inclusion of a second system changes the solvability at initialization (k = 1) from m1 ≥ 5, for the single-system case, to m1 + m2 ≥ 6, for the dualsystem case. Thus instead of a minimum of five satellites, as needed for the single-system case, now only three s1 t 2

1 t2 psu,j1 t2 + dt IF = ρsu1 t2 + μ j ιsu,GF

s1 t 2

s1 t 2

ϕsu,j1 t2 + dt IF + δ,j

20.9.2

Dual-Frequency Multi-GNSS PPP-RTK

As the ambiguities in Eq. (20.35) are real-valued, these user equations are not yet in a form that enables integer ambiguity resolution. To make this happen, we follow the same approach as before and have the reference network provide next to the orbits and satellite clocks, the needed extra corrections, such as the ambiguities of a reference station, asr,j1 t2, s1 t 2

or equivalently, the satellite phase bias δ,j (cf. Eq. (20.36)), s1 t 2

δ,j

12 extra pair of real-valued terms, δ12 ru,j + μ j dru,GF

for j =

1, 2. Were the values of this pair a priori known, then 1 t2 the DD ambiguities zsru,j (j = 1, 2) would become estimable as integers and user integer ambiguity resolution can be applied to all DD ambiguities present in the user equations. This is not possible, however, in the absence of such a priori values. In that case, the extra terms cannot be separated from the between-system DD ambiguities and it is their combination that then would be estimated as the realvalued ambiguity: λj

j = 1, 2 20 39

Hence, in that case‚ there are two fewer DD ambiguities that the user can estimate as integers. Thus, with the DISB

= − λ j asr,j1 t2

s1 t 2 s1 t 2 12 12 δs,j1 t2 − δ12 r,j − dIF − dr,IF + μ j dGF − dr,GF

=

− λ j zsr,j1 t2

20 37 Application of the phase bias correction transforms the DF-PPP user equations (Eq. (20.35)) into + d12 ru,IF

12 1 t2 1 t2 = ρsu1 t2 − μ j ιsu,GF + λ j zsru,j + δ12 ru,j + μ j dru,GF

In the pair of phase equations we now recognize the pair of integer DD ambiguities. However, due to the betweensystem differencing, the phase equations also contain an

12 1 t2 + δ12 asu,j1 t2 = zsru,j ru,j + μ j dru,GF

satellites of each system are needed for the initialization of the dual-system case. This illustrates the increase in positioning availability that the integration of GNSSs brings. The extra redundancy that the inclusion of the second system brings is (m2 − 1) + 3m2(k − 1). Thus, already with two satellites of the second system the redundancy increases at initialization. With one satellite‚ the extra redundancy is absent as the four extra user equations are then just enough to solve for the extra ionospheric delay, the two ambiguities, and the ionosphere-free DISB d12 ru,IF .

j = 1, 2

(20.38)

values known, there would be 2(m1 + m2 − 1) ambiguities that could be estimated as integers, versus 2(m1 + m2 − 2) in the case where the DISBs are unknown. Figure 20.6 shows an example of multi-GNSS PPP. It shows the DF-PPP ambiguity-float (red) and ambiguityfixed (green) 1 h coordinate time series (East and North) for GPS (left) and GPS+BDS (right) for a user at the BULA station in Australia. Upon comparing the time series, the impact of both ambiguity resolution as well as the inclusion of a second system (BDS) is clearly visible.

20.9.3

Calibration of ISBs

The above has shown that a dual-frequency, dual-system user may have to incorporate three additional terms in the user equations, namely, d12 ru,IF in the between-system code equations in the case of PPP (cf. Eq. (20.35)) and an additional two,

12 δ12 ru,j + μ j dru,GF

for j = 1, 2, that

get lumped in with the DD ambiguities in the two

20.9 Multi-GNSS PPP

BULA(GPS) East

0.5

BULA(GPS+BDS) East

0.5

Float Fixed

0

–0.5

0

0.2

0.4

0.8

0.6

1

North

0.5

Float Fixed

0

–0.5

0

0.2

0.4

0.6

0.8

Position wrt ground truth [m]

Position wrt ground truth [m]

Float Fixed

0

–0.5

0.2

0.4

0.6

0.8

1

North

0.5

Float Fixed

0

–0.5

1

0

0

0.2

0.4

0.6

0.8

1

Figure 20.6 DF-PPP ambiguity-float (red) and ambiguity-fixed (green) 1 h coordinate time series (east and north) for GPS (left) and GPS +BDS (right) for a user at BULA station in Australia (DOY 2016, UTC, 10 cutoff elevation angle).

between-system phase equations in the case of PPP-RTK (cf. Eq. (20.38)). The strength of the user equations improves, of course, if one may assume these terms to be either absent or known. Several studies have demonstrated that DISBs are quite time stable and that they even may be assumed to be zero when taken between similar receivers (same make, type‚ and firmware); see, for example, [136–140]. This implies that when receivers of different make and type are involved (e.g. within the reference network and/or between network and user), one has the potential of calibrating the DISBs as proposed in [10]. Just as the user can use Eq. (20.38) to estimate the three DISB terms for the user receiver, the reference network itself

can be used to estimate these types of DISBs between any pair of its mixed receivers. Hence, by estimating them with sufficient precision‚ one can provide calibrated values in a look-up table (Figure 20.7) that users in their turn can use to correct for the DISB of their particular receiver. In this way‚ users effectively realize their own ISB-corrected user model, thereby strengthening their model and maximizing the number of integer-estimable user ambiguities. The above approach of estimating or calibrating the three DISBs has the advantage that there is no need to include an ionospheric model. The accommodation of ISBs when integrating different systems can therefore be taken care of

System: ✶ System: G

Correctioncomponent cϕ , cp r=1

~

~

~

~

~

~

~

~

G✶ G✶ δ 1,j , d 1,j , d 1,IF

Networkcomponent

r=2

~G✶

r=n

G✶ G✶ G✶ δ q,j , d q,j , d q,IF G✶ G✶ G✶ δ n,j , d n,j , d n,IF

r=3

u User-component

r=q

Figure 20.7 ISB look-up table: It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model [10].

521

522

20 GNSS Precise Point Positioning

(both on the network and user side) without having to make any additional assumptions about the ionosphere. The consequence of not having an ionospheric model included is, however, that with the above approach only three DISB terms can be estimated and not all four. The following transformation shows how the three DISB terms stand in relation to the original four DISBs: d12 ru,1 d12 ru,2

=

δ12 ru,1 + λ1 z,1 δ12 ru,2

μ1 μ2 − μ1

1 1

− μ2

+ λ2 z,2

δ12 ru,1 + δ12 ru,2 +

d12 ru,IF d12 ru,GF μ1 d12 ru,GF μ2 d12 ru,GF

1 1

20 40

+ λ1 z,1 + λ2 z,2

s1 t 2 s1 t 2

ϕsu,j1 t2 + dt IF + δ,j

s1 t 2 s1 t 2 12 s1 t 2 + δ12 ur,j = ρu − μ j ιu,GF − dru,GF + λ j zru,j

Hence, when all four DISBs are used as a priori corrections, these between-system user equations take the same form as the single-system PPP-RTK user equations (Eq. (20.25)). Also‚ note that now the ionospheric delay of the user, s1 t 2 12 s1 t 2 1 t2 − d12 ιsu,GF ru,GF = ιu − dGF − dr,GF , will have the same bias as the ionospheric delays of the network; this is in contrast to the ionospheric delays of Eq. (20.38).

20.9.4

Multi-Frequency, Multi-GNSS PPP-RTK

For multi-frequency, multi-GNSS PPP-RTK, the previous result (Eq. 20.38) can be generalized as s t

s1 t 2

12 1 t2 = ρsu1 t2 + μ j ιsu,GF + d12 ru,j − μ j dru,GF

s t

s1 t 2

12 1 t2 1 t2 = ρsu1 t2 − μ j ιsu,GF + λ j zsru,j + δ12 ru,j + μ j dru,GF

psu,j1 t2 + dtIF1 2 + d,j ϕsu,j1 t2 + dt IF1 2 + δ,j

20 42 (j = 1, 2, …), with the between-system, multi-frequency satellite code and phase bias corrections given as s1 t 2

d,j

s1 t 2

δ,j

= dsj1 t2 − d12 r,j − =

12 to determine all four DISBs, d12 ru,1 and δru,1 , j = 1, 2. Determination of this geometry-free DISB requires, however, additional ionospheric assumptions, such as, for instance, in the case of zero or short baselines, the absence of between-receiver ionospheric delays [135, 138], or alternatively, the inclusion of an explicit ionospheric model. If with such approaches all four DISBs would be determined and provided to the user, the user equations (Eq. (20.38)) can be rewritten as

s1 t 2 12 s1 t 2 + d12 ur,j = ρu + μ j ιu,GF − dru,GF

psu,j1 t2 + dt IF

s1 t 2

Note that since the phase-DISBs can only be estimated in combination with the DD ambiguities (cf. Eq. (20.39)), they are shown here modulo λjz,j. This is, however, of no consequence for the estimation process as such shifts will automatically be absorbed by the estimated integer ambiguities. The one-to-one relation Eq. (20.40) shows that it is the geometry-free code DISB d12 ru,GF that is additionally needed

s1 t 2 12 dsIF1 t2 − d12 r,IF + μ j dGF − dr,GF

s1 t 2 s1 t 2 12 12 δs,j1 t2 − δ12 r,j − dIF − dr,IF + μ j dGF − dr,GF

− λ j zsr,j1 t2

20 43 s1 t 2

Compare with Eq. (20.31). Note that d,j 12 12 d12 ru,j − μ j dru,GF = dru,IF for j = 1, 2.

= 0 and

(20.41)

j = 1, 2

The integration of multi-frequency GNSSs increases the redundancy and strengthens the positioning model. This will improve ambiguity resolution and shorten the convergence times. With the increase in the number of satellites, one can even use larger-than-customary cutoff elevation angles and thus increase the GNSS applicability in constrained environments, such as, for example, in urban canyons or when low-elevation-angle multipath is present [141, 142]. For a static user, with the same dynamic parameter assumptions as before, Table 20.7 shows the two-system, multi-frequency user-redundancy of Eq. (20.42), for the case when the (2f − 1) DISBs are known and unknown, respectively. Note that although with the ISB-unknown case we have (2f − 1) extra unknown parameters Table 20.7 Two-system, multi-frequency, single-epoch userredundancy for ISB-unknown and ISB-known cases (cf. Eq. (20.42)). Redundancy

ISB known

ISB unknown

Amb-float

(f − 1)(m1 + m2 − 5)

(f − 1)(m1 + m2 − 6)

Amb-fixed

(2f − 1)(m1 + m2 − 5) + 4f

(2f − 1)(m1 + m2 − 6) + 4f

Note: For multiple epochs (k >1) the redundancy increases by (2f − 1) (m1 + m2 − 1)(k − 1). m denotes the number of tracked satellites of system .

References

(f phase-DISBs and f – 1 code-DISBs), the redundancy in the ambiguities-float case only reduces by f – 1 when going from the ISB-known to the ISB-unknown case. This is due to the fact that in the ambiguity-float case, the f phase-DISBs will get lumped with the ambiguities. In the ambiguity-fixed case, however, this difference in redundancy is equal to the number of DISBs. Also note that with k epochs, the redundancy increases by (2f − 1)(m1 + m2 − 1) (k − 1), which is the difference between the number of extra equations and the number of extra ionospheric delays in the multiple epoch case.

9

10

11 12

Acknowledgments

13

The author thanks all his colleagues from Curtin University’s GNSS Research Centre. The first version of Curtin’s PPP-RTK network and user software platforms used in the computations of the examples were developed under Projects 1.01 and 1.19 of the Cooperative Research Centre for Spatial Information. The CORS data was made available by Geoscience Australia.

14

15

16

References 17 1 Zumberge, J., Heflin, M., Jefferson, D., Watkins, M., and

2

3

4

5

6

7

8

Webb, F. (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of Geophysical Research, 102, 5005–5017. Kouba, J. and Héroux, P. (2001) Precise point positioning using IGS orbit and clock products. GPS Solutions, 5 (2), 12–28. Wubbena, G., Schmitz, M., and Bagg, A. (2005) PPP-RTK: Precise Point Positioning using state-space representation in RTK networks, in Proceedings of ION GNSS, pp. 13–16. Mireault, Y., Tétreault, P., Lahaye, F., Héroux, P., and Kouba, J. (2008) Online precise point positioning: A new timely service from National Resources Canada. GPS World, 19 (9), 59–64. IGS (2015), IGS products, http://igscb.jpl.nasa.gov/ components/prods.html. URL http://igscb.jpl.nasa.gov/ components/prods.html. Petit, G. and Luzum, B. (2010) IERS Conventions (2010), IERS Technical Note No. 36, Verlag des Bundesamts für Kartographie und Geodäsie. Montenbruck, O., Steigenberger, P., Khachikyan, R., Weber, G., Langley, R.B., Mervart, L., and Hugentobler, U. (2014) IGS-MGEX: Preparing the ground for multiconstellation GNSS science. Inside GNSS, 9(1), 42–49. Kouba, J. (2009) A guide to using International GNSS Service (IGS) products, Tech. Rep., IGS. URL http://igscb.

18

19

20

21

22

23 24

25

jpl.nasa.gov/components/usage.html, http://igscb.jpl. nasa.gov/components/usage.html. Teunissen, P.J.G. (1995) The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70 (1–2), 65–82. Khodabandeh, A. and Teunissen, P.J.G. (2016) PPP-RTK and inter-system biases: The ISB look-up table as a means to support multi-system PPP-RTK. Journal of Geodesy, 90 (9), 837–851. Parkinson, B. and Spilker, J. (1996) Global Positioning System: Theory and Applications, vol. 1 and 2, AIAA. Teunissen, P.J.G. and Kleusberg, A. (eds.) (1998) GPS for Geodesy, Springer, 2nd Ed. Leick, A. (2015) GPS Satellite Surveying (4th Ed.), John Wiley & Sons. Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2008). GNSS – Global Navigation Satellite Systems, GPS, GLONASS, Galileo and More, Springer-Verlag. Dow, J., Neilan, R., and Gendt, G. (2005) The International GPS Service (IGS): Celebrating the 10th anniversary and looking to the next decade. Advances in Space Research, 36, 320–326. Schaer, S., Gurtner, W., and Feltens, J. (1998) IONEX: The IONosphere map EXchange format version 1. IGS AC Workshop, Darmstadt, Germany. Li, Z., Yuan, Y., Li, H., Ou, J., and Huo, X. (2012) Two-step method for the determination of the differential code biases of COMPASS satellites. Journal of Geodesy, 86 (11), 1059–1076. Montenbruck, O., Hauschild, A., and Steigenberger, P. (2014) Differential code bias estimation using multi-GNSS observations and global ionosphere maps. Navigation, 61 (3), 191–201. Wang, N., Yuan, Y., Li, Z., Montenbruck, O., and Tan, B. (2016) Determination of differential code biases with multiGNSS observations. Journal of Geodesy, 90 (3), 209–228. De Jonge, P. (1998), A processing strategy for the application of the GPS in networks. Publications on Geodesy, 46, Netherlands Geodetic Commission. Hopfield, H. (1969) Two-quartic tropospheric refractivity profile for correcting satellite data. Journal of Geophysical Research, 74, 4487–4499. Saastamoinen, J. (1972) Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging of Satellites, AGU, pp. 247–251. Øvstedal, O. (2002) Absolute positioning with singlefrequency GPS receivers. GPS Solutions, 5 (4), 33–44. Le, A.Q. and Tiberius, C. (2007) Single-frequency precise point positioning with optimal filtering. GPS Solutions, 11 (1), 61–69. Choy, S., Zhang, K., and Silcock, D. (2008) An evaluation of various ionospheric error mitigation methods used in

523

524

20 GNSS Precise Point Positioning

26

27

28

29

30

31

32

33

34

35

36

37

38

single frequency PPP. Journal of Global Positioning Systems, 7 (1), 62–71. van Bree, R. and Tiberius, C. (2012) Real-time singlefrequency precise point positioning: accuracy assessment. GPS Solutions, 16 (2), 259–266. Yunck, T. (1992) Coping with the Atmosphere and Ionosphere in Precise Satellite and Ground Positioning, AGU, chap. 1 in Environmental Effects on Spacecraft Positioning and Trajectories, A. V, Jones (Ed.), pp. 1–16. Montenbruck, O. (2003) Kinematic GPS positioning of LEO satellites using ionosphere-free single frequency measurements. Aerospace Science and Technology, 7 (5), 396–405. Chen, K. and Gao, Y. (2005) Real-time precise point positioning using single frequency data. Proc. ION GNSS 2005, Long Beach, CA, 1514 – 1523. Schüler, T., Diessongo, H., and Poku-Gyamfi, Y. (2011) Precise ionosphere-free single-frequency GNSS positioning. GPS Solutions, 15 (2), 139–147. Diessongo, H.T., Bock, H., Schüler, T., Junker, S., and Kiroe, A. (2012) Exploiting the Galileo E5 wideband signal for improved single-frequency precise positioning. Inside GNSS, 7 (5), 64–73. Hernández-Pajares, M., Juan, J., Sanz, J., Orus, R., GarcíaRigo, A., Feltens, J., Komjathy, A., Schaer, S., and Krankowski, A. (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. Journal of Geodesy, 83 (3–4), 263–275. van der Marel, H. and de Bakker, P. (2012) Single- vs. dual-frequency precise point positioning – what are the tradeoffs between using L1-only and L1+L2 for PPP? InsideGNSS, 7 (4), 30–35. Collins, P., Lahaye, F., Héroux, P., and Bisnath, S. (2008) Precise point positioning with ambiguity resolution using the decoupled clock model, in Proceedings of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2008), pp. 1315–1322. Landau, H., Chen, X., Klose, S., Leandro, R., and Vollath, U. (2008) Trimble’s RTK and DGPS solutions in comparison with precise point positioning, in International Association of Geodesy Symposia, 133, pp. 709–718. Cai, C. and Gao, Y. (2007) Precise point positioning using combined GPS and GLONASS observations. Journal of Global Positioning Systems, 6 (1), 13–22. De Bakker, P.F. (2016) On User Algorithms for GNSS Precise Point Positioning, PhD thesis, TU Delft, Delft University of Technology. Bevis, M., Businger, S., Herring, T.A., Rocken, C., Anthes, R.A., and Ware, R.H. (1992) GPS meteorology: Remote sensing of atmospheric water vapor using the Global

39

40

41

42

43

44

45

46

47

48

49

50

Positioning System. Journal of Geophysical Research: Atmospheres, 97 (D14), 15787–15801. Ware, R.H., Fulker, D.W., Stein, S.A., Anderson, D.N. et al. (2000) Suominet: A real-time national GPS network for atmospheric research and education. Bulletin of the American Meteorological Society, 81 (4), 677. Poli, P. et al. (2008) Weather report: Meteorological applications of GNSS from space and on the ground. InsideGNSS, 3 (8), 30–39. Karabatić, A., Weber, R., and Haiden, T. (2011) Near realtime estimation of tropospheric water vapour content from ground based GNSS data and its potential contribution to weather now-casting in Austria. Advances in Space Research, 47 (10), 1691–1703. Shi, J. and Gao, Y. (2012) Improvement of PPP-inferred tropospheric estimates by integer ambiguity resolution. Advances in Space Research, 50 (10), 1374–1382. Li, X., Dick, G., Ge, M., Heise, S., Wickert, J., and Bender, M. (2014) Real-time GPS sensing of atmospheric water vapor: Precise point positioning with orbit, clock, and phase delay corrections. Geophysical Research Letters, 41 (10), 3615–3621. Webb, S.R. (2015) Kinematic GNSS Tropospheric Estimation and Mitigation over a Range of Altitudes, PhD thesis, Newcastle University. Mannucci, A., Wilson, B., Yuan, D., Ho, C., Lindqwister, U., and Runge, T. (1998) A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Science, 33 (3), 565–582. Khodabandeh, A. and Teunissen, P.J.G. (2016) Arrayaided multifrequency GNSS ionospheric sensing: Estimability and precision analysis. IEEE Transactions on Geoscience and Remote Sensing, 54 (10), 5895–5913. Hernández-Pajares, M., Juan, J.M., Sanz, J., AragónÀngel, À., García-Rigo, A., Salazar, D., and Escudero, M. (2011) The ionosphere: effects, GPS modeling and the benefits for space geodetic techniques. Journal of Geodesy, 85 (12), 887–907. Wei, L., Pengfei, C., Jinzhong, B., Hanjiang, W., and Hua, W. (2012) Calibration of regional ionospheric delay with uncombined precise point positioning and accuracy assessment. Journal of Earth System Science, 121 (4), 989–999. Zhang, B. (2016) Three methods to retrieve slant total electron content measurements from ground-based GPS receivers and performance assessment. Radio Science, 51 (7), 972–988. Morton, J., Zhou, Q., and Cosgrove, M. (2007) A floating vertical TEC ionosphere delay correction algorithm for single frequency GPS receivers, in Proceedings of the 63rd Annual Meeting of The Institute of Navigation, pp. 479–484.

References

51 Julien, O., Macabiau, C., and Issler, J.L. (2009)

52

53

54

55

56

57

58

59

60

61

62

Ionospheric delay estimation strategies using Galileo E5 signals only, in Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), pp. 3122–3128. Li, X., Ge, M., Zhang, H., and Wickert, J. (2013) A method for improving uncalibrated phase delay estimation and ambiguity-fixing in real-time precise point positioning. Journal of Geodesy, 87 (5), 405–416. Wang, C., Wang, J., and Morton, Y. (2014) Regional ionospheric TEC gradients estimation using a single GNSS receiver, in China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II, Springer, pp. 363–373. Guyennon, N., Cerretto, G., Tavella, P., and Lahaye, F. (2007) Further characterization of the time transfer capabilities of precise point positioning (PPP). Joint IEEE Frequency Control Symposium and the 21st European Frequency and Time Forum, pp. 399–404. Orgiazzi, D., Tavella, P., and Lahaye, F. (2005) Experimental assessment of the time transfer capability of precise point positioning (PPP). Proceedings of IEEE FCS, pp. 337–345. Petit, G., Harmegnies, A., Mercier, F., Perosanz, F., and Loyer, S. (2011) The time stability of PPP links for TAI. Proceedings of the Joint IEEE FCS and 25th EEFTF, pp. 1–5. Delporte, J., Mercier, F., and Laurichesse, D. (2008) Time transfer using GPS carrier phase with zero-difference integer ambiguity blocking. Proceedings of 22nd EFTF, pp. 1–6. Larson, K.M., Levine, J., Nelson, L.M., and Parker, T. (2000) Assessment of GPS carrier-phase stability for time-transfer applications. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 47 (2), 484–494. Bruyninx, C. and Defraigne, P. (2000) Frequency transfer using GPS codes and phases: Short and long term stability. Proceedings of 31st PTTI Meeting, pp. 471–478. Altamimi, Z., Rebischung, P., Métivier, L., and Collilieux, X. (2016) ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. Journal of Geophysical Research: Solid Earth (DOI: 10.1002/2016JB013098). Collins, P., Henton, J., Mireault, Y., Héroux, P., Schmidt, M., Dragert, H., and Bisnath, S. (2009) Precise point positioning for real-time determination of co-seismic crustal motion, in Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), pp. 2479–2488. Guo, Q. (2015) Precision comparison and analysis of four online free PPP services in static positioning and

63

64

65

66

67

68

69

70

71

72

73

74

tropospheric delay estimation. GPS Solutions, 19 (4), 537–544. Abdallah, A. and Schwieger, V. (2016) Static GNSS precise point positioning using free online services for Africa. Survey Review, 48, 61–77. Muellerschoen, R.J., Bertiger, W.I., Lough, M.F., Stowers, D., and Dong, D. (2000) An internet-based global differential GPS system, initial results, in Proceedings of the ION National Technical Meeting, Anaheim, CA, p. 6. Leandro, R.F., Santos, M.C., and Langley, R.B. (2007) GAPS: The GPS analysis and positioning software: A brief overview, in Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007), pp. 1807–1811. Doucet, K., Herwig, M., Kipka, A., Kreikenbohm, P., Landau, H., Leandro, R., Moessmer, M., and Pagels, C. (2012) Introducing ambiguity resolution in web-hosted global multi-GNSS precise positioning with Trimble RTXPP, in Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville, Tennessee, pp. 1115–1125. Píriz, R., Mozo, A., Navarro, P., and Rodríguez, D. (2008) magicGNSS: Precise GNSS products out of the box, in Proceedings of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2008), Savannah, GA, pp. 1242–1251. Gurtner, W. and Estey, L. (2007) RINEX – the Receiver INdependent EXchange format version 3.00., Tech. Rep., Astronomical Institute, University of Bern. Hauschild, A. and Montenbruck, O. (2008) Real-time clock estimation for precise orbit determination of LEO satellites, in Proceedings of the ION GNSS Meeting 2008, Savannah, Georgia, USA, pp. 16–19. Elsobeiey, M. and Al-Harbi, S. (2016) Performance of realtime precise point positioning using IGS real-time service. GPS Solutions, pp. 565–571. Montenbruck, O., Schmid, R., Mercier, F., Steigenberger, P., Noll, C., Fatkulin, R., Kogure, S., and Ganeshan, S. (2015) GNSS satellite geometry and attitude models. Advances in Space Research, 56 (6), 1015–1029. Görres, B., Campbell, J., Becker, M., and Siemes, M. (2006) Absolute calibration of GPS antennas: laboratory results and comparison with field and robot techniques. GPS Solutions, 10 (2), 136–145. Schmid, R., Steigenberger, P., Gendt, G., Ge, M., and Rothacher, M. (2007) Generation of a consistent absolute phase center correction model for GPS receiver and satellite antennas. Journal of Geodesy, 81 (12), 781–798. Ashby, N. and Weiss, M. (1999) Global positioning receivers and relativity. NIST Technical Note 1385, US Government Printing Office.

525

526

20 GNSS Precise Point Positioning

75 Bidikar, B., Rao, G.S., and Ganesh, L. (2016) Sagnac effect

76

77

78

79 80

81

82

83

84

85

86

87

88

89

and set error based pseudorange modeling for GPS applications. Procedia Computer Science, 87, 172–177. Wu, J., Wu, S., Hajj, G., Bertiger, W., and Lichten, S. (1993) Effects of antenna orientation on GPS carrierphase. Manuscripta Geodaetica, 18, 91–98. Le, A.Q. and Tiberius, C.C.J.M. (2006) Phase wind-up effects in precise point positioning with kinematic platforms, in Proceedings of the 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, NAVITEC 2006, ESA, pp. 1–8. Bar-Sever, Y. (1996) A new module for GPS yaw attitude control, in Proceedings of IGS Workshop-Special Topics and New Directions, GeoforschungsZentrum, Potsdam, pp. 128–140. Kouba, J. (2009) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solutions, 13 (1), 1–12. Dilssner, F., Springer, R., Gienger, G., and Dow, J. (2010) The GLONASS-M satellite yaw-attitude model. Advances in Space Research, 47 (1), 160–171. Ifadis, I. (1992) The excess propagation path of radio waves: Study of the influence of the atmospheric parameters on its elevation dependence. Survey Review, 31, 289–298. Herring, T. (1992) Modeling atmospheric delays in the analysis of space geodetic data. In: Refraction of Transatmospheric Signals in Geodesy, pp. 157 – 164. Niell, A. (1996) Global mapping functions for the atmosphere delay at radio wavelengths. Journal of Geophysical Research, 101, 3227–3246. Kleijer, F. (2004) Troposphere Modeling and Filtering for Precise GPS Leveling, PhD thesis, Delft University of Technology. Boehm, J., Werl, B., and Schuh, H. (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. Journal of Geophysical Research, 111 (B02406), 1–9. Chen, G. and Herring, T.A. (1997) Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data. Journal of Geophysical Research, 102 (B9), 20489–20502. Bar-Sever, Y.E. and Kroger, P.M. (1998) Estimating horizontal gradients of tropospheric path delay with a single GPS receiver. Journal of Geophysical Research, 103 (B3), 5019–5035. Boehm, J. and Schuh, H. (2007) Troposphere gradients from the ECMWF in VLBI analysis. Journal of Geodesy, 81 (6), 403–408. Ghoddousi-Fard, R. (2009) Modelling Tropospheric Gradients and Parameters from NWP Models: Effects on GPS Estimates, PhD thesis, University of New Brunswick.

90 Odijk, D. (2002) Fast Precise GPS Positioning in the

91

92

93 94

95

96 97 98

99

100

101

102 103

104

105

Presence of Ionospheric Delays, PhD thesis, Delft University of Technology, Publication on Geodesy, 52, Netherlands, Geodetic Commission, Delft. Marques, H., Monico, J., and Aquino, M. (2011) RINEX_HO: second-and third-order ionospheric corrections for RINEX observation files. GPS Solutions, 15 (3), 305–314. Klobuchar, J. (1987) Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Transactions on Aerospace and Electronic Systems, 23, 325–331. Radicella, S. (2009) The NeQuick model genesis, uses and evolution. Annals of Geophysics, 52, 417–422. Memarzadeh, Y. (2009) Ionospheric Modeling for Precise GNSS Applications, PhD thesis, Delft University of Technology. Schaer, S., Beutler, G., and Rothacher, M. (1998) Mapping and predicting the ionosphere, in Proceedings IGS AC Workshop, Darmstadt, Germany. McCarthy, D.D. and Petit, G. (2003) IERS conventions (2003), IERS technical note 32, Tech. Rep., IERS. McCarthy, D.D. (1989) IERS standards (1989), IERS technical note 3, Tech. Rep., IERS. Wahr, J.M. (1981) The forced nutations of an elliptical, rotating, elastic and oceanless earth. Geophysical Journal International, 64 (3), 705–727. Petrov, L. and Boy, J.P. (2004) Study of the atmospheric pressure loading signal in very long baseline interferometry observations. J. Geophys. Res., 109, 14, doi:10.1029/2003JB002500. Urquhart, L. (2009) Atmospheric pressure loading and its effects on precise point positioning, in Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), pp. 658–667. Verhagen, S., Li, B., and Teunissen, P.J. (2013) PsLAMBDA: ambiguity success rate evaluation software for interferometric applications. Computers & Geosciences, 54, 361–376. Bisnath, S. (2018) Relative positioning and RTK, in ION PNT Book, pp. 1–36. Teunissen, P.J.G. (1998) GPS carrier phase ambiguity fixing concepts, in GPS for Geodesy, 2nd Ed. (eds. P.J.G. Teunissen and A. Kleusberg), pp. 319–388. Mervart, L., Lukes, Z., Rocken, C., and Iwabuchi, T. (2008) Precise point positioning with ambiguity resolution in real-time, in Proceedings of 21st International Technical Meeting of the satellite Division of the Institute of Navigation (ION GNSS 2008), pp. 397–405. Bertiger, W., Desai, S.D., Haines, B., Harvey, N., Moore, A. W., Owen, S., and Weiss, J.P. (2010) Single receiver phase

References

106

107

108 109

110

111

112

113

114

115

116

117

118

119

ambiguity resolution with GPS data. Journal of Geodesy, 84 (5), 327–337. Teunissen, P.J.G., Odijk, D., and Zhang, B. (2010) PPPRTK: Results of CORS Network-Based PPP with Integer Ambiguity Resolution. Journal of Aeronautics, Astronautics and Aviation, 42 (4), 223–229. Laurichesse, D. and Mercier, F. (2007) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP, in Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), pp. 839–848. Collins, P. (2008) Isolating and estimating undifferenced GPS integer ambiguities, in Proc. ION NTM, pp. 720–732. Ge, M., Gendt, G., Rothacher, M., Shi, C., and Liu, J. (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. Journal of Geodesy, 82 (7), 389–399. Geng, J. (2011) Rapid Integer Ambiguity Resolution in GPS Precise Point Positioning, PhD thesis, University of Nottingham, UK. Loyer, S., Perosanz, F., Mercier, F., Capdeville, H., and Marty, J.C. (2012) Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center. Journal of Geodesy, 86 (11), 991–1003. Teunissen, P.J.G. and Khodabandeh, A. (2015) Review and principles of PPP-RTK methods. Journal of Geodesy, 89 (3), 217–240. De Jonge, P. and Tiberius, C.C.J.M. (1996) The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects. Publications of the Delft Computing Centre, LGR-Series, 12, 1–47. Teunissen, P.J.G. (1999) An optimality property of the integer least-squares estimator. Journal of Geodesy, 73 (11), 587–593. Teunissen, P.J.G. (1998) Success Probability of Integer GPS Ambiguity Rounding and Bootstrapping. Journal of Geodesy, 72 (10), 606–612. Zhang, B., Teunissen, P.J.G., and Odijk, D. (2011) A novel un-differenced PPP-RTK concept. Journal of Navigation, 64 (S1), S180–S191. Odijk, D., Zhang, B., Khodabandeh, A., Odolinski, R., and Teunissen, P.J.G. (2015) On the estimability of parameters in undifferenced, uncombined GNSS network and PPPRTK user models by means of S-system theory. Journal of Geodesy, 90 (1), 15–44. Hernández-Pajares, M., Juan, J.M., Sanz, J., and Colombo, O.L. (2000) Application of ionospheric tomography to real-time GPS carrier-phase ambiguities resolution, at scales of 400–1000 km and with high geomagnetic activity. Geophysical Research Letters, 27 (13), 2009–2012. Jonkman, N., Teunissen, P., Joosten, P., and Odijk, D. (2000) GNSS long baseline ambiguity resolution: Impact

120

121

122

123

124

125

126

127

128

129

130

131

132

133

of a third navigation frequency, in Geodesy Beyond 2000, IAG Symposium 121, pp. 349–354. Teunissen, P.J.G. and Khodabandeh, A. (2013) BLUE, BLUP and the Kalman filter: Some new results. Journal of Geodesy, 87 (5), 461–473. Wackernagel, H. (2013) Multivariate Geostatistics: An Introduction with Applications, Springer Science & Business Media. Li, X., Zhang, X., and Ge, M. (2011) Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. Journal of Geodesy, 85 (3), 151–158. Collins, P., Lahaye, F., and Bisnath, S. (2012) External ionospheric constraints for improved PPP-AR initialisation and a generalised local augmentation concept, in Proceedings of 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), pp. 3055 – 3065. Odijk, D., Teunissen, P.J.G., and Zhang, B. (2012) Singlefrequency integer ambiguity resolution enabled GPS precise point positioning. Journal of Surveying Engineering, 138 (4), 193–202. Geng, J. and Bock, Y. (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. Journal of Geodesy, 87 (5), 449–460. Tegedor, J. and Øvstedal, O. (2014) Triple carrier precise point positioning (PPP) using GPS L5. Survey Review, 46 (337), 288–297. Monge, B.M., Rodríguez-Caderot, G., and De Lacy, M. (2014) Multifrequency algorithms for precise point positioning: Map3. GPS Solutions, 18 (3), 355–364. Elsobeiey, M. (2015) Precise point positioning using triple-frequency GPS measurements. Journal of Navigation, 68 (03), 480–492. Cai, C. and Gao, Y. (2013) Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS Solutions, 17 (4), 223–236, doi:10.1007/s10291-012-0273-9. Pan, L., Cai, C., Santerre, R., and Zhu, J. (2014) Combined GPS/GLONASS precise point positioning with fixed GPS ambiguities. Sensors, 14, 17530–17547. Odijk, D., Zhang, B., and Teunissen, P.J.G. (2015) MultiGNSS PPP and PPP-RTK: Some GPS+BDS results in Australia, in Proceedings Chinese Satellite Navigation Conference 2015, Vol. II (ed. J.S. et al.), Springer, pp. 613–623. Qu, L., Zhao, Q., Guo, J., Wang, G., Guo, X., Zhang, Q., Jiang, K., and Luo, L. (2015) BDS/GNSS real-time kinematic precise point positioning with un-differenced ambiguity resolution, in Proceedings of Chinese Satellite Navigation Conference 2015, Vol. III, Springer, pp. 13–29. Hegarty, C., Powers, E., and Fonville, B. (2004) Accounting for timing biases between GPS, modernized

527

528

20 GNSS Precise Point Positioning

134

135

136

137

GPS, and Galileo signals, in Proceedings of 36th Annual Precise Time and Time Interval (PTTI) Meeting, Washington, DC, pp. 307–317. Montenbruck, O., Hauschild, A., and Hessels, U. (2011) Characterization of GPS/GIOVE sensor stations in the CONGO network. GPS Solutions, 15 (3), 193–205. Odijk, D. and Teunissen, P.J.G. (2013) Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution. GPS Solutions, 17 (4), 521–533. Melgard, T., Tegedor, J., de Jong, K., Lapucha, D., and Lachapelle, G. (2013) Interchangeable integration of GPS and Galileo by using a common system clock in PPP, in Proceedings of ION GNSS+ 2013, Institute of Navigation, Nashville, TN. Nadarajah, N., Teunissen, P.J.G., Sleewaegen, J.M., and Montenbruck, O. (2014) The mixed-receiver BeiDou inter-satellite-type bias and its impact on RTK positioning. GPS Solutions, 19 (3), 357–368.

138 Paziewski, J. and Wielgosz, P. (2015) Accounting for

139

140

141

142

143

Galileo–GPS inter-system biases in precise satellite positioning. Journal of Geodesy, 89 (1), 81–93. Odijk, D., Nadarajah, N., Zaminpardaz, S., and Teunissen, P.J.G. (2016) GPS, Galileo, QZSS and IRNSS differential ISBs: Estimation and application. GPS Solutions, pp. 1–12. Jiang, N., Xu, Y., Xu, T., Xu, G., Sun, Z., and Schuh, H. (2016) GPS/BDS short-term ISB modelling and prediction. GPS Solutions, pp. 1–13. Teunissen, P.J.G., Odolinski, R., and Odijk, D. (2014) Instantaneous BeiDou+GPS RTK positioning with high cut-off elevation angles. Journal of Geodesy, 88 (4), 335–350. Li, X., Ge, M., Dai, X., Ren, X., Fritsche, M., Wickert, J., and Schuh, H. (2015) Accuracy and reliability of multiGNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. Journal of Geodesy, 89 (6), 607–635. Steigenberger, P. (2015) Accuracy of Current and Future Satellite Navigation Systems, Habilitation Thesis, Technische Universität München.

529

21 Direct Position Estimation Pau Closas1 and Grace Gao2 1 2

Northeastern University, United States Stanford University, United States

21.1

Introduction

This chapter presents an innovative concept that helps overcome some of the critical challenges and limitations in standard global navigation satellite system (GNSS) position, navigation, and timing (PNT). The concept is known as Direct Position Estimation (DPE) and was introduced in [1]. At a glance, a receiver implementing DPE computes the position directly from the sampled signal, unlike a conventional receiver in which range estimates (i.e. pseudoranges) are required before solving for the user’s position [2]. Therefore, conventional receivers are generally referred to as two-step receivers and DPE as one-step receivers. The direct search and joint optimization across multiple satellites makes DPE a robust GNSS position and time estimation technique [3]. In contrast, conventional techniques, such as scalar tracking, first estimate intermediate pseudorange and pseudorange rate measurements to each satellite in view [4, 5], then they solve for the navigation solution, typically via an iterative least-squares approach [6, 7]. Vector tracking, a more robust approach than scalar tracking, jointly processes intermediate measurements across multiple satellites in view by mapping intermediate measurement residuals into shared navigation residuals [8, 9]. However, it is an indirect navigation estimation process based on intermediate measurement residuals which are separately estimated across multiple satellites [10, 11]. When the signals are degraded, both scalar and vector tracking discard intermediate measurements which are likely experiencing a fault. [12, 13]. In contrast, DPE is able to preserve such information [14] and provide improved performance under challenging situations [2, 15]. A comparison of scalar tracking, vector tracking‚ and DPE is given in Table 21.1. The chapter is organized as follows. With the intention of facilitating the introduction of new material, Section 21.2 describes the signal model used through this chapter, as

well as the basics of the signal processing that apply to standard GNSS receivers. DPE is introduced in Section 21.3, where extensive details are provided regarding the signal model and the direct-positioning concept. Additionally, the section provides theoretical results demonstrating the performance enhancement of DPE with respect to twosteps approaches. Implementation details are discussed in Section 21.4, where we move from the purely theoretical results in the previous section to the more practical aspects. Section 21.5 discusses some variants and alternative applications of DPE. Finally, conclusions are provided in Section 21.6.

21.2 Conventional GNSS Signal Processing and Positioning This section provides a common framework to mathematically describe the basic signal processing pipeline of a conventional two-step GNSS receiver. Then, in Section 21.3, we will leverage these definitions to better understand DPE processing. First, we discuss the transmitted signal and channel models to characterize the signal received at the antenna. Then, we describe the signal processing and navigation solution equations, which ultimately yield a position, velocity, and time (PVT) estimate.

21.2.1

GNSS Signal Model

A general signal model for satellite navigation systems consists of a direct-sequence spread-spectrum (DS-SS) signal, synchronously transmitted by all the satellites in the constellation. This type of signal enables code division multiple access (CDMA) transmissions; that is, satellite signals are distinguished by orthogonal (or quasi-orthogonal) codes. At a glance, these signals consist of two main components:

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

530

21 Direct Position Estimation

Table 21.1 Comparison between scalar tracking, vector tracking, and Direct Position Estimation (DPE) Approach

Scalar tracking

Vector tracking

Direct Position Estimation

• •• • •

Remarks

Estimates intermediate range measurements of each satellite

Estimates intermediate measurement residuals Couples signal tracking and PVT estimation, so that all channels aid each other by sharing information Maps intermediate measurement residuals to navigation residuals Maximizes cross-correlation of expected GPS signal reception with received GPS signal at multiple navigation candidates

a ranging code using a pseudorandom noise (PRN) spreading sequence; and a low-rate data link to broadcast necessary information for positioning such as satellite orbital parameters and corrections. The complex baseband model of the signal transmitted by the i-th satellite is sT,i t = sI,i t + jsQ,i t ,

21 1

• • •

where its in-phase and quadrature components are defined as sI,i t =

2PI,i qI,i t N cI

∞

=

2PI,i

LcI

cI,i kI gI t − mI T bI − uI T PRNI − kI T cI

bI,i mI mI = − ∞

uI = 1 k I = 1

21 2 sQ,i t =

2PQ,i qQ,i t N cQ

∞

=

2PQ,i

LcQ

cQ,i k Q gQ t − mQ T bQ − uQ T PRNQ − k Q T cQ ,

bQ,i mQ mQ = − ∞

uQ = 1 k Q = 1

21 3 where the following definitions for the in-phase component – analogous to the quadrature signal, defined in (21.3) with subindex Q – hold:

•

• • • ••

Susceptible to intermediate range estimation errors Does not account for inter-link correlations Susceptible to intermediate residual estimation errors

Direct search Joint optimization across satellites

PI,i is the transmitted power, considered equal for all satellites, and is elevation-dependent due to the antenna pattern at the satellite [16]. bI,i(t) {−1, 1} is the sequence of low-rate data bits, with T bI being the bit period. cI,i(t) {−1, 1} is the PRN spreading sequence, not to be confused with c, the constant representing the speed of light. The chip length of the sequence and the chip period are denoted by LcI and T cI , respectively. Therefore, T PRNI = LcI T cI is the codeword period. N cI denotes the number of code epochs per data bit. Figure 21.1 aims to clarify the relation between these bits/chips parameters. The energy-normalized chip shaping pulse is denoted by gI(t).

Note that several carrier frequencies can be used at a time, with the presented baseband structure being thus replicated. Actually, GNSS systems typically transmit complementary signals over several frequency bands. One of the main reasons for this is to combat the frequency-dependent perturbations suffered by the signal when traveling through the ionosphere and troposphere. Satellite signals travel through a propagation channel which modifies its amplitude, phase‚ and delay. In fact, multiple replicas of the same transmitted signal can reach

TbI ···

NcI

1

2

···

NcI

1

··· t

TPRNI = LcITcI

Figure 21.1 Relation among the parameters defining bits and spreading sequences in a generic navigation signal (in-phase component) [17]. Source: Reproduced with permission of P. Closas.

21.2 Conventional GNSS Signal Processing and Positioning

a receiver’s antenna due to multipath propagation. In general, these replicas are caused by reflections of the line-of-sight (LOS) signal from surrounding obstacles (e.g. buildings, trees, ground). For the i-th satellite link, such a propagation channel is generically modeled by a linear time-varying impulse response with Ni propagation paths [18, 19]: Ni − 1

hi t =

αi,n t exp jϕi,n t δ t − τi,n t ,

n=0

21 4 where αi,n(t), ϕi,n(t), and τi,n(t) are the amplitude, phase‚ and delay of the n-th propagation path for the i-th satellite. δ(t) is Dirac’s delta function [20]. Notice that subindex n = 0 denotes the LOS parameters. Typically, the amplitudes are assumed to obey the Rayleigh or Rice distributions, depending on whether the LOS is blocked or not [21]. Time delays are assumed to be piecewise constant during the observation interval. In a first-order Taylor expansion, the time-varying phase ϕi,n(t) has a uniformly distributed independent term [22] and a linear term representing the effect of the Doppler spread (that is, a frequency shift caused by the relative motion between the satellite and the receiver). In general, we consider that paths are independent, which is referred to as the Wide Sense Stationary with Uncorrelated Scattering (WSSUS) [23] channel model. Extensive measurement campaigns have been performed to characterize the GNSS propagation channel model, and they support the WSSUS characterization; see, for instance, the results reported in [24, 25]. As a consequence, a GNSS receiver measures signals that are considered to be a superposition of plane waves corrupted by noise and, possibly, interferences and multipath. An antenna receives M scaled, time-delayed, and Dopplershifted signals with known signal structure. Each signal corresponds to the LOS of one of the M visible satellites after propagating through the WSSUS channel mode. The received complex baseband signal can be modeled as the convolutions of the channel (Eq. (21.4)) with the corresponding signal, resulting in: M

ai si t − τi exp j2π f di t + n t ,

x t =

21 5

21.2.2

Basics of GNSS Signal Processing

The primary goal of a GNSS receiver is to accurately estimate its PVT, which is typically accomplished by first estimating the parameters in the signal model (Eq. (21.5)). These estimates are used to construct a set of observables per satellite. Observables are a set of ranges computed from time-delay or phase-difference estimates, referred to as pseudoranges and carrier-phase measurements, respectively. Once a set of valid observables is computed, a geometrical problem is solved to compute the PVT solution for the receiver. The received signal (Eq. (21.5)) is sampled at a suitable sampling rate fs = 1/Ts, resulting in a discrete-time signal x[n] = x(nTs) from which we aim to extract the observables. The propagation time of a signal, the time between its transmission from the i-th satellite to the user, is continuously estimated by tracking algorithms. This timedelay estimate (denoted by τi ) provides an estimation of the distance between the i-th satellite and the user. Under the maximum likelihood (ML) principle, the unknown parameters in Eq. (21.5) are obtained by maximizing the cross-ambiguity function (CAF) of the received signal and the PRN sequence of the i-th satellite. In general, the CAF is computed over a coherent integration time, in which Nc PRN sequences are used to correlate with the incoming signal. Additionally, Nnc CAFs can be averaged over a non-coherent integration time to avoid bit transitions. Here, we do not consider non-coherent integration for the sake of simplicity, but some details can be found in [2]. More formally,1 the i-th channel estimates [26] are defined as 2

Lc N c

x n ci nT s − τi exp − j2π f di nT s

τi , f di = arg max τi , f di

,

n=0

21 6 where we recall that Lc is the length of the PRN sequence ci( ). For convenience, the CAF is typically parameterized as Λi τi , f di , showing the corresponding satellite indicator and the relevant synchronization parameters. More compactly, in vector form, we can rewrite Eq. (21.6) as

i=1

where si(t) is the transmitted complex baseband low-rate navigation signal spread by the pseudorandom code of the i-th satellite, which is considered to be known. ai is its complex amplitude, τi is the time delay, f di is the Doppler shift, and n(t) represents zero-mean additive noise with variance N0/2 and other unmodeled terms besides LOS. N0 is the one-sided power spectral density in dBW/Hz. Note that subindex n is omitted since only LOS signals are explicitly modeled, in contrast to Eq. (21.4).

τi , f di = arg max τi , f di

Λi τ i , f d i

2

≜ x H ci

2

21 7

1 We use the convention to denote the Euclidean norm of n-dimensional vector spaces in n and to denote the absolute value, the latter coinciding with the norm on the one-dimensional vector space.

531

532

21 Direct Position Estimation

where

f di = − v i − v

ui

fc , c

21 10

x0 x=

where v = (vx, vy, vz) and v i = vxi , vyi , vzi are the velocity vectors of the user and the i-th satellite, respectively. ui represents the unitary direction vector of the i-th satellite relative to the user, defined as

and x Lc N c ci − τ i

ui =

ci = ci Lc N c T s − τi exp − j2π f di Lc N c T s 21 8 correspond to the LcNc snapshots and the local replica, respectively. The time-delay estimate, τi , is used to construct the so-called pseudorange ρi = cτi Pseudoranges provide a nonlinear relation between the user’s position (p = [x, y, z] ) and the time delay of each satellite according to the model ρi = ϱi p + c δt − δt i + cΔTi + cΔIi + ϵi ,

21 9

where c is the speed of light, satellites are indexed by i {1, …, M}, and the following definitions apply:

• • • • • •

τi is the time-delay estimate at the receiver for the LOS emitted by the i-th satellite. ϱi(p) = pi − p is the geometric distance between the receiver and the i-th satellite. pi = (xi, yi, zi) are the coordinates of the i-th satellite in the Earth-Centered Earth-Fixed (ECEF) coordinate system, which can be computed from the ephemeris. δt is the bias of the receiver clock with respect to GNSS time, which is unknown. δti is the clock bias of the i-th satellite with respect to GNSS time, known from the ephemeris. ΔTi and ΔIi are the non-dispersive tropospheric delay and the frequency-dependent ionospheric delay terms. The term ϵi includes errors from various sources such as multipath biases, ephemeris errors‚ and relativistic effects‚ among others.

The other important effect experienced by the signal is a frequency shift. The observed carrier frequency at the receiver differs from its nominal frequency due to Doppler effect, which is caused by user-satellite relative motion. Additionally, frequency shifts due to clock drifts (δt ) and background errors are typically experienced on top of the Doppler shifts. Accurate Doppler estimates yield precise velocity calculations that are useful in positioning and navigation applications with high user dynamics. The Doppler shift due to the relative motion of the user and the i-th satellite is

pi − p pi − p

21 11

and fc represents the corresponding carrier frequency used by the GNSS. Doppler (and phase) estimates are used to compute carrier-phase observables much more accurately than the code observable described in Eq. (21.9). Summing up, the baseband operation of current GNSS receivers is briefly described. First, the receiver detects which satellites are visible and obtains rough estimates of the time delays and Doppler shifts of those satellites, expressed as f d1

τ1 τ=

and τM

fd =

21 12 f dM

respectively. This initial operation is referred to as acquisition, and it can also be seen as an open-loop processing of the data. Once the rough estimates are obtained, the receiver can start operating in tracking mode. The tracking mode is typically implemented in a closed-loop (CL) architecture – that is, with phase lock loops (PLLs) and delay lock loops (DLLs) – or an open-loop (OL) architecture in a challenging environment, to obtain the accurate time delay, Doppler shift, and carrier-phase estimations and thus ultimately acquire accurate user position solutions. Ultimately, acquisition and tracking operations aim at solving Eq. (21.7). Regardless of the receiver operating architecture (OL or CL), conventional GNSS receivers estimate user position, p, from the computed observables. In this second step, the position of the receiver is computed upon taking into account the geometrical relation between the set of observables and the user PVT. The resulting multilateration problem is typically solved by a least-squares (LS) algorithm. Note that in this process the receiver also needs to estimate the receiver clock bias δt that represents the offset between the receiver time and the GNSS time. In its most simple form, that is, the single point solution with code pseudoranges, the LS solution appears from a linearized geometrical problem [6, 26, 27]. Such linearization makes perfect sense, given that the nonlinearity is, in essence, a sphere whose radius is on the order of tenths of thousands of kilometers. Given that GNSS satellites orbit between 15 000 and 30 000 km, and given that a GNSS receiver tracking PRN code chip transitions must resolve

21.3 DPE

uncertainties on the order of 100s of meters, the geometric localization problem may be treated as linear for all but the most precise applications. The problem is to compute the user’s position and clock offset from a set of M estimated pseudoranges. Thus, from Eq. (21.9), we form the following system of equations: ρi + cδt i − ϵi = i

pi − p

1, …, M

+ cδt

21 13

M≥4 ,

which results in a nonlinear and possibly overdetermined system. The condition M ≥ 4 is due to the dimensionality of the problem. The system is usually solved iteratively by linearizing each ϱi(p) with respect to an initial position estimate (po = (xo, yo, zo) ) and iterating until convergence: ϱi p

ϱoi +

xi − xo yi − yo zi − zo δ + δ + δz , x y ϱoi ϱoi ϱoi 21 14

where δx = x − x, δy = y − y, δz = z − z and ϱoi ≜ ϱi po = pi − po The Bancroft algorithm [28] provides an initial guess as to the position and the clock offset of the user receiver without any prior knowledge. Considering Eq. (21.14), the system in Eq. (21.13) can be formulated as the following LS problem: o

o

y − Tδ

δ = arg min δ

where δ = δx , δy , δz , δt

2

o

,

21 15

,

ρ1 + cδt 1 − ϵ1 − ϱo1 ρM + cδt M − ϵM − ϱoM x1 − xo ϱo1

y1 − yo ϱo1

z1 − zo ϱo1

xM − xo ϱoM

yM − yo ϱoM

zM − zo ϱoM

21.3

1

T=

, 1

•

and the solution †

δ=T y≜ T T H

−1

H

T y

21 16

is straightforwardly given by the Moore–Penrose pseudoinverse (T†). Therefore, we have that p = po + δ is the classical position estimation provided by GNSS receivers. Notice that, once a new position is obtained, it can be used as initialization point for linearization iteratively until convergence. This is the simplest way of formulating the PVT solution as a LS optimization problem, which can be enhanced by incorporating side information, measurements weighting, and dynamics, for instance, using solutions based on weighted least-squares (WLS) or Kalman filtering techniques [17]. This positioning approach has established itself as

DPE

Proposals for new techniques are blooming due to the advances in digital signal processing devices, which allow increased computational complexity at faster rates [29]. Over the last years, advanced receiver techniques have been presented which substitute well-established components of two-step receivers by more sophisticated algorithms. These methods do not modify the architecture of the receiver, as depicted in Figure 21.2(a), where acquisition and tracking operations are as discussed in Section 21.2. For instance, substitution of tracking loops by more versatile filtering solutions can be consulted in [30]. In this chapter, we are interested in those approaches that not only substitute certain parts of the receiver by more advanced algorithms, but those which entail an essential modification of the receiver’s operation. Figure 21.2(b) shows an advanced architecture for a receiver which performs code/carrier estimation and position computation in a single step. This is the basis of the so-called DPE concept in the context of GNSS receivers [1]. It is worth noting the following here:

•

,

y=

the de facto technique for GNSS receivers. This is due to its modularity, reuse of well-known receiver blocks, and, importantly, notable performance over the years. The twostep technique will be referred to as the conventional approach throughout the remainder of the chapter.

In DPE, an absolute initial position (or PVT, to be more general) estimate has to be provided so that the method can start exploring the space. This initialization can be either provided by an initial two-step process, as depicted in Figure 21.2(b), where a coarse estimation of synchronization parameters is used to compute a rough navigation solution that is used as the initial estimate in DPE’s algorithm, or provided by external means such as cellular positioning or assistance GNSS data [31]. Whereas tracking mode is typically implemented in CL (through banks of parallel PLLs/DLLs) for two-step approaches, OL schemes are also explored in the context of snapshot receivers. Conversely, DPE’s tracking mode is in general implemented in OL, which involves the optimization of a cost function. This is the approach mainly discussed in this chapter. However, CL schemes can also be considered within DPE. This is mentioned in Section 21.4.3, where references are provided and a PVT filtering described.

DPE is a completely different approach to the receiver design, where the PVT solution is estimated in one step. Rather than estimating a set of observables (through time delay and Doppler shifts) to infer the associated PVT, a

533

534

21 Direct Position Estimation

(a) Two-step approach Acquisition (OL)

υˆc

υˆ f

Tracking (OL/CL)

Navigation Solution

γˆ

x[n]

(b) DPE approach(self-initialized) γˆc

Position initialization

DPE (OL/CL): arg max { Λ (γ) } γ

γˆ

x[n]

Figure 21.2 Acquisition and Tracking schemes for (a) two-step and (b) DPE positioning approaches. Coarse estimates of synchronization parameters are referred to as υc, which are typically the outcome of the acquisition stage, whereas fine estimates are provided by tracking loops, υ f . Similarly, γ c represents coarse PVT estimates and γ fine PVT estimates.

DPE-enabled receiver directly estimates PVT from the received signal x[n] (hence the name). The method was first introduced in the context of localization of narrowband radio frequency transmitters [32] and for multiple radio signals [33]. In the context of self-localization, [1] presented the approach for GNSS receivers, and related works exist in the collective detection literature [34–37]. The key idea is to realize that time delays and Doppler shifts of all satellites are intimately related to one another through the receiver PVT parameters (which we gather in a vector γ Rnγ ). Indeed, the fact that all those signals are received at the same location and at the same time instant is crucial. Inspecting Eqs. (21.9) and (21.10), we can readily identify that, actually, τ ≜ τ γ and f d ≜ f d γ , respectively. Therefore, a value for γ implies a value for all satellites’ time delays and Doppler shifts. One of the simplest configurations for γ could be γ = p , δt, v , δt

,

21 17

encompassing PVT parameters. In contrast, the classical solutions in Figure 21.2(a) aim to independently estimate the CAF parameters for each channel. That is, Eq. (21.6) is optimized over τi , f di . We can define the joint vector of synchronization parameters as υ ≜ υ1 , …, υM

with

υi = τi , f di

21 18

Intuitively, one can see DPE as a direct approach for estimating γ without individual channel estimates. On the one hand, the conventional approach estimates the different time delays by maximizing the correlation between the signal and the conditioned PRN sequence of each satellite in

view, υi, individually. On the other hand, DPE defines a set of candidate positions, determines the time delays associated with the positions, and computes the energy found at the different correlation outputs jointly. In a way, the local replica is generated by jointly combining all signals. Then the tentative position that jointly maximizes correlation with all considered satellites is selected through optimization of a cost function. The cost function appears as a result of deriving the ML estimator of the PVT parameters directly from the received signal (Eq. (21.5)), which maximizes the addition of autocorrelation functions over the M visible satellites [17, 38].

21.3.1 Qualitative Motivations for DirectPositioning Although it is agreed that conventional two-step positioning has multiple benefits, some of its limitations have been pointed out [6], which are precisely exploited by positiondomain techniques [39]. As mentioned earlier, thanks to the advances in computation and software-defined radio [29], some of the technological limitations that prevented technology from going beyond two-step positioning have been overcome. Some of these qualitative drawbacks or limiting factors are as follows:

•

Estimates of the synchronization in Eq. (21.18), υ, are obtained independently per satellite, omitting any potential correlation among channels and propagation effects. The errors are propagated to the LS solution, where a statistical characterization is deemed challenging due to nonlinearities. Therefore, the two-step approach does not take into

21.3 DPE

•

•

•

consideration possible dependencies among channels, which could improve the estimation performance. Related to the previous point, a conventional GNSS receiver may require 10-20 parallel channels in order to process LOS signals and actively search for new signals previously obscured by structures or the horizon. In case of multi-constellation receivers, the number of channels is even larger. Since the ultimate parameter of interest is the PVT solution (i.e. position, velocity‚ and time defined in a three-dimensional space, γ), it seems that there exists a possible redundancy because the receiver performs estimation in a higher-dimensional parameter space (delay and Doppler for each channel, totaling 2M unknowns). Thus, the conventional approach increases the dimensionality of the problem with respect to the amount strictly (and theoretically) required. The use of prior information is not straightforward when dealing with synchronization parameters. In the two-step method, as mentioned in Section 21.2.2, side information is typically introduced in the navigation solution once observables have been computed. Using prior information in the tracking loops is, in general, an involved task [40] and would require extensive test-field campaigns to produce the relevant data [25], and the algorithm would need to distinguish among a number of synchronization evolution models depending on the dynamics of the receiver. This is much more difficult than considering prior information when the parameter of interest is the user’s position itself, γ, where the physical meaning of the parameter aids the inclusion of side information. Although the cross-correlation properties of spreading sequences used in GNSS signals provide a rather high processing gain, there is indeed a remaining multiple access interference (MAI) that is not combated in conventional receivers. This issue becomes critical when the received power levels for the satellites are highly unbalanced. To overcome this limitation, one could incorporate multiple access techniques to GNSS receivers, jointly processing signals from different satellites [41], which is inherently achieved by DPE [2].

Direct positioning aims at addressing these shortcomings by jointly processing signals from all satellites at the sample level. The remainder of this section discusses quantitative reasons for the superiority of DPE when compared to the two-step approach. Then, we will derive the optimal position estimator, under the ML principle, which shares a similar structure as the two-step synchronization solution discussed in Eq. (21.6).

21.3.2 Quantitative Motivations for DirectPositioning In previous section‚ we discussed some qualitative reasons for adopting DPE, as opposed to the two-step approach.

This section provides additional motivations, quantitative in this case, to support DPE’s potential. First, we discuss a result showing that DPE outperforms two-step positioning in the mean square error (MSE) sense. Second, we discuss some results on the theoretical lower bounds of positioning accuracy, comparing both two-step and DPE approaches. 21.3.2.1

DPE Outperforms Two-Step Positioning

The following result provides a mathematical justification for the fact that DPE provides asymptotically lower, or equal, MSE than two-step positioning. In other words, the result proves that the covariance of the two-step approach cannot be smaller than the covariance of the one-step estimator [42, 43]. Thus, the estimation performance of the conventional approach can only be, at most, equal to the one provided by the DPE approach. This result is heavily based on [42]. Rnυ and γ Rnγ be two unknown Let υ υ γ parameters such that there exists an injective function g γ ↦ υ, υ=g γ , γ

21 19

γ

that relates them. In our case, function g( ) is given by the PVT-observables relationship in Eqs. (21.9)–(21.10). Function g( ) has a unique inverse mapping γ = g−1 υ , υ

υ

21 20

under the subset υ = υ υ = g γ , γ γ υ. The K-sample estimators of γ based on the single-step and two-step approaches are denote by γ DPE and γ 2S , respectively. Similarly, Σ γ DPE and Σ γ 2S represent the covariance matrix of each estimator. Then, C ≜ lim Σ γ 2S − Σ γ DPE K

∞

21 21

is a positive semi-definite matrix, which proves the main result. The complete proof can be consulted in [17, Appendix 4.A], where the details are provided. 21.3.2.2

A Note on Position Estimation Bounds

In the context of positioning (i.e. self-localization), results exist where the Cramér–Rao lower bound (CRB) for PVT estimation is derived for both positioning approaches, highlighting the potential benefits of adopting DPE [44, 45]. More recently, [46] provided additional results regarding MSE performance bounds that yield a better understanding of DPE and its potential. These bounds are based on the ZivZakai methodology. The so-called Ziv-Zakai bound (ZZB) provides a bound on the MSE over the a priori probability density function. The generic derivation of the bound can be found in [47–49]. The ZZB allows us to determine, for instance, the signal-to-noise ratio at which both DPE and two-step approaches are able to operate before breaking

535

536

21 Direct Position Estimation

down (that is, before entering the large-error region). It turns out from this analysis that, under certain scenarios, there is an increase in sensitivity for DPE on the order of 10log10(M) dB, M being the total number of used satellites [46]. Although this effect was already observed in earlier works, derivation of the new bound allows analytic interpretation of the enhanced performance of DPE. Particularly, the lower MSE bound when estimating γ is M

SNRi 2 i=1

ZZB γ = Rγ 2Q

+

−1

M

γ Γ3

2

SNRi 4 i=1

we have that M

2Q

x

1 Γa

Γa x =

e − v va − 1 dv

21 23

0

and Γ 3 2 =

π 2 . The signal-to-noise ratio (SNR) per a2i satellite is defined as SNRi = , assuming unitary N0 2 energy for si(t). This result allows us to analyze the bound in the high- and low-SNR regimes. At low SNRs,

0

and

Γ3

2

SNRi 4 i=1

1 21 28 that causes the bound to reach, in the asymptotic region, the FIM of γ ZZB γ

21 22 where Rγ is the a priori covariance matrix of γ, which models the degree of a priori uncertainty about the parameter; γ is the Fisher Information Matrix (FIM) of γ; Q x = ∞ 1 2π x exp − t 2 2 dt is the Q-function, expressed in terms of the complementary error function as Q x = 1 2 erfc x 2 ; and Γa(x) is the incomplete gamma function given by

M

SNRi 2 i=1

−1 SNR

∞

γ ,

21 29

which corresponds to the CRB expression. More precisely, γ = PT τ P with P = 1c u1 , …, uM being the derivative of τ with respect to γ. The FIM of τ can be written as τ = β2s Γ, where Γ = diag(SNR1, …, SNRM) is a diagonal M × M matrix with its diagonal elements given by the M × 1 ∞ s t 2 dt is the mean quadratic SNR vector‚ and β2s = −∞∞ 2 − ∞ s t dt bandwidth of s(t). For the sake of completeness, we provide here some insights on the ZZB of position estimates when two-steps is considered. The ZZB for the time-delay estimation problem was first given in [50], and then generalized for any a priori distribution of τi in [48]. The ZZB for estimating each individual time delay, τi, can be readily obtained following that methodology and expressed in compact form split in the low- and high-SNR terms:

M

SNRi

0,

21 24

i=1

E τi − τ i

2

≥ σ 2τi 2Q

SNRi 2

+

−1

τ i Γ3

2

SNRi 4

≜ ZZB τi

we have that

21 30 M

SNRi 2 i=1

2Q

1

Then, the position MSE bound conditioned to using a

and

−1

21 25

M

Γ3

2

SNRi 4 i=1

0

such that, asymptotically, the bound is dominated by the a priori covariance matrix ZZB γ

SNR

Rγ

0

21 26

−1

Conversely, in the high-SNR regime, M

SNRi i=1

∞,

two-step scheme turns out to be PT ZZB − 1 τ P , where ZZB τ = diag ZZB τ1 , …, ZZB τ M is a diagonal M × M matrix constructed with the individual bound expressions for each satellite. The a priori variance of τi is represented by σ 2τi and (τi) is the FIM of τi [45]. In specific situations, for instance‚ when the satellites are received with the same power, one can show analytically the log10(M) dB improvement of DPE with respect to the two-step approach. A more general result can be obtained [46, 51] showing that

21 27

ZZB γ − PT ZZB − 1 τ P is a positive semi-definite matrix, although the improvement cannot be computed in closed form in the general case and can only be shown through Monte Carlo simulations.

21.3 DPE

concatenation of the M local codes, defined in Eq. (21.8), resulting in

21.3.3 ML Estimation of Position: Direct Positioning Parameter estimation methods have been thoroughly covered in the literature [52]. The ML principle presents an optimal paradigm to obtain a parameter estimator that asymptotically attains its lower variance bound (i.e. the bounds discussed earlier), as the number of samples goes to infinity. ML is based on maximization of the likelihood function, constructed from the conditional probability of measurements given a parameter value. In general, for a set of K recorded samples gathered in x, the maximum likelihood estimator (MLE) of a parameter γ is the solution to px γ γ ML = arg max γ

21 31

Under mild regularity conditions, the asymptotical distribution (for large data sets) of the estimator satisfies γ ML

γ,

−1

γ ,

21 32

where γ is the FIM evaluated at the true value of the parameter. Thus, the claim is that the MLE is asymptotically efficient; that is, it attains the lowest variance predicted by the CRB as K increases or the SNR is sufficiently high. The regularity conditions include the existence of the derivatives of the log-likelihood function and the FIM being nonzero. For further details, refer to [52, Appendix 7.B]. For the purposes of this chapter, we are interested in deriving the ML of position, γ , in a GNSS receiver due to the aforementioned asymptotic (and desirable) properties. Interestingly, the MLE of position [53], which is derived from the likelihood of x in Eq. (21.5), does not necessarily coincide with the position estimation computed in a twostep position. To derive the MLE of position from Eq. (21.5), we first express the observations in vector form. Assuming that K samples are processed and that the integration time is such that no bit transitions exist (or they can be removed by other means), we can write x = C υ a + n, or equivalently x = C γ a + n,

C γ = c1 , …, cM

21 34

We first take into account that the MLE is equivalent to the solution obtained by an LS criterion under the assumption of zero-mean AWGN. Neglecting additive and multiplicative constants, maximizing the likelihood function defined by Eq. (21.33) is equivalent to minimizing the following cost function: Λ a, γ = x − C γ a

2

21 35

with respect to a, γ. Expanding Eq. (21.35), Λ a, γ = xH x − xH C γ a − aH CH γ x + aH CH γ C γ a 21 36 and taking the derivative with respect to aH, we obtain ∂Λ a, γ = − CH γ x + CH γ C γ a ∂aH

21 37

which equated to zero gives us the desired estimation of complex amplitudes: −1

a = CH γ C γ

Cγ x

21 38

γ=γ

The first term, the one in the inverse, can be simplified taking into account the cross-correlation and autocorrelation properties of the PRN codes used in GNSS, although that simplification might not be accurate in binary offset carrier (BOC) modulations, which feature (multiple) secondary lobes. That is, we consider that the normalized CAF is such that cH i c j ≈ 0 if i cH i ci

21 39

j

=1

21 40

to simplify cH 1 CH γ C γ =

21 33

where x ℂK × 1 is the observed signal vector; a ℂM × 1 is a vector whose elements are the complex amplitudes of the M received signals a = (a1, …, aM) ; υ R2M × 1 gathers τ and fd, that is, time delays and Doppler shifts of each visible satellite. However, in DPE we make use of the reparameterization υ ≜ υ γ ; n ℂK × 1 represents K snapshots of zero-mean additive white Gaussian noise (AWGN) with piecewise constant variance σ 2n = N 0 2 during the observation interval; and C γ is composed of the

CK × M

c1 ,

, cM

cH M cH 1 c1

cH 1 c2

cH 1 cM

cH 2 c1

cH 2 c2

cH 2 cM

cH M c1

cH M c2

cH M cM

=

≈I

RM × M

21 41 and rewrite Eq. (21.38) as a = C γ x γ=γ

21 42

537

538

21 Direct Position Estimation

Substitution of a in Eq. (21.36) yields a cost function that depends on γ Λ a, γ = x x − x C γ C H

H

H

γ x

21 43

and the MLE of position is given by γ = arg min Λ a, γ

21 44

γ

= arg min xH x − xH C γ CH γ x

21 45

γ

γ

γ

2

xH C γ

= arg max xH C γ CH γ x = arg max

,

21 46 which can be further manipulated to obtain a more compact expression that depends on the individual CAFs associated to each satellite M

x H ci γ

γ = arg max γ

2

21 47

i=1

To obtain that expression, we used xH C γ = xH c1 , …, cM = xH c1 , …, xH cM 21 48 Note that the resulting cost function in the DPE approach is the non-coherent addition of the CAFs from the M 2

2 H satellites, M ≜ M = Λ γ , virtually i = 1 x ci γ i = 1 Λi γ augmenting the effective SNR proportionally. Additional coherent/non-coherent integrations can be considered to extend Eq. (21.48), as described in [2]. An example of the shape of Λ γ is shown in Figure 21.3. Since the MLE estimator is consistent, the cost function is optimized at the true PVT solution. It was shown that DPE provides additional robustness [54, 55] in challenging cases.

21.3.4

We conclude this section providing some additional qualitative intuition as to why DPE outperforms the two-step approach. We saw that, theoretically it does, and that the cost function is constructed such that the effective SNR is augmented. In this subsection‚ we carry out a small experiment comparing the cost functions of both two-step and DPE approaches to observe how they are affected by a multipath disturbance. For DPE, the cost function is plotted with only x and y coordinates as variable terms and fixing the rest of elements in γ to their true values. In particular, a constellation of M = 6 GPS satellites minimizing the geometrical dilution of precision is simulated, all received with a carrier-to-noise density ratio (C/N0) of 45 dB-Hz and transmitting the C/A code signal. At the receiver, the signal is bandpass-filtered at 2 MHz, and an integration time of 1 ms is configured. Note that, for the sake of a better visualization, the cost function is inverted and normalized in the plots, turning the optimization into the minimization in Eq. (21.45). The plots in Figure 21.4 represent the cost functions for both positioning approaches as a function of the error on the corresponding parameters. In benign situations, both functions have a clear global optimum. In contrast, when a multipath replica is present for one of the satellites the behavior of the cost function differs. In particular, Figure 21.5 is generated by adding an echo for one satellite (3 dB lower than the LOS). Whereas DPE’s cost function remains virtually unaltered by this effect, twostep’s cost function exhibits a strong secondary optimum due to the presence of a correlated signal. Furthermore, the two-step solution can be trapped in such a local optimum, yielding to potentially large biases in range and velocity estimation. Considering that position is jointly estimated with the information of all visible satellites, a sort of diversity is introduced in this estimation as the propagation path for each satellite link is independent.

vector correlation amplitude

highest vector correlation MLE solution

21.4

expected signal reception at a navigation candidate actual signal reception at GPS antenna position (E

ast)

Some Intuitions

)

rth

on siti

(No

po

Figure 21.3 The manifold of the vector correlation amplitudes Λ γ , shown in the east-north position domain [54]. Source: Reproduced with permission of Institute of Navigation.

Implementation Aspects

We have seen in Section 21.3 that the DPE’s solution involves an optimization problem that cannot be solved in closed form. In particular, each candidate solution γ requires evaluation of a certain number of correlator outputs, which is known to be computationally intensive. This section discusses some approaches when it comes to implementing DPE on a software-defined radio (SDR) receiver. Figure 21.6 depicts this situation. DPE performs a direct search, with inherent joint optimization across multiple satellites, for the navigation solution on the signal

(b) DPE

1

1

0.8

0.8

0.6

0.6

Λ (γ)

Λ (υ)

(a) The two-step approach

0.4

0.4

0.2

0.2

0 2

0 1000 500

4000

1 2000

0

0

–1

τi – τˆi [Tc]

–2000 –2 –4000

1000 500

0

0

–500

fdi – fˆdi [Hz]

y – yˆ [m]

–1000

–500 –1000

x – xˆ [m]

Figure 21.4 Comparison of cost functions for two-step and DPE optimization problems [2]. In the two-step approach, it is a function of the synchronization parameters of the locally generated code of the i-th satellite, υ. In DPE, the cost function is parametrized by the PVT parameters gathered in γ. Source: Reproduced with permission of IEEE.

(b) DPE

1

1

0.8

0.8

0.6

0.6

Λ (γ)

Λ (υ)

(a) The two-step approach

0.4

0.4

0.2

0.2

0 2

0 1000 4000

1

–2 –4000

–2000

1000 500

0

0

–1 τi – τˆi [Tc]

500

2000

0

0

–500

fdi – fˆdi [Hz]

y – yˆ [m]

–1000 –1000

–500

x – xˆ [m]

Figure 21.5 Comparison of cost functions for two-steps and DPE optimization problems in the presence of a replica for one of the satellites [2]. The echo has 3 dB less power than the corresponding LOS. In two-steps, a strong secondary optimum appears, whereas the DPE cost function is virtually unaltered. Source: Reproduced with permission of IEEE.

DPE solution

initialize multiple candidates in the navigation domain

correlate expected signal receptions at candidate states with received signal

perform MLE on correlations

Figure 21.6 Overview of the evaluation of candidate points of DPE. The grid points represent PVT candidates initialized in the navigation domain; the color saturation of the grid points represents cost function magnitude [58].

540

21 Direct Position Estimation

correlations [56–58]. The basic steps, found in Figures 21.2 (b) and 21.6, to implement DPE on a receiver would be 1) To provide some sort of initialization, which can be provided either by using two-step schemes or by external means. 2) The second step is optimization of the cost function in Eq. (21.48). This process involves the selection of candidate points for γ, which results in some τi , f di candidate pairs for each visible satellite. The τi , f di candidate pairs are then used to generate the expected signal reception at candidate states. Next, correlations are computed between the local replicas at candidate states and the received signal, and Λ( ) is evaluated. 3) The third step is to perform MLE through optimizing the cost function. These steps are performed each time new measurements are available. The main challenge of implementing DPE is the computational load. Related work on improving DPE’s computational efficiency includes use of sparsely located navigation candidates [59], reducing the number of required navigation candidates [3, 53, 60], efficient techniques for calculating multiple correlations [61], and efficient techniques for estimating the navigation solution given the vector correlation distribution [59]. To improve the efficiency of initialization, coarse-grid search [59] and initialization using Assisted-GNSS (A-GNSS) [62] were proposed. To improve the efficiency after initialization near the main vector correlation peak, optimization over navigation subsets was proposed. One such implementation used parameter grouping by position/clock bias and velocity/ clock drift [3, 59]. It has been shown that, according to this decoupling, parameters within subsets are strongly correlated‚ while parameters across subsets are weakly correlated. The subsets can then be separately optimized. Other subset optimization implementations used parameter grouping where each parameter formed its own subset [63, 64], which can be solved algorithmically through space-alternating generalized expectation-maximization (SAGE) [53]. These subset optimization methods reduce the number of required navigation candidates and thus the overall computational load. However, they are sensitive to initialization [53], which can be addressed using stochastic optimization methods such as accelerated random search (ARS) [60]. To increase the chances of initialization near the main navigation correlation peak for subsequent DPE measurement updates, motion model filtering can be performed between DPE measurement updates [3, 65]. In this section, we present some DPE implementation techniques in detail. The remainder of this section discusses (i) subset optimization strategies, (ii) faster local replica generation and correlation through fast Fourier transforms (FFTs), (iii) CL tracking schemes, and (iv) how to implement

low duty-cycling, performing DPE updates only a fraction of the time instead of calculating it continuously.

21.4.1

Grid Optimization by Divide and Conquer

Divide and conquer [66] is an algorithmic approach adopted in many signal processing applications, which breaks down a complex problem into two or more subproblems that are easier to solve. In addition, this methodology allows the exploitation of parallel structures in hardware architectures, and makes use of concurrency and multithreading scheduling when designing under the SDR paradigm. This is one of the reasons for adopting two-step architectures in GNSS receivers: independent per-satellite channel track delay-Doppler maps, which are then fused in an LS solution as detailed in Section 21.2. In the context of DPE positioning, a similar approach can be adopted in selecting the candidate points. It might be desirable to split γ into sets of correlated parameters. One way to reduce the number of candidates is to group the navigation parameters into two subsets: position/clock bias γ 1 = p ,δt

and velocity/clock drift γ 2 = v ,δt

[3, 67].

Co-estimation of γ 1 and γ 2 reduces the number of navigation candidates from N 8c to 2N 4c, in the case of Nc candidate points for each of the eight navigation search dimensions. Estimation of γ 1 is relatively insensitive to departure from the γ 2 search center and vice versa [3]. This is because the correlation amplitude with respect to γ 1 is maintained over a relatively broad range; the same is true for the correlation amplitude with respect to γ 2. Thus, the estimation of γ 1 and γ 2 parameters can be safely decoupled γ 1 = arg max Λ γ 1 , γ 2

21 49

γ 2 = arg max Λ γ 1 , γ 2

21 50

γ1

γ2

When decoupled, the CAF’s amplitude Λi p, δt, v, δt for varying γ 1 candidates with respect to a γ 2 fixed near the γ 2 search center is given in Eq. (21.51). The normalized correlation amplitude Λi p, δt, v, δt

for varying γ 2 can-

didates with respect to a γ 1 fixed near the γ 1 search center is given in Eq. (21.52). Λi p, δt, v, δt

Λi p, δt, v, δt

≈

1−

Δτi , 0,

0 ≤ Δτi ≤ 1 otherwise 21 51

≈ sinc π Δ f di ΔT ,

21 52

where Δτi is the delay error between the candidate delay τi γ 1 and the search center. Similarly, Δ f di represents the frequency error between candidate f di γ 2 and the search center for γ 2 . Note that these ideas resemble those of DLLs and PLLs in standard receiver architectures.

21.4 Implementation Aspects ˆ δt ˆ correlations across candidates p,

width = 1 code chip

normalized amplitude

normalized amplitude

ˆ ˆ δt correlations across candidates p,

width = 1/ΔT

Δτi = 0

Figure 21.7

Δfd = 0 i

Shape and width of (left) correlation amplitude Λi p, δt, v, δt

fixed velocity/clock-drift; (right) correlation amplitude Λi p, δt, v, δt

for varying position/clock-bias candidates with respect to a

for varying velocity/clock-drift candidates with respect to a fixed

position/clock-bias [58].

21.4.2 Batch Pre-Processing of Correlations Using Fast Fourier Transforms As in two-step positioning, one can exploit the circular correlation properties of the PRN codes to speed up correlation through the FFT [27]. The correlation Λi p, cδt, v, c δt for

Normalized correlation amplitude

varying position/clock-bias candidates with respect to a fixed velocity/clock drift in Eq. (21.51) can be implemented in the frequency domain. Let us use ( ) to represent the Fourier transform operator and −1( ) the inverse Fourier transform. Then,

1.0 0.8 0.6 0.4 0.2 0.0 –300

–200 –100 0 100 200 code phase residual Δϕ (m)

300

Λi p, cδt, v, cδt =

−1

∗

x

ci p, cδt, v, cδt 21 53

Batch pre-processing using FFTs more efficiently calculates multiple correlations. The batch pre-process is a result of Eq. (21.53). To form the vector correlation, we first calculate the τ γ associated with each candidate p, cδt. We then assign the FFT results to the navigation candidates, using linear interpolation for τ γ values between FFT points. In addition, these operations can be performed in parallel for all navigation candidates. Similarly, the correlation Λi p, δt, v, δt

for varying velocity/clock-drift candidates

with respect to a fixed position/clock bias is approximated as the Fourier transform

∗

x ci p, cδt, v, c δt

.

The above computations are carried out in two parallel threads as in Figure 21.8, one for correlations and the other for the Fourier transforms.

Normalized spectrum magnitude

The expression for the CAF in Eq. (21.51) assumes successful navigation bit and carrier wipe-off of the received signal near the γ 2 search center. Likewise, the expression in Eq. (21.52) assumes successful navigation bit and code wipe-off near the γ 1 search center. The shape and width of the two CAFs, where one of the sets of parameters is fixed, is illustrated in Figure 21.7.

1.0 0.8 0.6 0.4 0.2 0.0 –300

–200 –100 0 100 200 carrier frequency residual Δf (m/sec)

300

Across N satellites for the kth receiver

Figure 21.8 Correlation amplitude with respect to code residuals (left) and magnitude of the spectral density with respect to carrier residuals across satellites (right) [68]. Source: Reproduced with permission of Institute of Navigation.

541

542

21 Direct Position Estimation

21.4.3

Filtering of DPE’s PVT Solution

The implementations considered so far operate in OL. To improve the accuracy of DPE, CL tracking of the navigation solution can be implemented, as suggested in [3, 17, 64, 69–72]. We mentioned earlier that DPE is a suitable framework to introduce a priori information about γ that one might have [73]. In the context of CL schemes, this is particularly relevant since dynamics can be exploited. A methodology for how this can be actually implemented using nonlinear filtering is described in [69]. A simpler, yet effective, alternative is to smooth DPE results using a low-pass filter. For instance, implementation with an optimal Kalman filter (KF) allows for easy incorporation of motion models and integration of information from prior measurements into the estimation process [73]. The KF has two main steps: a measurement update step and a time update step [74, 75]. Recall that, at the discrete time instant k, the observations of this KF are the estimated PVT parameters from DPE’s optimization process, which we denote by yk in the following discussion. These are noisy measurements of the true PVT, whose likelihood is assumed normally distributed as yk γk

γ k , Rk ,

21 54

where, according to Eq. (21.54), we know that Rk asymptotically reaches the FIM of the parameters of interest, − 1 γ . Therefore, the measurement update at time k is given by γ k k = I − Kk γ k k − 1 + Ky k

21 55

Σ k k = I − Kk Σ k k − 1

21 56

Kk = Σ k k − 1 Σ k k − 1 + R k

−1

,

21 57

where the state γ k k is estimated along with its covariance Σk k taking into account the new observations yk, and the predicted stated and covariance, γ k k and Σk k, respectively. In these equations‚ I represents the identity matrix. Those predictions incorporate historical information regarding previous observations. This scheme integrates prior navigation solutions into the estimation process [70]. In the time update step, the next receiver state γ k + 1 k is predicted using, for instance, a constant acceleration motion model [3, 65, 76]. This approach incorporates vehicle accelerations using a dynamic process noise model on the velocities [77–79]. Then, γ k + 1 k = Fk + 1 γ k k

21 58

Σk + 1 k = Fk + 1 Σk k FTk + 1 + Qk ,

21 59

where Σk + 1 k is the predicted state error at time k + 1, and Qk is the dynamic process noise. Fk + 1 is the propagation

matrix, which incorporates possible knowledge regarding the motion dynamics of the receiver. For instance, given that ΔT is the time in seconds between two consecutive instants k and k + 1, we can use Fk + 1 =

I4 04

Qk = F k + 1

ΔTI4 I4

21 60

0 0

0 0

0 0 0 0

0 0

0 0

0 0

0 0

0 0 0

0 0 0

0 0 0 0 0 0

0 0 σ 2v

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0 0 0 0

0 0 0

σ 2v 0 0

0 σ 2v 0

0 0 σ2

FTk + 1

δt

21 61 where I4 and 04 represent the identity and all-zero square matrices of dimension 4, respectively. The dynamic process noise model captures the intuition that it is more difficult for a vehicle’s velocity to change when its speed is large as compared to when its speed is small. Thus, vehicle acceleration, modeled as noise, is lower when the vehicle’s speed is large and higher when the vehicle’s speed is small.

21.4.4

Low Duty-Cycling

Low duty-cycling performs DPE for a fraction of the time instead of calculating constantly. Duty-cycling DPE is particularly promising to mitigate the high computation cost of DPE. Instead of computing DPE-based solutions for all integration times, some are skipped for the sake of saving computations. In other words, a DPE-based receiver can operate intermittently, which may not work so well for tracking loop-dependent conventional receivers. Research has demonstrated viable DPE operation even at quite low duty cycle rates [80]. The duty-cycled DPE receiver architecture is shown in Figure 21.9. The measurement update uses optimization over navigation parameter subsets, combines and computes batch signal replica generation and correlation using FFTs, and estimates the navigation solution. The exact computation time depends on signal sampling parameters and the number of satellites in view. During the time required to compute the DPE measurement update, we iteratively predict satellite movements, using the satellite broadcast ephemerides, and update the signal code phase and carrier Doppler frequency parameters. This DPE time update reduces the accumulation of signal tracking errors during the time in which the DPE receiver is not performing any DPE measurement update.

21.5 DPE Variants

Measurement update process

Time update process yes

Initialize over navigation subsets

20 ms snippet

Batch replica generation and correlation using FFT and linear interpolation

Correct signal state

MLE using weighted ave.

Get satellite transmit time

Correct receiver state

Increment receiver state

Correct signal state

Increment signal state

PVT

Figure 21.9

no Switch on?

Get satellite PVT

Block diagram of duty-cycled DPE receiver architecture [79]. Source: Reproduced with permission of Institute of Navigation.

20 ms ...

1s DPE time update

on

DPE measurement update PVT

PVT

on

DPE time update

DPE measurement update PVT

on

...

DPE ...

PVT

Figure 21.10 Overview of duty-cycled DPE receiver architecture with DPE measurement update and DPE time update [80]. Source: Reproduced with permission of Institute of Navigation.

An implementation with a duty-cycling factor of 2% has succeeded in providing positioning updates at 1 Hz [80]. The implementation has the following parameters, as shown in Figure 21.10: 1) Perform 1 DPE measurement update every second on a 20 ms GNSS raw signal snippet during which the GNSS receiver is “on.” 2) Perform 49 DPE time updates during the 980 ms in which the GNSS receiver is “off.”

21.5

DPE Variants

So far, we have analyzed DPE in the context of PVT estimation. This section discusses alternative uses of the DPE concept, which sometimes require additional tuning but are conceptually similar to what we have seen in previous sections. We intentionally wanted to keep this material at a basic level just to give the flavor, avoiding deep theoretical derivations and providing the main concept and references instead.

21.5.1

Direct Timing Estimation

Many GNSS-based applications do not need a full PVT solution. For example, GNSS provides timing and synchronization to critical infrastructures [81–84] such as cellular communication network, financial transactions‚ and the power grid. Such applications only require the time (i.e. clock and clock-drift) element‚ and the position information of the GNSS receivers are often known. By using the prior information available to the timingfocused receiver, the DPE search domain can be reduced to the two clock parameters in a Direct Time Estimation (DTE) problem. DTE naturally reduces the computation load challenge, while maintaining DPE’s advantage in terms of robustness [85]. The architecture of DTE is comprised of two main stages. First, a two-dimensional search space is generated with clock bias and clock-drift parameters δt and δt, respectively. A combined satellite signal replica is generated for each grid point by utilizing the known receiver and satellite three-dimensional position and velocity vectors. Then, non-coherent vector correlation is performed to obtain weights that are derived proportional to the likelihood of the point in the grid, as described in Eq. (21.47). After

543

21 Direct Position Estimation

Receiver 3D position and velocity

All satellites 3D position and velocity

Clock Bias

Across the candidates in search space

Clock Drift

Maximum likelihood clock state

)

cδt

as bi

oc k

cδ t

cδt cδt Cloc k dr ift (m /s

cδ t

cδt

(m

)

cδ t

Vector Correlation

cδ t

Incoming raw GPS signal

Correlation valve

Combined satellite signal replica

Cl

544

Figure 21.11 Diagram of the first stage of DTE, where the MLE cost function is the computed CAFs across satellites [85]. Source: Reproduced with permission of IEEE.

optimizing the ML cost function, an MLE of the clock parameters is computed tML =

δt, δt

Yaw

at that instant.

Figure 21.11 shows the first stage of DTE. Based on the predicted clock estimate, the error measurement values are computed and sent to the second stage, where a KF is in charge of computing the corrected clock bias and clockdrift parameters. This KF acts similarly as the low-pass filtering solution presented in Section 21.4.3.

21.5.2

Multi-Receiver DPE and DTE

Multi-receiver-DPE (MR-DPE) extends the DPE concept to the situation where a network of DPE-enabled receivers is available. Such multi-receiver architecture can provide performance benefits, as additional information redundancy is exploited. The receiver elements form a network to generate a unified, network-wise PVT solution. MR-DPE improves receiver robustness of the following aspects: (i) on the receiver level, MR-DPE inherits robustness from individual DPE receivers; (ii) on the network level, since the baselines among the antennas are fixed and assumed known, one can relate receivers’ measurements among them through linear transformations, providing measurement redundancy; and (iii) while each of these antennas associated with the GNSS receiver elements may have a different, incomplete sky view, they together create a more complete observation by aggregating the information these antennas respectively capture, providing geometric redundancy. As an example, Figure 21.12 depicts a potential use in the context of aircraft positioning. The measurement aggregation process takes place by fusing the different MLE cost functions of the form in Eq. (21.35) by projecting toward the centroid. In the figure, a rigid platform represented by a fixed-wing aircraft is shown with four DPE-enabled

Four manifolds are projected to and overlap at centroid

Figure 21.12 Example of aggregation of MLE cost functions. They are projected to the centroid of the network, with knowledge of antenna baselines and aircraft yaw, pitch, and roll (the latter two are not shown) [86]. Source: Reproduced with permission of Institute of Navigation.

receivers at its vertices. MR-DPE operates iteratively to estimate the network’s PVT coordinate [86]. Similarly, the multi-receiver concept has been applied to DTE as multireceiver DTE [68, 87].

21.5.3

Joint GNSS-Vision DPE

Here we briefly comment on the fusion of GNSS and camera measurements through DPE’s principle. The directpositioning concept can be applied similarly to both GNSS and vision-based positioning. It is possible to formulate the MLE for both cases. In other words, one searches for the underlying position parameters that maximize the correlation with the GNSS raw signals and camera images. In vision-based positioning, the image replicas are selected from a database of geotagged reference images. An example of a suitable database is Google Street View [89, 90], where

21.5 DPE Variants

Deep Coupling

LOS Projections

GPS DP

Feature Matching Vector Correlation

Initialization

x, y, z, cdt, x, y, z, cdt

Coor. Transform

Vision DP

Feature Matching Feature-based Homography

x, y, z

Filter x, y, z, cdt, x, y, z, cdt Time Update Measurement Update

PVT

Tracking

Figure 21.13

Block diagram describing joint GNSS-vision DPE [88]. Source: Reproduced with permission of IEEE.

the images are indexed by latitude, longitude, heading‚ and tilt. Image features, such as those obtained from the Oriented FAST and Rotated BRIEF feature extractor, can be used to match consecutive frames. By estimating the camera's translation through traditional computer vision approaches, navigation-domain measurements can be generated. These navigation-domain vision measurements are easily fused with the navigation-domain likelihood manifold of DPE, providing deep integration of the sensors [91]. The direct measurements from both GNSS and vision are then combined in a navigation filter. An example block diagram is shown in Figure 21.13. Each iteration of the joint GNSS-vision DPE begins from a prediction, provided by the navigation filter, of the current navigation

parameters. Navigation candidates may be initialized around the current navigation prediction. Constraints are used to eliminate candidates and reduce the computation load, for instance, by requiring that a road user has to be on the road. Initialization of the navigation guesses is followed by feature matching, as shown in Figure 21.14. GNSS DPE uses vector correlation to get the likelihood distribution across the navigation guesses, estimating the mean and variance. Vision DPE is unable to get a similar continuous likelihood distribution. The replica sampling in Vision DPE is discrete and depends on the reference database. In addition, vision feature matching is susceptible to spurious results. A robust Vision DPE algorithm is inspired by a combination of prior work by other researchers [92, 93]. Two rounds are involved.

Guessed candidates Perform feature matching

Vector Correlation

Feature Matching Homography

Figure 21.14 GNSS feature matching using the vector correlator (left). Vision feature matching using vision features and homography analysis (right) [88]. Source: Reproduced with permission of IEEE.

545

546

21 Direct Position Estimation

In the first round, 2D features are extracted from the reference images [94], after which feature matching is performed between the reference images and the observed image. The reference images are then ranked according to their overall feature distance to the observed image. The lower the overall feature distance, the better the match. A threshold on the overall feature distance is used to select potential reference images. In the second round, homography analysis is used to verify that the reference image and observed image are generated from a similar camera view [95–97].

Sriramya Bhamidipati for reviewing the chapter. Pau Closas has been partially supported by the National Science Foundation under Awards CNS-1815349 and ECCS-1845833.

References 1 P. Closas, C. Fernández-Prades, and J. Fernández-Rubio,

2

21.6

Conclusions

DPE is an emerging concept in the design of advanced GNSS receivers. At a glance, DPE estimates a receiver’s PVT using signals from all satellites jointly at the sample level, thus avoiding the intermediate step of computing observables. DPE-enabled receivers are known to improve metrics such as accuracy (reducing the positioning error, particularly in scenarios where conventional solutions fail, such as in urban canyons), reliability (allowing for nearly optimal operation in cases where the received signal is severely degraded), and availability (increasing the receiver sensitivity). The main drawback of DPE with respect to two-step positioning is its increased computational burden. However, researchers have begun to explore approximations, assumptions, and computing methods that reduce the limitations of this load. This chapter introduced standard GNSS signal processing and describes how DPE modifies existing architectures. Both qualitative and quantitative arguments were given in support of DPE, even providing theoretical estimation bounds. We derived the MLE of position, resulting in a cost function that shares many similarities with the popular CAF. The chapter also provided a deep discussion of practical implementation aspects as well as variants and applications in several fields. Future work includes designing more efficient methodologies for implementing DPE with less computational cost as well as principled methods to fuse heterogeneous information from several sources.

21.7

Acknowledgments

Pau Closas would like to highlight that the part of this work related to the estimation bounds is the fruit of joint works with his colleague Adrià Gusi-Amigó. Grace X. Gao would like to acknowledge that this chapter is based on a number of students’ theses, papers‚ and presentations in her research group, including by Yuting Ng, Arthur Chu, and Sriramya Bhamidipati. She is thankful to Matthew Peretic and

3

4

5

6

7 8

9

10

11

12

“Maximum likelihood estimation of position in GNSS,” IEEE Signal Processing Letters, vol. 14, no. 5, pp. 359–362, 2007. P. Closas and A. Gusi-Amigó, “Direct Position Estimation of GNSS Receivers: Analyzing main results, architectures, enhancements, and challenges,” IEEE Signal Processing Magazine, vol. 34, no. 5, pp. 72–84, 2017. L.R. Weill, “A high performance code and carrier tracking architecture for ground-based mobile GNSS receivers,” in Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, 2010, pp. 3054–3068. P. Ward, “The natural measurements of a GPS receiver,” in Proceedings of the 51st Annual Meeting of the Institute of Navigation, 1995, pp. 67–85. P.W. Ward, J.W. Betz, and C.J. Hegarty, ch. Satellite signal acquisition, tracking, and data demodulation, Understanding GPS: Principles and Applications Second Edition, Artech House, Boston, 2006, pp. 153–240. B.W. Parkinson and J.J. Spilker, Progress in Astronautics and Aeronautics: Global Positioning System, American Institute of Aeronautics and Astronautics, 1996. P. Misra and P. Enge, Global Positioning System, GangaJamuna Press, 2006. J.J. Spilker Jr, “Vector delay lock loop processing of radiolocation transmitter signals,” March 14 1995, US Patent 5,398,034. J.J. Spilker and B.W. Parkinson, Fundamentals of signal tracking theory, Progress in Astronautics and Aeronautics: Global Positioning System, American Institute of Aeronautics and Astronautics, 1996, pp. 245–328. M. Lashley and D.M. Bevly, “Vector delay/frequency lock loop implementation and analysis,” in Proceedings of the 2009 International Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2009, 2009, pp. 1073–1086. S. Bhattacharyya, “Performance and integrity analysis of the vector tracking architecture of GNSS receivers,” PhD dissertation, University of Minnesota, 2012. P.W. Ward, “Performance comparisons between FLL, PLL and a novel FLL-assisted-PLL carrier tracking loop under RF interference conditions,” in Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, 1998, pp. 783–795.

