China Satellite Navigation Conference (CSNC 2021) Proceedings [3] 9789811631450, 9789811631467

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Lecture Notes in Electrical Engineering 774

Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume III

Lecture Notes in Electrical Engineering Volume 774

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Changfeng Yang Jun Xie •

Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume III

123

Editors Changfeng Yang China Satellite Navigation Engineering Centre Beijing, China

Jun Xie China Academy of Space Technology Beijing, Beijing, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-16-3145-0 ISBN 978-981-16-3146-7 (eBook) https://doi.org/10.1007/978-981-16-3146-7 © Aerospace Information Research Institute 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

BeiDou Navigation Satellite System (BDS) is China’s global navigation satellite system which has been developed independently. BDS is similar in principle to Global Positioning System (GPS) and compatible with other global satellite navigation systems (GNSS) worldwide. The BDS will provide highly reliable and precise positioning, navigation and timing (PNT) services as well as short-message communication for all users under all-weather, all-time and worldwide conditions. China Satellite Navigation Conference (CSNC) is an open platform for academic exchanges in the field of satellite navigation. It aims to encourage technological innovation, accelerate GNSS engineering and boost the development of the satellite navigation industry in China and in the world. The 12th China Satellite Navigation Conference (CSNC 2021) is held during May 26–28, 2021, in Nanchang, China. The theme of CSNC2021 is “Spatio-Temporal Data Empowers Bright Future,” including technical seminars, academic exchanges, forums, exhibitions and lectures. The main topics are as follows:

Conference Topics S01 S02 S03 S04 S05 S06 S07 S08 S09 S10

Professional GNSS Applications GNSS Applications for the Mass Market GNSS and Their Augmentations Satellite Orbits and Precise Positioning Time Frequencies and Precision Timing Autonomous Navigation and Intelligent Operation GNSS Signal Processing GNSS User Terminals PNT Architectures and New PNT Technologies Policies, Standards and Intellectual Property Rights

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The proceedings (Lecture Notes in Electrical Engineering) have 201 papers in ten topics of the conference, which were selected through a strict peer-review process from 471 papers presented at CSNC2021, in addition, another 202 scientific committee of China Satellite Navigation Conference (CSNC). Papers were selected as the electronic proceedings of CSNC2021, which are also indexed by “China Proceedings of Conferences Full-text Database (CPCD)” of CNKI and Wan Fang Data. We thank the contribution of each author and extend our gratitude to 281 referees and 55 session chairmen who are listed as members of the editorial board. The assistance of CNSC2021’s organizing committees and the Springer editorial office is highly appreciated.

Organization

Editorial Board Topic: S01: Professional GNSS Applications Chairman Dangwei Wang

Beijing UniStrong Science and Technology Co., Ltd., Beijing, China

Vice-chairman Dun Wang Shuangcheng Zhang Caicong Wu Weiqiang Li

Space Star Technology Co., LTD. Beijing, China Chang’an University, Shaanxi, China China Agricultural University, Beijing, China Institute of Space Sciences, Spanish National Research Council

Topic: S02: GNSS Applications for the Mass Market Chairman Wenjun Zhao

Beijing Satellite Navigation Center, Beijing, China

Vice-chairman Shaojun Feng Changhui Xu Taosheng Wang

Qianxun Spatial Intelligence Inc., Shanghai, China Chinese Academy of Surveying and Mapping, Beijing, China BeiDou Application & Research Institute Co., Ltd. of Norinco Group, Beijing, China

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viii

Baoguo Yu Yang Gao

Organization

The 54th Research Institute of China Electronics Technology Group Corporation, Hebei, China University of Calgary, Alberta, Canada

Topic: S03: GNSS and Their Augmentations Chairman Rui Li

Beihang University, Beijing, China

Vice-chairman Long Yang Wenxiang Liu Xingxing Li Yansong Meng Liwen Dai

Beijing Future Navigation Technology Co., Ltd., Beijing, China National University of Defense Technology, Hunan, China Wuhan University, Hubei, China Xi’an Branch of China Academy of Space Technology, Shaanxi, China John Deere, Torrance CA, USA

Topic: S04: Satellite Orbits and Precise Positioning Chairman Xiaogong Hu

Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China

Vice-chairman Jianwen Li Jianghui Geng Bofeng Li Xiaolin Meng

Information Engineering University, Henan, China Wuhan University, Hubei, China Tongji University, Shanghai, China The University of Nottingham, Nottingham, UK

Topic: S05: Time Frequencies and Precision Timing Chairman Aimin Zhang

National Institute of Metrology, Beijing, China

Vice-chairman Liang Wang

The 203th Research Institute of China Aerospace Science and Industry Corporation, Beijing, China

Organization

Lijun Du Xiaohui Li Patrizia Tavella

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Xi’an Branch of China Academy of Space Technology, Shaanxi, China National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Bureau International des Poids et Mesures, Paris, France

Topic: S06: Autonomous Navigation and Intelligent Operation Chairman Xingqun Zhan

Shanghai Jiao Tong University, Shanghai, China

Vice-chairman Haihong Wang Wenbin Gong

Yuxin Zhao Caibo Hu Naser EI-Sheimy

Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Harbin Engineering University, Heilongjiang, China Beijing Satellite Navigation Center, Beijing, China University of Calgary, Alberta, Canada

Topic: S07: GNSS Signal Processing Chairman Xiaochun Lu

National Time Service Center, Chinese Academy of Sciences, Shaanxi, China

Vice-chairman Yang Li

Zheng Yao Xiaomei Tang Sherman Lo

The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China Tsinghua University, Beijing, China National University of Defense Technology, Hunan, China Stanford University, San Francisco, USA

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Organization

Topic: S08: GNSS User Terminals Chairman Hong Li

Tsinghua University, Beijing, China

Vice-chairman Zishen Li Liduan Wang Chengjun Guo Sang Jeong Lee

Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China ComNav Technology Ltd., Shanghai, China University of Electronic Science and Technology of China, Sichuan, China Chungnam National University, Daejeon, South Korea

Topic: S09: PNT Architectures and New PNT Technologies Chairman Zhongliang Deng

Beijing University of Posts and Telecommunications, Beijing, China