References

13 P.W. Ward and T.D. Fuchser, “Stability criteria for GNSS

14

15

16

17

18 19

20

21

22 23 24

25

26 27 28

receiver tracking loops,” Navigation, Journal of The Institute of Navigation, vol. 61, no. 4, pp. 293–309, 2014. P. Axelrad, J. Donna, and M. Mitchell, “Enhancing GNSS acquisition by combining signals from multiple channels and satellites,” in Proceedings of the 22nd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2009), 2009, pp. 2617–2628. A.M. Reuven and A.J. Weiss, “Direct position determination of cyclostationary signals,” Signal Processing, vol. 89, no. 12, pp. 2448 – 2464, 2009. [Online]. Available: http://www.sciencedirect.com/science/article/ pii/S0165168409001650 J. B.-Y. Tsui, Fundamentals of Global Positioning System Receivers: A Software Approach, vol. 173, John Wiley & Sons, 2005. P. Closas, “Bayesian Signal Processing Techniques for GNSS Receivers: From multipath mitigation to positioning,” PhD dissertation, Dept. of Signal Theory and Communications, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, June 2009. T.S. Rappaport, Wireless Communications: Principles and Practice, Prentice-Hall, 1996. F. Fontan, M. Vazquez-Castro, C. Cabado, J. Garcia, and E. Kubista, “Statistical modeling of the LMS channel,” IEEE Transactions on Vehicular Technology, vol. 50, no. 6, pp. 1549–1567, November 2001. A.V. Oppenheim, A.S. Willsky, and S.H. Nawab, Signals and Systems, vol. 2, Prentice-Hall Englewood Cliffs, NJ, vol. 6, no. 7, p. 10, 1983. M. Irsigler, J.A. Ávila Rodríguez, and G.W. Hein, “Criteria for GNSS multipath performance assessment,” in Proceedings of the ION GPS/GNSS 2005, Long Beach, CA, September 2005. W.C. Jakes, Microwave Mobile Communications, Wiley, New York, 1974. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw Hill, 1995. A. Steingass and A. Lehner, “Measuring Galileo’s multipath channel,” in Proceedings of the European Navigation Conference, ENC-GNSS 2003, Graz, Austria, April 2003. ——, “Measuring the navigation multipath channel – A statistical analysis,” in Proceedings of the ION GPS/GNSS 2004, Long Beach, CA, September 2004. E. Kaplan and C. Hegarty, Understanding GPS: Principles and Applications. Artech House, 2005. E.D. Kaplan (ed.), Understanding GPS: Principles and Applications, 2nd Ed., Artech House, 2006. K. Borre, D.M. Akos, N. Bertelsen, P. Rinder, and S.H. Jensen, A Software-Defined GPS and Galileo Receiver:

29

30

31

32 33

34

35

36

37

38

39

40 41

42

A Single-Frequency Approach, Springer Science & Business Media, 2007. S. Bancroft, “An algebraic solution of the GPS equations,” IEEE Transactions on Aerospace and Electronic Systems, vol. 21, no. 7, pp. 56–69, January 1985. J. Dampf, T. Pany, W. Bär, J. Winkel, C. Stöber, K. Fürlinger, P. Closas, and J.A. Garcia-Molina, “More than we ever dreamed possible: Processor technology for GNSS software receivers in the year 2015,” Inside GNSS, vol. 10, no. 4, pp. 62–72, 2015. J. Vilà-Valls, P. Closas, M. Navarro, and C. FernándezPrades, “Are PLLs dead? A tutorial on Kalman filter-based techniques for digital carrier synchronization,” IEEE Aerospace and Electronic Systems Magazine, vol. 32, no. 7, pp. 28–45, 2017. F.S.T. Van Diggelen, A-GPS: Assisted GPS, GNSS, and SBAS, Artech House, 2009. A.J. Weiss, “Direct position determination of narrowband radio frequency transmitters,” IEEE Signal Processing Letters, vol. 11, no. 5, pp. 513–516, 2004. A.J. Weiss and A. Amar, “Direct position determination of multiple radio signals,” EURASIP Journal on Advances in Signal Processing, vol. 2005, no. 1, p. 653549, 2005. P. Axelrad, B.K. Bradley, J. Donna, M. Mitchell, and S. Mohiuddin, “Collective detection and direct positioning using multiple GNSS satellites,” Navigation, Journal of The Institute of Navigation, vol. 58, no. 4, pp. 305–321, 2011. .A. García-Molina and J.A. Fernández-Rubio, “Collective unambiguous positioning with high-order BOC signals,” IEEE Transactions on Aerospace and Electronic Systems, vol. 55, no. 3, pp. 1461–1473, 2018. L. Li, J.W. Cheong, J. Wu, and A.G. Dempster,“ Improvement to multi-resolution collective detection in GNSS receivers,” The Journal of Navigation, vol. 67, no. 2, p. 277, 2014. L. Narula, K.P. Singh, and M.G. Petovello, “ Accelerated collective detection technique for weak GNSS signal environment,” In 2014 Ubiquitous Positioning Indoor Navigation and Location Based Service (UPINLBS), IEEE, 2014, November, pp. 81–89 F. Vincent, E. Chaumette, C. Charbonnieras, J. Israel, M. Aubault, and F. Barbiero, “Asymptotically efficient GNSS trilateration,” Signal Processing, vol. 133, pp. 270–277, 2017. T. Pany, Navigation Signal Processing for GNSS Software Receivers, Artech House, 2010. P. Closas, C. Fernandez-Prades, and J.A. Fernandez-Rubio, “A Bayesian approach to multipath mitigation in GNSS receivers,” IEEE Journal of Selected Topics in Signal Processing, vol. 3, no. 4, pp. 695–706, Aug 2009. R. Iltis and L. Mailaender, “An adaptive multiuser detector with joint amplitude and delay estimation,” IEEE Journal

547

548

21 Direct Position Estimation

43

44

45

46

47 48

49

50

51

52

53

54

55

on Selected Areas in Communications, vol. 12, no. 5, pp. 774–785, June 1994. A. Amar and A.J. Weiss, “New asymptotic results on two fundamental approaches to Mobile Terminal Location,” in Proceedings of the 3rd International Symposium on Communications, Control and Signal Processing, IEEE, March 2008, pp. 1320–1323. P. Closas, C. Fernández-Prades, and J.A. Fernández-Rubio, “Direct position estimation approach outperforms conventional two-steps positioning,” Proceedings of EUSIPCO ’09, August 2009. P. Closas, C. Fernandez-Prades, and J.A. FernandezRubio, “Cramér–Rao bound analysis of positioning approaches in GNSS receivers,” IEEE Transactions on Signal Processing, vol. 57, no. 10, pp. 3775–3786, October 2009. A. Gusi-Amigó, P. Closas, A. Mallat, and L. Vandendorpe, “Cramér-Rao bound analysis of UWB based localization approaches,” in Ultra-Wideband (ICUWB), 2014 IEEE International Conference on, 2014. ——, “Ziv-Zakai bound for direct position estimation,” Navigation, vol. 65, no. 3, pp. 463–475, Dec 2018. D. Chazan, M. Zakai, and J. Ziv, “Improved lower bounds on signal parameter estimation,” IEEE Transactions on Information Theory, vol. 21, no. 1, pp. 90–93, 1975. K. Bell, Y. Steinberg, Y. Ephraim, and H. Van Trees, “Extended Ziv-Zakai lower bound for vector parameter estimation,” Information Theory, IEEE Transactions on, vol. 43, no. 2, pp. 624 –637, March 1997. R.D.J. V. Nee, J. Siereveld, P.C. Fenton, and B.R. Townsend, “Synchronization over rapidly time-varying multi-path channels for cdma downlink receiver in timedivision mode,” IEEE Trans. on Vehicular Technology, vol. 56, no. 4, pp. 2216–2225, July 2007. J. Ziv and M. Zakai, “Some lower bounds on signal parameter estimation,” IEEE Transactions on Information Theory, vol. 15, no. 3, pp. 386–391, 1969. A. Gusi-Amigó, “Bounds on the accuracy of ultrawideband based positioning,” PhD dissertation, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, July 2015. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, Englewood Cliffs, New Jersey, USA, 1993. P. Closas, C. Fernández-Prades, and J. Fernández-Rubio, “Maximum likelihood estimation of position in GNSS,” IEEE Signal Processing Letters, vol. 14, no. 5, pp. 359–362, 2007. P. Closas, C. Fernández-Prades, A. J. Fernández, M. Wis, G. Veccione, F. Zanier, J. Garcia-Molina, and M. Crisci, “Evaluation of GNSS Direct Position Estimation in

56

57

58

59

60

61

62

63

64

65

66

Realistic Multipath Channels,” in in Proceedings of the ION GNSS 2015, Tampa, Florida (USA), September 2015. P. Closas, A. Gusi-Amigó, and J. Blanch, “Integrity measures in direct-positioning,” in Proceedings of the ION GNSS+ 2017, Portland, Oregon, September 2017. P. Closas, C. Fernández-Prades, and J. FernándezRubio, “On the maximum likelihood estimation of position,” in Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), Fort Worth, TX, 2006, pp. 1800–1810. A. Amar and A. J. Weiss, “Localization of narrowband radio emitters based on Doppler frequency shifts,” IEEE Transactions on Signal Processing, vol. 56, no. 11, pp. 5500– 5508, November 2008. Y. Ng, “Improving the robustness of GPS direct position estimation,” Master’s thesis, University of Illinois at Urbana-Champaign, 2016. B. Bradley, P. Axelrad, J. Donna, and S. Mohiuddin, “Performance analysis of collective detection of weak GPS signals,” in Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, 2010, pp. 3041–3053. P.C. Gómez, “Bayesian signal processing techniques for GNSS receivers,” PhD dissertation, Universitat Politecnica de Catalunya, 2009. J.W. Cheong, J. Wu, A.G. Dempster, and C. Rizos, “Efficient implementation of collective detection,” in IGNSS symposium, 2011, pp. 15–17. ——, “Assisted-GPS based snap-shot GPS receiver with FFT-accelerated collective detection: Time synchronisation and search space analysis,” in Proceeding of the 2012 International Technical Meeting of the Satellite Division of the Institute of Navigation, 2012. J. Liu, X. Cui, M. Lu, and Z. Feng, “A direct position tracking loop for GNSS receivers,” in Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, 2011, pp. 3634–3643. ——, “Direct position tracking loop based on linearised signal model for global navigation satellite system receivers,” IET Radar, Sonar & Navigation, vol. 7, no. 7, pp. 789–799, 2013. F. D. Nunes, J. M. S. Margal, and F. M. G. Sousa, “Lowcomplexity VDLL receiver for multi-GNSS constellations,” in Proceedings of 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC 2010), December 2010, pp. 1–8.

References

67 T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein,

68

69

70

71

72

73

74

75

76

77

78

79

Introduction to Algorithms, MIT press, Cambridge MA, 1990. P. Closas, C. Fernández-Prades, and J. FernándezRubio, “ML estimation of position in a GNSS receiver using the SAGE algorithm,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing–ICASSP ’07, vol. 3, April 2007, pp. III–1045–III–1048. JS. Bhamidipati and G.X. Gao, “ Multi-receiver GPS-based direct time estimation for PMUs,” in ION GNSS+ 2016, Portland, OR, 2016. P. Closas and C. Fernández-Prades, “Bayesian nonlinear filters for direct position estimation,” in Proceedings of IEEE Aerospace Conference, Big Sky, MT,IEEE, 2010, pp. 1–12. Y. Ng and G.X. Gao, “Mitigating jamming and meaconing attacks using direct GPS positioning,” in Proceedings of IEEE/ION PLANS 2016, Savannah, GA, IEEE/ION, 2016, pp. 1021–1026. J. Dampf, K. Frankl, and T. Pany, “Optimal particle filter weight for Bayesian direct position estimation in a GNSS receiver,” Sensors, vol. 18, no. 8, p. 2736, 2018. K. Strandjord, P. Axelrad, D. Akos, S. Mohiuddin, “Improved urban navigation with direct positioning and specular matching,” Proceedings of the 2020 International Technical Meeting of The Institute of Navigation, San Diego, California,.2020/1, pp. 787–800 T. Lin, J.T. Curran, C. O’Driscoll, and G. Lachapelle, “Implementation of a navigation domain GNSS signal tracking loop,” in Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, 2011, pp. 3644–3651. R.E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45, 1960. R. E. Kalman et al., “Contributions to the theory of optimal control,” Boletín de la Sociedad Matemática Mexicana, vol. 5, no. 2, pp. 102–119, 1960. P. Closas, C. Fernández-Prades, and J. Fernández-Rubio, “Bayesian direct position estimation,” in Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, 2008, pp. 183–190. D. Simon and T.L. Chia, “Kalman filtering with state equality constraints,” IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 1, pp. 128–136, Jan 2002. F.D. Busse, J.P. How, and J. Simpson, “Demonstration of adaptive extended Kalman filter for low-earth-orbit formation estimation using CDGPS,” Navigation,

80

81

82

83

84

85 86

87

88

89

90 91

92

93

Journal of The Institute of Navigation, vol. 50, no. 2, pp. 79–93, 2003. Mathworks. (2015, jun) State estimation using timevarying kalman filter. [Online]. Available: http:// www.mathworks.com/help/control/getstart/estimatingstates-of-time-varying-systems-using-kalmanfilters.html Y. Ng and G.X. Gao, “Computationally efficient direct position estimation via low duty-cycling,” in Proceedings of the Institute of Navigation GNSS+ conference (ION GNSS+ 2016), Portland OR, September 2016. J. Merrill, “Patriot watch vigilance safeguarding America,” in Presentation Telcordia-NIST-ATIS Workshop Synchronization Telecommun. Syst. (WSTS’12), 2012. M.G. Amin, P. Closas, A. Broumandan, and J.L. Volakis, “Vulnerabilities, threats, and authentication in satellitebased navigation systems [scanning the issue],” Proceedings of the IEEE, vol. 104, no. 6, pp. 1169–1173, June 2016. R.T. Ioannides, T. Pany, and G. Gibbons, “Known vulnerabilities of global navigation satellite systems, status, and potential mitigation techniques,” Proceedings of the IEEE, vol. 104, no. 6, pp. 1174–1194, 2016. E.G. Agency, “GNSS Market Report,” GSA, Prague, Czech Republic, Tech. Rep., May 2017. Y. Ng and G.X. Gao, “Robust GPS-based direct timing estimation for PMUs,” in Proceedings of IEEE/ION PLANS 2016, Savannah, GA, IEEE/ION, 2016, pp. 472–476. A. Chu and G.X. Gao, “ GPS multi-receiver direct position estimation for aerial applications,” IEEE Transactions on Aerospace and Electronic Systems. vol. 56, no. 1, pp. 249–262, February 2020. S. Bhamidipati and G.X. Gao, “GPS spoofer localization for PMUs using multi-receiver direct time estimation,” in ION GNSS+ 2017, Portland, OR, 2017. Y. Ng and G.X. Gao, “ Joint GPS and vision direct position estimation,” in Proceedings of IEEE/ION PLANS 2016, Savannah, GA, IEEE/ION, 2016, pp. 380–385. Google Inc. (2016, January) Google Maps. [Online], Available: https://www.google.com/maps/ Google Developers. (2016, January) Google Street View Image API. [Online],Available: https://developers.google. com/maps/documentation/streetview/ M.A. Fischler and R.C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Communications of the ACM, vol. 24, no. 6, pp. 381–395, 1981. [Online]. Available: http://doi.acm.org/ 10.1145/358669.358692 M. Salarian, A. Manavella, and R. Ansari, “Accurate localization in dense urban area using Google Street View

549

550

21 Direct Position Estimation

images,” in SAI Intelligent Systems Conference (IntelliSys), 2015, IEEE, 2015, pp. 485–490. 94 A.R. Zamir and M. Shah, “Accurate image localization based on Google Maps Street View,” in Proceedings of 11th European Conference on Computer Vision (ECCV 2010). Springer Berlin Heidelberg, 2010, pp. 255–268. 95 E. Rublee, V. Rabaud, K. Konolige, and G. Bradski, “ ORB: An efficient alternative to SIFT or SURF,” in 2011 IEEE International Conference on Computer Vision (ICCV), November 2011, pp. 2564–2571.

96 R. Hartley and A. Zisserman, Multiple View Geometry in

Computer Vision, vol. 23, no. 2, Cambridge University Press, 2005. 97 T. Sattler, B. Leibe, and L. Kobbelt, “Fast image-based localization using direct 2D-to-3D matching,” in 2011 IEEE International Conference on Computer Vision (ICCV), November 2011, pp. 667–674. 98 Z. Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004.

551

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals Gary A. McGraw1, Paul D. Groves2, and Benjamin W. Ashman3 1

Collins Aerospace, United States University College London, United Kingdom 3 National Aeronautics and Space Administration, United States 2

22.1

Introduction

GNSS signals can be blocked and reflected by nearby objects, such as buildings, walls, and vehicles. They can also be reflected by the ground and by water. These effects are the dominant source of GNSS positioning errors in dense urban environments, though they can have an impact almost anywhere. Non-line-of-sight (NLOS) reception occurs when the direct path from the transmitter to the receiver is blocked and signals are received only via a reflected path. Multipath interference occurs, as the name suggests, when a signal is received via multiple paths. This can be via the direct path and one or more reflected paths, or it can be via multiple reflected paths. Figure 22.1 illustrates this. Within the GNSS community, it is commonplace to classify NLOS reception as multipath. However, the two effects are not the same; their error characteristics are quite different. As a reflected path is always longer than the direct path, NLOS reception always results in a positive ranging error that is independent of the signal and receiver design. By contrast, the coherent nature of multipath interference can produce both positive and negative ranging errors‚ and these vary with the signal and receiver designs [1]. As their error characteristics are different, NLOS and multipath interference typically require different mitigation techniques, though some techniques are applicable to both. Antenna design and advanced receiver signal processing techniques can substantially reduce multipath errors. Unless an antenna array is used, NLOS reception has to be detected using the receiver’s ranging and carrier-power-to-noise-density ratio (C/N0) measurements

and mitigated within the positioning algorithm. Some NLOS mitigation techniques can also be used to combat severe multipath interference. Multipath interference, but not NLOS reception, can also be mitigated by comparing or combining code and carrier measurements, comparing ranging and C/N0 measurements from signals on different frequencies, and analyzing the time evolution of the ranging and C/N0 measurements. Section 22.2 describes the characteristics of reflected and diffracted signals and how they produce NLOS and multipath errors. Section 22.3 describes how multipath errors can be reduced using advanced receiver design and signal processing techniques, including antenna design considerations, correlation signal processing‚ and adaptive antenna array processing. Section 22.4 covers carrier smoothing of code measurements, which is a technique for mitigating both noise and multipath. Section 22.5 describes real-time navigation-processor-based NLOS and multipath mitigation techniques, including C/N0-based detection and weighting, outlier detection, and aiding from other sensors. Section 22.6 then describes multipath mitigation techniques for post-processed high-precision positioning that work by analyzing time series of GNSS measurement data. Finally, Section 22.7 describes three-dimensional-mapping-aided (3DMA) GNSS. This improves real-time positioning in dense urban environments by using 3D mapping to predict which signals are NLOS at which locations. This can be used to enhance conventional ranging-based positioning and to implement shadow matching, a complementary GNSS positioning technique that determines position by comparing predicted and measured C/N0 from several satellites.

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c22.3d 551

15/12/2020 6:30:03 PM

552

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

Non-line-of-sight Reception

Multipath Interference

Signal reflected by a building

Direct signal from satellite

User

Signal reflected by a building

Direct signal is blocked

User Signal reflected off the ground

Figure 22.1

Multipath interference and NLOS reception.

22.2 Characteristics of Reflected Signals, NLOS Reception, and Multipath Errors 22.2.1

Multipath/NLOS Signal Characteristics

For land applications, most GNSS signal reflections occur within the surrounding environment, such as the ground, buildings, vehicles, or trees. For air, sea, and space applications, reflections off the host-vehicle body are more common. Low-elevation-angle signals are more likely than high-elevation-angle signals to be received via reflections by vertical surfaces. Where the reflecting surface is rough compared to the signal wavelength (~0.2 m for GNSS), scattering occurs, resulting in weak signals being reflected in many different directions. Within a GNSS receiver, scattered signals typically manifest as additional noise. Where the reflecting surface is smooth and of sufficient size, specular reflection occurs whereby a strong signal is reflected at an angle equal and opposite to the angle of incidence of the direct signal at the reflecting surface. GNSS signals are right-hand circularly polarized (RHCP). Specular reflection from a surface at normal incidence results in a left-hand circularly polarized (LHCP) reflected signal. At other angles of incidence, the polarization is mixed. As the angle of incidence increases, the LHCP component of the reflected signal decreases, and the RHCP component increases. At Brewster’s angle, the two components are equal, while at larger angles, the RHCP component dominates. The value of Brewster’s angle depends on the frequency of the signal and the properties of the reflecting surface. For L-Band GNSS signal (~1.5 GHz), it is around 89 for metallic surfaces, 85 for sea water‚ and around 70 for soil [2, 3]. Reflected signals are always delayed with respect to direct signals and have a lower amplitude (unless the direct

c22.3d 552

signals are blocked or attenuated). In cases of NLOS reception, the ranging errors are potentially unbounded and always positive. Thus, errors of several kilometers occasionally occur when a signal is reflected by a distant tall building. The range-rate errors can result in the user’s apparent direction of motion being reflected in the object reflecting the signal. Consequently, reflectors perpendicular to the direction of travel can produce much larger velocity errors than those parallel to the trajectory. Also, for a reflector close to a moving user antenna, the pseudorange error may be small, but the range-rate error large. The signal path between satellite and user is not a simple ray, but is instead determined by Fresnel zones. The first Fresnel zone is defined as the region about a signal’s propagation path where the phase difference in path length is less than half a cycle and is the radius of the effective signal footprint where the signal interacts with an object in its path. For reflection geometries where the transmitter is quite distant from both the receive antenna and the reflecting surface, as is the case with GNSS signals, the first Fresnel zone can be approximated as rλL, where r is the distance of the object from the user antenna and λL is the carrier wavelength [4]. Irregularities in the object on this scale will therefore affect the properties of the reflected or diffracted signal. Where a signal is partially blocked by an obstacle, diffraction can occur. The part of the signal interacting with the object interferes with the part passing the object by re-radiating energy in different directions and with different phase shifts, bending the path of the signal and producing alternating bands of constructive and destructive interference. The difference between the maximum and minimum levels of this diffraction pattern reduces as the angle through which the signal bends to pass around the obstacle increases, with usable GNSS signals receivable at deflections of up to 5 [5]. Diffracted signals are also delayed,

15/12/2020 6:30:03 PM

22.2 Characteristics of Reflected Signals, NLOS Reception, and Multipath Errors

but typically only by decimeters, as the strongest scattering occurs along paths that only deviate slightly from the direct path. At the receiver, each reflected signal may be described by a relative amplitude, αi, range lag, Δi, and carrier phase offset, ϕi, with respect to the direct signal (or the strongest signal if no direct signal is received). There is also a carrier frequency offset, δfi, which is larger when the user is moving with respect to the reflecting surface [4]. The relative amplitude of the i-th reflected signal is given by αi =

Gi Ri k i G0 R0 k 0

22 1

where Gi and G0 are the antenna gains in the directions of the i-th and strongest signals, respectively, Ri and R0 are the reflection coefficients, and ki and k0 are the path attenuation coefficients. The path attenuation coefficients are approximately 1 unless one of the signals has been attenuated by passing through partially absorbing materials, such as foliage. When the strongest signal is the direct signal, R0 = 1. For reflected signals, the reflection coefficient depends on the properties of the reflecting surface. Calm water, metal, and metallized glass can produce particularly strong specular reflections with reflection coefficients of 0.5–0.7. Brick, stone‚ and concrete typically have lower reflection coefficients. Note that rainwater enhances the reflectivity of other surfaces, including the ground, walls‚ and foliage. The antenna gain is a function of the signal’s angle of incidence at the antenna and of its polarization. In practice,

553

there can also be variation in the gain with azimuth. A typical GNSS antenna has a gain of 1.6–2.5 (2–4 dB) for signals at normal incidence (i.e. at the antenna zenith). This drops as the angle of incidence increases and is generally less than 1 for angles of incidence greater than 75 . For a horizontally mounted antenna, a 75 incidence angle corresponds to a satellite signal at a 15 elevation angle. Placing the antenna on a ground plane significantly attenuates signals from below the plane of the antenna, reducing the impact of ground reflections. Fixed-site applications often use special designs, such as choke ring antennas that attenuate low-elevation (i.e. high-incidence) signals. GNSS antennas are often designed to have higher gain for RHCP signals. At normal incidence to an RHCP planar antenna, the gain for LHCP signals is about a factor of 10 (10 dB) less than the RHCP gain. The polarization discrimination drops as the angle of incidence increases such that the LHCP and RHCP gains are the same for signals incident parallel to the plane of the antenna. An RHCP GNSS antenna is effectively linearly polarized for signals from the side. Cell phone antennas, conversely, are usually linearly polarized to minimize size. These antennas offer no polarization discrimination at all, so smartphone receivers are more susceptible to both multipath interference and NLOS reception. Furthermore, signals with lines of sight along the axis of a dipole antenna are significantly attenuated, which can sometimes result in a reflected signal being stronger than the direct counterpart. The path delay is the additional distance traveled by a reflected signal compared to the direct path from the satellite to the receiver. Figure 22.2 shows the signal paths of direct,

Signal reflected by a building Direct signal from satellite a b

h

g e User

θ

Signal reflected off the ground

d

Figure 22.2 Direct, building-reflected, and ground-reflected signal paths in a multipath interference scenario.

c22.3d 553

15/12/2020 6:30:05 PM

554

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

building-reflected, and ground-reflected signals. For the building-reflected signal, the range lag is Δi = a + b, while for the ground-reflected signal it is Δi = e − g. It is also useful to define the path delay in code chips, δi = Δi/λC, where λC is the code chip length. The phase offset is given by [6] ϕi =

2πΔi + ϕRi MOD2π λL

22 2

where λL is the carrier wavelength, the MOD operator gives the remainder from division by 2π, and ϕRi is the phase shift on reflection, which is π radians for a totally flat specular reflector at an angle of incidence less than Brewster’s angle. The frequency offset from the direct signal carrier frequency is [6] δfi =

1 ∂ϕi ∂ Δi ϕ = + Ri 2π ∂t ∂t λL 2π

2 ∂d 2d ∂θ − cos θ sin θ λL ∂t λL dt

22 3

22 4

In the case of a ground-reflected signal, the range lag is Δi = 2h sin θ for antenna height h, and the resulting multipath fading frequency is δfi =

2 ∂h + sin θ λL ∂t

2h ∂θ cos θ λL ∂t

22 5

Thus, the multipath fading frequency is a function of the distance from the reflecting surface (i.e. d or h), along with the rate of change of the distance. In a case experiencing both types of multipath, as in Figure 22.2, the relative influence of d and h on the composite fading frequency is inversely proportional to their relative magnitudes – for a more extensive treatment, see [7]. Although this is a simplified scenario, some useful conclusions can be drawn. For a stationary antenna with ground reflections, for example, if h is 1 meter and ∂θ/∂t is approximately 180 /6 hours (~0.15 mrad/s), then the multipath fading frequency at low elevation angles is about 1.5 mHz. However, if the antenna is moving perpendicular to a reflecting wall at 1 m/s, such as a car backing out of a parking space, 2(∂d/∂t)/λL is on the order of 10 Hz. At a rate of perpendicular motion of only 10 m/s, δfi measures tens of hertz. Fading frequencies much greater than 10 Hz would typically exceed the carrier tracking loop bandwidth, appearing more as noise than an error source correlated with the geometry of the antenna environment. For

c22.3d 554

22.2.2

Receiver Signal Modeling

The total received GNSS signal after the antenna can be written as [6, 8, 9] n

αi C t − t0 −Δi c D t −t0 −Δi c

r t = 2P

In the case of a building-reflected signal, the range lag is Δi = 2d cos θ for satellite elevation θ and distance from the reflecting wall d. The resulting multipath fading frequency is δfi =

vehicles at highway speeds, multipath from stationary objects is usually insignificant, but in stop-and-go traffic, such multipath may be a problem. Multipath is much more of a concern when the reflector is stationary with respect to the antenna, as in the case of fixed terrestrial installations or on spacecraft or aircraft when structures on the vehicle are present near the antenna.

i=0

× exp j 2π fL + fD + δfi t − t0 −Δi c + ϕi

+w t 22 6

where P is the signal power, n is the number of reflected signals, C( ) is the pseudorandom noise (PRN) spreading code, D( ) is the downlink data, t0 is the propagation delay for the direct signal, c is the speed of light, fL is the carrier frequency, fD is the Doppler shift, ϕ0 is the carrier phase of the direct signal component, and w(t) is bandlimited white Gaussian noise (WGN). In a typical receiver, there is usually a mixing operation to an intermediate frequency (IF), but we will assume a direct conversion to baseband for modeling purposes. In addition, from this point on, the navigation data in Eq. (22.6) is omitted since it generally has little impact on multipath error. In an idealized basic GNSS receiver, illustrated in Figure 22.3, incoming signals are converted to baseband with the in-phase and quadra-phase numerically controlled oscillator (NCO) signals, sNCO(t), and then correlated with early, prompt‚ and late replica codes, sE, sP, and sL, respectively: sNCO t = exp − j 2π

fL + fD t + φ

sP t = C t − t 0 , sE t = C t + dT C − t0 , sL t = C t − dT C − t0

22 7 where d is the early-prompt and prompt-late correlator spacing in units of chips, and t 0, f D, and φ are estimated quantities. The correlation process is assumed to include an automatic gain control (AGC) normalization by noise power and the coherent pre-detection integration interval, TPDI. In the presence of multipath interference where the composite signal is given by Eq. (22.6), the accumulated correlator outputs become [6, 8–10]

15/12/2020 6:30:07 PM

22.2 Characteristics of Reflected Signals, NLOS Reception, and Multipath Errors

555

Carrier NCO SNCO Prompt 1

X

IP + jQP

TPDI dt

n0TPDI

0

Carrier Phase Error Detector

εφ

Carrier Phase Measurement

Carrier Tracking Loop

φ

SP

r(t)

TPDI

1

X

X

Received Signal

IE + jQE

0

Code Delay Error Detector

SE Late X

TPDI dt

n0TPDI

SE SL

dt

n0TPDI

1

SP

Reference Signal Generation

Early

0

ερ

Delay Locked Loop

ρ Pseudorange Measurement

IL + jQL

SL

Figure 22.3 Receiver signal processing block diagram.

n

IE =

αi R τ − δi T C + dT C sinc π δf + δ f i T PDI cos δφ + ϕi + wIE

2 c n0 T PDI i=0 n

IP =

αi R τ − δi T C sinc π δf + δ f i T PDI cos δφ + ϕi + wIE

2 c n0 T PDI i=0 n

IL =

αi R τ − δi T C − dT C sinc π δf + δ f i T PDI cos δφ + ϕi + wIL

2 c n0 T PDI i=0 n

QE =

(22.8) αi R τ − δi T C + dT C sinc π δf + δ f i T PDI sin δφ + ϕi + wQE

2 c n0 T PDI i=0 n

QP =

αi R τ − δi T C sinc π δf + δ f i T PDI sin δφ + ϕi + wQP

2 c n0 T PDI i=0 n

QL =

αi R τ − δi T C − dT C sinc π δf + δ f i T c sin δφ + ϕi + wQL

2 c n0 T PDI i=0

where I and Q denote in-phase and quadra-phase; E, P, and L denote early, prompt‚ and late; c/n0 is the carrier-power-tonoise-density ratio (non-decibel form); R( ) is the autocorrelation function of the PRN sequence; τ = t 0 − t 0 is the code tracking error in units of seconds; δf is the carrier frequency tracking error; δφ is the carrier phase tracking error; and without loss of generality‚ it is assumed that the AGC normalizes the I/Q noise terms wIE, wIP, wIL, wQE, wQP, and wQL to have zero mean and unit variance. Note that sinc θ =

sin θ θ, 1,

θ

0

θ=0

22 9

See Chapters 14 and 15 of this volume, and [6, 8–11] or [12] for further details of GNSS receiver signal processing. For an ideal PRN code, the autocorrelation function is

c22.3d 555

R τ = E C t C t−τ

=

1 − τ TC , 0,

τ < TC τ ≥ TC 22 10

In subsequent sections, we will also make use of the early-minus-late (EML) delay lock detector (DLD) function: DEML τ =

1 R τ + dT C − R τ − dT C 2

22 11

The factor of half yields unity slope near the origin for the infinite bandwidth case, giving an accurate measurement of the tracking error.

15/12/2020 6:30:07 PM

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

22.2.3

Code Multipath Error

The effect of multipath on the code pseudorange measurements is principally a function of how multipath manifests itself in the code delay error detector in Figure 22.3. Two common delay error detectors, that are power- and phase-insensitive approximations of Eq. (22.11), include the early-power minus late-power discriminator: εELP =

IE 2 + QE2 − IL2 + QL2 2 IP2 + QP2

22 12

and the dot product detector: IDEML IP − QDEML QP , IP2 + QP2 IDEML = IE − IL 2, QDEML = QE − QL 2

εD =

22 13 Figure 22.4(a) shows the direct-signal, reflected-signal, and combined code autocorrelation functions for an ideal biphase shift key (BPSK) GNSS signal subject to a single interfering signal with a relative amplitude αm = 0.4, a path delay in code chips δm = 0.125 code chips, and phase offsets, ϕm, of 0 and 180 . The correlator spacing is d = 0.25 chips. The plots are constructed using a normalized time offset τ = τ T C to make the results independent of the PRN chipping rate. The effect of pre-correlation bandlimiting on the shape of the correlation function is also neglected in this diagram. It can be seen that the multipath interference distorts the shape of the correlation function. A conventional code tracking loop works by adjusting the phase of the

(a)

Nominal Multipath MP In-Phase MP Out-of-Phase

Correlation Function

1.2 1

d = 0.25 chip α = 0.4 δ = 0.125 chip

0.6 0.4 Prompt

0 –0.2

Late

Early

–1

–0.5

0 Code Offest (chips)

22 14

The pseudorange error due to multipath is obtained from the solution of Eq. (22.14) as δρM = τT C. For example, for a short multipath delay such that τ − δ1 < d, Eq. (22.14) yields δρM =

− α1 cos ϕ1 − α1 cos ϕ1 δ1 T C = Δ1 1 − α1 cos ϕ1 1 − α1 cos ϕ1 22 15

In this case, the pseudorange error can be seen to be proportional to the multipath delay and amplitude. Upper and

EML Detector function with Multipath

0.4

0.8

0.2

DEML τ − α1 DEML τ − δ1 cos ϕ1 = 0

(b)

Correlation function with Multipath

1.4

receiver-generated code so that the signal powers in the early and late correlation channels are equal. Therefore, if the code autocorrelation function is asymmetric due to multipath interference, there will be a code-tracking error and, consequently, an error in the resulting pseudorange measurement. Figure 22.4(b) shows the EML detector functions as in Eq. (22.11) corresponding to the case in Figure 22.4 (a). It can be seen that the zero crossings for the directplus-multipath cases are biased from the nominal case. Assuming that the multipath fading frequency is within the delay-locked loop (DLL) code tracking bandwidth, determining the code multipath error involves computing where the delay error detector ερ = 0, In general this is best done with numerical methods, that is, computing Eq. (22.12) or (22.13) with the direct and multipath signal components. However, an analytical solution can be readily obtained for the case of infinite bandwidth and a single interfering signal. For the dot product detector Eq. (22.13), this can be done by solving

Nominal Delay Detector Output (Chips)

556

0.3

MP In-Phase MP Out-of-Phase

0.2 0.1 0 –0.1 –0.2

d = 0.25 chip α = 0.4 δ = 0.125 chip

–0.3 0.5

1

–0.4

–1

–0.5

0

0.5

1

Code Offest (chips)

Figure 22.4 (a) Correlation function and (b) delay-detector function of a BPSK GNSS signal subject to constructive and destructive multipath interference (d = 0.25 chips; α1 = 0.4; δ1 = 0.125 chips; pre-correlation bandlimiting is neglected).

c22.3d 556

15/12/2020 6:30:07 PM

22.2 Characteristics of Reflected Signals, NLOS Reception, and Multipath Errors

MP Error Envelopes, a1 = 0.4, d = ¼ chip

PR Error (Chips)

0.1

a1d

Error Bnd MP Bias

0.05

(1 + a1)d

1– (1 – a1)d

1+d

0 (1 – a1)d

1– (1 + am)d

–0.05

–a1d

–0.1 0

0.5

1

1.5

Multipath Delay (Chips)

Figure 22.5 Multipath error envelopes and multipath bias for a BPSK signal and EML tracking for a single multipath signal. Precorrelation bandlimiting is neglected.

lower error bounds for the dot product detector can be obtained by solving Eq. (22.14) for ϕ1 = 0 or π. The computed bounds for BPSK code modulation are indicated in Figure 22.5. The plot also shows the errors for the specific correlator spacing in Figure 22.4(b). Also shown in Figure 22.5 is a plot of the multipath bias, which was computed numerically by averaging the result of Eq. (22.14) over −π < ϕ1 ≤ π for each value of δ1. As seen in Figure 22.5, the maximum absolute multipath error is α1d, so a narrower correlator spacing often leads to a smaller tracking error. This is one of the benefits of narrow

(a)

correlator receiver designs [9]. For an ideal PRN code, the multipath error is zero if δ1 > 1 + d; however‚ for codes with non-negligible autocorrelation side peaks‚ a small residual error is possible [4, 13]. The code multipath error at any given instance will lie between the bounds shown in Figure 22.5 and will oscillate at a frequency determined by the rate of change in the direct and reflected signal geometry as discussed above. As the multipath fading frequency increases beyond the carrier tracking loop capability, the code multipath error will converge to the bias level shown in Figure 22.5. Higher-chipping-rate signals are less susceptible to multipath interference than low-chipping-rate signals as the range lag, Δ, must be smaller for the reflected signal to affect the correlation peak. Figure 22.6(a) compares the code multipath error envelopes for three different modulation types: BPSK(1), BPSK(10), and binary offset carrier BOC(1,1), assuming infinite bandwidth. It can be seen that the BPSK(10) signal has much better resistance to longer delay multipath. However in many high-accuracy applications, it is the short-delay multipath – with path delay less than 0.1 BPSK(1) chip (29.3 m for C/A code) – that is the dominant error source, and all the code types have similar errors. Real GNSS receivers are affected by pre-correlation filtering, which is necessary to eliminate out-of-band interference and bandlimit the signal spectrum prior to sampling. For high-chipping-rate signals, the bandlimiting at the transmitter is also significant. Figure 22.6(b) shows the corresponding simulated error envelopes for the signals in Figure 22.6(a) with the code signals filtered by a five-pole

(b)

MP Error Envelopes, a = 0.2, d = 1/20 BPSK(1) chip 3 BPSK(1) BPSK(10) BOC(1,1)

BPSK(1) BPSK(10) BOC(1,1)

2

1

PR Error (m)

PR Error (m)

MP Error Envelopes, a = 0.2, d = 1/20 BPSK(1) chip

3

2

0

1 0

–1

–1

–2

–2

–3

557

–3 0

0.2

0.4

0.6

0.8

Multipath Delay, BPSK(1)-Chips

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

Multipath Delay, BPSK(1)-Chips

Figure 22.6 Code multipath error envelopes for different code types: (a) infinite bandwidth, (b) filtered with 10 MHz low-pass filter.

c22.3d 557

15/12/2020 6:30:08 PM

558

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

10 MHz low-pass filter (corresponding to a 20 MHz bandpass filter in the receiver front-end) and the dot product detector Eq. (22.13). The peak multipath errors are actually slightly reduced from the infinite bandwidth case, but the broadening of the correlation function extends the error bounds, which can be observed in Figure 22.6 for BPSK (10). Bandlimiting rounds the correlation function, which reduces the benefit of narrowing the correlator spacing, as this causes the slope of the delay error detector to decrease. Bandlimiting also reduces the effectiveness of the receiver signal-processing-based multipath mitigation techniques described in Section 22.3.2.

22.2.4

Carrier Multipath Error

In most GNSS receivers, carrier tracking relies on a phase tracking error measurement from the prompt correlator signal. The carrier tracking loop attempts to drive this tracking error to zero. For a single reflected signal, the carrier phase error can be determined using a simple signal phasor model as depicted in Figure 22.7, yielding δφM = arctan

α1 R τ − δ1 sin ϕ1 R τ + α1 R τ − δ1 cos ϕ1 22 16

The peak carrier phase error can be derived from Eq. (22.16), which occurs when cos ϕ1 = − α1 R τ − δ1 R τ : δφMax = arctan

α 1 R τ − δ1 R τ 2 − α21 R τ − δ1

22 17

2

Unlike the code error, the worst-case carrier phase error occurs when δ1 = 0 and for α1 < 1 the carrier phase error does not exceed 90 , corresponding to 4.8 cm at the L1 carrier frequency. Similar to what was done for code multipath, error bounds can be computed from Eq. (22.16). The results for α1 = 0.2 are shown in Figure 22.8(a) for Composite Signal Phasor

Multipath Signal Phasor ϕ1

δφ1 Direct Signal Phasor

− R(τ)

−

α1R(τ – δ1)

Figure 22.7 Depiction of a carrier phase multipath error for a single reflected path. The relative phase of the multipath signal with the direct path dictates the measured carrier phase error.

c22.3d 558

the infinite bandwidth case and Figure 22.8(b) for a filtered case. As in the case of code multipath, the actual errors will oscillate between these extremes.

22.3 Receiver-Based Multipath Mitigation Mitigation of multipath in GNSS signals can be accomplished throughout the receiver signal processing chain, including the antenna. This section covers receiver multipath mitigation techniques that are hosted in the receiver up to the point of code and carrier measurement generation. Note that none of these techniques directly mitigate NLOS reception errors. Measurement-domain mitigation techniques are discussed in Sections 22.4 and 22.5.

22.3.1

Antenna Design Techniques

Attenuating multipath interference through antenna design techniques can be highly effective in many applications. Two general approaches are discussed here: (i) Enhancement of desired-to-undesired signal levels in fixed antenna response characteristics and (ii) Taking advantage of polarization diversity in the antenna to generate measurements of multipath parameters. 22.3.1.1

Desired/Undesired Signal Component Optimization

Attenuating multipath interference prior to entering receiver signal processing is highly desirable when this is possible. Primary examples where multipath mitigation drives antenna design are fixed-site, survey, aircraft‚ and other vehicular applications where the multipath generally arrives below the receiver mask angle. Figure 22.9 illustrates an idealized antenna response wherein gain in the direction of the satellite is enhanced and gain in the direction of multipath is attenuated. As discussed in detail in Chapter 26, enhancement of the desired/undesired signal ratio can be accomplished by a variety of design elements, including ground planes, choke ring assemblies‚ and spiral antenna elements. These multipath-mitigating antenna design features tend to increase the size of the antenna, limiting their application. An extreme example is the integrated multipath limiting array (IMLA) for the Ground Based Augmentation System (GBAS) [14], which is a special-purpose fixed-site design that approximates the ideal fixed antenna pattern by combining two separate antenna structures: (i) The multipath limiting antenna, which consists of a vertical array of dipole elements in a manner that creates a sharp cutoff in the gain pattern below 5 and provides high gain up to a 35 elevation angle; and (ii) a high zenith antenna, which

15/12/2020 6:30:11 PM

22.3 Receiver-Based Multipath Mitigation

MP Phase Error Envelope, a = 0.2

(a) 0.04

0.04 BPSK(1) BPSK(10) BOC(1,1)

0.03

MP Phase Error Envelope, a = 0.2 BPSK(1) BPSK(10) BOC(1,1)

0.03

0.02

Phase Error (Cycles)

Phase Error (Cycles)

(b)

0.01 0 –0.01 –0.02 –0.03

559

0.02 0.01 0 –0.01 –0.02 –0.03

–0.04 0

0.2

0.4

0.6

0.8

1

1.2

–0.04 0

0.2

0.4

0.6

0.8

1

1.2

Multipath Delay, BPSK(1)-Chips

Multipath Delay, BPSK(1)-Chips

Figure 22.8 Carrier multipath error envelopes for different code types: (a) infinite bandwidth, (b) filtered with 10 MHz low-pass filter.

Direct Signal Ground Bounce Signal

Direct Signal Gain

Antenna

Elev Cutoff Multipath Signal Gain

Ground Plane

Figure 22.9 Illustration of an idealized antenna pattern where the direct signal gain is enhanced and the multipath interference is attenuated.

provides for satellite tracking above 35 and more than 30 dB of attenuation of ground multipath reflections. The IMLA is more than a meter high and is typically installed an additional meter or more above the ground. For many applications, such as handheld devices, the antenna must be small and the device orientation can be almost arbitrary, so it is essentially impossible to include multipath limiting features; hence‚ other multipath mitigation techniques must be pursued. 22.3.1.2

Polarization Diversity Reception

As discussed in Section 22.1, transmitted GNSS signals are RHCP. In general, this circular polarization is lost upon reflection, but the resulting elliptically polarized signal is mostly LHCP if the grazing angle is greater than Brewster’s angle (i.e. the angle of incidence is sufficiently small). Higher-performance GNSS antennas are typically tuned to

c22.3d 559

receive RHCP signals, thereby already providing some resistance to multipath, although RHCP selectivity falls off at low elevation angles. Further improvement can be achieved, however, by employing an LHCP antenna to preferentially receive reflected signals and incorporate this additional information. Multipath mitigation techniques in this class can be categorized as measurement weighting, range domain correction, tracking domain correction, and adaptive antenna array processing. Measurement weighting and antenna array techniques are covered in Sections 22.5.1 and 22.3.4, respectively. Tracking domain correction has been shown in simulations [15, 16], but relies on a prohibitively detailed knowledge of the antenna gain patterns and the direction of the reflected signal arrival relative to the antennas [17]. Range domain correction is discussed briefly here. Pseudorange, carrier phase, and C/N0 measurements can be made from both polarizations. Estimation of multipath using dual-polarization techniques relies on differences in the behavior of direct and reflected signals under the two antenna polarizations. Under certain conditions, the multipath parameters αi, Δi, and ϕi can be estimated from the RHCP and LHCP measurements and then used to estimate the code and carrier errors, δρM and δφM. These error estimates can in turn be used to correct range measurements supplied to the navigation processor. Pseudorange and carrier phase errors are the result of the relative delay and amplitude of reflected signals, as indicated in Eqs. (22.14) and (22.16), respectively. However, these errors also depend on the direct/reflected signal mix produced by the polarization of the reflected signal and the cross-polarization discrimination of the antenna. Assuming good polarization reversal at reflection (i.e. reflected signals are LHCP), the pseudorange error due to

15/12/2020 6:30:12 PM

560

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

a single short-delay reflected signal in Eq. (22.15) can be expanded as GL α1 cos ϕ1 GR δρM = Δ1 GL α1 cos ϕ1 1− GR −

22 18

where the cross-polarization discrimination of the antenna – the ratio of the LHCP and RHCP gains, GL and GR, respectively [18] – has been separated from the relative amplitude defined in Eq. (22.1), such that αi = GR GL αi. For a very good LHCP antenna, GL/GR is large and in the limit δρM approaches Δ1, the multipath relative delay. In this case of good isolation, the difference between the measured LHCP and RHCP pseudoranges is approximately the geometric additional path length of the reflected signal relative to the direct signal: ρLHCP − ρRHCP = ρ0 + Δ1 − ρ0 + δρM = Δ1 +

α1 cos ϕ1 Δ1 1 − α1 cos ϕ1

≈Δ1 , for α1 δzmax 22 83

where σ ρj is proportional to the error standard deviation of the j-th pseudorange measurement; the weighting schemes described in Section 22.5.1 may be used. The MSS with the lowest cost function, Ci, and its associated CS then form the set of measurements, zf, used to compute the final position and timings solution using ra+ + δR

=

ra−

−

δR

+

Hf

T

Wρf H f

−1

Hf

T

Wρf z f − z

f−

22 84 where Hf are the rows of the measurement matrix, Wρf the rows and columns of the weighting matrix, and z f − the set of predicted pseudoranges corresponding to the final measurement set. They are computed using Eqs. (22.73), (22.74), and (22.71), respectively. It is not necessary to test all possible MSSs as there will typically be more than one combination of MSS and CS that form the final measurement selection. Instead, the random sample consensus (RANSAC) technique may be used [63]. This randomly generates MSSs until a sufficient number have been generated for the probability that none of the MSSs are outlier free to have dropped below a predetermined significance level [62]. Another approach based on applying chi-square tests to different measurement combinations is described in [64].

22.5.3

Using a Filtered Navigation Solution

As discussed in Section 22.4, carrier smoothing of code pseudoranges can provide substantial attenuation of code multipath. Carrier smoothing is performed separately for measurements from each satellite, producing a set of smoothed pseudorange measurements which are then processed in the same way as raw pseudoranges. Thus, signal weighting and consistency checking can be applied as

15/12/2020 6:30:20 PM

22.5 Real-Time Navigation Processor-Based NLOS and Multipath Mitigation

described in Sections 22.5.1 and 22.5.2, respectively. Therefore, while carrier smoothing does not directly mitigate NLOS reception errors – which affect the code and carrier measurements in the same way – the reduction in pseudorange noise does aid in detecting NLOS reception. Instead of filtering measurements in the range domain, separately for each satellite, filtering can also be accomplished in the position domain, as part of the navigation solution. This is done by replacing the weighted leastsquares navigation solution in Eq. (22.70) with an extended Kalman filter (EKF) that maintains a continuous position, velocity‚ and time (PVT) solution with an associated error covariance. This is predicted forward in time, using the velocity solution to predict the change in position, and the receiver clock drift to predict the change in clock offset. New GNSS pseudorange and pseudorange rate (Doppler) measurements are then used to correct the predicted PVT solution, weighted according to the relative error covariance of the measurements and the predicted solution. Further details are presented in [6] and in Chapter 46. Independent signal weighting to reduce the impact of multipath interference and NLOS reception can be implemented in an EKF using a similar approach as that described in Section 22.5.1. However, there are some differences. A measurement noise covariance matrix is used instead of a weighting matrix (noting that one is the inverse of the other). This represents only errors that vary rapidly with time, including multipath and NLOS reception where the receiver is moving. Unlike a weighting matrix, a measurement noise covariance matrix must also be correctly scaled to ensure optimal weighting of old and new information within the filter [6]. The other main difference is that there are carrier-derived pseudorange rate measurements to weight as well as the pseudoranges; carrier-phasederived measurements may also be used, where available. Weighting should be performed under the assumption that all measurements from a given satellite are affected when multipath interference and/or NLOS reception is present. Consistency checking can also be performed as described in Section 22.5.2, with those measurements that pass the consistency-checking process then input to the EKF. All measurements from the same satellite should be accepted or rejected together as propagation paths for different frequency components are highly correlated and are likely also corrupted, even if the errors have not yet been detected. However, an EKF also enables measurements to be compared for consistency with the navigation solution predicted from previous epochs. This is known as innovation filtering. The measurement innovation vector of an EKF is [6] δzk− = zk − h xk−

c22.3d 577

22 85

577

where zk is the set of measurements at epoch k; xk− is the set of state estimates (typically position, velocity, and time) at epoch k, predicted forward from the previous epoch; and h is a nonlinear measurement function that expresses the measurements as a function of the states. The measurement vector will typically comprise pseudoranges and pseudorange rates (or carrier phase delta ranges). − The covariance of the innovations, Cδz,k , is a step in the computation of the KF gain, and comprises the sum of the measurement noise covariance and the error covariance of the state estimates transformed into the measurement space: − = Hk Pk− HTk + Rk Cδz,k

22 86

where Pk− is the error covariance matrix of the predicted state estimates; Hk is the measurement matrix, comprising the Jacobian matrix of partial derivatives of each measurement with respect to each state; and Rk is the measurement noise covariance matrix. The normalized innovation for the i-th scalar measurement is given by − = δzk,i

− δzk,i − Cδz,k,i,i

22 87

Outlying measurements can then be detected by − with a threshold. A higher threshold comparing each δzk,i minimizes the false alarm rate, while a lower threshold minimizes the missed detection rate. If two thresholds are used, measurements above the higher threshold can be rejected while measurements falling between the two thresholds are de-weighted. Test statistics can also be computed from a sequence of normalized measurement innovations, increasing sensitivity at the expense of response time [6]. Examining a sequence of innovations also enables NLOS reception and multipath interference to be distinguished, with the former indicated by a bias and the latter by a larger variance than normal [65]. Vector tracking combines PVT estimation and GNSS signal tracking into a single estimation algorithm. The navigation filter inputs code and carrier discriminator measurements instead of ranging measurements, and its PVT solution is used to generate the NCO commands within the receiver that control the reference code and carrier generation. Full details are presented in Chapter 16. In vector tracking, low-C/N0 discriminator measurements are automatically de-weighted, so NLOS measurements have less impact on the position solution [66]. Innovation filtering can also be performed on the discriminator measurements to enable rejection or de-weighting of NLOS and strongly multipathcontaminated signals [67].

15/12/2020 6:30:20 PM

578

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

22.5.4

Using Aiding Information

A dead-reckoning navigation system measures motion using inertial sensors, wheel-speed sensors, Doppler radar, Doppler sonar, or another technology, and then integrates that motion to update its position solution. As the motion measurement errors are also integrated, the position accuracy degrades with time. Consequently, dead-reckoning technologies are normally integrated with position-fixing technologies, such as GNSS, typically using Kalman-filter-based estimation. Details are presented in Chapter 46 and in [6, 68, 69]. In such an integrated navigation system, the motion between GNSS epochs is measured instead of predicted. Consequently, in innovation filtering (Section 22.5.3), the predicted navigation solution used to compute the GNSS measurement innovations is more accurate, making the innovation filtering more sensitive and thus making NLOS reception and multipath interference easier to detect. As described in [6], GNSS can also be integrated with other radio positioning technologies, environmental feature matching systems (e.g. magnetic anomaly matching), map matching, and/or terrain height aiding (see Section 22.7). These all increase the amount of information available to the navigation filter, boosting the sensitivity of innovation filtering. Chapters 35–43 in this book are dedicated to techniques that use radio signals of opportunity for navigation, while Chapters 44–52 describe non-radio-based navigation technologies. A sky-pointing camera with a panoramic lens or an array of cameras can produce an image of the entire field of view above the receiver’s masking angle. Where the orientation of the camera is known (requiring integration with inertial sensors or multi-antenna interferometric GNSS), the blocked lines of sight may be determined from the image. By comparing these with the satellite azimuths and elevations, NLOS signals can be identified and excluded from the PVT solution [70, 71].

22.6 Post-Processing Techniques for Multipath Mitigation Some methods for removing multipath effects rely on postprocessing of collected GNSS data. Post-processing approaches can use batch estimation techniques; exploit constellation repeat cycles; leverage additional information, such as known antenna motion; and employ computationally intensive methods, such as electromagnetic (EM) ray tracing.

c22.3d 578

22.6.1

Fixed or Repeatable Geometry

For a stationary receiver, installed in an essentially static environment, the repeating satellite geometry of each GNSS constellation produces repeating multipath effects that can be identified and removed. This repeat time varies by constellation: the GPS constellation repeats every sidereal day, GLONASS every eight days, Galileo every ten days [72], and BeiDou every seven days [73]. Techniques exploiting repeating satellite geometry are referred to as sidereal filtering, in reference to the constellation repeat time of GPS for which the technique was first conceived [74]. Multipath corrections may be applied in the position domain or the observation domain. In position domain sidereal filtering (PDSF), a series of position residuals (e.g. east/north/ height errors) from one day are subtracted from a series of corresponding position states from a subsequent day [75]. The position residuals from the first day may be low-pass filtered to avoid amplifying noise. In the postprocessing case considered here, the input to the position estimation for each day should be checked to ensure only satellites visible on both days are used in case the constellation changes (e.g. a satellite outage) [76]. Observation domain sidereal filtering (ODSF) involves correction of the range measurements themselves: measurement residuals from one day are low-pass filtered and subtracted, per satellite, from a subsequent day’s series of corresponding measurements. The low-pass filter bandwidth must be sufficiently less than the multipath fading frequency (see Eqs. (22.4) and (22.5)). Greater accuracy in multipath removal can be achieved by using more sophisticated alignment techniques. Although the GPS constellation nominally repeats every 86 164 s, for example, modified sidereal filtering (MSF) uses a repeat time of 86 155 s, accounting for the westward drift of the satellite planes due to the oblateness of Earth [77]. Orbit periods of GPS satellites vary by about 8 s over a year, however, and spacecraft maneuvers can change orbit periods by more than 100 s [76]; the repeat of a satellite ground track is a better indicator of repeating multipath than the orbit period. The aspect repeat time (ART) method takes this approach by finding the time shift that maximizes the dot product between the two user-to-satellite LOS vectors [19, 78]. Note that in each of these methods, accurate alignment of the previous day’s residuals with the current observations relies on a sufficiently high rate data (on the order of 1 Hz or greater). Noise in the multipath correction may be reduced by averaging residuals from multiple days [79]. Another approach that exploits repeatable geometry is to map measurement residuals onto a sky plot by azimuth and elevation, thus forming a hemispherical template of

15/12/2020 6:30:20 PM

22.6 Post-Processing Techniques for Multipath Mitigation

multipath corrections [80, 81]. In most cases, however, accounting for high-frequency multipath effects would require a prohibitively fine discretization of the hemisphere‚ and generating a complete template can take months or years [75]. This technique is still useful for spacecraft applications, where reflectors are very close to the receive antenna, implying lower-frequency errors (see Eqs. (22.4) and (22.5)), and the environment may be indefinitely static.

22.6.2

Estimation of Reflected Ray Properties

Estimation of the multipath parameters (αi, Δi, and ϕi for each of i = 1, …, n reflected signals in Eq. (22.6)) allows for reconstruction of the signals themselves, thereby enabling correction of multipath errors via any of the previously discussed methods. While methods discussed in Section 22.3.3, such as MEDLL, perform estimation in real time, others benefit from a post-processing approach. Due to the impossibility of perfect isolation of direct and reflected signals in the cases of interest (i.e. cases with multipath-induced errors), one approach is to rely on differences in the evolution of direct and reflected signals in a time series of data. Another approach is to thoroughly model the receiver environment and estimate the reflected signal properties through EM ray tracing. Multipath error is highly sensitive to antenna motion – moving an antenna just half a wavelength will significantly change the relative phases of the direct and reflected signals. As an antenna is moved, projection of the antenna motion onto the different signal arrival directions varies. By generalizing the multipath model used in MEDLL to include antenna motion, a known antenna motion time history can be used to estimate the multipath parameters of each reflected signal from the in-phase and quadrature accumulations [82]. This has been demonstrated experimentally with some success (e.g. reduction of overall accumulated delta pseudorange RMS from 10 to 6 m) but is still in development. Rather than estimating multipath parameters from measurements, these parameters can be calculated from a known receiver environment and the laws that govern the propagation of EM radiation. Representing a propagating EM field as a ray is a simplification known as geometrical optics (GO) [83]. As long as object dimensions are much larger than a wavelength, the interaction of this ray with surfaces and different mediums is described by the GO laws of reflection and refraction – though these do not apply to edges. The uniform geometrical theory of diffraction (UTD) expands the GO laws to handle complex bodies by introducing diffraction to describe the scattering of rays at edges [84–86]. When the electrical properties of an

c22.3d 579

579

environment are fully defined, EM ray tracing can be used to describe the path taken by an EM ray, including cases of multipath. In a typical approach to calculating multipath through EM radiation modeling, structures in the receiver environment are first decomposed into simple geometric shapes. These shapes are assigned diffraction and reflection coefficients according to their material properties and the canonical shapes characterized in the UTD. All field components contributing to the field at the antenna phase center are traced through the environment‚ and finally the individual field components are summed together. For example, [87] describes an individual electric field component at point r’: Er,d r' = Ei r Dr,d Ar,d s e − jks

22 88

where the superscript r, d indicates that the field may arise from either interaction (reflection or diffraction), Ei(r) is the incident field arriving at r from the source or the previous interaction point, Dr, d is a complex reflection or diffraction coefficient, Ar, d(s) a spreading factor due to distance s, and e−jks a phase term with wavenumber k. The total field at the receive antenna is the sum of the LOS field, reflected fields, and diffracted fields. Ray tracing software is used to perform the computationally intensive task of tracing all significant field components through the receiver environment and applying interaction coefficients. Software must be selected according to a number of factors, such as ease of use, visualization capabilities, speed, and accuracy. Most software tools use UTD methods [88–90], but accuracy is highly dependent on the accuracy of structure models [87]. Ray tracing faces significant challenges in terrestrial applications, but has found use in simple or well-understood environments, such as spacecraft [91]. Correcting code multipath errors requires knowledge of reflected signal path delay to within one-tenth of a wavelength (~2 cm), and therefore centimeter-level knowledge of antenna position, phase center, and environment features is needed. This is further complicated by imperfect phase reversal upon reflection (most buildings or other structures are not flat over the Fresnel zone at GNSS wavelengths). As discussed in Section 22.7, however, it is practical to use ray tracing for NLOS correction, as much greater modeling errors can be tolerated. Similarly, ray tracing can be used to provide rough estimates of multipath relative amplitude, αi, which in turn can be used to determine pseudorange error weighting for the position solution as in Eq. (22.74).

22.6.3

Multipath Characterization

Characterization of the multipath environment is important for antenna placement and measurement weighting.

15/12/2020 6:30:20 PM

580

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

But it can be difficult to identify multipath-induced errors from among the many error sources. As described in Section 22.4.1, pseudorange multipath errors can be isolated by processing CMC data. These techniques exploit the fact that pseudorange and carrier phase share most signal-in-space error sources but have different multipath errors. Consider code and carrier measurements in Eq. (22.31). The single-frequency CMC multipath observable Eq. (22.38) is the difference between these two range measurements,

and correct phase errors [94]. The expression for carrier phase error for a single reflected signal stated in Eq. (22.16) can be expanded to an arbitrary number of signals and, for small range lag (|x - δ| < d/2) and small αi, approximated as δφM ≈

n

Ac ≈ Ad

≈ 2I L + δρML + ερL − N L λL

6 4 2

16:27 Time [UTC]

PRN01 Prompt Correlator PSD

130

8

16:28

22 92

where ωi is the angular frequency of the i-th multipath component and ϕ0,i is the initial phase offset, and the number of multipath components and their frequencies can be identified through spectral analysis (e.g. fast Fourier transform methods). An example is shown in Figure 22.22, in which the signal power exhibits a multipath-induced oscillation, and a single multipath component with frequency 0.25 Hz can be identified in the frequency domain, despite the constant frequency assumption in Eq. (22.92) only holding approximately. The amplitudes and initial phases of each multipath component are estimated through a least-squares fit to the model:

LHCP correlation PSD [dB]

LHCP corr.power

ϕi = ωi t + ϕ0,i ,

PRN01 Prompt Correlator Power

16:26

22 91

This multipath-induced variation in the amplitude of the combined signal is evident in the adjusted SNR and can be used to estimate the relative amplitude and phase of each multipath component. The sum of these components forms a profile for removing carrier phase multipath errors [95]. Assuming the multipath frequency is constant over the time interval considered,

in which the geometric range, tropospheric delay, and clock terms cancel [13, 92]. Carrier multipath error and carrier noise terms are negligible relative to the code terms and can be ignored. The integer carrier ambiguity can be removed by subtracting the mean of χ L, but note that this removes any bias associated with the multipath errors. Finally, the ionosphere terms must be removed. This can be achieved by estimating and removing slow trending in the measurement (on the order of hours) [13], or by producing an ionosphere-free combination of the code and carrier range measurements with multiple frequencies – see Section 22.4.3.3 and Eq. (22.78). The resulting measure of pseudorange multipath errors can be employed to de-weight or ignore corrupted measurements [93]. Carrier phase multipath errors can be isolated with differential phase techniques (i.e. the difference in phase measured by two antennas) by considering the relationship between the measured SNR and the carrier phase error. If known factors affecting gain are removed (e.g. first-order transmitter and receiver motion), variation in the adjusted SNR can be attributed to multipath and used to estimate

0

αi cos ϕi i=0

22 89

× 105

22 90

The amplitude of the combined signal, for direct signal amplitude Ad and small αi, can be approximated as

χ L = ρL − φL = 2I L + δρML − δφML + ερL − εφL − N L λL

10

1+

n i = 0 αi sin ϕi n i = 0 αi cos ϕi

LCP power 20 ms noncoherent avg

120 110 100 90 80 70 60

0

0.5

1

1.5

2

2.5

3

Frequency [Hz]

Figure 22.22 (Left) Prompt correlator power and (right) power spectral density of PRN 1 measured during Hubble Servicing Mission 4 [18]. Source: Reproduced with the author’s permission.

c22.3d 580

15/12/2020 6:30:20 PM

22.7 3D Mapping-Aided GNSS

cos ω1 t k

− sin ω1 t k

cos ωn t k

− sin ωn t k

581

δφM123 = λ23 φ1 − φ2 + λ22 φ3 − φ1 + λ21 φ2 − φ3 = λ23 − λ22 δφM1 + λ21 − λ23 δφM2 + λ22 − λ21 δφM3 + Noise + Ambiguities

α1 Ad cos ϕ0,1 α1 Ad sin ϕ0,1 ×

22 95

where the subscripts 1, 2, and 3 denote the frequencies. This can be done with a single antenna/receiver and can be used to estimate overall multipath error statistics, assessing error budgets and comparing different antenna sites.

SNRM t k =

αn Ad cos ϕ0,n αn Ad sin ϕ0,n

22 93 where the multipath SNR time series, SNRM, is computed by subtracting the estimated direct SNR (calculated according to a link budget and known geometry) from the measured and adjusted SNR [95]. Note that the real-time SNR estimate must not be too heavily filtered in order to observe changes in the total SNR. The resulting ωi, ϕ0, i, and αi estimates are used to calculate the multipath frequency via Eq. (22.92), and in turn the carrier phase error in Eq. (22.90). The spectral analysis used to determine ωi does not determine sign, however, so measurements from two antennas are required. An additional least-squares fit must be performed according to the model δφM,1,1 t k

δφM,n,1

δφM,1,2

δφM,n,2

s1,1

×

sn,1 s1,2

DPHSresid t k =

sn,2 22 94 where δφM, i, j is the estimated carrier phase error for multipath component i and antenna j, DPHSresid the motioncorrected difference between the phase measured at each of the two antennas, and si,j the carrier phase error sign [95]. After these signs are computed, a differential phase correction profile can be constructed and applied to the differential phase data to produce carrier multipath free differential phase measurements. With the availability of triple-frequency GNSS signals, geometry/ionosphere-free phase combinations can be formed [96]. These are useful for characterizing overall carrier phase multipath error levels, but not the multipath error on a single frequency. Using the measurement models in Eq. (22.31), the triple-frequency phase combination suggested in [96] can be expanded to obtain

c22.3d 581

22.7

3D Mapping-Aided GNSS

GNSS position accuracy is degraded in dense urban environments because buildings block and reflect signals. 3D mapping of buildings (together with knowledge of satellite positions) enables prediction of which signals are affected where. By using this information in GNSS positioning algorithms, position error may be reduced from tens of meters to a few meters. Techniques may be divided into terrain height aiding, 3D mapping-aided (3DMA) GNSS ranging, and shadow matching. These are described in turn, followed by a discussion of system implementation issues.

22.7.1

Terrain Height Aiding

For most land positioning applications, the GNSS receive antenna may be assumed to be at a known height above the terrain. By using a digital terrain model (DTM), also known as a digital elevation model (DEM), the position solution may be constrained to a surface. Terrain height aiding was used in the early days of GPS to enable positioning with a limited number of satellites. By effectively removing a dimension from the position solution, the accuracy of the remaining dimensions is improved. In an open environment, terrain height aiding significantly improves only the vertical positioning and timing accuracies. However, where the signal geometry is poor, such as in dense urban areas, horizontal accuracy can be significantly improved [62]. Terrain height aiding is incorporated into a conventional least-squares or EKF positioning algorithm by adding a virtual ranging measurement [6, 62, 97]. This comprises the distance, rea, from the center of Earth to terrain at the predicted horizontal position, adjusted for any known vertical displacement of the user antenna from the terrain. The DTM will provide the terrain height at a series of grid points, so interpolation is necessary. Clearly, the more accurate the predicted horizontal position is, the more accurate the terrain height will be. Therefore, the positioning algorithm should be iterated several times, using the horizontal position solution from the previous iteration to compute the terrain height at each iteration.

15/12/2020 6:30:21 PM

582

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

The positioning algorithm described in Section 22.5.1 can be augmented with terrain height aiding by adding an additional measurement, r Ea,T , to Eq. (22.70). The terrain height aiding measurement innovation, r Ea,T − ra− , is added to the measurement residual vector of Eq. (22.70). The measurement matrix, Eq. (22.73), is augmented with the additional row Hm + 1 = ea,x where eEa ≈ rEa − rEa −

ea,y

ea,z

0

22 96

in ECEF coordinates or eLa ≈

0 0 1 T in local level coordinates. An additional row and column is also added to the weighting matrix, Wρ, to weight the height-aiding measurement within the position solution. Terrain height aiding may also be used to improve the robustness of consistency checking (Section 22.5.2) [62, 98].

22.7.2

3D Mapping-Aided Ranging

Using ray tracing or projection techniques, 3D maps of cities can be used to predict which signals are blocked by buildings, and thus are NLOS when received, and which are directly visible. Direct LOS signals may or may not be subject to multipath contamination. This process can be accelerated by using pre-computed building boundaries. The building boundary at a given position comprises the elevation threshold below which satellite signals are blocked for each azimuth. Satellite visibility can then be predicted very quickly simply by comparing the satellite elevation with the building boundary elevation at the appropriate azimuth. These satellite visibility predictions can be used to aid ranging-based positioning in a number of different ways. Where the position is already known to within a few meters, it is possible to predict which signals are NLOS with reasonable accuracy and simply exclude them from the position solution (assuming there are sufficient direct LOS signals) [99, 100]. Otherwise, which signals are directly visible depends on the true position, which is not known. A simple approach is to determine the proportion of candidate positions at which each signal is predicted to be directly visible and use this to weight each measurement within the position solution and to aid consistency checking. To make the best use of satellite visibility prediction, a conventional least-squares (or EKF) positioning algorithm should be replaced by an algorithm that scores candidate position hypotheses according to the difference between the measured and predicted pseudoranges, assuming LOS propagation. The receiver clock offset and any interconstellation timing biases may be eliminated by differencing measurements across satellites. Different assumptions about the error distribution can then be made at different

c22.3d 582

candidate positions according to which signals are predicted to be LOS or NLOS at each position. For example, a symmetric error distribution could be assumed for LOS signals and an asymmetric distribution for NLOS signals with the scoring adjusted accordingly. The candidate positions may be distributed in a regular grid or semi-randomly (like in a particle filter). The search area containing those position candidates is centered at either the conventional GNSS position solution or a position predicted forward from previous epochs. The size of the search area is then based on the uncertainty of the initializing position. Ray tracing enables the path delay of a reflected GNSS signal to be predicted as discussed in Section 22.6.2. NLOS reception errors may then be corrected, enabling NLOS signals to contribute to an accurate position solution. However, accurate correction of NLOS errors requires an accurate position solution. If the position is already known to within a few meters, alternate computation of the position solution and NLOS corrections may be iterated until they converge. For larger uncertainties, multiple starting positions will be needed to ensure convergence. A more powerful approach adds NLOS error prediction to positioning by scoring candidate position hypotheses. Appropriate NLOS corrections are then computed for each candidate position. Both grid-based and particle-based methods have demonstrated positioning accuracies within 2 m [101–103].

22.7.3

Shadow Matching

Shadow matching is a complementary GNSS positioning technique that determines position by comparing predicted and measured C/N0. Unlike conventional GNSS positioning, it does not use the ranging measurements, but rather, is akin to “RF fingerprinting” techniques used for indoor location systems. Using 3D mapping and the satellite positions, each GNSS signal is predicted to be directly visible in some areas and blocked (shadowed) in other areas. Shadow matching therefore assumes that the user is in one of the directly visible areas if the received SNR is high and in one of the shadowed areas if the SNR is low or the signal is not received at all. Figure 22.23 illustrates the general principle. Repeating this for each GNSS signal enables the area within which the user may be found to be reduced [104]. In practice, there can be overlaps in the SNR distributions of direct LOS and NLOS signals, particularly when a smartphone antenna is used. Furthermore, real urban environments and signal propagation behavior are more complex than it is possible to represent using 3D mapping [105]. Therefore, a practical shadow-matching algorithm works by scoring a grid of candidate positions according to the degree of correspondence between the satellite visibility

15/12/2020 6:30:21 PM

22.7 3D Mapping-Aided GNSS

No direct signal received: user is here

Figure 22.23 D. Groves.

Direct signal received: user is here

Principle of shadow matching. Source: © 2016, Paul

predictions and the SNR measurements. This enables inaccuracies in the process to be treated as noise, so a correct position is still obtained provided there is sufficient “signal.” Figure 22.24 shows the stages of a typical shadowmatching algorithm [106]. Before using shadow matching, the context must be determined [107]. Shadow matching requires an outdoor urban environment as it does not work indoors and is not needed in an open environment where conventional GNSS positioning works well. The first step is to establish the search area using an approximate position (e.g. from conventional GNSS) and an associated uncertainty. A search radius of a few tens of meters is typically needed. Within this search area, a grid of candidate positions is established; indoor locations may be omitted. Shadow matching works well with a grid spacing of 1 m, but can operate with a larger spacing. Next, 3D mapping is used to predict the satellite visibility at each position, either directly or via pre-computed building boundaries. A 3D city model is necessarily an approximation of the true environment, and a ray is only an approximation of a GNSS signal, the Fresnel radius of which can exceed a meter in urban environments.

583

Thus, although the satellite visibility predictions are Boolean, it is better to treat the probability that a signal is direct LOS as non-Boolean. For example, experimental tests have shown that a LOS probability of 0.8 can be assumed if the signal is predicted from the 3D mapping to be LOS and a LOS probability of 0.2 can be assumed for signals predicted to be NLOS [106]. The third step is to determine which of the received signals are direct LOS from the C/N0 (or SNR) measurements output by the receiver. Clearly, if the C/N0 is close to nominal, the signal is likely to be direct LOS. Conversely, if the C/N0 is just above the code tracking threshold or no signal is tracked, then the direct signal path is almost certainly blocked. However, intermediate values of C/N0 can be more difficult to classify as some NLOS signals can be very strong while direct signals can be attenuated by people and foliage. As discussed previously, cell phone antennas are linearly polarized, and present a particular problem as they do not distinguish between RHCP and LHCP signals. Therefore, an empirically determined function that expresses the direct LOS probability as a function of C/N0 should be used. This function can be derived from C/N0 data collected at known locations [106]. Because of their different antenna characteristics, different models are needed for professional-grade, consumer-grade‚ and cell phone GNSS user equipment. The fourth stage is to score each of the candidate positions. The probability that the predicted and measured satellite visibility match is Pij = p LOS C N 0 j p LOS map + 1 − p LOS C N 0 = 1 − p LOS C N 0

j

j

ij

1 − p LOS map

− p LOS map

+ 2p LOS C N 0 j p LOS map

ij

ij

ij

22 97

1. Establish search area

GNSS receiver

2. Predict satellite visibility at each candidate position

3. Determine direct LOS probabilities from C/N0

4. Score candidate position hypotheses

3D mapping or building boundaries

5. Calculate position solution from the scores

Figure 22.24

c22.3d 583

Stages of a typical shadow-matching algorithm. Source: © 2016, Paul D. Groves.

15/12/2020 6:30:21 PM

584

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

where p(LOS | map) is the predicted direct LOS probability, p(LOS | C/N0) is the observed direct LOS probability, j is the satellite‚ and i is the candidate position. A score for each candidate position can then be determined by multiplying the match probabilities for each signal. Thus, Λi =

22 98

Pij j

The output of the scoring process is thus a likelihood surface, giving the likelihood of each candidate position. This can be converted to a probability density function by normalizing it so that it integrates to unity. The final step in the shadow-matching process is to compute the position solution. A simple approach is to take a weighted average of the candidate positions. Thus: Λi p i

p= i

Λi

22 99

i

where pi is the position of the i-th candidate, which may be expressed as Cartesian, curvilinear, or projected coordinates. However, the likelihood surface can sometimes be multimodal, resulting in a position solution that is the average of several possibilities. This can be accounted for by increasing the position uncertainty in these cases. More sophisticated approaches include extracting multiple position hypotheses from the likelihood surface and putting the full likelihood surface into an integration filter. Several groups have demonstrated multi-epoch shadow matching using a particle filter, achieving cross-street positioning accuracies of better than 3 m [108–111].

22.7.4

System Implementation

Terrain height aiding, 3DMA GNSS ranging, and shadow matching should not be thought of as competitors. Best performance is obtained using all three techniques together, as well as many of the techniques described in the preceding sections. Because of the building geometry, GNSS ranging (with or without aiding) is typically more accurate in the along-street direction than in the across-street direction. Conversely, shadow matching is more accurate in the across-street direction. 3DMA ranging and shadow matching can be integrated simply by forming a weighted average of the two position solutions. The weighting should be directional, which can be achieved either using the covariances of the two position solutions or by using the street direction extracted from the mapping. However, where both positioning algorithms score an array of candidate positions, it is better to combine the ranging and shadowmatching scores for each candidate and then extract the integrated position solution. Shadow-matching and 3DMA GNSS ranging likelihood surfaces can also be processed with a multi-epoch navigation filter.

c22.3d 584

Terrain height aiding is inherent in both shadow matching and in 3DMA ranging algorithms that consider multiple candidate positions. By assuming the receive antenna is a fixed distance above the terrain, the grid of candidate positions is constrained to two spatial dimensions instead of three, reducing the processing load by an order of magnitude. However, a terrain-height-aiding least-squares position solution should also be used to initialize the search region. As it is more accurate, it enables fewer candidates to be considered, again reducing the processing load. For 3DMA GNSS to be practical, the algorithms must be able to run in real time on a typical consumer device and have realtime access to suitable 3D mapping data. Computational load is not a major problem for the positioning algorithms. However, ray tracing can be computationally intensive. One solution is to use pre-computed building boundaries, though that can take up more space than the original 3D mapping. Another option is to use projection techniques run on a graphics processing unit (GPU). However, both of these approaches can only predict satellite visibility, not path delays. Real-time path delay determination using ray tracing is currently limited to a hundred or so candidate positions per second. Highly detailed 3D city models are expensive. However, simple block models, known as level of detail (LOD) 1, are sufficient for most 3D-mapping-aided GNSS implementations. Open Street Map provides freely available building mapping for the world’s major cities and many other places, much of it in 3D. Data is also available from national mapping agencies. Although coverage is far from universal, it tends to be available in the dense urban areas where it is most needed. Conventional GNSS positioning usually works well enough in low-density areas. 3DMA GNSS can be implemented on either a server or a mobile device. A server-based implementation can use the existing assisted GNSS protocols to communicate with a GNSS receiver, so no modifications to the mobile device would be needed, and the 3D mapping would all be kept at the server. However, a server can only provide positioning for a limited number of users at one time, so is best suited to applications requiring only a single-epoch position fix. For continuous navigation and tracking applications, 3D mapping or building boundary data can easily be streamed to users over modern cell phone connections, assuming an efficient binary format. Pre-loading of data is also possible, but not necessarily convenient as a mobile device could only hold data for a few cities at a time.

22.8

Summary

Multipath reception is a phenomenon that all GNSS receivers must contend with, and for many applications it is the dominant error source. This chapter has provided a survey

15/12/2020 6:30:21 PM

References

of the plethora of techniques available to mitigate multipath errors: antenna siting to avoid multipath; antenna types that enhance direct signals and attenuate reflected signals, particularly for fixed sites; adaptive antenna array processing; correlation signal processing; measurement processing techniques like carrier smoothing; navigation processing to de-weight or exclude measurements impacted by multipath; and post-processing and modeling techniques that provide estimates to correct multipath errors. The applicability of these techniques to different GNSS receiver types varies greatly, with cell phones being especially constrained. NLOS reception is an additional challenge faced by many applications, especially for users in urban environments. Many receiver multipath mitigation techniques, including antenna and signal processing approaches, do not address NLOS reception. However, navigation processing techniques that help to de-weight or exclude multipath can also be adapted to mitigate NLOS reception. Furthermore, 3DMA techniques, such as shadow matching, are an example of how signal propagation modeling can be applied to actually use NLOS reception and signal blocking as sources of positioning information. As computational capabilities available to GNSS receiver systems continue to improve, and with the increased availability of information from communication networks and aiding sensors, the next decades can expect to see continued improvements in mitigation of multipath and NLOS reception.

7 Hannah, B., Modeling and simulation of GPS multipath

8

9

10

11

12

13

14

15

References 1 Groves, P.D., “How does non-line-of-sight reception differ

2 3

4

5

6

c22.3d 585

from multipath interference?” Inside GNSS, pp. 40–42, 63, November/December 2013. Rama Rao, B., Kunysz, W., Fante, R., and McDonald, K., GPS/GNSS Antennas, Artech House, 2013. Larson, K.M. et al., “Environmental sensing: A revolution in GNSS applications,” Inside GNSS, pp. 36–46, July/ August 2014. Braasch, M. S., “Multipath effects,” In Global Positioning System: Theory and Applications, Volume Vol. I, B. W. Parkinson and J. J. Spilker, Jr. (eds.), pp. 547–568, Washington, DC: AIAA, 1996, pp. 547–568. Bradbury, J., “Prediction of urban GNSS availability and Signal degradation using virtual reality city models,” in Proc. ION GNSS 2007, Fort Worth, TX, pp. 2696–2706, September 2007. Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, 2nd ed., Artech House, 2013.

585

16

17

18

19

propagation, Ph.D. Dissertation, Queensland University of Technology, 2001. Misra, P. and Enge, P., Global Positioning System: Signals, Measurements, and Performance, 2nd ed., Ganga-Jamuna Press, 2006. Van Dierendonck, A.J., Fenton, P., and Ford, T., “Theory and performance of a narrow correlator spacing in a GPS receiver,” in Navigation, Vol. 39, No. 3, pp. 265–283, 1992. Van Dierendonck, A.J., “GPS receivers,” in Global Positioning System: Theory and Applications Volume I, B. W. Parkinson and J. J. Spilker, Jr. (eds.), ch. 8, pp. 329– 407, Washington, DC: AIAA, 1996. Ward, P.W., Betz, J.W., and Hegarty, C.J., “Satellite signal acquisition, tracking and data demodulation,” In Understanding GPS Principles and Applications, 2nd ed., E.D. Kaplan and C.J. Hegarty, (eds.), ch. 5, pp. 153–241, Norwood, Massachusetts: Artech House, 2006. Betz, J.W., Engineering Satellite-Based Navigation and Timing: Global Navigation Satellite Systems, Signals, and Receivers, IEEE Press/ Wiley, 2016. Braasch, M., “Multipath,” Springer Handbook of Global Navigation Satellite Systems, P. Teunissen, and O. Montenbruck (eds.), Springer, pp. 445–470, 2017. Thornberg, D.B., Thornberg, D.S., DiBenedetto, M.F., Braasch, M.S., van Graas, F., and Bartone, C., “LAAS integrated multipath-limiting antenna,” Navigation, Journal of The Institute of Navigation, Vol. 50, No. 2, pp. 117–130, Summer 2003. Dovis, F., Pini, M., and Mulassano, P., “Multiple DLL architecture for multipath recovery in navigation receivers,” 2004 IEEE 59th Vehicular Technology Conference, VTC 2004-Spring (IEEE Cat. No.04CH37514), Vol. 5, pp. 2848–2851, 2004. Yang, C. and Porter, A., “GPS multipath estimation and mitigation via polarization sensing diversity: Parallel iterative cross cancellation,” in Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, California, pp. 2707–2719, September 2005. Jiang, Z. and Groves, P.D., “NLOS GPS signal detection using a dual-polarisation antenna,” in GPS Solutions, Vol. 18, No. 1, pp. 15–26, 2014 (online: 2012). Ashman, B., “Incorporation of GNSS multipath to improve autonomous rendezvous, docking and proximity operations in space,” Ph.D. Dissertation, Purdue University, 2016. Axelrad, P., Larson, K. M., and Jones, B., “Use of the correct satellite repeat period to characterize and reduce site-specific multipath errors,” Proceedings of the 18th International Technical Meeting of the Satellite Division of

15/12/2020 6:30:21 PM

586

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

20

21

22

23

24

25

26

27

28

29

30

c22.3d 586

The Institute of Navigation (ION GNSS 2005), Long Beach, California, pp. 2638–-2648, September 2005. Katzberg, S., Garrison, J., and Howell, C., “Simple overwater altimeter using GPS reflections,” in Proceedings of the 12th International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, TN, pp. 1819–1828, September 1999. Masters, D., Axelrad, P., Zavorotny, V., Katzberg, S., and Lalezari, F., “A passive GPS bistatic radar altimeter for aircraft navigation,” in Proceedings of the 14th International Technical Meeting of the Institute of Navigation. Cambridge, MA: Institute of Navigation, pp. 2435–2445, June 2001. Vinande, E., Akos, D., Masters, D., Axelrad, P., and Esterhuizen, S., “GPS bistatic radar measurements of aircraft altitude and ground objects with a software receiver,” in Proceedings of the 61st Annual Meeting of the Institute of Navigation, Cambridge, Massachusetts, pp. 528–534, June 2005. Dowdle, J.R. Gustafson, D.E., and Elwell, J.M., “Geographical navigation using multipath wireless navigation signals,” US Patent 6,693,592, February 2004. Cohen, I., “Relative navigation for Hubble Servicing Mission using reflected GPS signals,” Master’s thesis, University of Maryland, 2007. Cohen, I. and Boegner, G. Jr., “Method and apparatus for relative navigation using reflected GPS signals,” US Patent 7,817,087, October 2010. Garin, L., van Diggelen, F., and Rousseau, J.-M., “Strobe & Edge correlator multipath mitigation for code,” Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, Missouri, pp. 657–664, September 1996. Hatch, R.R., Keegan, R.G., and Stansell, T.A., “Leica’s code and phase multipath mitigation techniques,” Proceedings of the 1997 National Technical Meeting of The Institute of Navigation, Santa Monica, California, pp. 217– 225, January 1997. McGraw, G.A. and Braasch, M.S., “GNSS multipath mitigation using gated and high resolution correlator concepts,” in Proceedings of the Inst. of Navigation National Technical Meeting, San Diego, California, January 25–27, 1999. McGraw, G.A., “Practical GPS carrier phase multipath mitigation using high resolution correlator techniques,” in Proceedings of International Association of Institutes of Navigation World Congress/Annual Meeting of the Inst. of Navigation, San Diego, California, June 26–28, 2000. Veitsel, V.A., Zhdanov, A.V., and Zhodzishsky, M.I., “The mitigation of multipath errors by strobe correlators in

31

32

33

34

35

36

37

38 39

40

41

GPS/GLONASS receivers,” GPS Solutions, Vol. 2, pp. 38– 45, 1998. Zhdanov, A.V., Veitsel, V.A., Zhodzishsky, M.I., and Ashjaee, J., “Multipath error reduction in signal processing,” Proceedings of the 12th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1999), Nashville, Tennessee, pp. 1217–1224, September 1999. Irsigler, M. and Eissfeller, B., “Comparison of multipath mitigation techniques with consideration of future signal structures,” Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, Oregon, pp. 2584–2592, September 2003. Mattos, P.G., “Multipath elimination for the low-cost consumer GPS,” Proc. ION GPS-96, Kansas, Missouri, pp. 665–672, September 1996. Townsend, B.R. and Fenton, P.C., “A Practical approach to the reduction of pseudorange multipath errors in a Ll GPS receiver,” Proceedings of the 7th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1994), Salt Lake City, Utah, pp. 143– 148, September 1994. Townsend, B.R., Fenton, P.C., Van Dierendonck, K.J., van Nee, R.D.J., “Performance evaluation of the multipath estimating delay lock loop,” Navigation, Journal of The Institute of Navigation, Vol. 42, No. 3, pp. 503–514, Fall 1995. Weill, L.R., “Achieving theoretical accuracy limits for pseudoranging in the presence of multipath,” Proceedings of the 8th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1995), Palm Springs, California, pp. 1521–1530, September 1995. Weill, L.R., “Application of superresolution concepts to the GPS multipath mitigation problem,” Proceedings of the 1998 National Technical Meeting of The Institute of Navigation, Long Beach, California, pp. 673–682, January 1998. Weill, L.R., “Multipath mitigation: How good can it get with new signals?” GPS World, pp. 106–113, June 2003. Fenton, P.C. and Jones, J., “The theory and performance of NovAtel Inc.’s vision correlator,” Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, California, pp. 2178–2186, September 2005. Bhuiyan, M.Z.H. and Lohan, E.S., “Multipath mitigation techniques for satellite-based positioning applications,” in Jin S. (ed.), Global Navigation Satellite Systems: Signal, Theory and Applications, InTech, Rijeka, Croatia, pp. 405– 426, 2012. Ray, J.K., Cannon, M.E., and Fenton, P.C., “Mitigation of static carrier-phase multipath effects using multiple

15/12/2020 6:30:21 PM

References

42

43

44

45

46

47

48

49

50

51

52

53

c22.3d 587

closely spaced antennas,” Navigation, Journal of The Institute of Navigation, Vol. 46, No. 3, pp. 193–202, Fall 1999. Gold, K. and Brown, A., “An array of digital antenna elements for mitigation of multipath for carrier landings,” Proceedings of the 2005 National Technical Meeting of The Institute of Navigation, San Diego, California, pp. 190–196, January 2005. McGraw, G.A., Young, R.S.Y., Reichenauer, K., Stevens, J., and Ventrone, F., “GPS multipath mitigation assessment of digital beam forming antenna technology in a JPALS dual frequency smoothing architecture,” Proceedings of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, California, pp. 561–572, January 2004. Soloviev, A. and van Graas, F., “Utilizing multipath reflections in deeply integrated GPS/INS architecture for navigation in urban environments,” Proc. IEEE/ION PLANS, Monterey, California, pp. 383–393, May 2008. Xie, P., Petovello, M.G., and Basnayake, C., “Multipath signal assessment in the high sensitivity receivers for vehicular applications,” Proc. ION GNSS 2011, pp. 1764–1776, Portland, Oregon. Pany, T. and Eissfeller, B., “Demonstration of a synthetic phased array antenna for carrier/code multipath mitigation,” Proc. ION GNSS 2008, Savannah, Georgia, pp. 663–668, September 2008. Draganov, S., Harlacher, M., and Haas, L., “Multipath mitigation via synthetic aperture beamforming,” Proc. ION GNSS 2009, Savannah, GA, pp. 1707–1715, September 2009. Hatch, R., “The synergy of GPS code and carrier measurements,” in Proc. of 3rd Int. Symp. on Satellite Doppler Positioning, 1982. Hwang, P.Y.C. and Brown, R.G., “GPS navigation: Combining pseudorange with continuous carrier phase using a Kalman filter,” Navigation, Journal of The Institute of Navigation, Vol. 37, No. 2, pp. 181–196, Summer 1990. Franklin, G.F., Powell, J.D., and Workman, M.L., Digital Control of Dynamic Systems, 2nd ed., AddisonWesley, 1990. Hwang, P.Y.C., McGraw, G.A., and Bader, J.R., “Enhanced differential GPS carrier-smoothed code processing using dual frequency measurements,” Navigation, Journal of The Institute of Navigation, Vol. 46, No. 2, pp.127–137, Summer 1999. Brown, R.G. and Hwang, P.Y.C., Introduction to Random Signal Analysis and Applied Kalman Filtering, 3rd ed., Wiley, 1997. McGraw, G.A., “Generalized divergence-free carrier smoothing with applications to dual frequency

54

55

56

57

58

59

60

61

62

63

64

65

587

differential GPS,” Navigation: Journal of the Institute of Navigation, Vol. 56, No. 2, pp. 115–122, Summer 2009. Henkel, P. and Günther, C., “Reliable integer ambiguity resolution: multi-frequency code carrier linear combinations and statistical a priori knowledge of attitude,” Navigation: Journal of the Institute of Navigation, Vol. 59, No. 1, pp. 61–75, Spring 2012. “Minimum Operational Performance Standards for Global Positioning System/Wide Area Augmentation System Airborne Equipment,” RTCA DO-229D, 2006. Hartinger, H. and Brunner, F.K., “Variances of GPS phase observations: The SIGMA-ε model,” in GPS Solutions, Vol. 2, No. 3, pp. 35–43, 1999. Groves, P.D., Jiang, Z., Skelton, B., Cross, P.A., Lau, L., Adane, Y., and Kale, I., “Novel multipath mitigation methods using a dual-polarization antenna,” in Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, Oregon, pp. 140–151, September 2010. Viandier, N. et al., “GNSS performance enhancement in urban environment based on pseudorange error model,” Proc. IEEE/ION PLANS, Monterey, California, pp. 377– 382, May 2008. Strode, P.R.R. and Groves, P.D., “GNSS multipath detection using three-frequency signal-to-noise measurements,” in GPS Solutions, Vol. 20, No. 3, pp. 399– 412, 2016 (online: 2015). Hilla, S. and Cline, M., “Evaluating pseudorange multipath effects at stations in the National CORS network,” in GPS Solutions, Vol. 7, No. 4, pp. 253– 267, 2004. Jiang, Z., Groves, P.D., Ochieng, W.Y., Feng, S., Milner, C. D., and Mattos, P.G., “Multi-constellation GNSS multipath mitigation using consistency checking,” Proc. ION GNSS 2011, Portland, Oregon, pp. 3889–3902, September 2011. Groves, P.D. and Jiang, Z., “Height aiding, C/N0 weighting and consistency checking for GNSS NLOS and multipath mitigation in urban areas,” in Journal of Navigation, Vol. 66, No. 5, pp. 653–669, 2013. Torr, P.H.S. and Zisserman, A., “MLESAC: A new robust estimator with application to estimating image geometry,” in Computer Vision and Image Understanding, Vol. 78, No. 1, pp. 138–156, 2000. Hsu, L.-T., Tokura, H., Kubo, N., Gu, Y., and Kmaijo, S., “Multiple faulty GNSS measurement exclusion based on consistency check in urban canyons” in IEEE Sensors Journal, Vol. 17. No. 6, pp. 1909–1917, 2017. Spangenberg, M. et al., “Detection of variance changes and mean value jumps in measurement noise for

15/12/2020 6:30:21 PM

588

22 Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

66

67

68 69

70

71

72

73

74

75

76

77

78

c22.3d 588

multipath mitigation in urban navigation,” in Navigation, Vol. 57, No. 1, pp. 35–52, 2010. Lashley, M. and Bevly, D.M., “Comparison in the Performance of the vector delay/frequency lock loop and equivalent scalar tracking loops in dense foliage and urban canyon,” Proc. ION GNSS 2011, Portland, Oregon, pp. 1786–1803, September 2011. Hsu, L.-T., Jan, S.-S., Groves, P.D., and Kubo, N., “Multipath mitigation and NLOS detection using vector tracking in urban environments,” in GPS Solutions, Vol. 19, No. 2, pp. 249–262, 2015 (online: 2014). Farrell, J.A., Aided Navigation: GPS with High Rate Sensors, McGraw Hill, 2008. Grewal, M.S., Andrews, A.P., and Bartone, C.G., Global Positioning Systems, Inertial Navigation, and Integration, 3rd ed., Wiley, 2013. Marais, J., Berbineau, M., and Heddebaut, M., “Land mobile GNSS availability and multipath evaluation tool,” in IEEE Transactions on Vehicular Technology, Vol. 54, No. 5, pp. 1697–1704, 2005. Meguro, J. et al., “GPS multipath mitigation for urban area using omnidirectional infrared camera,” in IEEE Transactions on Intelligent Transportation Systems, Vol. 10, No. 1, pp. 22–30, 2009. Springer, T.A., “High accuracy GNSS solutions and services,” Global Navigation Satellite Systems Overview, GNSS Overview, 6 Feb. 2017, www.positim.com/ navsys_overview.html. Jan, S. and An-Lin, T., “Comprehensive comparisons of satellite data, signals, and measurements between the BeiDou Navigation Satellite System and the Global Positioning System,” Sensors (Basel, Switzerland), MDPI, 13 May 2016, www.ncbi.nlm.nih.gov/pmc/articles/ PMC4883380/. Genrich, J.F. and Bock, Y., “Rapid resolution of crustal motion at short ranges with the Global Positioning System,” Journal of Geophysical Research, Vol. 97, pp. 3261–3269, 1992. Atkins, C., “Observation-domain sidereal filtering for highrate GPS precise point positioning,” Ph.D. Dissertation, University College London, 2016. Larson, C., Bilich, A., and Axelrad, P., “Improving the precision of high-rate GPS,” Journal of Geophysical Research, Vol. 112, No. B05422, pp. 1–11, 2007. Choi, K., Bilich, A., Larson, K.M., and Axelrad, P., “Modified sidereal filtering: Implications for high-rate GPS positioning,” Geophysical Research Letters, 31, L22608, 2004. Agnew, D.C. and Larson, K.M., “Finding the repeat times of the GPS constellation,” GPS Solutions, Vol. 11, pp. 71– 76, 2007.

79 Bishop, G.J., Coco, D.S., Kappler, P.H., and Holland, E.A.,

80

81

82

83 84

85

86

87

88

89

90

91

“Studies and performance of a new technique for mitigation of pseudorange multipath effects in GPS ground stations,” Proceedings of the 1994 National Technical Meeting of the Institute of Navigation, San Diego, California, pp. 231–242, January 1994. Reichert, A.K. and Axelrad, P., “Carrier-phase multipath corrections for GPS-based satellite attitude determination,” Navigation: JION, Vol. 48, No. 2, pp. 77– 88, 2001. Hodgart, S. and Wong, R., “Statistically optimized inflight estimation of GPS carrier phase multipath for LEO satellite attitude determination,” Navigation: JION, Vol. 53, No. 3, pp. 181–202, 2006. Psiaki, M., Ertan, T., O’Hanlon, B., and Powell, S., “GNSS multipath mitigation using antenna motion,” Journal of the Institute of Navigation, Vol. 62, No. 1, pp. 1–22, Spring 2015. Goodman, J., Introduction to Fourier Optics, Englewood, Colorado: Roberts & Co., 2005. Keller, J., “Geometrical theory of diffraction,” Journal of the Optical Society of America, Vol. 52, No. 2, pp. 116– 130, 1961. Borovikov, V.A. and Kinber, B. Ye., Geometrical Theory of Diffraction, London: The Institute of Electrical Engineers, 1994. Gomez, S., “Three years of Global Positioning Systems experience on International Space Station,” NASA Johnson Space Center, NASA Technical Publication NASA/TP-2006-213168, 2006. Gomez, S. and Hwu, S., “Comparison of space shuttle GPS flight data to geometric theory of diffraction predictions,” in Proceedings of the 10th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1997), Kansas City, Missouri, September 1997. Byun, S., Hajj, G., and Young, L., “Development and application of GPS signal multipath simulator,” Radio Science, Vol. 37, No. 6, pp. 10.1–10.23, November 2002. Weiss, J., “Modeling and characterization of multipath in global navigation satellite system ranging signals,” Ph.D. dissertation, University of Colorado Boulder, 2007. Lau, L. and Cross, P., “Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modeling,” Journal of Geodesy, Vol. 81, No. 11, pp. 713– 732, 2007. Axelrad, P., Gold, K., Madhani, P., and Reichert, A., “Analysis of orbit errors induced by multipath for the ICESat observatory,” Proceedings of the 12th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1999), Nashville, Tennessee, pp. 875–884, September 1999.

15/12/2020 6:30:21 PM

References

92 Braasch, M., Isolation of GPS multipath and receiver

93

94

95

96

97

98

99

100

101

c22.3d 589

tracking errors, Navigation, Journal of the Institute of Navigation, Vol. 41, No. 4, pp. 415–434, Winter 1994–1995. Bisnath, S. and Langley, R., “Pseudorange multipath mitigation by means of multipath monitoring and deweighting,” in Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Alberta, pp. 392–400, June 2001. Comp, C., “GPS carrier phase multipath characterization and a mitigation technique using the signal-to-noise ratio,” Ph.D. dissertation, University of Colorado, 1996. Axelrad, P., Comp, C.J., and Macdoran, P.F., “SNR-based multipath error correction for GPS differential phase,” in IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 2, pp. 650–660, April 1996. Simsky, A., “Three’s the charm: Triple-frequency combinations in future GNSS,” Inside GNSS, July/August 2006, pp. 38–41. Amt, J.R. and Raquet, J.F., “Positioning for range-based land navigation systems using surface topography,” Proc. ION GNSS 2006, Fort Worth, Texas, pp. 1494–1505, September 2006. Iwase, T., Suzuki, N., and Watanabe, Y., “Estimation and exclusion of multipath range error for robust positioning,” in GPS Solutions, Vol. 17, No. 1, pp. 53–62, 2013 (online: 2012). Obst, M., Bauer, S., and Wanielik, G., “Urban multipath detection and mitigation with dynamic 3D maps for reliable land vehicle localization,” Proc. IEEE/ION PLANS 2012, Myrtle Beach, South Carolina, pp. 685-691, April 2012. Peyraud, S. et al., “About non-line-of-sight satellite detection and exclusion in a 3D map-aided localization algorithm,” in Sensors, Vol. 13, pp. 829–847, 2013. Suzuki, T. and Kubo, N., “Correcting GNSS multipath errors using a 3D surface model and particle filter,” Proc. ION GNSS+ 2013, Nashville, Tennessee, pp. 1583-1595, September 2013.

589

102 Kumar, R. and Petovello, M.G., “A novel GNSS

103

104

105

106

107

108

109

110

111

positioning technique for improved accuracy in urban canyon scenarios using 3D city model,” Proc. ION GNSS+ 2014, Tampa, Florida, pp. 2139-2148, September 2014. Hsu, L.-T., Gu, Y., and Kamijo, S., “3D building modelbased pedestrian positioning method using GPS/ GLOANSS/QZSS and its reliability calculation,” in GPS Solutions, Vol. 20, No. 3, pp. 413–428, 2016 (online: 2015). Groves, P.D., “Shadow matching: A new GNSS positioning technique for urban canyons,” in The Journal of Navigation, Vol. 64, No. 3, pp. 417–430, 2011. Groves, P.D., Wang, L., Adjrad, M., and Ellul, C., “GNSS shadow matching: The challenges ahead,” Proc. ION GNSS+ 2015, Tampa, Florida, pp. 2421-2443, September 2015. Wang, L., Groves, P.D., and Ziebart, M.K., “Smartphone shadow matching for better cross-street GNSS positioning in urban environments,” in The Journal of Navigation, Vol. 68, No. 3, pp. 411–433, 2015. Gao, H. and Groves, P.D., “Environmental context detection for adaptive navigation using GNSS measurements from a smartphone,” Navigation, Vol. 65, No. 1, pp. 99–116, 2018. Suzuki, T. and Kubo, N., “GNSS positioning with multipath simulation using 3D surface model in urban canyon,” Proc. ION GNSS 2012, Nashville, Tennessee, pp. 438-447, September 2012. Isaacs, J.T. and Irish, A.T. et al., “Bayesian localization and mapping using GNSS SNR measurements,” Proc. IEEE/ION PLANS 2014, Monterey, CA, pp. 445-451, May 2014. Wang, L., “Investigation of shadow matching for GNSS positioning in urban canyons,” PhD Thesis, University College London, http://discovery.ucl.ac.uk, 2015. Yozevitch, R. and Ben-Moshe, B., “A robust shadow matching algorithm for GNSS positioning,” in Navigation, Vol. 62, No. 2, pp. 95–109, 2015.

15/12/2020 6:30:21 PM

591

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM) Sam Pullen1 and Mathieu Joerger2 1 2

Stanford University, United States Virginia Tech, United States

23.1 Introduction: Integrity in the Context of Safety This chapter describes the concept of integrity for GNSS applications. Previous chapters of this book have shown how integrity is addressed for specific GNSS system architectures (e.g. see Chapter 12 on Ground-Based Augmentation Systems (GBAS) and Chapter 13 on Satellite-Based Augmentation Systems (SBAS)) or in response to specific threats (e.g., see Chapter 10 on Signal Quality Monitoring). Integrity, in very simple terms, refers to the level of trust that can be placed in the outputs of GNSS or any other navigation system. For some applications, errors beyond specified limits would result in great levels of harm to users, possibly including the loss of human life (these are often called “safety-critical” applications). For these applications, it is necessary to go beyond quantifying accuracy (the extent of typical errors within confidence intervals of 50% to 95%) to estimating error bounds that apply at very low probabilities. Section 23.2 of this chapter defines integrity in the context of other navigation system parameters (accuracy, continuity, and availability) and explains the trade-off between integrity on one hand and continuity and availability on the other. Section 23.3 explains the key variables used to quantify integrity and discusses the context in which integrity risk probabilities (the probabilities of encountering unsafe errors without alerting the user) are estimated. Section 23.4 explains how and why integrity is evaluated by users in real time by computing protection levels (PLs) for the position, velocity, and time (PVT) outputs that matter to particular applications. Sections 23.5 and 23.6 examine the building blocks of protection level calculations: rare-event bounds under nominal conditions in Section 23.5 and bounds under faulted conditions in Section 23.6. Section 23.7 shows how these principles are applied to the design and analysis

of RAIM, which is a monitoring technique that exploits redundancy in user measurements and is applied by both stand-alone and augmented GNSS users. Section 23.8 expands this to what is known as “Advanced RAIM” or ARAIM, which can handle larger sets of possible failure hypotheses. Section 23.9 briefly summarizes this chapter. The principles and methods described in this chapter were mostly developed for civil aviation applications of GNSS. In this chapter, civil aviation is often shortened to “aviation” for simplicity, but it should not be assumed that military or unmanned aviation applications currently use the same definitions and techniques. However, these principles can be applied to all GNSS applications (air, land, marine, and space) that require protection of user (and bystander) integrity.

23.2 Requirements Definitions and Trade-Offs The definitions of integrity and other complementary navigation system performance parameters (accuracy, continuity, and availability) are based on those used in civil aviation and are similar to those provided in Chapter 12 on GBAS. These parameters quantify the usefulness of a navigation system in terms of technical performance, safety, operational utility, and economic benefits.

23.2.1

Accuracy

Accuracy is the most commonly used and best-understood performance parameter, as it is important to all navigation systems and applications. Accuracy represents a quantitative measure of navigation error, meaning the difference between the reported state output (range, position, time, etc.)

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

592

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

and the true value of that output. In real-time operations, true state values are generally unknown, but they can be measured under controlled conditions, such as when measurements are taken at a static position whose location was established previously. Even in these conditions, it is difficult to observe more than 100 to 1000 statistically independent measurements. Therefore, accuracy values usually represent errors under typical measurement conditions out to probabilities no greater than 99.9%. Accuracy is commonly expressed in several different forms. One form is “error probable,” which represents a 50th-percentile confidence interval on error. For example, circular error probable (CEP) represents the value that includes 50% of all 2-D horizontal position errors (this is determined numerically from the error vector ε of differences between each measured data point and the known or estimated true state). Because nominal errors are typically well described by Gaussian (Normal) distributions out to 99% or 99.9%, it is common to estimate the sample standard deviation of the error vector ε [1, 2] and use this to express a “one-sigma” accuracy value, which bounds about 68.3% of the errors if the mean error is small. A two-sigma accuracy value based on this estimate bounds about 95.4% of errors. Extrapolating the Gaussian accuracy model beyond three sigma is not recommended because, as will be discussed in Section 23.5, errors under rare conditions have non-Gaussian distributions with “tails” that are “fatter” than those of a Gaussian distribution. In many applications, a requirement is placed on accuracy in terms of not exceeding a certain accuracy value, whether specified as error probable, one-sigma, or twosigma values. This can be tested in real time by, for example, multiplying a single one-sigma range error estimate by the dilution-of-precision (DOP) values that apply to the user’s current visible satellite geometry (see Chapter 2). While most applications assess accuracy performance as an “ensemble” over time and do not prevent operations at times when the accuracy requirement is not predicted to be met, civil aviation is different in that operations are not allowed in this case. In other words, the accuracy requirement is assessed in real time, and if it is not met for the desired operation, that operation cannot be conducted at that time. In practice, availability for civil aviation (see Section 23.2.4 below) is much more limited by the integrity requirement that will be described next.

23.2.2

Integrity

Integrity is not one parameter but a collection of parameters that express the trust that can be placed in a navigation solution under rare-event conditions (in practice, this usually refers to conditions with probabilities of 10−5 per

operation or below). As with accuracy, what is often sought is an error bound that applies at such low probabilities, but a combination of factors must be considered in order to create and validate such an error bound. In safety-critical applications that rely on navigation, the concern for safety arises from the possibility of errors large enough to create collisions or accidents. In aviation, the boundary that defines unsafe errors for a particular application is called the alert limit (AL). The unsafe condition that we want to avoid is called misleading information (MI). At a minimum, misleading information occurs when a navigation error exceeds one or more relevant ALs (depending on the specific integrity requirement, MI can also be declared when the protection level is exceeded – see Section 23.4). If MI occurs, safety can be maintained if the MI condition is stopped, most likely by detecting the underlying anomaly and excluding the affected GNSS measurements, or if an alert is provided to the user (pilot, driver, automated system, etc.) indicating that the system is no longer safe to use. Either of these actions must occur within a specified time to alert (TTA), which again varies depending on the operation being conducted. If MI occurs without being alerted or mitigated in time, loss of integrity occurs. In other words, loss of integrity occurs when MI exists without annunciation (alerting the user) or mitigation (excluding measurements such that MI no longer exists) within the time to alert. Integrity risk is the probability of loss of integrity over a time interval (“exposure time”) that is relevant to the operation in question (e.g. the duration of an aircraft precision approach). The integrity requirement for a given operation is thus composed of three specified values: integrity risk, AL, and time to alert. Figure 23.1 shows how the integrity requirement is met or not met in real time. Integrity is threatened when the (unknown) position error (or other navigation output that is safety-critical) exceeds either the AL or, more conservatively, the user-computed protection level (which one governs integrity depends on the specific set of requirements used). If this occurs, integrity can be protected if an alert leading to the operation being aborted (loss of continuity – see Section 23.2.3) or the exclusion of the measurements causing the unacceptable error occurs. However, for these preventive measures to be successful in preserving integrity, they must occur within the TTA. Table 23.1 shows the accuracy and integrity requirements for two aviation approach applications that are similar in that they both provide instrument guidance to approach a runway in obstructed visibility down to a minimum height above threshold (HAT, or decision height (DH)) of 200 feet. The variation supported by SBAS is known as LPV 200 and is explained further in Chapter 13, while

23.2 Requirements Definitions and Trade-Offs

PL = protection level (computed by user) AL = alert limit (“safe zone” defined by requirements)

Is position error > [PL or AL]?

Yes

No

Loss of integrity No

Is an alert issued, or are affected measurements excluded?

No

Yes

Does this action take place within TTA?

TTA = time to alert Yes

No integrity risk (integrity maintained)

Figure 23.1 Flowchart showing events leading to protection or violation of integrity requirement.

Table 23.1 Comparison of accuracy and integrity requirements for SBAS (LPV 200) and GBAS (CAT I, GAST C) versions of aviation precision approach to 200 ft DH [3, 4] Parameter

SBAS LPV 200

GBAS CAT I (GAST C)

Horizontal accuracy (95%)

16 m

16 m

Vertical accuracy (95%)

4m

4m

Horizontal alert limit (HAL)

40 m

40 m

Vertical alert limit (VAL)

35 m

10 m

Loss of integrity probability

2 × 10−7 / approach (150 s)

2 × 10−7/approach (150 s)

Time to alert (TTA)

6.2 s

6s

the GBAS variant is equivalent to precision approach under Category I weather minima (“CAT I precision approach”) as defined by the long-established non-GNSS system known as the Instrument Landing System, or ILS (see Chapter 12). As one would expect, both the accuracy and integrity requirements for these two operations are essentially the same except for the vertical alert limit (VAL), which is much lower for GBAS than for SBAS. This difference is to a large extent illusory, as the largest error source for both systems is anomalous spatial decorrelation of ionospheric delay on GNSS signals, and errors larger than the 10 m VAL for CAT I GBAS are allowed in the case of worstcase ionospheric anomalies. This will be further discussed in Section 23.6. Note that, as expected, there is a large gap between 95% accuracy and ALs in both horizontal and vertical position axes. In 2-D horizontal position, the 95th-percentile accuracy requirement of 16 m equates to about 8 m one-sigma, which is one-fifth of the 40 m HAL. Under nominal

conditions, when no faults exist to detect and exclude or to alert the user of, a typical horizontal protection level (HPL) is about six times the one-sigma error value (see Section 23.4). This means that, in practice, the integrity requirement places a tighter constraint on nominal horizontal accuracy than does the accuracy requirement, and confirming in real time that the integrity requirement is met also confirms that the accuracy requirement is met. The same is true of vertical position error, where a ratio of 5 to 1 also applies between the GBAS VAL of 10 m and the required one-sigma vertical position accuracy of 2 m.

23.2.3

Continuity

Continuity risk is a measure of the probability of unexpected loss of navigation during an operation that requires that the operation be aborted to preserve safety. Loss of continuity occurs when a user is forced to abort an operation

593

594

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

during a specified time interval after it has begun, presuming that the operation was deemed to meet all requirements (and thus be available) at its outset. The continuity risk requirement is usually expressed as a maximum tolerable probability of loss of continuity. In the case of the approach operations shown in Table 23.1 above, this probability is 8 × 10−6 per 15 s, where each 15 s interval is 10% of the total approach duration of 150 s. Figure 23.2 shows a simplified fault tree that identifies the key contributors to continuity loss for GNSS applications. The left-hand branch under the first “OR” gate includes detected failures of GNSS satellite signals when an actual problem exists. This can occur due to the sudden loss of access to a satellite signal (e.g. the signal simply disappears or is flagged as unhealthy) or due to the detection of a faulted satellite by monitoring within the GNSS application. The middle branch represents the failure of other GNSS system components that are needed for operations

to be conducted. One example is the means for broadcasting corrections and integrity information from augmentation systems to users. In SBAS, this information is provided by geostationary (GEO) satellites, while in GBAS it is provided by nearby VHF transmitters. Another example is the ground-based reference receivers that generate this information. The right-hand branch is different in that it represents fault detection of healthy GNSS measurements or equipment due to integrity monitor “false alarms,” meaning fault-free alerts issued by these monitors due to rare-nominal errors when no actual fault exists. The nodes labeled “A1,” “A2,” and “A3” under each of these branches indicate that, for each one, the event breakdown shown below under the “OR” gate labeled “A” determines whether or not continuity is lost. This “OR” gate is reached when either an actual fault or a fault-free event is detected – in real time, the system will not know which is the case. The lower right-hand branch represents the

Loss of Continuity (Probability of Unexpected Mission Abort in specified time interval)

OR

Dectected Satellite Fault(s)

Detected System Component Fault(s)

Fault-Free Detections(s)

A1

A2

A3

All three “A” nodes have the same form.

A

OR

AND

Affected measurement(s) are excluded

Figure 23.2

Affected measurement(s) are critical

Exclusion of affected measurements(s) is not possible

Notional fault tree showing the primary causes of loss of continuity.

23.2 Requirements Definitions and Trade-Offs

scenario where the detected event cannot be confidently isolated to a specific measurement or small subset of measurements. In this case, rather than risk incorrect exclusion and thus potential loss of integrity, continuity is sacrificed instead. The lower left-hand branch represents the scenario where exclusion is possible with an acceptably low probability of incorrect exclusion, but the exclusion of the apparently faulty measurements results in loss of continuity because those measurements (assuming they were healthy) were needed to meet the integrity requirements. Individual satellites whose loss or exclusion would cause loss of continuity are called critical satellites. Because most users see many more satellites than are needed to meet their navigation requirements, relatively few visible satellites are critical. The concept of critical satellites can be extended to combinations of satellites that are jointly critical (all must be excluded for continuity to be lost) and to other critical system components. As with GNSS satellites, redundancy is often present such that failure of a single element (e.g. a single GEO satellite, or a single SBAS or GBAS reference receiver) does not by itself cause loss of continuity. Therefore, in practice, most single-measurement exclusions are not critical and thus do not lead to loss of continuity. This makes the capability for measurement exclusion crucial to minimizing continuity risk in many applications. While the effect of measurement detections and exclusions on continuity is the same regardless of the cause, actual faults are separated in the fault tree from fault-free conditions in order to clarify how continuity risk is allocated. Continuity risk due to actual faults is based on the probabilities of these faults, whereas continuity risk due to fault-free exclusions is based on the fault-free alert probabilities of each of the monitors used to protect integrity, and this depends on the impact of nominal (fault-free) measurement noise on the monitor test statistics. In practice, since the probabilities of GNSS satellite faults are outside the control of GNSS application designers, continuity risk is allocated first by assigning a certain probability to satellite faults (the upper left-hand branch in Figure 23.2), and this probability determines the number of critical satellites that are allowed in a satellite geometry that meets the continuity requirement. The remainder of the allocation is divided among the other two branches, where the application designer has some flexibility. The allocation to fault-free detections and exclusions must then be subdivided among the monitor algorithms used to protect integrity. Loss of continuity in Safety-of-Life applications poses a potential safety concern as well as an operational problem. When an operation must be aborted unexpectedly, the backup operation that must be carried out may carry some

safety risk as well, although it would be much less than continuing the original operation. For example, when a precision approach must be aborted, a missed approach is flown instead. This is a well-understood operation that pilots are familiar with, but because the abort may catch pilots slightly by surprise, and because the missed approach may begin close to the ground, this operation is considered to have “minor” (but not zero) severity in terms of the hazard risk index safety concept used in civil aviation [5]. This concern, combined with the operational hazard of having several approaching aircraft lose service at the same time, is what motivates the loss-of-continuity probability requirement for precision approach to a 200 ft DH given above. The need to limit the probability of fault-free alerts and exclusions within integrity monitoring creates a direct trade-off between the continuity and integrity requirements. Integrity monitor algorithms are used to detect and remove faulted measurements within the TTA to prevent loss of integrity, which poses a much larger safety threat than loss of continuity. To achieve this, the detection thresholds on these monitors need to be set as tightly as possible. However, doing this increases the fault-free exclusion probability by making it more likely that random noise under nominal conditions will lead to unnecessary exclusion. Managing this trade-off so that both integrity and continuity requirements are met simultaneously is one of the greatest challenges confronting the designers of GNSS applications with stringent Safety-of-Life demands.

23.2.4

Availability

Availability is a measure of the operational and economic utility of the navigation service. It is most commonly expressed as the probability over time (e.g. over different user locations and GNSS satellite geometries) that all of the requirements for a given operation (accuracy, integrity, and continuity) are simultaneously met so that the operation can be conducted safely and efficiently. This is often called service availability. Other definitions also exist, such as the maximum time interval between service outages (periods of non-availability), which is sometimes called operational availability. Availability is analyzed both in real time by users and offline by operators to predict near-term performance and to evaluate long-term performance (often for cost-benefit assessment). In real time, at the beginning of each new operation type of phase, the availability of integrity, accuracy (if not already covered by integrity), and continuity are numerically assessed to determine if it is safe to proceed with the intended operation. Depending on the duration of the operation, this might involve forward calculations of how the predicted satellite geometry and range-domain

595

596

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

errors will change over time. Offline, aviation operations centers assess the availability of all user locations over the next 12, 24, or 48 hours (using the known GNSS satellite orbits and current satellite health) in order to determine if any outages will occur within the aviation service volume. If any such outages are predicted to occur in the US National Airspace System (NAS), the Federal Aviation Administration (FAA) will issue Notices to Airmen (NOTAMs) that alert pilots to where and when loss of service is expected. Availability requirements are usually expressed in terms of minimum service availability (e.g. 0.999, or “three nines”), but these requirements vary greatly depending on the operational and economic criticality of the service being supported. For example, precision approach availability requirements for smaller airports where nearby alternates exist tend to be around 0.99, and availability as low as 0.9 may sometimes be acceptable in practice. However, busy airports with few adequate alternatives or severe consequences of disruption if outages occur may have availability requirements as high as 0.99999.

23.3 Interpretation of Integrity Requirements 23.3.1

Simplified Integrity Risk Model

Analysis and validation of the integrity requirements defined in Section 23.2 is based on a simplified model of how faults, navigation errors, and integrity monitors interact. This model can be summarized by the following expression: PLOI,i = PPL,i PMD,i Pprior,i

23 1

where PLOI,i is the probability of loss of integrity (LOI) due to fault condition i, where i = 0 denotes nominal conditions; Pprior,i is the prior probability of fault condition i, meaning the probability that fault condition i is present without any measurements to infer its presence (note that, for nominal conditions, Pprior,0 1); PMD,i is the probability of integrity monitor missed detection (MD) of fault condition i, given that this condition is present (thus, it is a conditional probability). MD here means that action is not taken to mitigate the fault condition within the required TTA. While monitor detection of nominal conditions sufficiently unusual to cause LOI is possible, this probability is usually conservatively taken to be 1 for i = 0 since no specific fault is present to be detected.

PPL,i is the probability that the error fault condition i exceeds one or more PLs that define MI given that both the fault condition exists and MD occurs. Note that this could be changed to the AL instead (PAL,i) if MI is defined relative to ALs for a particular application. The following two subsections explain how prior fault probabilities and missed-detection probabilities are defined and calculated, while Section 23.4 explains the derivation of PLs and ALs.

23.3.2

Prior Probability Calculations

Prior probabilities of anomalous conditions are difficult to determine in general because the anomalies that they represent are typically rare events. In addition, the prior probabilities used in Eq. (23.1) represent threats that are specific to a given GNSS application rather than generic GNSS system faults that might be assessed and reported by system operations. However, years of experience and data collection from GPS satellites has helped reduce this uncertainty for some failure modes. An important source for prior probabilities of different types of GPS satellite failures is the GPS Standard Positioning Service (SPS) Performance Standard issued by the US Department of Defense (DoD) [6], which was last updated in 2020. This document does not give guarantees of specific levels of performance, but the “standards” of performance that it provides are based on many years of observed GPS measurement quality and generally show that the original DoD specifications on GPS SPS performance have been significantly exceeded. For L1 C/A code from a particular satellite, the integrity standard given in Section 3.5.1 of [6] limits the probability of signal in space (SIS) user range error (URE) exceeding 4.42 times the one-sigma user range accuracy (URA) value broadcast by that satellite to 1 × 10−5 or less over any hour (note that this probability is equivalent to that of exceeding ±4.42 from a standard Gaussian distribution with zero mean and unity variance) without a timely alert. A timely alert is defined as one that arrives at the user’s GPS antenna within 10 s of the SIS URE exceeding 4.42 times URE. Alerts within this short time frame are possible, but many unexpected satellite faults require GPS operator intervention and may take some TTA. A worst-case TTA of 6 hours is stated as a conservative assumption in Section A.5.4.2 of [6], but actual alerts almost always occur within 1 to 3 hours of a fault violating the above error tolerance. In addition, Section 3.6.1 of [6] provides a limiting probability of unscheduled failure causing loss of the L1 C/A code broadcast from a particular orbit slot (at least among the 24 primary GPS orbit slots), covering the above fault

23.3 Interpretation of Integrity Requirements

scenarios that require user or operator alerting as well as faults that are obvious (e.g. the signal is no longer receivable or trackable). This probability is 0.0002 per hour or lower per orbit slot, meaning that the probability of no loss of signal per orbit slot per hour is at least 0.9998. These probabilities are useful in assessing the GPS satellite contribution to user continuity risk. Finally, Section 3.7.1 of [6] provides a per-orbit-slot probability (among the 24 primary GPS orbit slots) of 0.957 or greater that a given orbit slot has a functioning L1 C/A-code SIS. This value is useful for availability calculations. In practice, simulations of changing GPS satellite geometries over time are used to estimate the availability of particular user applications, and they depend on assumptions of how many GPS satellites are functioning. The above probability can be used to estimate the state probability of all 24 satellites in the traditional 24-satellite GPS constellation being healthy, all but one being healthy, and so on, and these results can be convolved with simulation-based availability results for a particular set of healthy satellites to (approximately) estimate availability over a larger set of possible constellation health states. Note that the probabilities given in [6] are of two forms. The integrity and continuity probabilities in sections 3.5.1 and 3.6.1 are given in terms of a failure (or success) probability per hour, making them probability rates. The per-slot health probability in section 3.7.1 is instead independent of time and represents a state probability, or a long-term average probability that a given orbit slot is in one state versus another. It is important not to confuse these two values. Most GNSS user applications provide tolerable integrity and continuity risk requirements as a probability per time period, where the cited time period (“exposure time”) is related to the duration of the intended operation. Thus, the most common use of Eq. (23.1) is with PLOI,i and Pprior,i being probability rates and PPL,i and PMD,i being state probabilities. However, this is not always the case, and it is important to check each probability input to see if it is implicitly defined per time interval or not. A prior probability expressed as a failure rate over time is traditionally defined in the following manner when it is based on observations over a known time period: Pprior_rate =

N fail T obs

23 2

where Nfail represents the total number of (discrete and independent) observed failure events over a time period Tobs. This represents a point estimate of the failure rate, which can have significant statistical uncertainty if the true failure probability is rare such that Nfail is zero or very small. Therefore, it is advisable to also consider confidence intervals on this failure rate estimate, which are given by the

binomial distribution if the period Tobs can be converted into a number of discrete trials Ntrials. One recommended method for computing binomial confidence intervals is the Clopper– Pearson interval described by Wikipedia [7]. General forms of this interval using both Beta and F distributions are given in [7] and are complex, but a relatively simple result for the case where Nfail = 0 is particularly useful: 0 ≤ Pprior_actual ≤ 1 –

α 2

1 N trials

23 3

where Pprior_actual is the actual (unknown) prior point probability with a mean value given by Pprior_mean = Nfail / Ntrials, which equals 0 for Nfail = 0, and α represents the probability of being left outside the confidence interval given in Eq. (23.3) (in other words, 1 – α represents the size of the desired confidence interval in terms of probability). Consider the example where no failures are observed over 106 hours (approximately 114 years; thus this is likely to be obtained by observing perhaps 5.7 years on each of 20 independent satellites), with each hour representing one discrete time period (thus Ntrials = 106 as well). With Nfail = 0, Pprior_mean = 0/106 = 0, and it is often assumed that the actual prior probability can be upper-bounded by assuming that, had one failure been observed, Pprior_6 −6 per hour. However, setting α = 0.1 bound = 1/10 = 10 (for a 90th percentile confidence interval with 5th and 95th-percentile lower and upper bounds) in Eq. (23.3), the 95th-percentile upper bound on this prior probability is actually 3 × 10−6 per hour. Creating a much smaller 40th-percentile confidence interval with α = 0.6 gives an 70th-percentile upper bound of 1.2 × 10−6 per hour, indicating that there is more than a 30% chance that the true prior probability exceeds the naïve bound of 1 × 10−6 per hour mentioned above. A prior probability equation expressed as a state probability uses different inputs, both of which are expressed in units of time: Pprior_state =

MTTR MTBF + MTTR

23 4

where MTBF represents the mean time between (discrete and independent) failure events, and MTTR represents the mean time to repair (or at least alert and remove) these events. The significance of MTTR comes from the fact that, if a fault is never repaired, its state probability trends toward one. Since prior probabilities refer to faults and repairs that occur before monitor intervention, MTTR may be much longer than the TTA required of the monitors included within a GNSS augmentation system (such as the hour or more needed for GPS SPS alerts of satellite service failures described above).

597

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

Note that all of these calculations assume a stationary failure process, meaning that the probability of failure (or mean time to failure or repair) does not change with time over the observation period used to estimate these parameters. This is rarely the case in practice when the observation period is long enough to produce useful estimates for low failure probabilities, but it is typically assumed due to the lack of alternatives. Keeping this and other simplifying assumptions in mind, it is important to be conservative when using the results of these calculations. This often means using upper bounds derived from confidence intervals and using judgment to apply higher probabilities than the computed values based on knowledge of the uncertainty in the underlying assumptions and the numbers used to derive these estimates. One example of how these issues are tackled for the prior probabilities of satellite failures used in the Advanced RAIM (ARAIM) technique described in Section 23.8 of this chapter can be found in [8]. Estimating prior probabilities of rare but threatening natural events, such as anomalous ionospheric or tropospheric conditions, is particularly challenging because little is known about the frequency of such conditions except that they change with time and place. Several models have been developed to express the prior probability of anomalous ionospheric conditions. In [9], a prior probability model for ionospheric anomalies that are hazardous to Category I precision approaches supported by GBAS is proposed, but this model is not generally accepted, as it averages over

100

conditions of the precision approach that are generally treated as “worst-case” in GBAS integrity analysis (see Section 23.3.4).

23.3.3 Missed-Detection Probability Calculations Figure 23.3 shows a model of the response of a generic integrity monitor test statistic to a fault that appears as a bias and changes the mean of the test statistic. Under nominal conditions (the blue curve), the test statistic distribution is bounded by a zero-mean Gaussian distribution with a known standard deviation (“sigma”). The test statistic is normalized by (divided by) this sigma so that the plot in Figure 23.3 is shown in terms of the number of sigmas on the x-axis, with the probability density of the normalized Gaussian distribution shown on the y-axis. Integrity monitors separate nominal from faulted conditions by establishing a detection threshold (the purple vertical line) and alerting the presence of a fault when the test statistic exceeds the threshold. However, under nominal conditions, there is a certain probability that fault-free noise will drive the test statistic over the threshold and cause a false detection or fault-free alert. The bounding zero-mean Gaussian model of nominal errors allows this noise magnitude to be evaluated for any sub-allocated probability of fault-free alert PFFA (and corresponding continuity loss – see the right-hand branch of Figure 23.2).

Thresh.

10 –2

Probability Density

598

10 –4

Nominal

Faulted

10 –6

PMD PFFA/2

10 –8 MDE 10 –10 –6

–4

–2

0

2

4 KFFA

6

8

10

12

14

KMD

Test Statistic Response (no. of sigmas)

Figure 23.3

Gaussian model of monitor response to faulted conditions.

16

23.3 Interpretation of Integrity Requirements

The calculation of the threshold to meet a given PFFA allocation is easily done in MATLAB or another engineering toolbox with statistics capability. The MATLAB function call is K FFA = norminv 1 – PFFA 2, 0, 1

23 5

where KFFA is the size of the threshold in sigmas. In other words, the threshold in test statistic space is KFFA times the bounding sigma value for continuity. Note that the total PFFA sub-allocated to this monitor is divided by two here and in Figure 23.3 because fault-free noise can push the test statistic over the threshold on either side of zero. When a failure occurs, the monitor test statistic is biased to one side of zero but (in this simplified model) retains the same fault-free noise sigma. This is shown by the green curve in Figure 23.3. If the size of this bias is equal to the monitor threshold established previously, fault-free noise is equally likely to push the actual test statistic above or below the threshold, meaning that the probability of missed detection of the fault (PMD) is 0.5. Each monitor has a required PMD for the fault that it is designed to mitigate based on a sub-allocation of the integrity requirement, and it is usually much smaller than 0.5. The red vertical line labeled MDE in Figure 23.3, to the right of the threshold, represents the size of the bias in the test statistic that will be detected with the sub-allocated PMD. As with the threshold above, the MDE can be calculated from the statistics of the Gaussian distribution as follows, starting with the size of the missed-detection buffer: K MD = norminv 1 – PMD , 0, 1

23 6

Here, note that PMD is not divided by two because the fault biases the test statistic to one side of zero, and the possibility of MD to the other side of zero is negligible. Finally: K MDE = K FFA + K MD

23 7

and the MDE in test statistic space is KMDE times the bounding test statistic sigma. Note that it is possible for different bounding sigmas to exist for continuity and integrity (e.g. when the constraints for averaging or combining collected data for integrity are stricter than for continuity – see Section 23.3.4), and in those cases, it would be necessary to compute the MDE as follows: MDE = K FFA σ cont + K MD σ integ

23 8

where σ cont and σ integ are the different bounding sigma values for continuity and integrity, respectively. Of course, Eq. (23.8) can also be used when these two sigma values are the same. Once the MDE is known for a given monitor and fault condition, the magnitude of the differential range error corresponding to the test statistic at MDE can be determined.

This potential error must be bounded by the PLs computed by the user, as shown in Eq. (23.1) and explained further in Section 23.4. Note that, while this approach to computing threshold and MDE values is based upon the zero-mean Gaussian model for nominal test statistic values, the concept extends to other probability distributions as well. The basic idea is to determine threshold values that satisfy a sub-allocation of the continuity risk requirement and, based on that value, determine the smallest fault impact that will be detected with the probability derived from a sub-allocation of the integrity requirement. This impact drives the calculation of user PLs.

23.3.4

Conservatism Within Integrity Risk Model

The integrity risk model described above is based on probability evaluations that can be done in several ways. It is important to understand how this has been done for aviation applications of GNSS and alternatives that have been used for other applications. Civil aviation applications are designed to meet integrity requirements defined in terms of what is known as “specific risk.” In simple terms, this means that integrity requirements must be met for the worst combination of knowable or potentially foreseeable circumstances under which an operation may be conducted. For GNSS, some variables important to integrity, such as the user’s satellite geometry, are known by definition. On the other extreme are variables, such as receiver thermal noise, which are random and unpredictable (even if the received signal strength is known). But several factors that are critical to GNSS performance, such as multipath and ionospheric errors, fall in the middle and are neither completely random nor completely known [10]. In evaluating integrity risk, “specific risk” treats all error sources that are not completely random in a worst-case manner. One definition of “specific risk” is as follows: “Specific risk is the probability of unsafe conditions subject to the assumption that all credible unknown events that could be known occur with a probability of one (on an individual basis) [10].” The key elements of this approach are “worstcase” evaluation (from the point of view of the analysis used to evaluate integrity risk) and the separation of “unknown events that could be known” from unknown events that are truly random and unpredictable. In contrast, most evaluations of integrity or safety risk outside of civil aviation use the more natural (and less conservative) approach of “average risk,” which does not stress “worst-case evaluation” and does not treat “unknown events that could be known” differently from other unknown events. One definition of average risk is as

599

600

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

follows: “Average risk is the probability of unsafe conditions based upon the convolved (‘averaged’) estimated probabilities of all unknown events [10].” One example of the contrast between average and specific risk is the treatment of integrity risk due to anomalous ionospheric spatial gradients in SBAS and GBAS, which are both based upon specific risk. Gradients large enough to threaten the integrity of SBAS and GBAS corrections are rare, but because SBAS can observe the state of the ionosphere over very large regions, the prior probability of threatening anomalous ionospheric gradients is usually treated as 1.0. SBAS will detect and exclude all anomalous ionospheric gradients above a certain level, and its evaluation of the worst-case undetected error is based on the largest error that is just below what is guaranteed to be detected with the suballocated PMD (this is based on the MDE concept explained in the previous subsection). Since the prior probability is 1.0, this PMD will be very low (a fraction of 10−7 per approach), as it needs to mitigate almost all of the integrity risk by itself. GBAS is different from SBAS in that it cannot observe the ionospheric state directly, as it is a single-frequency system. Even if GBAS made dual-frequency measurements of ionospheric activity on the satellites that it was tracking, it would only see snapshots of disparate regions of the sky and would not necessarily be able to spot a gradient approaching one or more of its tracked satellites. Therefore, GBAS can use a prior probability of threatening ionospheric gradients lower than 1.0 (see [9]), but the prior probability of threatening gradients should be computed assuming anomalous ionospheric conditions rather than all ionospheric conditions (including the vast majority of the time when the ionosphere is quiet and gradients are small). While an individual GBAS installation is not able to distinguish anomalous conditions by itself, it could do so if it were making use of broadcast SBAS ionospheric corrections and/or GIVE values (see [11]) or were connected to other GBAS installations with which it shared data. Thus, “specific risk” penalizes GBAS for not making use of information that it was originally designed not to use but could have been given access to with additional investment. GBAS also determines worst-case impacts of threatening ionospheric gradients, which in its case are often given by the largest gradients allowed by the ionospheric gradient threat model (see Section 23.6). In contrast, an “average risk” approach would not enforce this level of conservatism in the prior probability calculations. It would allow the probability of threatening ionospheric gradients to be assessed relative to all ionospheric conditions rather than the uncommon set of anomalous conditions that is more likely to produce them. In addition, worst-case conditions (given the presence of threatening gradients) need not be assumed. Instead, all

possible threatening conditions could be averaged over to determine the probability of hazardous errors given an undetected threatening condition (PPL,i in Eq. (23.1)). The benefit of the “average risk” approach is that the probability of LOI (PLOI,i in Eq. (23.1)) for each fault condition will be much lower than in the “specific risk” approach, all else being the same. Since the integrity risk probability must be met whichever approach is used, additional design effort and conservatism is required to achieve this in using “specific risk.” This has been achieved for aviation uses of SBAS and GBAS, but at a sacrifice in availability and continuity compared to what would result from the use of “average risk.” This loss appears in the form of inflated sigmas to bound satellite, ground system, ionospheric, and other error sources, which leads to higher PLs.

23.3.5 Integrity Design Overview for GNSS Applications The elements of integrity risk evaluation described in this section are typically evaluated in an iterative fashion. Figure 23.4 shows a generic example of this procedure. The starting point is an allocation or breakdown of the overall integrity risk requirement (e.g. 10−7 per approach) to nominal conditions and all foreseen anomalous conditions (potentially including a miscellaneous category for unforeseen and un-analyzed anomalies). The prior probabilities of the foreseen anomalies are then assessed and validated if they are not already known. “Validation” here means, if nothing else, review by an internal and external body of subject-matter experts who will be responsible for approval of the final integrity safety case. While unpleasant “surprises” during the development of safety-critical systems are unavoidable, they can be minimized by reviewing the key inputs to the safety case as widely and as early as possible. Once trustworthy prior probability estimates are available, it is possible to approximate the missed-detection probabilities needed for the integrity monitor algorithms targeting each anomaly scenario. The bulk of the design work is developing, analyzing (often via software simulation), and testing these monitors to show that they can meet these derived PMD requirements. This includes time-based evaluations to demonstrate that the integrity TTA is also met, meaning that the derived PMD requirement is achieved within the TTA, where the TTA “clock” starts when the position error created by a threatening condition first exceeds one or more protection levels. Because this must be achieved for all potentially usable GNSS satellite geometries, this assessment is done by conservatively converting position domain error bounds into range-domain error requirements. One means of doing this is known as “time-varying MERR” and is described in [12].

23.4 Integrity Protection Level Concept and Its Implementation

Allocate Integrity Risk to Nominal Conditions and Identified Anomalies

Identify and Validate Prior Probabilities for Each Anomaly

Identify Required Missed-Detection Probabilities (PMD) for Each Anomaly

Analyze/Simulate/Test to Verify that Monitor(s) can Achieve Required PMDs within Time to Alert

Iterate and Redesign/Re-analayze/Re-simulate/Re-test as needed until top-level integrity risk allocations are satisfied.

Figure 23.4 Integrity design and validation procedure for GNSS applications.

Once a preliminary analysis of all threats and associated monitors has been completed, re-consideration of the initial integrity risk allocation and the integrity monitor design usually occurs because the derived monitor PMDs for one or more anomalies cannot be met. Beyond improving the initial monitor designs, one option is simply to allocate more of the overall integrity risk allocation to the anomalies that need it, but there is often little room to do so (because the initial integrity risk requirement is so small). This is often the time that conservatism in the original assumptions and prior probability calculations and threat models describing each anomalous condition get re-assessed. Under the “specific risk” approach, it is usually best to make worst-case assumptions initially and then consider relaxing the subset of these assumptions that creates the largest difficulties in meeting the integrity requirement. Some relaxation of the initial assumptions is almost always possible within the general constraints of “specific risk,” but it needs to be considered carefully by the integrity review team before too much reliance is placed upon an assumption that cannot be validated in the final safety case.

23.4 Integrity Protection Level Concept and Its Implementation In high-integrity GNSS applications, PLs are computed by users to represent position domain error bounds at the small probabilities required by the integrity requirements

for a given application. In augmentation systems such as SBAS and GBAS, most of the integrity mitigation is performed by the augmentation system, but only the user knows which GNSS satellites it is tracking and the contribution of user measurements to the overall error budget. Protection level calculations make use of the bounding error information broadcast by augmentation systems and local user information to determine position error bounds (in each position axis of concern) that are relevant to that user. These bounds are generally re-computed at each epoch and compared to the ALs (maximum tolerable position errors to maintain safety) that apply to the operation being conducted. Figure 23.5 shows the equation for the vertical protection level under nominal conditions (the so-called “H0 hypothesis”), when a zero-mean Gaussian fault-free error distribution is assumed (and has been shown) to bound the actual error distribution. This equation converts that bounding range error variance (σ i2, combining all augmentation system and user contributions) to vertical position domain error (using the si,vert2 coefficients from the pseudoinverse of the weighted satellite geometry observation matrix) and then extrapolates it to the tail probability required by the component of the integrity risk requirement allocated to the vertical segment of H0 integrity risk. This probability determines the multiplier Kffmd, which must account for the possibility of errors on either side of zero since no faultdriven bias is assumed. The si,vert2 coefficients are determined by the standard weighted geometric approach to solving for user position (see Section 2.3.9.1 of [13] and

601

602

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

Bouding range error variance

N

VPLH 0 = Kffmd

𝛴 S2i, vert σ i2

i=1

Extrapolation to H0 integrity risk probability (for Gaussian dist.)

Figure 23.5

Geometric conversion: range to vertical position

Vertical protection level definition – nominal conditions (H0).

Vertical position error std. dev. under faulted condition

VPLf = Bf,vert + Kmd, f σ vert, f Error bias caused by faulted condition (converted to vertical position error)

Extrapolation to faulted integrity risk, incorporating prior probability (for Gaussian dist.)

Figure 23.6 Vertical protection level definition – faulted conditions (Hf).

Section 2.2 of Chapter 2). Note that other position axes, such as 1-D lateral and 2-D horizontal, have similar calculations performed for them, but the 1-D vertical axis is typically the limiting one for aircraft precision approach availability. Figure 23.6 shows the equation for the vertical protection level under faulted conditions in which the fault adds an error bias to nominal measurement errors (the “Hf hypothesis”). This does not necessarily describe all possible anomaly effects, but it covers all of the anomalies for which fault mode PLs have been computed to date for civil aviation. Here, the key change is the addition of the impact of the bias (already converted to the vertical position domain) in the first right-hand-side term. The bias magnitude depends on the fault being modeled and often depends on user-specific information, such as the distance between the user and the reference receiver centroid location in GBAS. The second term is very similar to the main term in Figure 23.5 in that it extrapolates one-sigma nominal error (again, converted to vertical position) to a certain low probability, but this probability, which determines the multiplier Kmd,f, is influenced by the prior probability of the anomaly whose (worst-case) impact is reflected by the first term. If, for example, the fault represented there has a prior probability of 10−4 per approach, and the integrity risk allocated to this fault is 10−9 per approach, the remaining probability to be covered by fault-free error is 10−5 per approach, and this probability would be used to determine Kmd,f using one side of the Gaussian distribution (since, as with MDE above, the fault-induced bias is either positive or negative). When faulted conditions are represented by PLs, multiple different faulted conditions are generally represented by different versions of the equation shown in Figure 23.6, and the largest protection level at any given user and time

is the one that applies to that user’s integrity determination. For GBAS, two separate faulted PLs are computed by users (in addition to the H0 protection level): one for singlereference receiver faults (H1) and one for ephemeris faults (Heph). The impact of a single-reference receiver fault is independent of user location relative to the GBAS site and is indicated to users by broadcasting “B-values,” which represent the errors that would be present in the differential corrections if any single reference receiver were providing MI. The impact of ephemeris faults increases linearly with user distance from the GBAS site, and a bound on this error is provided to users via broadcast of a parameter that gives the maximum ephemeris range-domain error impact with distance from the GBAS site (beyond this, GBAS ephemeris monitoring is guaranteed to detect and exclude the faulted condition with the required PMD). Not all possible faulted conditions have PLs defined for them in GBAS (see Section 12.6 of Chapter 12). Furthermore, SBAS does not define any faulted protection level equations – it only uses the nominal equation form shown in Figure 23.5 (see Section 13.4.5 of Chapter 13). This does not mean that these unrepresented faults are ignored. Instead, faults not directly represented by protection level equations must be bounded by the PLs that are computed or specifically shown as “faults not covered by PLs” in the system-level integrity allocation. For SBAS, this means that all fault conditions must be covered by the nominal protection level equation or be so improbable that they fall under the small allocation to “negligible” conditions. To satisfy this, the range-domain error variance in Figure 23.5 is inflated to bound worst-case anomalies as well as nominal conditions. For GBAS, a similar requirement applies to the anomaly conditions that are not included in the H1 and Heph hypotheses.

23.5 Bounding Uncertain Error Distributions

Operationally, integrity is maintained as long as the PLs computed at each epoch are below the ALs. If this condition is suddenly violated, integrity is no longer protected, and the operation is aborted – continuity is lost. To minimize the likelihood of predictable continuity losses due to changes in satellite geometry (e.g. a useful satellite that is about to set below the horizon), some applications perform a predictive protection level calculation to check availability at the beginning of an operation to confirm that PLs will remain below ALs throughout the operation as satellite geometry changes. Other applications avoid this step and count on the probability of predictable continuity loss over a single mission interval being low enough to ignore.

23.5 Bounding Uncertain Error Distributions One challenge to bounding user errors in the protection level calculations derived above is demonstrating that the standard deviations (“sigmas”) meant to bound nominal errors in Figures 23.3 and 23.4 actually do so to the very small probabilities required (this is also an issue for the test statistic sigmas used in Section 23.3.3). This is difficult because most distributions of actual errors and test statistics have tails that are fatter than Gaussian, meaning that as the probability of occurrence becomes smaller, the probability of a given magnitude becomes larger than what would be computed from Gaussian distributions. Probability distributions of actual errors and test statistics are usually derived or informed by data collection, and it is very difficult to collect more than 104 to 105 statistically independent samples in representative conditions. Thus, extrapolating the bounding Gaussian sigmas to 10−7 or lower, as typically done in the nominal protection level calculation of Figure 23.5, requires additional information. Several approaches have been developed in the academic literature to support this extrapolation (see [14–16]), but all of them make several assumptions about the shape and character of the actual distribution that must be overbounded by a Gaussian distribution at the required probabilities. As a result, most overbounding in practice is done empirically by fitting the cumulative distribution function (cdf ) of a Gaussian distribution with varying sigma values to actual data and increasing the assumed bounding sigma value until sufficient margin exists between the bounding Gaussian distribution and the actual data at the required probabilities. The amount of margin necessary for integrity is determined by engineering judgment and is influenced by the observed shape and tail probability of the actual distribution relative to that of the Gaussian as well as any theoretical knowledge regarding the actual distribution.

An example of observed vertical position error (VPE) data from the WAAS network from July to September 2010, inclusive, is shown in the histogram in Figure 23.7, which comes from one of a series of quarterly Performance Analysis Network (PAN) reports compiled by the William J. Hughes FAA Technical Center for GPS, WAAS, and GBAS installations in the United States [17]. VPEs based on using WAAS corrections were estimated by the 37 WAAS reference stations (WRSs) in operation at that time based on the known locations of each WRS. Recording error estimates once per second per WRS over three months generated the total of about 2.8 × 108 samples shown in Figure 23.7. Errors generated under conditions where the precision approach PLs exceeded either the vertical or horizontal ALs for WAAS localizer precision vertical (LPV) operations (for a 250 ft DH: VAL ≤ 50 m; HAL ≤ 40 m) were excluded from this data. Not all of the collected points represent statistically independent samples because errors measured within several seconds of each other have highly correlated errors in both WAAS corrections and WRS multipath errors. If the separation between independent samples is roughly 100 s, only about 2.8 × 106 of the samples in Figure 23.7 are actually independent. The blue curve in Figure 23.7 shows a binned histogram of the absolute value of actual VPEs in meters over this three-month period. As shown in the figure, the 95th-percentile error bound was about 1.2 m, while the 95th-percentile error bound was about 1.6 m. Given that the mean error should be and appears to be close to zero, a Gaussian one-sigma value would be computed from the 95th-percentile error by dividing by 1.96 (treating the actual error distribution as two-sided: positive and negative), giving σ95 0.61 m. The Gaussian divisor that applies to the 0.62 m. 99th-percentile error is 2.58, which gives σ99 Thus, at these relatively frequent error bounds, the Gaussian distribution appears to apply well to this data. As an aside, note that the appropriate Gaussian divisors for two-sided distributions with zero mean error can be computed in MATLAB using Eq. (23.5), where the desired two-sided probability bound replaces PFFA in that equation. Table 23.2 shows the results of looking further to the right in Figure 23.7 to observe the approximate bounds on less probable errors (or higher probabilities of bounding the actual error). As the bounding probability becomes higher, the bounding VPE increases at a significantly higher rate than would be projected by the tails of the standard Gaussian distribution, as shown by the increasing values of the Gaussian sigma value equivalent to each probability and the increasing ratio of these sigmas to the 95th-percentile sigma of 0.61 m. Therefore, if one wished to bound the entire range of probabilities up to 1–107 (or, equivalently, to conservatively represent errors down to a probability of 10−7) using

603

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

3rd Qtr 2010 WAAS LPV Vertical position Error (VPE) Distribution

109

Vertical Position Error (VPE) Normalized Vertical Error (NVE)

108 107 106 No. of Samples

604

105 104 Max. VPE ≈ 7 m at Barrow, AK

103 102

Meas. from 37 WAAS stations

101 100

0

1

2

95% Error (m) 99% Error (m) 1.2 1.6

3

4

5

VPE (m)

6

7

8

Receiver Days Total Samples (sec) 3243 280201434

Figure 23.7 Histogram of WAAS vertical position errors (VPEs) observed from July to September 2010 [17]. Source: Reproduced with permission of William J. Hughes Technical Center / Federal Aviation Administration.

Table 23.2 Bounding errors and equivalent one-sigma values for high probabilities in Figure 23.7 Bounding probability

Bounding VPE (m)

Equivalent σ (m)

Ratio to 95th-pct σ

1–103

2.2

0.67

1.10

4

1–10

2.9

0.75

1.23

1–105

3.6

0.82

1.34

6

1–10

4.8

0.98

1.61

1–107

6.6

1.24

2.03

a single zero-mean Gaussian distribution, the selected sigma value would need to be at least 1.24 m from Table 23.2, and significant margin would need to be added to this calculated value to protect against events that could affect WAAS (such as severe ionospheric storms) that did not happen to occur during the three months of observations in this dataset. Depending on knowledge of the conditions during these three months, a bounding one-sigma value of 1.5 to 2.0 m might be chosen, meaning that the level of sigma inflation relative to the 95th-percentile sigma value of 0.61 m is at least a factor of 2.45. This example of fatter-than-Gaussian tails is typical of most collections of error and test statistic data, even those

that come from well-behaved and well-controlled processes. The reasons that fatter-than-Gaussian tails exist in the real world, contrary to expectations that might be derived from the central limit theorem, are varied. For example, see [18] for a discussion of the effect of “mixing” of parameters derived from Gaussian distributions with different parameters in the same data set. What is important is to expect fatter-than-Gaussian behavior in the tails of distributions of real data, to take enough independent samples to roughly quantify this behavior (rather than making Gaussian extrapolations from 95th- or 99th-percentile bounds), and to be prepared to allow for its effect by making room in error budgets for significantly inflated sigma values.

23.7 Introduction to RAIM

23.6 Faults and Anomalies – The Role of Threat Models The evaluation of faults and anomaly impacts, including the bias component of faulted threat models in Figure 23.6, requires a model of each fault or anomaly considered. In the design of GNSS for civil aviation, these models are called “threat models,” and they have several important characteristics. Figure 23.8 illustrates these features along with the process of developing and using threat models to describe faults and anomalies [19]. Each threat model consists of a simplified physical model of the fault or anomaly of concern with bounded parameters, as indicated by the (multidimensional) cube in the center of Figure 23.8. Since faults and anomalies are rare, these bounds are unknown in general and must be estimated from the limited available data and theoretical knowledge. Once these bounds are established, the probability of faults with parameters outside these bounds (or faults that do not obey the simplified physical model) must be negligible relative to the integrity risk allocation to this fault mode. Once a physical model with bounded parameters has been developed for a given fault or anomaly, it is evaluated analytically or (more commonly) via simulation to determine its worst-case user impact given the presence of integrity monitoring. Under the “specific risk” approach to integrity assessment, every combination of parameters within the bounded threat model space must be evaluated, and the combination that gives the worst results in terms of maximizing integrity risk after monitoring must be assumed to be present with the full prior probability assigned to that fault mode. This is very conservative, as the parameter combination that creates this worst case may not be very likely, given that a fault of this type occurs. Under an “average risk” approach, the probability of each

combination of parameters within the threat model (as a fraction of the prior probability of this class of fault or anomaly) could be taken into account [10, 19].

23.7

GNSS measurements are vulnerable to rarely occurring faults including satellite failures, which can potentially lead to major safety threats for users. To mitigate their impact, fault detection and exclusion (FDE) algorithms such as RAIM can be implemented [20, 21]. The main challenge in RAIM is not only to design fault detectors but also to evaluate the impact of undetected faults on safety risk. Two RAIM methods in particular have been widely used over the past two decades: chi-squared residual-based (χ 2) [21–23] and solution separation (SS) RAIM [20, 24, 25]. The two methods are presented below, starting from common definitions of the integrity and continuity risks. Integrity and continuity set conflicting requirements on FDE algorithms [26]. The fault detection function reduces integrity risk by generating alerts when redundant measurements are deemed inconsistent, but also increases continuity risk due to potential false and true alarms. Conversely, the fault exclusion function reduces continuity risk by allowing a mission to be pursued after identifying and removing faults, but increases integrity risk due to potential incorrect exclusions.

23.7.1

Collected Data

Bounded, multidimensional parameter space

System/User Impact Model (incl. monitoring) Deterministic simulation

Worst-case user impact (and relevant points within threat model)

Figure 23.8 Threat model development and utilization.

Redundancy for FDE

The core principle of RAIM is to exploit redundant measurements to achieve self-contained fault detection at the user receiver. The solution separation approach provides an intuitive illustration of this concept. If five or more satellites are

Specific Threat or Anomaly Description

Theory/Physics

Introduction to RAIM

605

606

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

available to estimate three position coordinates and a receiver clock bias, then multiple sets of four or more satellites provide positioning solutions. Large separation between the solutions that include the faulted space vehicles (SVs) and the ones that do not is a strong indicator that a fault is present. This principle is illustrated in Figure 23.9. When estimating four unknown parameters, five satellites are needed for single-SV fault detection, six SVs are required for dual-SV detection, and so on. In addition, exclusion is described in Section 23.7.4 as a second layer of detection, and can therefore be performed using SV redundancy. With regard to exclusion, six satellites are needed for single-SV FDE, eight SVs are required for dual-SV exclusion, and so on. With the modernization of GPS, the full deployment of GLONASS, and the emergence of Galileo and BeiDou, the number of redundant ranging signals increases dramatically, which opens the possibility of fulfilling stringent navigation integrity requirements using RAIM FDE [27, 28]. Figure 23.10 shows nominal SV constellations for four GNSSs. In Figure 23.10, signals received at an example location (at Chicago, Illinois, United States) are represented with thick black lines. Whereas each individual constellation only provides about five to ten ranging measurements, the joint constellation can provide continuous, global coverage of 25 to 35 satellites, thereby substantially increasing SV redundancy.

RAIM not only aims at detecting and excluding faults, but also at evaluating the integrity and continuity risks, or as an alternative, a protection level, which is a probability bound on the position estimate error. Integrity and continuity risk evaluation is needed when designing a navigation system to meet predefined requirements, and it is needed operationally to inform the user whether a mission should be pursued or aborted. Integrity risk evaluation includes both assessing the fault detection capability and quantifying the impact of undetected faults on estimation errors. In order to avoid making assumptions on unknown fault distributions, a bound on the integrity risk corresponding to the worst-case undetected fault can be evaluated. This bound is then compared to a specified integrity risk requirement to assess availability, which is the fraction of time where position estimates can safely be used [29]. It is therefore of primary importance for system availability to derive a tight bound on the integrity risk. The tightness of this bound varies depending on how RAIM is implemented. χ 2 and SS RAIM can themselves be implemented in several ways in order to either reduce the safety risk bound or to decrease the computation load. Section 23.7.2 establishes common definitions of integrity and continuity risks, which are then used in Section 23.7.3 to describe the χ 2 and SS RAIM algorithms.

pdf(xˆ0)

1 FULL-SET SOLUTION using 5 SVs

using (1,2,3,4,5)

xˆ 0 x

impact of fault on SV1

pdf(xˆ i)

5 SUBSET SOLUTIONS using 4 SVs using (2,3,4,5)

using (1,2,3,4) using (1,2,3,5) using (1,2,4,5) using (1,2,3,5) xˆi

x

Figure 23.9 Exploiting measurement redundancy using solution separation. With five SVs available, six SV combinations can be used to estimate four unknowns. We note x i, for i = 0, …, 5, the six vertical position estimates. Subscript 0 designates the full-set solution using all SVs, and subscripts 1 to 5 correspond to the five subset solutions with a single SV removed. All sets that include SV1 have their mean shifted with respect to the fault-free subset, which is represented with a dashed curve. The maximum solution separation max x 0 − x i i = 1, …, 5 is an intuitive and efficient detection test statistic.

23.7 Introduction to RAIM

Joint Constellation

GPS (U.S.A.)

GLONASS (Russia)

Beidou (China)

Galileo (Europe)

Figure 23.10 Nominal satellite constellations for future GNSSs. Signals received at an example location (at Chicago, United States) are represented by thick black lines.

23.7.2 Integrity and Continuity Risk Definitions for Fault Detection In this section, the integrity and continuity risks are defined for fault detection only, followed by notations for the leastsquares (LS) estimator. The integrity risk criterion for fault detection is defined in [30] as h

P ε0 > ℓ

q < T H i PHi + PNM ≤ I REQ

i=0 ≥ PHMI

23 9 where PHMI is the integrity risk, or probability of hazardously MI (HMI), upper-bounded by the left-hand-side (LHS) term in Eq. 23.9. It captures the risk of hazardous information (event ε0 > ℓ) but no detection ( q < T); is the error on the estimated parameter of interest ε0 (also called “state” of interest); ℓ is a specified AL that defines hazardous situations (e.g. [31]); q is the detection test statistic (q is used here to represent both the χ 2 and SS test statistics); T is the detection threshold; for i = 0, …, h is a set of mutually exclusive, jointly Hi exhaustive hypotheses. H0 is the fault-free hypothesis. The remaining h fault hypotheses correspond to faults on subset measurement i (including single-satellite and multi-satellite faults);

PHi is the prior probability of Hi occurrence; IREQ is the integrity risk requirement (also specified in [31], for example, aviation applications); PNM is the prior probability of a set of very rarely occurring faults that need not be monitored against such that PNM ℓ f i P q2χ < T 2χ f i fi

i=0

Pi

where the (n − m) × n parity matrix Q is defined as: QQT = In − m and QH = 0(n − m) × m. The χ 2 RAIM detection test statistic can be written as: q2χ pT p = rT r [22, 35]. q2χ follows a non-central chi-square distribution with (n − m) degrees of freedom and non-centrality parameter λ2χ (λ2χ f T QT Qf ) [35]. In χ 2 RAIM, integrity and continuity risk evaluation can be performed directly using Eqs. 23.9 and 23.10. In order to avoid making assumptions on unknown fault distributions,

0 n − ni

× ni

In − ni

T

. Assum-

ing that n − ni ≥ m and that BTi H is full rank, x i is defined as x i sTi z , for i = 1, …, h, where sTi αT Pi HT Bi BTi and −1

HT Bi BTi H

. It follows that, under Hi, the estimate

αT Pi α . The soluerror εi can be expressed as εi N 0, σ 2i tion separations are defined as [20, 24, 25, 30] Δi

23 12

23 13

where we used the well-known fact that ε0 and q2χ are statistically independent [35], so that the joint probability in Eq. 23.9 can be expressed as a product of probabilities. Also, under the nominal, fault-free hypothesis (index i = 0), we use the definition f0 ≡ 0. In contrast to χ 2 RAIM, PHMI and PFA bounds are typically used in SS RAIM, which are looser than Eq. (23.13), but are computationally efficient because they do not require determination of worstcase fault vectors. In SS RAIM [24, 25], the full-set solution x 0 , obtained using all n measurements in z, is distinguished from the subset solution x i, derived using only the (n − ni) fault-free measurements BTi z under Hi, where following the same

The χ 2 RAIM detection test statistic can be derived from the (n − m) × 1 parity vector p, or equivalently from the n × 1 LS residual vector r, which both lie in the (n − m)dimensional parity space, or left null space of H, and can be expressed as [22, 35]: In − HP0 HT z

PHi + PNM

and PFA = P q2χ ≥ T 2χ H 0 PH 0

assumptions as for Ai, Bi

Qz = Q v + f and r

ATi P0 HT α, where

Ini 0ni × n − ni [30]. Second, the worst-case fault Ai magnitude, fi, can be determined using a line search method. Thus, the χ 2 RAIM integrity and continuity risk bounds can be expressed as

23.7.3 Residual/Parity-Based and Solution Separation RAIM

p

−1

x 0 − x i = ε0 − εi , and

Δi N sT0 − sTi f , σ 2Δi = σ 2i − σ 20 for i = 1, …, h 23 14 Let TΔi be the SS RAIM detection thresholds. The SS RAIM PHMI and PFA can be bounded by [30] h

PHMI ≤

P εi + T Δi > ℓ H i PHi + PNM and i=0 h

PFA ≤

P Δi ≥ T Δi H 0 PH0 i

23 15

23.7 Introduction to RAIM

u3

u2

p

6 4

u2

u3 6 4

qχ

Tχ TΔ1 σΔ1

2

2 p2

p2

q3 q2

0

TΔ3 σΔ3

0

u1

u1

–2

–2

TΔ2 σΔ2

–4 –4

q1

–6

Fault Lines

–6

–6 –6

–4

–2

2

0 p1

4

Figure 23.11 Test statistics for χ and SS RAIM in parity space. The χ 2 test statistic qχ is the norm of the parity vector p, whereas the SS test statistics qi, for i = 1, …, 3, are orthogonal projections of p onto the fault mode lines. In this example, p is a bivariate normally distributed random vector, with unit-variance i.i.d. elements. Curves of constant joint probability density describe circles (not represented) centered at the origin under H0, and centered along the i-th fault mode line under fault hypothesis Hi. 2

The PFA-bound in Eq. (23.15) is used to determine the values of the thresholds TΔi ensuring that the requirement CREQ, 0 is satisfied. TΔi can be expressed as TΔi = Q−1{CREQ, i/(2PH0)}σ Δi and CREQ,0 = hi= 1 CREQ,i , where the function Q−1{} is the inverse tail probability distribution of the standard normal distribution. For single-SV faults, that is, for ni = 1, Δi can be written as [30] qi

Δi σ Δi = uTi p , where ui

QAi ATi QT QAi

−1 2

T

for i = 1, …, n with Ai = 01 × i − 1 1 01 × n − i ; that is, ui is the unit direction vector of the ith column of Q. The n solution separations (h = n when ni = 1) are projections of p on ui. Both qχ and qi are represented in parity space in Figure 23.11 for an illustrative example used in [35]. Let us consider a scalar state x and a 3 × 1 measurement vector z that are expressed as z = Hx + v + f where H = 1 1 1 T and v ~ N(03 × 1, I3). Since m = 1 and n = 3, the (n − m) parity space is two-dimensional, which is convenient for display. The fault vector represents three single-measurement faults with unknown fault magnitude fi, for i = 1, 2, 3: f =

f1

–4

–2

6

0 0 T , or f = 0

f2

0 T , or

f = 0 0 f 3 T. Three “fault mode lines” are described by the mean of p as fi varies from −∞ to +∞. They have direction vectors ui defined above. Figure 23.11 illustrates the fact that qχ is the norm of p, whereas qi, for i = 1, …, 3,

0 p1

2

4

Single-SV Fault Lines X2 RAIM SS RAIM

Figure 23.12 χ 2 and SS RAIM detection boundaries. The detection boundaries for χ 2 and SS RAIM are a circle (or a hypersphere in higher-dimensional parity space) and a polygon (or a polytope), respectively [30]. In this example, the SS detection thresholds are all equal (TΔ1 = TΔ2 = TΔ3), so that the polygon is a hexagon. Source: Reproduced with permission of John Wiley & Sons.

are orthogonal projections of p onto each of the three fault mode lines. The resulting χ 2 and SS RAIM detection boundaries are represented in Figure 23.12. The combined impact of measurement noise and fault causes p to be nonzero. Detection is established if the parity vector p lands outside the detection boundary. Figure 23.12 illustrates that the probability of no detection (second joint event in Eq. 23.9) differs for χ 2 and SS RAIM: it is the probability of being inside the dashdotted circle for χ 2 RAIM, and inside the hexagon for SS RAIM. Further comparison of χ 2 and SS RAIM detection capability can be found in [36, 37].

23.7.4 Reducing Continuity Risk Using Fault Exclusion Section 23.7.3 was limited to fault detection and did not address exclusion. Detection provides a means of ensuring that PFA is lower than CREQ, 0 as expressed in Eq. 23.10. However, the complete continuity risk PLOC accounts for all events causing loss of continuity (LOC), and can be expressed as h

P D0 H i PHi + Pother

PLOC =

23 16

i=0

where D0 is the detection event. Note that PFA = P(D0| H0)PH0. The term Pother encompasses all other sources of LOC, including unscheduled SV outages [31, 38], jamming, and ionospheric scintillation.

609

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

If the detector is efficient, then

h i = 1P

D0 H i PHi ≈

The first term in Eq. 23.17 is the same as the bound given in Eq. 23.9 for detection only. The second term in Eq. 23.17 accounts for all fault hypotheses (subscript i), and all exclusion candidates (j) [40]. In parallel, the continuity risk is redefined as

h i = 1 PHi .

And if this probability is larger than the overall continuity risk requirement CREQ, which is likely to occur in multi-constellation GNSS where h is large, then faults need to be excluded to continue using the system. This is why fault exclusion procedures were designed in [32, 34, 39]. FDE procedures can be described in three main steps. (a) The first step is the detection test described in Sections 23.7.2 and 23.7.3. (b) If a fault is detected (event D0), candidate subset measurements to be excluded are considered (indicated below with subscripts j). A second set of detection tests is carried out to ensure that the remaining non-excluded measurements are fault-free. An “exclusion test” is passed (event D j) if no fault is detected in the remaining measurements. (c) Finally, if none of the exclusion tests is satisfied (event hj = 1 D j), the mission is interrupted, which impacts continuity. Conversely, if one or more candidate subsets meet the exclusion test, then any one of these subsets can be excluded. However, excluding a subset that does not eliminate HMI (wrong exclusion or fault-free exclusion causing HMI) impacts integrity. An upper bound on integrity risk for FDE can be defined as [40]

h

H i PHi + Pother 23 18

Equations (23.9) and (23.10) versus (23.17) and (23.18) capture a fundamental trade-off of exclusion methods, which aim at reducing continuity risk at the expense of integrity risk. The continuity risk in Eq. 23.18 is lowered using exclusion as compared to using detection only in Eq. 23.16 derived from (23.10). The price to pay for this continuity risk reduction is the second term in Eq. 23.17, the integrity risk of performing an exclusion, which was not present in (23.9). The above PHMI and PLOC definitions are implemented for SS and χ 2 RAIM in [40]. The SS and χ 2 RAIM no-detection and exclusion regions are represented in Figure 23.13, for the illustrative example described in Section 23.7.3. First, one can respectively recognize in the left and right charts the hexagonal SS-based and circular χ 2-based no-detection areas. Then, Figure 23.13 shows that, for both SS and χ 2 RAIM, exclusion areas (dark-gray) are bands surrounding the fault mode lines. These bands are sensible criteria for exclusion. If the parity vector is near a fault line, then it is easy to figure out which measurement to exclude. On the contrary, if the parity vector lands in between two fault mode lines, then it becomes extremely challenging to determine which of the two fault modes caused the error that was detected, and it is safer not to exclude and to trigger an alert.

P HI 0 , D0 H i PHi h

j = 1D j

i=0

i=0 h

+

h

P D0

PLOC

h

PHMI ≤

P HI j , D0 , D j H i PHi + PNM j=1i=0

23 17 where HIj designates hazardous information when using an estimation solution that excludes candidate subset j.

χ2 RAIM

SS RAIM

p2

610

4

4

2

2

0

0

–2

–2

–4

Single-SV Fault Lines

–6

–4 –6

No Detection –6

–4

–2

0 p1

2

Exclustion

–6

–4

–2

0 p1

2

4

6

Figure 23.13 Parity space representations of no-detection and exclusion areas for SS (left) and χ 2 RAIM (right). If the parity vector lands in the dark-shaded band surrounding fault line, there is a quantifiable probability that the faulty measurement is correctly identified. It can therefore be excluded [30]. Source: Reproduced with permission of John Wiley & Sons.

23.8 Advanced RAIM (ARAIM)

23.8

Advanced RAIM (ARAIM)

With the emergence of new GNSSs providing dualfrequency ranging signals, the number of redundant ionosphere-error-free measurements increases considerably, thereby opening the possibility of fulfilling stringent navigation requirements at the user receiver, using RAIM. In particular, RAIM can help alleviate requirements on ground monitors. This is why researchers in the European Union and in the United States are investigating Advanced RAIM (ARAIM), not only for en route navigation, but also for worldwide vertical guidance of aircraft [41–43]. The US–EU “Agreement on the Promotion, Provision and Use of Galileo and GPS Satellite-Based Navigation Systems and Related Applications” [44] was signed in 2004 with the objective of developing GPS–Galileo based applications for Safety-of-Life services. One goal in particular is to establish whether ARAIM can be the basis for a multiconstellation concept to support global air navigation. ARAIM complements SBAS (see Chapter 13) [43]. It is anticipated that ARAIM could support horizontal navigation (H-ARAIM) in cases where SBAS services are unavailable while providing superior performance as compared to traditional RAIM. One of the most ambitious operations that ARAIM could support is global vertical navigation of aircraft (V-ARAIM), with LPV or LPV-200 requiring guidance down to a 200 ft height above the runway. To achieve this, ARAIM leverages three major future developments:

• • •

An increased number of satellites from multiple GNSS constellations Dual-frequency satellite signals allowing to eliminate the impact of ionospheric errors An Integrity Support Message (ISM) providing integrity parameter values to be used in the airborne ARAIM algorithm

These elements are further discussed in Section 23.8.1. The ARAIM measurement error and fault model is described in Section 23.8.2, where an overview of the baseline airborne ARAIM multiple hypothesis solution separation (MHSS) algorithm is given. Section 23.8.3 presents an approach to designing the optimal estimator in RAIM, which minimizes integrity risk. This non-least-squares (NLS) estimator is implemented in ARAIM. Preliminary ARAIM performance evaluations are given in Section 23.8.4.

23.8.1

ARAIM Architecture

Unlike in SBAS, fault detection using ARAIM is autonomously performed at the airborne receiver. ARAIM also relies upon a ground segment to validate, over hour-to-year-long

periods, the assertions made at the airborne receiver. In contrast to SBAS, the ARAIM ground monitor does not issue alerts: it does not need to meet an integrity allocation or a time to alarm. It is continuously running in the background of the actual integrity monitoring process at the aircraft. To incorporate information from multiple constellations at different stages of their development, ARAIM employs an ISM generated at the ground and broadcast to airborne receivers. The ISM provides integrity parameters describing measurement errors and faults, including, for example, the prior probability of satellite fault, Psat, the prior probability of constellation fault, Pconst, the standard deviation of nominal ranging uncertainty due to satellite orbit and clock ephemeris errors, σ URA, and a maximum value bNOM on non-Gaussian ranging errors primarily due to signal deformation [41, 42]. These parameters are key inputs to the airborne ARAIM algorithm, which determines the PL. Candidate ARAIM architectures for ISM generation include offline and online architectures [42]. Differences between offline and online architectures are pointed out in Figure 23.14. Both architectures leverage the

GNSS 1

GNSS 2

GNSS 3

Avionics with integrity monitoring Data link to send hourly changes in range accuracy Psat & Pconst ephemeris

Performance commitments from CSPs

Offline Monitoring Integrity Support Message (ISM)

Overlay Ephemeris

Reference Stations ~15 globally Dedicated

Online Monitoring

Figure 23.14 Overview of Online ARAIM [42, 46]. Gray-shaded elements indicate differences from Offline ARAIM. Online ARAIM gives ANSP more control over ISM parameters by generating and sending its own precise orbit and clock parameters called “overlay” ephemeris. The overlay is generated using few dedicated ground reference stations (RSs). By contrast‚ Offline ARAIM uses data from hundreds of existing RS, for example, from SBAS and IGS. The ISM is broadcast hourly for Online ARAIM, versus quarterly or yearly for Offline ARAIM. Online ARAIM can help mitigate Offline ARAIM’s availability risk caused by potentially weak CSP commitments on achievable ranging performance. Source: Adapted from EU-US Cooperation on Satellite Navigation [42].

611

612

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

Constellation Service Providers (CSPs) Service Provider Commitments (SPCs), for example, as specified in [6, 45] for GPS. However, the SPCs are not intended for specific applications. Thus, additional ground monitoring by Air Navigation Service Providers (ANSPs) will likely be required, especially for V-ARAIM, because CSP SPCs may not be tailored to specific requirements such as LPV-200. Reference [43] foresees initial H-ARAIM operations with a static ISM (i.e., a fixed, unchanging ISM). After an evaluation period, interested ANSPs may seek operational approval for V-ARAIM.

23.8.2

2Q

VPL − b0 σ0

h

+

Q i=1

VPL − T Δi − bi PHi σi

+ PNM = I REQ

23 19

where bi, for i = 1, …, h, is the impact of the nominal measurement bias bNOM on the vertical positioning error; we use the notation b0 for the full-set solution and bi for the i-th subset solution. As detailed in Section 23.7, establishing a tight VPL, that is, a tight probabilistic bound on the vertical positioning error, is instrumental to ensuring high availability. The next section describes an approach to finding the optimal estimator, which minimizes VPL, or equivalently, minimizes integrity risk.

Baseline ARAIM Airborne Algorithm

References [42, 43] provide detailed descriptions of a baseline ARAIM MHSS airborne algorithm, which serves as an example integrity monitoring method to analyze ARAIM performance. The method is based on the SS RAIM principles described in Section 23.7 of this chapter. Many useful developments came from refining this baseline algorithm, including new results on the optimal detector in ARAIM [36, 37], computationally efficient approaches to deal with large numbers of subset solutions [43], and the derivation of an optimal estimator, which minimizes integrity risk in ARAIM as explained in Section 23.8.3. The design of this algorithm was in part driven by requirements [43]. This chapter focuses on vertical positioning performance to achieve LPV-200, based on an interpretation [43, 47] of the International Civil Aviation Organization (ICAO) Standards and Recommended Practices (SARPs) [48]. In parallel to a 8 × 10−6 continuity risk requirement, ARAIM assumes vertical positioning performance criteria, including a 10 m, 1−10−7 fault-free accuracy requirement, and a 35 m, 1−10−7 limit on the position error. This last integrity criterion is the driver for loss of availability; it captures the fact that the risk of the vertical protection level (VPL) exceeding a VAL of ℓ = 35 m should be lower than IREQ = 10−7. Accuracy criteria do not account for fault conditions, whereas VPL does. Consistent with these requirements, ARAIM uses two error models: an integrity error model and an accuracy (or continuity) error model. The accuracy error model assumes smaller values for σ URA and bNOM as compared to the integrity model. In addition, both accuracy and integrity error models account for residual tropospheric delay, multipath errors‚ and receiver noise [42]. The ARAIM VPL equation can be derived from Eq. (23.15) (by replacing the VAL ℓ by VPL), and is obtained by solving the following equation:

23.8.3

Optimal NLS Estimator in ARAIM

Three main research efforts have investigated the possibility of using NLS estimators, which, in exchange for a slight increase in nominal positioning error, can substantially lower the integrity risk in RAIM [49–51]. The first two references pioneered the use of NLS estimators in RAIM, but employed heuristic approaches to reduce integrity risk. In 2012, in the context of ARAIM, Blanch cast the NLS estimator design into a constrained optimization problem [51]. Further refinement of this method yielded practical, computationally efficient implementations [52, 53]. Using the same notations as in Section 23.7, the NLS estimate x NLS for the state of interest (as defined in Eq. 23.9 and in the text following Eq. 23.11) can be written as:x NLS sT0 z + βT Qz, where the state estimate sT0 z = x 0 lies in the column space of H, and βTQz lies in the left null space of H. The estimator design problem narrows down to finding the (n − m) × 1 estimator modifier vector β, which minimizes integrity risk while meeting continuity and accuracy requirements. The impact of β is best understood in comparison with a more conventional LS estimator (β = 0). To illustrate this, the example six-satellite geometry displayed on the left chart in Figure 23.15 is considered. The right-hand chart is a failure mode plot for a single-SV fault on SV4. In a failure mode plot, the estimate error ε is displayed versus normalized solution separation test statistic qi ≡ Δi/σ Δi (defined in Section 23.7). “ε” designates both ε0 for the LS estimator (represented using dashed lines) and εNLS for the NLS estimator (dark-gray color, solid lines). The AL (ℓ = 15 m in this example) and the detection threshold (approximately 5 (unitless)) define the boundaries of the HMI area. Lines of constant joint probability density are ellipses because ε and qi are normally

23.8 Advanced RAIM (ARAIM) LS

N 330 300

60

SV 4 210

15

5

5 2

10

0

5 2

15

5

150

S

e

15 2

5

120

240

25 0

or at

m sti

5

5

60 30 0 E

W

HMI area

20

15

Estimate Error ε (m)

30

25

15

25 2

4

2

NLS ator estim

15 5

8

6

Test Statistic q4 (unitless)

Figure 23.15 (LEFT) Azimuth-elevation sky plot for an example satellite geometry. (RIGHT) Failure mode plot for the single-SV fault hypothesis on SV4 [52]. Ellipses of constant joint probability density are represented using solid lines and dark gray areas for the new NLS-estimator-based method versus dashed lines when using the LS estimator. The ellipses are labeled in terms of −log10fηi(ε, qi), where fηi(ε, qi) is the integrity risk probability density function. The failure mode slope is lower for the NLS estimator than for the LS estimator, which reduces the risk of HMI. Source: Reproduced with permission of Cambridge University Press.

LS estimator optimal NLS

Estimate Error ε (m)

20

15

10

Figure 23.15 only showed a single fault hypothesis, but the complete integrity risk accounts for all hypothesized fault conditions. The six single-SV fault hypotheses are represented in Figure 23.16. One of the solid ellipses for the LS estimator overlaps with the HMI area. In contrast, the optimization method in [52] provides a means of pulling all gray-shaded ellipses away from the HMI area, thereby reducing PHMI. The optimal estimator is used in ARAIM performance analyses.

5

23.8.4 0

0

2

4

6

8

Test Statistic qi (unitless)

Figure 23.16 Failure mode plot displaying all single-SV fault hypotheses [52]. One of the solid ellipses for the LS estimator overlaps with the HMI area, whereas the NLS estimator optimization process provides a means of pulling the gray-shaded ellipses away from this area, thereby reducing the integrity risk. Source: Reproduced with permission of Cambridge University Press.

distributed. As the fault magnitude varies, the means of ε and of qi describe a “fault mode line” passing through the origin. The influence of the estimator modifier vector β is threefold. First, β provides a means of reducing the slope of the failure mode line, thereby reducing the risk of HMI. Second, for the LS estimator, ε0 and qi are statistically independent, so that the major axis of the dashed ellipse is horizontal. In contrast, β provides a means of changing the ellipse’s orientation. Third, as should be expected from an NLS estimator, the variance of εNLS is larger than that of ε0, which explains why lowering integrity risk comes at the cost of a decrease in accuracy performance.

ARAIM Performance Evaluation

The three ARAIM milestone reports provide availability performance analyses for a range of H-ARAIM and V-ARAIM requirements, measurement error and fault model parameters, and system configurations, including constellation scenarios. The baseline constellation comprises 24 GPS and 24 Galileo satellites [6, 54]. An example availability map is reproduced in Figure 23.17 for the baseline GPS/Galileo constellation, for Pconst = 10-4, Psat = 10-5 and σ URA = 1 m [42]. Availability is computed as the fraction of time where LPV200 requirements are met, for each location on a 5 × 5 latitude-longitude grid, for satellite geometries simulated at regular 10 minute intervals over a 24 hour period. In Figure 23.17, availability is color-coded: dark purple corresponds to availability greater than 99.9%, light purple represents more than 99.5%, and dark blue is better than 99%. Over the past ten years, research on dual-frequency multi-constellation ARAIM has focused on quantifying ARAIM’s potential to complement SBAS both in the short term with horizontal-ARAIM and in the longer term with vertical-ARAIM. ARAIM has been a driving force in the advancement of RAIM FDE methods. Current efforts are

613

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

Availability as a function of user location 80 60 40

Latitude (deg)

614

20 0 –20 –40 –60 –80 –150

–100

–50

0

50

100

150

Longitude (deg)

< 50%

> 50%

> 75%

> 85%

> 90%

> 95%

> 99%

> 99.5%

> 99.9%

VAL = 35, HAL = 40, EMTth = 15, σacc = 1.87, Coverage(99.5%) = 98.79%

Figure 23.17 LPV-200 Availability map using ARAIM for the baseline GPS/Galileo constellation, for Pconst = 10−4, Psat = 10−5, and σ URA = 1 m [42]. The coverage of 99% availability, which is a key metric in ARAIM, is defined as the percentage of grid point locations exceeding 99% availability. The coverage computation is weighted by the cosine of the location’s latitude, because grid point locations near the equator represent larger areas than near the poles. In this case, coverage of 99% availability is 99.9%. Source: Reproduced with permission of Cambridge University Press.

steered toward further refinement of standards for the ISM, the user and ground segments, toward ground and airborne algorithm prototyping and testing, and toward coordinated development of compatible commitments by CSPs.

23.9

Summary

This chapter has presented a review of the methods used to analyze and verify that integrity requirements are met in GNSS applications while also satisfying accuracy, continuity, and availability requirements. While a self-consistent approach to GNSS integrity design and verification has been developed, this task remains challenging because of the very strict requirements on integrity and continuity, which directly oppose each other and which must both be met simultaneously. In addition, the application of these methods to civil aviation requires conservative assumptions and “worst-case” probability and error assessments that fall under the philosophy of “specific risk.”

The second part of this chapter presents RAIM in detail as a specific technique to meet these requirements without relying on augmentation from ground systems such as SBAS or GBAS. It first presents traditional residuals and solution separation RAIM techniques and then shows how Advanced RAIM, or ARAIM, has been developed from the solution separation approach to RAIM. Performance results for worldwide ARAIM support of LPV precision approaches (which are provided by SBAS today within SBAS coverage regions) are shown.

References 1 R.V. Hogg, Tanis, E.A., and Zimmerman, D.L., Probability

and Statistical Inference, Boston, MA, Pearson, 9th Ed., 2015. 2 Matlab help page for “Standard Deviation” (Std) function, MathWorks, https://www.mathworks.com/help/matlab/ ref/std.html

References

3 Global Positioning System Wide Area Augmentation System

4

5

6

7

8

9

10

11

12

(WAAS) Performance Standard (U.S. Federal Aviation Administration, Washington DC), 1st Ed., October 31, 2008. Minimum Aviation System Performance Standards for the Local Area Augmentation System (LAAS),Washington, DC, RTCA SC-159, WG-4, DO-245A, December 9, 2004. FAA System Safety Handbook, U.S. Federal Aviation Administration, Washington, DC, December 30, 2000, Chapter 3. https://www.faa.gov/regulations_policies/ handbooks_manuals/aviation/risk_management/ ss_handbook/media/Chap3_1200.pdf Assistant Secretary of Defense for Command, Control, Communications and Intelligence, “Global Positioning System Standard Positioning Service Performance Standard,” Washington, DC, 5th Edition, 2020, available online: https://www.gps.gov/technical/ps/2020-SPSperformance-standard.pdf “Clopper-Pearson interval,” within Wikipedia webpage on “Binomial proportion confidence interval,” https://en. wikipedia.org/wiki/ Binomial_proportion_confidence_interval, accessed 29 January 2018. T. Walter, J. Blanch, M. Joerger, and B. Pervan, “Determination of Fault Probabilities for ARAIM,” Proceedings of IEEE/ION PLANS 2016, Savannah, Georgia, April 11–14, 2016, pp. 451–461. S. Pullen, J. Rife, and P. Enge, “Prior Probability Model Development to Support System Safety Verification in the Presence of Anomalies,” Proceedings of IEEE/ION PLANS 2006, San Diego, California, April 25–27, 2006, pp. 1127–1136. http://web.stanford.edu/group/scpnt/ gpslab/pubs/papers/Pullen_IEEEIONPLANS_2006.pdf S. Pullen, T. Walter, and P. Enge, “SBAS and GBAS Integrity for Non-Aviation Users: Moving Away from ‘Specific Risk,’” Proceedings of ION NTM 2011, San Diego, California, January 24–26, 2011, pp. 533–545. http://web. stanford.edu/group/scpnt/gpslab/pubs/papers/ Pullen_IONITM_2011_Integrity_for_NonAviation_Users.pdf S. Pullen, M. Luo, T. Walter, and P. Enge, “Using SBAS to Enhance GBAS User Availability: Results and Extensions to Enhance Air Traffic Management,” Proceedings of ENRI International Workshop on ATM/ CNS, Tokyo, Japan, September 2010. http://web.stanford. edu/group/scpnt/gpslab/pubs/papers/ Pullen_Japan_EIWAC_2010_Using_ SBAS_to_Enhance_GBAS_Availability.pdf J. Rife and R.E. Phelts, “Formulation of a Time-Varying Maximum Allowable Error for Ground-Based Augmentation Systems,” IEEE Transactions on IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 2, April 2008.

13 Minimum Operational Performance Standards for GPS

14

15

16

17

18

19

20

21

22

23

Local Area Augmentation System Airborne Equipment, Washington, DC, RTCA SC-159, WG-4, DO-253D, July 13, 2017. B. DeCleene, “Defining Pseudorange Integrity – Overbounding,” Proceedings of ION GPS 2000, Salt Lake City, Utah, September 19–22, 2000, pp. 1916–1924. https:// www.ion.org/publications/abstract.cfm?articleID=1603 T. Schempp and A. Rubin, “An Application of Gaussian Overbounding for the WAAS Fault Free Error Analysis,” Proceedings of ION GPS 2002, Portland, OR, September 24–27, 2002, pp. 766–772. https://www.ion.org/ publications/abstract.cfm?articleID=2079 J. Rife, S. Pullen, and B. Pervan, “Core Overbounding and its Implications for LAAS Integrity,” Proceedings of ION GNSS 2004, Long Beach, California, September 21–24, 2004, pp. 2810–2821. http://web.stanford.edu/group/ scpnt/gpslab/pubs/papers/Rife_IONGNSS_2004.pdf “Wide-Area Augmentation System Performance Analysis Report,” Report #34, Reporting Period: July 1–Sept. 30, 2010, FAA/William J. Hughes Technical Center, Atlantic City, NJ, Oct. 2010. http://www.nstb.tc.faa.gov/reports/ waaspan34.pdf T. Walter, P. Enge, and B. DeCleene, “Integrity Lessons from the WAAS Integrity Performance Panel (WIPP),” Proceedings of ION NTM 2003, Anaheim, California, January 22–24, 2003, pp. 183–194. http://web.stanford. edu/group/scpnt/gpslab/pubs/papers/ Walter_IONNTM_2003.pdf S. Pullen, “The Use of Threat Models in Aviation Safety Assurance: Advantages and Pitfalls,” Proceedings of 2014 International Symposium on Certification of GNSS Systems & Services (CERGAL 2014), Dresden, Germany, July 7–8, 2014. http://web.stanford.edu/group/scpnt/ gpslab/pubs/papers/ Walter_IEEEIONPLANS_2016_ARAIM.pdf Y.C. Lee, “Analysis of Range and Position Comparison Methods as a Means to Provide GPS Integrity in the User Receiver,” Proceedings of the 42nd Annual Meeting of The ION, Seattle, WA, pp. 1–4, 1986. B.W. Parkinson and Axelrad, P., “Autonomous GPS Integrity Monitoring Using the Pseudorange Residual,” in Navigation: Journal of the Institute of Navigation, vol. 35, no. 2, Washington, DC, pp. 225–274, 1988. M. Sturza, “Navigation System Integrity Monitoring Using Redundant Measurements,” in Navigation: Journal of the Institute of Navigation, Washington, DC, vol. 35, no. 4, pp. 69–87, 1988. R.G. Brown, “A Baseline GPS RAIM Scheme and a Note on the Equivalence of Three RAIM Methods,” in Navigation: Journal of the Institute of Navigation, vol. 39, no. 3, pp. 301– 316, 1992.

615

616

23 GNSS Integrity and Receiver Autonomous Integrity Monitoring (RAIM)

24 M. Brenner, “Integrated GPS/Inertial Fault Detection 25

26

27

28

29

30

31

32

33

34

35

36

37

Availability,” Navigation, vol. 43, no. 2, pp. 111–130, 1996. J. Blanch, Walter, T., and Enge, P., “RAIM with Optimal Integrity and Continuity Allocations Under Multiple Failures,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 3, pp. 1235–1247, 2010. B. Pervan, “Navigation Integrity for Aircraft Precision Landing Using the Global Positioning System,” PhD Dissertation, Stanford University, Stanford, California, 1996. T. Walter, Enge, P., Blanch, J., and Pervan, B., “Worldwide Vertical Guidance of Aircraft Based on Modernized GPS and New Integrity Augmentations,” in Proceedings of IEEE, vol. 96, no. 12, pp. 1918–1935, 2008. J. Blanch, Walter, T., and Enge, P., “Satellite Navigation for Aviation in 2025” Proceedings of IEEE: Special Centennial Issue, vol. 100, 1821–1830, 2012. R.J. Kelly and Davis, J.M., “Required Navigation Performance (RNP) for Precision Approach and Landing with GNSS Application,” in Navigation: Journal of the Institute of Navigation, vol. 41, no. 1, pp. 1–30, 1994. M. Joerger, Chan, F.C., and Pervan, B., “Solution Separation Versus Residual-Based RAIM,” in Navigation: Journal of the Institute of Navigation, vol. 61, no. 4, pp. 273– 291, 2014. RTCA Special Committee 159, “Minimum Aviation System Performance Standards for the Local Area Augmentation System (LAAS),” RTCA/DO-245, Appendix D, 2004. J. Blanch, Walter, T., Lee, T., Pervan, B., Rippl, M., and Spletter, A., “Advanced RAIM User Algorithm Description: Integrity Support Message Processing, Fault Detection, Exclusion, and Protection Level Calculation,” Proceedings of ION GNSS 2012, Nashville, TN, pp. 2828–2849, 2012. J. Blanch, Walter, T., Enge, P., Wallner, S., Fernandez, F.A., Dellago, R., Ioannides, R., Hernandez, I.F., Belabbas, B., Spletter, A., and Rippl, M., “Critical elements for a MultiConstellation Advanced RAIM,” in Navigation: Journal of the Institute of Navigation, vol. 60, no. 1, pp. 53–69, Spring 2013. F. van Graas and J. Farrell, “Baseline Fault Detection and Exclusion Algorithm,” Proc. of the 49th Annual Meeting of The ION, Cambridge, MA, pp. 413–420, June 1993. I.E. Potter, and Suman, M.C., “Threshold-less Redundancy Management With Arrays of Skewed Instruments,” AGARDOGRAPH – No 224, pp. 15–11 to 15-25, 1977. J. Blanch, Walter, T., and Enge, P., “Results on the Optimal Detection Statistic for Integrity Monitoring,” Proc. of ION ITM 2013, San Diego, CA, pp. 262–273, January 2013. M. Joerger, Stevanovic, S., Langel, S., and Pervan, B., “Integrity Risk Minimization in RAIM, Part 1: Optimal Detector Design,” Journal of Navigation of the RIN, vol. 69, no. 3, 2016.

38 S. Pullen, and Enge, P., “Using Outage History to Exclude

39

40

41

42

43

44

45

46

47

48

49

High-Risk Satellites from GBAS Corrections,” in Navigation: Journal of the Institute of Navigation, vol. 60, no. 1, pp. 41–51, 2013. B. Pervan, Lawrence, D., Cohen, C., and Parkinson, B., “Parity Space Methods for Autonomous Fault Detection and Exclusion Using GPS Carrier Phase,” Proceedings of IEEE PLANS, Atlanta, Georgia, 1996. M. Joerger and Pervan, B., “Fault Detection and Exclusion Using Solution Separation and Chi-Squared RAIM,” IEEE Transactions on Aerospace and Electronic Systems, vol. 52, no. 2, 2016. EU-US Cooperation on Satellite Navigation, WG C-ARAIM Technical Subgroup, “ARAIM Technical Subgroup Interim Report Issue 1.0,” 2012, available online: http://www.gps. gov/policy/cooperation/europe/2013/working-group-c/ ARAIM-report-1.0.pdf EU-US Cooperation on Satellite Navigation, WG C-ARAIM Technical Subgroup, “ARAIM Technical Subgroup Milestone 2 Report,” 2014, available online: http://www. gps.gov/policy/cooperation/europe/2015/working-groupc/ARAIM-milestone-2-report.pdf EU-US Cooperation on Satellite Navigation, WG C-ARAIM Technical Subgroup, “ARAIM Technical Subgroup Milestone 3 Report,” 2016, available online: http://www. gps.gov/policy/cooperation/europe/2016/working-groupc/ARAIM-milestone-3-report.pdf The United States, The European Union, “Agreement on the Promotion, Provision and Use of Galileo and GPS SatelliteBased Navigation Systems and Related Applications,” 2004, available online: http://www.gps.gov/policy/cooperation/ europe/2004/gps-galileo-agreement.pdf Global Positioning System Directorate Systems Engineering and Integration, “Interface Specification ISGPS-200,” Revision H, 2013, available online: http://www. gps.gov/technical/icwg/IS-GPS-200H.pdf M. Joerger, Zhai, Y., and Pervan, B., “Online Monitor Against Clock and Orbit Ephemeris Faults in ARAIM.” Proceedings of the ION 2015 Pacific PNT Meeting, Honolulu, Hawaii, pp. 932–945, 2015. J. Blanch and Walter, T., “LPV-200 Requirements Interpretation,” Report to ARAIM subgroup, version 4, November 2011. ICAO, Annex 10, “GNSS Standards and Recommended Practices (SARPs)” Aeronautical Telecommunications, Volume 1 (Radio Navigation Aids), Amendment 84, Section 3.7, Appendix B, and Attachment D, 20 July 2009. P.Y. Hwang and Brown, R. G., “RAIM-FDE Revisited: A New Breakthrough In Availability Performance With NIORAIM (Novel Integrity-Optimized RAIM),” in Navigation: Journal of the Institute of Navigation, vol. 53, no.1, pp. 41–52, 2006.

References

50 Y.C. Lee, “Two New RAIM Methods Based on the

53 J. Blanch, Walter, T., Enge, P., and Kropp, V., “A Simple

Optimally Weighted Average Solution (OWAS) Concept,” in Navigation: Journal of the Institute of Navigation, vol. 54, no.4, pp. 333–345, 2008. 51 J. Blanch, Walter, T., and Enge, P, “Optimal Positioning for Advanced RAIM,” in Navigation: Journal of the Institute of Navigation, vol. 60, no. 4, pp. 279–289, 2012. 52 M. Joerger, Langel, S., and Pervan, B., “Integrity Risk Minimization in RAIM, Part 2: Optimal Estimator Design,” Journal of Navigation of the RIN, vol. 69, no.4, 2016.

Position Estimator that Improves Advanced RAIM Performance,” accepted for publication in IEEE Transactions on Aerospace and Electronic Systems, 2016. 54 European Commission newsroom, “Galileo Launch,” August 2014, available online: http://ec.europa.eu/ enterprise/newsroom/cf/itemdetail.cfm? item_id=7713&lang=en

617

619

24 Interference: Origins, Effects, and Mitigation Logan Scott LS Consulting, United States

24.1

Introduction

GNSS has been described as the stealth utility. When interference to GNSS occurs, as you might expect GNSS receiver performance becomes degraded but unexpected effects are also commonly seen. Among them, medical paging systems have turned themselves off, and cellular base stations have lost their ability to perform handoffs and so drop calls [1]. Marine radar displays have shown dire warnings to the effect that position has been lost, and shipboard satellite communications systems have completely failed [2]. GNSS is deeply integrated into diverse systems, often to the point where it almost becomes invisible, that is, until it fails.

• •

•

The medical paging system used GPS to provide frequency discipline to control the transmitter’s center frequency, and when GPS was lost, the transmitter turned itself off in accordance with FCC regulations regarding frequency stability [1]. In the same incident, about 150 cellular base stations lost their ability to perform handoffs. Why? GPS provided precise timing to the base stations allowing them to synchronize their code-division multiple access (CDMA) signal transmission timings to a common time base. Without GPS, they drifted with respect to each other‚ and the precisely coordinated hand off between base stations failed. People could initiate a call but when a handover was attempted, the new base station was not where it was expected to be and the call would drop, much like a pair of trapeze artists who are out of sync. In the Pole Star experiment [2], the shipboard GNSS kept reporting position long after it had completely lost the real signals. The shipboard satellite communications system, unaware of the huge position errors, pointed its high-gain antenna in the wrong direction and so missed its intended target, the communications satellite (see Figure 24.1).

GNSS is a critical part of international infrastructure. Not only does it provide low-cost methods for obtaining precise position, it is also the world’s backbone system for precise time and frequency dissemination. In the United States, 14 of 16 critical infrastructure (CI) sectors have been identified as having critical dependencies on GNSS. These sectors include transportation, emergency services, energy distribution, financial services, agriculture, and information technology. From the US Department of Homeland Security (DHS) website, the definition of CI: Critical infrastructure is the backbone of our nation’s economy, security, and health. We know it as the power we use in our homes, the water we drink, the transportation that moves us, and the communication systems we rely on to stay in touch with friends and family. Critical infrastructure are the assets, systems, and networks, whether physical or virtual, so vital to the United States that their incapacitation or destruction would have a debilitating effect on security, national economic security, national public health or safety, or any combination thereof. In a 2015 presentation to the PNT Advisory Board [3], Irv Leveson estimated that the total economic impact of GPS amounted to $68 billion per year. In short, GNSS is somehow integrated into just about everything we do, and the trend is accelerating in part because of autonomous vehicles, but also because in the Internet of Things (IoT), knowing where the Things are is often important. Widespread reliance on GNSS has a darker side, though: GNSS has become part of the attack surface for adversaries seeking to damage and/or exploit systems reliant on GNSS. Attacks on GNSS are fundamentally a security question, and so the question of “Why would someone do that?” has to be answered in order to develop a more nuanced

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c24.3d

619

15/12/2020 5:42:09 PM

620

24 Interference: Origins, Effects, and Mitigation

Used By Permission: George Shaw, General Lighthouse Authorities of the UK and Ireland

Figure 24.1 The “Voyage” of the Pole Star, a ship, shows how interference can cause massive positioning errors. These in turn led to a failure in shipboard SATCOM due to antenna pointing errors.

understanding of probable locations, methods used‚ and effective mitigations. Without motivation, an attack is very unlikely. In the case of military systems, motivations for attacking GNSS are often pretty straightforward: deny navigation to opposing forces so as to create confusion, make coordination hard, and lessen their effectiveness; make GNSS-guided weapons miss their targets, prevent forward controllers and sensors from determining target coordinates, deny emitter location systems precise time and position so they can’t accurately determine emitter locations; make sensor data less useful by limiting georeferenced overlay effectiveness. In the civil arena, the motivation most often has something to do with a GNSS-dependent tracking and reporting system. Criminal enterprises may use jammers to cover car thefts and cargo thefts, victims of domestic violence may use jamming to prevent stalkers from tracking them, and city construction workers may use jammers to cover the fact that they are paving someone’s private driveway. Commercial fisherman may be tempted to jam vessel monitoring systems (VMSs), but the mere fact of an attack gives rise to suspicion if the VMS can recognize onboard jamming. Similarly, the city construction workers may be looking for a little extra income or perhaps, just a longer nap. This might give rise to more civil spoofing attacks, particularly as they become easier and less expensive to mount. Attacks on GNSS follow a continuum but can be broadly divided into two categories: jamming and spoofing. Jamming is a denial-of-service style of attack where GNSS signals are masked by stronger interference signals to prevent

c24.3d

620

reception. As such, jamming’s objective tends toward area denial of navigation (though the area may be just one vehicle). Spoofing’s objective is basically to convince a GNSS receiver or dependent system that it is somewhere (or some time) that it is not. Often, but not always, this attack has a specific “victim” in mind, for example‚ a locationmonitored fishing vessel, a location-monitored cargo container, or a Pokémon Go gaming app (see Figure 24.2). RF spoofing may also be used as a denial-of-service type of attack where the objective is to create a more effective jamming attack. Spoofing attacks are not necessarily RF based. Broadly speaking, spoofing attacks come in three flavors: 1) Cyberspoofing, where the spoofer captures or becomes the device’s location object and then lies about position. Essentially a man-in-the-middle attack, this is a particularly powerful attack since it gives the attacker complete control over reported location, and it can be launched from anywhere in the world. Relative location spoofing may be achieved using correct location information from compromised system elements as a basis. The key to understanding and defending against these attacks is to recognize that GNSS receivers and their operating environments (e.g. a cell phone) are fundamentally computers, often running a full operating system and connected to the Internet. The difficulty of launching cyber attacks ranges from trivially simple to fairly complex depending on the “victim.” Variations include malicious software updates, root attacks,

15/12/2020 5:42:09 PM

24.2 The Effects of Jamming on GPS/GNSS Signals

Cyberspoofing

621

RF Spoofing

Figure 24.2 Two ways to cheat at Pokémon Go; cyberspoofing and RF spoofing.

man-in-the-middle attacks, falsified maps, incorrectly georeferenced maps, reference station manipulation‚ and theft of signing credentials. 2) Differential corrections/data spoofing, where substitute corrections are used to create relatively small but important errors in navigation solutions. Many networkconnected receivers (e.g. Assisted-GNSS) do not read data directly from satellites as a matter of course since the process is so slow. For these receivers, ephemeris data describing satellite orbits and/or clock corrections may be manipulated to achieve the desired effects. Public key infrastructure (PKI) cryptographic authentication methods (data signing) can make these sorts of attacks much harder to mount. 3) RF overlay attacks using a coordinated signal constellation broadcast, basically a GNSS signal generator [4–6]. Once found only in the military realm because of their technical complexity, the advent of software-defined radio (SDR) has made this sort of attack available to script kiddies in recent years [7, 8]. The attack can be very effective against an unwary receiver (most civil receivers) but is more difficult to launch at a distance since many exploits require knowing the true location of the “victim.” RF overlay attacks are difficult to mount against a wary receiver since numerous techniques can detect the attack (more on this later). That said, RF spoofing attacks can be extremely effective as an area denial jamming attack since the receiver is fundamentally a matched filter receiver for spoofing signals. Contrasting the military and civil interference use cases, military interference is more likely caused by an external agent, whereas in the civil environment, internal agents with close physical proximity to the affected equipment are more likely. Civil attacks are much more likely to be insider attacks. The specific motivations are myriad‚ but

c24.3d

621

understanding them is important when it comes to mitigations. First though, an examination of how interference affects GNSS receivers.

24.2 The Effects of Jamming on GPS/GNSS Signals Figure 24.3 shows two range-Doppler (RD) maps, one under nominal signal reception conditions and the other where there is an in-band, spectrally matched jammer that is 10,000 times stronger than the GPS P(Y)-code signal. In both cases, a receiver could easily track the signal, the pointy bit in the RD map, albeit with slightly less accuracy in the jammed case. This sounds like very strong resistance to jamming until we take a look at the received GPS signal levels. The L1 C/A signal is transmitted at a 25 W power level into a 13 dBiC (times 20) antenna for an effective isotropic radiated power (EIRP) of 25 ∗ 20 = 500 W. Nominally, these are about the same parameters as a cellular base station, but instead of having to travel only a couple of miles to the receiver, GPS signals travel from satellites in a circular medium Earth orbit (MEO) 20 200 km above Earth’s surface. By the time it reaches Earth, the signal is weak, very weak, about 20 times weaker than galactic noise. The L1 P(Y) signal is even weaker, about half the power of the L1 C/A signal. A jammer 10,000 times more powerful than a very weak signal is still very weak. More formally, Table 24.1 shows specified nominal received L1 signal levels from a GPS Block III satellite. Levels for earlier-generation satellites are similar, except for L1C, which debuted with Block III. Referring back to Figure 24.3, received jamming levels are usually described in terms of a power ratio J/S expressed in units of decibels. Specifically:

15/12/2020 5:42:11 PM

622

24 Interference: Origins, Effects, and Mitigation

No Jamming (Just Thermal Noise)

Jamming (10,000 x Signal | J/S=40 dB) P(Y)-Code Correlation Response (J/S=40 dB, 20 msec PIT)

Amplitude (volts)

Amplitude (volts)

P(Y)-Code Correlation Response (No Jamming, 20 msec PIT)

40 20 0 500

40 20 0 500

15 0

15 0

10

10

Doppler Offset (Hz)

Doppler Offset (Hz) 5 –500

5

Time Offset (chips)

–500

0

Time Offset (chips) 0

Figure 24.3 Two range-Doppler (RD) maps, one under nominal signal reception conditions (left) and the other where there is an in-band, spectrally matched jammer that is 10,000 times stronger than the GPS P(Y)-code signal(right). In both cases, a receiver can track P(Y)-code military signal. Table 24.1

Received minimum terrestrial RF signal strength

Signal

Specification

Isotropic signal level

L1 C/A

IS-GPS-200J

−158.50 dBW RHCP

L1 P(Y)

IS-GPS-200J

−161.50 dBW RHCP

L1C Pilot

IS-GPS-800E

−158.25 dBW RHCP

L1C Data

IS-GPS-800E

−163.00 dBW RHCP

J S dB = 10 log 10 j s

24 1

where j is the received jammer power in watts s is the received signal power in watts Thus, a situation where the received jamming power is 10,000 times the received signal power corresponds to a J/S of 40 dB. Table 24.1 shows that the nominal isotropic P(Y) received level is −161.5 dBW, and so a J/S of 40 dB means the jammer is received at −161.5dBW + 40 dB = −121.5 dBW. This is not a difficult amount of power to put on a target victim receiver. So‚ how does a GNSS receiver operate in the presence of jamming that is thousands of times more powerful than the signal? Figure 24.4 is a notional jamming scenario involving a direct sequence spread spectrum (DSSS) GPS satellite, a continuous wave (CW) jammer, and a receiver. Also shown are spectrum plots at various points in the signal/processing chain. Focusing on P(Y)-code transmission, the satellite starts with a 50 bps non-return-to-zero (NRZ) data stream, multiplies that by a 10.23 MChip/s NRZ PN code which also switches between values of 1 and −1. The resultant is used to binary phase shift keying (BPSK)-

c24.3d

622

modulate a sine wave at the L1 frequency of 154fo = 1575.42 MHz. The spectrum of the signal (point 1) is sin(x) / x centered at L1 with an equivalent noise bandwidth of 10.23 MHz. The jammer in this case is a simple tone jammer broadcasting CW at the L1 center frequency. Its spectrum is basically a narrowband spike at the L1 center frequency (point 2). The receiver antenna is stimulated by these two signals (plus thermal noise), and the summation of the various signals is output. The composite spectrum is shown at Point 3. Note that two separate signals are not seen, just the summation. The receiver then multiplies the composite signal by a local reference of the PN code time phased to account for propagation delay from the satellite to the receiver. Point 4 shows the composite output spectrum. The bandwidth of the satellite signal collapses from 10.23 MHz to 50 Hz because whenever the received signal is a 1, the local reference is a 1; and whenever it is a −1, the local reference is a −1. The PN code is stripped off‚ and all that’s left is the 50 bps data stream with a bandwidth of 50 Hz. The jammer though, goes from negligible bandwidth to a 10.23 MHz bandwidth mirroring what happened at the satellite when the PN code multiplied the sine wave centered at L1. Finally, the receiver passes the code mixing output through a 50 Hz band pass filter (BPF). The GPS signal passes through largely un-attenuated but the jammer, now with a 10.23 MHz bandwidth‚ mostly gets filtered out. Table 24.2 presents a simplified J/S threshold analysis where the objective is to quantify how much stronger a CW jammer has to be in order to cause the receiver to lose lock. Focusing on the P-code signal and following the previous discussion, the fraction of the jammer energy that gets through the 50 Hz BPF is 50Hz/10,230,000 Hz = 1/204,600.

15/12/2020 5:42:12 PM

24.2 The Effects of Jamming on GPS/GNSS Signals

1

623

4

Satellite D(t) data PN(t) PN Code Generator

50 Hz BPF Sin(2πfct)

Jammer

PN(t-τ) PN Code Generator

D(t) data

Receiver

3 2

5

Sin(2πfct)

Figure 24.4 A notional jamming scenario involving a direct sequence spread spectrum (DSSS) GPS satellite, a continuous wave (CW) jammer, and a receiver. Table 24.2

Simplified J/S threshold analysis

Stated another way, if a jammer is 204,600 times as powerful as the signal, it will yield equal power out of the 50 Hz BPF. Now, in order to track a legacy signal (C/A code or P(Y) code), the signal power needs to be around 10 times greater than noise, so to a good approximation, a P(Y) receiver will lose track once the j/s is greater than 20,460 or stated in decibels, once the J/S exceeds 43 dB. For C/A code, the analysis follows similar lines, but the calculated maximum J/S is a factor of ten less since the chipping rate is a factor of 10 slower. The caveat though is that C/A code has some structural vulnerabilities (explored later) that make the analysis overly optimistic for C/A code receivers.

address interference effects for binary offset carrier (BOC) signal formats, and it doesn’t take into account interference with spectrum shapes other than that of a CW jammer at the center frequency. Also, it does not take into account the effects of thermal noise due to amplifiers and cosmic noise. The Betz equation [9–11] shown below provides a method for calculating effective baseband C/No accounting for signal and interference spectral shapes assuming noise-like responses. C N0

= effective

C N+I Cs

24.2.1

The Betz Equation

Figure 24.5 shows L1 GPS signal spectra after modernization. The preceding analysis, while useful as a general introduction, is severely limited in its scope of applicability. It doesn’t

c24.3d

623

2

βr 2

Gs f df − βr 2

=

βr 2

βr 2

Gs f df + Ct

N0 − βr 2

Gt f Gs f df − βr 2

24 2

15/12/2020 5:42:13 PM

624

24 Interference: Origins, Effects, and Mitigation Normalized Source Spectrum

Source Type BPSK(1), Peak at = 0 MHz Source Type BPSK(10), Peak at = 0 MHz Source Type BOC(1,1), Peak at = –0.765 MHz Source Type BOC(10,5), Peak at = –9.495 MHz

–60

L1C* P(Y)-Code –70

C/A-Code

M-Code

dBW/Hz

–80

–90

–100

–110

Center Frequency of 1575.42 MHz

–120

–130 –15

–10

–5

0

5

10

15

Frequency (MHz)

Figure 24.5

L1 GPS signal spectra after modernization.

where Gs f

Signal's Normalized Power Spectrum ∞

Gs f df = 1 −∞

Cs Received Signal Power Gt f

Jammer's Normalized Power Spectrum

coefficient (SSC). SSC is a measure of how strongly interference couples into baseband noise at a zero hertz frequency offset assuming the two signals are uncorrelated and act like noise with respect to one another. The inverse of the SSC is sometimes referred to as processing gain. Also, note that the receiver’s front-end filtering is represented as a rectangular response extending from −βr/2 to +βr/2 Hz centered on the signal’s center frequency.

∞

Gt f df = 1 −∞

Ct Received Jammer Power N0 Thermal Noise Power Spectral Density βr Front End Filter Bandwidth Hz C numeric C No No Baseband C/No is basically the signal-to-noise ratio in a 1 Hz bandwidth. The above equation comprises three terms: in the numerator the signal power, and in the denominator two terms: the contribution due to thermal noise effects and the contribution due to interference effects. Of particular note, the contribution due to interference is equal to the jamming power Ct scaled by the spectral separation

c24.3d

624

βr 2

Spectral Separation Coefficient SSC

=

Gt f Gs f df − βr 2

Evaluation of the Betz equation is typically performed using numerical integration‚ but first a discussion of how to compute No, the thermal noise power spectral density. No comprises two sources, noise due to external blackbody radiation and noise internally generated by the receiver. If NF is the noise figure in dB of the receiver referenced to 290K, then N 0 = 10 log 10 k T antenna + T receiver

dBW

24 3

where Tantenna = Antenna Noise Temperature K Treceiver = Receiver Noise Temperature K = 290 10NF dB 10 − 1 k = Boltzman Constant = 1 38 x 10 − 23 Watts degree Kelvin

15/12/2020 5:42:14 PM

24.2 The Effects of Jamming on GPS/GNSS Signals

Numerically integrating the Betz equation for a 10-kHzwide, narrowband jammer at the center frequency analogous to that of Figure 24.4, Figure 24.6 plots effective C/ No as a function of J/SP for three signal types: C/A code, P(Y)-code, and the L1C Pilot signal, a BOC(1,1) signal. A few preliminary comments are in order:

• • •

The antenna temperature Tant used is 130 K. If a directional antenna is pointed toward the Milky Way, at L1 frequency the apparent blackbody radiation temperature is about 140 K. Away from the Milky Way but not toward the Sun, the apparent blackbody radiation temperature is about 70 K. Point the antenna toward the ground or operate indoors and the apparent temperature will be something around 250 K to 300 K. The receiver noise figure is usually set by the pre-amp, and for GPS receivers is anywhere from about 1.5 to 5 dB, with 2 dB being typical. GNSS signals are normally below thermal noise, and so most GNSS receivers use very low-precision A/D converters going into the correlators to save on power. The most common is a 1.5-bit converter that puts out one of three values: 1, 0, −1. Properly tuned and in Gaussian noise, the loss relative to a high-precision converter is less than 1 dB [12, 13].

• •

625

To provide meaningful comparisons between signals under a particular interference condition, it helps to use a common reference power level for the S in J/S. The chosen reference level in this and subsequent plots is S = −161.5 dBW, the power level of the P(Y) code as specified in Table 24.1. Hence the tem J/SP. In all cases, the front-end bandwidth is 24 MHz.

Comparing C/A code performance with P(Y) code performance, at low J/SP values the C/A code yields a C/No that is 3 dB (a factor of two) higher. This is because the C/A code signal is received with a 3 dB higher power level. It is a stronger signal‚ and until jamming levels exceed thermal noise levels, it will yield a higher C/No. As J/SP increases, the 10× wider spreading bandwidth of P(Y)-code provides 10 times better rejection against the jammer but, because the P(Y) signal is only half as strong, the net gain is a factor of 10∗1/2 = 5, or 7 dB. Holding off on a fuller discussion for now, the minimum required C/No to track C/A or P(Y) code is around 27 dB-Hz. This corresponds to an SNR of 27(dB-Hz) − 10∗log10(50 Hz) = 10 dB in a 50 Hz bandwidth consistent with the earlier discussion surrounding Table 24.2.

All Cases:Tant. = 130K, NF = 2 dB, L = 1 dB,Gsig = 0dBiC, Gjam = 0dBiC, 24 Mhz Passband 50

3 dB

Higher 45 Is Better

L1CP-Code

40

C/A-Code

35

Effective C/N0 (dB–Hz)

BPSK(10) @–161.5dBW, Brick(10 kHz) Jammer @ 0 kHz Offset BPSK(1) @–158.5dBW, Brick(10 kHz) Jammer @ 0 kHz Offset BOC(1,1) @–158.3dBW, Brick(10 kHz) Jammer @ 0 kHz Offset

P(Y)-Code

30

Assuming No Receiver Saturation!

25 20

Nominal Unaided Tracking Threshold Legacy Signal

15

Block III Signal Levels

10

7 dB

5 0

10x 0

10

100x 20

J/S = 43 dB (20,000 x)

1000x 30

40

50

60

70

Incident J/SP (dB wrt S=–161.5 dBW)

Figure 24.6 Effective C/No as a function of J/Sp given a narrowband jammer at 0 Hz offset relative to the center frequency.

c24.3d

625

15/12/2020 5:42:15 PM

626

24 Interference: Origins, Effects, and Mitigation

c numeric T i n0 C SNR dB = dB − Hz + 10 log 10 T i N0 C dB − Hz − 10 log 10 Bi SNR dB = N0

snr numeric =

24 4 where Ti predetection integration time in seconds Bi equivalent noise bandwidth is 1 Ti Turning now to the L1C Pilot channel response to jamming, there is very little effect until the jamming becomes extremely powerful, at least under the assumption that the front-end doesn’t saturate. Returning to the spectrum plots of Figure 24.5, note that the L1C Pilot Signal is a BOC(1,1) format signal and so has essentially no spectral content at the center frequency. The SSC in the Betz equation is thus very small for this particular jammer. In fact, there would have been no effect if the jammer was truly a pure tone at the center frequency. The only reason there is an effect is that the jammer is 10 kHz wide. Again returning to Figure 24.5, we might ask, “is there some other frequency where L1C Pilot signal might be

more sensitive to jamming”? Its peak spectral response is at −765 kHz with respect to the center frequency. What happens if we jam there? Figure 24.7 shows C/No plots for this case‚ and sure enough, the L1C Pilot signal is strongly affected and has the lowest C/No of the three signals once jamming becomes strong. In another interesting observation, the P(Y) code signal’s performance is much the same as for 0 Hz offset jamming‚ but the C/A code now performs about 4 dB better than P(Y) code in this type of jamming. Again, Figure 24.5 offers some insight. The C/A code is a BPSK(1) format signal and has relatively low spectral content at a −765 kHz offset. The SSC will therefore be smaller‚ and so relatively small amounts of jamming couple into the baseband response. Up to this point‚ discussion has focused on narrowband interference. Figure 24.8 considers the case where jamming energy is uniformly distributed over a 24 MHz bandwidth. Interestingly, the P(Y) signal consistently yields the lowest C/No (worst performance), while the C/A and L1C Pilot signals offer similar C/No. Why is this? Shouldn’t P(Y) code offer 10 times the resistance to in-band jamming given its 10 times faster chip rate? The answer once again is found in Figure 24.5. For the C/A code and L1C Pilot signals, a

All Cases:Tant.=130K, NF=2 dB, L=1 dB,Gsig=0dBiC, Gjam=0dBiC, 24 Mhz Passband 50

BPSK(10) @–161.5dBW, Brick(10 kHz) Jammer @ –765 kHz Offset BPSK(1) @–158.5dBW, Brick(10 kHz) Jammer @ –765 kHz Offset BOC(1,1) @–158.3dBW, Brick(10 kHz) Jammer @ –765 kHz Offset

Higher 45 Is Better 40

C/A-Code

Effective C/N0 (dB–Hz)

35 30

P(Y)-Code

Block III Signal Levels

25 20

Assuming No Receiver Saturation!

15

L1CP-Code

10 5

10x

0 0

10

100x 20

1000x 30

40

50

60

70

Incident J/SP (dB wrt S=–161.5 dBW)

Figure 24.7

c24.3d

626

Effective C/No as a function of J/Sp given a narrowband jammer at 765 kHz offset relative to the center frequency.

15/12/2020 5:42:15 PM

24.3 Jamming Effectiveness as a Function of Range

627

All Cases:Tant.=130K, NF=2 dB, L=1 dB,Gsig=0dBiC, Gjam=0dBiC, 24 Mhz Passband 50

BPSK(10) @–161.5dBW, Brick(24000 kHz) Jammer @ 0 kHz Offset

Higher 45 Is Better

BPSK(1) @–158.5dBW, Brick(24000 kHz) Jammer @ 0 kHz Offset BOC(1,1) @–158.3dBW, Brick(24000 kHz) Jammer @ 0 kHz Offset

40

P(Y)-Code Block III Signal Levels

Effective C/N0 (dB–Hz)

35

C/A-Code

30 25

Unaided Tracking Threshold Legacy Signal

Military Signals Do Not Always Outperform Civil Signals In Jamming!

20 15

L1CP-Code Unaided Tracking Threshold Modernized Signal

10

J/S =46 dB (40,000 x)

5

10x

0 0

10

100x

1000x

20

30

40

9 dB

50

60

70

Incident J/SP (dB wrt S=–161.5 dBW)

Figure 24.8 Effective C/No as a function of J/Sp given a 24-MHz-wide jammer at 0 Hz offset relative to the center frequency.

24-MHz-wide jammer is mostly out of band‚ and the SSC is correspondingly low. Also, note that compared to the narrowband jammer case (Figure 24.6), the P(Y) code C/No is 3 dB higher for a given J/S. This is a consequence of the code mixing process in the receiver of Figure 24.4. Multiplication in the time domain is equivalent to convolution in the frequency domain. A wideband jammer will be spread even further than a narrowband jammer‚ and so after code mixing (point 4) even less of its energy will show up in the frequency range of the 50 Hz BPF. Regarding tracking thresholds, the C/A and P(Y) code signals are what is referred to as “legacy” signals‚ meaning that they carry the 50 bps data stream on the same channel as the primary navigation signal. Absent data wipe-off, the maximum predetection integration time is 20 ms, and phase lock loops have to use a twoquadrant discriminator; for example, atan(Q/I) or sign(I)∗Q. The penalty for this is roughly 6 dB in threshold C/No performance compared with the case where there is no data on the carrier and a four- quadrant discriminator (atan2(Q,I)) is used. “Modernized” signal architectures comprise two channels, a pilot channel with no data on it and a separate data channel to carry ephemeris data, and so on. Typically, the pilot and data channels use distinct spreading codes but maintain a specific carrier and code phase relationship with

c24.3d

627

respect to each other. In the case of L1C, the pilot and data channels have the same carrier phase‚ and the data channel is 4.75 dB weaker. The data channel is usually not tracked directly‚ but its carrier and code phase is inferred from the pilot channel using the known relationships between the signals. Returning to Figure 24.8, tracking the P(Y) signal requires a C/No of about 27 dB-Hz while‚ the L1C Pilot requires a C/No of greater than 21 dB-Hz. This, combined with the fact that L1C Pilot is a 3 dB stronger signal‚ means that the L1C Pilot signal can withstand 9 dB greater jamming, for this type of jamming. The C/A signal, being a “legacy” design, performs only 3 dB better because of its power level relative to P(Y).

24.3 Jamming Effectiveness as a Function of Range In assessing jamming effects, the role of RF propagation effects is extremely important. Many analyses use free space propagation to estimate jammer power as a function of range‚ and as we shall see, they may overestimate effective ranges by orders of magnitude. First though, the free space model. The free space model predicts that signal strength falls off with range at a rate of 1/R2.

15/12/2020 5:42:15 PM

628

24 Interference: Origins, Effects, and Mitigation

λ 4πR

Sreceived = Stransmitted + Gt + Gr + 20 log 10

24 5

where: Sreceived is received signal power (dBW) Stransmitted is transmitted signal power (dBW) Gt is transmitter antenna gain in the direction of the receiver (dBiC) Gr is receiver antenna gain in the direction of the transmitter (dBiC) λ is the signal’s wavelength (19 cm@L1, 24 cm@L2) R is the spatial Tx/Rx separation in the same units as wavelength EIRP dBW = Stransmitted + Gt Figure 24.9 plots J/S as a function of range for jammer EIRP of 1, 10, 100, and 1000 W using the free space model. EIRP is a function of both transmitter power and its antenna gain toward a receiver. For purposes of this computation, a 10 W transmitter driving a highly directional 20 dBiC gain antenna is the same as a 1000 W transmitter driving a 0 dBiC omni-directional antenna; both have an EIRP of 30 dBW. Using a J/S of 43 dB as a benchmark, Figure 24.9 shows that an unaided P(Y) code receiver would lose track at a range of 350 km against a 1000 W EIRP jammer. This might be true in outer space, but on Earth, as a minimum, the curvature of Earth would limit the range depending on the

Median J/S (dB wrt –160 dBW

Higher 60 Is Worse (for the GPS 50 Receiver)

height above the ground. Is a 1000 W jammer even feasible? The answer is yes; look in your kitchen. A microwave oven uses a magnetron to put out roughly 500 to 1000 W at 2.45 GHz. In a military environment, providing prime power to operate a high-power jammer is likely the more challenging problem. Jammers and GNSS receivers are often ground based. In a smooth field, at low angles of incidence, the ground is a nearly perfect reflector. Figure 24.10 shows a notional two-ray propagation model [14] where a signal from the transmitter follows two paths to the receiver: a direct path and a reflected path. To a close approximation, receive and transmit antenna gains are the same for the direct and reflected paths. Depending on geometry, the reflected path can add to the direct path either constructively or destructively. At close ranges, when direct and reflected path signals add constructively, the received power can exceed free space predictions by 6 dB‚ but at a slightly different range, signals can cancel and nothing is seen. Finally, once the range exceeds the first Fresnel break point, the direct and reflected signals add together with a relative phase that leads to signals falling off at a rate of 1/R4. In reality, ground mobile propagation is nowhere near as simple as the two-ray model [15]. Buildings, terrain, reflections, and vegetation all affect the received interference power, especially when the interference source

10

00

10 10

1W

0W

tt

att

Can’t Track

40 Can Track 30

1000x

20

100x

Nominal Unaided P(Y)-code Receiver J/S Threshold of 43 dB

350 km 10

10x 10 km

0 100

Figure 24.9

c24.3d

628

Wa

tt

att

Wa

1 Watt EIRP, Free Space 10 Watt EIRP, Free Space 100 Watt EIRP, Free Space 1000 Watt EIRP, Free Space

101

100 km

1000  km

102

103

Range (km)

Incident J/S as a function of range assuming free space propagation.

15/12/2020 5:42:16 PM

24.4 GPS L1 C/A Code Structural Vulnerabilities

629

Frequency = 1.5754 GHz, h1 = 30’, h2 = 5’, Fresnel Breakpoint at 0.18189 miles, Link Pt*Gt*Gr of 10 Watts –10 –20 Two Ray Model

Power (dBm)

Higher –30 Received Power –40 –50 –60

R2 Slope (Free Space)

–70 R4 Slope

–80 –90 –100 10–2

10–1

100

101

Range (miles)

Figure 24.10

Ground reflection can cause +6 dB power relative to free space prediction at short ranges.

is also ground based. Propagation effects are particularly important in cellular systems‚ and numerous empirical models have been developed based on measurement campaigns that measure the median path loss as a function of frequency, antenna heights, urban environment, and so on [16]. The tendency toward 1/R4 propagation predicted by the two-ray model is well supported. One of the earlier (and simpler) models is the Hata– Okumura models and the variant described in 3GPP TR 43.030 which divides environments into four categories:

•• ••

Hata Hata Hata Hata

Urban Suburban Rural Quasi-Open Rural Open

The distinctions between different area types are somewhat subjective‚ and it should be emphasized that a Hata Urban environment is still fairly open with median building heights of around 15 m. It is not an urban canyon such as is seen in large cities. Figure 24.11 repeats the analysis of Figure 24.9 for a 1000 W EIRP jammer but with different propagation models. Under free space conditions, the predicted threshold range is 350 km as before, but in an urban environment, the median threshold jamming range is only 2.5 km.

c24.3d

629

24.4 GPS L1 C/A Code Structural Vulnerabilities The GPS L1 C/A code signal presents a bit of a conundrum. It is by far the single most popular navigation signal; every GNSS receiver can receive it and for many, it is the only signal type used. It is the easiest signal to work with from an acquisition and power consumption perspective [17]. It is usually the ultimate fallback signal for when all else fails. It is also, by far, the most easily interfered with since it uses a short PN code that repeats every millisecond and there are no authentication features. Figure 24.12 shows the actual spectrum of L1 C/A code PRN3. Broadly speaking‚ it has the sin(x)/x spectrum of a BPSK signal but, because the PN code repeats itself once every millisecond, the actual spectrum is a line spectrum. Figure 24.13 shows a close-up of the spectrum over the range 150 kHz to 170 kHz. The lines are separated by 1000 Hz due to the PN code repetition rate and have a nominal width of ±50 Hz due to the 50 bps data stream. The specific line structure is specific to each PRN code, and the lines can be as large as −21 dB with respect to the total power. Figure 24.14 shows an RD map for a receiver centered on zero Doppler and matched to PRN 3. Input comprises an PRN 3 L1 C/A signal centered at 500 Hz Doppler and

15/12/2020 5:42:17 PM

630

24 Interference: Origins, Effects, and Mitigation

1000 Watt EIRP Jammer at 100 feet AGL, Receiver at 5 feet AGL

Higher 60 Is Worse (for the GPS 50 Receiver)

Free Space Hata Urban Hata Suburban Hata Rural Quasi-Open Hata Rural Open

Median J/S (dB wrt –160 dBW)

Can’t Track 40 Can Track 30

1000x

20

100x

10

10x

Nominal Unaided P(Y)‐code Receiver J/S Threshold of 43 dB

2.5 km

350 km

10 km 0 100

100 km

101

102

1000 km 103

Range (km)

Figure 24.11

Using more realistic near-Earth propagation models, median received J/S is much less than predicted by free space model.

L1 C/A PRN3 Power Spectra

0

Power (dBr total)

–10

–20

–30

–40

–50

–60 –2

–1.5

–1

–0.5 0 0.5 Frequency (Hz)

1

1.5

2 x 106

Power Average of 1 x 262144 pt-FFTs, Hamming Window, Noise BW = 67.6688 Hz

Figure 24.12

GPS PRN 3 C/A code spectrum with respect to the center frequency.

30 chips code phase offset, and a CW jammer at the L1 center frequency + 159 kHz = 1575.579 MHz. The jammer is 250 times more powerful than the C/A code signal, or stated another way, the J/S is 10 log10 (250) = 24 dB. The CW jammer creates responses in the RD map whose magnitudes follow the line spectrum of the code but in reverse order. Starting at 159 kHz in Figure 24.13 and moving up in frequency, we see medium, bigger, biggest, and small

c24.3d

630

amplitudes. In Figure 24.14, we see the same pattern of line responses moving from left to right from 0 Doppler offset. In principle, a receiver could track the PRN3 signal response in this situation‚ but if the jammer were to shift frequency by +500 Hz to 159.5kHz, the line spectra responses also move by 500 Hz and now sit on top of the signal response (which does not move except in response

15/12/2020 5:42:17 PM

24.4 GPS L1 C/A Code Structural Vulnerabilities L1 C/A PRN3 Power Spectra

–20 –22

C/A Code Repeats Itself with 1 msec Period So Lines are 1 kHz Apart

–24 Power (dBr total)

631

–26

159 kHz 1,000 Hz Separation

–28 –30 –32 –34 –36 –38 –40 1.5

1.52

1.54

1.56

1.58

1.6

1.62

1.64

1.66

Frequency (Hz)

Figure 24.13

1.68

1.7 x 105

Close-up of C/A code line spectrum from 150 to 170 kHz offset relative to the center frequency.

C/A Search Correlation Responses 16000

A Continuous Wave (CW) Jammer Is Just a Sine Wave

J/S = 24 dB (250 x) & 159 kHz Offset

14000 12000

PRN3 Signal Response

10000 8000

0.3

6000

0.4 Time

0.5

4000 2000 0 100

Time

90 80

Offs

70 60

)

hips

et (C

50 40 30 20 10 0

Figure 24.14

6000

4000

2000

0

•

c24.3d

631

–4000

–6000

Doppler Offset (Hz)

In the range-Doppler map, the response to a CW jammer follows the PN code’s line spectrum.

to changes in relative geometry). In the absence of any checks, the receiver’s phase lock loop could lock onto one of the stronger jammer lines and track it off into oblivion. In point of fact though, there are several ways to identify the presence of a CW jammer. A few possibilities:

•

–2000

Detect the fact that Early, Late, and Prompt signals all have the same power level. With a real signal, Early and Late are about 6 dB down relative to Prompt for 1 chip E/L separation. Look at the RD map‚ and see that certain Dopplers have strong responses at all code phases.

• • •

Look at the probability density function of the precorrelation samples‚ and note that they are not Gaussian distributed. Perform a spectrum analysis using FFTs to detect tone jamming. This works surprisingly well even on 1.5-bit precision samples (e.g. Figure 24.26) and is often part of a receiver’s diagnostic capabilities. Finally, some receivers even have the capability to notch out CW interference. For military receivers, the reasons are obvious but many civil receivers also have this capability, so they can operate in complex EMI environments, namely, cell phones.

15/12/2020 5:42:19 PM

632

24 Interference: Origins, Effects, and Mitigation

At lower J/S levels, the effects of CW jamming can become more pernicious since the jammer’s presence is harder to detect. Figure 24.15 depicts an RD map where the jammer is offset 161 kHz with respect to the PRN 3 center frequency. The J/S is 12.3 dB, or 6 dB below thermal noise in a 2 MHz bandwidth, so the net rise in power is only 1 dB, which is too small to be reliably observable by a precorrelation jamming meter. A receiver tracking PRN 3 might think it is tracking fine‚ but in fact the jammer can distort the code correlation envelope and bias the code tracking point by several meters as is shown in Figure 24.16. Here, the top curve shows the distorted correlation envelope‚ and the three lower curves show Early– Late envelope responses for 1 chip, ½ chip, and ¼ chip E/L separations, respectively. A naïve receiver looking only at C/No meters, phase lock indicators‚ and code lock indicators might think it has much better accuracy than it actually does, which can prove critical in applications like harbor navigation and aircraft landing. As a final observation on CW jammers, the receiver’s predetection integration time (PIT) is also very important. Lower-end receivers using short predetection times, for example, 1 or 2 ms, have greater susceptibility to CW jamming. This is because the range of line interaction frequencies is inversely proportional to the PIT. With a 20 ms PIT, the line response needs to be within ±25 Hz of the desired signal for strongest effect. With a 1 ms PIT, the line response needs to be within ±500 Hz for strongest effect, and since lines are spaced 1000 Hz apart, there is always at least one line with a potentially strong interaction. The length 1023 L1 C/A codes defined in IS-GPS-200J are a subset of a family of 1025 distinct Gold codes with

well-defined auto- and cross-periodic correlation properties described in Tables 24.3 and 24.4. Figure 24.17 shows the autocorrelation response for PRN3 with temporal sidelobes identified. At zero Doppler offsets‚ any two equal power C/A codes will yield a cross-correlation response where at 25% of relative code phases, the response is down by only 24 dB. Figure 24.18 illustrates how an adversary can take advantage of this. Here, the jammer transmits PRN1 at the same nominal chip rate as GPS (1.023 MChip/s) and has a J/S of 24 dB relative to PRN 3, the desired signal. The Doppler offset between the two signals is 500 Hz. Trying to receive other real signals, for example‚ PRN 23, would yield similar RD maps where the specific structure is distinct but similar looking. Presented with this sort of correlation response on all signals, the receiver would likely have a difficult time acquiring and maintaining lock on the real signal but might be quite happy to lock onto the multitude of false peaks. This is exactly what happened in the Pole Star experiment [2] described in Figure 24.1. Receiver autonomous integrity monitoring (RAIM) could easily have detected that the receiver was tracking false “signals,” but such algorithms are often not included in receivers. Detecting the presence of this jammer type at the signals level can be done using methods similar to those used to detect CW interference but with the following caveats:

• •

Early, Prompt‚ and Late power levels will tend to be correct‚ and so that is not a great detection method. The jammer’s spectrum is that of a C/A code. Spectrum analysis for detection is less reliable‚ and notch filtering is not effective.

Case 1, C/A Search Correlation Response Track Bias is 31 meters

Amplitude (volts)

PRN 3 Signal Response

10 5 0 6000 4000 100

2000

90 80

0

Doppler Offset (Hz)

70 –2000

40

50

60

30

–4000

20 –6000

10 0

Time Offset (chips)

Figure 24.15 PRN3 range-Doppler map with 161 kHz offset CW at J/S = 12.3 dB (precorrelation interference is 6 dB below thermal noise in 2 MHz bandwidth). At lower interference levels, interference can degrade accuracy by distorting the correlation envelope.

c24.3d

632

15/12/2020 5:42:21 PM

24.4 GPS L1 C/A Code Structural Vulnerabilities

Late

Prompt

633

Early

Volts

1 0 –1 –2

Correlation Envelope

–1.5

–1

–0.5

0 Early-Late

0.5

Volts

1

2

1-chip Separation DLL Discrim

–1.5

–1

–0.5

31 meters 0.5

0

1 Volts

1.5

0 –1 –2

1

1.5

2

0.5-chip Separation DLL Discrim

0 –1 –2

–1.5

–1

–0.5

19 meters 0.5

0

1 Volts

1

1

1.5

2

0.25-chip Separation DLL Discrim

0 –1 –2

19 meters –1.5

–1

–0.5

0 Time (chips)

0.5

1

1.5

2

Figure 24.16 Correlation envelope and delay lock loop (DLL) discriminator responses with J/S=12.3 dB, thermal noise set to zero, and CW jammer @ 161 kHz offset as in Figure 24.15.

Table 24.3 C/A Code periodic autocorrelation values (integer code phase offsets) Autocorrelation Value

Probability

0 dB wrt peak

0.098%

−23.9 dB wrt peak

12.5%

−24.2 dB wrt peak

12.5%

−60.2 dB wrt peak

75%

Table 24.4 C/A Code periodic cross-correlation values (integer code phase offsets) Cross Correlation Value

Probability

−23.9 dB wrt peak

12.5%

−24.2 dB wrt peak

12.5%

−60.2 dB wrt peak

75%

Finally, before leaving the topic of structural vulnerabilities, modernized signals incorporate several techniques to mitigate these structural effects. They tend to use longer codes with better cross-correlation properties that repeat less frequently so as to break up the line structure. This is done either by simply using a longer code and/or by concatenating a shorter code with an overlay code. The L5 signal architectures (IS-GPS-705D) provide a good example of

c24.3d

633

the latter with their Neumann–Hoffman codes. The L1C Pilot signal uses a 10× longer code (10230 chips vs. 1023 chips), and it imposes an additional 100 Hz overlay code that repeats only once every 18 s. The result is that these signals offer much better resistance to structural jamming as is demonstrated in Figure 24.19. The top two RD maps show correlation responses at nominal C/No’s and with PRN1 (per ICD-GPS-800E) jamming for the L1C Pilot signal. The bottom two figures show corresponding results for the legacy L1 C/A signal. The L1C signal shows no particular sensitivity toward this sort of jamming, whereas the L1 C/A receiver is overwhelmed in a sea of confusion. The L1C Pilot signal has jamming resistance against most jammer types that is similar to that of the P(Y) code. Its 3 dB higher signal power, combined with a 6 dB lower tracking threshold and no particular structural vulnerabilities, makes up for its lower processing gain relative to P(Y). Figure 24.20 plots J/S as a function of range where the jammer has an EIRP of 0.2 W, typical of many so-called “personal privacy devices” (PPD). Using a very optimistic J/S threshold of 24 dB for the C/A code signal, such a jammer could, in theory, be effective at ranges from 400 m in urban environments to 30 km under free space conditions. Corresponding ranges for the L1C signal are 150 m and 4 km, respectively. In point of fact, the effective range of most PPDs is much less. Their antennas are often of such poor quality that more radiation occurs through the jammer casing than

15/12/2020 5:42:22 PM

634

24 Interference: Origins, Effects, and Mitigation

Case 1, Basic 1 msec PIT C/A Search Correlation Responses C/Nomax = 80.1105 dB-Hz

1500

Amplitude (volts)

20 msec Total PIT C/A Code Temporal Sidelobes

1000

500

0 500 100 80

0

DO

60

PPL

ER

–500

40

20 0

Time Offset (chips)

Doppler Offset (Hz)

Figure 24.17

E RANG

C/A code correlation response for Case 1, basic 1 ms PIT C/A search.

Tracking Loops Can Lock on To These Amplitude (volts)

PRN 3 Response 40 20 0 6000 4000 2000 0 Doppler Offset (Hz)

–2000 –4000 –6000

Figure 24.18

0

10

20

30

40

Jamming Mitigation

Military and civil defenses against jamming share many commonalities‚ but there are distinctions. Military defenses tend to emphasize protecting specific

c24.3d

634

60

70

90

100

Time Offset (chips)

PRN3 range-Doppler map with PRN1 Gold code jammer at J/S = 24 dB (250x) at 500 Hz offset, 20 ms PIT.

the antenna. The waveforms used, usually some form of fast chirp [18], are not particularly effective against C/A codes (Figure 24.21). And finally, the quality of manufacture is such that they often have poor control over the center frequency, and so they may miss hitting GNSS frequencies directly and rely instead on front-end saturation effects.

24.5

50

80

signals (e.g. P(Y) code), whereas civil defenses tend to focus more on jammer detection and avoidance. Possible jamming (and spoofing) mitigation approaches include

•• • •• ••

Strong out-of-band signal rejection Maintaining situational awareness Frequency excision [19] and adaptive A/D conversion [20, 13] Avoid relying on civil signals Signal diversity Tightly coupled IMU aiding Adaptive array antennas

15/12/2020 5:42:23 PM

24.5 Jamming Mitigation

635

PRN1 Jamming (J/S=24)

No Jamming

PRN 3 Response

PRN 3 Response

L1C

PRN1 Jamming (J/S=24)

No Jamming

PRN 3 Response

PRN 3 Response

L1 C/A

Figure 24.19 Correlation responses at nominal C/No’s and with PRN1 jamming for the L1C Pilot signal (top) and for the legacy L1 C/A signal (bottom). The plots show that modernized signals have much better resistance to structure jamming.

0.2 Watt EIRP Jammer at 5 feet AGL, Victim Receiver at 30 feet AGL with 0 dB Gain Towards Jammer –157 dBW Signal with 0 dB Gain towards Jammer 60 55

Fr

ee

42 dB L1C Matched Spectrum Jamming Threshold

50

ac

Nominal GPS Signal: –157 dBW into 0 dBiC

tio

n

n a ag op Pr

24 dB L1 C/A Capture Jamming Threshold

n

tio

Median J/S (dB)

ga

ba Ur

30

pa

ta

Ha

35

eP

ro

45 40

Sp

25 20

A Factor of 75 Variation in Range Depending on Propagation

15 10 10–1

400 meters

100

Range (km)

101

30 km

102

Figure 24.20 J/S as a function of range where the jammer has an EIRP of 0.2 W. The plot shows that the effective range of a jammer varies widely depending on propagation and upon the GNSS signal type.

c24.3d

635

15/12/2020 5:42:24 PM

636

24 Interference: Origins, Effects, and Mitigation

Jammer Found in the Wild 111.11 kHz Sweep Rate –8.6 to +5.4 Mhz

J/S = 24 dB / 250x

J/S = 34 dB / 2,500x

Figure 24.21

Most jammers being sold in civil markets do not use effective waveforms‚ and their antennas are of poor quality.

The topics of adaptive array antennas and tightly coupled IMU aiding are covered in Chapter 26 and 46 in this book and so will not be covered here other than to note that in the absence of these sorts of technologies, a determined adversary will usually win in the battle to deny access to a particular signal. Adaptive arrays can provide 30 to 70 dB of additional interference rejection by creating spatial nulls in the direction of the jammer(s), and so are by far the most effective means for preserving access to a given signal. Their main drawback, aside from being potentially ITAR controlled (the rules are complex), is that the array manifold is physically large. Standard seven (7) element array manifolds are 14” in diameter. The main drawback with tightly coupled IMU aiding is that in order to provide significant jamming protections to a moving user, the IMU has to be of very good quality (read expensive) so as to provide meaningful dynamic aiding to a GNSS receiver so that its signal tracking bandwidths can be reduced. Even then, the J/S gains are usually no more than 10 to 20 dB since oscillator phase noise and signal propagation effects (e.g. tree-induced scintillation) not measured by the IMU begin to limit how narrow tracking bandwidths can become. The real utility of an IMU is often that it allows a user to ride out extended periods of signal denial and efficiently reacquire signals in jamming.

c24.3d

636

So, is the situation for civil users hopeless? Far from it. As Table 24.5 shows, the civil user in principle has a plethora of signals available at diverse frequencies from a host of international satellite navigation systems, and they can also rely on diverse network-assisted methods to determine position and time. The core challenge for civil users is to identify and discard suspect signals‚ or in other words, maintain situational awareness. Also, civil users enjoy the protection of the law; jamming and RF spoofing are illegal and subject to major fines, $100,000 per incident in the United States [21]. With the above as prelude, for both military and civil communities, strong out-of-band interference rejection is important. Computed using the Betz equation but with no jamming, Figure 24.22 illustrates one of the key receiver design trade-offs, namely‚ front-end bandwidth. For a given desired signal, narrowing the front-end bandwidth usually makes the receiver more resistant to the effects of out-ofband interference but it also leads to greater SNR loss. The earlier the filtering occurs in the RF chain, the less chance of driving subsequent components into saturation. Naturally narrowband antennas and low insertion loss BPFs prior to pre-amplification deserve consideration. For military receivers in particular, high-intercept-point amplifiers and mixers prove beneficial in keeping operation linear even with high interference input levels. The penalty‚ of course,

15/12/2020 5:42:26 PM

24.5 Jamming Mitigation

linearity as a function of frequency is also improved‚ which is important for RTK and PPP applications. For these reasons, precision receivers often use 20 MHz or wider front-ends even though they may use only relatively narrowband signals like the L1 C/A signal. This is also the reason precision receivers consistently show up as more sensitive to harmful interference caused by LightSquared (now Ligado) LTE transmissions. Finally, before leaving the topic of front-ends, in the case of the L1C Pilot signal, there is a 4/33 duty factor BOC(6,1) component included expressly for improved multipath rejection, but to receive it, the front-end bandwidth has to be at least 14 MHz wide. Military receivers tend to be fairly good at recognizing the presence of jamming‚ whereas civil receivers are often abysmal in this task. Maintaining situational awareness is crucially important in jamming mitigation. If you don’t know you have a problem (potentially), you won’t apply the correct tools to provide for continued operation, and you won’t provide timely warnings to operators. A few examples:

Table 24.5 Navigation sensors are getting inexpensive (green indicates common smartphone capabilities) Satellite navigation systems

Other navigation sensors

Global SatNav Systems GPS

Microphone/Speaker (Ultrasonic Chirp)

GLONASS

WiFi (RSS and RTT modes)

BEIDOU

Cellular TOA/TDOA

GALILEO

Bluetooth iBeacon 6DOF MEMS IMU

Regional SatNav/ Augmentation Systems

3DOF Magnetic Field Sensor Camera(s) (Point Space Database)

QZSS

LTE Proximity Services

SBAS

Atomic Clock or Equivalent

IRNSS

LocataLites

637

NextNav (920–928 MHz) SAR Imagery

•

Iridium (1617.775–1626.5 MHz) Barometric Altimeter eLoran

is higher power consumption by active components since higher drive levels are usually needed to maintain linearity. Conversely, widening bandwidths makes multipath rejection techniques such as narrow correlator tracking [22] and strobe correlators [23] more effective. Phase

In 2012, Gary P. Bojczak, an engineering firm employee, used a cigarette lighter GPS jammer to jam the GPS-based tracking device his employer had installed on the truck he was driving [24]. He also inadvertently jammed the recently relocated GPS ground reference stations at Newark International Airport. He was caught by the FCC (unusual), fined $32,000 and lost his job. If his employer’s tracking device had been able to detect and inform his employer of jamming, the results would probably have been different. He might have been called into his supervisor’s office for the following conversation: “Gary,

0 BPSK(1)

–1 BPSK(10)

SNR Loss (dB)

–2

BOC(1,1) BOC(6,1) BOC(10,5)

–3

–4 Better Out of Band Interference Rejection

Better Multipath Rejection Possible

More Signal Loss

Higher A/D Sample Rates

Higher Cost/Power

–6 100

101 2-Sided Bandpass Filter Bandwidth (MHz)

Figure 24.22

c24.3d

637

Front-end filter bandwidth selection is a performance trade-off.

15/12/2020 5:42:28 PM

638

24 Interference: Origins, Effects, and Mitigation

•

I notice that you are jamming our tracker. I’d like it to stop.” In the civil environment, jamming mitigation can often be effected by social engineering, but only if it is identified and reported appropriately. Commenting on test results where timing receivers, some with chip-scale atomic clocks, were exposed to interference, Sarah Mahmood of DHS noted: “All the receivers were vulnerable to jamming and spoofing … it is one thing to say that you can switch over to backup timing if GPS is unavailable but if your receivers aren’t able to recognize that GPS is unavailable, or you’re being spoofed, the capability of backup timing is almost irrelevant. We need to make our receivers smarter” [25].

to ~0.5 dB. In another even more popular variation, the 1.5bit A/D converter, the “zero” threshold is not implemented‚ and the three possible output values are {−1, 0, and −1}. Such a converter has only about 0.9 dB of conversion loss if VT% is set to 40%, and it considerably simplifies subsequent correlator processing. Of particular interest for interference detection purposes, the control voltage to the variable gain AGC amplifier Vi can also be used to measure (jammer+noise) to noise power ((J+N)/N). Under unjammed conditions, the nominal input power to an L1 C/A receiver in a 2 MHz bandwidth is about −110 dBm, most of this due to naturally occurring thermal and amplifier noise. In recent years, the aggregate power from diverse GNSS satellites has further elevated noise levels in the neighborhood of the GPS L1 center frequency. The C/A code signal at −127 dBm is a factor of 50 (17 dB) weaker and so does not influence AGC operation. Small jammers or spoofers will also not influence AGC operation since the AGC only reacts to the composite of jamming + noise. If, however, interference starts rising above the thermal noise floor, the AGC will respond by decreasing the gain GA so as to maintain the correct percentage of “large” outputs. Response times to a change in input power level are very fast, typically less than 1 ms, and so pulse jamming characteristics can also be determined. If the receiver knows the control characteristics of the AGC amplifier (β,α), then the receiver can determine the

So how can interference be detected and characterized? The receiver’s automatic gain control (AGC) can play a crucial role [26, 27]. All current GNSS signals are received at power levels below thermal noise levels in their operating bandwidth when using typical antennas. Anything that raises power in the precorrelation bandwidth of a receiver is likely to be due to interference. Figure 24.23 depicts the A/D conversion/AGC loop found in virtually all GPS receivers in some form. The AGC’s core objective is to set the gain GA so a set percentage of 2-bit A/D converter outputs correspond to “large” values of 3 and −3. In the feedback control portion, depicted in yellow, VT% is set to 35% in a Gaussian noise environment to hold A/D conversion losses

GAGC

VT% 1

–

1 s

+

(J+N)/N Reading Pickoff

N

N

∑

For 1.5 bit ADC Want ~40% “1” & “–1”

A/D Converter Clock D/A + Vi Low IF Analog Signal

VB

–

Bits: 2

D-Type FlipFlop

VB

+

GA 0

–

D-Type FlipFlop

–VB A/D  Conversion Requires Automatic Gain Control (AGC)

–

1

1

1

0

1

–1

0

–1

–3

–1

–1

D-Type FlipFlop

+ 1.3VB

638

3

+

GA = αe βVi

c24.3d

1

0 –VB

Figure 24.23

1.5

–

D-Type FlipFlop

LPF (correlator)

Constant Envelope Detection Channel (CW, Swept CW, Gold)

Knowing you are jammed (or spoofed) is the first step‚ and the AGC can provide the first indications of interference.

15/12/2020 5:42:28 PM

24.5 Jamming Mitigation

change in (J+N)/N given Vi. Additionally, if the receiver knows the quiescent Vi associated with a thermal-noiseonly input, it can measure (J+N)/N, the jam-to-noise ratio, on an absolute scale. To obtain the quiescent value, the receiver can short the antenna on power-up as part of a built-in test prior to operation. Alternatively, it can maintain and refine a historical value during normal operations, the caution being that spoofers and jammers may try to manipulate history-based values. Figure 24.24 depicts (J+N)/N as a function of J/S for specific signals and associated minimum receiver front-end bandwidths. Equation 24.6 shows the process for computing such curves. Recalling the prior discussion surrounding the effects of low-power jamming on L1 C/A code (Figures 24.15, 24.16), the AGC has minimal response to low-power jammers. At a J/S of 12.3 dB, the rise in (J +N)/N is only about 1 dB, and so such a jammer is unlikely to be detectable via AGC monitoring. Computing and examining the RD maps (Figure 24.15) can yield better low-power jamming observability. J+N N where J dBW N dBW j Watts n Watts

dB = 10 log 10

j+n n

= J S dB + S dBW = 10 log 10 B + N 0 dBW = 10J 10 = 10N 10

24 6

from Equation 24 3

The probability density function of a Gaussian source’s amplitude is distinctly different from that of a constant

envelope (CE) source (CW, swept CW, or Gold code jammer types) [20, 13]. Referring back to Figure 24.23, in an additional refinement depicted in red, receivers can include an additional comparator set to threshold at 1.3 VB. If a CE jammer is present, this threshold will be crossed ~1% of the time versus ~14% of the time for Gaussian-distributed jamming if VT% is set to 40%. With the jammer type identified, the receiver can adapt VT% if it is seeing CE jamming to obtain several decibels of additional jamming resistance [20, 28]. The TI-420 L1 C/A receiver developed by the author’s team at Texas Instruments in the 1986 time frame routinely outperformed P(Y)-code receivers against CE jammers using this technique. Figure 24.25 shows an example of AGC responses to pulsed CW jamming at a J/N of 30 dB and with a 100 Hz pulse repetition frequency. Gain adjustment is fast, submillisecond, because the AGC operates on wide bandwidth precorrelation signals. Of particular note, the CE detection channel, shown in green on the lower trace, provides a clear indication as to jammer type. With pulsed Gaussian noise, it would hold steady at ~2 × 14% except for short transients due to changes in input power level. With a bit of additional FFT-based processing on AGC gain and 1.5-bit ADC samples, the jammer’s pulse and spectral characteristics can be determined. Figure 24.26 shows that a 1.5-bit ADC output spectrum has a surprising degree of spectral fidelity. The CW jammer is clearly visible‚ and its center frequency is readily determined. The additional spectral line artifacts in the 1.5-bit ADC spectrum vary depending on the ADC sample rate and the jammer’s

All Cases:Tant.=300 K, NF=2 dB

50

BPSK(10) @–161.5dBW, Inband Jamming, 17 MHz Passband BPSK(1) @–158.5dBW, Inband Jamming, 1.7 MHz Passband BOC(1,1) @–158.3dBW, Inband Jamming, 3.5 MHz Passband

40

C/A-Code

30 (J+N)/N (dB)

639

L1CP-Code

20

P(Y)-Code 10

0

–10

0

10

20

30

40

50

60

70

Incident J/S (dB)

Figure 24.24

c24.3d

639

The AGC responds to a composite of J+N and will not react to small jammers.

15/12/2020 5:42:29 PM

640

24 Interference: Origins, Effects, and Mitigation

Signal AM (voltage gain)

1

Input Signal AM Characteristics

ON

Gaussian: –170 dBm/Hz CW: –80 dBm at 1350.5 kHz

0.5 OFF

0 0

5

10

15

20

25

30

35

40

45

50

30

35

40

45

50

Front End Gain (GA) 80 70 Gain 60 (dB) 50 40 0

5

10

15

20

25

Large Value Percentages

100

= 40%

AGC Control Channel, V

Percent Large 50

CE Monitor Channel, V

0 0

5

10

15

20

CE Detection Channel (x2)

25 Time (msec)

30

35

40

= 1.3V

45

50

Not CW

CW

Figure 24.25 The AGC and A/D conversion process can measure J/N, pulse rate, and jammer type. In this example, for illustrative purposes, the jammer is pulsed CW at 30 dB J/N (50 dB J/S) with a 100 Hz PRF.

ADC input spectrum

–140

Power (dBW/Hz)

–160 –180 –200 –220 –240 –260 –280 –2.5

–2

–1.5

–1

0

0.5

1

1.5

2

2.5 x 106

0.5

1

1.5

2

2.5 x 106

ADC output spectrum

–40

Power (dBW/Hz)

–0.5

–50 –60 –70 –80 –90 –2.5

–2

–1.5

–1

–0.5

0 Frequency (Hz)

Figure 24.26 A 1.5-bit A/D converter output has reasonable spectrum fidelity. The top curve shows the spectrum of the unquantized signal‚ while the bottom figure shows the spectrum of the quantized signal.

c24.3d

640

15/12/2020 5:42:30 PM

24.6 Spoofing Detection

frequency. Additional A/D conversion precision reduces such artifacts. The takeaway from the above discussions is that with very simple hardware, a GNSS receiver can measure (J +N)/N and also identify the approximate type of jamming that it is seeing: pulse, CE, and Gaussian. More sophisticated identification strategies are certainly possible‚ but the point is this: receivers that take steps to develop situational awareness know something is going on, and so can take action. Like a smoke alarm, situational awareness doesn’t put out the fire‚ but it does give warning to allow for more effective action. Referring back to Table 24.5, the action may be to not use signals identified as having jamming present. Timing receivers with atomic clock backups can start riding the atomic clock until jamming ceases. Hybrid GPS/eLoran receivers can place greater reliance on the eLoran signal when GNSS signals are denied due to jamming. Knowing you have a problem is the first step.

24.6

Spoofing Detection

First‚ a caveat; the intent of this section is to educate the reader on spoofing detection and mitigation, not on how to build a spoofer. Descriptions of spoofing techniques are deliberately vague and incomplete by design. Over the last few years‚ the possibility of RF spoofing has received a lot of attention‚ and there have been a couple of successful open literature demonstrations [8, 29]. More recently, there have been numerous spoofing incidents in which spoofing has been used as a denial-of-service form of jamming [30, 31]. The success of these demonstrations is more a testament to the utter naiveté of the victim receivers than to the sophistication of the spoofers. Spoofing is fairly easy to detect, but only if the receiver is looking for it. Performing basic signal validations will usually reveal that an RF spoofer is present, and depending on the methods, may allow for discrimination between real and faux signals [32, 33] so as to allow continued operation even while under attack. What are some of the possible indicators that spoofing is present and how hard are they to implement? Broadly speaking, some of the more important techniques include the following:

• ••

c24.3d

641

Checking for inconsistencies between diverse navigation sources and signals Continuity checks in estimated time and position Looking for anomalous signal characteristics with regard to the signal-to-noise ratio, tracking glitches, and in the appearance of RD maps

• •

641

Detecting multiple signals having a common point of origin or direction of arrival; most spoofers transmit all faux signals from one location Cryptographic verification that each signal originated from a real satellite

None of the techniques is 100% reliable in all scenarios‚ but in concert, they can make undetected spoofing very unlikely. If a significant percentage of civil receivers maintained basic situational awareness, it would establish a form of herd immunity by making attempts at RF spoofing less attractive to adversaries since the reliability of such attacks would be lessened. Receivers that use multiple signal types from multiple sources (e.g. GPS, BeiDou, Glonass, and Galileo) and multiple frequencies (e.g. L1, L2, and L5) can makes the RF spoofer’s task more onerous. In the Humphrey’s spoofing demonstrations, the victim receivers were GPS L1 C/A-only receivers. If the receivers had been looking for other signals, for example‚ Glonass, RAIM-style tests would have quickly revealed major inconsistencies and raised suspicion. That said, in the United States, there are legal impediments imposed by the FCC to using all GNSS signals available, particularly in safety-critical applications where the benefit would be greatest. Many of the technical objections to using foreign GNSS signals can be overcome by using authenticated out of band sources for ephemeris and clock corrections. Using additional sources such as WiFi positioning, cellular ranging and timing signals, and IMU, previously enumerated in Table 24.5, can make the spoofer’s task that much harder‚ but as the Portland spoofing incident demonstrated, only if those information sources are properly used [34]. It is little wonder that cyberspoofing (discussed in the chapter introduction) is often the preferred attack method, especially for insider attacks where the “victim” is the attacker (e.g. Automatic Identification System (AIS) spoofing). The ability to recognize attacks and discard questionable data is a key requirement for hardening navigation and timing systems. Situational awareness is the first step. Focusing on RF attacks for now, the first task of an RF spoofer is to get the victim receiver to lock on to its navigationally consistent set of false signals instead of the real signals. It needs to do this without being detected and with a high probability of success. If the receiver locks onto some mix of real and spoof signals, spoofing can be detected using RAIM-style algorithms. Sudden jumps in position and time are highly detectable‚ and so the spoofer needs to mask this as well. One approach is to jam first so the receiver is “lost” and then present a more powerful set of faux signals to be acquired. If the target receiver hasn’t maintained a last

15/12/2020 5:42:33 PM

642

24 Interference: Origins, Effects, and Mitigation

known good position and time bias, the receiver might accept the faux signals as valid even though they make no physical sense. For example, a very simple spoofer might use a signal generator with a canned scenario (e.g. circles)‚ or it might play back previously recorded signals. The receiver should really be asking itself, why did the time estimate change by 3 years upon reacquisition? Receivers need to be extremely cautious after jamming and during initial acquisition after having been off for a while. Another approach, possibly used in combination with a prior jamming attack, is to synchronously slide faux signals in underneath real signals at low power, then slowly raise the power, and then draw off the receiver. The attack has strong similarities to range gate walk-off methods used in radar deception but with the additional requirement that multiple satellite signal trackers have to be drawn off in a coordinated and navigationally consistent pattern. While straightforward in principle, this technique requires precise knowledge of where the target receiver is, and, it requires the spoofer to synchronize with the satellite navigation system(s). Humphrey’s spoofing demonstrations aboard a superyacht (see Chapter 25) were successful because the spoofer was a limpet type [4] placed on the vessel under attack. The spoofer knew the precise location

of the vessel in real time based on its own unspoofed GNSS receiver and so was able to generate faux signals with precise offsets and drive the victim’s navigation solution. Without this physical access, the spoofer would have had to use sophisticated and complex remote tracking methods to achieve the levels of accuracy needed for success. One important exception to this requirement is if the intended victim is a stationary timing receiver. Once the attacker has accurately located the target receiver’s antenna, perhaps using Google Earth, this becomes a fixed set of variables. At the RF/signals level, one of the more important antispoofing techniques is to monitor C/No and jamming levels to look for inconsistencies. If a spoofer transmits with too little power, it risks a failure to capture the target receiver. If it transmits too much power, the spoofer rises above thermal noise and becomes visible to the AGC. Figure 24.27 depicts a simplified spoofing scenario where the spoofer is trying to spoof 12-signals simultaneously, each with an equal power allocation, and all of the real signals are at specified minimum levels. All four curves are drawn as a function of the incident total spoofer power. The top curve shows the apparent C/No of authentic signals as a function of the incident total spoofing power assuming

12-SV Spoofer with Tant=250 K, NF=2 dB, L=1 dB, 2 MHz Passband, Csigi=–157 dBW, Gsig=0dBIC, Gjam=0dBiC Real Signal C/N0 60 C/N0 true (dB-Hz) 40 20 –155

Noise-like Assumption –150

–145

–140 Spoof Signal C/N0

–135

–130

–125

–145

–140

–135

–130

–125

–135

–130

–125

–135

–130

–125

60 C/N0 spoof (dB-Hz) 40 20 –155

–150

Spoof+Thermal Noise Power to Thermal Noise Power (J+N)N

20 (J+N)/N 10 (dB) 0 –155

–150

–145

–140 Spoof Signal1 / True Signal1 (dB)

20 Spoof Signal1 10 /True Signal1 (dB) 0 –10 –155

–150

–145

–140

Incident Total Spoof Power (dBW)

Figure 24.27

c24.3d

642

Without careful power control on the spoofers’ part, they are easily detected since they will elicit an AGC response.

15/12/2020 5:42:33 PM

24.6 Spoofing Detection

spoofing acts like noise with respect to the authentic signal. The second curve shows the corresponding apparent C/No of the faux signals. Both of these curves can be computed using the Betz equation (Eq. 24.2). Of special note, depending on the receiver’s PIT and the specific placement of faux signals in range and Doppler, real signals may be visible with little or no degradation in C/No, and hence the dashed red line. The third curve, computed using Eq. 24.6, shows (J+N)/N assuming a 2 MHz passband. The final curve depicts the relative power of one spoof signal relative to one true signal. In general, if a spoofer is generating N simultaneous equal power signals, the power devoted to any one signal is −10log10(N) dB relative to the total power. For a 12-channel spoofer, the power devoted to any one signal is −10log10(12) = −10.8 dB with respect to the total power. The significance of this last curve is that in order to reliably draw off a tracker and not cause obvious amplitude modulation, the inserted faux signal needs to be about 9 dB stronger than the real signal. This happens when the incident total spoof power is −137 dBW. The corresponding rise in (J +N)/N is a readily detectable 4.4 dB, and the apparent C/ No of the faux signal is 51 dB-Hz. An intelligent receiver will notice this discrepancy; if it sees that jamming is present and the measured C/No is higher than expected‚ it will become suspicious and perhaps compute a RD map to see what is happening (more on this later). Complicating the spoofer’s task, it may not have complete knowledge of the target’s antenna gain pattern, orientation‚ and polarization‚ and the propagation channel may not be a simple free space channel. To ensure tracking loop capture, additional power is needed‚ but this makes the attack that much more visible.

643

For receivers with capable search engines, periodic or cued examination of RD maps provides another good strategy for detecting spoofing. Figure 24.28 shows responses when a real signal and a faux signal are present simultaneously at similar power levels. It may not be obvious which signal is the real one‚ but the mere presence of two strong responses is enough to label the signal as questionable for incorporation into the navigation solution. In situations where real and faux signals overlap with similar correlation responses at a particular code phase and frequency, the net result has similarities to multipath. The correlation envelope becomes distorted in shape and, depending on the relative carrier phase, the signals may add constructively or destructively. During the initial walk-off phase, these effects are observable unless the faux signal is much stronger and can be used to detect the presence of spoofing. If the spoofer tries to perform a coordinated walk-off with code phase and carrier phase aligned like a real signal, the relative carrier phase of the real and faux signals will change 360o for each wavelength of the relative pseudorange shift (19 cm at L1). The resultant observable is a rapid fluctuation in the apparent signal power with a frequency equal to [dRwalkoff/dt]/λ Hz. Depending on the relative postcorrelation amplitudes, the apparent phase of the composite signal will show varying levels of deviation synchronous with the amplitude deviations. The spoofer may try to avoid creating these artifacts by setting its frequency equal to that of the real signal and then walking off only the code phase. This in turn yields another observable. Presuming coherent tracking, changes in pseudorange as measured by

Case 15 PRN 6 C/A Search Correlation Responses to TEXBAT3 @300 Seconds

Amplitude (volts)

IQ Vector Data Courtesy of T.E. Humphreys, J.A. Bhatti, D.P. Shepard, and K.D. Wesson, “The Texas Spoofing Test Battery: Toward a Standard for Evaluating GPS Signal Authentication Techniques,” Proc. ION GNSS, Nashville, TN, 2012.

10

Spoof Signal

5

Real Signal

0 1500 1000 500 0 Doppler Offset (Hz)

–500 –1000 –1500

0

1

2

3

4

5

6

7

8

9

10

Time Offset (chips)

Figure 24.28 With sufficient range-Doppler separation between real and faux signals, in the range-Doppler map both signals are plainly visible (but not conveniently labeled)

c24.3d

643

15/12/2020 5:42:36 PM

644

24 Interference: Origins, Effects, and Mitigation

accumulated carrier Doppler will diverge from changes in pseudorange as measured by the accumulated code Doppler. Either way, the intelligent receiver should be on the lookout for these effects. Real GNSS signals arrive at a receiver from diverse directions. When multiple signals arrive with a common direction of arrival‚ the receiver should be suspicious. This is because spoofers typically broadcast all of their signals via a single antenna‚ and so spoofing signals arrive at a target receiver with a common direction of arrival and/or correlated fading [35] and polarization characteristics [36]. Correlated fading is characteristic of ground mobile channels and can be detected without any special antenna capabilities provided the spoofer and the receiver move with respect to each other. Referring to Figure 24.29, the direction of arrival sensing can be accomplished using two or more antennas and measuring the relative phase of the two post-correlation outputs for each desired signal (e.g. PRN 2, PRN 6). Coherent tracking is not required since this is a relative phase measurement, and in fact, the array manifold doesn’t have to be well calibrated for this to work. The objective is not so much to determine the actual direction of arrival but to detect signals with a common direction of arrival. If several signals are seen to have arrived from the same direction, one strategy is to not use any of them, even those seeming to come from some other direction. This strategy might manifest as: don’t use L1 C/A, spoofing is present; but none was detected on civil L1 Glonass, so use it. A somewhat riskier strategy is to discard signals with a common direction of arrival and use those remaining as inputs for developing a navigation solution. It should also be noted that this technique continues to be viable even if antenna elements have

somewhat high mutual coupling that would be unacceptable for an interference-cancelling adaptive array.

24.7

Authenticatable Signals

Encrypting the spreading codes is a powerful anti-spoofing technique since it denies the spoofer ready access to the spreading codes; an adversary can no longer go to the appropriate ICD and look up precisely how to generate a faux signal for, say, PRN 23. Even if the adversary has access to the relevant ICDs, he still needs the cryptographic keys. Aside from stealing the keys, his only method for accessing spreading codes is to listen for them off the air as they are broadcast and then repeat them with appropriate delays and frequency shifts, a daunting but not impossible task referred to as meaconing. Even then, the composite set of faux signals will always be delayed with respect to real signals since meaconing is essentially a bent-pipe repeater‚ while real signals follow a shorter direct path to the receiver. An intelligent receiver will always search from early to late in the code phase and look for anomalies in time bias and time bias rate estimates symptomatic of spoofing and meaconing. It should be emphasized that finding an anomaly does not mean that spoofing is present; it simply means that caution is warranted‚ and further investigation is needed before making a definitive declaration. For systems using encrypted spreading codes in real time, protecting the cryptographic keys is a formidable challenge. Unlike communications systems where different subgroups can use distinct keys, in satellite navigation systems, every single authorized user ultimately has to be able to derive the

Can Detect Spoofing Using Two Antennas Interfering Source at Frequency fc

Excess Delay τ=d sinθ/c θ A sin(2πfc(t – τ) + ψ ) d sin θ ) = A sin(2πfct + ψ – 2πfc c

Relative Phase Delay Is Mesurable Even Without Phase Lock

2πfc

d sin θ c

d

radians

A sin(2πfct + ψ )

[0]radians

Technique described in Hartman USP 5,557,284 issued 17 Sept, 1996

Figure 24.29

c24.3d

644

Signals coming from a spoofer can be detected by looking for signals with a common direction of arrival.

15/12/2020 5:42:37 PM

24.7 Authenticatable Signals

same key used to generate the spreading sequence at the satellite. A compromise of any one user can have systemwide ramifications. For this reason, encrypted real-time spreading codes for SATNAV are likely to remain the purview of military and government entities for the foreseeable future. Civil entities are simply not secure enough to provide the level of symmetric key protection needed. That said, asymmetric cryptography can play an important role in securing civil signals by providing methods to authenticate signals without requiring the user segment to hold secrets. This is an active area of research that is expected to culminate in future satellite and terrestrial deployments for civil use. As a first line of defense, satellite data broadcasts can be cryptographically signed using public key/ private key cryptography [4, 37–40]. In such schemes, an associated key pair is generated comprising a private key and a public key. The private key is used to sign data by creating a cryptographic signature‚ and the corresponding public key is used to verify signatures. The data itself is not encrypted‚ but the appended signature can establish the provenance of the data and that the data has not been altered. The private key is closely held by the signer (the satellite), and the public key is widely disseminated to the user community. To prove the origin of the public key and prevent key spoofing, the public key is signed by a well-known trusted entity and distributed in the form of an X.509 certificate (or equivalent). Certificate publication and distribution is needed only when the key pair changes and might happen only once a year via out-ofchannel means, for example‚ Google Play. Again, there is nothing secret about the public key; it can be widely disseminated. There are numerous signing algorithms available‚ but the Elliptic Curve Digital Signature Algorithm (ECDSA) detailed in FIPS-PUB 186-4 is representative of current best practices for digital signing. Table 24.6 shows the security performance and signature lengths for NIST-recommended elliptic curves. To a close approximation, for a given security level, the length of an ECDSA digital signature is about four times as long. Signature lengths are important since broadcast GNSS data rates are generally quite slow, somewhere in the 25 bps to 250 bps range depending on signal type. Using the L1CData signal as an exemplar, elements of the 50 bps data stream (and the time of interval, TOI) can be cryptographically signed by each satellite using a private signing key unique to that satellite or to the satellite constellation. Again, this does not encrypt the 50 bps data stream; it just appends a digital signature to the data stream to authenticate it. Subframe 3 messages, one of which is transmitted every 18 s, carry up to 232 bits of payload. Two subframe

c24.3d

645

645

Table 24.6 ECDSA security strength and signature size for NIST-recommended elliptic curves

Elliptic curve

Security strength (bits)

(r,s) Signature length (bits)

P-192

96

384

P-224

112

448

P-256

128

512

P-384

192

768

P-521

256

1024

3 messages would be needed to convey one digital signature based on the P-224 elliptic curve [40]. In Transmitted once every 3 min in a pair of subframe 3 messages, digital signing would occupy a 20% duty factor on subframe 3 of the L1C signal’s navigation message stream. For the interested reader, there are more complex signing schemes [38] described in the literature that achieve similar results with fewer bits per second required, most notably approaches based on the TESLA protocol. Such schemes may prevail in practice‚ but their description is beyond the scope of this book. Maintaining adequate protections in a post-quantum environment may also influence the choice of algorithm and key lengths. Continuing, message signing allows security-conscious receivers to verify that the data stream originated from a real satellite, that it is correct, and that it is not fictitious. Message signing forces potential spoofers to use off-theair, collected data streams — a difficult proposition against receivers that read data, have accurate and secure a priori knowledge of time, and check for excess signal delay observable in time bias states. It also prevents malformed 50 bps data message attacks such as described in Nighswander et al. [41]. Cryptographic data signing is an important anti-spoofing step but is inadequate for several reasons: 1) The spreading codes used to measure the signal’s apparent time of arrival (pseudorange) are not cryptographically bound to the signed message stream. A valid, offthe-air data stream can be modulated onto an ICD-specified spreading code stream with spoofer controlled delay and Doppler. There is an inherent delay in doing this‚ but under nominal C/No conditions, the delay can be held to less than 1ms, mainly to allow for accurate demodulation of off-the air data symbols [4, 42]. If the target receiver doesn’t know time to better than 1 ms, it may buy into the faux signals and with a high degree of confidence that they are real since the signature verification process succeeds.

15/12/2020 5:42:37 PM

646

24 Interference: Origins, Effects, and Mitigation

2) Many battery-operated GNSS receivers don’t read low rate data (e.g. 50 bps for L1CD, the L1C data channel). They turn on for only a few milliseconds to measure pseudoranges and pseudorange rates to available satellites, and then they turn off. Access to satellite ephemeris and other 50 bps data is obtained via a network connection, or the receiver sends the measured pseudoranges to a remote site for position computations. Chiplevel binding is needed for these receivers. 3) Data signing does not provide a mechanism for proving location to a remotely located second party (more on this in the next section). Figure 24.30 shows a signal construct to overcome these limitations [4, 40, 43, 44], again using the L1C signal as an exemplar. Here, 90% of the data channel’s timeline is devoted to transmitting normal L1CP (IS-GPS-800E) signal‚ while the remaining 10% of the timeline is repurposed to transmitting an encrypted spread spectrum security code (SSSC) based on the aforementioned data stream signature. Specifically, the digital signature, known only to the satellite until it is transmitted, is also used to construct a watermark-generating key that is used up until the time that the signature is transmitted. In the Chimera signal specification, IS-AGT-100, the watermark-generating key is constructed by hashing the signature. Using the previously described data signing approach, the watermarkgenerating key changes once every 3 min. The watermark insertions are performed at the PN chip level and feature both an encrypted SSSC and a cryptographically controlled time-hopping insertion pattern. This latter feature combats certain power-modulation attacks by making it difficult for a forger to be certain which chips are SSSC versus normal IS-GPS-800 chips. In a further refinement and if the satellite modulator can support it, inserted chips can have cryptographically generated pseudorandom carrier phase relative to the nominal signal [45].

Watermark Generation key

Seed Value

10 msec

Cipher stream Generator

Type 2 Format

From an SNR perspective, the individual watermark chips (SSSC) have the same properties as the normal ISGPS-800 chips‚ and they are not individually visible to a receiver. They are visible only after a period of correlation. Receivers cannot correlate against watermark insertions in real time since they don’t know the watermark-generating key until it is published (broadcast). Receivers can‚ however‚ record raw A/D samples and store them in memory. When the watermark-generating key becomes known, the receiver can correlate against the watermark insertions and check to make sure they correlate to an appropriate power level and that they are correctly aligned in time and phase with the nominal L1C code and carrier phase. As long as the receiver knows the trusted time to within the authentication epoch (3 min in this case), it can be assured that the only way a spoofer could generate an authenticatable signal would be if it had received and manipulated off-the-air signals in a meaconing-style attack. Such an attack, while possible, is very complex to mount. In regard to the watermark correlation process, it should be noted that the reference waveform generated at the receiver uses nonzero values only when the watermark is expected to be present. The watermark reference waveform is equal to zero for intervals where a normal IS-GPS-800 signal is expected. The other unusual aspect is that the correlation response is computed only for the prompt channel aligned with the code and carrier tracking provided by the pilot channel. The receiver is not trying to track the watermark signal; it is simply trying to make sure it is there. Figure 24.31 shows the probability of not detecting watermarks (1-PDetection) assuming a 1000 ms collection interval, a 5% watermark duty factor‚ and perfect phase lock. This correspond to a 1000 ms coherent integration time‚ but because of the 5% duty factor, from an SNR perspective the effective integration time is 1000 ms ∗ 5% duty factor = 50 ms. Also, because phase lock is assumed, its envelope can be computed using only the in-phase channel. Probabilities of detection

Spread spectrum Security code (SSSC) & Time Hopping (TH) Pattern

10 msec

10% Duty Factor Time Hopped SSSC Normal L1CDiSignal flow per IS-GPS-800

Normal L1CDiSignal flow per IS-GPS-800

•••

Figure 24.30 Time-hopping insertion of spread spectrum security codes creates a watermark that is hard to observe without the watermark-generating key.

c24.3d

646

15/12/2020 5:42:37 PM

24.7 Authenticatable Signals

Probaility of NOT Dectecting Watermark (1.00 sec segment, WM DF = 5.0%, pfa = 1.00E-03) 1.E+00

Probability of NOT Detecting valid watermark using sum of N partitions

Probability of a False Positive

1.E-02

Is Better

99%

1.E-03

99.9%

1.E-04

99.99%

1.E-05

99.999% 99.9999% 18

21

24

27

30 33 c/No(dB-Hz)

36

39

42

45

Watermarks can provide an extremely low false positives rate and a high probability of detecting spoofing.

can be computed using the Marcum’s Q function and/or via simulation. It is important to recognize that failure to detect the watermark is tantamount to saying that the signal is not valid‚ and so failure to detect the watermark on a valid signal is essentially a false positive. The false positives rate on spoofing detection schemes needs to be extremely low since this is in many ways like yelling “fire” in a crowded theater; a good idea, but only if there really is a fire. Similarly, the probability of a false alarm is the probability of declaring the watermark present when presented with an invalid signal‚ and so 1-Pfa is actually the probability of detecting spoofing. The takeaway from this is that watermarks offer an extremely reliable method for discriminating between real and faux signals. Incorporating the watermarking features of Figure 24.30 reduces the apparent SNR on the punctured channel by 0.9 dB [Loss (dB) = 20log10 (Normal Flow Duty Factor)], a small penalty. Also note that the satellite must know the digital signature before it is transmitted‚ and so data message updates for signature-covered elements would need to be restricted to the signing interval. From the description so far, the reader may have the impression that location authentication occurs only once every 3 min and that time to first authentication could be as long as 6 min. This would be true if all satellites changed their watermark keys at the same time‚ but one refinement is to have them change keys on a time-staggered basis. Having even one or two authenticated signals places some strong constraints on where the receiver can actually be. Typically, anywhere from 8 to 13 GPS satellites are visible in an unobstructed sky‚ and so the average time to first L1C

647

Nominal C/No

N=1 15

c24.3d

99.9% Probability of Detecting Spoofing

90%

1.E-06

Figure 24.31

Pfa = 10–3

PDwatermark

1.E-01 Lower

647

signal authentication can be held to around 3 min, and the authentication refresh interval (time between authentications) might be 45 s assuming four time staggers. That said, a fast key/slow key watermarking approach such as the one shown in Figure 24.32 might be warranted for fast authentication. Here, fast keys change every 6 s, while the slow keys change once every 3 min as previously described. Fast keys have the advantage of providing speedier location authentication, but the watermarking keys would have to be provided “via network”; possibly by a set of secured key servers. The 50 bps L1CD data channel is inadequate to convey keys that change every 6 s. This is the approach planned for the IS-AGT-100 signal planned for initial broadcast by the NTS-3 satellite in 2022 [46, 47]. In closing this section, it is important to recognize that as of 2019, there are no civil signals in space with any form of authentication either at the message level or at the chip level. This situation appears to be changing though. Both the United States and EU [48] have strong candidates for adding signal authentication to their WAAS & EGNOS SBAS signals‚ and the EU has committed to including authentication on their commercial services signals [49]. For SBAS, chip-level watermarking and data message signatures can both be carried on a new quadrature signal component first proposed in [4] and added to the legacy signal provided the signal is range disciplined. A particular attraction of SBAS signals is that the modulator is located on the ground‚ and the signals are relayed to users through a bent-pipe GEO satellite transponder. No modifications are required to the space component. Having even one authenticatable ranging signal makes RF spoofing much

15/12/2020 5:42:38 PM

648

24 Interference: Origins, Effects, and Mitigation

10 msec

Type 3 Format

10 msec

5%fast key / 5% slow key Duty Factor Time Hopped SSSC Normal L1CDi Signal Flow per IS-GPS-800)

Figure 24.32

Normal L1CDi Signal Flow per IS-GPS-800)

Fast Key (6 s) and Slow Key (3 min) SSSC streams support distinct user communities.

more difficult and, it provides a basis for beginning to do Proof of Location.

24.8 Proof of Location and Receiver Verification Location is a key identity attribute in security-sensitive applications. Security credentials can be lost or stolen. When authenticating a user to receive sensitive information from a server, we should be asking, “Where is the request coming from and is the information requested relevant and permissible at that location?” When a remotely located device, for example‚ a traffic light or an electrical generator, receives an actionable command, “Where did that command come from?” should be a key question; similarly a bank transfer. Crowd-sourced databases and knowledge bases are subject to manipulation and poisoning by adversaries using false georeferences. As a hypothetical, an adversary could create a botnet of smartphones by sending specially crafted MMS text messages to vulnerable phones and using the Stagefright vulnerability (now patched CVE-2015-6602). This would allow the adversary to perform arbitrary operations on victim devices through remote code execution and privilege escalation. Then, the adversary could “place and distribute” those phones on West Manchester Boulevard in Los Angeles to create an apparent traffic jam whose appearance would divert real vehicles, particularly autonomous driving vehicles, from the area. Then he could have a pleasant drive over to Randy’s Donuts and not have to wait in line for his chocolate Long John w/cream. Admittedly, this is a trivial example, but it doesn’t take much imagination to come up with other more nefarious and profitable exploits. Assuring the “truthfulness” of reported PVT is a cybersecurity issue. An attack on location and timing information may not use RF spoofing or jamming methods on the GNSS receiver itself. Even if a GNSS receiver is working correctly, a man-in-the-middle attack may simply inject false positions into the system data stream – in short, lie about position. Receiver attestation and PVT signing can defend

c24.3d

648

•••

against simple variants of this attack, but it is not foolproof; signing keys can be stolen or lost, particularly when dealing with civil equipment with limited physical security capabilities. To fight this, position reports can be verified and validated by looking for hard-to-forge elements of an authenticatable GNSS signal, in short, the watermarks. Proofs of location need to be operable on untrusted receivers and systems – that is, proofs of location should seek to minimize trust in the reporting party or any intervening parties and systems such as cell phone modems, communications links, routers, switching centers, and so on. Trust is dangerous. So, how can location be proven to a remote site? Conceptually, the process might work much like a police detective trying to verify someone’s alibi by asking overlapping questions. Questions might include: “Who were you with? What movie were you at?” Witnesses of varying credibility and observational capability might be interviewed to establish an overall perspective. Ideally, a location proof should use similar methods and be based on multiple sources (multiple witnesses). GNSS position reports, reports about what WiFi access points were seen, video feeds of the area, photographs, audio feeds, and so on can all aid in establishing the veracity of a location report. That said, it is important to recognize that location proofs also need strong time stamping. A location proof without a trusted time stamp is not much of a proof; you could have moved. Figure 24.33 outlines how authenticatable signals described in the last section signal might be used as part of a Proof of Location. A GNSS front-end downconverts the signal to a low intermediate or zero intermediate frequency, an A/D converts the ensemble of all L1C GPS signals in view and forwards them to a location authentication object (LAO), where they are sequestered. The nominal duration of the location-signature burst would be anywhere from about 50 to 200 ms and would be about 125 to 500 kilobytes in size; roughly 1/16th to 1/4th the size of a typical smartphone photograph. Once the watermark-generating key(s) are published, a location authentication object can validate that signal by checking to see that its watermark component is present (see Figure 24.31). Then, using snapshot positioning techniques [50–52], the authenticator can

15/12/2020 5:42:39 PM

24.8 Proof of Location and Receiver Verification

649

Authenticatable GNSS Signals Location Signature Stream Is Sent Before Watermark Keys Are Published TGHU307703022G1

RF Front End & Downconversion

A/D

Communications Interface

Local GPS Receiver (Optional in Some Cases)

“Golden” GNSS Receiver(s)

Secure Server(s)

Location Authentication Object No RFNeeded Can Be All S/W Local, Remote, or Cloud Based

• Ephemeris / Symbol Stream • Watermark Generating Keys • 3 minutes/SV

• Location Signature is 125‐500 Kbyte (Nominal) • Diverse Trust Models Are Possible

Figure 24.33 Process flow for Proof of Location using location signatures. By sending snippets of raw A/D samples to a location authentication object before the watermark key has been published, a remote user can verify the reported location.

establish the position and time at which the raw A/D samples were collected. As an additional signal-level verification, the authenticator can establish that the watermark component has the same C/No as the regular IS-GPS-800 signal. Figure 24.34 shows how accurately a watermark’s C/No can be measured as a function of L1CD signal C/No. Under nominal conditions‚ L1CP C/No is about 44 dB-Hz (corresponding to an incident power of −158.25 dBW, 0 dBiC antenna gain, a 2 dB noise figure, and an antenna noise temperature of 130 K). Processing a 200 ms locationsignature segment yields 20 ms of watermark signal‚ and the watermark C/No can be placed within an accuracy band of ±0.7 dB 99% of the time (red bands). At an L1CP C/No of 30 dB-Hz, the watermark C/No can be determined to an accuracy of ±1 dB about 50% of the time (green bands). This might correspond to a case with 10 dB of attenuation due to environmental factors. Returning to Figure 24.33, it is extremely important to note that the authentication object does not expressly require any RF reception capabilities. The first-party GPS front-end has done the required GPS signal reception. Authentication objects can be constructed entirely as software entities using well-known SDR techniques to process samples. Additionally, the supplicant receiver might also be asked to provide track state side information to aid in processing the location signature and as a further source of validation. Examples might include phase histories for PLLs and DLLs, location and time, inertial states, and so on. Another important aspect to keep in mind is that the LAO does not have to operate in real time. It can run in a general-purpose computing environment, a graphics

c24.3d

649

processing unit, another cell phone, a Raspberry Pi, or on specialized hardware. In short, location authentication objects can physically be anywhere – local, remote, or cloud-based. This opens the way to diverse trust models. For the LAO to determine and authenticate a supplicant receiver’s location, in addition to the location signature (raw A/D samples), it needs the watermark-generating keys and satellite ephemeris data. This data might be made available in several ways: 1) Secured server(s) with attached GPS receivers could collect required information and publish it as the data becomes available. 2) A local receiver might provide the information from offthe-air received satellite signals. This last option is quite interesting as it raises the possibility of independent location verification within a standalone device. Figure 24.35 illustrates how a smartphone’s location might be secured using authenticatable signals. A LAO in the form factor of a microSD (Secure Digital) card slips into the phone. Ideally, the LAO device would be tamper-resistant and have trusted platform module (TPM)-style cryptographic capabilities [53] in addition to timekeeping, bulk encryption/decryption, and a position-computing engine. The GNSS receiver integral to the phone would feed location signatures (raw A/D samples) to the microSD for sequestration. Once authentication keys are published via either satellite or Internet, it could compute the location and sign the results. In effect, the microSD LAO device provides independent verification of the phone’s intrinsic internal position solution. Additionally, location-based security paradigms (e.g. no reading sensitive documents

15/12/2020 5:42:39 PM

650

24 Interference: Origins, Effects, and Mitigation

Watermark C/No Estimation Error (dB wrt Truth)

4.0 50.0% High 50.0% Low 90.0% High 90.0% Low 99.0% High 99.0% Low

200 msec Collection Interval 10% Watermark Duty Factor Coherent Integration

3.0 2.0 1.0 0.0 –1.0 –2.0

Nominal L1CP C/No is 44 dB‐Hz at ICD Minimum Power Levels

–3.0 –4.0 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

L1CP Signal C/No (dB-Hz)

Figure 24.34

Watermark C/No estimation accuracy using 200 ms data record at 10% SSSC duty factor.

Small Sequestration Delay

«

+

Local Location Authentication Object Tamper Resistance TPM Capability Time Keeping & Time Stamping Computing Engine

+

: Even Better

Remote Location Authentication Object

Figure 24.35

Civil devices can use watermarks in diverse ways to improve location assurances.

at Starbuck’s) could be enforced by the microSD device‚ and so this device could play an important role in developing secure cell phones and devices usable in a wide variety of government, military‚ and civil applications. Expanding on the concept, occasionally, location signatures could be sent from the phone to external authentication objects at remote locations for additional independent verification. This might be required only when accessing particularly sensitive data, or it might be done to check the local microSD device (“Quis custodiet ipsos custodes?”). Following the police detective model, other data such as inertial measurement unit and compass outputs, cell tower IDs, WiFi BSSIDs, AGC settings, or signals from other GNSS systems, might also be sent to LAOs

c24.3d

650

as additional location-signature elements for further corroboration.

24.8.1 Other SATNAV Proof of Location Schemes Other techniques for proving location have been proposed – such as those in papers by Denning and MacDoran [54], Psiaki et alia [55], Lo et alia [56], Zhefeng Li et alia [57], Heng et alia [58], and Scott [59]. Basically, these approaches use military signals as a watermark of opportunity. This is a good idea; the watermarking schemes described in the last section face several programmatic and national policy hurdles if they are to be implemented. The schemes developed

15/12/2020 5:42:40 PM

References

by these authors face no such obstacle, but there are some significant drawbacks. First, there is a presumption that military codes are secure. This is hopefully true from a sovereign perspective, but it is important to recognize that these schemes place trust not only in the control segment and the space segment, but also in the hundreds of thousands of keyed military user equipment fielded around the world. An adversary may not choose to advertise the fact of a successful compromise. SNR is another issue. Civil uses are unlikely to have access to military-code-generating keys. To minimize squaring loss and thus reduce signature sizes, authenticators need access to high-gain, multiple-beam antenna systems to provide more accurate military code sequence references. This may be a shared resource between several authenticators or unique to a particular one. A supplicant and an authenticator must have shared satellite visibility for several satellites. The approach described in the last section does not suffer from such limitations since watermark-generating keys are implicitly available to the user community (with a delay). Another important issue is that military signals have different bandwidths and often are spectrally segregated from civil signals. Consequently, specialized receiver front-end designs and higher sampling rates may be needed by both the supplicant and the authenticator to access military signals for use as a watermark. Referring back to Figure 24.22, a 2-MHz-wide front-end passes most of the C/A code signal energy and causes less than 1 dB of SNR loss for C/A code signal reception. The same filtering leads to a 7 dB loss for the BPSK(10) format Y-code. This means that associated location signatures would need to be 7 dB (5 times) longer to achieve the same confidence level. Another significant limitation is that military code as watermark schemes can’t easily operate in a stand-alone device configuration as was depicted in Figure 24.35. The alternative approaches all require strong network connectivity to convey location signatures to a remote third party authenticator. There are numerous strong use cases for stand-alone, limited connection bandwidth applications. For instance, in Figure 24.35, the cell phone might use a FIPS-140 physical security hardened microSD device to act as a location authenticator and signer for most security transactions. Raw signatures could be sent at very modest rates to authenticate the authenticator. Again, it needs to be emphasized that military signal as watermark schemes are workable in many applications and would prove invaluable. But, considering the above limitations and weaknesses, they should be regarded as less than optimal and a temporary stopgap solution.

c24.3d

651

24.9

651

Closing Remarks

The topic of interference effects and mitigations encompasses diverse elements including RF signal processing, propagation modeling, cybersecurity, cryptography, national policies, and law [60]. GNSS is becoming ever more deeply embedded in national infrastructures and social fabric‚ and so we can expect attacks and need to defend against them. Toward this end, here are some actionable recommendations, some at a manufacturer level, others at a policy level: 1) Recognize that PNT (GNSS) is CI and harmonize location assurance efforts across constituencies. 2) Build and integrate validated augmentation systems (e.g. eLoran), and integrate them into a national PNT architecture 3) Civil receivers need to develop situational awareness. Exposure testing is crucial. Establish voluntary, pragmatic receiver certification, attestation‚ and threat information sharing programs. Provide a basis for purchase decisions in critical applications. 4) Negotiate an end to unfettered jammer manufacture and proliferation. Jamming affects everyone and has no legitimate role in civil society. 5) Create authenticatable clock and ephemeris data and differential corrections data with PKI data signing. Consider both in-band and out-of-band distribution models 6) Provision for physical layer anti-spoofing and Proof of Location using chip-level watermarking techniques. 7) Support secure and traceable time distribution (IEEE P1588/eLoran/WWVB). 8) Explore methods for interference reporting and locating using point defenses as well as crowd-sourced methods. 9) Protect spectrum for both US and foreign GNSSs. There are tremendous benefits in having access to multiple GNSS systems.

References 1 J. Carrol and K. Montgomery, “Global Positioning System

Timing Criticality Assessment—Preliminary Performance Results,” in 40th Annual Precise Time and Time Interval (PTTI) Meeting, 2008. 2 A. Grant, P. Williams, N. Ward, and S. Basker, “GPS jamming and the impact on maritime navigation,” The Journal of Navigation The Royal Institute of Navigation, vol. 62, pp. 173–187, 2009. 3 I. Leveson, “The Economic Value of GPS: Preliminary Assessment,” in National Space-Based Positioning,

15/12/2020 5:42:41 PM

652

24 Interference: Origins, Effects, and Mitigation

4

5 6

7

8 9

10

11

12

13 14

15 16

17 18

19

20

c24.3d

652

Navigation and Timing Advisory Board Meeting, June 11, 2015, 2015. L. Scott, “Anti-Spoofing & Authenticated Signal Architectures for Civil Navigation Systems,” in ION GPS/ GNSS 2003, 2003. L. Scott, “Expert Advise: Location Assurance,” GPS World, July 2007. T. Humphreys, B. Ledvina, M. Psiaki, B. O’Hanlon, and P. Kitner, “Assessing the Spoofing Threat: Development of a Portable GPS Civilian Spoofer,” in ION GNSS 2008, Savannah, GA, 2008. C.D. Hacker, "GPS Spoofing w/BladeRF - Software Defined Radio Series #23," [Online]. Available: https://www. youtube.com/watch?v=VAmbWwAPZZo. [Accessed 26 December 2017]. L. Huang and Y. Qing, “GPS Spoofing,” in Defcon-23, Las Vegas, NV, 2015. J. Betz, “Effect of Narrowband Interference on GPS Code Tracking Accuracy,” in ION NTM 2000, Anaheim, CA, 2000. M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, Spread Spectrum Communications, Computer Science Press, 1985. A. Van Dierendonck and B. Elrod, “Pseudolites,” in Global Positioning System: Theory and Applications, AIAA, 1996, pp. 51–79. J. Betz, “Bandlimiting, Sampling, and Quantization for Modernized Spreading Modulations in White Noise,” in ION NTM 2008, San Diego, CA, 2008. T.L. Lim, “Digital Matched Filters: Multibit Quantization (PhD Thesis),” University of California, Berkeley, 1976. W. Lee, “Path Loss Over Flat Terrain,” in Mobile Communications Engineering, McGraw-Hill, 1982, pp. 87–114. J. Parsons, The Mobile Radio Propagation Channel, 2nd Ed., Wiley, 2000. M. Hata, “Empirical Formula for Propagation Loss in Land Mobile Radio Services,” IEEE Transactions on Vehicular Technology, Vols. VT-29, no. August, pp. 317–325, 1980. F. v. Diggelen, “Who’s Your Daddy?: Why GPS Rules GNSS,” in Stanford PNT, 14 Nov 2013, Palo Alto, CA, 2013. R. Mitch, D. Ryan, M. Psiaki, S. Powell, J. Bhatti, and T. Humphreys, “Signal Characteristics of Civil GPS Jammers,” in ION GNSS 2011, Portland, 2011. J. Young and J. Lehnert, “Sensitivity Loss of Real-Time DFT-Based Frequency Excision with Direct Sequence Spread-Spectrum Communication,” in Proceedings of the 1994 Tactical Communications Conference, 1994. Vol. 1. Digital Technology for the Tactical Communicator, 1994. F. Amoroso and J. Bricker, “Performance of the adaptive A/D converter in combined CW and Gaussian

21 22

23

24

25 26

27

28

29

30 31 32

33 34 35

36

37

interference,” IEEE Transactions on Communications, vol. 34, no. March, pp. 209–213, 1986. FCC, “FCC Enforcement Advisory No. 2012-02,” 2012. A. Van Dierendonck, P. Fenton, and T. Ford, “Theory and performance of narrow correlator spacing in a GPS receiver,” Navigation: Journal of the Institute of Navigation, vol. 39, no. Fall, 1992. L. Garin, F. van Diggelen, and J. Rousseau, “Strobe and Edge Correlator Multipath Rejection for Code,” in ION GPS 1996, Kansas City, MO, 1996. FCC, “$32K Penalty Proposed for Use of a GPS Jammer by an Individual,” 2 August 2013. [Online]. Available: https:// www.fcc.gov/document/32k-penalty-proposed-use-gpsjammer-individual. [Accessed 23 Sept. 2016]. D.A. Divis, “Homeland Security Researching GPS Disruptions, Solutions,” Inside GNSS, June 2014. L. Scott, “J911: The Case for Fast Jammer Detection and Location Using Crowdsourcing Approaches,” in ION GNSS2011, Portland, 2011. D. Akos, “Who’s afraid of the spoofer? GPS/GNSS spoofing detection via automatic gain control (AGC),” Navigation: Journal of the Institute of Navigation, vol. 59, no. Winter, 2012. L. Scott, “Making the GNSS Environment Hostile to Jammers & Spoofers,” in ION GNSS2011, Portland, OR, 2011. J. Bittel, “Superyacht Owner Lets College Kids Hack and Hijack $80 Million Ship in Name of Science,” Slate, 1 August 2013. E. Groll, “Russia Is Tricking GPS to Protect Putin,” Foreign Policy, 19 April 2019. T. Humphreys, “Above Us Only Stars,” C4ADS, 2019. M. Psiaki, B. O’Hanlon, S. Powell, J. Bhatti, K. Wesson, T. Humphreys, and A. Schofield, “GNSS Spoofing Detection using Two-Antenna Differential Carrier Phase,” in ION GNSS+2014, Tampa, FL, 2014. R. Hartman, “Spoofing Detection System for a Satellite Positioning System,” Patent 5,557,284, 17 September 1996. L. Scott, “The Portland Spoofing Incident,” in PNT Advisory Board, Redondo Beach, 2017. A. Broumandan, A. Jafarnia-Jahromi, V. Dehghanian, J. Neilsen, and G. Lachapelle, “GNSS Spoofing Detection in Handheld Receivers based on Signal Spatial Correlation,” in Position Location and Navigation Symposium (PLANS), 2012 IEEE/ION, Myrtle Beach,SC, 2012. E. McMilin, D. De Lorenzo, T. Walter, T. Lee, and P. Enge, “Single Antenna GPS Spoof Detection that is Simple, Static, Instantaneous and Backwards Compatible for Aerial Applications,” in ION GNSS+2014, Tampa, FL, 2014. A. Kerns, K. Wesson, and T. Humphreys, “A Blueprint for Civil GPS navigation Message Authentication,” in ION/ IEEE PLANS, Monterey, CA, 2014.

15/12/2020 5:42:41 PM

References

38 G. Caparra, S. Sturaro, N. Laurenti, and C. Wullems, “A

39

40 41

42

43

44

45

46

47

48

c24.3d

653

Novel Navigation Message Authentication Scheme for GNSS Open Service,” in ION GNSS+2016, Portland, OR, 2016. P. Walker, V. Rijmen, I. Fernández-Hernández, L. Bogaardt, G. Seco-Granados, J. Simón, D. Calle, and O. Pozzobon, “Galileo Open Service Authentication: A Complete Service Design and Provision Analysis,” in ION GNSS+2015, Tampa, FL, 2015. AFRL, “IS-AGT-100, CHIMERA Signal Specification,” 2019. T. Nighswander, B. Ledvina, J. Diamond, R. Brumley, and D. Brumley, “GPS Software Attacks,” in CCS’12, Raleigh, NC, 2012. M. L. Psiaki and T. E. Humphreys, “GNSS Spoofing and Detection,” IEEE Proceedings, vol. 104, no. June, pp. 1258–1270, 2016. L. Scott, “Proving Location Using GPS Location Signatures: Why it is Needed and a Way to Do It,” in ION GNSS+2013, Nashville, TN, 2013. J. Anderson, K. Carroll, J. Hinks, N. DeVilbiss, J. Gillis, B. O’Hanlon, J. Rushanan, R. Yazdi, and L. Scott, “Signal-in-Space Methods for Authentication of Satellite Navigation Signals,” in ION GNSS+2017, Portland OR, 2017. L. Scott, “Location Signatures: Proving Location to Second Parties without Requiring Trust,” in Joint Navigation Conference, Colorado Springs, CO, 2012. L. Scott, “The Role of Civil Signal Authentication in Trustable Systems,” in PNT Advisory Board, Alexandria, VA, 2019. D. A. Divis, “New Chimera Signal Enhancement Could Spoof-Proof GPS Receivers,” InsideGNSS, May/June 2019. A. Dalla-Chiara, I. Fernandez-Hernandez, E. Chatre, V. Rijmen, G. D. Broi, O. Pozzobon, J. C. Ramon, J. Fidalgo, N. Laurenti, G. Caparra, and S. Sturaro, “Authentication Concepts for Satellite-Based Augmentation Systems,” in ION GNSS+2016, Portland, OR, 2016.

653

49 D. Calle, S. Cancela, E. Carbonell, I. Rodríguez, G. Tobías,

50

51

52 53

54

55

56

57

58

59

60

I. Fernández, J. Simón, and G. Seco-Granados, “First Experimentation Results with the Full Galileo CS Demonstrator,” in ION GNSS+2016, Portland, OR, 2016. B. Peterson, R. Hartnett, and G. Ottman, “GPS Receiver Structures for the Urban Canyon,” in ION GPS-95, Palm Springs, CA, 1995. S. Lannelongue and P. Pablos, “Fast Acquisition Techniques For GPS Receivers,” in ION AM, Denver, CO, 1998. F. van Diggelen, A-GPS: Assisted GPS, GNSS, and SBAS, Artech House, 2009. Trusted Computing Group, “Trusted Platform Module (TPM),” [Online]. Available: http://www. trustedcomputinggroup.org/work-groups/trustedplatform-module/. [Accessed 24 Sept 2016]. D. Denning and P. MacDoran, “Location-Based Authentication: Grounding Cyberspace for Better Security,” in Computer Fraud & Security, Elsevier Science Ltd., 1996. M. Psiaki, B.W. O´Hanlon, J.A. Bhatti, and T. E. Humphreys, “Civilian GPS Spoofing Detection based on Dual-Receiver Correlation of Military Signals,” in ION GNSS2011, Portland, OR, 2011. S. Lo, D.D. Lorenzo, P. Enge, D. Akos, and P. Bradley, “Signal Authentication, A Secure Civil GNSS for Today,” Inside GNSS, Sept/ Oct. 2009. Z. Li and D. Gebre-Egziabhery, “Performance Analysis of a Civilian GPS Position Authentication System,” Navigation: The Journal of the ION, vol. 60, no. 4, 2013. L. Heng, D. Work, and G. Gao, “GPS Signal Authentication from Cooperative Peers,” IEEE Intelligent Transport Systems, vol. 16, no. 4, pp. 1794–1805, 2015. L. Scott, “Multilevel Authentication Approaches for Location Assurance,” in Joint Navigation Conference, Orlando, FL, 2015. L. Scott, “Towards a Sound National Policy for Civil Location and Time Assurance; Putting the Pieces Together,” Inside GNSS, Sept/ Oct 2012.

15/12/2020 5:42:41 PM

655

25 Civilian GNSS Spoofing, Detection, and Recovery Mark Psiaki1 and Todd Humphreys2 1 2

Virginia Tech, United States University of Texas at Austin, United States

25.1

Introduction

25.1.1 The Growing Concern Regarding GNSS Spoofing GNSS spoofing is the deliberate transmission of false GNSS signals or data with the intent of confusing or misleading a GNSS user. Typical military GNSS receivers are very hard to spoof due to their use of symmetric private-key encryption to define their spreading codes. Civilian receivers use publicly known, predictable spreading codes, which makes them much more vulnerable to spoofing attack. Attacks against civilian receivers have been demonstrated in tests going back to 2003 [1–4]. Attacks “in the wild” have been alleged starting in 2011 [5], though it remains debatable whether the incident in question involved GPS spoofing. There is convincing evidence of at least one such attack. It occurred in the Black Sea in June 2017, and it affected the navigation of a number of ships [6–8]. Cooperative spoofing, in which the spoofer owns or controls the victim receiver, is also on the rise [9–11]. The “victim,” e.g., a ship’s captain or Pokémon Go player, gains the ability to fish in forbidden waters or hunt Pokémon from the comfort of a couch. In the case of smartphone cooperative spoofing, a downloadable application [9] poses as the GPS receiver on a smartphone in order to fool the game application into believing that the player and phone are in some exotic location.

25.1.2

History of Spoofing Concerns

Spoofing has long been recognized as a threat to civilian GNSS receivers [12]. Early defenses focused on pseudorange-based receiver autonomous integrity monitoring (RAIM). These defenses assumed that a spoofing attack

would consist of one or more false signals that produced pseudoranges which were inconsistent with other measured pseudoranges. Given five or more measured pseudoranges, the post-fit residuals could be computed as part of the navigation solution and an alert generated whenever a chi-squared consistency test statistic based on the residuals was too large. In 2001, the Volpe Report alerted the GNSS community to the possibility that a sophisticated spoofer might generate a set of self-consistent pseudoranges that could deceive a receiver without generating a pseudorange-based RAIM alert [13]. Further alarms were raised in 2003 [1, 14] and 2007 [15]. Nevertheless, these warnings were largely ignored by civil receiver manufacturers and were unknown to the general public until a working receiver-spoofer device was developed, tested, and announced in 2008 [2, 16]. In addition to producing self-consistent pseudoranges, this class of spoofer could drag its victim off to a false position fix in a seamless, gentle manner that would avoid raising any alerts about the operation of the victim’s GNSS receiver. It accomplished this task by receiving the same GNSS signals as the victim and by using knowledge of its geometry relative to the victim in order to lay down the initial false signals on top of the true signals. It seems likely that military researchers were aware of the possibility of this type of spoofer. They may have developed a similar device, but no such work has been publicly acknowledged. The advent of this new class of receiver-spoofer generated a great deal of interest and concern within the GNSS community. It spawned a growing body of research into spoofing and detection. This chapter’s goal is to report on the state of this body of research. Related reporting can be found in the GNSS spoofing and detection survey papers [17–19].

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

656

25 Civilian GNSS Spoofing, Detection, and Recovery

25.1.3

Current Status

Two important developments in spoofing and detection have countervailing impacts. One is the lowering of barriers to the development of spoofers. A GPS signal simulator that is software defined was posted to the GitHub code sharing site in June 2015 [20]. Such software can be run on a commercial-off-the-shelf (COTS) GPS simulation hardware platform that costs less than $1000 [21]. Universal Software Radio Peripherals (USRPs) [22] can also be used to run the GitHub GPS signal simulator, albeit at a somewhat higher price tag. These software and hardware technologies can be combined to synthesize GNSS spoofing attacks. They will enable many actors, perhaps even bright high-school students, to mount attacks. In fact, the authors know of multiple cases where individuals with no technical background in GNSS or even in RF successfully built and tested simulator- or record-and-playback-based spoofers. The countervailing development is the introduction of the first commercial receiver that has a new defense against spoofing attacks which goes beyond the monitoring of pseudorange consistency [23]. It is a rudimentary form of defense that works only if the signals are initially authentic. It detects changes that are characteristic of a spoofing attack. If the receiver starts with spoofed signals or if the detection methods somehow fail during the change from authentic to spoofed signals, then this COTS spoofing detector will fail. Despite its limitations, it is a hopeful sign for the future that a receiver manufacturer saw fit to make spoofing detection capabilities commercially available. It is hoped that more manufacturers will follow suit and will implement increasingly sophisticated defenses.

25.1.4

The Dangers of Spoofing

There are many reasons why a spoofer might mount an attack and why GNSS users would want spoofing defenses. Two tests demonstrated the possibility of steering a vehicle off-course via GNSS spoofing. A helicopter drone was nearly forced to the ground when it was programmed to hover at White Sands Missile Range in June 2012 [3]. A superyacht was steered gently off-course in the Mediterranean in July 2013 [4] without the bridge crew being able to detect the fault. Such tactics could be used to cause an airplane to crash or a ship to run aground. Another form of attack would spoof a target receiver in such a way that only its reported time, not position, would be erroneous. GNSS receivers are used as time standards for cell phone towers, power grid monitors, and financial

transactions. Spoofing attacks that induced timing errors in such devices could be used to disrupt communications, trigger power outages, or confuse automated financial trading. Some driverless automobiles depend on GNSS signals as part of their position/velocity/attitude estimation systems. GNSS spoofing might confuse such a system and cause the car to take a wrong exit, act erratically, or stop. Other cooperative “victims” besides Pokémon Go cheaters may try to mount attacks on their own receivers. Fishing boat captains might be tempted to do this in order to evade GNSS monitoring of whether they have entered restricted waters. Accused criminals under house arrest might try to spoof the GNSS-equipped ankle bracelets that monitor their whereabouts. Gig-economy drivers are employing spoofing technology to cut in line at virtual airport queues [24]. The victims in such scenarios are the agencies or companies that rely on GNSS technologies. No end user of GNSS services wants to be the victim of a malicious spoofing attack. Users can hope that few, if any, attacks will ever be mounted. Given the trends, however, prudence suggests a need to develop and field economical defenses that will reliably defeat the most likely attacks.

25.1.5

Goals and Organization of Chapter

The authors have been developing civilian GNSS spoofers and defensive countermeasures since early 2008. This chapter reviews the fundamental approaches that can be used for GNSS spoofing and spoofing detection. It discusses progress in these areas and defines the state of the art at the time of writing. The remainder of this chapter is divided into five sections. Section 25.2 describes various types of spoofing attacks and the technology used to mount them. Section 25.3 covers spoofing detection systems. Section 25.4 discusses methods for recovering authentic position, navigation, and timing (PNT) information after an attack has been detected. Section 25.5 reviews the methods of testing defenses against spoofing.

25.2

GNSS Spoofing Attack Methods

25.2.1

Definition of an Attack

A GNSS spoofing attack is any manipulation of GNSS signals or a GNSS receiver that induces the receiver to report an incorrect position, velocity, or time, or to base these

25.2 GNSS Spoofing Attack Methods

outputs on signals that do not originate from the authentic GNSS satellites. The first part of this definition is straightforward. The second part is needed in order to include the attack mode of [2] in which the spoofer gently drags the victim receiver off of its true PNT fix in a continuous manner that is difficult to detect. More will be said about this mode in Section 25.2.5.

25.2.2 Software-Only Attacks on Smartphone GNSS Software-only spoofing represents a kind of attack that was not foreseen in the Volpe Report. This type of spoofer is shown schematically in Figure 25.1. This spoofer does not transmit false RF signals. It does not spoof the smartphone’s GNSS receiver at all. Rather, it is an extra application within the smartphone that poses as the smartphone’s GNSS receiver. It sends position fixes to the GNSS-dependent application in a way that makes the victim application believe that these positions originate from the smartphone’s built-in GNSS receiver. This type of spoofer is applicable only to systems where the possibility exists for interposing the spoofer software between the true GNSS receiver and the software module that needs GNSS position, velocity, or timing fixes as inputs. Smartphone applications are obvious examples. They are the only known victims to date [9, 10]. Other systems with this vulnerability may exist. A software-only spoofer is economical. Unlike all other spoofers, it requires no extra spoofing hardware. It does not violate any FCC or international telecommunications regulations because it does not broadcast any RF signals. It is inexpensive and legal, at least for the time being.

25.2.3

RF-Based Attacks

A conventional spoofing attack is carried out via broadcast of false GNSS RF signals, as depicted in Figure 25.2. The spoofer generates signals that appear to the victim receiver to be authentic GNSS signals. They have the correct nominal carrier frequency, the correct civilian spreading codes, and believable navigation data messages. The spoofer transmission antenna must be located in a region of the victim receiver antenna’s gain pattern that has sufficient gain to enable the victim to receive and process the false signals. The victim antenna may also receive the true GNSS RF signals. Therefore, the spoofer must apply sufficient power to induce the victim to lock onto and track the false signals. There are various ways to accomplish this‚ and various corresponding needed power advantages of the spoofer. Assuming an attack at a single frequency, the composite signal that is received by the victim takes the form N

y t = Re

A i Di t − τ i t C i t − τ i t e

j ωc t − ϕi t

i=1 Ns

Asl Dsl t − τsl t C sl t − τsl t e

+

j ωc t − ϕsl t

l=1

25 1 where N is the number of true signals‚ and Ns is the number of spoofed signals. The carrier amplitude of the i-th true signal is Ai, and that of the l-th spoofed signal is Asl. The respective data bit streams for the i-th true and l-th spoofed signals are Di(t) and Dsl(t). The corresponding true and spoofed spreading codes are Ci(t) and Csl(t). The i-th true signal’s code phase and beat carrier-phase time histories are, respectively, τi(t) and ϕi(t). Those of the l-th spoofed GNSS constellation

Built-in GNSS antenna True RF signals

Smartphone GNSSdependent App

GNSS receiver

Sreen joystick to input false position

Disrupted GNSS output link

App that poses as GNSS receiver

Figure 25.1 Spoofing of a GNSS-dependent application in a smartphone using another application that masquerades as the phone’s GNSS receiver.

GNSS spoofer False spoofer RF signals Victim GNSS receiver

Figure 25.2 Spoofing attack via RF transmission of false GNSS signals.

657

658

25 Civilian GNSS Spoofing, Detection, and Recovery

signal are τsl(t) and ϕsl(t). The nominal carrier frequency is ωc. It is common to the true and spoofed signals. The carrier Doppler shift of the i-th true signal is − ϕi, and the carrier Doppler shift of the l-th spoofed signal is − ϕsl . Often the number of spoofed signals equals or exceeds the number of true signals: Ns ≥ N, and all of the existing true signals have spoofed counterparts. Thus, one can often assume that the corresponding spoofed spreading codes are Csi(t) = Ci(t) for all i = 1, …, N. In order for the spoofer to overpower the true signals, it is necessary that Asi > Ai for all i = 1, …, N so that the victim will lock onto and track the false signals. Additional strategies may be required to induce the victim to follow the false signals. Such strategies vary by spoofing technique. They are discussed below in the context of each specific technique. The spoofer may transmit navigation bits identical to those of the true signal: Dsi(t) = Di(t) for all i = 1, …, N. In this case, its means of inducing a false position or timing fix lies in its choice of the false code phases τsi(t) and beat carrier phases ϕsi(t) for i = 1, …, N. Another potential strategy is to spoof only the navigation data bits so that the only differences between the spoofed signals and the true signals, besides the increased power levels, are the different Dsi(t) time histories. The spoofer can adjust parts of the satellite data message in order to induce a false PNT fix in the victim receiver.

25.2.4

Blind GNSS-Signal-Simulator-Based Attack

One of the simplest spoofing attacks transmits signals from a GNSS RF signal simulator with little or no consideration of the authentic GNSS signals. One could use an expensive research-grade simulator, for example,[25], or one could use publicly-accessible software [20] and a relatively inexpensive hardware platform [21]. The attacker pre-programs a GNSS satellite/signal scenario, hooks the simulator output to an RF amplifier and antenna, points the antenna at the victim receiver’s antenna, and turns on the system. Such an attack typically starts with a short jamming interval, which causes the victim receiver to lose lock on all of the authentic signals. The spoofer is engaged after the jamming prelude. The victim receiver will start to reacquire GNSS signals. If there is a stronger spoofed signal for each authentic signal, then the victim receiver will typically acquire only spoofed signals. Jam-then-spoof might be deemed a “clumsy” attack mode because the initial jamming could alert the victim receiver. If the spoofer transmits particularly strong signals, then the spoofer signals themselves may serve to jam the true signals and induce the receiver to re-acquire the spoofed signals. The initial attack still seems like jamming to the victim, which affords it a possible mode of detection. The subsequent very

high power of the tracked inauthentic signals could give the victim a second method of generating an alert. After the onset of the attack, the victim receiver will obtain its PNT fixes from the spoofer signals that it has acquired and tracked. These fixes will be those that have been pre-programmed into the spoofer. They can induce an arbitrary erroneous position. The victim might have thought it was in the Black Sea at the onset of the jamming attack. After the jamming is over and after the victim has re-acquired GNSS signals, it might find itself in Chicago or even in low-Earth orbit. It behooves the spoofer not to generate outlandish fixes if it wants to maintain its deception of the victim. The authors speculate that the June 2017 Black Sea spoofing incident described in [6–8] may have been an attack by a spoofer in this blind signal-simulator class. Reference [7] indicates that 20 ships were spoofed to show the same coordinates. Thus, the spoofer was acting over a wide area with the same signal in order to affect many ships in an identical manner. Information that was reported by a ship’s master is contained in [7]. He provided pictures of his charts to confirm his statement that many ships were showing an identical location. He also indicated that his GPS receiver experienced one or more temporary outages. These outages might indicate an initial jamming event or an extremely high power of the spoofer relative to the true signals, which would seem like a jamming attack at first. In any event, this attack was not a stealthy attack of the kind that is described in the next subsection.

25.2.5

Receiver-Spoofer Attack

A receiver-spoofer can mount attacks that are more sophisticated than those from a simple simulator-based spoofer. GNSS constellation

True RF signals

→

∆rtr GNSS receiver/ spoofer

Figure 25.3

→

∆rvs

False spoofer RF signals for all visible satellites

Receiver-spoofer attack mode.

Victim GNSS receiver

25.2 GNSS Spoofing Attack Methods

This type of spoofer is depicted in Figure 25.3. It still uses a signal simulator, but it also uses its own GNSS receiver. It is able to acquire and track all visible GNSS signals, and it uses those signals to determine its own position vector r rs and its own receiver clock offset δrs. It knows the relative position vector from its own receiver antenna to that of the victim, Δ r vs . Some sort of survey or sensing system is needed in order to determine this vector. Similarly, it knows the position vector from its own receiver antenna relative to its own transmitter antenna, Δ r tr . The receiver-spoofer uses this information in order to reconstruct the range-induced part of each satellite’s code phase as it appears at the victim receiver. This takes the form Δτi = τrsi − δrs +

ρiv − ρirs c

25 2

This delay component does not include the effect of the victim receiver’s clock offset. The new quantities used in this equation are the code phase for the i-th GNSS satellite as received by the receiver-spoofer, τrsi, and the ranges from the victim receiver to the i-th satellite and from the receiverspoofer to this same satellite, respectively‚ ρiv and ρirs . The receiver-spoofer uses its knowledge of the true signals and of the spoofer-victim relative geometry to synthesize spoofed spreading codes and spoofed data bit streams that have a well-defined relationship to the true spreading codes and data bit streams at the victim receiver antenna. Suppose that the spoofer wants to induce a code phase offset of δτsi of the spoofed spreading code relative to the authentic code at the victim receiver so that the spoofed code for the i-th satellite is Ci[t − τi(t) − δτsi]. This offset can be positive or negative. Then the receiver-spoofer must synthesize the following spreading code internally: Ci[t − τrsi(t) − δτrsi]. The quantity δτrsi is an internal code-phase offset that the receiver-spoofer uses to perturb its spoofed version of the spreading code from the code replica Ci[t − τrsi(t)] that it synthesizes as part of its standard receiver baseband de-spreading operations. The needed internal offset in the receiver-spoofer is related to the target offset at the victim receiver through a function frsi that combines various delay inputs to produce the needed offset: δτrsi = f rsi δτsi , Δτi , τrsi , δrs , Δ r vs − Δ r tr

A stealthy attack scenario begins with each code-delay offset set to 0 at the victim so that the spoofed signals lie exactly on top of the true signals. That is, δτsi = 0 for all i = 1, …, N initially. Each of the spoofed amplitudes starts at zero: Asi = 0 for all i = 1, …, N. The Asi values are all ramped up to be slightly larger than their corresponding authentic values Ai while the corresponding δτsi offsets are held constant at 0. After all of the Asi values are sufficiently larger than the corresponding authentic signal values, the code-phase offsets δτsi for i = 1, …, N are slowly drawn away from zero in order to capture the receiver’s code-phase tracking delay-lock loops (DLLs). The spoofed carrier phase is synthesized in a way that drifts in concert with the spoofed code phase so that the spoofed carrier Doppler shift equals the non-dimensional spoofed codephase Doppler shift multiplied by the nominal carrier frequency. Some attack strategies lock the spoofed carrier phase to the authentic carrier phase (to within a constant offset) during the initial drag-off. This approach prevents a timevarying interference between the code correlation functions of the true and spoofed signals as drag-off is effected. Drag-off must be done very slowly in this so-called “frequency-locked” spoofing attack, but it has the advantage of avoiding telltale thrashing in the carrier-to-noise ratio. This frequency lock feature is turned off after the spoofed code phase has been dragged far enough from the true code phase to eliminate interference between the two codes’ correlation functions. The receiver-spoofer attack scenario for a single channel is depicted in Figure 25.4. The black dash-dotted curve in this figure is the spoofed signal. The blue solid curve is the sum of the authentic signal and the spoofed signal. The horizontal axis is the code-phase offset axis of a typical code correlation

c, δline 25 3

The one new term in this equation is δline. It is the total delay in the receiver-spoofer from the time that a given part of a spreading code arrives at its receiving antenna to the time that a synthesized version would exit its transmitting antenna if δτrsi were zero.

Figure 25.4 Evolution of a spoofed signal’s amplitude and codephase offset during the initial stages of a receiver-spoofer attack. Spoofed signal: black dash-dotted curve; sum of spoofed and authentic signals: blue solid curve; receiver tracking points: red dots [19, 26]. Source: Reproduced with permission of IEEE.

659

660

25 Civilian GNSS Spoofing, Detection, and Recovery

function. The three red dots are the early, prompt, and late accumulation points of the victim receiver’s DLL. The figure’s five plots show successive snapshots of the initial part of the attack. The top three plots show the interval when δτsi = 0 while Asi is ramped up from 0 in the top plot to slightly more than Ai in the middle plot. The lower two plots show the initial drag-off of δτsi from 0 as the spoofer captures the DLL. In the fourth trace, δτsi equals about one full code chip, and the authentic and spoofed spreading code autocorrelation functions interfere with each other. In the fifth trace, δτsi equals about three chips, the spoofed and authentic peaks are distinct, and the three receiver DLL tracking points are centered on the spoofed peak. The three-chip δτsi code-phase difference between these two peaks equals the amount by which the spoofer is deceiving the victim about its measured pseudorange. Figure 25.4 depicts an attack in which the spoofed and authentic carrier phases are equal‚ or nearly so. In typical cases, close carrier-phase alignment will not occur. Even if carrier-phase alignment does occur initially, it cannot be maintained during drag-off if the spoofer’s carrier-phase rate is held proportional to its code-phase rate. In these more typical cases, the curves shown in Figure 25.4 would be three-dimensional (i.e. having in-phase and quadrature components of their correlation peaks), and the corresponding plots would be more complicated. Nevertheless, the sequence of events and the relative code-phase alignments would be the same as are shown in this figure. The receiver-spoofer must be careful to synthesize a selfconsistent set of false pseudoranges. Otherwise, the victim receiver will be able to detect the attack using simple pseudorange-residuals-based RAIM calculations. A good way to synthesize self-consistent spoofed pseudoranges is to base them on a target spoofed position, r s, and a target spoofed increment to the victim receiver clock offset, Δδs. Given the three components of r s and the scalar Δδs, a self-consistent set of target spoofed code-phase offsets at the victim receiver takes the form δτsi = f si

rs− r

i

c, r rs + Δ r vs − r

i

c, Δδs

for all i = 1, …, N

25 4 i

where fsi is an appropriately defined function, and r is the position vector of the i-th GNSS satellite. The spoofer chooses the spoofed position time history r s t and the spoofed receiver clock offset increment time history Δδs(t). It uses these time histories to synthesize a set of N spoofed code-phase offset time histories using Eq. (25.4) to compute the δτsi values followed by Eq. (25.3) to compute the δτrsi values. Consistent with the initial attack profile in Figure 25.4, the initial spoofed

position r s must equal the victim receiver antenna position r v = r rs + Δ r vs , and the initial spoofed clock offset increment Δδs must be zero. The problem of choosing spoofed power levels Asi for i = 1, …, N can be tricky. The receiver-spoofer can measure the received power levels at the output of its own receiver RF front-end. If it knows its automatic gain control setting and if it knows its attitude and its receiver antenna gain pattern, then it can deduce the signal amplitudes at the victim antenna. These amplitudes, however, are not the actual Ai values that the victim receiver sees for the authentic signals because those values depend on the victim receiver’s antenna gain pattern and attitude. In addition, the spoofed Asi values that will be seen at the victim antenna output depend on the spoofer transmission power amplification, its transmission antenna gain pattern, and the distance from the spoofer transmission antenna to the victim receiver antenna. The transmitter power amplification and transmission antenna gain in the direction of the victim can be known to the spoofer in principle, but accurate knowledge will require calibration. The spoofer will be faced with uncertainties about the victim antenna gains in the directions of the authentic and spoofed signals. A sophisticated spoofer might ascertain the victim antenna model and measure its attitude. Given a nominal gain pattern for the victim antenna model, this information would give the spoofer some idea about gains. Suppose that the spoofer seeks to achieve a spoofed amplitude Asi = fiAi at the victim receiver, where fi is an amplitude advantage factor. Typically this factor is chosen to be larger than 1. Given a value of fi, the synthesized carrier amplitude in the receiver-spoofer should be Atsi = f i Arsi gtsi i

r rs − r

i

r rs + Δ r vs

− r , Gvi , Gvs , Δ r vs − Δ r tr

λ, Grsri , Grst 25 5

where gtsi is an appropriately defined amplitude re-scaling function. The quantities in this equation have the following definitions: Atsi is the carrier amplitude of the digitally synthesized spoofed signal. Its digital units are the input units of the digital-to-analog converter (DAC) that lies at the start of the spoofer’s analog transmission chain. Arsi is the carrier amplitude that the receiver-spoofer’s receiver tracking loop estimates based on discriminator values. It is given in the digital output units of the analog-to-digital converter (ADC) that lies at the end of the spoofer’s analog reception chain. Gvi is the victim receiver’s antenna gain above a 0 dBic omnidirectional antenna in the direction of the authentic signal from the i-th satellite. Gvs is the victim

25.2 GNSS Spoofing Attack Methods

receiver’s antenna gain in the direction of the spoofer transmission antenna. Grsri is the gain of the spoofer’s entire RF reception chain, starting at the input to the antenna and ending at the output of the ADC for the direction of the signal from the i-th satellite. Its units are (ADC units)2/Watt. Grst is the gain for the spoofer’s entire RF transmission chain, starting at the input to the DAC and ending at the output of its antenna for the direction from the spoofer to the victim receiver. Its units are Watts/(DAC units)2. λ is the GNSS signal’s nominal carrier wavelength. The challenges of computing the spoofed signal amplitude using Eq. (25.5) concern the four gains Grsri, Grst, Gvi, and Gvs. Calibration of the receiver-spoofer antenna and analog RF chains can be used to get reasonable ideas of Grsri and Grst if the receiver-spoofer attitude is known. Knowledge of Gvi and Gvs will require both an antenna calibration and attitude knowledge for the victim receiver. Approximations of the victim antenna gain pattern may be available from nominal data sheets if the antenna model is known, but these nominal calibrations are likely to differ from the actual victim unit. The attitude of the victim antenna will be determinable only if the spoofer has a very sophisticated sensing system, perhaps a vision-based system. In many situations, it will be too difficult to synthesize an Atsi that precisely achieves a given target amplitude advantage fi. A typical spoofer will make estimates of the various gains, and it will compute a lower bound for Atsi that will guarantee a sufficiently large amplitude advantage to ensure capture of the victim tracking loops. In practice, the residual gain factor uncertainties in Eq. (25.5) dictate that the actual amplitude advantage may be significantly larger than a target fi value in order to ensure capture of the victim tracking loops. This difficulty for the spoofer can be used to advantage when implementing spoofing defenses. Three different groups are known to have built receiverspoofers of the kind described in this section [2, 27, 28]. It seems likely that additional receiver-spoofers have been built.

25.2.6

Meaconing Attacks

Meaconing is the simple reception and re-transmission of GNSS signals. This attack mode looks similar to that of the receiver-spoofer in Figure 25.3. The difference is that the meacon is a very simple device which receives, amplifies, and re-broadcasts the entire GNSS signal spectrum. A meacon simultaneously attacks simple civilian signals, “hardened” civilian signals that include Navigation Message Authentication (NMA) or spreading code authentication, and encrypted military signals. The effect of a meaconing attack can be understood in terms of Eqs. (25.3) and (25.4). The extra code-phase offsets

introduced at the meacon are δτrsi = 0 for all i = 1, …, N. One can put this value on the left-hand side of Eq. (25.3) and solve this equation to determine the effective code-phase offsets at the victim receiver, δτsi for all i = 1, …, N. One can then equate these with their values defined in terms of the intended spoofed location r s and spoofed clock offset increment Δδs. The resulting equations for i = 1, …, N can be used to determine that the “chosen” spoofed location is r s = r rs and the chosen spoofed clock offset increment is Δδs =

Δ r vs − Δ r tr

c + δline > 0. That is, the location

of the meacon receiver antenna is the location that the victim receiver will deduce, and the added clock offset at the victim receiver will be the net path delay from the input to the meacon antenna to the input to the victim antenna. This result is somewhat obvious. The added delay Δδs indicates that the spoofed “true” time will always be earlier than the actual true time at the victim receiver. This fact can enable a detection strategy in which the victim compares its estimated clock offset time history with reasonable values based on the known level of stability of its oscillator. Note that the line delay δline is not necessarily fixed. The spoofer may modulate this value to satisfy its own purposes. In all cases, it will obey δline > 0.

25.2.7

Spoofing Navigation Data Bits

The navigation data bit stream Di[t − τi(t)] must be generated and broadcast by the spoofer. A good signal simulator automatically generates a believable bit stream. A meacon returns the true bit stream. A receiver-spoofer may use estimates of the true Di[t − τi(t)] time history. These data bits are unpredictable a priori, but many of the bits repeat periodically. For example, the legacy GPS L1 C/A code uses 50 Hz navigation data bits. The full navigation data message largely repeats every 12.5 min, and much of the message repeats every 30 s. Most of the non-repeating part consists of time-of-week counters that can be predicted accurately. A reasonable strategy for a receiver-spoofer operating on a largely periodic data bit stream is to delay spoofing until one full period of the bit stream has been received. It can then use this period’s worth of bits and any needed counter predictions to synthesize a very good estimate of Di[t − τi(t)] – actually Di[t − τrsi(t) − δτrsi]. If there are a few unpredictable bits in this stream that do not repeat periodically, then the spoofer may just synthesize guesses for such bits and adjust any error-detecting (e.g., parity) bits accordingly. At changeovers of the periodic message, which occur every 2 h for the GPS L1 C/A code legacy message, the receiverspoofer performs the changeover one full period late, that is, 30 s late for the part that repeats every 30 s and

661

662

25 Civilian GNSS Spoofing, Detection, and Recovery

12.5 min late for the other part. The receiver-spoofer of [2] forms its spoofed navigation data bits in this manner. There are proposals to add special unpredictable bits to the Di[t − τi(t)] data streams of future signals [29]. These unpredictable bits would constitute a security code that can be used for spoofing detection. In order to avoid detection, the spoofer would need to determine good estimates for these bits and include them in its spoofed navigation data bit stream. This type of attack is called a Security Code Estimation and Replay (SCER) attack because the unpredictable navigation bits constitute a security code [30]. The authentic signal’s limited signal-to-noise ratio forces the spoofer to wait a certain amount of time after the start of such a data bit in order to estimate its value with high reliability. Suppose that this time delay is δτsD. The spoofer has two options in this case. One option is to choose all δτrsi values to respect δτrsi ≥ δτsD. This option places limitations on the possible combinations of spoofed locations r s and spoofed clock offset increments Δδs due to the impact of this constraint on the calculations in Eqs. (25.3) and (25.4). The spoofed scenario must lie between two extremes. At one extreme, the spoofed victim location could be further away from each satellite than the effective signal path from the satellite through the spoofer and on to the victim. At the other extreme, the spoofed location could be arbitrary while the spoofed clock offset increment Δδs was sufficiently positive to ensure that δτrsi ≥ δτsD for all i = 1, …, N. It is possible to design a combination of the spoofed position and the spoofed clock offset increment that lies between these two extremes; that is, the spoofed location would not be completely arbitrary, but Δδs would be large enough to allow some flexibility in the choice of the spoofed location. These limitations on the spoofer offer detection options to the victim. If the spoofed location needed to be further away from all the visible GNSS satellites than the true location, then the spoofed altitude might lie below sea level, which could trigger a spoofing alarm. A sudden increase in Δδs to avoid this situation might be noticed by the victim as being inconsistent with its oscillator’s known stability characteristics. The other option for a SCER attack is to allow δτrsi < δτsD. In this case, the spoofer will have to send some guess or poor estimate of each unpredictable security code navigation data bit during the uncertainty window of duration δτsD − δτrsi that occurs at the start of the bit’s spoofed transmission interval. The resulting errors offer another avenue for detection of this type of attack [30].

25.2.8

Additional Attack Possibilities

The basic ideas of blind signal simulation attacks, receiverspoofer attacks, and meaconing attacks have numerous

potential variations. These variations tend to complicate the attacks and make them more expensive to mount. They also tend to make defense countermeasures more difficult. This subsection reviews some possible additional attack features.

25.2.8.1

Nulling Attack from a Receiver-Spoofer

A nulling attack by a receiver-spoofer broadcasts two signals for each signal that it seeks to spoof. The first is the exact negative of the true signal. This first signal cancels the true signal so that no evidence of it can be found at the victim receiver. The second signal is the spoofed signal, as in the second line of Eq. (25.1). Referring again to Eq. (25.1), the number of spoofed signals is Ns = 2N. The first N of these signals are the nulling signals. Nulling demands that Asl = Al, Dsl(t) = Dl(t), Csl(t) = Cl(t), τsl(t) = τl(t), and ϕsl(t) = ϕl(t) + π for all l = 1, …, N. The final 180o (π radians) carrier-phase shift achieves cancellation of the N authentic signals by the nulling signals. The second N spoofed signals, the l = (N + 1), …, (2N) signals, are the spoofed versions of the signals that induce the spoofed receiver location r s and the spoofed clock offset increment Δδs. This type of attack is illustrated in Figure 25.5 by five successive plots of the resulting code-phase correlation function for a single GNSS signal that would be seen by the victim receiver during the attack’s onset. As in Figure 25.4, the five successive plots in this figure show five successive stages of the attack, with the initial stage depicted in the top plot and the final stage shown in the bottom plot. Initially the spoofed signal is aligned with the true

Figure 25.5 Onset of a nulling attack as viewed using the codedelay correlation function. Nulling signal: green dashed curve, spoofed signal: black dash-dotted curve; sum of nulling, spoofed, and authentic signals: blue solid curve; receiver tracking points: red dots.

25.2 GNSS Spoofing Attack Methods

signal in code-phase. The green dashed nulling signal and the black dash-dotted spoofed signal for this channel start with zero amplitude: Asl = 0 and As(l + N) = 0, as in the top plot. Both amplitudes are slowly ramped up simultaneously, as shown in the second and third plots, until the nulling amplitude equals the true amplitude: Asl = Al. The two signals from the spoofer cancel each other in these two plots. Therefore, the solid blue curve stays unchanged and represents the authentic signal’s code-phase correlation function. Starting in the fourth plot, the spoofer begins to drag the spoofed code phase away from the authentic code phase. That is, the black dash-dotted curve migrates to the left. The green dashed nulling curve remains in the center in order to cancel the true signal. By the bottom plot, the early, prompt, and late receiver tracking points have been dragged off to the left by about three full code chips. There is a slight residual ripple at the location of the true signal because the nulling signal’s correlation function does not exactly match the negative of the true signal. Therefore, it does not exactly cancel the true signal. It matches well enough, however, to make the ripples very small. By comparing the blue curves in the bottom two plots of Figure 25.4 with their counterparts in the bottom two plots of this figure, it is apparent that a nulling attack is harder to detect by looking for distortions of the code correlation function. It is very difficult to mount a good nulling attack. First, the amplitude matching between the true signal and the nulling signal must be very close. Referring to Eq. (25.5), matching would require an accurate calibration of the receiver-spoofer’s reception and transmission gains and accurate calibration of the victim antenna’s gain ratios between the authentic and spoofed signal reception directions. The receiver-spoofer would also need to know the attitudes of the receiver-spoofer and victim antennas. Probably the victim antenna calibration knowledge requirement is the hardest to meet. An additional set of requirements would apply to the carrier phase. The receiver-spoofer would have to know and control the absolute change between the received carrier phase at its receiver antenna and the transmitted carrier phase at its transmission antenna. The receiver-spoofer would need to know the precise distance between its transmitter antenna and the victim receiver antenna Δ r vs − Δ r tr . The error in its estimate of this quantity would need to be a small fraction of the carrier wavelength.

25.2.8.2

High-Frequency Sensing of Victim Motion

Equations (25.3)–(25.5) all require knowledge of the position of the victim receiver antenna relative to the

receiver-spoofer’s receiver antenna, Δ r vs . If the victim is stationary relative to the spoofer, then the spoofer can pre-survey this displacement vector. If the victim can move relative to the spoofer, then the spoofer will need an active sensor for use in determining the relative motion time history Δ r vs t . There exist spoofing detection strategies that rely on the victim antenna undergoing small high-frequency motions that the victim knows. In order to defeat such detection strategies, the receiver-spoofer must have a sensor that can produce high-bandwidth measurements of Δ r vs t . In addition, its spoofed signal synthesis mechanization must be able to respond to any sensed rapid changes in Δ r vs t . It is possible for a spoofer to have this capability at the cost of increased hardware complexity.

25.2.8.3

Multi-Channel Meaconing Attack

An advanced form of meaconing attack could be mounted if the meacon were equipped with a small phased-array receiving antenna instead of a single-element antenna. This array could be used to implement multiple independent meaconing channels. Each channel could steer its gain to a different GNSS satellite. Each channel’s output could be delayed in an independently steerable manner. Afterward, it could be amplified, combined with the other channels’ signals, and re-broadcast through the spoofer transmission antenna. An attack by this type would be similar to an attack by the receiver-spoofer of Section 25.2.5. The one important difference would be that the choice of delays would be restricted to respect the limits δτrsi ≥ 0.

25.2.8.4

Patient Receiver-Spoofer Attacks

Another aspect of receiver-spoofer attacks is the speed with which they drag the victim receiver off to false position or timing fixes. Viewed in terms of Figure 25.4 or Figure 25.5, patience concerns the speed at which the spoofed correlation peak moves to the left. Stated in terms of the codephase spoofing calculations in Eqs. (25.3) and (25.4), patience concerns the speed at which the spoofed position r s moves away from the true victim position r rs + Δ r vs and the speed at which the spoofed clock offset increment Δδs changes from zero. If the spoofed position error r s − r rs + Δ r vs

changed too rapidly, then the victim

might notice an inconsistency with the expected changes from an inertial navigation system (INS) – assuming it had one. If Δδs(t) changed too rapidly, then the victim might notice that its clock offset estimate exhibited large rates of change that were inconsistent with its oscillator stability.

663

664

25 Civilian GNSS Spoofing, Detection, and Recovery

A sophisticated receiver-spoofer could assess its victim’s ability to monitor both position movement and clock offset drift. It could induce spoofing offsets slowly so that changes in r s − r rs + Δ r vs and changes in Δδs(t) are small enough to lie within the expected variations that might be caused by INS measurement error or oscillator drift. 25.2.8.5

Multi-Agent Attack

If expense is no object, then a spoofer might mount a multiagent attack like the one shown in Figure 25.6. Each of the three single-channel spoofers is either a receiver-spoofer or a meacon. It outputs just one spoofed signal, that of the GNSS satellite with which it and the victim receiver antenna form a line. One of the main benefits of a multi-agent attack is that the spoofed signals arrive at the victim antenna from a diversity of directions. Some spoofing detection methods use multiple antennas or a moving-antenna synthetic aperture with INS aiding in order to measure the direction of arrival of each GNSS signal. If all signals arrive from the same direction, then the signals are obviously from a spoofer or a meacon. A multi-agent spoofer can avoid being detected by this method.

25.2.9

mount. Therefore, the potential set of actors who would mount such an attack is limited. The set of possible victims is limited to those that the small set of actors might want to spoof. Reference [19] lists 13 attack techniques. It ranks them by a subjective assessment of their cost, where cost is a measure of the difficulty of developing and deploying the spoofing system. Reference [31] defines categories of threat sources, ranging from truck drivers up to terrorist organizations and governments. It also defines categories of threats, which are spoofing attack modes that map to some of the spoofing attack methods defined above. These types of analyses are useful for assessing what type of spoofing defenses one should implement. Some spoofing attack methods are easy to detect. A user equipment designer would rather develop defenses only for such attacks, thereby minimizing the complexity and cost of the detector. Some users, however, may feel threatened by attackers with enough resources to develop advanced spoofers. Such users should consider devoting the resources that are needed to develop stronger spoofing defenses.

25.3 Methods for the Detection of Spoofing Attacks

Spoofing Attack Categories

One can categorize spoofing attacks by the level of sophistication or difficulty. An attack with a higher level of sophistication or difficulty will require more resources to GNSS constellation

True RF signals

Single channel receiver-spoofers or meacons (possibly drone-mounted)

This section presents methods to detect that a spoofing attack is underway. Such methods constitute the first part of a defense. A victim receiver must know that it is under attack in order to institute appropriate responses. Each detection method presented in this section is accompanied by a discussion of its effectiveness against various methods of attack.

25.3.1

False spoofer RF signals

Victim GNSS receiver

Figure 25.6 Spoofing attack mounted by multiple agents in order to achieve correct diversity of spoofed signal directions of arrival. Note that the true signals also arrive at the victim receiver, despite appearances to the contrary in this figure.

Fake GNSS Apps in Smartphones

The problem of detecting fake GNSS applications in smartphones lies partly in the realm of cybersecurity. One could thwart malicious software by checking whether the platform should or should not be trusted. Pokémon Go has added a check of whether the user has gained root privileges. If so, the user gets locked out of playing the game [32]. GNSS-specific approaches might analyze the time histories of the smartphone’s position and clock offset. A detection strategy might try to discern micro- or macro-level variations that were highly improbable. For example, if a claimed position time history showed a smartphone user walking straight across the Grand Canyon, then a GNSS-dependent application might issue a spoofing alert. Such approaches would be analogous to credit card companies’ strategies for detecting fraud.

25.3 Methods for the Detection of Spoofing Attacks

Methods for detecting and quarantining navigation impostor software have not been studied extensively at the time of the writing of this chapter. This is a topic that deserves more attention.

25.3.2 Pseudorange Consistency for NavigationLevel RAIM Pseudorange consistency checks operate on the standard pseudorange equations of a GNSS receiver: Pi = cτi = r v − r

i

+ c δv − δi + νPi

25 6

where δv is the victim receiver’s clock offset, δi is the clock offset of the i-th GNSS satellite, and νPi is the pseudorange measurement noise. The measurement noise consists primarily of thermal noise and multipath error. Ionosphere and neutral atmosphere delays are neglected in this model for the sake of simplicity. They should not be neglected in actual receiver calculations. Suppose that the pseudorange measurement noise is assumed to be Gaussian with the following statistics: E{νPi} = 0

for all i = 1, …, N

E νPi νPl = σ 2Pi δi,l

for all i, l = 1, …, N

25 7

where σ Pi is the i-th pseudorange measurement error standard deviation and δi, l is the Kronecker delta, which equals 1 if i = l and 0 if i l. A reasonable value of σ Pi can be deduced from the corresponding received carrier-to-noise-density ratio, the accumulation bandwidth, the DLL bandwidth, and the elevation. The elevation angle is used to get an idea of the multipath contribution to the error. The thermal noise and multipath contributions are combined in a root-mean-square manner to yield σ Pi. Navigation-level RAIM calculations start by solving the standard least-squares problem for the navigation solution: find r v and δv to minimize J r v , δv

1 N Pi = 2i=1

rv

i

r σ Pi

c δv

δi

2

25 8 i

where r and δi for i = 1, …, N are known from the satellites’ navigation data messages. Suppose that r vopt and δvopt are the optimized victim receiver position and clock offset. Then the optimized value of the cost function is Jopt = J r vopt , δvopt . The quantity 2Jopt should be a sample from a degree-(N − 4) chi-squared distribution. This type of RAIM-based spoofing detection determines whether 2Jopt is too large to be a random sample from a degree-(N − 4) chi-squared distribution. The mean of this

distribution is N − 4, and its standard deviation is 2 N − 4 . Therefore, values of 2Jopt larger than a threshold such as γ = N − 4 + 3 2 N − 4 should occur rarely. If such a threshold is exceeded by the navigation solution, then a spoofing alert is issued. This method can detect attacks that spoof only a subset of the available signals in a way that fails to produce a selfconsistent navigation solution. This method is ineffective against attacks that use Eqs. (25.3) and (25.4) to generate all of the spoofed signals and that break the victim receiver’s lock on all of the authentic signals. The advent of the spoofer of [2] rendered this detection method unreliable as a stand-alone defense. It still may have merit if used in combination with other defenses. As new constellations augment the number of navigation satellites, however, a spoofer faces the increasing challenge of ensuring that it successfully spoofs each and every available signal. Otherwise, a victim will be able to detect its attack using this method.

25.3.3 Signal Distortion/Anomaly Monitoring for Tracking-Level RAIM Newer forms of RAIM look at other quantities besides pseudorange that are or can be computed autonomously within a receiver. These quantities include the received signal power, distortion of the complex code-delay/carrier-phase autocorrelation function, and jumps in carrier phase or carrier Doppler shift [33–38]. Examples of the kinds of distortion that might be monitored are shown in Figures 25.7–25.10. Figure 25.7 shows a strong gain in received signal power across the entire GPS L1 C/A code spectrum during an attack. This is an attack where the spoofer power advantage factors, fi for i = 1, …, N, were probably set to about 2 so that the spoofed power advantages were about 6 dB. A sudden jump in received power could be used to issue a spoofing alert [35]. Many receivers use an automatic gain control (AGC) module to maintain the power levels at the outputs of their RF front-ends. Such a receiver would need to report the AGC gain to the digital part of its signal processing chain in order to detect absolute power changes. This type of defense will work against spoofers that have a high level of uncertainty in their Eq. (25.5) calculations. They typically capture the victim receiver’s tracking loops by overwhelming the authentic signals’ power, as in Figure 25.7. If the spoofer has less uncertainty about gains and can mount a successful attack using less spoofer power, or using a nulling spoofer, then this method of detection will fail. Figure 25.8 shows attack-induced distortion of the complex correlation function of the receiver. This figure plots two views of the three-dimensional I and Q versus codephase offset. The left-hand panel of this figure is like the

665

25 Civilian GNSS Spoofing, Detection, and Recovery

× 109 7

Spoofed Signal Non-Spoofed Signal

Power Spectral Density

6 5 4 3 2 1 0 –1

–0.5

0 0.5 Frequency Offset (MHz)

1

Figure 25.7 Non-spoofed (red dash-dotted) and spoofed (blue solid) power spectral densities in the GPS L1 band prior to and after the onset of an attack.

1.2

1.2 Non-Spoofed Spoofed No apparent spoofed distortion in correlation magnitude vs. code offset

0.8

0.6

0.4

0.2

0

Telltale spoofer/true-signal interaction distortion: complex autocorrelation is non-planar

1 In-Phase Accumulation

1 In-Phase Accumulation

666

0.8

0.6

0.4

0.2

–2

–1

0

1

Code Offset (chips)

2

0

–0.5

0

0.5

Quadrature Accumulation

Figure 25.8 Two views of the three-dimensional I and Q versus code-phase offset immediately prior to an attack (blue solid curve) and during the initial stage of a receiver-spoofer attack (red dash-dotted curve) [19]. Source: Reproduced with permission of IEEE.

code-offset correlation functions that are shown in Figures 25.4 and 25.5. This figure is from an actual spoofing attack against a GPS L1 C/A signal. The three-dimensional I and Q versus code-phase plot should be a simple C/A-code correlation with some rounding at its edges due to the finite bandwidth of the receiver’s RF front-end. It should lie along a single line on the I versus Q projection of this plot. The left-hand panel shows the expected C/A-code correlation function before the attack (blue solid curve) and after the

attack onset (red dash-dotted curve). The right-hand panel shows the distortion that is caused by the attack. The unspoofed blue solid curve lies along a single line in the I versus Q plane. The spoofed red dash-dotted curve is not confined to a line in this plane. Another possibility is distortion in the I 2 + Q2 versus code-offset view of this function. No such distortion exists in the left-hand panel of Figure 25.8, but Figure 25.4 clearly illustrates this type of distortion in the fourth plot of its

25.3 Methods for the Detection of Spoofing Attacks

attack sequence. This distortion occurs during the initial drag-off of the spoofed code phase from the true code phase, when the spoofed and authentic curves lie within two code chips of each other. A spoofing detector that is based on distortion monitoring must evaluate its computed in-phase and quadrature accumulations, I(δτk) and Q(δτk) for k = 1, …, Noffsets. The delays δτk for k = 1, …, Noffsets are the code-phase offsets, relative to the prompt replica, of the spreading code replicas that are used to compute the corresponding accumulations. A typical receiver might use Noffsets = 3: δτ1 = −0.5τchip, δτ2 = 0, and δτ3 = +0.5τchip, where τchip is the spreading code’s chip duration. It might be wise to use a larger number of offsets and corresponding accumulations in order to detect spoofing based on this method. A spoofing detection algorithm would compare these accumulations to a nonspoofed model of their values: I(δτk) = AaccumR(τerr + δτk) cos (ϕerr) + νI(δτk) for k = 1, …, Noffsets Q δτk = Aaccum R τerr + δτk sin ϕerr + νQ δτk for k = 1, …, Noffsets

25 9

where Aaccum is the accumulation amplitude, τerr is the code-phase error of the prompt replica, ϕerr is the carrierphase error of the baseband mixing signal, R(τ) is the code-offset correlation function that includes rounding due to finite RF front-end bandwidth, and νI(δτk) and νQ(δτk) are in-phase and quadrature noise. Statistical models of the in-phase and quadrature noise exhibit nonnegligible cross-correlations between νI(δτl) and νI(δτk) and between νQ(δτl) and νQ(δτk). One way to develop a spoofing detection test is to form a cost function for the fit error in the accumulation models in Eq. (25.9) and to optimize it by finding the best-fit values of Aaccum, τerr, and ϕerr. The optimization problem would take a form similar to that given in Eq. (25.8), except that the measurements and models would involve I(δτk) and Q(δτk) rather than pseudorange, the summation would be performed over k, and the correlations between different noise terms would be taken into account in defining the cost function, which would require inversion of a noise correlation matrix. If the resulting optimized cost were JIQopt, then 2JIQopt would be a sample from a chi-squared distribution of degree 2Noffsets − 3 if the signals were authentic. This fact could be used to set a threshold value for this measurement residuals cost function. If the optimized cost exceeded this threshold, then a spoofing alert would be issued. There are three challenges for this detection method. The first is that distortions only occur during the initial signal drag-off. This is best illustrated by the fourth and fifth plots

of Figure 25.4. The distortions are evident in the fourth plot during the drag-off, but not in the fifth plot after drag-off has caused the spoofed code phase to differ from the authentic code phase by more than two code chips. The second challenge for this detection method is that of high spoofer amplitude. If the spoofer amplitude Asi is much larger than the authentic amplitude Ai, then not much distortion will exist because the spoofed signal will dominate the I(δτk) and Q(δτk) signal models. Of course, this challenge for a distortion-monitor-based detector represents an opportunity for a power-based detector. The third challenge is that of multipath. The distortions being monitored for spoofing detection are the same as the distortions caused by specular multipath. The spoofer must somehow distinguish multipath from spoofing and issue a spoofing alert only when a true spoofing attack is occurring. Otherwise, there may be too many false alarms. The problem of multipath false alarms during distortion monitoring and the opportunity afforded by simultaneous power monitoring are addressed in [39]. A variant of this detection method would be to look at all possible code-phase offsets and all possible carrier Doppler shifts on a continuous basis. Such calculations constitute the standard search operations during a signal acquisition. Thus, continuous implementation of a re-acquisition signal search could be implemented as part of a spoofing detection algorithm. This strategy would locate the second peak on the bottom plot of Figure 25.4 even after the spoofer had dragged the code phase more than two chips away from the authentic signal. This detection strategy places a greater processing burden on the receiver. A weakness of this strategy is exposed if the spoofer signal power is much larger than that of the authentic signals. In this case, the spoofer will also effectively jam the authentic signal, and the latter signal may not be found during the re-acquisition search due to its peak not rising high enough above the spoofed noise floor. Of course, an over-powering spoofer presents an easy target for a power-based detection method. Signal distortion monitoring has the potential to detect a variety of spoofing attacks. The only attacks that it cannot detect are nulling attacks and over-powered attacks. In both of these cases, the looked-for distortion does not exist. This method only works during the initial drag-off phase of a receiver-spoofer attack unless the costly continuous-reacquisition version of this method is implemented. Another detection method is to look for jumps or slope changes in typical quantities that are computed by the receiver tracking loops. An example of a spoofing-induced jump is shown in Figure 25.9. An example of a spoofinginduced slope change is shown in Figure 25.10. The jump in Figure 25.9 occurs in the time histories of the prompt

667

25 Civilian GNSS Spoofing, Detection, and Recovery

× 108 1

In-Phase Accum

0.5

Sudden [I;Q] jump at onset of spoofing attack

0

–0.5

–1 1 0 × 108 Quadrature Accum

Figure 25.9

–1

193.5 194

194.5 195

195.5 196

Three-dimensional plot of I and Q versus time at the onset of a receiver-spoofer attack.

2240 Onset of spoofing attack

2220

Onset of drag-off (sudden 0.02 g increment in carrier acceleration/ Doppler rate)

2200 2180 2160 2140 2120

0

196.5

Time (sec)

2260

Doppler Shift (Hz)

668

100

200 300 Time (sec)

400

500

Figure 25.10 Carrier Doppler shift versus time at the onset of an attack by a receiver-spoofer.

in-phase and quadrature accumulations, I(0) and Q(0). The onset of spoofing produced a sudden jump in the twodimensional vector [I(0); Q(0)], because of a sudden amplitude change, code-phase change, or carrier-phase change. Although not obvious from the perspective used in this plot, the amplitude Aaccum suddenly increased by a factor of 3, and the carrier-phase error ϕerr suddenly increased by 40o. Such changes are unphysical for a stationary or slowly moving receiver. Simple spoofing detector calculations could be implemented that computed the magnitudes of changes in the [I(0); Q(0)] vector from sample to sample.

If the change magnitude were too large relative to the original magnitude, then a spoofing alert would be issued. This approach would work well for static receivers. Its reliability would degrade for dynamic receivers operating in harsh environments such as an urban area. In this case, pure non-line-of-sight (LOS) signals and severe multipath could distort the correlation function in a way that could easily trigger false spoofing alarms. Figure 25.10 shows a receiver’s computed carrier Doppler shift from its phase-lock loop (PLL) at the onset of an attack by a receiver-spoofer. There are no anomalies during the initial part of the attack, starting at t = 200 s. This period corresponds to the top three panels of Figure 25.4 when the spoofer is ramping up the amplitude of the spoofed signal. At t = 320 s, there is a sudden change in the slope of the PLL’s computed carrier Doppler shift. This change corresponds to the onset of code-phase drag-off, which occurs between the third and fourth panels of Figure 25.4. The spoofer generates a false carrier phase that diverges from the authentic carrier phase in order to avoid code-carrier divergence of the spoofed signal. The resulting sudden change in the slope of the received carrier Doppler shift time history offers a means of detecting the attack. This change might seem small to the spoofer. It amounts to a 0.02 g change in the projection of the acceleration of the spoofed location onto the LOS to the spoofed satellite. This small change, however, is easily detectable by the victim receiver. An implementation of this type of detection strategy might use the beat carrier-phase acceleration output of a

25.3 Methods for the Detection of Spoofing Attacks

typical third-order PLL. This output is the slope of the plot in Figure 25.10. The detector would look for sudden changes in this output and issue a spoofing alert if any unphysical changes were detected. The levels of change that should result in an alert would be dependent on the type of application. A large ocean-going vessel would experience only small jumps in the beat carrier-phase acceleration during normal cruising. A fighter jet could expect much larger jumps during unspoofed operation. Thus, the problem of detecting spoofing using this method would be more difficult for a highly maneuverable vehicle. This “jumps” method has the potential to detect a variety of spoofing attacks. It cannot detect a very patient receiverspoofer because the attacker will not produce any sudden jumps if it raises the amplitudes of its spoofed signals very slowly and if it performs its post-capture drag-off very slowly. In this case, however, the slowness of the attack will afford greater opportunities for distortion-based methods to detect the spoofer. Therefore, the challenge posed by a patient spoofer to this detection strategy offers a corresponding benefit to distortion-based detection methods. If a receiver-spoofer uses a combination of nulling and patience, however, then neither this method nor the distortion-monitoring method will detect the attack. As with the distortion method, this method can work only during the initial phases of a spoofing attack. Vector-based tracking loops have been proposed as means of detecting a spoofing attack. A vector technique couples the DLL and PLL tracking for all of the signals through the requirement that they yield consistent position and velocity solutions. Suppose that the spoofer attacks only a minority of the signals. Then the remaining true signals can help the attacked signals’ tracking loops coast through the attack onset and eventually recover lock on the true signals [40]. Note, however, that navigation-level RAIM, as in Section 25.3.2, could also detect such an attack. Neither type of defense would be effective against the current state of the art in receiver-spoofers, which attack all signals simultaneously [2]. A vector tracking loop might be a useful component of a defense that also monitored sudden changes in carrier Doppler shift, as in Figure 25.10. A spoofer might employ intentional code/carrier divergence during its initial drag-off in order to avoid a sudden jump in the rate of change of carrier Doppler shift. A vector tracking loop might detect an unreasonable level of code/carrier divergence and use it as the basis for a spoofing alert. Another potential anomaly that can be monitored within the receiver is unusual PNT drift. Drift-based detection methods look at temporal changes in the navigation solution’s receiver clock offset δv(t), position vector r v t , and velocity

vector r ν t Large changes in these quantities that are unphysical can be used to generate spoofing alerts. Changes in the estimated clock offset can be compared to the receiver oscillator’s known root Allan variance. Suppose that the root Allan variance curve is σ osc(τ) versus τ. Then the receiver can ask whether δv t − δv t − τ τσ osc τ

> γ osc

25 10

where γ osc > 1 is the spoofing detection threshold. A value on the order of γ osc = 3 might be used. Violation of this limit would indicate an oscillator drift that was too large to be physically believable and, therefore, likely the result of spoofing. A clock drift test requires a good characterization of the receiver oscillator’s root Allan variance curve. If that curve might be affected by rapid changes in temperature or by vibration or acceleration of the receiver, then appropriate measures must be taken to ensure that the system does not produce false alarms due to these environmental factors. Spoofing detection based on position or velocity drift can look for unphysical motions like the abrupt acceleration change shown in Figure 25.10. Such techniques, however, go beyond a channel-by-channel analysis of drift. Instead, they look at the position and velocity solutions computed by the receiver and assess whether they are reasonable for the given user platform. For example, a spoofed ship’s altitude that is much different from sea level should trigger an alert. Some of the best methods for detecting physically unrealistic motions fuse INS data with GNSS data. Detection methods based on INS data are the subject of the next subsection. The authors conjecture that the commercially available spoofing detection system of [23] uses one or several of this subsection’s techniques. The system is implemented entirely within the receiver’s signal processing unit. It does not require any of the external modifications or signals that are required by the methods that will be discussed below. It can detect spoofing only if it sees the onset of a spoofing attack, which is consistent with most of the methods discussed in this subsection. There is some question about whether it uses power monitoring. One might expect that power monitoring would enable it to detect spoofing even if it did not see the change from unspoofed operation to spoofed operation. If the absolute power were significantly higher than expected under normal operation, what would prevent a power-based method from generating an alert? Perhaps the system has a power monitor that is only good at detecting

669

670

25 Civilian GNSS Spoofing, Detection, and Recovery

changes. Alternatively, perhaps the possible range of normal power levels is too large to be able to identify the presence of spoofed signals based purely on a certain absolute power threshold.

25.3.4 Methods that Exploit INS Data and GNSS/INS Data Fusion Data from an INS can be used to detect spoofing in various ways [41–46]. The idea of all such systems is to compare motion time histories sensed by the GNSS receiver with motion time histories sensed by the INS. If there is too much disagreement between the two systems, then a spoofing alert is issued. Any comparison between GNSS and INS data is complicated by the fact that their data types are very different. Therefore, some sort of data fusion approach must be used. The INS data most directly comparable to GNSS data are the accelerometer outputs. The comparable GNSS data are carrier Doppler shifts, which can be used to deduce velocity, and pseudoranges, which can be used to deduce position. An additional complication is that INS data are sensed in a body-fixed INS coordinate system, whereas GNSS data are most directly related to Earth-Centered/ Earth-Fixed (ECEF) coordinates. Comparisons can be made if the INS accelerometer outputs are integrated to produce velocity or position time histories that are directly comparable to corresponding GNSS-derived velocities or positions, as in [42]. Conversely, GNSS outputs can be differentiated to produce accelerations that are directly comparable to INS outputs [45]. A powerful, but complicated, INS-based spoofing detection method uses a nonlinear Kalman filter to fuse the GNSS data with the INS data in a tightly coupled manner, as in [46]. Such a filter typically estimates position, velocity, three-axis attitude, accelerometer biases, rate-gyro biases, receiver clock offset, and receiver clock offset rate. It might use the following 18-by-1 Kalman filter state vector rv t rν t qt x t =

b acc t

25 11

b rg t cδv t cδv t where q t is the 4-by-1 attitude quaternion that parameterizes the rotation from ECEF coordinates to INS coordinates, b acc t

is the 3-by-1 accelerometer bias vector

given in INS coordinates, and b rg t is the 3-by-1 rate-gyro bias vector given in INS coordinates. Standard Kalman filter operations can be used to determine the sum of the squares of the filter’s normalized innovations. The innovations are the differences between measured data and the Kalman filter’s a priori predictions of the measurements. The filter’s normalized sum of squares should be a sample from a chi-squared distribution with degree equal to the number of scalar measurements [47]. A spoofing detection alert is issued if this quantity is too large to have been a random sample from the corresponding chi-squared distribution. The measured data that should be used in a tightly coupled GNSS/INS system are the pseudorange measurements and the carrier Doppler shift measurements. The INS accelerometer and rate-gyro measurements are used within the dynamic propagation model for the state vector. This type of INS-based filter is known as a modelreplacement filter. It is possible to use beat carrier-phase measurements in place of the carrier Doppler shift measurements, but their use would require the addition of beat carrier-phase bias states to the filter. The use of either carrier Doppler shift or beat carrier phase is highly recommended for spoofing detection applications. These data types are much more sensitive to small changes in position and velocity than are pseudorange measurements. Their use in a tightly coupled INS-based spoofing detector will greatly lower the missed-detection probability for a given type of attack and a given false-alarm probability. A tightly coupled GNSS/INS spoofing detection approach will work very well if the victim GNSS antenna location r v t undergoes oscillations whose amplitudes equal a significant fraction of a wavelength and whose frequency is too high for the spoofer to measure and adjust its corresponding Δ r vs t input to Eq. (25.4). The oscillations will induce large normalized-innovations-squared measurement residuals when under attack. The residuals will be small when the received GNSS signals are all authentic because the authentic signals respond correctly to the r v t oscillations. In order for this type of spoofing detection system to work properly, it is necessary to use good tunings of its Kalman filter process noise and measurement noise statistical models. The process noise model is defined by the bias drift rates, the velocity random walk, and the angular random walk statistics of the INS accelerometers and rate gyros. The measurement noise model is defined by the thermalnoise-induced and multipath-induced errors in the pseudorange and carrier Doppler shift measurements. If any of these sources of uncertainty are assigned erroneous

25.3 Methods for the Detection of Spoofing Attacks

statistical models, then the chi-squared test will not achieve its designed false-alarm and missed-detection probabilities. Good INS-based methods can detect an attack that does not reproduce the GNSS characteristics of the true highfrequency motions of the victim receiver antenna. Any such shortcoming will create a discrepancy between the INS and GNSS data that the victim can notice and use to detect the attack. A Kalman-filter-based INS method can also detect any attack that is impatient about the rate at which the spoofed

authentic shortly after their reception. This approach has some similarities to symmetric secret-key encryption of military GNSS signals. The main difference is that the victim receiver is not able to predict the features prior to receiving them. This inability has the benefit of precluding the need for a secret key to enable generation of the features. There are three classes of methods of this type. One method exploits the presence of an encrypted military spreading code that is broadcast by the same satellite on the same carrier with known code and carrier offsets from the civilian spreading code. The second method uses unpredictable data bits that can be authenticated after the fact through the use of a digital signing protocol. The third method uses short segments of the spreading code that are unpredictable [14]. They are called “digital watermarks.” The generation key for each such segment is broadcast after the fact within the navigation data bit stream.

location r s t diverges from the true victim receiver location r v t . If the divergence is too much larger than the known drift statistics of the victim’s INS, then a spoofing alert will be generated by the Kalman filter innovations test statistic. On the other hand, if an attacker is patient enough to avert INS-based detection, then it may become vulnerable to detection by a signal monitor that looks for telltale distortions like the ones described in the discussion of Figure 25.8.

25.3.5

25.3.5.1 Receiver-Receiver Cross-Correlation Methods

Methods that use military signals are described in [48–52]. These particular methods use the encrypted P(Y) signal on the GPS L1 frequency in order to detect spoofing on the L1 C/A signal. The C/A and P(Y) signals are known to be in phase quadrature with each other. This quadrature relationship of their baseband spreading codes is depicted in Figure 25.11.

Encryption-Based Methods

Encryption-based methods rely on the presence of encrypted signal features. The spoofer must not be able to produce these features at the time of the attack, but the intended victim must be able to estimate these features from the received signal and evaluate whether they are

Known in-phase C/A code used for tracking in both receivers

Unknown encrypted quadrature P(Y) code used for cross-correlation spoofing detection

Victim receiver signal

2

C/A Signal

C/A Signal

Secure reference signal

0 –2

P( 2 Y) 0 Si –2 gn al

4

6

8 T

0 –2

12

10

ps)

chi

( ime

2

P( 2 Y) 0 Si –2 gn al

4

6

8 e Tim

12

10 )

ips

(ch

Correlated portions of P(Y) code based on C/A code to match timing between receivers

Figure 25.11 Code-phase and carrier-phase relationship of known C/A spreading code and encrypted P(Y) spreading code in two receivers [49, 51]. Source: Reproduced with permission of IEEE.

671

672

25 Civilian GNSS Spoofing, Detection, and Recovery

Spoofing detection is carried out by using a secure receiver to aid the victim receiver. The secure receiver is located in a place where a spoofer is not able to attack it. It is likely far away from the victim receiver, perhaps in another country or on another continent. The only requirements on the secure receiver are that it be in a secure, unspoofable location and that it see the same GNSS satellites that the victim sees. It can only provide authentication for signals that are visible to both receivers. The secure receiver tracks its civilian spreading code using standard DLL and PLL techniques. It steers its PLL so that the civilian code is located on its in-phase baseband-mixed signal. It then reads a noisy version of the military signal from the quadrature baseband-mixed signal. Identical operations are carried out on the victim receiver. The resulting quadrature samples take the forms [51] yqak = APaPY(tak) + νqak yqbk = APb PY t bk + νqbk

25 12

with yqak being a quadrature sample from the secure receiver and yqbk being a quadrature sample from the victim receiver. The received carrier amplitudes of these two baseband signals are APa and APb. These amplitudes can be deduced from the C/A code amplitudes that are measured by the receiver and by a cataloged relationship between the C/A transmitted power and the P(Y) transmitted power on the various GPS satellites [50]. The unknown function PY(t) is the encrypted P(Y) spreading code, and the respective sample times of the two receivers’ quadrature signals are tak and tbk. The terms νqak and νqbk are the quadrature baseband noise terms in the two receivers. The two receivers’ C/A code DLLs measure their respective code delays. These code delays can be used to match P(Y) samples between the two receivers. Suppose that this matching procedure determines that tak and t b k + Δkab correspond to the same portion of the C/A code. The method uses Δkab and the quadrature samples to compute the following cross-correlation detection statistic: K

γ cc =

yqak yqb k + Δkab

25 13

These inputs include the received carrier-to-noise density ratios of the C/A code in the two receivers, the known relationship between the C/A code transmitted power and the P(Y) code transmitted power, the noise variances of νqak and νqbk, the sampling interval Δt = tak + 1 − tak = tbk + 1 − tbk, the number of correlated samples in Eq. (25.13), K, and the target false-alarm probability [51]. This method has the drawback of needing to bring the quadrature samples from the two receivers, yqak and yqbk, to a common location. These samples may have a frequency of 5–10 MHz, and it may be necessary to sum them over a full second in order to produce a high probability of detection for a low probability of false alarm. This fact implies the need for a high-bandwidth data link between the receivers or between each receiver and a third location. This extra data link imposes a significant infrastructure cost on this type of system. Semi-codeless P(Y) signal processing techniques provide a means of economizing on bandwidth while increasing the probability of detection for a given falsealarm probability [49]. These techniques exploit knowledge that the encrypted P(Y) code is the product of a publicly known P code that chips at 10.23 MHz and an encrypted W code that chips at slightly less than 0.5 MHz. The semi-codeless technique forms estimates of the unknown W chips based on the raw quadrature samples and the known P code. These estimates are formed independently in each of the two receivers. The semicodeless technique cross-correlates these W-chip estimates. The decreased communications bandwidth is caused by only needing to assemble W-chip estimates in a common location. Their frequency is smaller than the frequency of the raw samples by a factor of 10 or more, leading to bandwidth savings. The increase in the probability of detection occurs because of the processing gain that results from integrating the product of the quadrature samples and the P code over the W-chip intervals in order to estimate those chips. Correlation intervals of 0.2 s duration have been shown to produce reliable spoofing detections when using semi-codeless crosscorrelation techniques [49].

k=1

25.3.5.2

This statistic is compared to the threshold value γ th. If γ cc < γ th, then a spoofing alert is issued. Otherwise, the C/A code signal in the victim receiver is deemed to be authentic because of the large correlation between its noisy version of the P(Y) code and the secure receiver’s noisy version of this same encrypted spreading code. The value of the spoofing detection threshold γ th is designed based on a formula that uses a number of inputs.

NMA

NMA techniques are a means of authenticating the navigation data bit stream Di(t). Suppose that this bit stream takes the form Dl ΠT t − lT

Di t =

25 14

l

where Dl is the l-th data bit, T is the data bit transmission interval, and ΠT(t) is the usual finite support function that

25.3 Methods for the Detection of Spoofing Attacks

equals 1 if its argument lies in the range 0 ≤ t < T and that equals zero otherwise. The Dl values are either +1 or −1. Suppose that a certain subsequence of the Dl bits constitute a single NMA block. Suppose, without loss of generality, that this sequence is D1 , …, DL. In practice, the NMA bits might not be contiguous. It is certain, however, that they will occur in known locations within the data stream. NMA works by using a public-key/private-key cryptographic technique to generate a digital signature that constitutes the NMA sequence D1 , …, DL . After receiving this sequence, the victim receiver uses the known public key to check whether the signature is correct. If it is correct, then the navigation data block signed by the digital signature is declared authentic. If the signature is incorrect, then a spoofing alert is issued [29]. Only the GNSS constellation knows the private key that has been used to generate the signature. Therefore, a spoofer cannot generate a correct signature a priori. One drawback of NMA is the long time that is required to transmit an entire digital signature. The interval can be minutes. Thus, its latency is typically much longer than that of the cross-correlation method. The only latencies of the cross-correlation method are the time for the two receivers to process enough quadrature samples to form a good detection statistic, the time to transmit both sets of quadrature samples to a common location, and the time to compute the detection statistic in Eq. (25.13). The latency of this competing system can be on the order of 1 s or less [50]. The most significant drawback of NMA is that it requires a change of the transmitted navigation signal. This can be challenging or even impossible for satellites that are already in orbit with navigation message structures that are already defined. The European Galileo system plans to implement an NMA component within its data stream [53], and simulation-based tests of Galileo NMA spoofing detection have been conducted [54]. It is unclear when other GNSS constellations will follow suit.

it has a good estimate of the bit. Afterward, it transitions to the true bit value if its guess is wrong. An NMA defense can be augmented to look for this faulty bit guessing on the part of the spoofer. This defense looks for telltale bit transients in the initial part of each NMA data bit interval [55]. It can average its assessment of whether such transients are occurring over many NMA bits. If it sees suspicious initial transients in about 50% of the bit intervals or more, then it issues a spoofing alert. Spreading Code “Digital Watermarks”

25.3.5.4

This technique places unpredictable spreading code segments in predictable locations within the otherwise-known civilian spreading code sequence [14]. The receiver does not use these short segments of the received signal for tracking purposes. Instead, it records each segment’s basebandmixed samples. Afterward, it receives the key for generating the spreading code segment. This key is sent through the navigation data message. It uses this key to generate a replica of the spreading code segment, which it then uses to compute correlations with its stored baseband samples. If a high correlation value is achieved, then the signal is deemed authentic. Otherwise, a spoofing alert is issued.

25.3.6 Antenna Array Methods that Sense Direction of Arrival A victim receiver that has an antenna array can exploit the array’s direction-finding capabilities to implement spoofing detection based on direction of arrival (DoA), as in Figure 25.12. Example investigations of DoA-based spoofing detection are [56–66]. The authentic signals arrive along a diverse set of unit direction vectors, for example, i−1

ρv

i

i+1

, ρ v , and ρ v

for GNSS satellites i − 1, i, and

GNSS satellite i − 1 GNSS satellite i GNSS satellite i + 1

25.3.5.3

NMA with Bit Distortion Detection

A spoofer may attempt to estimate the NMA bits on the fly and replay the authentic bits on the spoofed signal. This type of attack has been discussed in Section 25.2.7. It is called a SCER attack. The SCER attack has two options. One is to delay the spoofed signal enough to enable correct estimation of the NMA bits before they are needed to construct the spoofed signal. In this case, the SCER attacker runs the risk of producing a suspiciously large spoofed victim clock offset δv. The other SCER attack option is to broadcast a guess of each NMA data bit during the short initial interval before

→i – 1

ρv

GNSS spoofer

→i

ρv

→i +1 →

ρv

ρvs

Antenna array of victim receiver with direction-finding capabilities

Victim GNSS receiver

Figure 25.12 Victim receiver with an antenna array that enables direction-of-arrival measurement.

673

674

25 Civilian GNSS Spoofing, Detection, and Recovery

i + 1. All of the spoofed signals from a single transmitter, i − 1, i, and i + 1, arrive along a common unit direction vector, ρ vs . One method of spoofing detection measures all of the DoA vectors [58]. Let these measured vectors be designated i−1

i+1

i

as ρ vm , ρ vm, and ρ vm . One way to make these measurements is to consider only the beat carrier-phase single differences between the antenna elements. Another method exploits calibrations of the directional dependence of the signal phase and amplitude at each antenna feed. The measured unit direction vectors are given in a coordinate system that is defined relative to the antenna array. There are challenges to making these measurements, such as the need to calibrate the unknown antenna manifolds [67]. Nevertheless, DoA measurement has proved to be an effective technique for use in spoofing detection [61]. The DoAs are also computable from the navigation solution and the satellite ephemerides. Let the computed unit i−1 ρ vc ,

i+1 ρ vc .

i ρ vc ,

and direction vectors be designated as These computed vectors are defined relative to reference coordinates, typically‚ ECEF coordinates. As an example, consider one possible DoA-based spoofing detection algorithm: It solves two optimal estimation problems and forms the difference of their minimum costs in order to compute its spoofing detection test statistic. The first optimal estimation problem fits the measured direction vectors to the hypothesis that the signals are authentic. It takes the form find q to minimize Jns

1 N q = 2i=1

qT q = 1

subject to

i

ρ vm

i

A q ρ vc

2

σ vmi

25 15

where q is the 4-by-1 unit-normalized attitude quaternion that parameterizes the three-axis rotation from ECEF coordinates to antenna coordinates, A q is the corresponding 3-by-3 orthonormal direction cosines matrix, and σ vmi is the per-axis direction measurement error standard deviai

tion for the ρ vm measurement. A description of quaternions and a formula for the direction cosines matrix are contained in [68]. This is a constrained nonlinear optimization problem. Normally such problems are difficult to solve and require some sort of iterative numerical solution. This particular problem is a version of Wahba’s problem and admits a closed-form solution for the global minimum using Davenport’s q-method. Davenport’s method computes the optimal quaternion by solving for an eigenvector of a 4by-4 symmetric matrix [68]. The spoofing detection method’s second optimal estimation problem fits the measured direction vectors to the

hypothesis that all of the signals are spoofed and that they all arrive from the same direction. This common direction vector is estimated in antenna coordinates, where it is designated as ρ vsm. The optimal estimation problem for this vector takes the form find ρ vsm to minimize subject to

1 N = 2i=1

Js ρ vsm

i

ρ vm ρ vsm σ vmi

T

ρ vsm ρ vsm = 1

2

25 16

This is also a constrained nonlinear optimization problem. It too can be solved in closed form. The solution algorithm starts with the over-determined system of equations whose half-sum-squared error cost is J s ρ vsm . This equation is linear in the unknown vector ρ vsm y = H ρ vsm , where y =

1 ρ vm

It takes the form N

σ vm1 ; …; ρ vm σ vmN

is a 3N-

by-1 vector and H = [I3 × 3/σ vm1; …; I3 × 3/σ vmN] is a 3Nby-3 matrix. By using a Lagrange multiplier to adjoin the constraint to the cost function, one can show that the optimal solution takes the form ρ vsm = H T H + μI 3 × 3

−1

H T y . The quantity μ is the unknown scalar Lagrange multiplier. It can be determined by substitution of the solution back into the unit normalization constraint for ρ vsm and finding the value of μ that causes this constraint to be satisfied. The resulting equation can be transformed into a sixth-order polynomial in μ that can be solved using standard numerical polynomial solution techniques. A singular value decomposition of the H matrix and a corresponding transformation of the ρ vsm solution vector will simplify the derivation of the μ polynomial. Suppose that the optimal quaternion for the non-spoofed problem in Eq. (25.15) is qopt and that the corresponding minimum cost is J nsopt = J ns qopt

Suppose, also, that

the optimal spoofer direction vector for the spoofed problem in Eq. (25.16) is ρ vsmopt and that the corresponding minimum cost is J sopt = J s ρ vsmopt

Then the spoofing

detection test statistic for this method equals the difference of these two optimal costs: γ DoA = J sopt − J nsopt

25 17

This test statistic should be a large positive number if the signals are authentic. This will be true because Jnsopt will be small due to the good fit of the non-spoofed hypothesis while Jsopt will be large due to the poor fit of the spoofed hypothesis. If the signals are all spoofed, then γ DoA should be a negative number with a large magnitude based on similar reasoning: Jnsopt will be large due to the poor fit of the non-spoofed hypothesis‚ while Jsopt will be small due to

25.3 Methods for the Detection of Spoofing Attacks

the good fit of the spoofed hypothesis. A spoofing alert threshold γ DoAth can be defined based on a worst-case analysis of the false-alarm probability, similar to the analysis given in [57]. A spoofing alert will be issued if γ DoA < γ DoAth. It is possible to develop DoA-based spoofing detection methods that use antenna configurations which give directional sensitivity without enabling full measurement of i

each ρ vm direction vector. One such system uses known one-dimensional antenna motion to create a synthetic aperture [57]. Another system uses two antennas and estimates i

dot products of the satellite directions ρ v with the direction vector between the antennas [26]. A third system uses two antennas with differing gain patterns, and it computes received amplitude ratios between the two antennas for each satellite [56]. Spoofing detection is based on a fit of the DoA-sensitive data to a model of the non-spoofed hypothesis, to a model of the spoofed hypothesis, or to both types of models. The spoofed hypothesis postulates directional metrics that lack diversity among the different received signals. The non-spoofed hypothesis looks for an expected level of diversity in the metric that is consistent with the DoA diversity of the true signals. The spoofing detection system of [69] might reasonably be lumped with this class of detectors. It uses a single antenna element that has two feeds, one primarily responsive to right-hand circularly polarized (RHCP) signals and the other primarily responsive to left-hand circularly polarized (LHCP) signals. The spoofing detection mode of this system exploits two expected features of spoofed signals: (i) the presence of significant power in the LHCP component and (ii) a lack of diversity of the spoofed DoAs. Authentic signals should be primarily RHCP and should have DoA diversity. The two assumed properties of spoofed signals enable the system to distinguish between spoofed and non-spoofed signals when operating in a special mode that combines the RHCP and LHCP feeds using a time-varying relative phase offset. A DoA-based system can detect all spoofing attacks that originate from a single spoofing transmitter antenna and that cause the victim receiver to track only the spoofed signals. It may be possible to develop techniques that relax this requirement to allow the victim receiver to track some spoofed signals and some authentic signals. In that situation, it may be helpful to use pseudorange measurement residuals from the navigation solution of Eq. (25.8) to distinguish spoofed and authentic signals. In any case, the arrival of multiple signals from a common direction is a dead giveaway that a spoofing attack is underway if the authentic signals should be arriving from different directions.

DoA-based spoofing detection can fail against a multiagent spoofer like the one shown in Figure 25.6. If the multiple spoofers are aligned properly, then their measured directions from the victim antenna will yield a good fit to the non-spoofed problem in Eq. (25.15) and a poor fit to the spoofed problem in Eq. (25.16).

25.3.7

Network-Based Defenses

Spoofing detection strategies have been proposed that exploit networks of receivers [52, 70–73]. The common theme of these methods is that multiple receivers collaborate to detect the presence of the spoofer. Some of these techniques are similar to network-based methods for detecting and locating GNSS jammers [74]. The network method proposed in [52] is the P(Y)-code cross-correlation approach that has been discussed in Section 25.3.5. This approach exploits the existence of a receiver network to look for differences in the vestigial encrypted components of received signals that could indicate an attack on one receiver or on a subset of receivers. Other networked approaches exploit the possibility that multiple receivers are under attack by the same spoofer. This class of networked methods includes a strategy which uses the receiver network to derive DoA information that can be used to distinguish between spoofed and nonspoofed signals, as in methods based on antenna arrays [71]. Other methods look for suspicious similarities between pseudoranges or estimated positions [70, 73]. The method of [72] looks for telltale overlaps of reported victim aircraft positions, as reported through ADS-B or similar systems. This method also uses time differences of arrival of ADS-B signals at a network of ground-based ADS-B receivers in order to form an independent estimate of an aircraft’s location. It compares that location with the reported location based on its GNSS receiver. Thus, this networked-based method uses a form of data fusion to detect GNSS spoofing. Most network-based methods will fail if the spoofer has enough transmission antenna directivity to target only a single victim receiver. Reference [72] explicitly discounts this possibility. That could be a rash assumption in certain situations. On the other hand, the only known “in-thewild” spoofing attack is consistent with the multi-victim assumption [7]. Therefore, networked approaches have some merit.

25.3.8

Combined Defenses

It should be possible to enhance spoofing detection performance by using multiple complementary techniques. INSbased methods and clock-drift-based methods, if used in

675

25 Civilian GNSS Spoofing, Detection, and Recovery

combination, constrain the spoofer to move the false position and clock fixes slowly away from the true values. This slowness causes transient signal distortions to last longer and therefore to be easier to detect by the methods of Section 25.3.3. INS/clock-drift-based methods also prevent a SCER attack on the NMA defense from quickly moving the spoofed navigation bits late enough to enable accurate estimation of the NMA digital signature bits prior to their initial broadcast. The foregoing are just two examples of how combined techniques can yield stronger defenses than either technique used alone. There are additional combinations of detection methods that have the potential to enhance detection. The enumeration of all such combinations is beyond the scope of this chapter.

25.4 Methods for Recovery of Authentic PNT Services During a Spoofing Attack A desirable component of a spoofing defense is a method to recover the authentic PNT solution. Spoofing detection is useful even if an authentic PNT solution is not recoverable. In that case, the user receiver is lost, but it is better to know that one is lost than to believe a false position fix. Best of all, however, would be a recovery that allowed the victim receiver to resume navigation using authenticated GNSS signals.

25.4.1

Steps of Recovery

A full defense that includes recovery of PNT services can be broken into four steps. The first step is detection of the spoofing attack. The second step is to find the authentic signals among the spoofed signals. The third step is to verify the authenticity of these newly found signals. The fourth step is the re-computation of an authentic navigation solution from these signals. Methods for accomplishing the detection step have been covered in detail in the preceding section. Computation of an authenticated navigation solution in the final step is also straightforward. The difficult steps are the second and third steps. How does one find the authentic signals? How does one verify their authenticity?

25.4.2 Recovery and Verification of the Authentic Signals Recovery of the authentic signals can start with a standard signal acquisition search over all possible code phases and carrier Doppler shifts. A search of this type is illustrated in

x 108 Spoofed signal 2 1.5 Λ

676

Authentic signal

1 0.5 0 1

5000

0.5 τ (msec) 0

–5000

0 ωD /(2π) (Hz)

Figure 25.13 Re-acquisition search for the true signal when there is also a spoofed signal.

Figure 25.13. It yields two distinct peaks that rise above the noise floor. One is the authentic peak, and the other is the spoofed peak. The spoofed peak is higher than the authentic peak due to the spoofer’s use of an amplitude advantage in order to capture the victim receiver’s tracking loops. It is straightforward to find the authentic signal in this example. It is clearly visible in the search space. Furthermore, it will be the one with a different code phase or a different carrier Doppler shift than the spoofed signal that the receiver is already tracking. Recovery of the authentic signal is much more difficult if the spoofed signals have too much of a power advantage. They can act as jammers and raise the effective noise floor so that the authentic signals cannot be found. Additional measures must be taken to find the true signals in this case, if they can be found at all. One strategy for finding a weak authentic signal is to lengthen the coherent integration time of the acquisition search accumulations. If the spoofed signal reproduces the broadcast navigation data bit stream Di(t), then this decoded data bit stream from the spoofed signal can be used to lengthen the coherent integration interval beyond the data bit period. One of the authors has used this technique successfully in a data set associated with the spoofing and detection tests of [26]. There is another possible way to deal with jamming of the authentic signals if the victim receiver has an antenna array. The array can be used to steer nulls in the directions of the strongest spoofed signals. This approach may provide enough reduction in the effective jamming power to enable detection of the authentic signals. This technique should work particularly well if the spoofing signals all come from a common direction.

25.5 Testing of Defenses

It is important that the victim receiver’s ADC have a sufficient number of bits to pass the authentic signals with sufficient resolution after the AGC has adjusted the input power to avoid saturating the ADC due to the high power of the spoofed signals. If the effective jammer power is too much higher than the authentic signal power and if the ADC has too few bits, then it may become impossible to recover the authentic signals. Fortunately, a sophisticated spoofer probably will not use an inordinate power advantage for fear of allowing easy detection based on the power test of Section 25.3.3. Once the authentic signals have been found, the victim is faced with two problems. Presumably the victim will have found two signals for each satellite, one spoofed and the other authentic. If there are N such signal pairs, then there will be 2N possible ways of splitting the pairs into the spoofed and authentic sets of N signals. The victim receiver must apply an authentication test to each of these sets in order to determine which one constitutes the authentic set. Authentication methods will vary depending on the available hardware in the victim receiver. If it has an antenna array with DoA capabilities, then each combination can be used to compute the DoA-based spoofing detection statistic γ DoA. The combination that gives the lowest value of the statistic is the best candidate for the authentic set. The pseudorange residuals test of Section 25.3.2 and Eq. (25.8) can also be applied to the question of which signals are authentic. Presumably only two combinations will produce a very low optimal cost in the solution to the problem in Eq. (25.8). One combination will be the spoofed set, and the other combination will be the non-spoofed set. If the receiver has already determined that several of the signals in one combination are spoofed signals, then it can use this information in order to decide between the two sets. It is possible that there will be just one detected signal for several of the GNSS satellites. This one signal may be a spoofed version, or it may be authentic. In this case, the combinations that must be tried involve including or not including this signal in a given set rather than including one of two versions of this signal. It is likely possible to combine the DoA fit test and the pseudorange fit test to develop an improved authentication test. This would be a good topic for further work. There may be other practical ways to authenticate reacquired signals. One might consider the shape of the correlation function. Perhaps the spoofed signals would have sharper or more rounded shapes than the authentic correlation peaks. Alternatively, the victim receiver could execute a movement that the spoofer might find hard to track and emulate in its signals. Only the authentic signals would correctly respond to such purposeful position dithering. This problem of developing additional

authentication strategies is another good topic for further work. There could be situations in which it is impossible to recover and authenticate four or more GNSS signals. The victim receiver would have to give up at that point and seek other means of dealing with its loss of GNSS PNT information.

25.5

Testing of Defenses

Any proposed spoofing defense needs to be tested against a set of spoofing attacks. The ideal tests would be against a sophisticated receiver-spoofer that was broadcasting its false signals over the air, as in [3, 4]. Such tests are difficult to conduct because of prohibitions against broadcast in protected navigation RF bands. An alternative is to connect the spoofer to the RF frontend of a receiver via a signal combiner that is placed downstream of the victim antenna and upstream of the front-end. This configuration is legal because the spoofer never actually broadcasts its signals over the air. This is the method that was used in [50]. This method suffices to test certain types of defenses, but it is not appropriate for other types of defenses. In particular, DoA-based techniques and coupled GNSS/INS techniques cannot be tested in this manner. Some high-end GNSS signal simulators provide the capability of simulating a receiver-spoofer attack against the simulated authentic signals. Such simulators can be used to test the same types of defenses that can be tested by connecting a receiver-spoofer between the receiver antenna and the RF front-end. DoA spoofing detection can be tested if the spoofer and the victim receiver are both placed in an anechoic chamber. A signal simulator or a repeater from an outdoor antenna can be used to generate spoofer signals that are broadcast over the air within the chamber. The chamber’s shielding prevents illegal leakage of the signals into the open air. Single-direction spoofing DoA geometry can be easily reproduced in a chamber, which ensures that the DoA test is valid. This is the first test technique that was used in [57]. If a receiver-spoofer is unavailable, then one can use the recorded data in the Texas Spoofing Test Battery [75, 76]. These data can be replayed through a special system that produces RF signals which are based on recordings of both authentic signals and spoofer signals. The output of the replay system is hooked to the receiver in place of an antenna. Similar to wire-based combining of the spoofer signal, this technique cannot be used to evaluate defenses that employ DoA measurements or GNSS/INS coupling.

677

678

25 Civilian GNSS Spoofing, Detection, and Recovery

References

14 L. Scott (2003) “Anti-Spoofing and Authenticated Signal

1 J. Warner and R. Johnston. (2003) A Simple Demonstration

2

3

4

5

6

7

8

9

10

10

12 13

that the Global Positioning System (GPS) Is Vulnerable to Spoofing. Los Alamos National Lab. [Online]. Available: http://permalink.lanl.gov/object/tr?what=info:lanl-repo/ lareport/LA-UR-03-2384 T.E. Humphreys, B.M. Ledvina, M.L. Psiaki, B.W. O’Hanlon, and P.M. Kintner, Jr. (2008) “Assessing the spoofing threat: Development of a portable GPS civilian spoofer,” in Proc. ION GNSS, Savannah, GA, pp. 2314–2325. A.J. Kerns, D.P. Shepard, J.A. Bhatti, and T.E. Humphreys (2014) “Unmanned Aircraft Capture and Control Via GPS Spoofing,” Journal of Field Robotics, vol. 31, no. 4, pp. 617–636. J. Bhatti and T. Humphreys (2017) “Hostile Control of Ships via False GPS Signals: Demonstration and Detection,” Navigation, vol. 64, no. 1, pp. 51–66. A. Rawnsley (2011, Dec.) “Iran’s Alleged Drone Hack: Tough, but Possible,” http://www.wired.com/ dangerroom/2011/12/iran-drone-hack-gps. Anon. (2017, June) 2017-005A-GPS Interference-Black Sea. Maritime Administration, U.S. DoT. [Online]. Available: https://www.marad.dot.gov/msci/alert/2017/2017-005agps-interference-black-sea/ D. Goward. (2017, July) Mass GPS Spoofing Attack in the Black Sea? – Maritime Executive. Resilient Navigation & Timing Foundation. [Online]. Available: https://rntfnd. org/2017/07/12/mass-gps-spoofing-attack-in-the-blacksea-maritime-executive/ S. Goff. (2017, July) Reports of Mass GPS Spoofing Attack in the Black Sea Strengthen Calls for PNT Backup. Inside GNSS. [Online]. Available: http://www.insidegnss.com/ node/5555 Ajinkya. (2016, Nov.) How to Play Pokemon GO without Moving in Android (No Root). Devs-Lab. [Online]. Available: https://devs-lab.com/how-to-play-pokemon-gowithout-moving-no-root-required.html Anon. (2017, Feb.) In 2017, GPS Spoofing is the Real Bane of Pokémon GO. Go Hub. [Online]. Available: https:// pokemongohub.net/post/featured/2017-gps-spoofing-realbane-pokemon-go/ Anon. (2017, Mar.) Android Security Update Disables GPS Spoofing in Pokémon GO. Go Hub. [Online]. Available: https://pokemongohub.net/post/breaking-news/android7-1-security-update-disables-gps-spoofing-pokemon-go/ E.L. Key (1995) “Techniques to Counter GPS Spoofing,” Internal Memorandum, MITRE Corporation. John A. Volpe National Transportation Systems Center (2001) “Vulnerability Assessment of the Transportation Infrastructure Relying on the Global Positioning System.”

15 16

17

18 19

20 21

22 23

24

25

26

27

28

Architectures for Civil Navigation Systems,” in Proc. ION GPS/GNSS, Portland, OR, pp. 1543–1552. ——,. (2007, July) “Expert Advice: Location Assurance,” GPS World, vol. 18, no. 7, pp. 14–18. T.E. Humphreys, P.M. Kintner, Jr., M.L. Psiaki, B.M. Ledvina, and B.W. O’Hanlon (2009, Jan.) “Assessing the Spoofing Threat,” GPS World, vol. 20, no. 1, pp. 28–38. A. Jafarnia-Jahromi, A. Broumandan, J. Nielsen, and G. Lachapelle (2012, July) “GPS Vulnerability to Spoofing Threats and a Review of Antispoofing Techniques,” International Journal of Navigation and Observation, vol. 2012, no. 127072, pp. 1–16. C. Günther (2014, Fall) “A Survey of Spoofing and CounterMeasures,” Navigation, vol. 61, no. 3, pp. 159–177, M.L. Psiaki and T.E. Humphreys (2016, June) “GNSS Spoofing and Detection,” Proc. IEEE, vol. 104, no. 6, pp. 1258–1270. T. Ebinuma. (2015) GPS-SDR-SIM. GitHub. [Online]. Available: https://github.com/osqzss/gps-sdr-sim Anon. (2017) bladeRF – the USB 3.0 Superspeed Software Defined Radio. Nuand, LLC. [Online]. Available: http://nuand.com/ ——,. (2017) Products. Ettus Research. [Online]. Available: https://www.ettus.com/ ——,. (2017) u-blox 8/u-blox M8 Receiver Description. u-blox. [Online]. Available: https://www.u-blox.com/sites/ default/files/products/documents/u-blox8M8_ReceiverDescrProtSpec_(UBX-13003221)_Public.pdf ——,. (2017, June) GPS Spoofing: A Growing Problem for Uber. SolidDriver. [Online]. Available: http://soliddriver. com/GPS-Spoofing-A-Growing-Problem-for-Uber ——,. (2017) Positioning, Navigation, and Timing Solutions: Professional Equipment and Services for all your GPS/GNSS Testing Needs. Spirent Communications. [Online]. Available: https://www.spirent.com/Solutions/ Position-Navigation-Timing M.L. Psiaki, B.W. O’Hanlon, S.P. Powell, J.A. Bhatti, K.D. Wesson, T.E. Humphreys, and A. Schofield (2014) “GNSS Spoofing Detection using Two-Antenna Differential Carrier Phase,” in Proc. ION GNSS, Tampa, FL, pp. 2776–2800. M. Nicola, L. Musumeci, M. Pini, M. Fantino, and P. Mulassano (2010, Oct.) “Design of a GNSS Spoofing Device Based on a GPS/Galileo Software Receiver for the Development of Robust Countermeasures,” in Proc. ENC GNSS 2010, Braunschweig, Germany. O. Pozzobon, C. Sarto, A. Dalla Chiara, A. Pozzobon, G. Gamba, M. Crisci, and R. Ioannides (2012) “Status of Signal Authentication Activities within the GNSS Authentication and User Protection System Simulator (GAUPSS) Project,” in Proc. ION GNSS, Nashville, TN, pp. 2894–2900.

References

29 A.J. Kerns, K.D. Wesson, and T.E. Humphreys (2014, May)

42 P.F. Swaszek, S.A. Pratz, B.N. Arocho, K.C. Seals, and R.J.

“A Blueprint for Civil GPS Navigation Message Authentication,” in Proc. IEEE/ION PLANS Meeting, Monterey, CA. T.E. Humphreys (2013) “Detection Strategy for Cryptographic GNSS Anti-Spoofing,” IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 2, pp. 1073–1090. P. Walker, V. Rijmen, I. Fernández-Hernández, L. Bogaardt, G. Seco-Granados, J. Simón, D. Calle, and O. Pozzobon (2015) “Galileo Open Service Authentication: A Complete Service Design and Provision Analysis,” in Proc. ION GNSS, Tampa, FL, pp. 3383–3396. R. Behar (2018, Aug.) Pokémon GO is Locking out Users after Scanning Internal Storage for Evidence of Rooting. Android Police. [Online]. Available: https://www. androidpolice.com/2018/08/20/pokemon-go-updatelocks-users-suspects-rooted-phones-digging-internalstorage/ M. Pini, M. Fantino, A. Cavaleri, S. Ugazio, and L. Lo Presti (2011) “Signal Quality Monitoring Applied to Spoofing Detection,” in Proc. ION GNSS, Portland, Oregon, pp. 1888–1896. F. Dovis, X. Chen, A. Cavaleri, K. Ali, and M. Pini (2011, Sept.) “Detection of Spoofing Threats by Means of Signal Parameters Estimation,” in Proc. ION GNSS, Portland, Oregon, pp. 416–421. D.M. Akos (2012) “Who’s Afraid of the Spoofer? GPS/GNSS Spoofing Detection via Automatic Gain Control (AGC),” Navigation, vol. 59, no. 4, pp. 281–290. M. Mosavi, Z. Nasrpooya, and M. Moazedi (2016, July) “Advanced Anti-Spoofing Methods in Tracking Loop,” Journal of Navigation, vol. 69, no. 4, pp. 883–904. E.G. Manfredini and F. Dovis (2016, Dec.) “On the Use of a Feedback Tracking Architecture for Satellite Navigation Spoofing Detection,” Sensors, vol. 16, no. 12. E.G. Manfredini, D.M. Akos, Y.-H. Chen, S. Lo, T. Walter, and P. Enge (2018) “Effective GPS Spoofing Detection Utilizing Metrics from Commercial Receivers,” in Proc. ION International Technical Meeting, Reston, VA, pp. 672–689. K.D. Wesson, J.N. Gross, T.E. Humphreys, and B.L. Evans (2018) “GNSS Signal Authentication via Power and Distortion Monitoring,” IEEE Transactions on Aerospace and Electronic Systems. A. Jafarnia-Jahromi, T. Lin, A. Broumandan, J. Nielsen, and G. Lachapelle (2012, Jan.) “Detection and Mitigation of Spoofing Attacks on a Vector-Based Tracking GPS Receiver,” in Proc. ION National Technical Meeting, Newport Beach, California, pp. 790–800. S. Khanafseh, N. Roshan, S. Langel, F.-C. Chan, M. Joerger, and B. Pervan (2014) “GPS Spoofing Detection using RAIM with INS Coupling,” in Proc. IEEE/ION PLANS Meeting. IEEE, pp. 1232–1239.

Hartnett (2014, Sept.) “GNSS Spoof Detection Using Shipboard IMU Measurements,” in Proc. ION GNSS+, Tampa, Florida, pp. 745–758. S. Manickam and K. O’Keefe (2016, Sept.) “Using Tactical and MEMS Grade INS to Protect Against GNSS Spoofing in Automotive Applications,” in Proc. ION GNSS+, Portland, Oregon, pp. 2991–3001. C. Tanil, S. Khanafseh, and B. Pervan (2016, Sept.) “An INS Monitor Against GNSS Spoofing Attacks During GBAS and SBAS-Assisted Aircraft Landing Approaches,” in Proc. ION GNSS+, Portland, Oregon, pp. 2981–2990. S. Lo, Y.H. Chen, T. Reid, A. Perkins, T. Walter, and P. Enge (2017, May) “The Benefits of Low Cost Accelerometers for GNSS Anti-Spoofing,” in Proc. ION 2017 Pacific PNT Meeting, Honolulu, Hawaii, pp. 775–796. C. Tanil, S. Khanafseh, M. Joerger, and B. Pervan (2018, Feb.) “An INS Monitor to Detect GNSS Spoofers Capable of Tracking Vehicle Position,” IEEE Trans. on Aerospace and Electronic Systems, vol. 54, no. 1, pp. 131–143. Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan (2001) Estimation with Applications to Tracking and Navigation. New York: J. Wiley & Sons. P. Levin, D. De Lorenzo, P. Enge, and S. Lo (2011, June) “Authenticating a Signal Based on an Unknown Component Thereof,” U.S. Patent No. 7,969,354 B2. M.L. Psiaki, B.W. O’Hanlon, J.A. Bhatti, D.P. Shepard, and T.E. Humphreys (2011) “Civilian GPS Spoofing Detection based on Dual-Receiver Correlation of Military Signals,” in Proc. ION GNSS, Portland, Oregon, pp. 2619–2645. B.W. O’Hanlon, M.L. Psiaki, J.A. Bhatti, D.P. Shepard, and T.E. Humphreys (2013) “Real-Time GPS Spoofing Detection via Correlation of Encrypted Signals,” Navigation, vol. 60, no. 4, pp. 267–278. M.L. Psiaki, B.W. O’Hanlon, J.A. Bhatti, D.P. Shepard, and T.E. Humphreys (2013) “GPS Spoofing Detection via DualReceiver Correlation of Military Signals,” IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 4, pp. 2250–2267. S. Bhamdipati, T.Y. Mina, and G.X. Gao (2018, April), “GPS Time Authentication against Spoofing via a Network of Receivers for Power Systems,” in Proc. IEEE/ION PLANS Meeting, Monterey, California, pp. 1485–1491. Anon. (2017, Feb.) Commission Implementing Decision (EU) 2017/224. Official Journal of the European Union [Online]. Available: http://eur-lex.europa.eu/legal-content/ EN/TXT/PDF/?uri=CELEX:32017D0224&from=EN D. Margaria, G. Marucco, and M. Nicola (2016, April) “A First-of-a-Kind Spoofing Detection Demonstrator Exploiting Future Galileo E1 OS Authentication,” in Proc. IEEE/ION PLANS Meeting, Savannah, Georgia, pp. 442–450.

30

31

32

33

34

35

36

37

38

39

40

41

43

44

45

46

47

48

49

50

51

52

53

54

679

680

25 Civilian GNSS Spoofing, Detection, and Recovery

55 K. Wesson, M. Rothlisberger, and T. Humphreys (2012,

56

57

58

59

60

61

62

63

64

65

Fall) “Practical Cryptographic Civil GPS Signal Authentication,” Navigation, vol. 59, no. 3, pp. 177–193. M. Trinkle, Z. Zhang, H. Li, and A. Dimitrovski (2012, Sept.) “GPS Anti-Spoofing Techniques for Smart Grid Applications,” in Proc. ION GNSS, Nashville, Tennessee, pp. 1270–1278. M.L. Psiaki, S.P. Powell, and B.W. O’Hanlon (2013) “GNSS Spoofing Detection Using High-Frequency Antenna Motion and Carrier-Phase Data,” in Proc. ION GNSS, Nashville, Tennessee, pp. 2949–2991. A. Konovaltsev, M. Cuntz, C. Haettich, and M. Meurer (2013) “Autonomous Spoofing Detection and Mitigation in a GNSS Receiver with an Adaptive Antenna Array,” in Proc. ION GNSS+, Nashville, Tennessee, pp. 2937–2948. T. Bitner, S. Preston, and D. Bevly (2015, Jan.) “Multipath and Spoofing Detection Using Angle of Arrival in a MultiAntenna System,” in Proc. ION National Technical Meeting, Dana Point, California, pp. 822–832. D. Borio and C. Gioia (2015, Sept.) “A Dual-Antenna Spoofing Detection System Using GNSS Commercial Receivers,” in Proc. ION GNSS+, Tampa, Florida, pp. 325–330. M. Appel, A. Konovaltsev, and M. Meurer (2015, Sept.) “Robust Spoofing Detection and Mitigation based on Direction of Arrival Estimat ion,” in Proc. ION GNSS+, Tampa, Florida, pp. 3335–3344. S.-H. Seo, G.-I. Jee, B.-H. Lee, S.-H. Im, and K.-S. Kim (2017, Sept.) “Hypothesis Test for Spoofing Signal Identification using Variance of Tangent Angle of Baseline Vector Components,” in Proc. ION GNSS+, Portland, Oregon, pp. 1229–1240. A. Broumandan and J.T. Curran (2017, Nov.) “GNSS Spoofing Detection in Covered Spoofing Attack using Antenna A rray,” in Proc. International Technical Symposium on Navigation and Timing, Toulouse, France,. S. Zorn, T. Bamberg, and M. Meurer (2018, Jan.) “Accurate Position and Attitude Determination in a Jammed or Spoofed Environment Using an Uncalibrated MultiAntenna-System,” in Proc. ION National Technical Meeting, Reston, Virginia, pp. 690–702. Y. Hu, S. Bian, B. Li, and L. Zhou (2018, April) “A Novel Array-Based Spoofing and Jamming Suppression Method

66

67

68 69

70

71

72

73

74

75

76

for GNSS Receiver,” IEEE Sensors Journal, vol. 18, no. 7, pp. 2952–2958. Y. Hu, S. Bian, B. Ji, and J. Li (2018) “GNSS Spoofing Detection Technique Using Fraction Parts of DoubleDifference Carrier Phases,” Journal of Navigation, pp. 1–19. M. Niestroj, M. Brachvogel, S. Zorn, and M. Meurer (2018, Sept.) “Estimation of Antenna Array Manifolds based on Sparse Measurements,” in Proc. ION GNSS+, Miami, Florida, pp. 4004–4011. J. Wertz, Ed. (1978) Spacecraft Attitude Determination and Control. Boston: D. Reidel Pub. Co. E. McMilin, Y.-H. Chen, D.S. De Lorenzo, S. Lo, D. Akos, and P. Enge (2015, Sept.) “Field Test Validation of Single-Element Antenna with Anti-Jam and Spoof Detection,” in Proc. ION GNSS+, Tampa, Florida, pp. 3314–3324. E. Axell, M. Alexandersson, and T. Lindgren (2015, June) “Results on GNSS Meaconing Detection with Multiple COTS Receivers,” in International Conf. on Location and GNSS (ICL-GNSS), Gothenburg, Sweden. Z. Zhang and X. Zhan (2016) “GNSS Spoofing Network Monitoring Based on Differential Pseudorange,” Sensors, vol. 16, no. 10. K. Jansen, M. Schafer, D. Moser, V. Lenders, C. Popper, and J. Schmitt (2018, May) “Crowd-GPS-Sec: Leveraging Crowdsourcing to Detect and Localize GPS Spoofing Attacks,” in IEEE Symposium on Security and Privacy (SP2018), San Francisco, California, pp. 189–202. F.A. Milaat and H. Liu (2018, June) “Decentralized Detection of GPS Spoofing in Vehicular Ad Hoc Networks,” IEEE Communications Letters, vol. 22, no. 6, pp. 1256–1259. L. Strizic, D.M. Akos, and S. Lo (2018, Jan.) “Crowdsourcing GNSS Jammer Detection and Localization,” in Proc. ION International Technical Meeting, Reston, Virginia, pp. 626–641. T.E. Humphreys, J.A. Bhatti, D.P. Shepard, and K.D. Wesson (2012) “The Texas Spoofing Test Battery: Toward a Standard for Evaluating GPS Signal Authentication Techniques,” in Proc. ION GNSS, Nashville, Tennessee, pp. 3569–3583. UT Radionavigation Laboratory. (2014, July) Texas Spoofing Test Battery (TEXBAT). Version 1.1. [Online]. Available: http://radionavlab.ae.utexas.edu/datastore/texbat/

681

26 GNSS Receiver Antennas and Antenna Array Signal Processing Andrew O’Brien, Chi-Chih Chen, and Inder J. Gupta The Ohio State University, United States

An antenna is one of the primary components of all GNSS receiver systems. Its performance and characteristics play critical roles in driving the received signal quality as well as relating the receiver’s position solution to a precise point in physical space. A testament to the importance of antennas in the GNSS community is the sheer variety of antennas that are available for different navigation, surveying‚ and timing applications. For receiver system designers and their users, it is essential to understand how a particular antenna could affect a specific GNSS receiver application. It is also important to be familiar with antennas that offer special capabilities. This applies to both simple, single-element antennas as well as more advanced antenna arrays, which have found increasing utility in the state-of-the-art GNSS receiver systems. The goal of this chapter is to provide an understanding of the key features of modern GNSS receiver antennas and antenna arrays. The first half of the chapter is devoted to single-element antennas. The first section begins with a review of important antenna concepts and terminology. Next, the reader is shown how an antenna can be modeled as a simple direction-dependent filter, which provides a convenient and accurate means of understanding how an antenna will affect a GNSS receiver’s pseudorange and phase measurements. This is followed by a survey of different GNSS antenna types used in modern practice, and the motivations behind their use in different applications will be discussed. The second half of this chapter is devoted to multielement antenna arrays. A review of important antenna array design parameters is provided along with a discussion of how antenna arrays are used in GNSS receiver systems. The final sections address a variety of array signal processing techniques used to provide enhanced capabilities to GNSS receivers.

26.1 Overview of Antenna Concepts and Terminology Figure 26.1 shows a high-level diagram of how an antenna fits in with other important components of a GNSS receiver system. At the most fundamental level, an antenna is the part of the system designed to radiate or to receive electromagnetic waves. In many applications, the low-noise amplifier (LNA) and passband filtering is moved into the antenna itself and becomes part of the physical antenna assembly. These antennas are called active antennas. This allows the antenna to be connected to the receiver using long cables that would otherwise create attenuation and degrade performance. Passive antennas do not have these active components, or these components are a part of the receiver front-end, and the cable length to the receiver is kept very small. It should also be noted that the passive antennas encountered in common practice are reciprocal antennas. That is, their behavior is identical whether they are transmitting or receiving. Although GNSS antennas are only used to receive signals, one commonly encounters antenna specifications that discuss GNSS antenna radiation. This wording is true even for active GNSS antennas, where the components in an active GNSS antenna would prevent it from actually being used for transmission. The most important parameter for quantifying the performance of an antenna is its gain, G(θ, ϕ), which is the ratio of the signal intensity (received at the antenna terminal) in a given direction (θ, ϕ) to the signal intensity that would be received if the antenna were isotropic. An isotropic antenna is a hypothetical, ideal antenna that receives or radiates its power uniformly in all directions at all polarizations. An isotropic antenna is often used as a reference antenna from which to define the antenna gain, among other things. Since incident GNSS satellite signals are weak, it is important for a GNSS antenna to have enough antenna

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c26.3d

681

15/12/2020 5:48:22 PM

682

26 GNSS Receiver Antennas and Antenna Array Signal Processing

Passive Antenna

Active Antenna

Filters & LNA

Front End

GNSS Receiver

Cable (RF & Power)

Cable (RF)

Front End

GNSS Receiver

Figure 26.1 Block diagram of receiver system components showing a typical (left) active antenna system and (right) passive antenna system.

θ

0 –30

5.00

30

0.00 –5.00

–60

60

–10.00 –15.00 –20.00 90

–90

–120

0

20

120

Antenna Gain (dB)

40 (mm)

150

–150 –180

Figure 26.2

Example simulated gain pattern (right-hand circular polarization) of a simple GPS L1 patch antenna.

gain in order to ensure a sufficiently high signal-to-noise ratio (SNR) prior to demodulation and decoding. An antenna pattern may refer to the angular distribution of any quantity that characterizes the antenna; however, when used in performance specifications, the term typically refers to the antenna’s gain pattern. When no direction is specified, the gain of an antenna is understood to refer to the maximum of the gain pattern. Figure 26.2 shows the simulated gain pattern of a simple GPS patch antenna. The antenna pattern typically has a preferred direction, and the lobe surrounding the maximum radiated field region is called the main lobe‚ while the other features are called sidelobes. For a good antenna, the sidelobe level is much lower than the main lobe level. The angular extent of the main lobe defines the antenna beamwidth. Conventionally, beamwidth refers to the half-power beamwidth, which is the angular size of the region over which the

c26.3d

682

received signal gain drops by a factor of two relative to the peak gain. In some cases, beamwidth might be redefined to mean the region over with a specified minimum gain level is achieved. The desired beamwidth of an antenna depends on the application. Typically, GNSS receivers are meant to receive signals arriving from satellites distributed over the entire sky, and GNSS antennas should have very wide beamwidths. In other cases, such as handheld GNSS receivers, the antenna orientation is arbitrary, and antennas are designed to be omnidirectional, making the concept of a beamwidth less relevant. The antenna terminal is the part of the antenna used to connect it to a receiver. Most commonly, for antennas that are not integrated with a receiver, this terminal would be a TNC, BNC, F-type‚ or SMA port that a cable connects to. One must keep in mind that this connection is a transmission line, and the antenna presents a particular input

15/12/2020 5:48:22 PM

26.1 Overview of Antenna Concepts and Terminology

683

0.00 Antenna S11 (dB) –5.00 m1

m2

–10.00

–15.00

–20.00

Name m1

X Y 1.5605 –9.5055

m2 m3

1.5895 –10.0307 1.5760 –24.4400

–25.00 1.50

1.52

m3 1.55

1.58

1.60

1.63

1.65

Freq [GHz]

Figure 26.3 Example simulated S11 versus frequency in the zenith direction for a simple GPS L1 patch antenna.

impedance that must be matched to the cable and the rest of the receiver system. If the antenna input impedance is poorly matched to the cable and receiver system, then there will be a loss of received power. The realized gain of an antenna, GR, accounts for the mismatch between the antenna and the rest of the receiver: GR θ, ϕ = M G θ, ϕ

26 1

Here, M is the impedance mismatch factor. If we consider an antenna that is transmitting, the impedance mismatch factor is defined as the ratio of the power accepted by an antenna to the power incident at the antenna’s terminal. For a receiving antenna, the realized gain relates the incident power to the power of the signal actually delivered to the rest of the receiver system. Therefore, it is the gain value that should be used when calculating a GNSS signal’s received power. The impedance mismatch is commonly represented in terms of an input reflection coefficient, Γ: M = 1− Γ 2

26 2

It is also common to see the impedance matching properties of an antenna specified in terms of the voltage standing wave ratio (VSWR): VSWR =

1+ Γ 1− Γ

26 3

The reflection coefficient is also directly related to the return loss of the antenna. In terminology used for microwave component characterization, the return loss is often determined by an S11 measurement, which characterizes the signal returned from port 1 for a signal input to port 1.

c26.3d

683

An example simulated S11 measurement for a simple GPS antenna is shown in Figure 26.3. This is a measurement of the amount of signal power that is returned from the antenna terminal when a signal has been input into it. Since we expect the antenna to radiate this input power away, S11 should be very low. This measurement cannot quantify the power actually radiated by the antenna, since the power could have been lost to other factors in the antenna. Nonetheless, it is a useful metric for checking antenna behavior. For a well-designed antenna, S11 should be quite small (less than −15 dB) and should typically not exceed −10 dB. Here, we have assumed the antenna is passive and reciprocal; an S11 measurement such as this cannot be meaningfully performed with an active antenna. It is also common to further decompose the antenna’s absolute gain into a product of two components: the antenna radiation efficiency η and the antenna directivity pattern D(θ, ϕ): G θ, ϕ = ηD θ, ϕ ,

26 4

For a passive reciprocal antenna, the reception efficiency is equivalent to the radiation efficiency. The antenna radiation efficiency is defined as the ratio of the total power radiated by an antenna to the net power accepted by the antenna from its terminal. No antenna perfectly radiates all the energy it accepts from the feed cable. Power is lost due to conversion of electromagnetic energy into thermal energy and is often attributed to electrical conduction loss in conductors and resistors. Loss may also be attributed to material (i.e. dielectric or ferromagnetic) absorption. The directivity pattern is the ratio of the radiation intensity in

15/12/2020 5:48:23 PM

684

26 GNSS Receiver Antennas and Antenna Array Signal Processing

a given direction from the antenna to the radiation intensity integrated over all directions. When no direction is specified, it is implied that the directivity of the antenna is the maximum value of the directivity pattern. Though we have not explicitly denoted it, all of the antenna parameters defined above (gain, beamwidth, S11, etc., …) are frequency dependent. The antenna bandwidth is the frequency range over which the antenna offers sufficient performance for a particular application. An antenna might be designed to operate over a single band or multiple, separate frequency bands; as such, bandwidth would be specified separately for each band. For commercial GNSS receivers that receive a single GNSS signal, the bandwidth could be as small as 2 MHz, whereas, for GNSS receivers using all available satellite constellations, the bandwidth could be as large as 500 MHz. For well-designed antennas, the gain will be relatively flat over the frequency range of interest. Often, flatness characteristics will be specified to ensure that signal distortion will be minimized. Although antennas are designed for particular frequencies, this does not mean they necessarily offer sufficient rejection of signals at other frequencies. Antennas exhibit out-of-band rejection that does not meet the level necessary for protection of GNSS receiver applications. Hence, antennas are almost always combined with additional passband filters. The passband filter can be integrated into the antenna, inserted as a discrete connectorized component between the antenna and receiver, or be part of the receiver frontend electronics. For active antennas, power is typically provided by the receiver as direct current (DC) over the same RF cable over which GNSS signals are received. One should ensure compatibility between the power requirements of the antenna and the power supply specifications of the receiver. If one uses an active antenna with a receiver that does not provide power for it, the antenna will not function correctly and no signal will reach the GNSS receiver. In this case, one can use a bias-T to provide external power to the antenna. If one uses a passive antenna with a receiver that provides DC power, one must be careful to ensure the passive antenna does not short DC. In this case, a capacitor can be used to block DC and allow the system to operate. The gain of an active antenna is commonly specified as the sum of both the passive antenna component and the gain of the integrated LNA. For an active antenna, the gain must be understood in relation to the amount of thermal noise introduced by the LNA. In this case, the gain-totemperature ratio (G/T) is normally used as the performance measure. The total gain of an active antenna is given by G θ, ϕ = Ga θ, ϕ + G f + Gb + Gl ,

c26.3d

684

26 5

where all quantities are in dB. Ga is the gain of the antenna, Gf is the gain of the feed line, Gb is the gain of bias-T, and Gl is the gain of the LNA. Note that Gf and Gb are negative quantities. The total temperature of an active antenna is given by T = Ta +

F f −1 Fb − 1 Fl − 1 + + To, G f Gb G f Gb Gl Gf 26 6

where Ta is the antenna temperature. Ff, Fb, and Fl are the noise figures for the filter, bias-T, and LNA, respectively. In the above equation, To is the ambient temperature (290 K in most applications). Higher G/T corresponds to better active antenna performance. In this section, we provided only a brief overview of the most important antenna terminology. Definitions followed from IEEE Standard Definitions of Terms for Antennas (145-1983). The reader is referred to other sources [1] and [2] for more detailed information. We note that antenna polarization has not been explicitly mentioned in the above discussion. Since GNSS satellite signals are right-hand circularly polarized (RHCP), it is typically implied that the antenna parameters are quantified for RHCP polarization unless otherwise specified. Polarization and its important effects are discussed later in this chapter.

26.2 Effects of Antennas on GNSS Signals One can imagine a hypothetical, ideal GNSS antenna that occupies a single infinitesimal point in space. In this case, all of the delay and phase measurements made by a GNSS receiver using this ideal antenna would be geometrically related to this point in a perfect manner. In fact, most mathematical models of GNSS measurements treat antennas as a perfect point. Unfortunately, real antennas do not behave as an infinitesimal point in space; rather, real antennas alter the received GNSS signals in significant ways. In this section, we will discuss how to model these effects on GNSS signals.

26.2.1

Modeling an Antenna as a Filter

To begin, we define a coordinate system for the antenna called the antenna reference frame (ARF). The origin of the ARF is a point commonly referred to as the antenna reference point (ARP). The ARF and ARP are not intrinsic electromagnetic properties of the antenna but instead are arbitrary and often chosen to be an easily identifiable location or marking on the exterior of the antenna. As we will see, the reference point plays an important role in connecting GNSS receiver measurements to the physical world.

15/12/2020 5:48:24 PM

26.2 Effects of Antennas on GNSS Signals

The behavior of a linear device or system is often characterized by its frequency response, H(f), which is the ratio of the magnitude and phase of the output signal relative to that of the input. In the frequency domain, the relation between an input signal X(f) and output signal Y(f) is simply Y f =H f X f

26 7

An antenna also acts as a linear system with respect to electromagnetic fields and can be characterized by a complex-valued antenna response, Ap(θ, ϕ, f). Y f = Ap θ, ϕ, f X f

Magnitude (dB)

Antenna Reference Frame

Reference Point

2

26 9

A GNSS signal is modulated onto the magnitude and phase of each plane wave, so an antenna can be modeled as a direction-dependent linear time-invariant (LTI) filter acting on the GNSS signal. That is, if x(t) is the GNSS signal after it has reached the geometric point in space located at the ARP, then the output signal y(t) after going through the antenna is completely characterized by yt =

26 8

For an antenna, the input to the system is an incident electromagnetic plane wave that is characterized by an incident signal direction (θ, ϕ) and frequency f. A given antenna response only applies to waves incident with a certain type of polarization, which we will label p. A plane wave occupies all of space with a phase that varies based on location, so we will define the input to our system X (f) as the magnitude and phase of the electric field at the ARP location. The output Y(f) is the corresponding voltage produced on the antenna terminal when the antenna is in the presence of this incident field. In this way, the antenna response is defined as the magnitude and phase of the antenna output signal relative to the signal that would have been received by an isotropic antenna located at the reference point. Note that the realized gain GR of a GNSS antenna corresponds to the magnitude squared of the RHCP component of the antenna response, AR,

θ

GR θ, ϕ, f = AR θ, ϕ, f

685

AR θ, ϕ, f X f e j2πft df

26 10

This is a simple and accurate way to conceptualize what an antenna is doing to a GNSS signal, and such response functions are routinely provided by an antenna measurement or a computational antenna simulation software. It is important to understand the a particular response is relative to the ARP and corresponding coordinate system, although the reference can be shifted to a new location by applying a transform to the antenna response. Figure 26.4 shows an example antenna response for a simple GPS patch antenna. The magnitude and phase of the antenna response is shown over the GPS L1 band for a signal incident from the zenith. Note that the antenna response varies with frequency. Later in this chapter, we will discuss how these variations create directiondependent errors in the GNSS receiver measurements. The RF front-end for a GNSS receiver system contains components – located in the receiver and within active

4.5 4 3.5 3 1560

1565

1570

1575

1580

1585

1590

1580

1585

1590

Freq (MHz) Phase (deg)

20

ϕ X (f)

10 0 –10 1560

Ap(θ, ϕ, f )

Y (f)

1565

1570

1575 Freq (MHz)

Figure 26.4 (Left) Example antenna reference frame and (right) a simulated antenna response versus frequency in the zenith direction for a simple GPS L1 patch antenna.

c26.3d

685

15/12/2020 5:48:24 PM

686

26 GNSS Receiver Antennas and Antenna Array Signal Processing

antennas – including a number of devices such as amplifiers, filters, mixers, limiters, and diodes. Although these components could act nonlinearly, a well-designed frontend maintains a high degree of linearity over the range of signal inputs for the application for which it has been designed. As a result, it is common practice to also model the front-end effects as an LTI filter. In some cases, it might be difficult to delineate what is the antenna. Many GNSS antennas are integrated into other equipment or mounted on complex structures that could encompass entire platforms (i.e. vehicles, ships‚ and aircraft). Many antennas, such as patch antennas, are designed to be placed on large flat metal structures referred to as ground planes. The size and shape of the ground plane (or the platform serving as one) has effects on the antenna performance that cannot be separated from the antenna itself. The antenna will couple to nearby structures and received fields will scatter, creating platform multipath. For improved accuracy, the effects of the platform should be incorporated into any analysis involving characterization of antenna performance [3]. To model the effects on GNSS signals, the entire platform can be incorporated into the antenna response given in Eq. 26.8. When this is the case, it is referred to as an in situ antenna response, as the antenna has been characterized in the environment for which it is intended to be used. This method can even be extended to environments where the platform varies in time, such as helicopters and other rotorcraft, through the use of linear time-varying (LTV) filters [4].

26.2.2

Effects on GNSS Receiver Measurements

As discussed in the previous section, antennas behave as spatial-temporal filters for GNSS signals. Instead of acting as a perfect point in space, real antennas introduce additional direction-dependent delay and phase shifts into received GNSS signals. This introduces bias errors into carrier-phase and pseudorange measurements made by GNSS receivers and are known as antenna-induced biases. It is only by understanding the effects of these biases that one can understand to which point in space and time a particular GNSS receiver solution actually corresponds. The antenna-induced carrier phase and code delay bias are defined as direction-dependent functions, which we will denote as ϕa(θ, ϕ) and τa(θ, ϕ), respectively. These are the additional phase and delay caused by the antenna for a signal received from a given direction. These biases are different for each GNSS signal type and each GNSS signal frequency band. That is, strictly speaking, they could also be different for signals on the same frequency band with different spectra (i.e. GPS L1 C/A-, P/Y-, and M-coded signals may have different antenna-induced biases);

c26.3d

686

however, for many simple antennas, these differences could be negligible. The biases are always defined as relative to the ARP. That is, if we choose a different ARP, the biases would be different. If one were to correct for these biases by subtracting them from the raw phase and pseudorange measurements, the receiver position and time solution would correspond perfectly to the ARP in physical space. If not corrected, the error introduced into the position and time solution is more complicated. How these biases affect the receiver position and time solution will depend on how the receiver forms a solution using the individual raw measurements – it is not a property of the antenna alone. Therefore, the focus of this section is on how the biases effect raw phase and delay measurements. Conventionally, it has been useful to utilize the concept of an antenna phase center (APC) when one talks about relating a position solution to a particular point in space [5, 6]. Unlike the ARP, which can be chosen arbitrarily, the APC is an inherent property of the antenna. The standard definition of the APC is the point in space that lies at the center of a sphere (whose radius extends into the far field) such that the phase of the antenna’s radiation pattern is effectively constant. The APC is found by only considering the phase over angular regions where the gain is significant, which, for typical GNSS antennas, means the upper hemisphere. The APC represents the best-fit approximation of the antenna carrier-phase biases to a point in space (a point which need not actually be located on the physical antenna itself ). If this approximation is very good for all incident signal angles, the antenna is said to have a stable phase center and the antenna can be treated as if it were a point in space when using the carrier-phase measurements, such as for carrier-phase differential positioning. In some cases, the APC is very closely aligned with the centerline of the antenna, and only a vertical phase center offset need be specified. In other cases, the APC approximation needs to be extended to account for offsets that depend on other factors. There are extensions to the APC concept that allow satellite elevation-angle dependence or general direction dependence. While mostly used for carrier phase, the same concept has also been used to characterize delays. In any case, one should keep in mind that the concept of an APC is an approximation. That is, it is the best fit of the directiondependent phase behavior of an antenna that only applies to certain types of antenna, whereas direct usage of direction-dependent antenna-induced biases provides a general and complete characterization. If a measured or simulated antenna response Ap(f, θ, ϕ) is available, one can easily calculate the antenna-induced biases in the carrier-phase and pseudorange measurements. Let α represent the phase of the RHCP component of the antenna response in radians:

15/12/2020 5:48:24 PM

26.2 Effects of Antennas on GNSS Signals

α θ, ϕ, f = AR θ, ϕ, f

26 11

For a GNSS signal with center frequency fc, the carrierphase bias ϕa of the antenna on that signal is often approximated as the phase of the response the center frequency, and the code delay bias τa is often approximated as the group delay at the center frequency: ϕa θ, ϕ = α θ, ϕ, f c τa θ, ϕ =

1 dα θ, ϕ, f c , df 2π

S f AR θ, ϕ, f e − j2πf τa df ,

τa θ, ϕ = arg max τ

26 13

26 14

S f AR θ, ϕ, f e − j2πfτ df 26 15

While these equations are very accurate in cases where the antenna response is well behaved, they are also an approximation. The tracking loops in GNSS receivers use discriminators to estimate the phase and delay of the signal. A typical delay-lock-loop (DLL) discriminator function is based on assumptions regarding the shape and symmetry of the received GNSS signal’s cross-correlation function [7]. Since the antenna acts as a filter that can introduce general distortion into the signal, the shape of the crosscorrelation function could affect the delay estimate. The expected value for the cross-correlation function between the signal received by the antenna and the one received by an ideal isotropic antenna located at the reference point is given by Rτ =

S f AR θ, ϕ, f e − j2πf τ df ,

26 16

and a more accurate calculation of the antenna-induced biases can account for receiver tracking-loop implementations acting on this cross-correlation function. For example, in a GNSS receiver with an early-minus-late discriminator, the antenna-induced code delay bias will satisfy R τa − τ s = R τ a + τs ,

26 17

where τs is the spacing between the early, prompt, and late correlator taps. While our discussion has focused on usage of the antenna response to calculate antenna-induced biases, in practice

c26.3d

687

one can also use differential GNSS receiver measurements to measure antenna-induced biases and to calibrate GNSS antennas. Extensive work describing these approaches is provided in the following references [8–11]. Finally, it should also be noted that significant variations can exist between antennas of the same model due to mechanical tolerances during fabrication, temperature‚ and aging.

26 12

which are given here in units of radians and seconds, respectively. However, if the antenna response varies appreciably with frequency, these equations are approximations. For more accuracy, one must account for the antenna response over its entire frequency range and power spectral density S(f) of the GNSS signal. In this case, the antenna-induced biases are given by ϕa θ, ϕ =

687

26.2.3

Effects due to Antenna Polarization

If one were to look toward a GNSS satellite and observe the electric field vector at a particular point in space as an incident GNSS signal passed through it, one would observe the electric field vector rotating in a counter-clockwise direction in a plane perpendicular to the direction of propagation. Much like the fingers of your right-hand curl counter-clockwise when your thumb points toward you, we say that the signal transmitted from a GNSS satellite is RHCP. Antennas, like GNSS signals, are also polarized, and this polarization affects both the antenna design as well as GNSS receiver phase measurements in ways that are important to understand. Most GNSS antennas have been designed to receive RHCP signals. Left-hand circular polarized (LHCP) electric fields are orthogonal to RHCP ones, and if the antenna were perfectly designed, then it would not receive any signals that were LHCP. However, real antennas are never perfect‚ and they do receive some LHCP waves. The polarization purity of an antenna in different directions is often quantified by plotting gain pattern of co-polarized and cross-polarized components levels together. For example, Figure 26.5(a) shows the gain of the RHCP and LHCP components of a simple GPS patch antenna on a small ground plane at the L1 center frequency. The figure also includes plots of gain for the horizontal (H) and vertical (V) polarizations. For this figure, the angle of ascension θ varies from behind the ground plane (θ = ± 180 ) to boresight (θ = 0 ), which emphasizes the effects of polarization at low elevation angles. Alternatively, the axial ratio is a commonly used metric to describe the polarization purity of an antenna. The axial ratio of an antenna is the ratio of the major to minor axes of a polarization ellipse, which in our case corresponds to the antenna response AR(θ, ϕ, f) for the RHCP component and the antenna response AL(θ, ϕ, f) for the LHCP component AR θ, ϕ, f =

AR θ, ϕ, f AL θ, ϕ, f AR θ, ϕ, f AL θ, ϕ, f

+1 −1 26 18

and is often specified in dB. Note that for a perfect RHCP antenna, the axial ratio is close to unity. For linearly polarized antenna, the axial ratio is ∞.

15/12/2020 5:48:24 PM

688

26 GNSS Receiver Antennas and Antenna Array Signal Processing

(a)

(b) 10

20

RHCP LHCP H V

5

18 16 Axial Ratio (dB)

Gain (dB)

0 –5 –10 –15 –20

12 10 8 6 4

–25 –30

14

2 –150

–100

–50

0

50

100

150

0

θ (deg)

–150

–100

–50

0

50

100

150

θ (deg)

Figure 26.5 (Left) Example simulated gain pattern plots for four different polarizations and (right) the corresponding axial ratio of a simple GPS L1 patch antenna on a small ground plane.

The response of an antenna is completely characterized given the complex antenna response for two polarizations. Using this information, the response of the antenna to incident signals with any polarization can be calculated. Typically, these two polarizations are provided as a pair of RHCP and LHCP or a pair of horizontal and vertical polarizations. One can use a transformation such as AR θ, ϕ, f =

1 2

AH θ, ϕ, f − jAV θ, ϕ, f

26.2.3.1

26 19 1 AL θ, ϕ, f = 2

AH θ, ϕ, f + jAV θ, ϕ, f 26 20

to convert horizontal (H) and vertical (V) polarization antenna responses into RHCP and LHCP components, and vice versa. It is important to keep in mind that when an incident electromagnetic wave reflects and scatters off of surfaces, its polarization can change. When an RHCP incident wave reflects off a large flat surface, its polarization changes to be LHCP. In this way, antennas that are designed to only receive RHCP signals can provide some degree of multipath suppression. When RHCP waves scatter off more complicated structures with edges and corners, the signal will have arbitrary polarization. Unfortunately, most circular polarized antennas tend to become linearly polarized near the horizon (as in Figure 26.5), which is exactly where the multipath is expected to originate for many GNSS applications. Consequently, geodetic GNSS antennas are specifically designed to improve the rejection of LHCP signals near

c26.3d

688

the horizon. Alternatively, some GNSS antennas have actually been developed that are LHCP, as this offers the best reception of reflected GNSS signals for applications such as reflectometry for GNSS remote sensing. For some handheld or vehicle-mounted GNSS receivers that are used in environments with high multipath and limited line-of-sight to GNSS satellites, linearly polarized antennas are used. Phase Wind-Up due to Polarization

An often-observed phenomenon related to circular polarized GNSS antennas is known as phase wind-up. When a GNSS antenna is rotated, a predictable change in the receiver’s carrier phase of measurements occurs, even if the position of the antenna remains constant. We distinguish two components of this phase wind-up phenomenon: the component caused by the antenna and the component caused by the polarization properties of the signal. The carrier-phase bias introduced by most GNSS antennas exhibits a predictable variation versus the azimuth angle that we refer to as antenna phase wind-up. Figure 26.6(a) shows the carrier-phase bias of a simple GPS L1 RHCP polarized patch antenna. If one were to rotate the antenna azimuthally 360 in a counter-clockwise direction, one would observe the carrier-phase “wind-up” 360 . This behavior is due to the fact that the timeharmonic currents introduced on an antenna by an incident GNSS signal tend to be rotationally symmetric. In this way, physical rotation of the antenna produces a current distribution that is similar to advancing the phase in time. As a result, the phase wind-up behavior extends down to the horizon of circular polarized antennas, and even its

15/12/2020 5:48:25 PM

26.2 Effects of Antennas on GNSS Signals

antenna pattern becomes linear polarized at those angles. Figure 26.6(b) shows the effect of subtracting the azimuth angle from the phase. Unwinding of the phase in this manner reveals more subtle carrier-phase effects of this particular antenna. Carrier-phase wind-up needs to be accounted for in a number of GNSS applications in which phase information is used on a moving receiver. Note that it is a property of the antenna and cannot be universally applied to all GNSS antennas. One important thing to note is that if a signal passes through the zenith, Figure 26.6 indicates that its phase will jump by 180 , but this is not what actually happens. One must also account for phase wind-up due to the orientation of the polarized signal‚ as described next. A second important phenomenon is known as polarization phase wind-up. Unlike azimuthal phase wind-up, which is a property of the antenna, polarization phase wind-up is due the inherent polarization orientation of the incident signal [12]. To convey the effect, it is easiest

689

to consider the case of a rotating antenna. Let us assume there is an incident signal from direction (θ, ϕ), and define a pair of basis vectors in a spherical coordinate system, cos θ cos ϕ θ θ, ϕ =

cos θ sin ϕ , − sin θ

− sin ϕ ϕ θ, ϕ =

cos θ 0

,

26 21 as depicted in Figure 26.7. Next, let us assume that the antenna undergoes a rotation around its reference point. Let the antenna rotation be specified by the rotation operator R( ), which rotates vectors from the original coordinate system into the new prime coordinate system, where the new incident signal direction from the perspective of the antenna is (θ , ϕ ). We have two basis vectors θ θ , ϕ and ϕ θ , ϕ ,

but we also bring along the old basis

vectors by rotating them as well, θ θ, ϕ = R θ θ, ϕ

(a)

(b)

θ

(deg)

(deg)

10

150

0

–10

100

–20 50

–30 –40

0

ϕ

ϕ

–50

θ

–50

–60

–100

–70 –80

–150

–90

Figure 26.6 Example simulated carrier phase over the upper hemisphere for a simple GPS patch antenna at the L1 center frequency (left) before and (right) after removal of azimuthal phase wind-up.

(a)

(b)

z ‸ ϕ′

R

‸ θ′

‸ ϕ′

‸ ϕ

‸ θ′

‸ θ

‸ ϕ (θ′, ϕ′) ψ

y

x

‸ θ (θ′, ϕ′)

Figure 26.7 Diagram of the coordinate system basis vectors of a polarized electromagnetic field before and after rotation of the antenna.

c26.3d

689

15/12/2020 5:48:25 PM

690

26 GNSS Receiver Antennas and Antenna Array Signal Processing

and ϕ θ, ϕ = R ϕ θ, ϕ . These two sets of vectors will be rotated with respect to one another. We can define the amount of rotation by an angle ψ, ψ = tan − 1

θ θ, ϕ

ϕ θ ,ϕ

θ θ, ϕ

θ θ ,ϕ

26 22

which is simply the amount of rotation that occurs along the axis corresponding to the signal direction. In doing so, we will find that the antenna responses for linear polarizations transform in the following ways: AV θ , ϕ = cos ψ AV θ , ϕ + sin ψ AH θ , ϕ

26.3.1

Single-Band GNSS Antennas

The majority of low-cost commercial GNSS receivers operate over a single frequency band. The antennas used with these receivers are small and are narrow bandwidth (2 MHz to 50 MHz). As such, these antenna are the simplest to design and the least expensive. Microstrip patch antennas (MPA) and its variants are the most ubiquitous of all single-band GNSS antennas. The other popular antenna for low-cost receivers is the quadrifilar helix antenna (QHA). The operation and design of these two antenna types are reviewed below.

26 23 AH θ , ϕ = sin ψ AV θ , ϕ + cos ψ AH θ , ϕ 26 24 For certain rotations of the antenna, vertical polarization becomes horizontal and vice versa – as expected. On the other hand, circular polarizations undergo a phase shift proportional to the rotation angle: AR θ , ϕ = AR θ , ϕ ejψ AL θ , ϕ = AL θ , ϕ e

− jψ

26 25 26 26

What this is telling us is that the effect of an antenna on an incident signal cannot be characterized by only its direction (θ, ϕ); instead, there is an additional angle ψ that is related to the orientation of the incident field (or equivalently, the transmitter). Although we have rotated the antenna in this example, the results are the same if the antenna remains fixed and we allow the incident signal direction to change as GNSS satellites move. Fundamentally, the incident field has an orientation that must be accounted for. As indicated in Eq. 26.25, this phase change is not captured in antenna pattern data implicitly, but instead must be captured in the geometric model between the receiver and transmitter. The reader is referred to [13] for more detailed information. In many differential carrier-phase applications with fixed antennas, the act of differencing carrier-phase measurements cancels out these effects, which are often neglected in mathematical measurement models.

26.3

Example GNSS Antennas

This section provides an overview of some of the more popular GNSS antenna types. Due to space limitations, it is not possible to cover the wide variety of available GNSS antennas. For a more thorough discussion, the reader is referred to [13, 14].

c26.3d

690

26.3.1.1

Microstrip Patch Antenna

The basic MPA consists of a metallic conductor that is typically square or circular in shape and is etched on the top surface of a dielectric substrate. In general, the dielectric substrate is a little larger than the metallic conductor. The opposite side (bottom) of the dielectric substrate has copper cladding. Often the antenna is placed over a ground plane that is much larger than the antenna. In that case, the bottom surface becomes part of the ground plane. The antenna is often excited with a coaxial cable where the inner conductor is connected to the top patch and the outer conductor is connected to the ground plane. Alternative feeding techniques are also possible, such as aperturecoupled feeds and proximity probes. There could also be multiple points of excitation. Figure 26.8 shows a typical MPA for the GPS L1 band. The metallic patch and the ground plane form a highly resonant radio-frequency cavity. The energy stored inside the cavity radiates out from the edges of the metallic patch. The resonant frequency of the cavity depends on the shape and size of the metallic patch and the permittivity of the dielectric substrate. In general, increasing the size of the patch lowers the resonant frequency. Increasing the permittivity also lowers the resonant frequency. Thus, by using a substrate with high permittivity, one can reduce the size of an MPA. The thickness of the substrate is strongly related to the bandwidth of the antenna, with larger bandwidths corresponding to thicker substrates. However, increasing the thickness beyond a certain value leads to higher-order modes in the antenna, which is usually undesired. For substrates with high permittivity, this puts a limit on the substrate thickness, and it becomes increasingly difficult to design small MPAs with a large bandwidth [15]. The bandwidth of a patch is about 2%. With advanced designs, this can be increased to 10%. These MPAs use low-permittivity substrates, and thus are large in size (cross section and height). Since MPAs are resonant antennas, their bandwidth is dictated by the return loss (i.e. how well the antenna is matched to the receiver input impedance). An

15/12/2020 5:48:26 PM

26.3 Example GNSS Antennas

691

Z

30 mm m

30

m

24 mm 24 mm

6 mm 2.8 mm Dielectric Constant = 16

Figure 26.8 Example GPS microstrip patch antenna with a single probe feed (Chen et al. [14]). Source: Reproduced with permission of John Wiley & Sons.

MPA, when operating in its fundamental mode, has the greatest gain along boresight direction (perpendicular to the patch), and the gain drops toward the horizon. The boresight gain drops with an increase in the thickness of the dielectric substrate. Low-permittivity substrates are used in better-performing GNSS antennas, but highpermittivity substrates lead to reduced size. For multielement GNSS antenna arrays, patches with highpermittivity substrates are used to make individual elements more compact. To obtain RHCP polarization in MPAs, two feed probes are often used that are located orthogonally at specified distances from the edges of the patch. The probes are connected to a quadrature hybrid, such as a branch-line coupler, in order to obtain an equal-magnitude but 90 phase difference, which leads to RHCP radiation. Sometimes a single asymmetrical (see Figure 26.9) probe feed is placed on a square patch in order to obtain RHCP polarization. In this case, the patch is slightly modified near the corners in order to help generate RHCP polarization. Figure 26.9 shows an example of a very common commercial L1-band GPS antenna design. This design is based on the popular dielectric-loaded patch whose circular polarization is achieved by using two quadrature-phased orthogonal resonant modes that could be excited by employing a corner-cut, offset feed with a rectangularshaped patch [16, 17]. Figure 26.9(b) shows the gain patterns in two orthogonal elevation planes for both RHCP (solid line) and LHCP (dashed line) components, which exhibits excellent gain level and coverage down to 10 elevation angle. The LHCP gain remains low compared to the RHCP gain over the entire sky. Figure 26.9(c) shows the impedance bandwidth based on the −10 dB reflection coefficient criterion to be approximately 29 MHz. Figure 26.9(d) shows the polarization bandwidth based on the RHCP/ LHCP > 10 dB criterion, and it is approximately 15 MHz.

c26.3d

691

26.3.1.2

Quadrifilar Helix Antenna

A QHA, also known as a “volute,” is especially suitable for use in handheld receivers and mobile terminals [18]. It consists of four helical resonant elements wrapped around a cylinder. The four elements (arms) are driven in phase quadrature to produce a broad RHCP beam. A QHA can be fed from the top or at the bottom with the other end either shortened or left open. When it is fed from the top, the bottom end is normally shortened to provide radiation from the top; whereas, when it is fed from the bottom, the top end is left open to provide forward radiation. Its size can also be controlled by using a dielectric material cylinder. Moreover, one can use printed circuit technology to reduce the cost. Two types of QHAs are used with GNSS receivers: self-phasing QHAs and externally phased QHAs. Self-phasing QHAs use a balun (balance to unbalance) approach to feed the four elements. The two adjacent arms are connected to the center conductor of the coaxial cable, whereas the other two adjacent arms are connected to the outer conductor of the coaxial cable. Thus, these two sets of arms have a 180 phase difference. The lengths of the adjacent arms are adjusted to produce another 90 phase difference. The other ends of the four arms of this top-fed QHAs are short-circuited, and, after reflection from the shorted end, the field is radiated from the top. Since a circular polarized signal changes its polarization after reflection, the four arms of this QHA are wound in the left sense. Though it is cost-effective to build a self-phased QHA, its design is little bit more involved. Also, because of the feeding mechanism, it has a smaller bandwidth as compared to an externally phased QHA. In an externally phased QHA, the four arms of the QHA are fed using an external broadband phasing network. It consists of a 180 hybrid ring coupler and two 90 branch-line couplers. This network feeds the four arms with equal amplitude and with a relative phase of 0 , −90 ,

15/12/2020 5:48:26 PM

692

26 GNSS Receiver Antennas and Antenna Array Signal Processing

(a)

(b)

0.00

Gain (dB)

–60

Z

25 mm

–30

30

–5.00

0.00

4 mm X

25 mm

Feed Offset (x)-1.7 mm (y)-1.8 mm

PEC ground plane (70mm × 70mm)

60

–10.00

Gain –10.00 (dB) –15.00

–60

–15.00

ϕ

–120

–20.00

0°

–150

120

90

–150

150

5 10dB

15 MHz

10dB

–5

–15

Gain (dBI)

Reflection Coefficient (dB)

–10

120

–180

0

29 MHz

90°

ϕ

–120

150

(d)

0 –5

60

90 –90

–90

–180

(c)

30

–5.00

–20.00 Y

εr = 20

0

0

–30

(X = 20.05 mm, Y = 20.47 mm) cutoff (2 mm × 2 mm) PEC patch

θ

θ

–20 –25

–10

LHCP Gain

RHCP Gain

–15

–30

–20

–35

–25

–40 –30 1.520 1.530 1.540 1.550 1.560 1.570 1.580 1.590 1.600 1.610 1.620 1.520 1.530 1.540 1.550 1.560 1.570 1.580 1.590 1.600 1.610 1.620 Freq [GHz]

Freq [GHz]

Figure 26.9 An microstrip patch antenna for GPS L1-band receivers showing (a) antenna geometry, (b) elevation patterns in principal planes for RHCP (solid line) and LHCP (dashed line), (c) reflection coefficient as a function of frequency, and (d) RHCP- and LHCP-realized gain at zenith (Chen et al. [14]). Source: Reproduced with permission of John Wiley & Sons.

−180 , and −270 resulting in RHCP end-fire radiation. The use of the external phasing network leads to easy design of the individual arms in that all the arms are of equal length and are easy to tune. Also, as will be discussed in the next section, one can easily design the antenna for multi-band GNSS receivers. The cylindrical core used in QHAs, in general, is made either from foam or other low-permittivity material such as Teflon. As pointed out earlier, high-permittivity cores, such as ceramic cores, can be used to reduce the overall size of QHAs. The presence of the high-permittivity core alters the phase velocity of the radio-frequency currents and affects the radiation pattern of the antenna. The pitch angle and length of the four helix elements are adjusted to compensate for these effects. Leisten [19] has used highpermittivity cores to design very-small-sized QHAs for GNSS receivers. Figure 26.10 shows a 16-cm-tall open-ended QFA above a 6 cm × 6 cm ground plane with left-hand helix winding and external right-hand phasing. Note that the antenna has good upper hemispherical coverage and an excellent axial ratio. The height of the QFA can be further reduced by

c26.3d

692

using a short-ended QFA, as shown in Figure 26.11, where the helical arm length is approximately 1/2 wavelengths. Although the axial ratio of the short-ended QFA is not as good as that of the open-ended QFA, its shorter height makes it a popular antenna choice for small mobile devices. However, since both the open-ended and short-ended QFAs are narrowband, they are limited to a single GNSS frequency band.

26.3.2

Multi-Band GNSS Antennas

Modernized GNSS receivers receive signals from multiplefrequency bands (L1 and L2, or L1, L2 and L5, etc.). In each band, the bandwidth of the satellite signal could be as large as 30 MHz. These receivers, as expected, use multiple band antennas resulting in complex antenna design and increased cost. The conventional MPAs and QHAs described in the previous section are narrowband antennas and are not good for modern applications. One can, however, use multiple collocated microstrip patches or quadrifilar helices for multi-frequency operation.

15/12/2020 5:48:27 PM

26.3 Example GNSS Antennas

10

RHCP end-fire pattern

693

RHCP

0

–10 Realized Gain (dBic)

left-hand winding

Z

end-fire

–20

–30 LHCP –40

right-hand phasing –50

–180° –270°

Y X

–90° 0°

1GHz –60 –180 –150

–120

–90

–60

–30

30

0

60

90

120

150

180

Theta [deg]

Figure 26.10

Axial-mode 1 GHz QHA. LH helix and RH phasing produce RHCP end-fire pattern.

10 RHCP 0

Realized Gain (dBic)

–10

end-fire

–20

LHCP

–30

–40

–50 1GHz –60 –180

–150

–120

–90

–60

–30

0

30

60

90

120

150

180

Theta [deg]

Figure 26.11

26.3.2.1

Short-ended QHA with a ground plane size of 9.3 cm by 9.3 cm.

Stacked-Patch Antennas

Stacked-patch antennas are very popular for multiplefrequency band operation [20, 21]. In these antennas, multiple resonant patch antennas are stacked on top of each other with the topmost patch resonating at the highest

c26.3d

693

frequency band. Figure 26.12 shows an example stackedpatch design [22]. The top-feed technique is the most popular approach for feeding stacked-patch antennas. In this technique, the inner conductor of each feed probe passes through the bottom patches without making any electrical

15/12/2020 5:48:29 PM

694

26 GNSS Receiver Antennas and Antenna Array Signal Processing

Single-fed LP stacked patch antenna 5

d1 h1

d2

Duroid 6010LM

d

w2

–5

K30

h2 Vertical strips

0

K16

dB

D

–10 –15

w1

Chip resistor: Coaxial 50 Ω connector

–20 1.1

L5/E5a

Gain S11

E5b L2

1.2

1.3

L1

1.5

1.4

1.6

frequency (GHz)

Figure 26.12 Example stacked-patch GPS antenna supporting L1 and L2 frequency bands (Zhou et al. [22]). Source: Reproduced with permission of IEEE.

W l3

l1 l2 r1

TMM10i εr = 9.8

D L h1 h2

Parameters L W l1 l2 l3

Figure 26.13

Value(mm) 9.52 0.58 2.29 0.61 1.02

Parameters r1 h1 h2 h3

h3

Jsurf[A_per_n]

εr = 45

Value (mm) 2.5 1.27 10 9.8

694

L2 band

L1 band

Compact dual-band (L1 and L2) GPS antenna (M. Chen and C.-C. Chen [24]). Source: Reproduced with permission of IEEE.

contact and is soldered to the topmost patch. The location of each probe is optimized to provide a good impedance match at multiple-frequency bands. The larger bottom patch acts as a ground plane for the next upper patch. Since there is strong coupling between various patches, the design of a stacked patch is not straightforward‚ and many iterations are needed to come up with a working antenna. When high-permittivity substrate are used to reduce the size of a stacked-patch antenna, the integrity of the bond between the two substrates and/or between the metal patch and the substrate can be problematic. Also, holes for the internal feed probes can weaken the high-permittivity substrates. One can avoid the internal feed probes by using proximity probes [23]. A unique compact dual-band GPS antenna with external probes was developed by Chen et. al. [24] and is shown in Figure 26.13. The proposed antenna is composed of a single slot-loaded conducting patch fabricated on a Rogers TMM10i board (h1 = 1.27 mm, ϵr = 9.8, tan δ = 0.002) using

c26.3d

1.0000e+002 9.2929e+001 8.5857e+001 7.8786e+001 7.1714e+001 6.4643e+001 5.7571e+001 5.0500e+001 4.3429e+001 3.6357e+001 2.9286e+001 2.2214e+001 1.5143e+001 8.0714e+000 1.0000e+000

standard PCB fabrication processes. The bottom substrate is a high-dielectric ceramic puck (h2 = 10 mm, ϵr = 45, tan δ ~ 0.0001). The two substrates are bonded together using ECCOSTOCK dielectric paste (ϵr = 15) to avoid air gaps and the low-dielectric bonding layer formed by common glues, both of which cause detuning of resonant frequencies. This new design is also mechanically superior to conventional stacked-patch designs where the presence of the middle conducting patch weakens the bonding between the top and bottom layers. Two conducting strips (width=2 mm, height=9.8 mm) on the side serve as proximity feeds for the new design. The bottom ends of these strips are connected to the outputs of a 0 –90 hybrid to obtain the RHCP property. These two external probes made of conducting strips are conveniently located on the side. The probes are connected to a feeding circuitry on a 1.27mm-thick FR4 board (ϵr = 4.4) as shown in Figure 26.14. The bottom of the antenna and feeding circuitry shares the same ground. Two equal-length microstrip lines with

15/12/2020 5:48:31 PM

26.3 Example GNSS Antennas

695

5 0 –5 Realized Gain (dBic)

–10 –15 –20 –25 –30 –35 –40 –45 –50 –55 –60 1.1

Simulated RHCP Gain Simulated LHCP Gain Measured RHCP Gain Measured LHCP Gain 1.2

1.3

1.4

1.5

1.6

1.7

Frequency (GHz)

Figure 26.14 Measured and simulated RHCP and LHCP gain at the zenith (M. Chen and C.-C. Chen [24]). Source: Reproduced with permission of IEEE.

a characteristic impedance of 50 Ω connect the outputs of a commercial broadband 0 –90 chip hybrid to the bottom of the two antenna probes. The right images of Figure 26.13 show the computed magnitude of the equivalent currents on the top patch at 1227 MHz (left) and 1575 MHz (right). This shows that the resonant current distribution occupies the entire patch in L2 mode‚ and the current is mostly concentrated around the meandered slots in L1 mode. The meandered slots, the center circular hole, and the high-dielectric substrate help to establish L2 mode resonance within the physically small antenna volume. The concentration of fields only around slots in the L1 band also makes it possible to tune the L1 frequency independently by adjusting the length, l3, of the inner tuning stub. Figure 26.14 shows the simulated and measured broadside gain of a fabricated antenna element mounted on a 117.2 mm × 117.2 mm FR4 board containing the feeding circuitry. The RHCP antenna gain is around 3.2 dBi at 1.227 GHz and 3.5 dBi at 1.575 GHz. The RHCP to LHCP isolation is 20 dB at the L2 band and 15 dB at the L1 band. The axial ratio is found to be 1.3 dB at 1.227 GHz and 1.9 dB at 1.575 GHz. The 3 dB bandwidth of the lower mode is 45 MHz from 1200 MHz to 1245 MHz and that of the higher mode is 50 MHz from 1545 MHz to 1595 MHz at the zenith. These bandwidths are sufficient to support GNSS signals with modern coding schemes.

26.3.2.2

Multi-Band QHA

QHAs can also be designed for multi-band operation. In this case, one QHA is either placed on top of or is enclosed

c26.3d

695

within the other QHA. One can also rotationally offset the two QHAs such that their arms are interleaved. As expected, design of multi-band QHAs is more involved‚ and these do not perform as well as individual single-band QHAs. A triple-band ceramic-loaded QHA has been reported by Liu [25] for operation in GPS L1, L2, and L5 bands. It consists of two separate antennas mounted on top of each other, a dielectric-loaded QHA at the top and a dielectric-loaded octo-filar helix at the bottom. The two antennas work in combination to provide triple-band coverage. However, due to the ceramic core, the bandwidth is quite small. An interesting dual-band, externally fed QHA has been designed by Lamensdorf and Smolinski [26, 27]. Basically, the QHA is designed for operation at the L2 GPS frequency band. However‚ using trap filters along the four helical arms, the antenna is forced to radiate at the L1 band. The trap filters act as open circuits at the L1 band and short circuits at the L2 band. Thus, the antenna radiates at both frequency bands. The antenna has a good match at the L1 band and L2 band frequencies with more than 2% bandwidth in each band.

26.3.3

Wideband GNSS Antennas

The state-of-the-art GNSS receivers utilize all available GNSS satellite signals. The frequency range of all of these signals extends from approximately 1150 MHz to 1300 MHz and 1550 MHz to 1620 MHz. The antennas used with these receivers are wideband antennas that may, in general, operate over the 1150 MHz to 1620 MHz frequency band. MPAs and QHAs are very hard to design for this large

15/12/2020 5:48:32 PM

696

26 GNSS Receiver Antennas and Antenna Array Signal Processing

50 mm

raise above reference point 54.3 mm A

67.2 mm

C z

B z

z x

(b)

10

0 –5

A&B 1

1.1

(c)

1.2

1.3 1.4 1.5 1.6 Frequency [GHz]

1.8

A&B

–20 –60

–30

0

30

B C

–100 –150

A 1

1.1

60

1.2

1.3 1.4 1.5 1.6 Frequency [GHz]

1.7

1.8

50

–10

–30 –90

0 –50

(d) C

0

100

–200

Phase [deg]

RHCP Gain [dBi]

10

1.7

x add a infinite ground plane

50

C 5

Phase [deg]

RHCP Gain [dBi]

(a)

x

90

C

0 –50

B

–100 –150 –90

Elevation angle, θ [deg]

A –60

–30

0

30

60

90

Elevation angle, θ [deg]

Figure 26.15 Cross bowtie antenna with and without a PEC ground plane backing. (a) RHCP gain response at the zenith‚ (b) phase response at the zenith‚ (c) RHCP gain elevation pattern at 1380 MHz, (d) phase elevation pattern at 1380 MHz (Zhou et al.[22]). Source: Reproduced with permission of IEEE.

frequency band. Three common wideband GNSS antennas are discussed in this section. 26.3.3.1

Bowtie Antennas

It is well known that one can increase the thickness of a dipole or a monopole antenna to increase its bandwidth. Based on this principle, bowtie dipole antennas [28, 29] have been designed for wideband operation. Bowtie dipoles are linearly polarized; however, one can use multiple bowtie antennas with proper phasing to produce RHCP radiation. The cross bowtie turnstile antenna is a broadband version of the original turnstile dipoles introduced in [28, 29]. The two orthogonal dipoles are fed 90 out of phase from a unique balun design with only a single coaxial waveguide. The dipoles in all three designs droop down from the horizontal plane in order to achieve a better axial ratio at lower elevation angles. The droop angle in the turnstile element varies between 30 and 45 . Figure 26.15 shows an example cross bowtie antenna design. RHCP polarization can be achieved by combining the signals of two orthogonal bowtie dipole elements with the quadrature phase difference. Figure 26.15(a) plots the

c26.3d

696

simulated realized RHCP gain versus frequency in the zenith direction for three different cases: (A) a free-standing cross bowtie antenna on a reference plane where the ARP is located at the origin of the coordinate system, (B) an antenna elevated vertically at 54.3 mm (λ/4 at 1380 MHz) above the ARP, and (C) same as case (B) except that an infinite perfect conducting plane is added. The signal phase versus frequency at the zenith is shown in Figure 26.15 (b). The phase variation is related to the impedance matching condition and the location of the antenna’s effective aperture (or phase centers). The nonlinear phase behavior is caused by the finite impedance bandwidth associated with finite bowtie dipole antennas. Figures 26.15(c) and 26.15(d) show the antenna gain and phase along an elevation cut at 1380 MHz. Note that the antenna has good upper hemispherical coverage and a constant phase. 26.3.3.2

Planar Spiral Antenna (PSA)

Spiral antennas were introduced in the 1950s by Edwin Turner‚ who experimentally demonstrated that an Archimedean spiral delivered a constant input impedance and circular polarization (CP) over a wide frequency range.

15/12/2020 5:48:33 PM

26.3 Example GNSS Antennas

His work generated great interest in spiral and frequencyindependent antennas [30, 31], including those of Dyson for the planar and equiangular antenna [32–36]. PSAs fall into the category of traveling wave antennas, where the radiation occurs while electromagnetic waves are traveling along a guided structure. Spiral antennas are made from either spiral wires or spiral slots cut into a metal conductor. Figure 26.16 shows the top view of the two typical twoarm planar spiral antennas. The outer diameter of the antenna determines the lowest frequency of operation, whereas the diameter at the feed region determines the highest frequency of operation. In a self-complementary spiral, the width of the conductor is the same as the gap between the two adjacent conductors. Four-arm spirals are typically used in GNSS antennas to achieve better azimuth symmetry. The radiation from a conventional spiral is bidirectional (in the upper hemisphere as well as in the lower hemisphere). To prevent undesired back lobes, the spiral is backed by a metallic cavity whose depth is

Archimedean Spiral

c26.3d

697

697

approximately equal to quarter of the wavelength at the lowest frequency. To decrease the height of the cavity, it can be filled with some dielectric material or absorber; however, this can introduce additional loss. This cavity makes the spiral frequency dependent, and the design of the cavity is very important for proper operation of the spiral. Many GNSS antennas using a spiral configuration have been developed and are available in the open market [37–39]. 26.3.3.3

Conical Spiral Antenna (CSA)

Another common type of circular polarized traveling wave antenna is the CSA. As shown in Figure 26.17, it is a threedimensional version of the planar spiral antenna. By extending a spiral antenna in the third dimension, one can make the antenna more directive (upward radiation) and thus can avoid the use of the cavity. For GNSS applications, one needs to cover the whole upper hemisphere, and the CSA should be designed to not be very directive. For a

Equiangular Spiral

Figure 26.16 McGraw-Hill.

Example two-arm Archimedean and equiangular spirals (Volakis et al. [15]). Source: Reproduced with permission of

Figure 26.17

Conical spiral antenna (CSA) examples. (Left) Archimedean CSA, (right) Log CSA.

15/12/2020 5:48:33 PM

698

26 GNSS Receiver Antennas and Antenna Array Signal Processing 10

10 1.1 GHz 1.2 GHz 1.3 GHz 1.4 GHz 1.5 GHz 1.6 GHz

5 RHCP

–5 –10 –15

LHCP

–20 –25

–5 –10

–20 –25 –30

–35

–35 –60

–30

0

30

60

90

120

150

180

Theta [deg]

LHCP

–15

–30

–40 –180 –150 –120 –90

1.1 GHz 1.2 GHz 1.3 GHz 1.4 GHz 1.5 GHz 1.6 GHz

RHCP

0 Realized Gain [dBic]

Realized Gain [dBic]

0

5

–40 –180 –150 –120

–90

–60

–30

0

30

60

90

120

150

180

Theta [deg]

Figure 26.18 (Left) Resistively terminated three-turn log CSA without ground plane and (right) resistively terminated log CSA above a finite 23 cm conducting ground plane.

given CSA height, one can adjust the directivity by controlling the pitch angle (the number of turns). A loosely wound spiral is less directive; however, it will have more back radiation, increased cross-polarization, and a worse axial ratio. As expected, these are design trade-offs. The CSA can also be mounted on a ground plane in order to reduce the back lobe and cross-polarized fields. Figure 26.18 plots the elevation gain patterns of the RHCP and LHCP components for the three-turn, 155mm-tall resistive-coated (at the bottom) free-standing CSA at six sample frequencies within the GNSS frequency range. These results exhibit very good and stable RHCP gain patterns versus frequency and a more than 20 dB RHCP/LHCP gain ratio from −45 to 45 . However, there is significant LHCP polarization below the 45 elevation angle. This is not desirable as it will pick up multipath signals and cause position estimation errors. This high-LHCP back lobe is a consequence of trading off low directivity for broad sky coverage and can be mitigated by placing a conducting ground plane beneath the antenna. The ground plane will reflect the downward LHCP waves into RHCP waves into the sky region as demonstrated in the right plot of Figure 26.18. This plot shows a significant reduction in the LHCP gain at low elevation angles and below the horizon. The interference from this additional RHCP component in the sky region will also produce different variations in the RHCP gain patterns at different frequencies in the sky region. A lower antenna height can reduce this interference effect, but this will also lower the maximum gain.

26.3.4

High-Precision GNSS Antennas

Antennas for high-precision applications should have good coverage over the horizon to receive signals from all

c26.3d

698

satellites in view, low cross-polarized (LHCP) response and back lobes (to deemphasize signal multipath), and a very stable phase center. In order to minimize the back lobes, these antennas are mounted on a ground plane. For most applications, this ground plane cannot be very large, and diffracted fields from the rim of the ground plane lead to back lobes in the gain pattern as well as high crosspolarized gain near the horizon. Most commercial high-precision GNSS antennas employ some sort of choking rings to improve the axial ratio at lower elevation angles and suppress aforementioned undesired edge diffractions. However, such treatments can add significant size and weight and can narrow the antenna pattern, weakening satellite reception at low elevation angles. The design of choke rings that are able to operate over wide bandwidths can also be difficult. Electronic band-gap (EBG) ground planes [40] have been proposed for a low profile solution to reduce edge diffraction in some GNSS antennas. If these treatments are narrowband, they might be unsuitable for multi-band and multi-GNSS receivers. The use of resistive treatment near the ground plane has been successfully used to reduce the edge diffraction from the ground plane. For example, the antenna presented in [41] uses a resistive tapered ground plane with a resistivity that varies from zero (perfect conductor) at the center to 800 ohms/square at the outer perimeter. This ground plane design covers the entire GNSS frequency band. One novel high-precision GNSS antenna is shown in Figure 26.19. The antenna is based on a conical spiral design with additional lightweight resistive treatments that include a vertical cylindrical wall, a circular array of vertical fins, and a resistive rim around the ground plane edge. These treatments were used for controlling the RHCP gain and improving the axial ratio with minimal impact on satellite reception at low elevation angles. Figure 26.20 shows

15/12/2020 5:48:34 PM

26.3 Example GNSS Antennas

699

155 mm

Arm Width = 60°

Inner Spiral radius r1 = 4 mm Outer Spiral radius r2 = 58 mm

Resistive Terminator 25 Ω/sq

Resistive Wall 130 Ω/sq Resistive Rim 130 Ω/sq

Resistive 25 Ω/sq

80 mm

95 mm

44 mm 13 mm

381mm ground (229 mm PEC + 152 mm resistive sheet)

Radome

Resistive Wall d Resistive Rim Conical Spiral Resistive Fine Conducting Ground Plastic Base GNSS antenna prototype without radome and R-fence

Figure 26.19

GNSS antenna prototype stackup

Novel lightweight high-precision GNSS antenna design.

10

10 1.1 GHz 1.2 GHz 1.3 GHz 1.4 GHz 1.5 GHz 1.6 GHz

5 RHCP

–5

0 Realized Gain [dBic]

Realized Gain [dBic]

0

–10 –15 LHCP

–20 –25

–10 –15

–25

–35

–35 –60

–30

0

30

60

90

120

150

180

LHCP

–20

–30

–90

RHCP

–5

–30

–40 –180 –150 –120

–40 –180 –150 –120

–90

Theta [deg]

Figure 26.20

699

–60

–30

0

30

60

90

120

150 180

Theta [deg]

Comparison of (left) simulated and (right) measured realized gain patterns.

the simulated and measured RHCP and LHCP elevation gain patterns. The antenna exhibits a good polarization isolation and low LHCP gain near the horizon. It also has excellent sky-to-ground gain ratio, making it more effective in suppressing multipath interference as compared to other GNSS antennas. Figure 26.21 shows the measured

c26.3d

1.1 GHz 1.2 GHz 1.3 GHz 1.4 GHz 1.5 GHz 1.6 GHz

5

performance at the center frequency of L1, L2, and L5 bands. The center of each circular plot corresponds to the zenith and the outer edge corresponds to the horizon. Four separate rows of plots are shown, each of which corresponds to a different performance metric: RHCP realized gain, axial ratio, carrier-phase bias, and code delay bias.

15/12/2020 5:48:35 PM

700

26 GNSS Receiver Antennas and Antenna Array Signal Processing

GPS L1

GPS L2

ϕ

GPS L5 5 2.5

(a) 0[dBic] –2.5 –5

(b)

ϕ

3 2.5 2 1.5[dB] 1 0.5

(c)

ϕ

0 15 10

5 0 deg –5 –10

(d)

ϕ

–15 10

8 6 4 2 0 cm –2 –4 –6 –8 –10

Figure 26.21 Measured performance of the antenna shown in Figure 26.19 for GPS L1, L2‚ and L5 bands, showing upper-hemisphere metrics: (a) gain, (b) axial ratio, (c) carrier-phase bias, and (d) code delay bias.

26.3.5 Reconfigurable GNSS Antennas for Beam Switching and Nulling It is expected that most GNSS signal multipath as well as intentional or unintentional radio-frequency interference (RFI) will originate from directions near or below the horizon for a number of important GNSS applications. To suppress these undesired signals, reconfigurable antennas that perform beam switching and simple nulling have been proposed. These antennas possess a pattern that is switched between two primary modes. In the normal mode, the antenna pattern has a wide main beam to receive signals from all satellites in view. In multipath environments and/or in the presence of interfering signals, the antenna pattern is switched to a narrow main beam mode with reduced gain or nulls around the horizon. While this can

c26.3d

700

lead to loss of low-elevation satellites, it will tend to improve the overall receiver performance. A few beamswitchable nulling antennas are described below. A simple beam-switching antenna for the GPS L1 band is described in [42], which consists of two stacked patches. The upper patch element is used in the normal mode, and this element has a wide main beam to receive signals from GPS satellites down to the horizon. The lower patch antenna has high gain (9 dBic) toward the zenith and low gain (−15 dBic) toward the horizon, which is desirable for suppressing signal multipath and/or RFI. Switching between the two patches can be performed manually or automatically by varying the DC voltage on the center conductor of the coaxial cable connecting the antenna to the GPS receiver. When the antenna is in narrow beamwidth

15/12/2020 5:48:37 PM

26.4 Antenna Arrays for GNSS Receivers

mode, the gain around the horizon is approximately 8 dB lower than while operating in normal mode. A different beam-switchable antenna design for both GPS L1 and L2 bands is reported in [43] and [44]. The antenna, shown in Figure 26.22, consists of three dielectric layers, each approximately 22 cm in linear dimension. The bottom dielectric layer has a metallic coating at the bottom surface and a 5 cm square patch at the top that is designed to radiate at the GPS L2 frequency band. The middle layer has a 2.5 cm square patch at the top to radiate at the GPS L1 band. This patch is surrounded by a 2-cm-thick dielectric strip to control surface waves. The top layer has a metallic strip of the same dimensions as the strip on the middle dielectric layer. The top layer strip, however, is switch-loaded to vary the mode of operation of the antenna. The switches are turned on and off in order to vary the beam pattern of the antenna for vertical polarization. When the switches are turned on, the antenna has a wider main beam; whereas, when the switches are turned off, the antenna has a narrower main beam. Also, the narrower beam has a higher response along the zenith. Thus, one can switch between the two beams to provide some degree of multipath and/or RFI suppression. An antenna that has been designed to steer a ring null toward the horizon is described in [45]. It consists of two concentric microstrip patch elements. The signal received by the inner patch is used in nulling the RFI received by the outer angular ring antenna. Though the ring antenna is resonant in a higher mode, it is forced to generate RHCP

Figure 26.22 Beam-switchable dual-band GPS antenna based on characteristic modes (Lee et al. [44]). Source: Reproduced with permission of John Wiley & Sons.

c26.3d

701

701

lower-order (TM11) far fields. This allows the needed comodal phase tracking between the two elements for signal cancellation. Both elements are connected to sets of four coaxial probes that are symmetrically spaced at 90 intervals. This forces RHCP fields and suppresses higher-order modes from being excited in the outer ring element. To generate a spatial ring null around the horizon, the signals received by the inner patch and outer ring are combined through an adaptive nulling network. First, the signal received by the inner patch is attenuated such that its magnitude is equal to the signal received by the outer ring element from the selected direction. Next, the phase is adjusted until the two signals are out of phase. The resulting antenna radiation pattern has a null that covers all azimuthal angles at the selected elevation angle. Reconfigurable single-element antennas that perform beam switching and nulling provide limited multipath suppression and RFI mitigation capability. For operation in severe RFI environments, one uses multiple element antennas with GNSS receivers. With multiple antennas, the signals received by various antenna elements are adaptively weighted and summed together such that RFI is suppressed by orders-of-magnitude improvement. These antennas, called adaptive antennas, are discussed in the following sections.

26.4 Antenna Arrays for GNSS Receivers Antenna arrays have found widespread use in many GNSS receiver systems used today. Two-element antenna arrays provide precise heading/attitude sensors for use as marine compasses and high-precision heading aiding for IMUs [46]. Arrays are able to determine the direction of GNSS signals, which is useful for security applications that want to confirm the authenticity of received GNSS signals [47]. By combining the signals received from multiple elements, the antenna has increased gain and reduced beamwidths in controllable directions, which is useful for multipath and interference mitigation in critical military and civilian applications [48]. High-gain GNSS antennas with multiple polarizations are used in receiving weak scattered signals for remote sensing applications. In all, arrays are important for the GNSS community to understand. This section begins with an overview of the important features of antenna arrays before a discussion of array signal processing later in this chapter. In Section 26.2.1, we defined the antenna response Ap(θ, ϕ, f) for a single-element antenna. When dealing with an antenna array where each element has a single port, the

15/12/2020 5:48:38 PM

702

26 GNSS Receiver Antennas and Antenna Array Signal Processing

antenna responses for each element are collected into a single set that we refer to as the antenna array manifold. It is important to note that the antenna array has a single ARP. The antenna response for each element in the array is defined relative to this common reference point. Also, the antenna response of each element should be found in the presence of the other elements so that the effects of mutual coupling are accounted for. Under these conditions, the antenna array manifold can be used to characterize the effects of the antenna array on the received GNSS signals, as will be discussed later. For typical GNSS receiver applications, there are two main methods for utilizing multiple antennas. In the first method, the signals from multiple antennas enter the receiver‚ where they are processed separately‚ and satellite signals acquired and tracked from all antennas. This is commonly done when using antenna arrays for heading and attitude determination or GNSS signal direction-ofarrival estimation, where the differential GNSS measurements made between the two antennas carry the relevant information. The second method for utilizing multiple antennas is to weight and sum the RF signals together before that signal is used by the receiver. The content of the rest of this chapter is primarily focused on the latter. When the signals received by various elements are weighted and summed together to produce an array output signal, the effect of the antenna response of each antenna element can be observed in the composite antenna array pattern. An example antenna array pattern is shown in Figure 26.23. By summing up the signals from multiple antennas, an increase in the received power relative to a single-element antenna can occur, which is called the array

gain. If K is the number of antenna elements in the array, an approximation for the array gain is 10 log10(K), although this is not the case in general since each antenna element might not have the same gain in a given direction. The antenna array pattern will have a decreased beamwidth and will have a different number of sidelobes and levels. The most important factor determining an array’s performance is the number and geometric distribution of antenna elements. The most typical distribution is a planar array, in which elements form a two-dimensional arrangement on a plane in a circular form. The array aperture is the rough size of a planar array. Within this aperture, array elements are typically distributed with half-wavelength spacing at some target frequency. When this is the case, the array aperture is “full.” If one packs additional antenna elements into this aperture, the increase in performance (i.e. gain and beamwidth) might only improve by a small amount. In this sense, it is the size of the aperture that drives performance, not necessarily the number of elements. This is one of the key physical limitations driving the limits of what performance can be achieved with miniaturized antenna arrays. GNSS antenna arrays in use today have 4–9 antenna elements filling apertures on the order of 10 to 40 cm in diameter. For adaptive nulling applications, the number of interference sources that can be nulled is roughly is the number of elements minus one; however, one must be careful since this is an approximation. Certain array processing algorithms make use of the concept of a reference antenna element. Typically, circular antenna arrays will have one antenna element in the center that will serve as the reference. For circular arrays, the

15

Array Pattern

Z

Y

x

0

50

100 (mm)

Realized Gain (dB)

10

Element Patterns

5 0 –5 –10 –15

–80

–60

–40

–20

0

20

40

60

80

θ (deg)

Figure 26.23 Example seven-element GPS L1 patch array showing the simulated gain pattern of each element (dashed) and the composite array pattern (solid).

c26.3d

702

15/12/2020 5:48:38 PM

26.5 Array Signal Processing for GNSS Receivers

elements will sometimes be clocked, that is, rotated based on their location around a circular distribution in order to create a symmetry in antenna patterns. The reader is referred to a variety of different array configurations in literature. Antenna arrays could have a three-dimensional distribution of elements to increase resolution at low elevation angles [49]. Array elements might be packed so densely that the array becomes a continuous aperture [50]. In some cases, arrays are sparsely distributed over larger distances. In other cases, the arrays include analog hardware, such as Butler matrices, that forms beams or modes before analogto-digital conversion. Arrays for handheld applications have also been developed [51], as well as arrays that are distributed around platforms for increased coverage during arbitrary rotations [12]. When multiple antenna elements are brought close together, they begin to electromagnetically couple to one another‚ and their antenna patterns and performance begin to change as compared to each element in isolation. This is known as mutual coupling. Since the individual antenna elements were likely designed and optimized in isolation, the effect of mutual coupling typically has a degrading effect on performance. As multiple elements are brought together in different geometrical configurations, the primary effect is to make each element’s pattern dissimilar from one another. Figure 26.24 shows the effects on mutual coupling between two simple patch antennas. Traditionally, there has been an emphasis on minimizing mutual coupling when designing an array; however, one should be aware that it is not always an important factor nor is it feasible to keep closely spaced antenna elements from

703

coupling without compromising other performance metrics [52]. It is important to note that the effects of mutual coupling are often modeled as a frequency- and/or directionindependent mutual coupling matrix; however, this is an approximation, and the accuracy of this approximation becomes worse as antenna elements become more wideband and packed closer together.

26.5 Array Signal Processing for GNSS Receivers This section reviews the signal processing techniques and algorithms used with GNSS antenna arrays. Although there are different ways arrays can be used, the focus of this section is on antenna arrays for adaptive interference suppression, which is one of the most important uses of arrays for GNSS applications. There are many different ways to design and implement this array signal processing, which are driven by a number of different motivations, including computational complexity, optimization criteria, available information, and tightness of integration with the GNSS receiver hardware itself. We have chosen to limit the discussion to the most popular techniques currently in use today. This section begins with an analytic model for adaptive antenna array using space-time adaptive processing (STAP). Different types of STAP adaptive filtering algorithms will be introduced, as well as how the adaptive filters are numerically implemented. Adaptive antennas can have a significant effect on the GNSS signals, and equations will

Antenna Element in Isolation (No Mutual Coupling ) 7 Z

6

1

2

Y

x

0

50

100 (mm)

Realized Gain (dB)

5 4 3 2

Antenna Element #1 (With Mutual Coupling)

1

Antenna Element #2 (With Mutual Coupling)

0 –1 –2

Figure 26.24

c26.3d

703

–80

–60

–40

–20

0 θ (deg)

20

40

60

80

Simulated gain pattern of two antenna elements before and after incorporating mutual coupling.

15/12/2020 5:48:39 PM

704

26 GNSS Receiver Antennas and Antenna Array Signal Processing

be provided for understanding how to analyze these effects. Finally, alternative adaptive filtering architectures will be introduced, including space-frequency adaptive processing (SFAP) as well as post-correlation designs.

26.5.1

Space-Time Adaptive Processing

Figure 26.25 shows a simplified model of an adaptive antenna array with adaptive filtering. There are K antenna elements, and Ak(f, θ, ϕ) represents the frequency response of the k-th element for a given polarization in the (θ, ϕ) direction. Each antenna element is backed by front-end electronics, represented by Fk(f), which downconvert the signal to baseband and perform analog-to-digital conversion. The front-end electronics include LNAs, filters, mixers, and other components. The digitized signal for each element is sent through a finite impulse response (FIR) filter with L taps each that is represented by Wk(f) in the frequency domain. Note that a system with L = 1 (i.e. a single complex weight behind each element) is known as spaceonly processing (SOP), and a system with L > 1 is known as STAP. The outputs from each of the adaptive FIR filters are summed to form a single array output. The output is said to correspond to an adaptive channel. A particular adaptive antenna system could have several adaptive channels. The digitized signals from all elements could be sent to each adaptive channel and processed with different sets of adaptive filter weights to produce multiple array output signals. For a desired GNSS signal d(t) incident along the (θd, ϕd) direction, the n-th discrete sample after passing through the antenna element and the front-end electronics in the k-th channel is given by dk n =

D f Ak f , θd , ϕd F k f e j2πfnT s df ,

26 27

where D(f) is the Fourier transform of d(t), and Ts is the discrete sampling period. Here‚ it is implied that the antenna response Ak(f, θd, ϕd) polarization corresponds to RHCP polarization for GNSS signals. The integration is carried over the frequency band of the desired signal. Similarly, for an interference signal i(t) incident along the (θi, ϕi) direction, the n-th discrete sample after passing through the antenna element and the front-end electronics in the k-th channel is given by ik n =

I f A k f , θ i , ϕi F k f e

j2πfnT s

df ,

26 28

where I(f) is the Fourier transform of i(t). Again, it is implied that the polarization of the antenna response used in this equation corresponds to the polarization of the interference signal. For a signal scenario with M number of interference signals, the n-th sample of the total combined signal in the k-th channel after the front-end electronics stage is then given by M

ik,m n + νk n ,

x k n = dk n +

26 29

m=1

where νk[n] is the thermal noise in the k-th channel. The thermal noise, in general, is assumed to be independent between channels. Note that for this formulation, xk[n] contains just a single GNSS signal of interest (SOI). In reality, multiple GNSS signals reside in the same frequency band. However, assuming that the cross-correlations between the satellite signals are small and that the satellite signal powers are much lower than the interference signal powers and the noise, the presence of other satellite signals can be ignored. For an adaptive array system with L taps, the n-th snapshot of the signal from the k-th channel prior to the adaptive filtering stage can be represented in vector form by

A1(f,θ,ϕ)

A2(f,θ,ϕ)

AK(f,θ,ϕ)

Antenna Array

F1(f)

F2(f)

FK(f)

Front-End Electronics

W1(f)

W2(f)

WK(f)

Adaptive Filters

Σ Adaptive Antenna Output

Figure 26.25

c26.3d

704

Simplified model of space-time adaptive processing for GNSS antenna arrays.

15/12/2020 5:48:40 PM

26.5 Array Signal Processing for GNSS Receivers T

xk n = x k n …x k n − L + 1

,

26 30

where the superscript T denotes the matrix transpose operation. The snapshots from all antenna elements can be combined into a single vector given by x1 n 26 31

xn = xK n

From Eq. 26.29, it can be seen that the received signals in the k-th channel can be decomposed into three distinct components: desired signal, interference signal, and the noise. Thus, x[n] can also be decomposed into the three components, given by x n = x d n + xi n + x ν n

26 32

The subscripts d, i, and ν denote the desired, interference, and noise components, respectively. The adaptive FIR filter weights for the k-th channel can also be represented in vector form as wk =

wk1

wkL

T

,

26 33

where wkl is the complex weight for the l-th tap of the k-th channel. The weights from all the antenna elements can be combined into a single weight vector w1 w=

,

26 34

wK and the array output signal is given by y n = wT x n

26 35

In reality, the adaptive filter weights will also vary in time at an update rate determined by the specific implementation of the adaptive filtering algorithm. However, in this model, we are interested in capturing the steady-state performance of the adaptive antenna and treat the weights as fixed. The expected output power from the adaptive antenna can be written as 1 E y∗ n y n 2 1 = w H E x∗ n x T n w 2 1 = wH Φw, 2

P=

26 36

where Φ is the KL × KL signal correlation matrix of the adaptive antenna. In Eq. 26.36, the superscripts ∗ and H denote the complex conjugate and complex conjugate of

c26.3d

705

705

the transpose, respectively. Assuming that the desired signal is uncorrelated with the interfering signals and the thermal noise is uncorrelated with all the signals incident on the antenna array, the expected output power from the adaptive antenna can be separated into separate components P = Pd + Pi + Pu

26 37

with a separate correlation matrix for each signal component 1 H 1 w E x∗d n xTd n w = wH Φd w 2 2 1 H 1 Pi = w E x∗i n xTi n w = w H Φi w, 2 2 1 H 1 ∗ T P u = w E x u n x u n w = w H Φu w 2 2 Pd =

26 38 26 39 26 40

Using Eqs. (26.38)–(26.40), one can calculate the SNR, signal-to-interference ratio (SIR), and signal-to-interference-plus-noise ratio (SINR) at the array output. For a GNSS receiver equipped with an adaptive antenna, the array output is fed into the receiver‚ where it is crosscorrelated with a locally generated reference signal r(t). The cross-correlation function estimate R using N samples is given by Rτ =

1 N y n r ∗ nT s + τ , Nn=1

26 41

where τ is the relative delay introduced in the reference signal. If we let τ0 be the delay that maximizes the crosscorrelation function, then substituting Eq. 26.35 into Eq. 26.41 produces 1 N x n r ∗ nT s + τ0 Nn=1

R τ0 = w T ∗

= wT s τ0 ,

26 42

where s τ0 is called the correlation vector. Using Eq. 26.32, the correlation vector can be written as the sum of sd τ0 and su τ0 , which are the desired and undesired (interference and noise) components of the correlation vector. The receiver carrier-to-noise ratio (C/N0) is given by [53] C N0 =

1 w H sd τ 0 T E w H su τ 0

=

1 w H Φd τ 0 w T w H Φu τ 0 w

2 2

26 43

where T is the coherent integration time‚ and the postcorrelation matrices for the desired and undesired components are defined as

15/12/2020 5:48:40 PM

706

26 GNSS Receiver Antennas and Antenna Array Signal Processing

Φd τ0 = sd τ0 sH d τ0 ,

26 44

H

Φu τ0 = E su τ0 su τ0

26 45

For a given set of antenna array weights, one can use Eq. 26.43 to calculate the C/N0 for the antenna array in a given signal and interference environment. In the following section, some popular algorithms for adapting the antenna weights are discussed.

26.5.2

Adaptive Filtering Algorithms

There are a variety of adaptive filtering algorithms available that can be used to determine the filter weights in real time based on the received signals. Here, we differentiate between the adaptive filtering algorithm (which analytically defines the steady-state solution to some optimization equation) from the actual numerical implementation of the adaptive filter, which is discussed in the next section. This section describes a few of the most popular adaptive filtering algorithms used in GNSS adaptive antennas, although a significant number of alternative designs have been proposed in the literature. The most common algorithms used in modern adaptive antennas are based on minimizing the total output power (Eq. 26.36) of the array subject to a single constraint. Mathematically, the approach can be written as wc = arg min w

1 H w Φw 2

such that

uH c w = 1, 26 46

where uc is the constraint vector. One can use Lagrange multiplier method to solve Eq. 26.46, which yields wc =

Φ − 1 uc −1 uH uc c Φ

26 47

The weight vector wc satisfies the constraint Eq. 26.46 and varies based on the RF environment via the correlation matrix Φ. These weights are known as the linearly constrained minimum power (LCMP) weights [54]. Since we typically assume the GNSS signals are below the noise floor and that the interference and noise are zero mean, it is sometimes implied that Φ is also the covariance matrix of the undesired signal and that Eq. 26.47 is also the linearly constrained minimum variance (LCMV) solution as well. The following subsections review algorithms that have the form of Eq. 26.47. Note that we will specify the constraint vector by uc =

u1,1 u1,2 … u1,L u2,1 … uK,L

T

,

26 48

where its entries uk, l correspond to the k-th antenna element and l-th filter tap.

c26.3d

706

26.5.2.1

Simple Null Steering

A common constraint that is frequently used in GNSS antenna arrays is to fix the weight of the center tap lr of a selected antenna element kr (i.e. the reference element) to unity. This constraint vector is defined as uk,l =

1 0

k = k r , l = lr else

26 49

where the nonzero entry corresponds to the center tap of the reference element. Note that the constraint vector is the same for all satellites in view. Thus, in a given frequency band, the same set of weights can be used to receive signals from all satellites in view. The weights will be adapted to suppress strong (above the noise floor) interfering signals. In the process of suppressing the interfering signals, the antenna response in the signal direction can vary significantly. The antenna gain in the satellite direction can increase or drop. For this reason, adaptive antennas based on this constraint vector are referred to as null-steering adaptive antennas [55]. These are very popular in the current GNSS receivers as the weights can be adapted very efficiently‚ and no knowledge of the antenna array and/or satellite signals is needed.

26.5.2.2

Beamforming/Null Steering

The next most common algorithm used for GNSS adaptive antennas forms array pattern beams in GNSS satellite directions while simultaneously adaptively forming nulls in interference directions [54]. Algorithms that operate like this are referred to as beamforming/null-steering antennas. The constraint vector is chosen so that the sum of the signals received at the center taps of various antenna elements from the satellite direction (θd, ϕd) at the carrier frequency fc is fixed to unity. This constraint vector can be written as uk,l =

A∗k f c , θd , ϕd F ∗k f c

l = lr

0

else

26 50

Note that the nonzero entries correspond to the center tap (lr) of various antenna elements. This constraint vector depends on the satellite direction, and thus differs from one satellite in view to the next satellite in view. Also, one needs to know the in situ antenna response of the individual antenna elements as well as the response of the front-ends. Therefore, an adaptive antenna using this algorithm requires additional implementation complexity as compared to simple null-steering adaptive antennas. These adaptive antennas, however, have the advantage of providing additional gain and reduced antenna-induced biases in the received GNSS signals.

15/12/2020 5:48:40 PM

26.5 Array Signal Processing for GNSS Receivers

26.5.2.3

Correlation Vector

Another choice of constraint vector is based on the desired signal component of the correlation vector. In order to calculate the correlation vector, one would normally need to know the delay and carrier phase associated with the locally generated PRN sequence; however, we can let the reference signal have the same phase and delay as the signal received by the center tap of an isotropic antenna element located at the phase reference point of the antenna array followed by an ideal front-end. In this case, the entries of the constraint vector are given by uk,l =

S f A∗k f , θd , ϕd F ∗k f e j2πf

l − N 2+ 1 T s

df 26 51

where S(f) is the power spectral density of the GNSS SOI, and Ts is the sampling period. Note that this constraint vector not only depends on the satellite direction but also depends on the satellite signal spectra. Thus, adaptive antenna weights will be different for different GNSS satellite signals, which increases the implementation requirements. In the absence of interfering signals, this constraint vector leads to direction-independent carrier phase and delay for all satellites. Both the beamforming/null-steering and the correlation vector algorithms require the angular locations of the GNSS satellites in the antenna array coordinate system. This information can be obtained from the GNSS receiver, so it is implied there is communication from the receiver to the adaptive antenna electronics, and it can be said that the two are loosely coupled. On the other hand, the simple null-steering algorithm requires no information from the GNSS receiver and can operate completely independently.

and the locally generated reference signal, r[n]. sr is given by sr = E x∗ n r n

26 54

If one compares Eq. 26.53 with Eq. 26.47, one will notice that the two are quite similar except that the constraint vector, uc, has been replaced with the correlation vector, sr. In general, α is selected such that the weight corresponding to the center tap of the reference element is kept fixed, and other weights are adjusted to minimize the MSE. These weights are referred to as the MMSE weights. In this case, the reference signal could be the prompt PRN sequence generated by the GNSS receiver, and the adaptive antenna electronics would need to be tightly coupled with the GNSS receiver in order to receive this information. In practice, a finite number of samples are used to estimate the correlation vector, sr. In the presence of strong interfering signals, the estimated correlation vector sr is, therefore, dominated by the undesired signals. Nevertheless, the antenna weights will still converge to their desired values as long as the reference signal is perfectly correlated to the GNSS signal. MMSE-based adaptive antennas yield the same C/N0 as correlation-vector-based GNSS adaptive antennas.

26.5.2.5

Optimal C/N0 Weights

Rather than minimizing the output power in Eq. 26.46, a more GNSS-specific optimization of the weights would be to maximize the C/N0 at the output of the array. In Eq. 26.43, the C/N0 for an incident GNSS signal was specified in terms of a specific set of adaptive filter weights. This allows the optimization to be mathematically stated as 1 H w Φu τ 0 w 2 wH Φd τ0 w = 1,

w 0 = arg min w 26.5.2.4

MMSE Adaptive Antennas

The last two constraint vectors require knowledge of the in situ antenna manifold as well as knowledge of the front-end response of the antenna electronics. This information is not only hard to obtain but can also vary with time. To overcome this obstacle, one popular approach is based on minimizing the mean-squared-error (MSE) between the array output and a locally generated reference signal r[n]. Using Eq. 26.35, the MSE is given by ϵ=E

w x n −r n T

∗

x n w−r n T

26 52

The antenna weights that lead to minimum MSE are then given by w m = αΦ − 1 sr ,

26 53

where α is a scalar, and sr is the correlation vector between the signal received at each tap of each antenna elements

c26.3d

707

707

such that

26 55 The solution to this optimization problem has the form [56] −1

w 0 = λ Φu

τ 0 Φd τ 0

w0 ,

26 56

where λ is a scalar constant. Thus, w0 is equal to the eigen−1

vector of Φu τ0 Φd τ0 , and λ is the associated eigenvalue. Equation 26.56 can be further simplified to yield −1

w 0 = α0 Φ u

τ0 sd τ0 ,

26 57

where α0 is another scalar constant. Note that one needs to know τ0 to calculate the optimal weights; however, C/N0 is not very sensitive to τ0, and it can be set equal to the delay associated with the center tap of the reference element.

15/12/2020 5:48:40 PM

708

26 GNSS Receiver Antennas and Antenna Array Signal Processing

26.5.3 Effects of Antenna Arrays on GNSS Signals In Section 26.2, we discussed how a single-element antenna acts as a linear filter for incident GNSS signals. The effect of an antenna array can also be modeled as a filter. Starting with the STAP-based antenna array model in Figure 26.25, the total system response of the adaptive antenna with K elements can be described as K

Ak θ, ϕ, f F k f W k f

H θ, ϕ, f =

26 58

k=1

The individual antenna element responses Ak are quantified in the presence of the other antenna elements such that they include the effects of mutual coupling. The total system response also incorporates the front-end antenna electronics Fk and the fixed or adaptive array weighting Wk, where the details of various quantities are defined as before. In this case, for an incoming signal with power spectral density of S(f), the cross-correlation between the incident GNSS signal at the antenna phase reference point and the antenna output is given by R θ, ϕ, τ =

S f H θ, ϕ, f e

− j2πf τ

df

26 59

If all the quantities in Eq. 26.58 are known, then the antenna array is completely characterized‚ and one can use Eq. 26.59 along with the GNSS receiver discriminator characteristic to calculate the antenna-induced biases. If desired, the GNSS receiver measurements can then be corrected for the antenna-induced biases. In the case of adaptive antenna arrays, the adaptive filter weights change based on the RFI environment and other factors. Therefore, the weights are not known ahead of time‚ and simple precalibration of the antenna-induced biases is not possible. While one can calibrate the antenna-induced biases in the absence of all interfering signals, these calibrated values may not hold in the presence of interfering signals. For precision GNSS applications, one should attempt to minimize the errors associated with antenna-induced biases. For single-element antennas, certain antenna designs can be utilized to minimize these biases, and, similarly, one would expect that a well-designed antenna array might help in reducing the antenna-induced biases. However, for many GNSS adaptive antennas, this may not be a practical approach. First, many modern GNSS receiver antenna arrays have small apertures with closely packed elements. There is demand to make the aperture even smaller so that even small platforms can be equipped with GNSS receivers protected by adaptive antennas. These arrays will necessarily have strong coupling between various antenna elements, leading to large antenna-induced biases. Second,

c26.3d

708

even if an antenna array is well designed, it is typically mounted on complex platforms that will couple with the antenna or scatter incident fields, creating bias errors. Finally, adaptive antenna arrays with STAP or SFAP form patterns to suppress interference, and conventional adaptive weighting algorithms can lead to large antenna-induced biases [7, 57, 58]. In order to overcome antenna-induced errors caused by adaptive antenna arrays, a variety of different approaches have been proposed. One method is to predict and correct for the adaptive antenna-induced biases in the receiver [59, 60]. This requires that real-time information about the adaptive filter weights be sent to the receiver. Another method is to design new adaptive filtering algorithms specifically to mitigate antenna-induced biases [56, 61]. However, these algorithms can have increased implementation complexity and require very accurate antenna manifold information. Another approach is to implement MMSE methods that can provide reduced antenna-induced biases without excessive information [62].

26.5.4 Example Adaptive Antenna Simulation Results Simulations were performed to demonstrate the performance differences between adaptive filtering algorithms. A seven-element circular array of GPS L1 patch antennas mounted on a small ground plane was simulated in computational electromagnetic codes. The array is shown in Figure 26.23. Each element was simulated in the presence of the others in order to capture the effects of mutual coupling. Arrays similar to this are commonly used for GNSS applications. The front-end electronics are assumed to be ideal and are effectively neglected. The front-end thermal noise is assumed white, zero-mean Gaussian. The antenna electronics implement seven-tap STAP with 24 MHz system bandwidth and sampling rate. The SOI is a GPS P-coded signal with an incident signal power of −30 dB SNR, and its angle of arrival is varied. The STAP filter weights are analytically computed using equations described in the previous sections assuming the weights have converged to a steady state in a constant signal scenario. Receiver performance metrics are also evaluated using the analytic equations. The interference scenarios include wideband and partial-band interferers. Wideband interferers occupy the entire system bandwidth‚ while partial-band interferers have a narrower bandwidth and are offset from the L1 carrier frequency. All interferers are strong with a 50 dB interference-to-noise ratio (INR) and are incident from angles near the horizon as indicated in each figure. Figure 26.26 shows the simulated performance of the different adaptive filtering algorithms in two interference

15/12/2020 5:48:40 PM

26.5 Array Signal Processing for GNSS Receivers

(b) 55

50

50 C/N0(dB–Hz)

55

45 40

Code Delay Bias (cm)

30 –90

40

–60

–30

0 θ (deg)

30

60

30 –90

90

50

50

0

0

–50

NS BF/NS CV

–60

–30

0 θ (deg)

30

60

NS BF/NS CV

150 100

–30

0 –50

–100 –150

0 θ (deg)

30

60

90

–100 NS BF/NS CV

–60

–30

0 θ (deg)

30

60

90

30

60

90

NS BF/NS CV

150

50

–90

–60

–50

–150 –90

90

Carrier Phase Bias (deg)

–150 –90

NS BF/NS CV OP

35

–100

Carrier Phase Bias (deg)

45

NS BF/NS CV OP

35

Code Delay Bias (cm)

C/N0(dB–Hz)

(a)

709

100 50 0 –50 –100 –150

–60

–30

0 θ (deg)

30

60

90

–90

–60

–30

0 θ (deg)

Figure 26.26 Simulated performance of an adaptive antenna array showing C/N0, code delay bias, and carrier-phase bias versus elevation angle (a) in the absence of interference and (b) in the presence of a single wideband interferer.

environments. Each row of plots shows the C/N0, carrierphase bias, and code delay bias. In each plot, the incident angle of ascension θ of the GNSS signal is varied from −90 to 90 (i.e. a principal plane cut going from horizon to horizon passing through the zenith). The performance of three different adaptive filtering algorithms is compared: simple null steering (NS), beamforming / null-steering (BF/NS), and correlation vector (CV). In the plots showing

c26.3d

709

the C/N0 performance, the optimal C/N0 (OP) algorithm is also included. The left column shows results in the absence of interference. In this case, we can observe that the simple null-steering algorithm has reduced C/N0 performance as compared to the other algorithms because it does not perform beamforming and lacks array gain. We also observe that the other algorithms come very close to the optimal C/N0 performance. We observe that the beamforming/

15/12/2020 5:48:40 PM

710

26 GNSS Receiver Antennas and Antenna Array Signal Processing

null-steering algorithm does not introduce carrier-phase biases, while the CV algorithm has neither carrier phase nor code delay biases. The right column of Figure 26.26 shows the performance in the presence of a single wideband interferer. The direction of the interference is indicated by the arrow. While performance has degraded in the angular region around the interferer, we see that all algorithms provide protection against it and allow sufficient C/N0 at other angles. It should also be noted that the antenna-induced biases introduced by certain algorithms have changed as compared to the scenario without interferers. This highlights the fact that antenna calibration in the absence of interference cannot be applied to adaptive antennas. Figure 26.27 shows the performance in two additional interference scenarios. The interference directions are indicated by the arrows. The left column shows results in the presence of two wideband interferers. Again, the use of adaptive interference suppression has allowed the receiver system to provide good C/N0 over a large portion of the sky. The right column shows the case with three partial-band interferers. Since these interferers occupy only a small portion of the frequency band, STAP is able to null them and still provide good C/N0 even in directions near the interferers. However, the act of temporally nulling the interference has caused distortions in the GPS signal, resulting in a larger antenna-induced bias.

26.5.5

Sample Matrix Inversion (SMI)

It is clear that if the covariance matrix Φ is known, then it is straightforward to calculate the adaptive antenna weights. One can use multiple snapshots of the signals received at various taps of K elements to estimate the covariance matrix; that is, Φn =

1 M−1 ∗ x n − m xT n − m , Mm=0

26 60

where M is the number of samples used in estimation of the covariance matrix. Note that the larger M is, the better the estimated covariance matrix will be. As a rule of thumb, M > 2KL + 3, where K is the number of elements‚ and L

c26.3d

710

26.5.5.2

Recursive Least Squares (RLS)

In an RLS implementation, the latest snapshots of x[n] are used to calculate the inverse of the covariance matrix directly. Let Φ n = λ f Φ n − 1 + x∗ n x T n ,

Adaptive Filtering Implementations

The adaptive filtering algorithms described above make use of the received signal correlation matrices in order to adapt to the signal environment. Traditionally, forming and inverting this matrix has been computationally costly, and a number of approaches were developed to allow efficient implementation of the adaptive filter weight algorithms [63–67]. 26.5.5.1

is the number of taps. This method of calculating the adaptive antenna weights is called SMI. SMI implementation leads to converged weights (no past memory) and a stable solution as long as the estimated covariance matrix is full rank. However, for a large value of the product KL, it is computationally inefficient as many operations are needed to estimate the covariance matrix (Eq. (26.60)) and to solve the system of equations. Though many approaches, such as systolic arrays, have been developed to decrease the computation requirements, it still might not be sufficient for many systems. Also, there will be some time lag between the input samples and the output samples unless one is willing to use the “stale” weights (i.e. weights calculated from the previous snapshots are applied to the current snapshots). These are the two main drawbacks of SMI implementation. In the case of the MMSE algorithm, one also needs to estimate the CV, sr. Again, one can use multiple snapshots of x[n] to estimate sr. The number of samples used in the estimation of sr can be different from the number of snapshots used to estimate the covariance matrix. In general, many more snapshots are used in the estimation of sr.

26 61

where λf is a real number called “forget factor.” Then assuming that Φ(n − 1) is invertible, it can be shown that Φ−1 n =

1 λf

Φ−1 n − 1 −

Φ − 1 n − 1 x∗ n xT n Φ − 1 n − 1 λ f + x T n Φ − 1 n − 1 x∗ n

26 62 Therefore, Φ−1[n] can be calculated very efficiently. To guarantee inversion, one can assume Φ[0] = I. This implementation has excellent performance in time-varying RF environments. The forget factor, λf, is generally chosen between 0.95 and 0.99. Note that in RLS implementations, one can update the weights with every snapshot; however, it is neither practical nor recommended. Many snapshots are skipped between weight updates, and the adaptive weights are stale. Furthermore, many updates may be needed before the weights to converge to a steady-state value, and it can exhibit stability problems in finite-precision implementations. 26.5.5.3

Least Mean Squares (LMS)

In an LMS implementation, one does not calculate the inverse of the covariance matrix or solve a system of

15/12/2020 5:48:41 PM

26.5 Array Signal Processing for GNSS Receivers

(a) 55

55

50

50 C/N0(dB–Hz)

C/N0(dB–Hz)

(b)

45 40 NS BF/NS CV OP

35 30 –90

–60

–30

0

45 40 NS BF/NS CV OP

35

30

60

30 –90

90

–60

–30

50

0

0

Code Delay Bias (cm)

50

–50

–100

–150 –90

NS BF/NS CV

–60

–30

0 θ (deg)

30

60

NS BF/NS CV

150 100

0 –50 –100

60

90

NS BF/NS CV

–60

–30

0 θ (deg)

30

60

90

30

60

90

NS BF/NS CV

100 50 0 –50 –100 –150

–150 –90

30

–100

150

50

0 θ (deg)

–50

–150 –90

90

Carrier Phase Bias (deg)

Code Delay Bias (cm)

θ (deg)

Carrier Phase Bias (deg)

711

–60

–30

0 θ (deg)

30

60

–90

90

–60

–30

0 θ (deg)

Figure 26.27 Simulated performance of an adaptive antenna array showing C/N0, code delay bias, and carrier-phase bias versus elevation angle in the presence of (a) two wideband interferers and (b) three narrowband interferers.

equations. Instead, the covariance matrix Φ is used directly to update the antenna weights, which leads to a very efficient implementation. Originally, LMS was developed for MMSE-based adaptive antennas [68]. It was suggested that the weights be updated using w n + 1 = w n + μ n E x∗ n ϵ n ,

26 63

where μ[n] is a scalar constant‚ and ϵ[n] is the error between the array output and the reference signal. That is,

c26.3d

711

ϵ n = r n − xT n w n

26 64

Substituting Eq. 26.64 into Eq. 26.63 yields w n + 1 = w n + μ n E x∗ n r n − μ n E x∗ n xT n w n

26 65 = w n + μ n sr n − μ n Φ n w n

26 66

Note that in a static signal environment, the weights will converge to their steady-state values as given in Eq. (26.53).

15/12/2020 5:48:41 PM

712

26 GNSS Receiver Antennas and Antenna Array Signal Processing

Also, Φ is used directly in updating the antenna weights, so the weights can be updated very efficiently. In an LMS implementation, like an RLS implementation, the weights can be updated with every snapshot. However, it is not recommended‚ as the weights can become noisy. In practice, many samples are skipped between weight updates. One can use all these samples or a fraction of these samples to estimate sr[n] and Φ[n]. LMS implementations also lead to stale weights in the sense that previously updated weights are used with the most recent snapshots. In an LMS implementation, weights go through a transition before reaching their steady-state value. The transition period or convergence time depends on μ[n]. The larger μ[n] is, the faster the convergence will be. If μ[n] is selected to be too large, the system becomes unstable as it (LMS) is a closed-loop implementation in that input as well as output are used to update the antenna weights. For a stable system, μn =

E

xT

γ n x∗ n

=

γ , Pn

26 67

where 0 < γ < 1 and P[n] is the total power in all the signals incident on the antenna array. μ[n] decreases with an increase in P[n]. Also‚ the strongest signal dictates the selected value of μ[n]. For signal scenarios consisting of jammers with a large dynamic range, the convergence rate can be quite slow. In fact, the convergence rate depends on the eigenvalue spread of the covariance matrix. The larger the spread is, the slower the convergence will be. Nevertheless, the implementation is stable, converges to steady-state values of the weights‚ and is efficient to implement. The weights in Eq. 26.66 can also be written as w n + 1 = I − μ n Φ n w n + μ n sr n ,

26 68

which represents the LMS implementation of MMSE-based adaptive antennas. For LCMV-based adaptive antennas, the LMS implementation is given by w n + 1 = P I − μ n Φ n w n + f,

26 69

where P and f depend on the constraint vector, uc, and are defined as P = I − fuH c , uc f= H uc uc

712

Space-Frequency Adaptive Processing

In the above discussion, STAP was used to calculate and apply the antenna filtering in the time domain. One can also carry out this processing in the frequency domain using the fast Fourier transform (FFT) to transfer the antenna snapshots back and forth to the frequency domain [69, 70]. Frequency domain processing provides the ability to process individual frequency bins independently. That is, instead of dealing with a single KL × KL correlation matrix, one deals with L, K × K matrices. While this technically leads to suboptimal performance, the increase in computational efficiency allows one to make up for the loss in performance by increasing the number of frequency bins. Thus, when the number of taps becomes large, single-bin processing becomes quite attractive. For example, if a STAP system has 15 taps, single-bin frequency processing can have 32 or 64 bins. The use of this single-bin frequency processing is sometimes referred to as narrowband STAP or SFAP. It has been shown that the implementation requirements of SFAP are significantly lower than those of STAP as the length of the adaptive filter increases [71]. For improved performance in an SFAP implementation, time domain snapshots can be multiplied by a window function before the application of the FFT. This limits spectral leakage of strong narrowband interference to a few frequency bins. The inverse of the window function is applied to the time domain samples obtained after the inverse FFT is applied to the output frequency domain samples. SFAP processed the received signals in batches, and the processing can distorts the end samples of a batch of the time domain samples. To minimize this distortion, some overlapping of the time domain samples is carried out. In general, 50% overlapping is carried out; that is, each time domain sample is processed twice, although it has been shown that one can easily reduce the overlapping to 25% in order to further reduce the implementation requirements [71]. SFAP has many other attractive features, such as its increased frequency resolution over large bandwidths, and the ability to completely remove the antenna-induced biases when performing beamforming.

26 70

H Note that uH c f = 1, uc P = 0 , and the weights in Eq. 26.69 meet the selected constraint (i.e., uH c w n + 1 = 1). Many variants of RLS and LMS implementations have been proposed in the open literature. In fact, before the digital revolution, this was one of the most researched topics. While implementations that lead to faster convergence and are still stable have been proposed, they come with an increased cost of implementation.

c26.3d

26.5.6

26.6

Summary

Modern GNSS receiver systems must meet a number of increasing demands, including higher precision, a larger number of supported GNSS signals, incorporation into smaller platforms, and increased reliability in a wider range of environments. The antennas chosen for these systems play an important role in satisfying these requirements. This chapter has provided a high-level review of the key

15/12/2020 5:48:41 PM

References

features of antennas for modern GNSS receiver systems. It is by no means comprehensive. The reader is referred to alternate references, such as [13], for more detailed information. The importance of the antenna in the overall system should not be disregarded, since it plays a crucial role in determining signal quality and driving error budgets for state-of-the-art precision applications. The use of antenna arrays with GNSS receiver systems has now become commonplace. Although we have focused on one of their most advantageous capabilities – adaptive interference suppression – they offer numerous other uses, including precise attitude determination, high gain, and direction-of-arrival verification. Recent work has gone into the miniaturization of antenna arrays to open up the range of applications and platforms. Although array processing has been computationally demanding in the past, steady improvements in computation performance have eased this burden‚ and we will likely see improvements as array signal processing is more deeply integrated with receiver processing in the near future.

9 G. Wubbena, “A new approach for field calibration of

10

11

12

13 14

15

16

References 1 C.A. Balanis, Antenna Theory: Analysis and Design (3rd 2 3

4

5

6

7

8

c26.3d

713

Ed.), John Wiley & Sons, Hoboken, NJ, 2005. J.D. Kraus and R.J. Marhefka, Antennas, McGraw-Hill, New York, 2002. A.J. O’Brien, I.J. Gupta, C.J. Reddy, and F.S. Werrell, “Space-time adaptive processing for mitigation of platform generated multipath,” in Proc. 2010 Int. Tech. Meeting of The Inst. of Navigation, San Diego, California, January 2010, pp. 646–656. A. OBrien, K. Hayhurst, and I.J. Gupta, “Effect of rotor blade modulation on GNSS receivers,” in Proc. ION GNSS 2009, Savannah, Georgia, September 2009. Y. Yashcheshyn et al., “Evaluation of the impact of the virtual phase centre effect on the accuracy of the positioning system,” 3rd European Conf. on Ants. Prop., March 2009, pp. 2930–2933. W. Kunysz, “Antenna phase center effects and measurements in GNSS ranging applications,” 14th Int. Symp. Ant. Tech. App. and Am. EM. Conf. (ANTEMAMEREM), 2010. C. Church, I.J. Gupta, and A. O’Brien, “Adaptive antenna induced biases in GNSS receivers,” in Proc. 63rd Annu. Meeting of The Inst. of Navigation (ION 2007), Cambridge, Massachusetts, April 2007, pp. 204–212. G.L. Mader, “GPS antenna calibration at the national geodetic survey,” GPS Solutions, 3 (1): pp. 55–58, 1999.

713

17 18 19

20 21

22

23

24

25

26

absolute antenna phase center variations,” in Proc. ION GPS-96, Kansas City, Missouri, 1996. R. Schmid, “Absolute phase center corrections of satellite and receiver antennas,” GPS Solutions, 9: pp. 283– 293, 2005. B. Gorres et al., “Absolute calibration of GPS antennas: Laboratory results and comparison with field and robot techniques,” GPS Solutions, 10: 136–145, 2006. A.S.C. Svendsen, “GPS antenna and receiver for small cylindrical platforms,” PhD dissertation, Dept. Elect. & Comput. Eng., The Ohio State University, Columbus, 2012. B. Rama Rao et al., GPS/GNSS Antennas, Artech House, Boston, 2013. C.-C. Chen, S. Gao, and M. Maqsood, “Antennas for Global Navigation Satellite Systems (GNSS) receivers,” Chap.14, Space Antenna Handbook (eds. W.A. Imbriale, S. Gao, and L. Boccia), Wiley, May 2012. J.L. Volakis, C.C Chen, and K. Fujimoto, Small Antennas: Miniaturization Techniques and Applications, McGrawHill, New York, 2010. G. Kumar and K. Ray, Broadband Microstrip Antennas, Artech House, Boston, 2003 K.R. Carver, J.W. Mink, “Microstrip Antenna Technology,” IEEE Trans. Ants. Prop., 29, pp. 2–24, January 1981. C.C. Kiglu, “Resonant Quadrifilar Helix,” IEEE Trans. Ants. Prop., 17, pp. 349–351, May 1969. O. Leisten, et al., “Miniaturized Dielectrically Loaded Quadrifilar Antennas for Global Positioning Systems (GPS),” Electron. Lett., 37, pp. 1321–1322, October 25, 2001 R. Garg et al., Microstrip Antenna Design Handbook, Artech House, Norwood, Massachusetts, 2001 J.R. James and P.S. Hall, Handbook of Microstrip Antennas, Volumes 1 and 2, IEE Electromagnetic Series, Peter Peregrinus Ltd., 1989. Y. Zhou, C. Chen and J.L. Volakis, “Single-fed circularly polarized antenna element with reduced coupling for GPS arrays,” in IEEE Trans. Ants. Prop., Vol. 56, No. 5, pp. 1469– 1472, May 2008. Y. Zhou, C.C. Chen and J.L. Volakis, “Dual band proximity-fed stacked patch antenna for tri-band GPS applications,” IEEE Trans. Ant. Prop., Vol. 55, pp. 220–223, January 2007. M. Chen and C.-C. Chen, “A compact dual band GPS antenna design,” IEEE Ant. Wireless Prop. Lett., 12, pp. 245– 248, January 2013. S. Liu and Q.-X. Chu, “A novel dielectrically loaded antenna for triband GPS applications,” Proc. 38th Eur. Microwave Conf., pp. 1759–1762, 2008. D. Lamensdorf and M.A. Smolinski, “Dual-band quadrifilar helix antenna,” Digest of IEEE Ant. Prop. Soc. Symp., 3, pp. 488–491, June 2002.

15/12/2020 5:48:41 PM

714

26 GNSS Receiver Antennas and Antenna Array Signal Processing

27 D. Lamensdorf et al., “Dual-band quadrifilar helix

46 T. Ford et al., “Magnetic beeline – Satellite derived attitude

antenna,” US Patent 6,653,987, November 25, 2003. 28 G. Brown, “The Turnstile antenna,” Electronics, April 1936. 29 G. Brown, “Antenna system,” US Patent 2086976, July

13, 1937.

47

30 V. Rumsey, “Frequency independent antennas,” IRE

National Convention Record, Pt. 1, pp. 114–118, 1957. 31 J. Donnellan and R. Close, “A spiral-grating array,” IRE 32 33 34

35

36

37 38

39 40

41

42

43

44

45

c26.3d

714

Trans. Ants. Prop., 9, pp. 291–294, May, 1961. J. Dyson, “The equiangular spiral antenna,” IRE Trans. Ants. Prop., 7, pp. 181–187, April 1959. W. Curtis, “Spiral antennas,” IRE Trans. Ants. Prop., 8, pp. 293–306, May 1960. J. Kaiser, “The Archimedean two-wire spiral antenna,” IRE Trans. Antennas Prop., Vol. AP-8, pp. 312–323, May 1960. J.D. Dyson, R. Bawer, P.E. Mayes and J.I. Wolfe, “A note on the difference between equiangular and Archimedes spiral antennas,” IEEE Trans. Micro. Theory Tech., 9, pp. 203–205, March 1961. J. Dyson and P. Mayes, “New circular-polarized frequencyindependent antennas with conical beam or omnidirectional patterns,” IEEE Trans. Ants. Prop., 9, pp. 334–342, July 1961. Roke Manor Research Ltd., Data Sheet, Triple GNSS Geodetic Grade Antenna. J.J.H. Wang and D.J. Triplett, “High performance universal GNSS antenna based on SMM Antenna Technology,” Proc. IEEE Int. Symp. Microwaves, Antennas, Propagation, and EMC Technologies for Wireless Communications, 2007. W. Kunysz, “High performance GPS pinwheel antennas,” Proc. ION GNSS Conf., pp. 2506–2511, September 2000 F. Scire-Scappuzzo and S.N. Makarov, “A low-multipath wideband GPS antenna with cutoff or non-cutoff corrugated ground plane,” IEEE Trans. Antennas and Propagation, 57, pp. 33–46, January 2009. E. Krantz, S. Riley and P. Large, “The design and performance of Zephyr Geodetic Antenna,” Proc. ION GNSS Conf., pp. 1942–1951, September 2001. F.N. Bauregger et al., “A novel dual-patch anti-jam GPS antenna,” Proc. 58th Annu. Meeting of The Inst. of Navigation and CIGTF 21st Guidance Test Symposium (2002), Albuquerque, New Mexico, pp. 516–522, June 2002. N. Surittikul, “Pattern reconfigurable printed antennas and time domain method of characteristic modes for antenna analysis and design,” PhD dissertation, Dept. Elect. & Comput. Eng., The Ohio State University, Columbus, 2006. K.W. Lee, R.G. Rojas, and N. Surittikul, “A pattern reconfigurable microstrip antenna element,” Microw. Opt. Technol. Lett., 48: 1117–1119. Doi:10.1002/mop.21555. B.R. Rao and E.N. Rosario, “Spatial null steering microstrip antenna array,” US Patent 6,597,316 B2, July 22, 2003.

48

49

50

51

52

53

54

55

56

57

58

for marine navigation,” Proc. 11th Int. Tech. Meeting of the Satellite Division of The Inst. of Navigation (ION GPS 1998), Nashville, Tennessee, pp. 1245–1255, September 1998. M. Appel, A. Konovaltsev, and M. Meurer, “Robust spoofing detection and mitigation based on direction of arrival estimation,” Proc. 28th Int. Tech. Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, pp. 3335–3344, September 2015. R.L. Fante and J.J. Vaccaro, “Wideband cancellation of interference in a GPS receiver array,” IEEE Trans. Aerosp. Electron. Syst., Vol. 36, April 2000. D. Wilson and S. Ganguly, “Flexible GPS receiver for jammer detection, characterization and mitigation using a 3D CRPA,” Proc. 19th Int. Tech. Meeting of the Satellite Division of the Inst. of Navigation (ION GNSS 2006), Fort Worth, Texas, pp. 189–200, September 2006. B.A. Kramer, M. Lee, C-C. Chen, J.L. Volakis, “A miniature conformal spiral antenna using inductive and dielectric loading,” Proc. 2007 IEEE Ant. Prop. Soc. Int. Symp., pp.1004–1007, June 2007. A.S.C. Svendsen and I.J. Gupta, “Adaptive antenna for handheld GPS receivers,” Navigation, Journal Inst. Navigation, Vol. 58, No. 3, pp. 221–228, Fall 2011. A.S.C. Svendsen and I.J. Gupta, “The effect of mutual coupling on the nulling performance of adaptive antennas,” IEEE Ant. Prop. Mag., Vol. 54, No.3, pp. 17–38, June 2012. A.J. O’Brien and I.J. Gupta, “Comparison of output SINR and receiver C/N0 for GNSS adaptive antennas,” IEEE Trans. Aerosp. Electron. Syst., Vol. 45, No. 4, pp.1630–1640, October 2009. H.L. Van Trees, Optimum Array Processing: Part IV of Detection, Estimation and Modulation Theory, Wiley Interscience, 2002. Compton, R.T. Jr., “The power-inversion adaptive array: Concept and performance,” IEEE Trans. Aerospace Elect. Sys., Vol. 15, pp. 803–814, November 1979. A.J. O’Brien and I.J. Gupta, “An optimal adaptive filtering algorithm with zero antenna-induced bias for GNSS antenna arrays,” Navigation, J. Inst. Navigation, Vol. 57, No. 2, pp. 87–100, Summer 2010. U.S. Kim, “Analysis of carrier phase and group delay biases introduced by CRPA hardware,” Proc. 18th Int. Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, California, pp. 635–642, September 2005. D.S. De Lorenzo, J. Rife, P. Enge, and D.M. Akos, “Navigation accuracy and interference rejection for an adaptive GPS antenna array,” Proc. 19th Int. Tech. Meeting of the Satellite Division of The Inst. of Navigation (ION GNSS 2006), Fort Worth, Texas, pp. 763–773, September 2006.

15/12/2020 5:48:41 PM

References

59 A.J. O’Brien and I.J. Gupta, “Mitigation of adaptive

60

61

62

63

64

65

c26.3d

715

antenna induced bias errors in GNSS receivers,” IEEE Trans. Aerosp. Electron. Syst., Vol.47, No.1, pp. 524–538, January 2011. Y.C. Chuang and I.J. Gupta, “On-the-fly estimation of antenna induced biases in SFAP based GNSS antenna arrays,” Navigation, J. Inst. Navigation, Vol. 61, No. 4, pp. 323–330, Winter 2014. A. Konovaltsev, D.S. De Lorenzo, A. Hornbostel, and P. Enge, “Mitigation of continuous and pulsed radio interference with GNSS antenna arrays,” Proc. 21st Int. Tech. Meeting of the Satellite Division of The Inst. of Navigation (ION GNSS 2008), Savannah, Georgia, pp. 2786–2795, September 2008. Y.C. Chuang, “Blind adaptive beamforming for GNSS receivers,” PhD dissertation, Dept. Elect. & Comput. Eng., The Ohio State University, Columbus, 2015. I.L. Frost III, “An algorithm for linearly con- strained adaptive array processing,” Proc. IEEE, Vol. 60, pp. 926– 935, August 1972. L.J. Griffiths and C.W. Jim, “An alternative approach to linearly constrained adaptive beam-forming,” IEEE Trans. Ant. Prop., January 1982, Vol. AP-30, pp. 27–34. L.S. Resende, J.M.T. Romano, and M.G. Bellanger, “A fast least-squares algorithm for linearly constrained adaptive

66

67

68 69

70

71

715

filtering,” IEEE Trans. Signal Process., Vol. 44, pp. 1168– 1174, May 1996. M.L.R. de Campos, S. Werner, and J.A. Apolinario, Jr., “Constrained adaptation algorithms employ ing householder transformation,” IEEE Trans. Signal Process., Vol. 50, pp. 2187–2195, September 2002. J.A. Apolinario, Jr., S. Werner, and M.L.R. de Campos, “On the equivalence of RLS implementations of LCMV and GSC processors,” IEEE Signal Process. Lett., Vol. 10, pp. 356–359, December 2003. B. Widrow et al., “Adaptive antenna systems,” Proc. IEEE, Vol. 55, pp.2143–2159, December 1967. R.T. Compton, Jr., “The relationship between tapped delay-line and FFT processing in adaptive arrays,” IEEE Trans. Ant. Prop., Vol. 36, pp. 15–26, January 1988. I.J. Gupta and T.D. Moore, “Space-frequency adaptive processing for radio frequency interference mitigation in spread spectrum receivers,” IEEE Trans. Aerosp. Electron. Syst., 52: 1611–1616, June 2004. T.D. Moore, “Analytic study of space-time and spacefrequency adaptive processing for radio frequency interference suppression,” PhD dissertation, Dept. Elect. Eng., The Ohio State University, Columbus, 2002.

15/12/2020 5:48:41 PM

717

Part C Satellite Navigation for Engineering and Scientific Applications

719

27 Global Geodesy and Reference Frames Chris Rizos1, Zuheir Altamimi2, and Gary Johnson3 1

University of New South, Wales, Australia Institut National de l’Information Géographique et Forestière, France 3 Geoscience, Australia, Australia 2

27.1

Global Geodesy

27.1.1

Background

Geodesy is the science of the study of Earth’s properties of shape, gravity, and rotation [1] – requiring their measurement in both a spatial and temporal sense. These properties change with time because Earth is a dynamic system comprising fluid atmosphere and oceans, mobile tectonic plates and active geological faults, changing distributions of ice, snow, surface and ground water, and numerous deep Earth processes. In the past half century or so, geodetic science has been revolutionized by the expansion of the geodetic measurement toolkit to include a number of space techniques, based primarily on the tracking of artificial Earth satellites, such as the global navigation satellite system (GNSS), satellite and lunar laser ranging, and Doppler frequency measurements; as well as the radio-astrometric technique known as Very Long Baseline Interferometry (VLBI). In modern geodesy, “shape” can be considered synonymous with “position” – the mathematical description of location of any point on or above the surface of Earth with very high accuracy – for which GNSS is ideally suited. The focus of modern geodesy is now the monitoring of changes with time of the three fundamental Earth properties of shape: 3D position of ground stations, gravity, and rotation. This requires the definition, realization, and maintenance of high-fidelity, high-accuracy geodetic reference systems – the one most relevant for the aforementioned space geodetic techniques being the Terrestrial Reference System (TRS). Its practical realization – the Terrestrial Reference Frame (TRF) (see Section 27.3) – allows comparison of geodetic measurements that have been made over periods of up to several decades, so that variations in the size and shape, gravity field‚ and rotational characteristics of Earth can be

reliably determined. Geodesy is therefore providing vital insights into dynamic Earth System processes (Chapter 28). Geodesy is also a geospatial discipline that provides the foundation for surveying and mapping (Chapter 55). Geodesy does this by providing the TRF so that the temporal coordinates of any object, built structure, or land feature can be unambiguously expressed; as well as by aiding the development of the tools and methodologies for precise positioning and mapping. It is not surprising that geodesy performs these dual functions because the same GNSS technology, and the TRF that services geodetic science, are also used by many other geospatial applications in engineering, surveying, navigation, and mapping. In the context of this chapter, GNSS geodesy comprises the following:

• • •

Precise GNSS positioning methodologies that have been developed over the past three or so decades – the mathematical modeling of carrier-phase observations, the operational procedures for determining sub-centimeterlevel coordinate accuracies, the field receivers that track the GNSS signals, the measurement processing software, and so on [2–4]. Ground infrastructure used to augment GNSS accuracy – the networks of permanent GNSS receivers installed at ground stations which substantially improve GNSS positioning accuracy, and which, in addition, are vital to both the definition of national TRFs as well as providing a means of connecting to the appropriate TRF for the geospatial or geoscience application of interest. GNSS services to support precise geodetic positioning – to overcome some of the systematic errors of GNSS positioning, such as satellite orbit and clock errors, satellite signal biases, and atmospheric signal disturbances, such as provided by the International GNSS Service (IGS) [5].

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

720

27 Global Geodesy and Reference Frames

•

TRFs defined at the global, regional‚ or national level in which the precise coordinates are expressed – in this regard‚ special mention should be made of the role of the IGS in providing the means to connect to the global TRF (see Section 27.2).

This chapter is organized into three parts. The first part is an introduction to space geodesy, the principles of GNSS geodesy, and the International Association of Geodesy (IAG). The IAG is the scientific association that organizes the space geodetic services that support high-accuracy GNSS positioning for scientific and societal applications. The most important of the IAG services is the IGS, and the second part of the chapter gives a short description of the IGS and its role in providing the geodetic infrastructure and services that underpin precision GNSS positioning. The third part describes one of the most important products of modern geodesy, the TRF. A brief explanation is given of how the International Terrestrial Reference Frame (ITRF) is realized, including some information on the current ITRF2014.

27.1.2

The IAG

At the invitation of the Prussian General Johann Jacob Baeyer, representatives of the states of Prussia, Austria, and Saxony met in 1862 in Berlin to discuss Baeyer’s “Proposal for a Central European Arc Measurement.” By the end of that year, 16 nation-states had agreed to participate in the project: Austria, Belgium, Denmark, France, seven German states (Baden, Bavaria, Hannover, Mecklenburg, Prussia, Saxony, and Saxe-Gotha), Italy, the Netherlands, Poland, Sweden, Norway, and Switzerland. The IAG counts this international scientific initiative, and the organization it spawned, as its origin [6]. The idea for the project had been submitted by Baeyer to the Prussian Ministry of War in his document “On the Size and Figure of the Earth: A Memorandum on the Establishment of a Central European Arc Measurement, Along with a Sketch Map” (“Über die Größe und Figur der Erde: eine Denkschrift zur Begründung einer Mitteleuropäischen Gradmessung nebst einer Übersichtskarte”). The aim was to connect the numerous Central European astronomical observatories by the existing or planned triangulation networks, in order to determine the regional and local anomalies of the curvature of the figure of Earth. This was the basis for all precise point positioning in science and practice, and the beginning of interpreting these anomalies with respect to the structure and composition of the outer layer of Earth, which was explicitly mentioned by Baeyer as a scientific challenge. The project extended rapidly to other European states‚ and consequently the name of the

organization was changed in 1867 to “Europäische Gradmessung,” and in 1886 to “Internationale Erdmessung” (“Association Internationale de Géodésie”) with additional member states Argentina, Chile, Japan, Mexico, and the United States. A primary motivation for the founding of these associations was to encourage international cooperation for a practical geodetic project, with the outcome being improved reference frame and geoid knowledge to support continent-wide mapping [6]. It must be acknowledged that the (perhaps utopian) goals of close European cooperation and unfettered sharing of geodetic data were not substantially achieved until well after World War II. However, in the past few decades‚ the IAG again strongly promoted global collaboration to advance the science and practice of geodesy. Today, the IAG is an important association under the umbrella of the International Union of Geodesy and Geophysics, which in 2019 celebrated its founding centenary [7]. The IAG [8] accomplishes its mission through the activities of its commissions, inter-commission committees, services, and the Global Geodetic Observing System (GGOS – [9]). The IAG services span the relevant geometric, gravimetric, oceanographic, and related properties of Earth. GGOS was established by the IAG in 2007 to support the ambitious goals of modern geodesy, derived from the recognition that geodesy is an observational science that nowadays deals with [10] (Figure 27.1):

• • • • • • •

Monitoring of the solid Earth (i.e. displacement, subsidence or deformation of the ground and structures, due to tectonic, volcanic‚ and other natural phenomena, as well as human activity). Monitoring of variations in the liquid Earth (e.g. sea level rise, ice sheets, mesoscale sea surface topography features, mass transport). Monitoring variations in the Earth’s rotation (polar motion, length of day). Monitoring the atmosphere with satellite geodetic techniques (ionosphere and troposphere composition, and physical state). Monitoring the temporal variations in the gravity field of the Earth, as well as mapping the geoid with increasing accuracy and spatial resolution. Determining satellite orbits (including those of Earth observation and navigation satellites). Determining positions, and their changes with time, of points on or above the surface of the Earth with the utmost accuracy.

The IAG services of the four primary space geodesy techniques are the cornerstones of GGOS: the IGS [5, 11], the International Laser Ranging Service (ILRS – [12, 13]), the

27.1 Global Geodesy

adjustments due to deglaciation since the last glacial maximum and to current mass change of the ice sheets; pre-, co-, and post-seismic deformations associated with large earthquakes; early warnings for tsunamis, landslides, earthquakes, and volcanic eruptions; as well as deformation and structural monitoring.

27.1.3

Figure 27.1 The Global Geodetic Observing System (GGOS): applications, geoscience parameters‚ and space geodetic techniques. Source: Reproduced with permission of GGOS.

International VLBI Service for Geodesy and Astrometry (IVS – [14, 15]), and the International Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) Service (IDS – [16, 17]). These services generate products, including precise satellite orbits and clocks, ground station coordinates, Earth rotation parameters, atmospheric refraction quantities, and others. Networks of the space geodesy observing stations of these geometric IAG services are the physical realization of the ITRF [18]). The International Earth Rotation and Reference Systems Service (IERS – [19]) is responsible for combining the necessary analyses of the individual geometric IAG services to produce the ITRF – so as to satisfy the requirements for science and society for a stable, high-accuracy, global geodetic reference frame. The latest realization is known as ITRF2014 (see Section 27.3 [20]). The majority of the fundamental observing stations underpinning the ITRF realization belong to the IGS tracking station network (Figure 27.4 [21]). A challenge that geodesy is now facing is to maintain the ITRF accuracy and stability over time at the level of millimeter and sub-millimeter per year, respectively, that is required for Earth science applications [10], such as the determination of global sea level change; glacial isostatic

The Impact of GNSS on Modern Geodesy

What has enabled geodesy to change from an obscure applied science to today’s cutting-edge geoscience? There are a number of reasons for this. First, modern geodesy relies on space technology, and enormous strides have been made in accuracy, resolution, and coverage due to advances in satellite sensors and an expanding suite of satellite missions. Second, geodesy can determine Earth parameters to an accuracy that no other remote sensing technique can. These include the position and velocity of points on the surface of the Earth, the shape and variations of the ocean, ice and land surfaces, and the spatial and temporal features of the gravity field. However, what relentlessly drives geodesy into the future is the innovative use of GNSS signals. GNSS is the most versatile space geodetic technology ever developed for high-accuracy positioning of points on or above the surface of the Earth. GNSS is therefore crucial to studying the faint signatures of the Earth that find expression in changes in shape of the Earth’s surface via time-varying coordinates of sampled ground points. This also requires a highly accurate ITRF. Furthermore, GNSS is the "go-to" technology for precise orbit determination of satellite altimetry, gravity mapping, and remote sensing satellites (Chapter 28). In addition, GNSS is a technology for monitoring important parameters of the atmosphere and Earth’s surface – the former by virtue of the distortion of GNSS signals as they propagate through the ionosphere (Chapter 31) and troposphere (Chapter 30), and the latter from an analysis of reflected GNSS signals off the ocean and land surfaces (Chapter 34). High-accuracy GNSS positioning is synonymous with the differential positioning mode that utilizes (a minimum of ) two receivers, with one antenna set up at a reference station of known coordinate, and the other at the point whose coordinate needs to be determined – which may be a static ground station or a moving platform [22, 23] (Chapter 19). As a result, GNSS positioning accuracy can be defined in relative terms, for example‚ as a ratio of coordinate error (typically expressed as a 95% uncertainty) to distance (separating the two GNSS receivers). The coordinate error can then be expressed in distance units by scaling the ratio by this baseline distance. For example, “0.1 parts-per-million” (or ppm) is a relative accuracy measure of 1 cm (95% confidence value) between two receivers 100 km

721

722

27 Global Geodesy and Reference Frames

apart, or 10 cm error over a 1000 km baseline distance, and so forth. The differential GNSS techniques based on carrierphase measurements can deliver relative coordinate accuracies as low as a few millimeters when top-of-the-line GNSS receivers are used, following strict operational guidelines, and the measurements are processed using sophisticated software [23]. The reader is referred to such texts as [3, 4] for a detailed treatment of the measurement models and algorithms that make possible such high-accuracy positioning performance. However, in addition to hardware, software, and operational procedures, there are several other innovations of GNSS geodesy that have contributed to making it such a powerful technology. The first one was the widespread establishment of permanent GNSS reference receivers, or continuously operating reference stations (CORSs). In the early 1980s, use of GPS for geodetic applications required the measurement of baselines between pairs of simultaneously operating receivers over distances from several tens to hundreds, and even thousands of kilometers. The research organizations and government agencies that conducted such surveys were responsible for the setting up, operation, and demount of all the receivers. This would be done in the context of a geodetic survey to establish (typically) a network of coordinated ground marks to define a nation’s reference frame. For geoscience applications, changes in ground

mark coordinates were measured by GPS surveys that were repeated on (for example) an annual basis. There was a considerable logistical challenge in executing GNSS geodetic surveys in this way. A network of CORSs would obviate the need to operate reference receivers during GNSS surveys, and would be especially useful for geodetic tasks such as the monitoring of continuous (as opposed to episodic) changes in the coordinates of ground marks used to characterize crustal motion or ground deformation. CORSs range from single-receiver installations to vast networks of CORS across entire countries (as in Japan’s GEONET [24]), regions (e.g. EUREF’s permanent CORS network [25]), and globally (for example‚ the IGS station network with more than 500 stations [21]). Most CORS networks are not homogeneous, with different agencies and organizations being responsible for their operation. CORSs may have different equipment configurations, different types of antennas and ground mark monuments, addressing the needs of different user communities. However, GNSS geodesy, particularly via the IGS (Section 27.2), strives to standardize the site and equipment guidelines [26]. Figure 27.2 shows a typical choke-ring antenna installed on a concrete pillar (left, without radome) and on a rigid tripod (right, with radome). Not shown in either image is the instrument cabinet where the receiver itself is housed (together with communications, batteries, and

Figure 27.2 Two examples of geodetic-grade continuously operating reference station GNSS installations. (Left) On concrete pillar at Mount Stromlo, outside Canberra, Australia, without radome, in front of the satellite laser ranging (SLR) tracking station; (right) drilledbraced monument at Petrof Lake, Alaska, United States, part of the EarthScope Plate Boundary Observatory (left photo credit: Geoscience Australia; right photo credit: UNAVCO). Source: Reproduced with permission of Geoscience Australia; Reproduced with permission of UNAVCO.

27.1 Global Geodesy

other ancillary equipment), power systems such as solar panels, lightning protection, additional pillars or witness marks, and so on. CORS installations such as these are a considerable investment by an agency or organization in GNSS ground infrastructure for accuracy augmentation. CORS ground infrastructure is a defining characteristic of GNSS geodesy and surveying. A second innovation is the availability of a variety of GNSS products and services, including those provided directly by the IGS [27], by web services for GNSS measurement processing [28–30], and by service providers for realtime GNSS positioning for surveying and engineering applications [31–33]; as well as standardized data and transmission formats that support GNSS interoperability [34, 35]. The third innovation is the increasing adoption of the ITRF [18] (Section 27.3). There are a number of reasons for this: 1) The ITRF is globally applicable and maintained by the IERS as a scientific service. 2) The coordinates of many GNSS CORSs provide a connection to the ITRF. 3) Any GNSS receiver can be easily connected to the ITRF using a variety of positioning techniques (Chapters 19 and 20), via CORS measurements and the aforementioned IGS GNSS products and services.

whose coordinate was to be determined. The processing was undertaken one observation session at a time, to compute the single-session baseline vectors between the pair of simultaneously operating receivers, which were then combined into a geodetic network. A network of coordinated ground points observed in this way is an effective realization of a geodetic datum that can be used for subsequent surveying and mapping tasks. In summary, GNSS geodesy is characterized by the following:

• • •• • • •

Records carrier-phase measurements in the field, during a specified observation period. Uses top-of-the-line geodetic-grade receivers and antennas. Installed on stable ground monuments. Facilitates the determination of relative coordinates between a minimum of two simultaneously operating stationary receivers. Used for continental-scale projects and (typically) long baselines. Subsequently processed using sophisticated multi-station, multi-session software. Incorporates additional information on reference frame and measurement errors from geodetic service providers.

27.1.4.2

27.1.4 27.1.4.1

Geodetic GNSS Surveying and Geodesy

GNSS is a fundamental tool for the geodetic, land, engineering‚ and hydrographic surveyor [23]. As already mentioned, GNSS survey tasks relate to the determination of highaccuracy coordinates in a well-defined reference frame, using positioning techniques based on the processing of carrier-phase measurements. This enhanced GNSS positioning accuracy is possible because of the refinement of the special instrumentation, the sophisticated software, and field operations that has taken place over the last three decades or more. Differential GNSS (DGNSS) is capable of achieving positioning accuracies three orders of magnitude higher than using the standard single-receiver GPS technique (Chapter 2). GNSS geodesy is an extension of GPS geodesy principles. All mathematical concepts, measurement principles, operational procedures‚ and applications were first developed using GPS technology. The first decade of GPS geodesy was characterized by static positioning‚ in which two GPS receivers recorded measurements during an observation session, and subsequent measurement processing back in the office computed the baseline vector connecting a ground mark of known geodetic coordinate to a point

Static GNSS Positioning Techniques

One of the key features of DGNSS techniques compared to terrestrial geodetic techniques is that inter-visibility between pairs of observing GNSS receivers is not necessary. In fact, the distance between GNSS receivers may range from several kilometers to hundreds, and even thousands of kilometers. The ground marks whose coordinates are to be determined are static. For many geodetic applications, great care is taken to build stable monuments upon which the GNSS antennas are mounted – concrete pillars, steel pins, metal tripods‚ or poles – fixed to bedrock or attached to structures (Figure 27.2). These coordinated ground marks can be used as datum control marks to which all other lower-accuracy surveys are connected using standard terrestrial or GNSS-based surveying and mapping techniques. When resurveyed on a regular basis (or monitored continuously), they can measure ground displacement or subsidence, either locally or in the context of large-scale tectonic movements, and so on. Surveys (and hence coordinates derived from them) were (and still are to a large extent) classified in a hierarchical sense – from the highest geodetic categories through to lower-accuracy control, engineering, and mapping surveys. The accuracies of such GNSS surveys range from the subcentimeter to perhaps the decimeter level. There is a complex relationship between the accuracy required and the

723

724

27 Global Geodesy and Reference Frames

GNSS hardware, field procedures, augmentation services, and measurement processing software that should be used [2, 23]. GNSS hardware varies the least – typically multifrequency, multi-constellation GNSS receiver equipment is used. In contrast, the measurement modeling within the processing software exhibits considerable variation, from commercial systems designed for land and engineering surveying that are optimized for short-baseline scenarios and ease of use, to geodetic software used for the long-baseline geoscientific applications referred to earlier. The pertinent characteristics of several GNSS geodesy methodologies are discussed below. Global GNSS Geodesy. GNSS geodesy makes use of ultra-accurate, long-baseline GNSS techniques – capable of relative positioning accuracies as high as a few parts-perbillion over baseline lengths of hundreds to thousands of kilometers. Applications are ITRF definition and maintenance (see Section 27.3), connecting national geodetic reference frames to the ITRF, precise satellite orbit determination, and tectonic motion studies. Some characteristics of GNSS geodesy are listed below:

• • • •

The carrier-phase measurements are made by top-of-theline, multi-frequency, multi-constellation GNSS receivers installed at stable ground marks or monuments. To date‚ GPS satellites are mostly being tracked, though increasingly measurements are also made to GLONASS, BeiDou, and Galileo satellites. Observation sessions are many hours (and even days) in length during which carrier-phase measurements are recorded for post-survey analysis. However, at CORS sites‚ this typically involves the segmentation into 24hour observation session measurement files for subsequent processing. The measurement processing is undertaken using complex geodetic software, which typically involves not only the computation of the coordinates of the GNSS receivers, but also a variety of signal biases, GNSS satellite orbits, atmospheric delay biases, and Earth Orientation Parameters (EOPs). Such analysis is typical of what IGS Analysis Centers undertake on a continuous basis (see Section 27.2).

GNSS for Geodetic Control. Geodetic surveying is concerned with the establishment of geodetic reference frames. These are typically at national scale, but they may also refer to individual project applications – though these are sometimes referred to as “control surveys”. Geodetic datums are realized by ground marks with known ellipsoidal coordinates that can be used by any surveyor or engineer as starting coordinates for subsequent surveys to support mapping, surveying, construction‚ or engineering activities. Precise GPS static positioning has revolutionized geodetic

surveying because it has replaced traditional laborintensive terrestrial surveying techniques. As in the case of global GNSS geodesy techniques, geodetic-grade receivers are used. Multiple receivers may be deployed (a minimum of two), which are used to record simultaneously tracked GPS (and increasingly other GNSS) satellites. Some characteristics of geodetic control GNSS surveys are listed below, for two field deployment scenarios:

•

•

Campaign mode single-baseline or multi-station: – Observation sessions are typically several hours in length, and measurements are recorded in data files for subsequent processing [35]. – Logistical considerations are important, so that receivers are moved to pre-established ground marks, and operated according to a carefully defined timetable [36]. – Recorded measurements from the pair (or more) of simultaneously operating receivers are processed, one observation session at a time, to compute the singlesession baseline vectors. The software that is used may be commercial (capable of ppm-level relative accuracy for relatively short inter-receiver distances, of several tens of kilometers or so), or geodetic-grade (when longer baselines are processed, or more complex multi-station/multi-session processing is undertaken). – Subsequently these single-session solutions may be combined in a secondary network adjustment when datum constraints are applied – typically in the form of “fixed” known coordinates of one or more datum points – if commercial software has been used. (This step may not be necessary if using state-of-the-art, multi-session geodetic-grade software.) In this way, the datum is propagated to other GNSS-surveyed ground marks. Surveys with the aid of CORS infrastructure: – Ground marks to be surveyed in the national datum are occupied as in the above scenario. The logistical challenges are substantially reduced, as the geodetic surveyor needs only to be responsible for transporting, setting up, and operating their own GNSS receiver(s). – Measurement processing is undertaken using the techniques mentioned above. The data files from the CORS are downloaded for subsequent measurement processing. – As an alternative to processing the measurement data themselves – a task that requires considerable analyst skill – surveyors can submit data files to one of several Web processing engines such as NGS’s OPUS [28], NRCAN’s CRCS-PPP [29], GA’s AUSPOS [30], and others.

GNSS Deformation Surveys. Ground deformation surveys are undertaken to measure the change in the

27.2 The IGS

coordinates of stable points or monuments fixed to the Earth’s surface or to engineered structures [23]. The points may move in a horizontal or vertical sense, or in three dimensions, with signature characteristics across a wide range of time and spatial scales, from motion on the order of millimeters or centimeters per year, to rapid ground or structural shaking reaching magnitudes of many decimeters. The sub-categories of deformation surveys include building or structural monitoring (during or after construction), building or structural movement due to wind or load effects, landslide monitoring, co-seismic displacement, ground subsidence (due to underground fluid extraction or mining) or inflation (due to build-up of magma below volcanoes), tide gauge stability monitoring, local tectonic fault motion, and post-seismic response. We can distinguish two typical deformation scenarios: small, slow, and (in general) steady motion, in contrast to large, rapid and (in general) unpredictable displacement. Some characteristics of GNSS deformation surveys are listed below:

•

•

•

Rapid ground displacement due to catastrophic events such as earthquakes, volcanic eruptions, landslides, and so on: – Continuous operations are ideal, and typically in realtime, remote monitoring mode. – Real-time (RT) continuous is typically in so-called "realtime kinematic" (RTK) mode [37] (Chapter 19), otherwise non-RT simplified measurement processing with commercial software in single-baseline mode [22]. – Monumentation, from highly stable, permanent antenna mounts to low-cost, temporary marks. – CORS, but installations may use low-cost, singlefrequency GNSS receivers, in circumstances where many monitoring receivers are required and/or there is a possibility they could be destroyed. Rapid deformation of structures due to wind and loads: – Continuous operations in real-time monitoring typically using the RTK GNSS technique (if in alarm mode), otherwise post-processing of recorded measurements using commercial software in singlebaseline mode. – Monumentation on buildings or ground marks, and may vary from stable, permanent antenna mounts to temporary marks. – Choice of either top-of-the-line GNSS receivers, possibly augmented with accelerometers or inclinometers for deformation monitoring of high-value structures, or low-cost GNSS receivers. Slow subsidence, for example‚ due to extraction of ground fluids or underground mining, or movement of tide gauges:

•

– CORS installation for high-value projects, or repeat GNSS surveys of low-cost ground marks (varying time intervals). – Use standard commercial static or rapid static GNSS surveying techniques, of comparatively short baselines (perhaps up to a few kilometers in length). Slow horizontal motion, such as pre-seismic deformation, would employ similar techniques to those above, with the critical parameters influencing selection of GNSS surveying technique being the expected magnitude of ground or structural deformation, and the interreceiver distances.

27.2

The IGS

27.2.1

Background

It would not be possible to talk about modern global geodesy and reference frames without referring to the contribution of the IGS. The IGS has been mentioned earlier in this chapter (Section 27.1) as well as with reference to the ITRF (Section 27.3). By the late 1980s‚ it was becoming obvious that GPS would significantly change global geodesy. The densification and application of reference frames would come to rely heavily on high-accuracy, differential GPS measurement analysis. To facilitate this outcome, it was agreed that a civilian global reference receiver network would be needed to make the measurements that would allow for the estimation of constellation parameters and the reference frame. This would alleviate the need for the temporary deployment of globally distributed reference receiver infrastructure for specific regional studies (Section 27.1.3). Consequently, regional studies could be undertaken more efficiently, and more consistently, thus increasing both the quality and number of such studies. This concept provided the impetus to begin planning what ultimately became one of the largest collaborative GNSS research programs ever undertaken, the International GPS Service, which was in 2005 renamed the International GNSS Service in recognition of the fact that other GNSS constellations could be utilized to fulfill the mission of the IGS. The impact of the IGS has extended well beyond the establishment of the globally consistent network of reference stations. The generation of the IGS products required collaboration across many research institutions, resulting in a new era of benchmarked geodetic science, and inter-comparison of geodetic analyses. It also demanded the standardization of data and product formats, and the open sharing of data and products. Lastly‚ the establishment of the IGS has facilitated dialogues between

725

726

27 Global Geodesy and Reference Frames

system infrastructure owners, constellation providers, instrument manufacturers, and the research community, about specific characteristics and biases of GNSS measurements that would not have been possible if GNSS geodesy progressed only on an individual researcher basis.

27.2.2

IGS Mission

The IGS provides, on an openly available basis, the highest-quality GNSS data, products, and services in support of the TRF; Earth observation and research; Positioning, Navigation and Timing (PNT); and other applications that benefit the scientific community and society. (IGS Terms of Reference 2017 [38]) The combination of open data policies with high-quality data, products‚ and services has resulted in the widespread reliance on the IGS for contributions to a range of scientific, industrial‚ and societal endeavors. These endeavors far exceed those originally envisioned when the IGS was launched as an IAG service in 1994. In fact, even today IGS products are being used in new science and applications as the quest for positioning precision becomes ever more entrenched in society.

27.2.3

IGS Organizational Values

Fundamental to the IGS are key values that are shared across the organization:

• • • • •

Advocacy of an open data policy, with data and products readily available to all users at no cost. Contributions from, and participation by, all organizations willing to adopt these values. Very high degree of IGS product reliability through redundancy of the IGS components. Technical evolution through friendly competition between different IGS analysis centers. Dedicated engagement with policy entities to raise awareness of the IGS, and geodesy in general.

It is these organizational values that have facilitated the contribution the IGS has made to global geodesy and reference frames over the last two decades. Readers are referred to [39] for a detailed description of the IGS structure, products‚ and services. These are summarized in Figure 27.3.

27.2.4 Advocacy of an Open Data Policy, with Data and Products Readily Available to All Users IGS data, products, and services support a wide variety of geodetic research and scholarly endeavors. For instance, application of IGS products to local, regional‚ and global

neo-tectonic studies is now commonplace, with submillimeter relative site velocity precisions being achievable (Chapter 28). Similar products, albeit in real time, are also utilized to support mainstream precise positioning applications that touch millions of users in virtually all segments of the global economy. IGS offers free and open access to the highest accuracy data products available. The data and products are actually produced by participating organizations with the IGS fulfilling a coordination role (Figure 27.3). These products include GNSS tracking data from over 500 worldwide reference stations (Figures 27.4 and 27.5), satellite orbits and clocks with the highest precision, EOPs and weekly geocentric site coordinates and velocities, tropospheric zenith path delays‚ and ionospheric total electron content grids [27]. The products are distributed via 4 global data centers and 24 regional or product data centers. With such a distributed network of data centers, high levels of product availability are achieved, resulting in many agencies and organizations considering the IGS as part of the GNSS fundamental infrastructure. This unfortunately is often demonstrated by users utilizing products from the IGS without due recognition or acknowledgment of the contribution of the IGS. In order to facilitate the exchange of data, and the efficient distribution of products, the IGS has developed a number of common data and product standards, including RINEX, SP3, and ANTEX [26]. While initially developed for use within the IGS community, these standards have been adopted more broadly by many GNSS user communities, driven largely by software vendors, ensuring their utilities can input IGS data and products.

27.2.5 Contributions From and Participation by Many Organizations The IGS is a service of the IAG [8] (Section 27.1.2), and accordingly a component of the GGOS [9]. With over 350 self-funded organizations from 118 countries, the IGS is the largest collaborative geodetic research project in the world. Participating agencies include space agencies with globally distributed networks of CORS, national mapping and surveying agencies, universities, research centers, private companies‚ and individuals. Having the largest number of participating agencies of any IAG service, and the largest network of ground stations, the IGS is a fundamental contribution to the IAG’s efforts to enhance society’s understanding of the so-called “Earth System”. The IGS associate members, nominated by the contributing organizations, elect a Governing Board as per the IGS Terms of Reference [38]. The Governing Board organizes participants into working groups, pilot projects, and services; and elects individuals to coordinate or chair each

27.2 The IGS

Figure 27.3 IGS at a glance – extracted from the IGS Strategic Plan 2017. Courtesy NASA/JPL-Caltech IGS Central Bureau.

component. Pivotal to the ongoing operation of the IGS is the Central Bureau, which is the only component of the IGS that is specifically funded to undertake this task, in this case by NASA. All other contributions to the IGS are made voluntarily by agencies, institutions, or individuals. While contributions are encouraged from new participants, benchmarking occurs by product coordinators before new contributions are included in the routine IGS product releases to ensure the overall quality of product is maintained. Reliability and sustainability of product

submissions is also assessed before products are integrated into the IGS combined products.

27.2.6 Effective Reliability Through Redundancy of IGS Components The IGS is a distributed multi-national collaboration. Not only are the GNSS reference stations of the IGS network distributed across all regions of the Earth, but data centers (DCs), product centers and, to a lesser extent, analysis

727

728

27 Global Geodesy and Reference Frames

IGS Network 2017 GPS GPS + GLONASS Multi GNSS

Figure 27.4

Global IGS tracking network stations. Source: From IGS. Reproduced with permission of IGS.

IGS Real Time Service Network 2017

Figure 27.5

Global distribution of tracking sites in the IGS Real-Time Service. Source: From IGS. Reproduced with permission of IGS.

centers (ACs) are also widely distributed. This distribution is intended to help load-balance internet traffic from DCs, but also to encourage regional participation in the IGS. This cooperative characteristic of the IGS has resulted in multiple agencies undertaking similar activities independently,

and then inter-comparing the results, allowing effective product generation reliability through redundancy. The IGS has a long-held philosophy that a combined product will, in general, be of better quality than any of the independent contributions, provided suitable specification of

27.2 The IGS

input parameters and constraints are applied across all contributions. The net effect is that a combined solution can still be computed even when one or more of the independent source solutions are unavailable. Hence, while the IGS does not claim to offer or guarantee a specific service level performance, in reality very high levels of availability and reliability are achieved. With so many different product types, and teams of interested researchers focusing on specific issues, the IGS segments its activities into working groups and pilot projects. Each of these components reports its progress to the Governing Board on a biannual basis, with targeted biennial IGS workshops arranged to bring associate members together to develop work plans for the coming two years. During the intervening period‚ working groups continue to function independently, generating products, undertaking comparisons, and producing peer-reviewed scientific literature. The current WGs are [40] the following:

• • • • • •

Antenna Working Group (AWG) – To increase the accuracy and consistency of IGS products, the AWG coordinates research on GNSS receiver and satellite antenna phase center determination, and manages official IGS antenna files and their formats. Bias and Calibration Working Group (BCWG) – Different GNSS observables are subject to different satellite biases that can degrade the IGS products. The BCWG coordinates research on computing and monitoring GNSS biases, and develops guidelines for handling these biases. Clock Products Working Group (CPWG) – The CPWG is responsible for aligning the combined IGS products to a highly precise timescale traceable to the world standard, Coordinated Universal Time (UTC). Data Center Working Group (DCWG) – The DCWG works to improve the provision of data and products from the operational, regional‚ and global DCs. Ionosphere Working Group (IWG) – The IWG produces global ionosphere maps of Ionosphere Vertical Total Electron Content (TEC). A major task of IWG is to make available global ionosphere maps from the TEC maps produced independently by the Ionosphere Associate Analysis Centers within the IGS. Multi-GNSS Working Group (MGWG) –The MGWG supports the MGEX Project by facilitating estimation of inter-system biases and comparing the performance of multi-GNSS equipment and processing software. The MGEX Project was established to track, collate‚ and analyze all available GNSS signals, including those from BeiDou (Chapter 6), Galileo (Chapter 5), and QZSS (Chapter 8), in addition to GPS and GLONASS (Chapter 4) satellites.

• • • • • • •

Precise Point Positioning with Ambiguity Resolution Working Group (RFWG) – The WG investigates the interoperability of PPP-AR products generated by various ACs, with a view to analyzing the feasibility and benefits of having the IGS adopt a modernized combination process considering the consistency of the satellite clock and bias products. Reference Frame Working Group (RFWG) – The RFWG combines solutions from the IGS ACs to form the IGS station positions and velocity products, and Earth rotation parameters, for inclusion in the IGS realization of ITRF (see Section 27.3). Real-Time Working Group (RTWG) – The RTWG supports the development and integration of real-time technologies, standards‚ and infrastructure to produce highaccuracy IGS products in real time. The RTWG operates the IGS Real-Time Service (RTS) to support Precise Point Positioning (PPP) (Chapter 20) at global scales, in real time (see Figure 27.5). RINEX Working Group (RINEX-WG) – The RINEX-WG jointly manages the RINEX format with the Radio Technical Commission for Maritime Services-Special Committee 104 (RTCM-SC104) [34]. RINEX has been widely adopted as an industry standard for archiving and exchanging GNSS observations, and newer versions support multiple GNSS constellations. Space Vehicle Orbit Dynamics Working Group (SVODWG) – The SVODWG brings together IGS groups working on orbit dynamics and attitude modeling of spacecraft. This work includes the development of force and attitude models for new GNSS constellations to fully exploit all new signals with the highest accuracy possible. Tide Gauge (TIGA) Working Group – TIGA is a pilot study for establishing a service to analyze GPS data from stations at or near tide gauges in the IGS network to support accurate measurement of sea level change across the globe. Troposphere Working Group (TWG) – The TWG supports development of the IGS troposphere products by combining tropospheric delay solutions from individual ACs to improve the accuracy of PPP solutions.

27.2.7 Technical Evolution Through Friendly Competition The evolution of products within the IGS is driven strongly by friendly competition within each of the components mentioned above, and by utilizing products that are estimated independently by other observing services. The minimization of modeling errors is often completed using empirical estimation in purpose-built analysis software tools at each of the research centers. Inter-comparison of

729

27 Global Geodesy and Reference Frames COD EMR ESA GFZ GRG JPL MIT NGS SIO IGR

Final Orbits (AC solutions compared to IGS Final) 300

(smoothed)

250

Weighted RMS [mm]

730

200

150

100

50

0 700

800

900

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Time [GPS weeks]

Figure 27.6 Weighted RMS of final GPS orbits. Source: From Geoscience Australia / MIT Analysis Center Coordinator. Reproduced with permission of Geoscience Australia MIT Analysis Center Coordinator.

results then provides evidence-based validation of adopted modeling improvements. As an example, Figure 27.6 shows the convergence of the weighted RMS (mm) of the individual AC orbit solutions with respect to the IGS Final Orbits for the period 1994–April 2019. Clearly‚ significant improvements in coherence have been achieved over this long period of operation. Importantly‚ each AC uses their own software utilities‚ ensuring that group errors caused by repeated use of faulty software are detected through inter-comparison. The IGS network has also evolved over its life from a sparse, and often unreliable‚ network to today’s network with over 500 stations globally distributed across Earth (Figure 27.4). While the distribution of the network is still not optimal in some regions, it is significantly better than the network available in the mid-1990s. Observation data quantity, quality, and consistency have had a considerable effect on the quality of the resultant analysis products. Importantly, each individual AC can choose their own network configuration from the available IGS network‚ allowing for an additional degree of independence of products. The availability of observation data is likely to have been the largest contributor to improved product precision. GNSS modeling improvements have also had a very significant impact on product quality. While implementation of model improvements has sometimes proved to be problematic, further validating the benefit of solution intercomparisons [41], the eventual correct implementation has certainly contributed to the overall improvement.

The following list summarizes the primary modeling issues that have benefited from considerable research and eventual implementation in the routine product generation within the IGS:

• • • • •• • • ••

Network density, distribution and quality, and reference frame alignments. Solar radiation pressure, yaw and attitude models, including the handling of satellite eclipse periods. Tropospheric modeling, parameterization including mapping functions and frequency of zenith tropospheric delay (ZTD) estimation, and horizontal gradients. Ambiguity resolution refinement, including longbaseline algorithms. Satellite and station phase center variation parameters. Observation weighting, including elevation dependency. Clock modeling, including correction for radial orbit error. Earth rotation parameter modeling, including International Astronomical Union (IAU) recommendations on precession and nutation, and application of the pole tide corrections (solid Earth and ocean). Application of ocean tide corrections. Albedo models and antenna thrust models.

Although much has been achieved by the IGS, the quest for new and improved products continues. Consideration of error budgets is now extending beyond consistency within the IGS. As the GGOS aims to understand and model the “Earth System,” it is important that consistency be

27.2 The IGS

achieved across all of the observing elements of the GGOS [9, 10]. As such, IGS, along with the other geodetic services [12, 14, 16], are now examining common parameters and determining the appropriateness of agreeing on unified parameter values or a methodological approach. For instance, the gravity fields used in the GNSS orbit integrations should be updated to match modern fields to make them consistent with the fields being used by the other IAG services. Similar consideration needs to be given to whether sitedependent physical parameters should be managed in an integrated way across all observing systems at a site. The IGS, through the GNSS technology, can offer far greater temporal and spatial variability of site displacement estimates than the other geodetic techniques, reinforcing the crucial role the IGS plays within GGOS. However, technique-specific errors need to be well understood before constraints on site displacement can be applied uniformly across all techniques. For instance, the site-dependent calibration of GNSS antennas is needed since these have a direct effect on the ITRF realization and position offsets when antennas are changed (Section 27.3). The IGS is developing procedures aimed at resolving these uncertainties without disturbing an existing antenna installation, or the resultant long-term coordinate time series. Investigation and potential development of an in situ antenna calibration system are a key element of this investigation. Ultimately the inter-comparison of products across the geodetic techniques allows for identification and possible quantification of some of the system-dependent artifacts. As an example, researchers have noted the appearance of the GPS draconitic signal and harmonics of this period in time series of various geodetic products (e.g. site positions and EOPs). Assessments are currently being undertaken to determine if other GNSS constellations suffer the same artifacts, and what the impact of this signal is on time series estimates of site coordinate and velocity. Inter-comparisons with SLR [13] and VLBI [15] time series may prove valuable.

27.2.8 Dedicated Engagement with Policy Entities to Raise Mutual Awareness of the IGS and Geodesy in General The capability generated by the IGS has applicability in many fields of science, and therefore informs policy making at the national government level. The need to provide highquality evidence-based science to policy makers continues to grow as society grapples with Earth-change-related issues such as sea level rise, environmental degradation, and management of natural hazards. The push toward automation and intelligent information technologies is also creating a growth in precise positioning applications as part

of an increase in geospatial enablement. This also creates a growing need for engagement between geodesy and policy. The IGS is directly engaged with policy entities in order to raise awareness of the capability the IGS offers, and geodesy more generally. These include the Committee on Earth Observation Satellites (CEOS), Global Sea Level Observing System (GLOSS), Group on Earth Observations (GEO), ISC World Data Service (WDS), UN Global Geospatial Information Management (UNGGIM), and the International Committee on Global Navigation Satellite Systems (ICG). While the majority of the above engagements concern sharing information about the IGS products and services with communities who are likely to obtain value from them, the engagement with the ICG is particularly important as it facilitates a two-way conversation with GNSS constellation providers on behalf of the research community about specific satellite characteristics and biases that would not have been possible on an individual researcher basis. Similar exchanges with instrument manufacturers have occurred in the past‚ resulting in information being shared about instrument data formats and biases that are now integrated into common utilities such as TEQC [42]. By engaging with policy making entities, the IGS aims to maximize its impact, and to remain relevant to society.

27.2.9

Looking Forward

The IGS strives to be the premier source of GNSS-related data, products, services‚ and expertise in support of science and society. In order to achieve this goal, the participants need to be agile in how operations are undertaken and very connected to stakeholders, ensuring the IGS understands their current requirements and future needs. The transition from a GNSS service supporting reference frame and the geosciences to an RTS is an example of how the IGS has evolved to embrace whole new user communities, and how it has had to modify its processes to achieve this outcome. In doing so, the IGS needs to regularly reassess and restate its organizational values, ensuring any new activities or projects undertaken are aligned with the broader interests of the contributing agencies. As such‚ the IGS has developed a strategic plan which is refreshed every four years [43]. A new version was released in late 2017. Recently the IGS has joined with the ICG’s International GNSS Monitoring and Assessment (IGMA) Task Force to create the Joint GNSS Monitoring Project and Working Group. This project aims to utilize existing expertise from within the IGS, supplemented with new groups not currently participating in the IGS, to monitor key system parameters from all GNSS constellations. The objective of the project is to provide some level of public trust in the performance of these systems. It is also intended to provide a

731

732

27 Global Geodesy and Reference Frames

forum for discussion between the IGS and the GNSS constellation providers about system performance in general. In this way‚ the IGS hopes to become more openly utilized by the system providers as a source of GNSS expertise. It is abundantly clear that society will embrace GNSS positioning with ever-increasing accuracy and integrity requirements. The IGS has demonstrated its capabilities for over two decades of continuous operation, and shown that its capabilities have been significantly improved. The prevailing strength of cooperation between infrastructure providers, government agencies, research institutions, and individual researchers within the IGS has proved to be its key strength. As society calls for greater positioning accuracy for applications in a huge variety of devices needing open standards, the need for a service like the IGS can only continue to grow.

Earth investigations and precise satellite orbit determination. It is also needed for operational geodetic users who wish to align their national or even local reference frames to it using GNSS technology. When constructed, a secular reference frame retains, by definition, only the linear part of ground station motion that is due (mainly) to plate tectonics. A secular reference frame is accessible to the users through station positions (X) at a given epoch (t0) and station velocities (X ), so that a station position at any epoch (t) is obtained by X t = X t0 + X t − t0 and its variance at epoch t is obtained by var X t

Terrestrial Reference Systems

27.3.1

Background

A standard and long-term stable reference frame is required for the quantification of Earth changes in space and time due to various geodynamic processes and for the determination of precise positions of objects on the Earth’s surface or the centers of mass of artificial satellites in space. There are several vocabularies used to describe mathematical geodetic references, but in the context of space geodesy we adopt here the terminology of chapter 4 of the IERS Conventions [44]. We distinguish between the theoretical or mathematical definition of that reference, the TRS and its practical or numerical realization accessible to the users, the TRF, being a global, regional‚ or national reference frame. The mathematical and physical properties of a TRS at the theoretical level or a TRF at the realization level are fully specified by an origin, a scale, and an orientation, as well as the time evolution of these three fundamental defining parameters. The reader may refer to [44] for a more detailed mathematical definition and description of TRS and TRF, but also of the International Terrestrial Reference System (ITRS) and the International Terrestrial Reference Frame (ITRF). Although it is important to distinguish between the TRS and the TRF, we focus in this chapter on the TRF, because of its easy accessibility and use by operational and scientific geodetic users.

27.3.2

Types of TRFs

In practice there are two categories of TRFs: secular and quasi-instantaneous TRFs. The former is the critical reference needed for scientific applications, including all solid

+ 2 t − t 0 cov X, X

= var X t 0 + t − t0

27.3

27 1

2

var X

27 2

A quasi-instantaneous reference frame provides mean station positions at a given epoch (with no information about time variations or coordinate changes), adjusted using data collected over a short time span: a few hours, one day, and up to perhaps one week. A time series of such reference frames may embed all types of station motions and variations: linear, periodic, position offsets caused by instrument changes or geophysical events (earthquakes, volcanic eruptions, or landslides), and post-seismic deformations for stations impacted by major earthquakes. Quasi-instantaneous reference frames still rely on the availability of a secular reference frame, such as the ITRF, for at least the definition of the orientation and its time evolution. One of the fundamental subjects that geodesy has always dealt with is the definition, realization, and maintenance of reference systems and frames [1]. Before the era of space techniques, traditional geodesy was based on the so-called triangulation method, where ground station coordinates were determined using classical terrestrial measurements. Such reference frames (or datums) are by nature hybrids, since they are constructed by adjusting 2D measurements (directions and distances) together with 1D height measurements determined with spirit leveling methods, and involve geoid undulations and the choice of an ellipsoid of reference; see, for example, [1]. With the advent of space geodesy since the early 1980s, reference systems and frames became three dimensional and global by nature, making use of satellite observations and other celestial objects, obviating the need of any ellipsoid or geoid of reference.

27.3.3 Space Geodetic Techniques and Reference Frames In general, space geodetic techniques rely on two types of methods: the dynamic method, which makes use of the

27.3 Terrestrial Reference Systems

laws of motion of artificial satellites, and the kinematic (or astrometric) method, which is based on the directions to celestial objects, such as stars and radio sources. The dynamic method of satellite orbit determination is itself divided into two positioning techniques: the bidirectional and unidirectional techniques. The two-way method of SLR or lunar laser ranging (LLR) is based on the round trip of a laser pulse emitted from an Earth-fixed telescope, reflected by a target (reflector), and then collected by a receiver placed next to the transmitter [13]. The unidirectional method relies on the propagation of radio waves. In addition to the GNSS techniques, which are described in this book, the French DORIS system (developed by CNES and IGN) is based on the Doppler frequency shift – frequency difference between the time of transmission and reception – which is a function of the satellite-receiver relative speed. In contrast to GNSS, DORIS is an uplink system where signals are emitted from Earth-fixed beacons to satellites with onboard DORIS receivers. The astrometric methods have made considerable progress since the 1970s with the VLBI technique [15]. This technique relies on the simultaneous reception by at least two antennas (radio telescopes) of the same wavefront in the same radio frequency band. The received signals are then processed by a correlator which determines the frequency of the fringes and the arrival delay of the signal at the two antennas. This delay permits the determination of the baseline between the electrical phase centers of the two radio astronomy antennas. None of these four space geodetic techniques on its own – GNSS, DORIS, SLR, and VLBI – is able to provide the full reference-frame-defining parameters (origin, scale, and orientation). While satellite techniques are in theory sensitive to the Earth’s center of mass (a physical natural origin of the TRF – a point around which the satellite orbits), differences in origin components between estimated SLR, GNSS‚ and DORIS frames exist, and reach up to several centimeters. A VLBI-derived TRF can only be realized if its origin is specified via mathematical constraints, with respect to external satellite data. While the TRF physical parameters (origin and scale) are critical for science applications, the orientation and its time evolution are of less consequence and are arbitrarily defined. Combining multi-technique reference frames is therefore recognized to be the method that not only takes advantage of the strengths, and compensates for weaknesses and systematic errors, of the different techniques, but it also allows a more accurate global reference frame and its defining parameters. This is the fundamental basis of the implementation of the ITRF, which rely on the contributions of the four space geodetic techniques. These techniques are organized as scientific services within the IAG

[8]: the IDS [16], the IGS [5], the ILRS [12], and the IVS [14] (see Section 27.1).

27.3.4 Global, Regional‚ and National Reference Frames Truly global reference frames started to become available with the advent of space geodesy, as individual technique-specific frames, or as combined frames such as the ITRF. The ITRF history dates back to 1985 when a first combined TRF was constructed using space geodesy data, and called at that time the BIH (Bureau International de l’Heure) Terrestrial System 1984 (or BTS84) [45]. The proliferation of modern regional and national reference frames effectively started from the beginning of the 1990s, with the progress made in GPS/GNSS technology, in particular its ease of use and low cost, and the availability of the IGS satellite orbit and clock products (Section 27.2). Consequently‚ regional and national reference frames used today are GNSS-based reference frames, but are all connected and compatible with the global ITRF via the universal use of IGS products (which themselves are consistent with the ITRF). A detailed description of GNSS-based regional and national reference frames can be found in [46]. In addition, general guidelines on how to realize GNSS-based local, regional, and global reference frames, fully consistent with and optimally aligned to the ITRF, are provided in [46]. One of the global reference frames worth mentioning here, other than the ITRF, is the series of IGSyy frames. At its inception‚ the IGS adopted the ITRF solutions as the reference frames for the IGS orbits [46]. However, the IGS started in 2000 to establish its own, internally more consistent GPS-only frame, but still inheriting the ITRF definition in terms of origin, scale, and orientation. When the IGS switched from relative to absolute model corrections to account for antenna phase center variations (PCV) [47], the IGS adopted the ITRF2005 [48] so as to establish its specific frame known as IGS05. It is composed of about 100 IGS stations whose coordinates were corrected to account for relative-to-absolute PCV differences. In order to preserve the ITRF2005 origin, scale, and orientation, the IGS05 was aligned to the ITRF2005 using a 14-parameter similarity transformation [49]. Similar to the IGS05, on 17 April 2011, the IGS established the IGS08 frame, derived from the ITRF2008, where corrections were applied to 65 IGS stations to the ITRF2008 positions in order to comply with the antenna calibration models [50]. A similar procedure has been applied to the ITRF2014 [51] coordinates of 252 stable IGS stations to form the IGS14 frame, with corrections applied in order to account for antenna calibration models used in present-day GNSS data analysis.

733

734

27 Global Geodesy and Reference Frames

27.3.5

Building the ITRF

Thirteen versions of the ITRF were published since the creation of the IERS [19] in 1988. The current one is the ITRF2014. The complete list of ITRF solutions can be found in Table 27.1. Up to the ITRF2000 [52], the input space geodetic data used were long-term (station positions and velocities) solutions provided by individual ACs of the four space geodetic techniques. Starting with the ITRF2005 [48], the input data are in the form of time series (weekly from satellite techniques and 24-hour sessions from VLBI) of station positions

Table 27.1 Frame rates

and daily EOPs. In the following, we describe the current ITRF combination strategy based on time series analysis, provide more details about the ITRF2014, and briefly summarize the means of access to the ITRF products. 27.3.5.1

Combination Strategy

The ITRF determination fundamentally depends not only on space geodetic solutions but also on the availability of terrestrial measurements, or local tie surveys, connecting the reference points of geodetic instruments at co-location sites.

Transformation parameters at epoch 2010.0 and their yearly rates from the ITRF2014 to past ITRF frames. Tx (mm) mm/yr

Ty (mm) mm/yr

Tz (mm) mm/yr

D (ppb) ppb/yr

Rx (mas) mas/yr

Ry (mas) mas/yr

Rz (mas) mas/yr

ITRF2008

1.6

1.9

2.4

−0.02

0.00

0.00

0.00

rates

0.0

0.0

−0.1

0.03

0.00

0.00

0.00

ITRF2005

2.6

1.0

−2.3

0.92

0.00

0.00

0.00

rates

0.3

0.0

−0.1

0.03

0.00

0.00

0.00

ITRF2000

0.7

1.2

−26.1

2.12

0.00

0.00

0.00

rates

0.1

0.1

−1.9

0.11

0.00

0.00

0.00

ITRF97

7.4

−0.5

−62.8

3.80

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF96

7.4

−0.5

−62.8

3.80

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF94

7.4

−0.5

−62.8

3.80

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF93

−50.4

3.3

−60.2

4.29

−2.81

−3.38

0.40

rates

−2.8

−0.1

−2.5

0.12

−0.11

−0.19

0.07

ITRF92

15.4

1.5

−70.8

3.09

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF91

27.4

15.5

−76.8

4.49

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF90

25.4

11.5

−92.8

4.79

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF89

30.4

35.5

−130.8

8.19

0.00

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

ITRF88

25.4

−0.5

−154.8

11.29

0.10

0.00

0.26

rates

0.1

−0.5

−3.3

0.12

0.00

0.00

0.02

−9

Note: Tx, Ty and Tz are the translation components in millimeters, D is the scale factor in ppb (10 ), and Rx, Ry and Rz are the rotation parameters, around the three axes X, Y, Z, in milli-arc-seconds.

27.3 Terrestrial Reference Systems

Dedicated software – known as CATREF (Combination and Analysis of Terrestrial Reference Frames) – was developed in the early 1990s, and continuously updated to enable time series analysis and ITRF computations. The CATREF combination model used for the ITRF combination is described in several publications [48, 51–53]. There are basically two steps used for the ITRF construction: (1) “stacking” the individual time series to estimate a long-term solution per technique comprising station positions at a reference epoch, velocities, and daily EOPs; and (2) combining the resulting long-term solutions of the four techniques together with the local ties in co-location sites. The CATREF combination model involves a 14-parameter similarity transformation, station positions and velocities, and EOPs. When stacking time series of station positions and EOPs, the reference frame definition over the 14 defining parameters is specified via the application of minimum and/ or internal constraints, as detailed in [48]. The ITRF definition of origin, scale, orientation, and their respective time evolutions is specified in the second step, when combining the four long-term solutions together using information on local ties. The ITRF long-term origin coincides with that of the SLR frame over the time span of the observations, that started in 1993.0 with the availability SLR observations of the two LAGEOS satellites. In practice, there are zero translations and zero translation rates between the ITRF and the long-term SLR frame constructed using observations from 1993.0. The ITRF long-term scale coincides with (i.e. no scale and scale rate with respect to) the average of SLR and VLBI long-term intrinsic scales. The ITRF orientation and its time evolution are continuously maintained to be the same, by successive alignments between ITRF solutions. Local ties are incorporated into the ITRF combinations with full variance covariance information, and considering the time epoch of each site survey. 27.3.5.2

The ITRF2014 Solution

Compared to past ITRF releases, the ITRF2014 generation involved two main innovations concerned with nonlinear station motions: (1) modeling the periodic seasonal signals for ground stations with sufficient time span; and (2) postseismic deformation (PSD) for sites affected by major earthquakes [51]. The submitted solutions cover the entire observation history of each one of the four space geodetic techniques. The IVS [14] contribution involves 5789 session-wise solutions [54, 55]; 407 sessions involving only two stations were discarded from the ITRF2014 processing since they were not designed for TRF determination. The majority (86%) of the VLBI sessions include only a small number of stations, ranging between 3 and 9. Among the remaining

sessions, 391 involve 10–19 stations, 8 with 20 stations, and 2 include 21 and 32 stations. The ILRS [12] contribution comprises 244 fortnightly solutions, with polar motion and length of day (LOD) estimated every 3 days for the period 1983.0–1993.0, using LAGEOS I satellite data, and 1147 weekly solutions with daily polar motion and LOD estimates thereafter, using data acquired on LAGEOS I, LAGEOS II, ETALON I, and ETALON II satellites [56]. The IGS-submitted time series comprise 7714 daily solutions spanning the time period 1994.0–2015.1 [56]. Two IGS ACs have used available GLONASS data in addition to GPS [57]. The IDS [16] contribution is a combined time series involving six ACs, using data from all available satellites with an onboard DORIS receiver, and comprises 1140 weekly solutions spanning the period 1993.0–2015.0 [58]. Figure 27.7 shows the full ITRF2014 network, comprising 1499 ground stations located at 975 sites, where about 10% of them are co-located with two, three, or four distinct space geodetic instruments. Modeling the station seasonal signals is accomplished by adding to the combination model the appropriate parameters (coefficients) of sinusoidal functions, while the PSDs were accounted for, before the stacking, by applying parametric models that were first fitted to IGS daily station position time series solutions [51]. We then applied the corrections predicted by the GNSS-fitted models to the nearby stations of the other three space geodetic techniques at earthquake colocation sites, before stacking their respective time series. The main motivation of modeling the periodic (annual and semi-annual) signals is to ensure the most robust estimation of station linear velocities, and so they are not part of the ITRF2014 products. On the other hand, the fitted PSD parametric models are effectively part of the ITRF2014 products‚ and the users should be aware of their importance and how to apply them, depending on their applications. Failure to do so could introduce position errors at the decimeter level for many ground stations impacted by PSD. Full details of the PSD functions and their usage are provided in [51] and at the ITRF2014 website [20].

27.3.6 27.3.6.1

Usage of and Access to the ITRF Using ITRF Coordinates

The ITRF products are provided to the users in the form of station positions at a given (arbitrary) epoch, station linear velocities, and EOPs. The choice of the epoch for the ITRF coordinates does not in principle matter, though it is chosen to be approximately in the middle of the time span of the most significant set of observations. In fact, the user can actually propagate the ITRF station positions, and their

735

736

27 Global Geodesy and Reference Frames ITRF2014 sites 90°

90°

60°

60°

30°

30°

0°

0°

–30°

–30°

–60°

–60° –90°

–90° VLBI

SLR

GNSS

DORIS

Figure 27.7 ITRF2014 network highlighting VLBI, SLR, and DORIS sites co-located with GNSS [Altamimi et al. 51]. Source: Reproduced with permission of IERS/ITRF.

associated variances, from the reference epoch t0 to any other epoch t using Equations 27.1 and 27.2. Note that by definition, and by construction, the ITRF is a linear (secular) frame, and hence the coordinates vary only linearly, defined by the provided linear station velocities, even for earthquake sites that experience significant PSD. However, in the case of the ITRF2014, the user interested in ground positions during the post-seismic trajectory of a station subject to PSD should add the sum of all PSD corrections, XPSD(t), to the linearly propagated position using the following equation: X PSD t = X t 0 + X t − t 0 + δX PSD t

27 3

where δXPSD(t) is the total sum of PSD corrections at epoch t. The ITRF2014 PSD parametric models, together with all equations allowing the computation of the PSD correction, XPSD(t), are available at [20]. 27.3.6.2 Frames

Transformation Parameters Between ITRF

For some applications, users might need to transform from one ITRF frame to another. Table 27.1 lists the set of 14 transformation parameters from the most recent ITRF solution, the ITRF2014, to past ITRF solutions. Note that the transformation parameters listed in the table are valid at epoch 2010.0. If the transformation parameters are

needed at another epoch t, they should be computed using the following equation. For a given parameter P and its rate P, its value at any epoch t is obtained as P t = P 2010 0 + P t − 2010 0

27.3.6.3

27 4

Access to the ITRF Using IGS Products

Guidelines for GNSS-based reference frame implementation and their alignment to the ITRF are provided in [46]. For completeness, we summarize here the steps to follow in computing the coordinates of GNSS ground stations in the ITRF using IGS products. The following general steps are valid for: (1) any type of network, being local, national, regional or global; and (2) observations spanning short intervals, ranging from a few hours, one day, and to one week. The steps are as follows: 1) Select a reference set of ITRF/IGS stations‚ and collect RINEX data from the IGS DCs. 2) Process data from your ground stations together with the selected ITRF/IGS stations. 3) Fix IGS satellite orbits, satellite clocks, and EOPs. 4) Eventually, add minimum constraint conditions in the processing (see [46]). The resulting solution for ground station coordinates will be expressed in the ITRF frame that is consistent with the

References

IGS orbits that are used. Further steps for consistency checks are as follows: 5) Propagate the official ITRF coordinates of the ground stations included in the processing, using Eq. 37.1 or 37.3 at the central epoch (tc) of the observations used. 6) Compare the estimated coordinates of the ITRF stations included in the processing with the official ITRF values propagated at (tc) in Step 5, and check for consistency by fitting a seven-parameter similarity transformation. The seven parameters should be statistically zero with no outliers (post-fit residuals larger than a certain threshold, say 1 cm). Regarding the reference set of ITRF/IGS stations that are included in the processing, it is advised to include ground stations with global coverage, selected from the set of IGS reference frame stations, such as the IGS14 network. The resulting station coordinates can also be transformed to another ITRF frame using the transformation parameters listed in Table 27.1, using Eq. 27.4 and the seven-parameter similarity transformation given by (from Frame 1 to Frame 2): X Y Z

X Y

=

Z

2

+

+ 1

Tx Ty

+D

Tz

X Y

− Rz

Ry

Rz − Ry

0 Rx

− Rx 0

7 8 9 10

11

12 13

14

Z

0

6 W. Torge, “The International Association of Geodesy 1862

1

15

X ×

Y Z

1

27 5

16 17

Note that Eq. 27.5 is valid at a given epoch, which should be the same for not only the coordinates in the two frames, but also for the set of transformation parameters. 18 19

References 1 W. Torge and J. Müller, Geodesy, 4th Ed., de Gruyter, 2012. 2 C. Rizos, “Making sense of the GNSS techniques,” in

Manual of Geospatial Science and Technology (eds. J. Bossler, J. B. Campbell, R. McMaster, and C. Rizos), 2nd Ed., Taylor & Francis Inc., 2010, ch. 11, pp. 173–190. 3 A. Leick, L. Rapoport, and D. Tatarnikov, GPS Satellite Surveying, 4th Ed., Wiley, 2015. 4 B. Hofmann-Wellenhof, H. Lichtenegger, and E. Wasle, GNSS—Global Navigation Satellite Systems: GPS, GLONASS, Galileo and More, Springer Verlag, 2008. 5 International GNSS Service (IGS) website, http://www.igs. org,

20

21 22

23

to 1922: From a regional project to an international organization,” Journal of Geodesy, vol. 78, pp. 558– 568, 2005. International Union of Geodesy & Geophysics (IUGG) website, http://www.iugg.org, International Association of Geodesy (IAG) website, http://www.iag-aig.org, Global Geodetic Observing System (GGOS) website, http://www.ggos.org, H.-P. Plag and M.R. Pearlman (eds.), Global Geodetic Observing System: Meeting the Requirements of a Global Society on a Changing Planet in 2020, Springer Verlag, 2009. J. Dow, R.E. Neilan, and C. Rizos (2009), “The International GNSS Service in a changing landscape of Global Navigation Satellite Systems,” Journal of Geodesy, vol. 83, no. 3-4, pp. 191–198, 2009, doi:10.1007/s00190-0080300-3. International Laser Ranging Service (ILRS) website, http://ilrs.gsfc.nasa.gov, M. Pearlman, J.J. Degnan, and J.M. Bosworth, “The International Laser Ranging Service,” Advances in Space Research, vol. 30, no. 2, pp. 135–143, 2002. International VLBI Service for Geodesy & Astrometry (IVS) website, http://ivscc.gsfc.nasa.gov, H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” Journal of Geodynamics, vol. 61, pp. 68–80, 2012, doi:10.1016/j.jog.2012.07.007. International DORIS Service (IDS) website, http://idsdoris.org, P. Willis et al., “The International DORIS Service: Toward maturity,” Advances in Space Research, vol. 45, no. 12, pp. 1408–1420, 2010, doi:10.1016/j. asr.2009.11.018. International Terrestrial Reference Frame (ITRF) website, http://itrf.ign.fr, International Earth Rotation and Reference Systems Service (IERS) website, http://www.iers.org, International Terrestrial Reference Frame 2014 (ITRF2014) website, http://itrf.ign.fr/ITRF_solutions/ 2014/, IGS global tracking network website, http://igs.org/ network, C. Rizos and D. Grejner-Brzezinska, “GPS positioning models for single point and baseline solutions,” in Manual of Geospatial Science and Technology (eds. J. Bossler, J.B. Campbell, R. McMaster, and C. Rizos), 2nd Ed., Taylor & Francis Inc., 2010, ch. 9, pp. 135–149. C. Rizos, “Surveying,” in Springer Handbook of Global Navigation Satellite Systems (eds. P.J.G. Teunissen and O.

737

738

27 Global Geodesy and Reference Frames

24

25

26

27 28

29

30

31

32

33 34

35

36

37

38

Montenbruck), Springer, ISBN 978-3-319-42926-7, 2017, ch. 35, pp. 1011–1037. Japan’s GNSS Earth Observation Network (GEONET) website, http://datahouse1.gsi.go.jp/terras/terras_english. html, European Reference Frame permanent GNSS network (EPN) website, http://epncb.oma.be, IGS Data and Product Formats website, http://kb.igs.org/ hc/en-us/articles/201096516-IGS-Formats, IGS Products website, http://igs.org/products, National Geodetic Survey’s (NGS) OPUS web processing site, http://www.ngs.noaa.gov/OPUS/, Natural Resources Canada (NRCAN) Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) web processing site, http://www.nrcan.gc.ca/earthsciences/geomatics/geodetic-reference-systems/toolsapplications/10925#ppp, Geoscience Australia’s AUSPOS online GPS processing service, http://www.ga.gov.au/scientific-topics/ positioning-navigation/geodesy/auspos/, Trimble CenterPoint RTX website, http://www.trimble. com/positioning-services/centerpoint-rtx.aspx, Navcom Starfire website, https://www.navcomtech.com/ navcom_en_US/products/equipment/ cadastral_and_boundary/starfire/starfire.page, Veripos website, https://www.veripos.com, Radio Technical Commission for Maritime Services (RTCM) website, http://www.rtcm.org, RINEX v3.04—Receiver Independent Exchange Format, see ftp://ftp.igs.org/pub/data/format/rinex304.pdf,

C. Rizos, D. Smith, S. Hilla, J. Evjen, and W. Henning, “Carrying out a GPS surveying/mapping task,” in Manual of Geospatial Science and Technology (eds. J. Bossler, J. B. Campbell, R. McMaster, and C. Rizos), 2nd Ed., Taylor & Francis Inc., 2010, ch. 13, pp. 217–234. Canada’s “Guidelines for Real-Time Kinematic (RTK) Surveying,” http://canadiangis.com/guidelines-for-realtime-kinematic-rtk-surveying.php, IGS Terms of Reference, https://kb.igs.org/hc/en-us/ articles/115003535547-IGS-Terms-of-Reference-v-02-2017-,

39 G. Johnston, A. Riddell, and G. Hausler “The International

40 41

42

43

44

45

46

47

48

49

50

51

GNSS Service,” in Springer Handbook of Global Navigation Satellite Systems (eds. P.J.G. Teunissen and O. Montenbruck), Springer, ISBN 978-3-319-42926-7, 2017, ch. 33, pp. 967–982. IGS working groups, http://igs.org/wg, G. Beutler, A.W. Moore, and I.I. Mueller, “The International Global Navigation Satellite Systems Service (IGS): Development and achievements,” Journal of Geodesy, vol. 83, pp. 297–307, 2019. L.H. Estey and C.M. Meertens, “TEQC: The multi-purpose toolkit for GPS/GLONASS Data,” GPS Solutions, vol. 3, no. 1, pp. 42–49, doi:10.1007/PL00012778, 1999. IGS Strategic Plan, https://kb.igs.org/hc/en-us/articles/ 360001150012-2017-Strategic-Plan, G. Petit and B. Luzum, “ IERS Conventions (2010) ,” IERS Tech. Note 36, Verlag des Bundesamts für Kartographie und Geodäsie, 179 pp., Frankfurt am Main, Germany, 2010. C. Boucher and Z. Altamimi, “Towards an improved realization of the BIH terrestrial frame,” in Proceedings of the International Conference on Earth Rotation and Reference Frames, MERIT/COTES Rep., vol. 2 (ed. I. I. Mueller), 551 pp., Ohio State University, Columbus, Ohio, 1985. Z. Altamimi and R. Gross, “Geodesy,” in Springer Handbook of Global Navigation Satellite Systems (eds. P.J.G. Teunissen and O. Montenbruck), Springer, ISBN 978-3319-42926-7, 2017, ch. 36, pp. 1039–1061. R. Schmid, M. Rothacher, D. Thaler, and P. Steigenberger, “Absolute phase center corrections of satellite and receiver antennas,” Journal of Geodesy, vol. 81, pp. 781–798, 2007. Z. Altamimi, X. Collilieux, J. Legrand, B. Garayt, and C. Boucher, “ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters,” Journal of Geophysical Research, doi: 10.1029/2007JB004949, 2007. R. Ferland and M. Piraszewski, “The IGS-combined station coordinates, Earth rotation parameters and apparent geocenter,” Journal of Geodesy, vol. 83, no. 3–4, pp. 385– 392, 2009. R. Schmid, R. Dach, X. Collilieux, A. Jäggi, M. Schmitz, and F. Dilssner, “Absolute IGS antenna phase center model igs08.atx: status and potential improvements,” Journal of Geodesy, vol. 90, no. 4, pp. 343–364, 2016. Z. Altamimi, P. Rebischung, L. Métivier, and X. Collilieux, “ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions,” Journal of Geophysical Research: Solid Earth, doi:10.1002/ 2016JB013098, 2016.

References

52 Z. Altamimi, P. Sillard, and C. Boucher, “ITRF2000: A new

56 V. Luceri and E. Pavlis, “The ILRS contribution to

release of the International Terrestrial Reference Frame for Earth science applications,” Journal of Geophysical Research, vol. 107(B10), p. 2214, doi:10.1029/2001JB000561, 2002. 53 Z. Altamimi, X. Collilieux, and L. Métivier, “ITRF2008: An improved solution of the International Terrestrial Reference Frame,” Journal of Geodesy, doi:10.1007/s00190011-0444-4, 2011. 54 S. Bachmann, L. Messerschmitt, and D. Thaller, “IVS contribution to ITRF2014,” in IAG Commission 1 Symposium 2014: Reference Frames for Applications in Geosciences (REFAG2014), pp. 1–6, Springer, Berlin, 2015. 55 A. Nothnagel et al., “The IVS data input to ITRF2014,” IVS, GFZ Data Services, Helmholtz Centre, Potsdam, Germany, 2015.

ITRF2014,” available at http://itrf.ign.fr/ITRF_solutions/ 2014/doc/ILRS-ITRF2014-description.pdf, . 57 P. Rebischung, Z. Altamimi, J. Ray, and B. Garayt, “The IGS contribution to ITRF2014,” Journal of Geodesy, vol. 90, no. 7, pp. 611–630, doi:10.1007/s00190-016-08976, 2016. 58 G. Moreaux, F.G. Lemoine, H. Capdeville, S. Kuzin, M. Otten, P. Stepanek, P. Willis, and P. Ferrage, “Contribution of the International DORIS Service to the 2014 realization of the International Terrestrial Reference Frame,” Advances in Space Research, doi:10.1016/j. asr.2015.12.021, 2016.

739

741

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment Yehuda Bock1 and Shimon Wdowinski2 1 2

Scripps Institution of Oceanography, United States Florida International University, United States

28.1

Introduction

The original concept in the 1970s of a global positioning system as a real-time positioning and navigation tool with several meters precision did not anticipate the major role that it would play in unraveling the complexities of tectonic plate motion, plate boundary deformation, volcanism, hydrology, glaciology‚ and climate, all applications requiring millimeter-level precision. Space geodetic positioning provided the first direct measurement of tectonic plate motion; it was only a few years earlier when the theory of plate tectonics had become the paradigm for geologists and geophysicists. The primary advantage of GPS is that it provides highly accurate three-dimensional positions and changes in position (displacements) of static, kinematic‚ and dynamic platforms with respect to a global terrestrial reference frame. Today, there are thousands of GPS stations at regional and global scales (Figures 28.1 and 28.2), and numerous precise GPS field surveys have been conducted (Figure 28.3). Increasingly, real-time GPS observations are contributing to early warning systems for mitigating the effects of natural hazards such as earthquakes, volcanoes‚ and tsunamis. We describe in this chapter how GPS geodesy has become an increasingly important discipline in Earth sciences by providing critical observations for modeling and understanding of physical processes at local to global scales. We cover only briefly the technical aspects of GPS fully described in other chapters, but provide enough detail to understand the fundamentals of GPS geodesy as it pertains to physical applications. We refer the reader to earlier pertinent reviews on tectonic geodesy [1, 2], seafloor geodesy (GPS-Acoustics) [3], volcano geodesy [4, 5], grand challenges facing geodesy [6], GPS geodesy [7], and global navigation satellite systems – GNSSs [8]. An important complementary geodetic

measurement system mentioned in this chapter is Interferometric Synthetic Aperture Radar (InSAR) [9].

28.2

Geodetic-Quality GPS

28.2.1

History

Geodesy, the oldest science, studies the size, shape‚ and deformations of Earth, first determined through terrestrial (distance – trilateration, angles – triangulation) and extraterrestrial observations (of the Sun, Moon‚ and stars), and precise timekeeping. Astronomic positioning‚ the predecessor of satellite (space) geodesy‚ required an inertial and terrestrial reference frame and consideration of the effects of precession and nutation, polar motion‚ and Earth rotation to relate the two [10]. Geodetic astronomy is an intensive observational technique that provided a precision of about 0.1 to 1 arcsecond (~0.3–30 m) in latitude, longitude‚ and orientation (azimuth) for triangulation and trilateration networks. Triangulation is a surveying technique that measures angles between survey monuments with optical instruments, and a short baseline measured with an invar tape to determine network scale. The technique of trilateration, measuring distance by an electromagnetic instrument, replaced triangulation and was used extensively for crustal deformation and volcano surveys, notably by the US Geological Survey [11]. In the early 1980s‚ geodesists demonstrated that GPS could achieve millimeter-accuracy relative positioning, well beyond the constellation’s original design specifications, by utilizing the dual-frequency carrier phase observations and resolving the integer-cycle phase ambiguities [12–14]. These early efforts were demonstrated on short baselines (several kilometers), and were limited by the number of available satellites within a narrow window of

Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, First Edition. Edited by Y. T. Jade Morton, Frank van Diggelen, James J. Spilker Jr., and Bradford W. Parkinson. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.

c28.3d 741

15/12/2020 5:57:53 PM

0°

60°

120°

180° –120°

–60°

0°

60°

60°

0°

0°

–60°

–60°

0°

60°

120°

180° –120°

–60°

0°

Figure 28.1 Continuous GPS stations and tectonic environment. Shown are thousands of continuous GPS (cGPS) stations (white triangles) established for global and regional geodetic applications, earthquakes greater than magnitude five (brown squares) since 1990, major tectonic plate boundaries (black lines), and earthquake centroid moment tensor (CMT) solutions (“beach balls”) (Section 28.4.2) for significant earthquakes observed by GPS over the last 25 years. The map is centered on the Pacific Rim, which along with the Indonesian archipelago, contain the world’s major subduction zones – the area has produced 9 of the largest 10 earthquakes in recorded history. Produced by Dara Goldberg.

Figure 28.2 Typical continuous GPS station. Deeply-anchored braced Southern California Integrated Network (SCIGN) monument and antenna (under the radome) of a typical cGPS station (SIO5 in La Jolla, California) for monitoring tectonic plate boundary deformation (Section 28.3), earthquake early warning (Section 28.4.2) and GPS meteorology. The small white box on the monument’s vertical leg contains a MEMS accelerometer used for seismogeodesy (Section 28.2.3). In the background are equipment enclosures, solar panels, a radio antenna for real-time transmission of data‚ and meteorological instruments. Source: Photo courtesy of D. Glen Offield.

c28.3d 742

15/12/2020 5:57:53 PM

28.2 Geodetic-Quality GPS

743

Figure 28.3 GPS survey. Buried National Geodetic Survey GPS benchmark located in the seismically active Imperial Valley of Southern California. It is part of a network of hundreds of buried markers established in the late 1970s to measure crustal deformation associated with the Imperial fault, and initially surveyed with trilateration [31]. Source: Courtesy of Prof. David Sandwell, the surveyor in the picture, standing near a tripod and GPS choke ring antenna.

several hours that shifted by nearly 4 s each day according to Earth’s sidereal rotation. Initial precision was expressed in parts per million starting with parts in 106 or 1–10 mm at distances of 1–10 km [15, 16]. As the baselines increased in length‚ the effects of tropospheric refraction and residual orbital errors became apparent and required enhancements in GPS analysis methods. Techniques for estimation of tropospheric refraction and other effects were well developed from analyses of very long baseline interferometry (VLBI) [17, 18]. At this point, precision was expressed in parts in 107 [19]. The GPS broadcast ephemeris with meter-level orbital precision was insufficient for longer baselines, so techniques were developed for regional orbit determination [20]. For regional networks (hundreds of kilometers in extent), 5–10 cm error in satellite position was sufficient to produce millimeter-level relative positions, suitable for investigating plate boundary deformation. At larger scales, in particular for studies of global plate motion at the requisite accuracy, improved orbit determination was required [21]. The earliest concept was a bootstrapping procedure referred to as the fiducial approach [22], where well-determined Earth-centered Earth-fixed coordinates available through VLBI, laser ranging to satellites (LRS), and GPS were constrained to

c28.3d 743

estimate orbital elements and positions of new GPS stations. Using this approach enabled integer-cycle phase ambiguity resolution at distances of 1–2000 km [23, 24], with a precision on the order of 1–2 parts in 108. To extend this capability to global scales‚ it was necessary to apply the fiducial concept globally. The earliest effort in the mid1980s was the Cooperative International GPS Network (CIGNET) led by the US National Geodetic Survey (NGS) [25, 26]. This effort was followed by the establishment of the International GPS Service for Geodynamics (IGS) [27] in the early 1990s. Today, the renamed International GNSS Service (IGS) (http://www.igs.org/), a mostly volunteer global cooperative effort, provides precise orbit and Earth orientation estimation from several hundred globally distributed GPS tracking stations (Figure 28.1). The service consists of multiple global analysis and global data centers, and a central bureau. The global analysis centers provide precise GPS satellite orbits and clock estimates and Earth Orientation Parameters (EOPs), which are consistent with the latest International Terrestrial Reference Frame (ITRF2014 – http://itrf.ign.fr/ITRF_solutions/2014/) and international conventions [28]. The IGS also maintains standards for instrumentation and station deployments, data formats, data analysis‚ and data archiving [29, 30].

15/12/2020 5:57:56 PM

744

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

The availability of IGS products and access to the ITRF allow for precision on the order of 1 part in 109; effectively there is no longer the need to specify a distance-dependent term. To maintain millimeter-level position precision, however, it is essential to properly record and archive the appropriate “metadata” including, for example, antenna type and serial number, receiver type, serial number and firmware version, antenna eccentricities (height and any horizontal offsets), antenna phase calibration values, and dates when changes in any of these have occurred. Keeping metadata up to date is the responsibility of the station operators and the IGS global data centers, and other regional data centers. Another notable community resource is UNAVCO founded in the United States in the mid-1980s. Today it is a nonprofit university-governed organization with global extent that supports and promotes Earth science, and other related fields of study, by advancing highprecision geodetic techniques such as GPS and InSAR (http://www.unavco.org/).

28.2.2

Analysis Methods

There are two basic approaches to geodetic GPS analysis, relative (interferometric) positioning, and precise point positioning. As in the early demonstration experiments, relative positioning of a “baseline” between two stations requires a reference station, whose precise coordinates are known, and estimation of the coordinates of the second station [12, 14]. This can be easily extended to a network of many stations and a number of reference stations [16]. The practical limit in distance or network scale for geodetic precision is dependent on the ability to resolve integer-cycle phase ambiguities after doubly differencing dual-frequency phase and pseudorange observations between stations and satellites [23, 24]. However, as the observation span increases‚ the benefit of ambiguity resolution is reduced. Also important in relative positioning is the reduction in correlated troposphere and ionospheric errors, which are a function of the baseline distance. For the troposphere, the correlation length is on the order of tens of kilometers; for the ionosphere‚ the effect is approximately proportional to the distance. The network positioning (fiducial) approach is required to estimate satellite orbits and EOPs from a global network of reference stations. Precise point positioning (PPP) [32] was introduced as a way to individually and very efficiently estimate local and regional station positions with respect to the global reference network (ITRF), the same network used to estimate the satellite orbits and EOP [33]. However, PPP requires the estimation of satellite and receiver clock parameters,

c28.3d 744

which are eliminated in relative positioning. When first introduced, PPP did not include ambiguity resolution‚ so the precision was poorer than network positioning. Since then, techniques have been developed to allow PPP with ambiguity resolution [34–37]. The main advantage of PPP is the speed of computations. The efficiency of network positioning rapidly decreases approximately as the cube of the number of stations. To compensate, the network can be divided into subnetworks with overlapping stations and then re-combined through a least-squares network adjustment. The success of PPP is primarily due to the fact that baselines in a GPS network are only weakly correlated [38].

28.2.3

GPS Seismology and Seismogeodesy

High-rate, ≥1 sample per second (sps – also expressed as Hz), instantaneous surveying with geodetic precision was first applied in tectonic GPS to measure freely slipping (creeping) geological faults [39]. High-rate GPS has also been used in support of dynamic applications such as movement of ice sheets for climate studies, georeferencing of airborne LiDAR surveys [40], GPS-Acoustics (GPS-A) for seafloor positioning [41], and engineering seismology [42]. GPS seismology provides estimates of dynamic displacements during earthquake shaking [43–47], in addition to permanent (static) ground displacements. A comprehensive archive of GPS high-rate displacements of 29 earthquakes from 2003–2018 with moment magnitudes of Mw 6.0–9.0 is described by Ruhl et al. (2018) [48]. Seismogeodesy, the optimal combination of collocated high-rate GPS and seismic data, provides coseismic (static and dynamic) displacements and seismic velocities [49] (Table 28.1). GPS networks have captured large-amplitude teleseismic waves (seismic signals greater than about a thousand kilometers from an earthquake’s location), first for the 2002 Mw7.9 Denali fault, Alaska earthquake with stations up to 4000 km away [50–52], 14 000 km from the 2004 Mw9.3 Sumatra-Andaman earthquake [60], and several thousand kilometers from the 2011 Mw9.0 Tohoku-Oki earthquake [67]. However, at these distances‚ dynamic GPS displacements are only accurate enough to discern large earthquakes (~M>7.5), while traditional seismic measurements at any location on Earth can resolve earthquakes as small as > M 5.3, a factor of 1000 better than geodesy. GPS seismology and seismogeodesy are particularly advantageous in the near field (within tens of kilometers) of large earthquakes (Figure 28.4) for local earthquake and tsunami warning and rapid response (Section 28.4). Broadband seismometers that measure ground velocities go off-scale (“clip”) when close to an earthquake’s epicenter, while GPS does not [52]. Therefore, seismic stations are

15/12/2020 5:57:56 PM

28.2 Geodetic-Quality GPS

equipped with strong-motion instruments (accelerometers) that do not clip – some operate continuously while others are triggered by the broadband instrument before it clips. Absolute station displacement is the most useful measurement for downstream modeling of the earthquake source (Section 28.3.7), but seismology requires single integration of observed broadband velocities or a double integration of accelerations. The accuracy of absolute displacements from broadband seismometers is poor because of its limits in dynamic range. Doubly integrating accelerations to displacements is subject to various spurious breaks, termed “baseline” errors (not to be confused with GPS baselines), due to numerical errors in the integration procedure, mechanical hysteresis, and cross-axis sensitivity between the test mass/ electromechanical system used to measure each component of motion [74–77]. The main disadvantage is that accelerometers are incapable of discerning between rotational and translational motions [78, 79], leading to unphysical drifts in the resulting displacements. Baseline corrections are usually taken into account by a high-pass filter [80], resulting in accurate recovery of the mid- to high-frequency portion of the displacement record. However, in the process long-period information‚ in particular‚ the static offset is lost [81]. The static offset (permanent motion) is critical for rapid estimation of earthquake magnitude and mechanism, an essential element for earthquake and tsunami early warning (Section 28.4). Finally, unlike GPS, seismic instruments are subject to magnitude saturation, meaning that is not possible to distinguish between, say, a magnitude 8 and 9 earthquake

Table 28.1 Significant earthquakes measured with GPS seismology and seismogeodesy Earthquake

Mw

References

2002 Denali fault, Alaska

7.9

[50–52]

2003 San Simeon, California

6.6

[53]

2003 Tokachi-oki, Japan1

8.3

[54–57]

2004 Parkfield, California

6.0

[58, 59]

2004 Sumatra-Andaman, Indonesia

9.3

[60]

2005 West off Fukuoka Prefecture, Japan

7.0

[61]

2008 Wenchuan, China

8.0

[62]

2010 Mentawai, Indonesia

7.7

[63]

2010 Maule, Chile1

8.8

[63, 64]

2010 El Mayor-Cucapah, Mexico1

7.2

[57]

2011 Tohoku-oki, Japan1

9.0

[57, 65–67]

2012 Nicoya, Costa Rica

7.5

[63, 68]

2014 Napa, California1

6.1

[63]

2014 Aegean Sea, Greece

6.5

[63]

2014 Iquique, Chile

8.2

[69]

2015 Illapel, Chile1

8.3

[69]

2016 Kumamoto, Japan1

7.0

[70]

2016 Kaikōura, New Zealand

7.8

[71]

2017 Chiapas, Mexico1

8.2

[72]

2019 Ridgecrest, California

7.1

[73]

1

Sufficient GPS/accelerometer collocations available for seismogeodesy.

Broadband

Accelerometer

GPS

250 Hz

100-200 Hz

1-10 Hz

Singly Integrate velocities

Doubly Integrate Accelerations

Lose Static offset

745

Seismogeodetic

Direct Displacements + Static offset

Lose Static offset

Magnitude Saturation Clips in Near Field

Magnitude Saturation Integration Biases

P-wave Detection

P-wave Detection

No Magnitude Saturation Cannot Detect P-wave

kalman Filter: displacement

velocity

Figure 28.4 Displacements derived from GPS and seismic instruments: advantages and disadvantages. The seismogeodetic combination of GPS displacements, broadband velocities, and strong motion accelerations using a Kalman filter maintains the advantages of each data type and minimizes their disadvantages.

c28.3d 745

15/12/2020 5:57:57 PM

746

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

(a factor of about 30 difference in energy release), since the scaling relationships between seismic wave arrivals and earthquake magnitude break down at higher magnitudes [82, 83]. There are other differences between GPS and seismic sensors. Seismic observations are local, with respect to an inertial reference frame as they involve the movement of a test mass inside an electromechanical system. On the other hand, GPS instruments provide spatial (non-inertial) observations with respect to a global terrestrial reference frame. Siting requirements are also different. Seismometers are ideally located in stable underground seismic vaults or in boreholes to minimize temperature- and pressure-induced tilts and to shield against electromagnetic interference. GPS stations must be located aboveground to view the GPS satellites and avoid significant obstructions. It is not surprising, then, that there are few collocations of seismic and geodetic-quality GPS instruments. Seismic stations generally sample at very high rates (e.g. 100–200 sps) compared to “high-rate” GPS stations with a typical sample rate of 1–10 sps. The very-high-rate seismic data mitigates the aliasing effect of lower-rate GPS data [84]. As a practical matter, seismic data are less verbose than GPS data‚ so that communication requirements for GPS stations are more severe even with the difference in sampling rate, and more so with the availability of other GNSS constellations. It is clear that collocating GPS and seismic instruments for recovery of seismic motion at the full range of frequencies from high frequencies up to the static displacement with high precision is preferred (Figure 28.4). For earthquake early warning‚ where timely near-source observations is critical, GPS is not sensitive enough to detect seismic P-waves, particularly in the vertical direction where the P-wave with millimeter-level amplitudes is most pronounced; the precision of real-time GPS instantaneous displacements is about 1 cm in the horizontal components and 5–10 cm in the vertical [46]. The displacement precision observed with seismogeodesy during dynamic shaking is reduced by a factor of two in the vertical and by about 20% in the horizontal component, compared to GPS alone, though still dominated by long-period errors in the GPS observations due to multipath [42]. Since the dynamic range of GPS instruments has no upper limit, GPS and broadband seismic sensors cover together the entire possible range of dynamic and static surface displacement. To this end, GPS displacements were used as long-period constraints for the deconvolution (integration) of accelerometer data for 30 s data collected during the 1999 Mw7.1 Hector Mine, California earthquake [85] and 1 sps GPS data for the 2003 Mw8.3 Tokachi-Oki, Japan earthquake [55].

c28.3d 746

Displacements and baseline offsets in the accelerometer records were estimated by weighted least squares, after correcting for possible spurious rotations of the accelerometers. These early efforts were not suitable for realtime applications such as early warning. A multi-rate Kalman filter suitable for real-time implementation was proposed to optimally combine high-rate (1 sps) GPS displacements and very-high-rate (100–250 sps) accelerometer observations, first targeted for structural monitoring and engineering seismology [86]. This method was used to monitor the loads of runners on the Verrazano suspension bridge at the start of the 2004 New York City marathon [87]. Retrospective real-time capabilities were demonstrated for the 2010 Mw7.2 El Mayor-Cucapah earthquake in northern Baja California, Mexico [49] and the 2011 Mw9.0 Tohoku-oki, Japan earthquake [65] (Section 28.4). A study comparing the displacements and seismic velocities obtained with observatory-grade accelerometers and inexpensive microelectromechanical (MEMS) accelerometers demonstrated the same level of precision in seismic velocity at distances of tens of kilometers for earthquakes as small as ~M4, where there is no permanent displacement [42, 88]. It is possible to remove much of the GPS error contributed by multipath noise with sidereal filtering, taking advantage of the nominally 12-h satellite periods that result in daily repeated signatures in the GPS data and positions [39, 89, 90]. However, this is only effective for seismically quiescent periods and may even reduce precision during strong ground motion [46, 91], because multipath is not dominant at these frequencies [52, 92]. In any case, reducing multipath effects, which is challenging in a real-time environment, is still not sufficient to allow P-wave detection, compared to accelerometer or velocity waveforms [88], even with observations from multiple GNSS constellations such as GLONASS, Galileo, and BeiDou [91]. However, the satellite orbit periods of these constellations do not follow the 12-h nominal value, so that standard sidereal filtering is mostly ineffective.

28.2.4 28.2.4.1

Observation Models Basic Concepts

Here we only present the basic mathematics of precise GPS positioning. Other chapters cover this and related topics such as orbit determination and GPS meteorology in detail. The basic elements of precise GPS positioning can be summarized as a quartet of idealized equations for the carrier phase observations (φ1, φ2), in distance units, and pseudorange observations (P1, P2) at frequencies f1 (L1) and f2 (L2) for a single satellite and single station as,

15/12/2020 5:57:57 PM

28.2 Geodetic-Quality GPS

φ1 φ2 P1

−1

1 =

−

1 1 1

P2

f1 f2 1 f1 f2

r I

1 0 2

2

0 1 0 0

λ1 N 1

0 0

λ2 N 2

,

28 1 where r denotes the non-dispersive signal travel distance (the “geometric term”), I is the dispersive ionospheric effect, and N1 and N2 are integer-cycle phase ambiguities. The objective is to estimate the station position (embedded in r), while fixing the ambiguities to their integer values [93] in the presence of ionospheric refraction. The range for station i and satellite j is given by r ij t, t − τij t

=

r j t − τij t

− ri t

,

28 2

at any instant of time [21]. Access to accurate satellite ephemerides at the 1–2 cm level in instantaneous satellite position, available today through a series of IGS products (ultra-rapid, rapid‚ and final orbits), is essential to achieving millimeter-level positioning in geophysical applications; the broadcast ephemeris transmitted by the GPS satellites has meter-level precision, not sufficient for many geodetic applications. Although the effects of the ionosphere are dispersive and can be eliminated to first order by the “ionosphere-free” linear combination of the L1 and L2 phase observations, residual ionospheric refraction and antenna multipath (also dispersive) are the limiting factors in phase ambiguity resolution. The “ionosphere-free” linear combination is given by

tion vector ri at the time of reception t. The receiver position is defined in a right-handed Earth-fixed Earth-centered terrestrial reference frame by ri t =

Xi t Yi t Zi t

28 3

1−

f2 f1

f2 f2 φ1 − φ2 ; f1 f1

2

= 1227 6 1575 42 = 60 77

28 6

so that the non-integer ambiguity term for φLC is N φLC

0 56N 1 − 1 98 N 2 − N 1

28 7

The variance in the ionosphere-free combination is by error propagation 2

By convention, the X and Y axes are in Earth’s equatorial plane with X in the direction of the point of zero longitude and the Z axis in the direction of Earth’s pole of rotation. The satellite position at any epoch of time is described by the satellite’s equations of motion in a geocentric inertial reference frame as d j r = rj dt

28 4

d j GM j r = 3 r j + r Perturbing dt r

28 5

The station position in a terrestrial reference frame and the satellite position in an inertial frame are related through a series of rotations to account for precession, nutation, Earth rotation‚ and polar motion [10]. The first term on the right of Eq. (28.5) is the spherical part of Earth’s gravitational field. The second term represents perturbing forces (accelerations) acting on the satellite, including the non-spherical part of Earth’s gravitational field, luni-solar gravitational effects, solar radiation pressure, and other perturbations such as satellite maneuvers. Solving the equations of motion for each GPS satellite based on observations from a global network of GPS stations, referred to as “orbit determination” and covered in Chapter 11, provides estimates of the satellite’s state (“the satellite ephemeris”)

c28.3d 747

1

φLC =

a nonlinear function of the satellite position vector rj at the time of signal transmission t − τij t and the receiver posi-

747

σ 2φLC =

1 f2 1− f1

2

1+

f2 f1

2

σ 2 ≈ 10 4σ 2 ,

28 8 assuming that the L1 and L2 variances, σ 21 and σ 22 , are of equal weight (=σ 2) and uncorrelated. In most cases (except for very short baselines in network positioning described below), phase observations φ1 and φ2 are combined to form φLC since the increase in variance by an order of magnitude is negligible compared to that of the ionospheric signal delay. The direct GPS signals from the satellite antenna to the receiver antenna are also perturbed by the non-dispersive neutral atmosphere (the troposphere) and are interfered with indirect signals (multipath), for example, reflections off objects near the GPS antenna. Furthermore, the signal is perturbed by imperfect receiver and satellite clocks, introducing timing and “clock” biases. The clock errors are eliminated in relative (network) positioning, but need to be taken into account for PPP [32]. The measurements themselves are subject to error due, for example, to thermal noise in the GPS receiver; errors can vary from one type of GPS receiver to the other. Other factors to be considered are phase wind-up on a dynamic platform, due to the electromagnetic nature of circularly polarized waves [94];

15/12/2020 5:57:57 PM

748

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

realization of the ITRF [95]; Earth tides, atmospheric loading [28]; and relativistic effects [96]. To achieve millimeter-level geodetic precision‚ it is necessary to clearly identify the phase centers of the transmitting satellite antenna [97] and receiving ground antenna [98], and the exact point to be positioned. Absolute phase center variations with and without antenna covers (“radomes”) at L1 and L2 frequencies for all known geodetic-quality antennas are estimated through single robot-mounted calibration by collecting thousands of observations at different orientations [99]. Tables of phase center values are maintained by the IGS. In practice, the corrections are imperfect‚ and changes in antenna types will often result in spurious offsets in position time series‚ so changing antennas is avoided to the extent possible. Antennas are oriented to true north to reduce azimuthal effects and to be consistent with the calibration corrections. The precise relationship of the geodetic marker to the phase centers must be clearly identified. This is typically given as the vertical antenna “height,” although there may be horizontal offsets, as well. The GPS antenna mount needs to be level with respect to the direction of the local gravity field and centered over the marker. The geodetic community has expended significant efforts to reduce systematic errors due to centering and leveling of the GPS antenna. For example, the Southern California Integrated GPS Network (SCIGN) project designed a precision antenna adapter (mount) with a fixed antenna height (0.0083 m), leveling capability, ensuring insignificant error in re-centering in the event that the antenna needs to be replaced. This adapter and the SCIGN radome (Figure 28.5) have been adopted by many other GPS geophysical monitoring networks. Geodetic GPS analysis software has been critical to the accomplishments described in this chapter. The earliest software packages, which are still being maintained today, include Bernese (at Astronomical Institute, University of Berne – [100, 101]), GAMIT (“GPS at MIT” – [102]), and GIPSY-OASIS (“GNSS-Inferred Positioning System and Orbit Analysis Simulation Program” at the National Aeronautics and Space Administration (NASA), Jet Propulsion Laboratory) [32, 35].

Figure 28.5 Custom GPS equipment for cGPS monitoring stations. (Top) SCIGN short antenna radome; (bottom) antenna adapter/mount. Source: Courtesy of SCIGN project.

j

The model for an L1 or L2 phase measurement li at a particular epoch of time can be expressed in distance units by the observation equation . lij = r ij t, t − τij t +

j MH i

− I ij

+ c dt i t + dt j t − τij t

j ZHDi

+λ

N ij

+

j MW i

+ Bi − B

j

j ZWDi

+

mij

+ +

j MGi

+

GN cos α + GE sin α −

εij

28 9 where r ij (Eq. (28.2)) denotes the geometric (in vacuum) range between station i and satellite j, t is the time of signal reception, τij is time delay between transmission and reception, and c is the speed of light. The second term on the right includes dti the receiver clock error, and dtj is the satellite clock error; for our purposes, we will simply refer to it as the j

28.2.4.2

Physical Models and Observation Equations

Here we describe the basic functional and stochastic models (“observation equations”) that relate the GPS observables and the physical parameters of interest, for example‚ station position. We assume that the satellite orbits are known without error, the satellite and receiver antenna phase centers and geodetic mark are well determined‚ and the metadata are accurate.

c28.3d 748

clock error dt. ZHDi is the tropospheric zenith hydrostatic delay‚ MH ij is the hydrostatic mapping function that maps the ZHD to lower elevation angles, ZWDij is the zenith j

“wet” delay with the wet mapping function MW i , and gradient parameters GN in the north and GE east components, j azimuth α, and the gradient mapping function MGi to model azimuthal asymmetries in the atmospheric refractive index due to atmospheric conditions [103, 104]. I ij is

15/12/2020 5:57:57 PM

28.2 Geodetic-Quality GPS

the total effect of the ionosphere along the signal’s path. N ij denotes the integer-cycle phase ambiguity, Bi and Bj denote the non-integer (fractional) parts of receiver- and satellitespecific clock biases, respectively, and λ is the wavelength. j

The term mi denotes total signal multipath effects at the transmitting and receiving antennas; here we will neglect multipath at the satellite transmission antenna and refer j

to this term as mi. Similarly, we replace εi by εi. The observation equations for a P1 or P2 pseudorange measurement are the same as the phase measurements (Eq. (28.9)) except that there is no ambiguity term N ij and the sign is reversed for the dispersive ionosphere term I ij . The integer cycles are counted once tracking starts to a satellite‚ so only the initial integer-cycle phase

surface pressure and temperature measurements can be used to estimate atmospheric water vapor, in particular precipitable water (PW) [106]. Multipath effects are considered to be “noise” in most applications although receiver multipath mi can also be exploited as a “signal” for local environmental applications (Section 28.6.4 and Chapter 34; e.g. soil moisture, snow cover, ocean wave heights [107]). Except for very short baselines in relative positioning, we form the ionosphere-free linear combination (Eq. (28.6)). The linearized observation (Eq. (28.9)) is δlij LC = Dij δx i + cδΔt + MH ij δ ZHDij + MW ij δ ZWDij + + λLC δ N ij + Bi − B j + mLCi + εLCi ,

28 11

j

ambiguities N i need to be estimated. However, in practice, phase observations may include losses of receiver phase lock and cycle slips (jumps of integer cycles) due to a variety of factors including signal obstructions, severe multipath, gaps in the data due to communication failures, satellite rising and setting, severe ionospheric disturbances, and so on. Losing count of the number of integer cycles in the signal propagation complicates phase ambiguity resolution and reduces the precision of the parameters of interest, if not taken into account. Therefore, efficient geodetic GPS algorithms include automatic detection and repair of cycle slips. We assume that the phase measurement error term is distributed as E ε = 0; D ε = σ 20 C ε

28 10

E denotes statistical expectation, D denotes statistical dispersion, Cε is the covariance matrix of observation errors, P= C ε− 1 is the weight matrix, and σ 20 is an a priori variance factor. If we further assume that the observations are uncorrelated in space and time‚ then the covariance matrix Cε is diagonal. The uncertainties in the longer wavelength pseudorange measurements are about two orders of magnitude larger than the phase errors, on the order of about a meter. Depending on the application, three-dimensional positions (Eq. (28.3)), zenith troposphere delays ZTDi, ionospheric delays I ij , and multipath effects mi may be parameters of specific interest (“signals”). Three-dimensional positions/displacements are the primary parameters of j

interest for tectonic geodesy. Ionospheric parameters I i may be eliminated to first order through the linear combination of phase measurements (Eq. (28.6)), but are of interest in tsunami modeling based on gravity wave and acoustic wave disruptions of the ionosphere [105], as discussed in Chapter 32. The troposphere parameters are of interest in GPS meteorology, as discussed in Chapter 30; ZWD with

c28.3d 749

749

where λLC = c/(f1 + f2), and δ is the incremental adjustment to an estimated parameter relative to its a priori value. For j

example, Di is the partial derivative for the position parameters such that j

Di =

xi − x j j

di

28 12

We assume that E εLC = 0 and D εLC = σ 20 C εLC 10 4σ 20 Cϵ. The estimated parameters N lj + Bi − B j are real-valued. We assume that the precise satellite orbits xj and satellite clock parameters are available from the IGS, or another external source, and held fixed. The a priori station coordinates are their best true-of-date values with respect to the ITRF. For simplicity, we have ignored the troposphere horizontal gradients and lumped the clock term into Δt. Note that multipath is dispersive‚ so mLCi denotes the magnified effect. The estimation of the parameters of interest can be performed through the well-known weighted least-squares inversion or other inversion methods. In relative positioning‚ the bias terms Bi and Bj are eliminated by differencing the observation equations between stations and satellites (“double differencing”), isolating the ambiguity term N ij. The phase ambiguity term resulting from the ionosphere-free linear combination has a noninteger value since it is multiplied by λLC. Precise pseudorange measurements, although much less precise than the phase measurements, provide valuable constraints for ambiguity resolution. The pseudoranges are used to extract the integer-cycle phase ambiguities N1 and N2 by first estimating N2 − N1, the so called “wide-lane” or “Melbourne– Wübbena” combination with an effective wavelength of 86.2 cm, compared to the narrower wavelength (“narrowlane”) L1 (~19 cm) and L2 (~24 cm) phase observations [108, 109] such that

15/12/2020 5:57:58 PM

750

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

N 2 − N 1 = φ2 − φ1 +

f1 − f2 P 1 + P2 f1 + f2

28 13

Once the N2 − N1 ambiguities are resolved‚ then one can try to resolve the “narrow-lane” N1 ambiguities (now with an effective wavelength of 10.7 cm). Usually, the wide-lane ambiguity can be resolved, even for networks of global extent, by inverting multiple data epochs at static stations, as long as the pseudorange errors are a fraction of the widelane wavelength. This is more complicated for real-time (single epoch) observations and dynamic platforms [43]. Another approach to resolving the wide-lane ambiguities, appropriate to network positioning, is to apply a realistic a priori stochastic constraint (a “pseudo” observation) on the ionosphere term I ijas a function of the inter-station distance [110]. The introduction of modernized GPS signals and other GNSS constellations requires additional treatment [8]. Algorithms for ambiguity resolution have been the subject of numerous studies since the early 1980s [93], and the reader is referred to Chapters 19 and 20 for the details. One of the most successful approaches is the “least-squares ambiguity decorrelation adjustment” (LAMBDA) method that decorrelates the phase ambiguities to reduce the ambiguity search space bounding all possible integer candidates [111]. Let us focus now on PPP. This method calculates “absolute” positions at any location on the globe with respect to the ITRF, which is accessible through the given satellite clock parameters and precise ephemeris available through the IGS [32, 33]. These parameters are estimated by the IGS analysis centers through a separate network adjustment, including orbit determination and estimation of EOP constrained to epoch-date ITRF coordinates of the IGS reference stations, and merged into a series of precise orbital products (ultra-rapid, rapid, final). This information is then available to PPP clients to individually position unknown stations. The parameters estimated in the PPP inversion j are then the station’s position, zenith troposphere delays Z 1 at that location (i=1), the receiver clock parameter dti, and the non-integer bias term N 1j + B1 − B j for each satellite j (Eq. (28.11)). The ionosphere parameters I ij are eliminated to first order by a linear combination of the L1 and L2 phase observations (Eq. (28.6)). It is important that the physical models (e.g. Earth tides, antenna phase center corrections) used by the PPP client be consistent with those used in the global network analysis. There are several approaches to PPP with ambiguity resolution (PPP-AR) within a limited region, up to several thousand kilometers in extent [34, 36, 37]. In one approach, a regional network solution is performed to estimate

c28.3d 750

weighted averages of all Bj satellite bias terms (Eq. (28.11)), called fractional cycle biases (FCBs; [112]), which are then made available to the PPP client. The receiver bias B1 can be eliminated by differencing the observation equations (Eq. (28.11)) between satellites. The FCBs are then computed for each satellite j over the n reference stations by j

B = Σni= 1 B j

i

n

28 14

Increasing the number and distribution of stations in the reference network will improve the reliability and accuracy of the FCB estimates. Now that the integer-valued phase j

ambiguities N i have been decoupled from the satellite and receiver phase biases, ambiguity resolution for a single station can then be attempted, first for the wide-lane ambiguities and then the remaining narrow-lane ambiguities. This approach is well suited to earthquake monitoring by relying on reference stations outside the expected area of coseismic deformation (Section 28.3.5). In practice, the inversion of Eq. (28.11) includes realistic uncertainties assigned to a priori estimates of particular parameters, for example, to station positions to improve ambiguity resolution or for GPS meteorology (see Chapter 30). Kalman filters or similar extensions of the least-squares method may be used to take into account temporal correlations. For example, troposphere delays and receiver clock parameters may be parameterized by piecewise continuous functions with assumed stochastic processes, such as first-order Gauss– Markov. Besides the requirement for external real-time satellite clock information and FCBs for ambiguity resolution, a serious disadvantage of both PPP and PPP-AR methods, in particular in real-time applications, is that they require a convergence period until the epoch-by-epoch positions stabilize, and possible re-initializations due to loss of data, ionospheric disturbances, severe multipath, and so on. This process can extend to 1-2 h for PPP and less time for PPPAR. In a real-time environment, for example in earthquake early warning (Section 28.4.2), it is critical to minimize re-initializations and repeated convergence periods. An active area of research is reducing the convergence period by taking advantage of multiple GNSS constellations, and GPS modernization with a third carrier frequency [91, 113]. In Section 28.2.3, we introduced seismogeodesy, the optimal combination of GPS and accelerometer data as a useful method for real-time applications. In a “tightly coupled” Kalman filter approach, the GPS observation equations are extended to include accelerometer data so that the inversion is performed at the observation level [112, 114]. The extended system of equations is then inverted to estimate displacements and seismic velocities during strong

15/12/2020 5:57:58 PM

28.2 Geodetic-Quality GPS

motion. In a “loosely coupled” Kalman filter approach, first, GPS displacements are estimated, and then optimally combined with seismic data [49].

28.2.5 28.2.5.1

GPS Daily Position Time Series Introduction

Noth Displacement (mm)

GPS receiver manufacturers each provide a different proprietary receiver-specific data format. Therefore, typically, phase and pseudorange data are binned into 24-h files corresponding to a GPS day (00:00-24:00) and converted to the internationally recognized RINEX (receiver independent exchange) format. Likewise, real-time GPS data are mostly streamed in universal Radio Technical Commission for Maritime Services (RTCM) format (www.rtcm.org), for example, version 3.1 – these are then translated and stored in RINEX format. Many of the archived RINEX files for GPS geodesy are freely available from global and regional data centers under the auspices of the IGS and other geodetic organizations, such as UNAVCO. The typical

40

East Displacement (mm)

RMS = 1.4 RMS = 2.4

PIN1

2010 Mw7.2 El mayour-Cucapah

VNDP

0 –20

East velocity sigmas: ~0.05 mm/yr

–40 1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

RMS = 2.7 JPLM 2012

2014

2016

2018

40 RMS = 2.0

20 0

RMS = 2.0 –20 –40 1994

1996

1998

RMS = 1.5

North velocity sigmas: ~0.05 mm/yr

1994 Mw6.7 Northridge 1992

Up Displacement (mm)

sampling and storage rate is 15 s for long-term crustal motion studies. For GPS seismology, typically real-time data are collected and archived at 1 sps (1 Hz). Data are often buffered in the GPS receivers at higher rates (5–10 sps) – they are downloaded and archived when a significant earthquake or other event occurs. The cGPS data are analyzed using methods such as those described in Section 28.2.2 to estimate daily position time series, which are then modeled for tectonic or other signals (Sections 28.3–28.5). Secular (interseismic) deformation can be as large as 250 mm/yr at the fastest plate boundaries [115], sudden coseismic motions can be as large as 10 m‚ and postseismic deformation can accumulate over years to be greater than the coseismic magnitude, or even over several decades for great earthquakes such as the 1964 Mw9.2 Alaska earthquake [116]. After modeling these effects, the time series residuals may reveal transient signals (Section 24.3.8). Figure 28.6 shows a 22-year displacement time series for three stations spanning the southern San Andreas Fault System (SAFS) in Southern California,

1999 Mw7. Hector Mine

20

751

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

100 Up velocity sigmas: ~0.2 mm/yr

50

RMS = 6.4

0 –50

RMS = 4.6

–100 RMS = 4.9 1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

Figure 28.6 Twenty-five-year GPS daily displacement time series. Stations JPLM, PIN1 and VNDP in southern California. Detrended modeled time series revealing coseismic and postseismic deformation for the 1999 Mw M7.1 Hector Mine earthquake and the 2010 Mw7.2 El Mayor-Cucapah earthquake and an Mw5.7 aftershock. The large earthquakes caused significant coseismic motion at all cGPS stations in southern California. Vertical lines denote modeled non-tectonic offsets, primarily related to antenna replacements. Time series are from http://garner.ucsd.edu/pub/timeseries/measures/ats/WesternNorthAmerica/.

c28.3d 751

15/12/2020 5:57:58 PM

752

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

showing the effects of coseismic and postseismic deformation for two large earthquakes, coseismic deformation due to an aftershock of one of the events, and two unlike antenna changes. 28.2.5.2

Coordinates and Displacements

For most geodetic applications‚ GPS data are analyzed for daily (X, Y, Z) positions with respect to the ITRF. The coordinates are transformed into more intuitive and physically meaningful horizontal and vertical displacements (ΔN, ΔE, ΔU) at epoch ti with respect to station positions (X0, Y0, Z0) at an initial epoch t0, according to ΔN i t i ΔE i t i

sinϕcosλ sinλ

=

ΔU i t i

sinλsinϕ cosϕ cosλ 0

cosλcosϕ

cosϕsinλ

X i ti

X t0

Y i ti Zi ti

Y t0 Z0

sinϕ

28 15

The relationship between “geodetic” coordinates (ϕ, λ, h), (ellipsoidal latitude, longitude‚ and height) and spatial (X, Y, Z) coordinates is

H denotes the discrete Heaviside function, H=

0, t i − T k j < 0 1, t i − T k j ≥ 0

The coefficient a is the value at the initial epoch t0, and ti denotes the time elapsed from t0 in units of years. The linear rate (slope) b represents the interseismic secular tectonic motion, typically expressed in mm/yr. The coefficients c, d, e, and f denote the unmodeled annual and semi-annual variations present in GPS position time series. The magnitudes g of ng jumps (offsets, steps, discontinuities) are due to coseismic deformation and/or non-coseismic changes at epochs Tg. Most non-coseismic discontinuities are due to the replacement of GPS antennas with different phase center characteristics. Possible nh changes in velocity are denoted by new velocity values h at epochs Th. Coefficients k are for nk postseismic deformation (Section 24.3.8) starting at epochs Th and decaying exponentially with a time constant τj. The “logarithmic” model is another parameterization associated with afterslip on the fault surface; the exponential model is associated with motion below the crust (mantle) [118]. The logarithmic model is expressed as nk j=1

X Y Z

=

η + h cos ϕ cos λ η + h cos ϕ sin λ ; η η 1 − e2 + h sin ϕ

= a 1 − e2 sin 2 ϕ

1 2

; e2 = 2f − f 2

28 16

with semimajor axis a, inverse flattening (1/f), and ellipsoidal eccentricity e. The US Department of Defense WGS84 system used for GPS is consistent within ±1 m with the ITRF, which is internally consistent at the sub-centimeter level. The WGS84 ellipsoidal parameters are semimajor axis a = 6 378 137 and 1/f = 298.257 223 563. 28.2.5.3

Time series analysis can be performed component by component since the correlations between them are small [38, 117]. An individual component time series (ΔN, ΔE, or ΔU) at discrete epochs ti can be modeled by [85] y t i = a + bt i + csin 2πt i + dcos 2πt i + esin 4πti + fcos 4πt i + ng

g j H ti − T gj +

+ j=1

h j H ti − T hj ti +

j=1

nk

+

nh

k je

1−

t i − T kj τj

H t i − T kj + εi

j=1

28 17

c28.3d 752

k j log 1 +

t 1 − T kj H t i − T kj τj

28 19

and was applied, for example, to the 2004 Mw6.0 Parkfield, California earthquake [119]. The event times T (g, h, k) can be determined from earthquake catalogs, site logs, automatic detection algorithms [120], or by visual inspection. The postseismic decay times τj are typically estimated separately by maximum likelihood methods, so that estimation of the remaining time series coefficients can be expressed as a linear inverse problem y = Ax + ε; E ε = 0; D ε = σ 20 Cε

28 20

where A is the design matrix and x is the parameter vector, x = abcdef ghk

Parameterization and Estimation

28 18

T

28 21

As before (Eq. (28.10)), E denotes statistical expectation, D denotes statistical dispersion, Cε is the covariance matrix of observation errors, P= C ε− 1 is the weight matrix, and σ 20 is an a priori variance factor. The observation equations can be solved by weighted least squares. Examination of the post-fit residuals ε = y − Ax often reveals common signatures within a geographical region (e.g. western United States), indicating a global source. Spatiotemporal filtering of the residuals can be used to estimate and remove the “common mode,” allowing for improved discernment of tectonic signals. An early study suggested

15/12/2020 5:57:59 PM

28.2 Geodetic-Quality GPS

a simple stacking procedure [121], a simple form of principal component analysis (PCA) [122]. Using these approaches, daily displacement time series of stations on the North America plate indicated spatial coherence across a 2000 km scale with 95% of that within the first 1000 km [123]. PCA analysis of time series in Western North America in the period 1995–2017 based on a combined analysis by Jet Propulsion Laboratory using the GIPSY analysis software and Scripps Institution of Oceanography using the GAMIT software reduces the root mean square (rms) of north, east and up post-fit residuals by about 20–50%, from about 1–2 mm to 0.5–1.0 mm for horizontal components and from about 3–5 mm to 2.5–4.5 mm in the vertical component [124].

28.2.5.4

Error Analysis

Obtaining realistic estimates of model parameter uncertainties, for example‚ the velocity term, coefficient b in Eq. (28.21), is fundamental to identification, verification‚ and interpretation of physical signals. Often the magnitude of the underlying physical process is small against a background signal, for example, a transient motion (Section 28.3.8) that deviates from the empirical time series model. The nature of the errors in daily displacement time series (Eq. (28.17)) is introduced into the weighted leastsquares process (Eqs. (28.17) and (28.18)) through the covariance matrix Cε. Experience with long records of geodetic measurements including spirit leveling [125], trilateration (electronic distance measurement) [126, 127], and tiltmeters [128, 129] indicates significant temporal correlations (“colored” noise). Besides instrumental noise approximated by a white noise process, time series analysis of these observations indicate that the temporal errors resemble a random walk process (sometimes called “red” noise or Brownian motion), primarily attributed to the instability of geodetic monuments caused by soil contraction, desiccation, or weathering, for example, by expansive clays in near-surface rocks. Based on this earlier geodetic record, a permanent and rigid monument was designed by the SCIGN project to minimize non-tectonic local surface deformation (Figure 28.2). The monument consists of five deeply anchored drill-braced stainless steel rods, one vertical and four slanted (~10 m) rods, isolated from the surface down to ~3 m [130]. The SCIGN monument (Figure 28.5) has been adopted by other geophysical networks such as UNAVCO’s Plate Boundary Observatory (PBO). Less expensive, and supposedly less stable mounts, include, for example, shallow-braced monuments, rock pins, spike mounts, masts, and building mounts.

c28.3d 753

753

In general, the power spectra of geophysical and atmospheric noise can be approximated by a power law process [131] Px f = P0

f f0

k

28 22

where f is the temporal frequency, k is the spectral index, and P0 and f0 are normalizing constants. The value of k for physical processes may range from k = 0 to k = −3 [132]. Special cases of integral spectral indices include white noise (k=0), flicker noise (k=−1), and random walk noise (k=−2). A good approximation of the noise ε in GPS daily displacement time series has been found to be a combination of white noise and time-correlated (colored) noise with an appropriate choice of k [133, 134]. Neglecting the temporal correlations will result in underestimation of the time series model terms. A more realistic covariance matrix can be expressed by Cε t = α2WN I + β2k J k t

28 23

For a white noise process, βk = 0 and with no colored noise, the covariance matrix Cε(t) is a diagonal matrix with elements α2WN . The uncertainty in the weighted leastsquares estimate (Eq. (28.18)) for the station velocity, coefficient b in Eq. (28.17), is then [133] σb2 =

α2WN 12 n − 1 T2 n n + 1

12α2WN ; for large n nT 2

28 24

where n is the number of time series data points equally spaced in time‚ and T is the total time span. For a random walk process with a rise of f−2, the temporal component of the covariance matrix is 1 1 1 … 1 1 2 2 … 2 2 β T 1 2 3 … 3 β22 J 2 t = 2 n−1

28 25

1 2 3 … n The contribution of the time-correlated component is surprisingly simple [132] σb2 =

β2k T

28 26

indicating that unlike the white noise case (Eq. (28.24)), it depends solely on the time interval T between the first and last data points. However, power spectra of increasingly long GPS displacement time series indicate that flicker noise (sometimes referred to as “pink” noise) with a rise of f−1 may be more dominant. In this case [133],

15/12/2020 5:57:59 PM

754

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

β21 J 1 t = β21

3 4

2

24 I − J 0 12

28 27

where element (i, k) of the symmetric matrix J0 of dimension n is J0 =

0; i = k log k − i + 2; i < k log 2

28 28

Note that here is no explicit reference to time or sampling frequency as flicker noise is on the asymptotic boundary between stationary and nonstationary processes and often exhibits odd behavior. There is no simple analytic expression for σ b 2 for a flicker noise process. An approximate expression is given by (Williams 2003b) [135]: σb2

9β2k , 16ΔT 2 n2 − 1

28 29

where ΔT is the sampling interval. Empirical formulas are available for the contribution of the colored noise component to station velocity uncertainty in the general case of a fractal spectral index k (Williams 2003b) [135]. The variance coefficients α2WN and β2k in Eq. (28.23) can be obtained through maximum likelihood estimation (MLE) of the displacement time series residuals ε = y − Ax assuming a certain power law [133, 135, 136]. With the increasing amount of data and large matrix inversion required, methods have been presented to speed up the computations and deal with missing data [137, 138]. The appropriate spectral index k and its uncertainty can be obtained by linear leastsquares fitting (Eq. (28.18)) of the slope of the amplitude spectrum of the modeled displacement time series residuals [133]. Once the spectral index and white noise and colored coefficients are determined, the proper covariance matrix Cε(t) can be then be constructed for the weighted leastsquares inversion (Eq. (28.18)) and the uncertainties obtained for all the time series model parameters. If only the velocity uncertainties are of interest, a simpler and less time-consuming approach is to apply an empirical formula to properly scale the velocity uncertainties [135]. Other schemes for estimating velocity uncertainties in the presence of colored noise approximate the more rigorous spectral approaches described above when the displacement time series are well behaved [137, 139]. Estimates of the most appropriate spectral indices and the relative contribution of white noise and colored noise components have been obtained by a growing number of studies of daily displacement time series with longer and longer time spans. The conclusions have provided a range of results on the magnitude of the white noise and colored noise coefficients and the most appropriate spectral index,

c28.3d 754

with or without spatial filtering (Eq. (28.25)) and under a variety of geologic settings and monuments. Early results with a time span of about a decade with spatial filtering indicated that a white plus flicker noise assumption is preferred with white noise on the order of 0.5–1.0 mm in the horizontal components and 3.0 mm in the vertical component with flicker noise on the order of 2.0 mm/yr1/4 in the horizontals and 7.0 mm/yr1/4 in the vertical [140]. With non-filtered, globally distributed stations the noise coefficients (Eq. (28.23)) were about three times larger in the horizontal components and five times larger in the vertical, for both white noise and flicker noise components. The least noisy results were related to two long-lived regional cGPS networks designed for plate tectonic studies in the western United States – the Basin and Range GPS Network (BARGEN) and SCIGN, both using the SCIGN monument (Figure 28.5). The BARGEN results were the least noisy, which is thought to be due to the dry desert conditions. Other monument types (e.g. building mounts, metal tripods, rock pins, concrete slabs, concrete piers‚ and steel towers) indicated larger white noise and colored noise components, but with similar spectral values, k. A third network, the US Pacific Northwest GPS Array (PANGA) had larger colored noise amplitudes thought to be due to the wetter climate and less stable monuments. Overall for this study, station velocity uncertainties were on the order of 0.05–0.1 mm/yr in the horizontal components and 0.2–0.3 mm/yr in the vertical; the contribution of the flicker noise was about 0.2 mm/yr1/4 for the horizontal components and 0.7 mm/yr1/4 for the vertical. An analysis of spatially filtered displacement time series of 256 stations from the BARGEN and SCIGN projects indicated the lowest white noise and flicker noise amplitudes‚ with the preferred noise model being a combination of white noise and flicker noise with a random walk noise component [141]; the flicker noise component was considered to be due to the GPS system itself (e.g. the receivers, satellites, local antenna environment) and fell in the frequency band between the higher frequencies (white noise) and the lower frequencies (random walk noise). The study of the error characteristics is an ongoing area of investigation, for example, [117, 141, 142], as the number and length of the available displacement time series grow and the causes of temporal correlations are better understood. The growing interest in detecting subtle transient motions has also stressed the importance of better understanding errors in GPS displacement time series. So, what can we conclude from these studies regarding monumentation? The time series analyzed in the GPS studies may not be long enough to reveal an underlying random noise component‚ and so it is yet unclear if the expensive SCIGN monument is essential for millimeter-level

15/12/2020 5:57:59 PM

28.2 Geodetic-Quality GPS

positioning [140, 141, 143]. Ultimately, the overriding issue for anchoring in many locales is the hydrology or freeze thaw cycle over an area much larger than the footprint of the anchor. The location of the GPS monument is an overriding factor – sites in dry climates have less noise‚ while sites with anthropogenic effects (e.g. oil extraction and groundwater pumping) have the most noise. 28.2.5.5

Considerations and Complications

There are other numerous considerations and complications in time series analysis of daily station displacements. Some time series span more than 25 years‚ and there are thousands of cGPS stations (Figure 28.1). The parameterization is subjective and depends on the application. In the last few years, the focus of many studies is to discover and interpret transient deformation through analysis of the residual displacement time series ε = y − Ax after known effects have been modeled. For crustal deformation studies, the time series parameters a (initial value), c-f (periodic terms), and h (non-coseismic offsets) are considered “nuisance” parameters. One problem is distinguishing between ng coseismic offsets and other offsets nh., primarily due to changes in GPS instrumentation, in particular, antenna and/or radome changes, receiver changes (though they rarely cause significant offsets), and other unknown issues. Here‚ the proper recording of metadata is critical. External calibrations of different antenna and radome combinations are not sufficient to eliminate offsets. When an antenna fails‚ it is usually preceded by degraded performance that is exhibited as an apparent wandering of the position or noisier model-fit residuals, which further complicates the analysis. The tagging and timing of coseismic offsets requires special treatment when modeling daily position time series. Furthermore, quickly determining the stations affected by an earthquake is critical in earthquake response, considering that large events can affect hundreds of cGPS stations. If an earthquake occurs near mid-day, the question arises whether to retain the data before or after the event, or exclude it altogether and assign the offset time to the start of the next day. Higher-resolution observations of coseismic and short-term postseismic deformation obtained through seismogeodesy, GPS seismology (Section 28.2.3), and higher-rate GPS positioning are addressing this issue. Although there are algorithms to automatically detect non-coseismic offsets [120, 144], considerable manual effort may still be required to detect all offsets and to minimize the number of false detections, which will increase the parameter uncertainties, in particular, those of station velocities. A recent study attempts to minimize the effects on station velocities of offsets, as well as outliers and seasonality, through an automatic median trend estimator

c28.3d 755

755

[145]. Although useful for some applications and as the number of cGPS stations increases, it can be problematic in studies of the earthquake cycle, in particular‚ the estimation of postseismic deformation for large earthquakes that can affect stations thousands of kilometers from their epicenters, and in the case of irregular ground subsidence. Seasonal effects in the displacement time series are modeled by annual and semi-annual terms (coefficients c, d, e, f in Eq. (28.21)). The presence of seasonal (periodic) effects necessitates longer data spans to reliably extract the secular velocities; velocity bias rapidly diminishes after ~4.5 years [146]. Based on increasingly long-time series (>~10 years), the effects of periodic signals on velocity estimates are less than 0.2 mm/yr [147]. The possible sources of seasonal effects were investigated and classified by three categories [148]: (1) the gravitational attraction of the Sun and Moon, including seasonal polar motion, Earth rotation variations, and loading displacements due to solid Earth, ocean and atmospheric tides, and pole tide loading; (2) hydrodynamics and thermal effects including atmospheric pressure loading, non-tidal sea surface fluctuations, anthropogenic groundwater and mineral extraction, snow accumulation, local thermal expansion, and seasonal changes in the reflecting surface (soil moisture and vegetation) that produce multipath errors [149]; (3) effects specific to GPS analysis such as satellite orbital errors, choice of atmospheric models including zenith delay mapping functions [150], and the underlying reference frame. Joint contributions from surface mass redistribution (atmosphere, ocean, snow, and soil moisture) and the pole tide are the primary causes for the observed annual vertical variations of site positions with amplitudes of about 5 mm [148]. Non-tidal atmospheric loading may also play a role [151], coupled with hydrological effects. Tidal forces including Earth tides and atmospheric pressure loading [152], most predominant at semi-annual and annual periods and most pronounced in the vertical direction, are accounted for by applying physical models in the GPS phase and code analysis. Mismodeled tidal forces and undersampling with 24-h position estimates can explain the annual and semi-annual signatures in GPS heights with amplitudes up to the several millimeter level, exhibiting long-period signals from 12 days to one year [153, 154]. Mis-modeled Earth tide effects on estimates of vertical positions may cause amplitudes of up to 0.4 mm for annual periods and 2 mm for semi-annual periods, increasing as a function of latitude, and 2 mm in zenith troposphere delay parameters with a dominant diurnal frequency [155]. Other complications in time series analysis include data gaps when a station fails to collect data or collects poorquality data and the detection and rejection of outliers; robust statistics (median, interquartile range) are useful

15/12/2020 5:57:59 PM

756

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

to better distinguish outliers compared to the mean and standard deviation [85]. A difficult problem is distinguishing tectonic sources from anthropogenic effects, for example, water, oil and mineral extraction, geothermal power generation [156], and snow accumulation [157], which appear as systematic features in the residual displacement time series. Note that some of these effects may be considered signals for other applications [158, 159] (Section 28.6).

28.3 Tectonic GPS and Crustal Deformation 28.3.1

Introduction

Tectonic geodesy seeks to measure and model crustal deformation at local to global scales to better understand the underlying physical processes of tectonic plate motion, plate boundary deformation, earthquakes‚ and volcanoes. Understanding these processes is critical to society’s efforts to mitigate the detrimental effects of natural hazards on civilian life and infrastructure. Two examples from a long list of catastrophic earthquakes and tsunamis in recent history make this point more tangible. The 26 December 2004 Mw9.3 Sumatra-Andaman earthquake and tsunami resulted in 250,000 casualties, the majority of them on the nearby island of Sumatra, Indonesia, with tsunami inundation heights of up to 30 m [160]. The 11 March 2011 Mw9.0 Tohoku-oki (Great Japan) earthquake generated a tsunami with inundation heights as high as 40 m resulting in over 18,000 casualties, with extensive and long-term damage to infrastructure, in particular the Fukushima nuclear facility, and the economic collapse of the near-source coastline [161–164]. To put this into perspective, damage and death from a great earthquake on the Cascadia megathrust in the US Northwest and Western Canada and a subsequent tsunami, the last event was in 1700 [165, 166], is likely to be comparable to that of the 2011 Mw9.0 Tohoku-oki event. Crustal deformation of Earth’s crust is driven by the motion of the tectonic plates. A simplified description of plate boundary deformation is of a “crustal deformation cycle” or “earthquake cycle” composed of three primary phases. The interseismic phase is the period between earthquakes from tens to thousands of years, depending on the particular tectonic setting, during which Earth’s crust deforms at a steady rate. An earthquake disrupts this secular motion during the coseismic phase, lasting from tens of seconds to no more than 10 min for great earthquakes such as the 2014 Mw9.3 Sumatra-Andaman event. The coseismic phase transitions into the postseismic phase as Earth relaxes and returns to its steady-state motion. The

c28.3d 756

postseismic phase can extend to decades for great earthquakes [167]. GPS along with other space geodetic methods provide direct measurements of surface displacements related to these processes. Typical cGPS displacement time series displaying the effects of three earthquakes in Southern California are shown in Figure 28.6. The period leading up to an earthquake is referred to as the preseismic phase‚ but there is scant observational data to support an unusual change in motion just prior to an event (Section 28.3.8.4). The availability of precise GPS measurements is contributing to a more nuanced view of crustal deformation. Plate boundary zones consist of multiple faults and fault segments that do not experience earthquakes according to a predictable pattern, and have complex geometries, patterns of motion, and underlying crustal properties and processes. Crustal deformation at subduction zones have recently been described in terms of “super-cycles” consisting of very large earthquakes interspersed with a sequence of smaller earthquakes, taken together rupturing an entire megathrust boundary, after which the process is repeated. These include historical sequences on the Sunda megathrust [168], the Chilean megathrust [169], the Ecuadorian subduction zone [170], the Northeast Japan trench, the Himalayan thrust, and the Cascadia subduction zone [171]. However, the record of geodetic measurements of fault motion to date is not long enough to measure a complete cycle or super-cycle in any one location. Thus, tectonic geodetic studies are comparative in nature, looking at plate boundaries at different stages of the cycle. These types of studies indicate changes in the interseismic rates of motion [118, 172]. GPS measurements have also revealed previously unknown transients (Section 28.3.8) such as episodic tremor and slip (ETS) reflecting small motions on the fault interface with an apparent regularity, first discovered from cGPS observations at subduction zones in Japan [173, 174].

28.3.2

History

The connection between earthquakes and faulting was first inferred from repeated triangulation surveys exhibiting surface deformation related to the 1872 Owens Valley earthquake [175] of magnitudes 7.4–7.9, the 1888 North Canterbury, New Zealand earthquake [176] of magnitude 7.0–7.3, and the Great Nōbi earthquake in central Japan of magnitude 8.0 [177]. The elastic rebound theory [178, 179] was developed based on the repeated triangulation measurements across the great Sumatra fault in the late 1880s [180–182] and triangulation measurements of surface offsets resulting from the 1906 magnitude ~7.9 San Francisco earthquake [183]. The theory postulates that there is an earthquake loading cycle consisting of elastic strain

15/12/2020 5:57:59 PM

28.3 Tectonic GPS and Crustal Deformation

accumulation along an active geologic fault until the stress on the fault exceeds the frictional resistance, leading to an earthquake. Crustal strain is manifested in relative changes in network size or shape, which can be geodetically measured. On a larger global scale, the hypothesis of continental drift [184–186], discredited at the time by geologists, required positions to change over time. Wegener wrote that “I have no doubt that in the not too distant future we will be successful in making a precise measurement of the drift of North America relative to Europe.” Although Wegener’s explanation was incorrect, the theory of plate tectonics [187–189] required such motions and gained wide acceptance in the 1960s. The first direct geodetic measurements of plate motion were made by the NASA Crustal Dynamics Project (CDP) from yearly estimates of the position of global tracking stations over about a decade by LRS [190, 191] and VLBI [192]. These early results showed generally good agreement, within the uncertainties of the geodetic measurements, with the ~3 Myr geologic record of the motion of rigid plates [193–195]. Expensive and geographically sparse space geodetic measurements of crustal deformation using VLBI and LRS were supplemented and essentially replaced by dense relatively inexpensive GPS networks starting in the mid1980s. GPS also replaced traditional terrestrial geodetic techniques (triangulation and trilateration) because of its distinct advantages; it can measure over long distances without the requirement of line of sight between stations‚ and it yields three-dimensional positions and displacements with respect to a global terrestrial reference frame. GPS measurements of surface displacement now play a dominant role in measuring crustal deformation from the scale of a single geological fault to tectonic plates.

28.3.3

Continuous and Survey-Mode GPS

In this section, we describe the underlying observational framework for GPS geodesy. In later sections‚ we show how GPS displacements are used to model tectonic processes. GPS observations of plate boundary deformation begun in the mid-1980s were limited to GPS “campaigns” or, as referred to here, “survey-mode GPS” or “sGPS.” In the early years, geodetic monuments in a network were surveyed, typically for ~3 consecutive days, over a period of several weeks. One or more monuments were occupied for the duration of the survey (these early surveys were done in network/relative positioning mode and so required local reference stations), while mobile crews were deployed until all the monuments were surveyed. This process was

c28.3d 757

757

repeated, typically annually. The early surveys were limited to several hours per day because of the limited GPS constellation at the time, so that depending on the time of the year, one could be surveying in the desert during the hottest day of the summer or atop a mountain at night in the heart of winter, with the satellite window shifting by ~3 h 56 min per day according to Earth’s sidereal rotation and the ~12 h period of the satellites. The multiple day surveys were typically scheduled at the same time of day for redundancy and to minimize repeating noise such as multipath. The first major efforts using sGPS for tectonic geodesy were focused on crustal deformation measurements at plate boundaries in California [197–199], Indonesia [200, 201], the South Pacific [115], the Mediterranean [202, 203], and the Andes [204]. Several of these projects included monuments that had been surveyed up to a century earlier by triangulation and/or trilateration [31, 182, 205, 206]. Figure 28.3 shows a sGPS survey station in the Imperial Valley, Southern California, a tectonically active area with frequent medium to large earthquakes [31, 207]. A representative list of sGPS projects can be found in Table 28.2. In the early 1990s, the first continuous GPS (cGPS) network for monitoring crustal deformation, the Permanent GPS Geodetic Array (PGGA) consisting of five stations, was established on the North America/Pacific plate boundary in Southern California [130]. With cGPS, instruments are continuously deployed with a source of power and a communications link to a central facility, and autonomously operated (Figure 28.2). The PGGA was the first cGPS network to capture a significant earthquake and measure coseismic displacements [210, 211]. This early effort was extended into the Los Angeles Basin with the Dense GPS Geodetic Array (DGGA), and expanded into the 250-station SCIGN project [212, 213]. The funding for this larger effort was spurred by loss of life (57 killed) and considerable damage to infrastructure (up to $40 billion) in the San Fernando Valley during the 1994 Mw6.7 Northridge earthquake [214]. About half of the SCIGN stations and other cGPS networks in the western United States (Pacific Northwest Geodetic Array – PANGA [215]; BARGEN [216]; Eastern Basin and Range and Yellowstone (EBRY) [217] were integrated in the PBO numbering about 1200 stations from Southern California to the Aleutian Islands [218]. Other early efforts included the San Francisco Bay Area Regional Deformation Array (BARD) [219], Western Canada Geodetic Array (WCDA) [220], and a network in Long Valley to monitor volcanic deformation [221]. The cGPS method quickly spread to other plate boundary zones (Table 28.2). Most notable is Japan’s national cGPS network, GEONET, with ~1200 stations [222]. Besides tectonic geodesy, these networks serve

15/12/2020 5:57:59 PM

758

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

Table 28.2 Representative list of crustal deformation measurements with GPS sorted by geographic region

1

Region

Studies

Pacific /North America

[198] [250, 251] [252, 253] [123] [167] [254] [255] 256] [216] [257] [258] [199] [197] [259] [238] [209] [231] [208] [210]1

Nazca/South America

[260] [261] [262] [263] [264] [265] [64] [204] [266, 267] [268, 269, 270]

South America/Scotia

[271] [259]

Caribbean

[272] [273] [274] [275]

India/Eurasia

[276] [277] [278] [279] [280] [281] [282]

Africa/East African Rift

[283] [284] [285]1 [286]1 [287]1 [288]

Mediterranean

[289] [203] [290] [202] [291] [292] [293] [294] [295] [203] [288]

Pacific Basin

[296] [297] [298]

Southeast Asia

[299] [300] ([301] [302] [198] [303] [199] [306] [307] [308] [304, 182] [305] [201]

South Pacific

[115] [309] [310] [311]

New Zealand

[312] [313, 314] [315]

Australia/Sunda

[316]

Japan

[222]1 [317] [318] [319] [320] [321] [246]2 [322] [41] [244]2

Mexico and Central America

[323] [324] [325] [326] 1 [327, 328]

Greenland

[329]1 [330]1

Antarctica

[331] [332] [333]1

cGPS; 2GPS-A

multiple purposes, for example‚ to support precise surveying, engineering and transportation applications [223], and GPS meteorology [224]. Initially, cGPS networks recorded phase and pseudorange measurements at a 15–30 s date rate. The data were downloaded usually daily to a central facility. With improvements in data communications and computing power and to support new applications such as earthquake and tsunami early warning systems (Section 28.24), many stations have been converted to allow real-time transmission of data, typically sampled at 1 sps or greater and continuously transmitted with a latency of about 1 s to a central server. Data transmission is performed in a variety of ways, including dedicated radios and microwave towers, cell modems, satellite dishes‚ and direct Internet connections. Japan’s GEONET and a majority of the Western North America cGPS stations have been converted to real-time operations. Although the number of cGPS stations has significantly increased, sGPS surveys are still performed for tectonic GPS applications. They are used for local transects across active geologic faults to distinguish between locked and creeping sections [225], often using kinematic and rapid static GPS methods with repeated short occupation times [31, 39, 226]. GPS surveys have also been conducted in the epicentral regions of large earthquakes to record coseismic

c28.3d 758

(Section 28.3.5) [227] and postseismic (Section 28.3.8.1) motions [228], often in combination with InSAR measurements [209, 229]. However, sGPS is often logistically complex and manpower intensive, especially when expeditiously performed after a significant seismic event.

28.3.4

Displacements and Velocities

The fundamental observation in GPS geodesy is displacement, the change in position over time. In this section‚ we discuss secular motion (velocities) as a representation of interseismic deformation, and the primary objective of many sGPS and cGPS efforts. Figure 28.7 shows the velocities estimated at North Island, New Zealand, at the PacificAustralian plate margin, the area of the 2016 Mw7.8 Kaikōura earthquake. Besides plate boundary deformation, horizontal station velocities at plate interiors are input to global plate motion models and to the realization of ITRF for space geodesy (Section 28.3.6). Early efforts focused on horizontal motions because of the lesser precision of vertical velocities. More recently the vertical motions are being exploited, especially at subduction zones where significant vertical tectonic deformation occurs. One of the longest-studied and most intensely instrumented plate boundaries, the 800-mile SAFS in California, consists of multiple mostly transform (strike-slip) faults on

15/12/2020 5:57:59 PM

28.3 Tectonic GPS and Crustal Deformation

759

Pacific Plate North Island

–38°

Australian Plate

Hi

ku

ra n

gi

Tr ou

gh

–40°

–42° 172°

174°

176°

178°

180°

Figure 28.7 Oblique subduction of the Pacific Plate beneath the Australian Plate at the Hikurangi Margin, North Island New Zealand. GPS velocities (black vectors) from sGPS campaigns between 1991 and 2003 are shown relative to the Pacific Plate. Red vectors show estimated long-term convergence rates (mm/yr) at the Hikurangi trough. The GPS velocities in the eastern North Island show that 50–60 mm/yr of convergence occurs offshore of the northeastern North Island with the rates decreasing to ~20 mm/yr in the southern North Island. The southward decrease in offshore convergence rates is accompanied by an increase in upper plate shortening and produces rapid clockwise tectonic rotation of the eastern North Island relative to the bounding Pacific and Australian Plates. The margin-parallel component of Pacific/Australia relative plate motion is accommodated by a combination of strike-slip faulting and clockwise rotation of the eastern North Island. The inset shows the location of the 2016 Mw7.8 Kaikoura earthquake. Source: Adapted from Wallace et al. [196] and the references therein. Reproduced with permission of John Wiley & Sons.

land and offshore. The last major earthquake on the San Andreas Fault itself was the 1906 Mw7.9-8.0 San Francisco earthquake [232, 233]; the central portion of the SAF last ruptured during the 1857 Mw7.9 Fort Tejon earthquake [234]. The long recurrence time inferred from paleoseismic observations [235, 236], the absence of significant rupture on the southernmost segment of the fault for at least 250 years‚ and the interseismic strain that has accumulated since then inferred from geologic and geodetic data suggest that the southern segment of the SAF is primed for a large earthquake [237], often referred to as the “Big One.” A velocity map of the SAFS is shown in Figure 28.8 [238], including 1981 horizontal velocity vectors over the period 1996–2010 compiled from numerous sGPS campaigns and cGPS networks, as well as some early trilateration surveys. Complicating these efforts are the effects of postseismic deformation. There have been several large earthquakes with significant postseismic motion affecting all Southern California GPS stations: the 1992 Mw7.3 Landers, 1999 Mw7.3 Hector Mine‚ and 2010 Mw7.2 El Mayor-Cucapah

c28.3d 759

in northern Baja California, Mexico (Figure 28.6). Other complications include non-secular deformation due to primarily to anthropogenic sources (Section 28.6), including, groundwater pumping and mineral extraction, aquifer recharge and injection and withdrawal of fluids in hydrothermal power generation [156, 239, 240] that may bleed into horizontal motions. These effects as well as episodic, transient, seasonal‚ and other motions must be considered in the estimation of velocity vectors. The measurement of interseismic deformation and the accumulation of strain over the earthquake cycle as indicators of the buildup of stresses in the crust is an important input for forecasting earthquake probabilities and the associated seismic risks. However, geodetic observations (GPS and InSAR) are not long enough to span a complete earthquake cycle. Therefore, tectonic geodetic studies have been comparative in nature to form a coherent picture of the underlying earthquake engine. GPS horizontal velocities are shown in Figure 28.9 for three subduction zones at different phases of their cycles. Other types of data provide complementary information over the longer term.

15/12/2020 5:57:59 PM

34

–1 14 °

°

–1 16 °

36

40

°

°

–1 18 °

°

–1 20

°

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

38

760

10 + –1 mm/yr

–1 22

°

–1 24

°

40 °

km 0

100

Figure 28.8 Horizontal GPS-derived velocities for the San Andreas Fault System (SAFS) and the Imperial fault in Southern California delineating the diffuse plate boundary between the North American and Pacific plates from sGPS and cGPS data. The velocities are shown with respect to a North America plate pole of rotation [208], with half of the plate motion subtracted, and mapped in an oblique Mercator projection. Stations furthest to the east of the boundary on the North America plate are moving to the southeast by about 25 mm/yr and those to the west of the boundary are moving to the northwest by up to the same amount with the maximum on the Channel Islands (with small residual motions, ~1–2 mm/yr, with respect to the Pacific plate). Source: Adapted from Tong et al. [209]. Reproduced with permission of John Wiley & Sons.

(a)

(b) 35° S GPS Model 20 ± 20 mm/yr

15° N BNKK

50° N

2010 GPS Model 1 20 ± 2 mm/yr –1 10 m yr 66 m

36 40° S

5 10

100 km

10

PHKT

1

30

10° N

– yr

5

CPN

mm

15

200 km

(c)

Cascadia

45° N

1

Chile

100 km

90° E

5

Sumatra

45° S

GPS Model 20 ± 2 mm/yr

1

52 mm yr–1

20

5° N

18 mm yr–1 95° E

100° E

75° W

70° W

125° W

120° W

Figure 28.9 Comparative study of three subduction zones at different stages of the earthquake cycle. GPS horizontal surface velocities in red and model-predicted velocities in blue. (a) One-year averaged postseismic velocities at the Sumatra trench one year after the Mw9.3 Sumatra-Andaman earthquake – all stations move seaward. Coseismic fault slip contours in meters. (b) At the Chile subduction zone, four decades after the Mw9.5 earthquake of 1960 – coastal and inland stations show opposing motion. The northernmost areas show landward interseismic motion before the 2010 M8.8 Maule earthquake, while inland stations show postseismic deformation following the 1960 event. (c) At the Cascadia subduction zone. Three centuries after the Mw 5 [424]. A CMT solution is described by 10 parameters: the 6 independent elements of the symmetric moment tensor [425–427], its geographic location (centroid), and time of occurrence. The geographic location of the moment tensor is the point of average moment release (centroid) and differs from the earthquake hypocenter (the point of initiation of rupture). Using the static (permanent) displacements allows for a rapid CMT estimate most useful for local earthquake and local tsunami early warning systems [428, 429]. The CMT is a point-source approximation. However, for great earthquakes the fault rupture can be longer than 1000 km. For example, the 2004 Mw9.3 Sumatra-Andaman megathrust earthquake ruptured a distance of >1,500 km and a width of ~150 km [430]; the rupture duration was close to 10 min [431]. The point-source approximation resulted in a significant underestimate of the full seismic moment release and, hence, the initial magnitude. A global CMT analysis using five-point sources to mimic a propagating slip pulse led to a more accurate estimate [432]. A more localized approach is to define a series of linear point sources (Figure 28.21), followed by a grid search for the optimum line azimuth and spatial location and then averaging the individual moment tensors over the line source. The final CMT solution is then

15/12/2020 5:58:06 PM

776

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

located at the location of mean moment release [65]. An important aspect of this approach is that no prior information on the fault geometry is required. Since tsunamigenic earthquakes generally (but not always) occur at subduction zones, it is most probable that a thrust fault will generate a local tsunami; the primary consideration is whether there is significant seafloor uplift. The line-source CMT approach was retrospectively demonstrated for the 2011 Mw9.0 Tohoku-oki earthquake with a rupture length of 340 km, available within 2–3 min of the event, well before the arrival of the first tsunami waves about (30–60 min after earthquake onset time); it agreed well with the final global CMT solution obtained from teleseismic data [65]. The next step is to derive a rapid finite fault slip model (Section 28.3.7) from the same data that is used for the

135˚

46˚

140˚

CMT analysis (Figure 28.21). To begin [65], the fault that is the closest one to the CMT line source can be extracted from a catalog of faults, for example, the Slab 1.0 model, a 3D model of global subduction zone geometries [433]. The slip model can then be used to generate maps of ground motion and seismic intensity [434], and as input to a tsunami model. As described in the next section, a finite source model along with accurate topography and bathymetry can be used to estimate the uplift of the seafloor, from which the tsunami extent, inundation‚ and run-up can be modeled before the first tsunami waves arrive at the coastline [435]. Note that the described slip model (Figure 28.21) is solely for rapid analysis. More refined models are computed later, usually by numerous investigators for major earthquakes, as part of crustal deformation studies [66].

145˚ 0848

GPS/Accelerometer station fastCMT inversion node fastCMT moment release Direction of slip

44˚

fastCM

0

GCMT

100 200 km

10

20

30

10

40˚

0

60 50 40 30 20

42˚

Slip(m) 38˚

0914/ MYG003

36˚

34˚

0

1.5 3 .0 x10 21Nm

32˚

Figure 28.21 Rapid line-source CMT solution and finite fault slip model for the 2011 M9.0 Tohoku-oki earthquake. Green circles represent the linear point sources. The fastCMT and global CMT solution (GCMT) beach balls are shown. The inset shows the moment release from the line source as a function of distance along the fault. Shown along the fault interface with 10 km depth contours from the Slab 1.0 model [433] is the fault slip model; the blue lines represent the direction of slip on the fault interface. The triangles indicate the locations of the input collocated GPS/accelerometer stations. The two large triangles represent the fixed GPS station (0848, red) and the GPS/accelerometer pair (0914/MYG003, blue). Source: Adapted from Melgar et al. [65]. Reproduced with permission of John Wiley & Sons.

c28.3d 776

15/12/2020 5:58:06 PM

28.4 Natural Hazards Mitigation

28.4.3

Local Tsunami Warning

Current tsunami warning systems are focused on Earth’s subduction zones and are well developed for ocean basinwide warnings. In the United States, the Pacific basin is monitored by the US National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) Pacific Tsunami Warning Center (PTWC) in Hawaii. The west coast and the Alaska region are the responsibility of the National Tsunami Warning Center in Alaska. They employ two basic methods. The direct method relies on NOAA’s Deep-ocean Assessment and Reporting of Tsunamis (DART) GPS-equipped buoys with real-time satellite links [436] tethered to deep-water (4000–6000 m) oceanbottom pressure sensors [437]. The pressure readings provide a measure of variations of the sea surface that are produced by tsunami waves. These readings are used to infer the vertical motion of the seafloor (that caused the tsunami), to model tsunami propagation and generate sitespecific warnings [438–440]. Since the DART buoys are deployed in deep water‚ the warnings are not timely enough for local tsunami warning and have been difficult to maintain. The indirect and most reliable method is based on measurement of teleseismic waves (20 to 0.003 Hz, greater than 1000 km) by globally and regionally distributed broadband seismometers to locate the earthquake from integrated displacements, and estimate its magnitude and fault mechanism as a basis for tsunami alerts and more refined tsunami models [441]. As discussed previously, seismic data have problems in the near field of large earthquakes‚ so reliance of traditional seismic instruments method is not suitable for timely local tsunami warning. Real-time GPS networks are not affected by these problems. Tsunami warning systems based on observed static GPS displacements became a focus of research following the 2004 Mw9.3 Sumatra-Andaman earthquake and the subsequent devastating tsunami (Table 28.3). An initial study proposed using GPS observations from global stations for Table 28.3 Year

777

rapid magnitude and slip estimation for great earthquakes as the basis for ocean basin-wide tsunami warnings [442]. Other studies focused on combining coastal near-source GPS and open-ocean DART buoy observations to rapidly estimate source energy and scale for tsunamis generated by seismically induced seafloor uplift and coastal landsliding [443, 444] . Related studies proposed coastal GPS networks (“GPS Shields”) [445] to rapidly calculate fault dimensions and average slip [446] as initial conditions for tsunami propagation [447]. Japan has the world’s most advanced tsunami warning systems operated by its Meteorological Authority (JMA). The system gained impetus after the 1993 Mw7.8 Hokkaido-Nansei-oki earthquake; the subsequent tsunami reached the nearby Okushiri Island in only 3 min and left 230 dead [448]. In their approach, tsunami propagation and inundation scenarios are simulated for different earthquake scenarios and stored in a database. Then, when an earthquake occurs‚ the most appropriate scenario is chosen, based on the estimated earthquake parameters, to guide the warning, The key to robust local tsunami warning is to be able to rapidly estimate earthquake magnitude and the faulting mechanism since not all large events in a subduction zone can be assumed to rupture the megathrust. For example, the 2012 Mw8.6 event off Sumatra, Indonesia, was a predominantly strike-slip event that did not generate a significant tsunami [449]. As described in the previous section, magnitude scaling relationships such as PGD can decrease the amount of time required for magnitude estimation, before seismic shaking is complete and before the coseismic static displacement is revealed. Once the coseismic displacement is estimated, then other methods are available such as the line-source CMT solution [65], further use of scaling relationships between magnitude and fault length and width [450] to initiate a rapid slip inversion [451], and other rapid slip inversion methods using real-time GPS static displacements [57, 447, 452, 453].

Tsunamigenic earthquakes observed by GPS and seismogeodesy Name

Mw

Dead/Missing

Max Tsunami Height (m)

2004

Sumatra-Andaman, Indonesia

9.3

230 000–280 000

15–30

2010

Maule, Chile

8.8

525/25

1.3

2010

Mentawai, Indonesia

7.7

408/303

3

2011

Tohoku-oki, Japan

9.0

15 894/2562

40.5

2014

Iquique, Chile

8.3

6

2.1

2015

Illapel, Chile

8.3

14/6

4.9

2016

Kaikōura, New Zealand

7.8

2

7

2017

Chiapas, Mexico

8.2

98

1.75

Source: https://en.wikipedia.org/wiki/List_of_historical_tsunamis

c28.3d 777

15/12/2020 5:58:07 PM

778

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

A recent retrospective real-time GPS analysis of four tsunamigenic events in Japan and Chile summarizes how rapid magnitude estimates can be used to generate timely estimates of maximum expected tsunami amplitude [69]. The timeliness of GPS-based tsunami warnings available from these rapid methods is important in issuing a general evacuation warning for local populations. However, more refined methods can provide additional and more accurate information on tsunami propagation and arrival times, geographical extent, inundation distance‚ and height. These approaches are based on inversion of some combination of geodetic and seismic data to estimate a finite fault slip model from which seafloor uplift is inferred. Using available topography and bathymetric maps‚ a tsunami propagation model can then be produced to issue a warning for coastal areas and islands adjacent to the earthquake rupture zone. The accuracy of the tsunami model is dependent on the source model [454] and can be assessed by comparison with direct deep-ocean DART buoys and coastal postevent field survey measurements [162]; the latter is most relevant for local tsunami warning. Using land-based data allows for an improved tsunami model without a significant increase in latency [435]. However, the resolving power of land-based data to the shallow fault slip responsible for large uplift and tsunamis can be quite limited [447, 455]. Incorporating direct data from offshore GPS buoys (kinematic displacements), ocean-bottom pressure sensors [456, 457], and tide gauges [458–460] as they become available can provide increased resolution and model accuracy [435, 454, 461–464], but with increased latency; in many cases‚ it can still provide sufficient time to issue a refined tsunami prediction. A study of the resolution of the different data used to model the 2011 Mw9.0 Tohoku-oki event shows that GPS displacement time series are most sensitive to slip closest to the coast and almost completely insensitive to slip close to the trench, while seismogeodetic velocities are sensitive to slip anywhere on the fault. The tsunami wave observations are most sensitive to slip near the trench. Each data set, used independently‚ provides limited resolving power, while the combination affords a substantial improvement [455]. To this end, an extensive network of seafloor cables has been installed in Japan to transfer seafloor data in real time to the JMA; displacements of GPS buoys are transmitted by satellite communications. Seafloor positioning by five ocean-surface GPS buoys and sea-bottom acoustic transponders, fortuitously installed off the Tohoku coast between 2000 and 2004 above the 2011 hypocenter‚ showed seafloor displacements up to 24 m in the horizontal and 3 m of vertical uplift [244]. An acoustic transponder within 50 m of the trench recorded 31±1 m of horizontal motion [465]. A submarine network for transmitting seafloor data,

c28.3d 778

S-net, has been established in the region of the 2011 Tohoku-oki event [466]. Japan also runs the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) to transfer real-time seafloor data through submarine cables at the Nankai Trough, a major tectonic feature off the Kii Peninsula and Shikoku Island (https://www.jamstec. go.jp/donet/e/).

28.4.4

Volcano Monitoring

Geodetic methods play an important role in volcano monitoring. Unlike earthquakes, volcano monitoring may be able to detect precursory signals from minutes to months prior to an eruption as a basis for early warning and hazard mitigation. We mentioned earlier (Section 28.4.1) that precursory signals were detected by GPS and other sensors prior to the eruption of the Merapi stratovolcano in central Java, Indonesia‚ in late October 2010 [411]. Although there were 400 deaths, early warnings issues by the Indonesian Center of Volcanology and Geological Hazard led to an evacuation of more than a third of a million people and is estimated to have saved 10 000–20 000 lives. However, there are several classes of instrumented volcanoes with different behaviors and multiple underlying physical processes that have lacked precursory signals. On the other hand, increased magmatic activity does not always lead to eruptions, for example‚ at the heavily instrumented Long Valley Caldera at Mammoth Lakes, northern California [467]. As a reference, there are several good reviews of volcano geodesy and seismology theory, methods, and observations [4, 5, 468–471]. The introduction of cGPS has the advantage of providing high-rate continuous observations of a volcano edifice and its flanks, but establishing reliable real-time communication links is not always reliable, nor practical. Other challenges to GPS include inaccessibility and dangerous deployments, obstruction of GPS signals due to the steep slopes of volcanic cones, and loss of equipment during eruptions. As an example, the Stromboli volcano, Aeolian Islands, Italy‚ is characterized by persistent but moderate (Strombolian) explosive activity within its shallow magma chambers, making installation of sensors hazardous. Landsliding is a serious problem and can be tsunamigenic; an eruption in late December 2002 accompanied by a landslide on the volcano’s northwest flank (Sciara del Fuoco) caused a tsunami at the southern Italian coast. In April 2003, a paroxystic explosion episode ejected basaltic rocks causing significant damage to its monitoring networks. One of the GPS stations recorded and transmitted data for only 90 s before being destroyed by lava; the station had been installed only 9 days prior to the event ([472]; Figure 28.22). InSAR does not have these limitations and provides high-spatial resolution of line-of-sight (LOS) measurements of displacement, making it the preferred

15/12/2020 5:58:07 PM

28.4 Natural Hazards Mitigation N

GPS permanent station operating since 1997 New “sciaradat” GPS station

38.81°

December 28th 2002 fissure Outpoured lava flows Slided area

38.80°

38.79°

38.78°

Tyrrhenian Sea

str om

bo

li Is

Aeolian Archipelago

lan

0

1

d

Sicily

km

Displacements (m)

15.19° 0.15 0.1

Stromboli

15.20°

15.21°

15.22°

SSBA station (relative to svin)

Italy

0

15.23°

50km

15.24°

N-S E-W

0.05 0 Date

–0.05

12

13

14

15

16

17

18

19 February ‘03

Figure 28.22 GPS real-time monitoring network of the Stromboli volcano on Stromboli Island, Italy. Data plot: Ten-minute average values of 1 sps displacement time series of the SSBA station from the start of operations on 11 February 2003 until a lava flow destroyed it on 20 February. Data gaps are due to radio communication outages. Source: Adapted from Mattia et al. [472]. Reproduced with permission of John Wiley & Sons.

122°20'

46°20'

122°15'

122°10'

122°05'

method for volcano monitoring. In particular, L-band measurements are able to penetrate vegetation. More than 110 volcanoes have been observed with InSAR, while only about 40 volcanoes with GPS [470]. For example, the Cascadia subduction zone includes an arc of 10 volcanoes along the Cascade ranges in the western United States. One of these, the Mount St. Helens stratovolcano, suffered a major explosive eruption in 1980 [473] with accompanying loss of life (over 50 dead) and property. Continued activity during 1981–1986 produced a new lava dome, and eruptions in 2004–2008 with a cumulative volume of lava of nearly 100 million cubic meters [474]. Monitoring of the volcano by sGPS and cGPS began in earnest in 2000 (Figure 28.23). A swarm of small earthquakes in September 2004 and a small eruption on October 1 provided the impetus for the USGS Cascadia Volcano Observatory and UNAVCO’s PBO to install additional cGPS stations; today there are a total of 25 cGPS stations. Although many GPS stations show significant velocities before 2004, there was no systematic premonitory pattern [475]. The 2004–2008 eruptions caused about 30 mm of widespread, inward‚ and downward movement of the ground, which reversed itself after the eruptions stopped (Figure 28.23). GPS observations also reveal a steady background northnortheastward movement of all stations at a rate of 6 mm/yr that is related to the subduction of the Juan de Fuca plate beneath the North American plate.

122°20'

122°00'

122°15'

122°10'

122°05'

WASHINGTON

P702

AREA OF MAP

779

122°00'

WASHINGTON

P702

AREA OF MAP

JRO1

JRO1

46°15' TSTU

TSTU TGAU

P693 TWRI P699 WGOT

46°10'

NEBU

LOOW

+

P690

P695 TWRI P699 NEBU

WGOT P698

LOOW

TGAU P693

TWIW P695 P696 P697

P697

TWIW P696

LVCY

P698

LVCY

P690

BIVO

BIVO

5

10

OBSERVED

0

P687 MODEL

KILOMETERS

46°05'

VELOCITY SCALE MODEL 10 MM/YEAR OBSERVED

-10 MM/YEAR

VELOCITY SCALE P687

KILOMETERS 0

5

10

Figure 28.23 GPS velocities from Mount St. Helens stratovolcano monitoring network. Large-aperture cGPS network is operated by the USGS Cascadia Volcano Observatory (CVO) and UNAVCO’s Plate Boundary Observatory (PBO). Shown are observed (with 95% confidence error ellipsoids) and modeled averaged 2004–2005 velocities (left – horizontal velocities; right – vertical). The model consists of a best-fitting, tilted point prolate spheroid (surface projection of center denoted by red plus sign in the left panel). Source: Adapted from Lisowski et al. [475]. Reproduced with permission of U.S. Geological Survey.

c28.3d 779

15/12/2020 5:58:07 PM

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment Dilatation

M PI PE

20

5 0

5

µ Str

10

ain

20 10

MOGI

0

–1 M

FEEDER DIKE

20 10

PE

10

20

5

PIPE

–20

–10

10 0 Distance, km

0 20

ain

Mogi/sphere: 9 km deep 595 m radius

10

PI

m

10

0

I OG

8 6 4 2 0

,k ce tan

Closed-pipe: 6.5 to 11 km deep 250 m radius

Dis

Depth, km

m

,k

ce

10

I

0

OG

8 6 4 2 0

an

t Dis

0 –2 0 –1 0

µ Str

780

Figure 28.24 Modeling the volcano source. (Left) Example of two volcano deformation sources used to model surface geodetic displacements and other data: (1) Mogi spherical source at 9 km and (2) a closed pipe extending from 6.5 to 11 km depth. The initial volume of both sources is chosen to be 0.88 km3, and both volumes are assumed to increase by 0.018 km3. Note that the inversion model parameters were chosen to approximate those inferred for the magma body that fed the 18 May 1980 eruption of Mount St. Helens; eruptions with this increase in volume are quite common. (Right) Calculated dilatations caused by a volume change of 0.018 km3 in each source. The uplift patterns produced by an inflating Mogi source and a closed pipe are very different in proximal areas (here within ~1/2 source depth) but not in distal areas. Thus, distinguishing between these two models requires distribution of cGPS stations in the proximal areas, as well as the distal areas. Source: Adapted from Dzurisin [469]. Reproduced with permission of John Wiley & Sons.

There are a variety of physical models for underlying volcano processes. Some of these include point/spherical (“Mogi”) sources and closed pipes (Figure 28.24), ellipsoidal chambers, and fault dislocations within homogeneous and elastic media. Inversion of geodetic and other data may require more complex models with viscoelastic rheology (Figure 28.24) and inhomogeneous materials. In the study of Mount St. Helens, the surface deformation was consistent with a vertically elongated magma chamber, modeled as a tilted prolate spheroid, with its center at a depth of around 7 to 8 km and with a total cavity-volume loss of about (16–24)×106 m3 [475]. Another example of volcano monitoring and implications for early warning is the moderately active Eyjafjallajökull stratovolcano in Iceland [476]. Iceland is located on the plate boundary between the North American and Eurasian plates with a relative spreading rate of 19.4 mm/yr. The Eyjafjallajökull volcano is situated in a propagating rift outside the main zone of plate spreading. Hundreds of people were evacuated prior to an explosive eruption of the summit beginning on 14 April 2010. There, after 18 years of intermittent volcanic unrest and a 3-month period of magmatic activity, GPS and InSAR observations recorded rapid deformation of >5 mm/day in the month prior to the first eruption. The summit eruption was preceded by

c28.3d 780

a flank eruption from 20 March to 12 April 2010. Deformation was rapid before the first flank eruption (0.5 mm per day after 4 March) as determined by cGPS, but negligible during the eruption (Figure 28.25). The authors of this study concluded that “signs of volcanic unrest signals over years to weeks may indicate reawakening of such volcanoes, whereas immediate short-term eruption precursors may be subtle and difficult to detect.”

28.5

Climate

28.5.1

Introduction

Climate change affects the livelihood of a large portion of the world’s population and impacts natural environments. Consequences include rising surface temperatures, continental ice melt, rising sea level, reduced water availability for human and natural consumption, and increased frequency of atmospheric and hydrological hazards, including tropical cyclones, hurricanes, heat waves, droughts, and floods. Therefore, mitigating the degree and extent of climate change and forecasting trends are pressing issues for reducing societal and environmental vulnerabilities. Geodesy, in particular GPS, provides valuable observations

15/12/2020 5:58:09 PM

28.5 Climate

Longitude (ºW)

(a) 63.8

19.8

19.6

19.4

19.2

19.8

25 Sep. 2009 − 20 Mar. 2010

63.7 Latitude (ºN)

781

19.6

19.4

19.2

11–22 Apr. 2010

63.7

STEI/STE2

63.6

63.8

63.6

SKOG THEY LOS displacement

LOS displacement

63.5 0.0

5 km

15.5 mm

0.0

5 km

15.5 mm

63.5

80

2.5

4 March

2010

(b)

STEI in N101°E direction 60

STEI

2

STE2

1.5

THEY at N185°E direction 0 −20

1

Flank eruption

−40 −60

SKOG at N121°E direction −80

Summit eruption

Displacement (mm)

20

Number of earthquakes x103

40

0.5

0 Sep.

Oct.

Nov.

Month in 2009

Dec.

Jan.

Feb.

Mar.

Apr.

Month in 2010

Figure 28.25 Monitoring deformation of the Eyjafjallajökull, Iceland stratovolcano. Results from the magma intrusive period of 2009–2010 prior to two eruptive events in March to April 2010, with GPS, TerraSAR-X interferograms and seismic data. (a) Interferograms are from descending satellite paths with black orthogonal arrows showing the satellite flight path and look direction. One color fringe corresponds to line-of-sight (LOS) change of 15.5 mm (positive for increasing range, that is, motion of the ground away from the satellite). Thick lines below indicate the time span of the interferograms. Triangles denote cGPS stations. Black dots show earthquake epicenters over this time period. The red stars show the flank and summit event locations. The white denotes snow cover. (b) cGPS displacement time series for stations THEY, SKOG, and collocated station STEI/STE2 labeled in upper left panel with one-sigma error bars, and offset for clarity. Gray shading shows the cumulative number of earthquakes, and black shading the corresponding daily rate. (c) Model of progressive sources of deformation in map view. (d) Schematic east–west cross section across the summit area, with sources plotted at their best-fit depth (vertical exaggeration by a factor of 2). Gray shaded background indicates overlapping source depth uncertainties (95% confidence). Source: Adapted from Sigmundsson et al. [476]. Reproduced with permission of Springer Nature.

c28.3d 781

15/12/2020 5:58:09 PM

782

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

(d)

(c) 63.8

Latitude (ºN)

(m) 2,000 63.7 0 Dike –2,000 63.6

–4,000

source 1994

–6,000 5 km

5 km

63.5

19.9 19.8 19.7 19.6 19.5 19.4 19.3 19.2 19.1

19.9

Longitude (°W)

Figure 28.25

28.5.2 Crustal Response to the Changing Climate Earth’s crust deforms in response to forces exerted on its surface, mainly due to redistribution of atmospheric, oceanic, hydrologic, and cryospheric masses, which are often termed load changes. The changing climate affects the distribution of both hydrological and cryospheric loads, resulting in measurable displacements of Earth’s surface by precise cGPS measurements. Earth’s response to load changes depends on the time scale of the deformation. From a mechanical view point, Earth can be approximated as a viscoelastic material with a characteristic Maxwell time of roughly 1000 years [477]. Thus, short-term load changes (1000 yr) also induce permanent deformation, manifested by viscous flow of the mantle (Figures 28.26c, d). Immediate Response

Short-term load changes induce time-independent elastic deformation. A short-term emplacement of a load, or an

c28.3d 782

1999

19.8

19.7 19.6 19.5 Longitude (ºW)

19.4

19.3

(Continued)

on three climate change frontiers, continental ice melt, variations in continental water storage, and sea level rise. Observations of ice melt and water storage changes are obtained as Earth’s crust deforms in response to cryospheric (ice) and hydrologic (water) load changes. Monitoring of glacier movements provides valuable information on ice flow rates and flow dynamics. GPS observations are also crucial for assessing sea level changes from tide gauge records by estimating biases due to vertical land movements.

28.5.2.1

Sill 2 Sill 1

increase in the load’s mass, results in an immediate subsidence beneath and in the vicinity of the load (Figure 28.26a). Complete or partial removal of the load results in an immediate uplift of the previously subsided area (Figure 28.26b). Very short-term load changes (orders of hours to days), due to ocean tides or a passage of low or high atmospheric pressure systems, induce small displacements of Earth’s surface, on the order of a few millimeters [478]. Seasonal hydrologic and cryospheric load changes result in periodic displacement of Earth’s surface that can reach an amplitude of several centimeters [479]. Multi-year hydrologic and cryospheric load changes can be induced by continental ice melt [480], drought [481], and variability in seasonal load from one year to another [482]. Examples of such load changes are presented in Sections 28.5.3 and 28.5.4 28.5.2.2

Delayed Response

Long-term load changes (>1000 yr) induce delayed viscoelastic deformation. The classic example of long-term delayed response is the emplacement and removal of the late Pleistocene ice sheets, which reached heights of several kilometers in North America and Fennoscandia. A large ice load displaces the crust downward beneath the load and upward away from the load, along the peripheral bulge (Figure 28.26c). These vertical movements induce a delayed outward viscous mantle flow (Figure 28.26c). Removal of the ice load induces uplift of the previously subsided area beneath the load and subsidence of the peripheral bulge (Figure 28.26d). However, both uplift and subsidence are delayed, due to the slow inward mantle flow toward the subsided region beneath the melted ice sheet. This process of delayed uplift and subsidence is termed GIA and is well captured by precise well GPS measurements (Figure 28.27). The

15/12/2020 5:58:10 PM

28.5 Climate

“Small” load change - immediate (elastic) response

783

“Large” load change - delayed (viscous) response

ICE

Ice/water

PERIPHERAL FORE-BULGE FLEXES UP

LOADED CRUST “SINKS”

Subsidence

MANTLE FLOWS OUTWARD

GLOBAL SEA LEVEL RISING

CRUST REBOUNDING

COLLAPSING PERIPHERAL FORE-BULGE

Uplift MANTLE FLOWS BACK

Figure 28.26 Crustal response to loading and unloading of cryospheric (ice) or hydrologic (water) load changes. Small short-term load changes result in immediate (predominantly elastic) (a) subsidence or (b) uplift. Long-term large load changes, as the emplacement or melt of the late Pleistocene ice sheets, induce (c) outward viscous mantle flow and (d) inward mantle flow and delayed crustal uplift after ice sheet melting. Panels (c) and (d) are courtesy of the Canadian Geodetic Survey, Natural Resources Canada. Source: Reproduced with permission of Canadian Geodetic Survey.

analysis of vertical GPS velocities in North America reveals a pronounced uplift signal in eastern and central Canada, which was the center of a massive ice sheet that covered most of North America during the last Ice Age [483]. The vertical velocity field also shows the subsidence of the peripheral bulge, south of the hinge line, roughly located along the United States–Canada border (Figure 28.27). The residual horizontal velocities reveal systematic outward crustal movements of the area along the hinge line, reflecting the release of flexural stresses that were absorbed during the formation of the peripheral bulge (Figure 28.27).

28.5.3

Polar Ice Melt

The increased warming of Earth’s atmosphere and oceans over the past century resulted in massive ice melt and significant mass decrease in continental glaciers, the polar ice sheet, and sea ice. Monitoring the rapid changes over the vast polar regions requires the use of multiple measuring techniques, including satellite altimetry, satellite gravity (e.g. Gravity Recovery and Climate Experiment – GRACE), and InSAR, as well as ground-based methods, including GPS and ground-based InSAR. Integration between the

c28.3d 783

various measurements provides the most complete assessment of current and recent changes in the polar regions. GPS observations are crucial for determining both local changes to individual glaciers, as well as integrated changes occurring over larger sections of the ice sheets. 28.5.3.1

Mass Balance of Ice Sheets

According to the report of the Intergovernmental Panel on Climate Change [484], the average rate of ice loss from glaciers around the world was 226 ± 130 Gt yr−1 over the period 1971 to 2009, and 275 ± 135 Gt yr−1 over the period 1993 to 2009. The rate of ice loss in the polar regions has significantly accelerated since the turn of the 20th century. The loss rates from the Greenland Ice Sheet were 34 ± 40 Gt yr–1 over the period 1992 to 2001 and 215 ± 70 Gt yr–1 over the period 2002 to 2011, and the rates from the Antarctic Ice Sheet were 30 ± 66 Gt yr–1 over the period 1992 to 2001 and 147 ± 65 Gt yr–1 over the period 2002 to 2011 [484]. These reported rates were obtained with large uncertainties, because some of the monitoring techniques measure integrated elevation (altimetry) or mass (gravity) changes, which are induced by both GIA and present-day ice loss. Assessing the present-day ice loss relies on good estimates

15/12/2020 5:58:10 PM

784

28 GNSS Geodesy in Geophysics, Natural Hazards, Climate‚ and the Environment

Vertical Velocities

Residual Velocities

6

4

8 6 10

2

–2 IGb00 0–1 5 mm/yr + ve –ve

1.5 mm/yr Rigid GIA Tect. Effect

Figure 28.27 GPS-detected crustal movements in North America, reflecting GIA response to the melt of the late Pleistocene ice sheets. (Left) Vertical movements with highest uplift rates around Hudson Bay, and subsidence to the south. Green line shows the “hinge line” separating uplift from subsidence. (Right) Residual horizontal movements after subtracting best-fit rigid plate rotation model defined by sites shown with black arrows. Red vectors represent sites primarily affected by GIA. Blue vectors represent sites that include effects of tectonics. Source: Adapted from Sella et al. [483]. Reproduced with permission of John Wiley & Sons.

of GIA [485]. GPS observations from polar regions are used both for constraining the magnitude and spatial distribution of GIA [486] as well as for determining ice loss independent of GIA-induced displacements [480, 487]. Greenland – Continuous GPS measurements along the rocky margins of Greenland have detected high rates of uplift (up to 30 mm/yr), reflecting crustal response to both GIA and present-day ice melt [488, 489]. Several methods were proposed for assessing the present-day component of the uplift and determining ice mass balance at the vicinity of measurement localities. Khan et al. (2010) [488] removed the GIA component using the global ICE-5G model and VM2 viscosity profile [490] to calculate the uplift component due to present-day ice loss and found spreading of ice mass loss into northwest Greenland. More recently, Khan et al. (2016) [330] used multiple observation types, including GPS, and detected that the northeast Greenland ice stream is undergoing sustained dynamic thinning, which is linked to regional warming, after more than a quarter of a century of stability. Jiang, Dixon, and Wdowinski (2010) [480] noticed that long-time series in the North Atlantic region contain an acceleration component, which is independent of long-term GIA displacement, and represents an acceleration in the rate of ice mass loss. Using

c28.3d 784

a simple elastic model, they estimated that western Greenland’s ice loss has accelerated at an average rate of 8.7 ± 3.5 Gt yr−2 and the acceleration rate for southeastern Greenland at a rate of 12.5 ± 5.5 Gt yr−2. Khan et al. (2016) [330] used observations from the Greenland GPS network (GNET) to directly measure GIA and estimate basin-wide mass changes since the Last Glacial Maximum and surprisingly found a large GIA uplift rate of 12 mm/yr in southeast Greenland (Figure 28.28). van Dam et al. (2017) [491] used GPS and gravity measurements to separate the viscoelastic GIA component from the GPS-observed uplift rate and estimated that the GIA component in their study area was inconsistent with most previously reported GIA model predictions. Antarctica – GPS measurements from bedrock sites in Antarctica are also used for estimating GIA models [492] and ice mass balance. Bevis et al. (2009) [332] noticed that the spatial pattern of vertical GPS velocities in West Antarctica is variable and not consistent with available GIA models. They suggested that GIA estimates for Antarctica are inaccurate and, most likely, affect the ice mass loss estimate measured by other techniques such as GRACE. MartinEspanol et al. (2016) [493] used multiple data types, including GPS, to estimate spatiotemporal mass balance trends

15/12/2020 5:58:11 PM

28.5 Climate 90°W

80°W

70°W 60°W50°W40°W30°W 20°W10°W

0°

785

10°E 80°N

75°N 75°N

70°N

70°N

65°N

65°N

GIA rates (mm/yr) 10

60°N

GIA rates (mm/yr) 10 60°N

–10 50°W

40°W

Uncertainties (mm/yr) 3

–10

0

30°W

Figure 28.28 GNET-based glacial isostatic adjustment (GIA) model for Greenland. (A) Estimated global isostatic adjustment (GIA) vertical displacement rates at GNET cGPS stations. Gray curves denote major drainage basins. (B) Interpolated GIA vertical displacement rates. (C) Uncertainties of GIA vertical displacement rates. Source: Adapted from Khan et al. [330]. Reproduced with permission of AAAS.

for the Antarctic Ice Sheet for the period 2003–2013. They revealed that Antarctica has been losing mass at a rate of −84 ± 22 Gt yr−1, in which West Antarctica is the largest contributor, mainly by high thinning rates of glaciers draining into the Amundsen Sea Embayment. 28.5.3.2

Glacier and Ice Sheet Flow

Ice mass loss of both glaciers and ice sheets occurs by surface melt runoff, basal shear and runoff, dynamic thinning due to the speedup of glacier flow, and calving in marine-terminus glaciers. Monitoring glacier and ice sheet movements and dynamics is conducted by both space-based and groundbased techniques. The space-based techniques – satellite altimetry and InSAR – provide high-spatial-resolution observations over wide study areas [494]. Ground-based techniques, including cGPS and seismic networks, provide high-temporal-resolution observations, which are crucial for understanding the kinematics and dynamics of glacier flow and ice sheet thinning. The quality and significance of GPS ice movement measurements has increased over time. Early GPS episodic measurements of the Jakobshavn Isbræ glacier in western Greenland revealed no significant variations in seasonal velocity rates, within the uncertainties of the geodetic measurements [495]. However, cGPS measurements in the same region detected significant seasonal variations in velocity ranging from 35–40 cm d−1 (127.8–146.0 m yr−1)

c28.3d 785

in the summer to 27–28 cm d−1 (98.6–102.2 m yr−1) in the winter [40]. The detected seasonal acceleration (summer) and deceleration (winter) coincides with period of surface melting, suggesting a strong coupling between surface conditions and ice sheet flow, which provide a mechanism for explaining the dynamic response of ice sheets to climate warming [40]. Continuous GPS has provided crucial observations for understanding the role of meltwater and basal pressure changes on glaciers and ice sheet movements. Bartholomaus, Anderson, and Anderson (2008) [497] monitored the motion of the Kennicott Glacier, Alaska, and detected velocity increase when englacial and subglacial water storage increased and proposed that the acceleration occurred due to an increase in basal pore pressure that promotes basal motion. Das et al. (2008) [498] used GPS, increased seismicity, transient acceleration, ice sheet uplift, and horizontal displacements to monitor rapid (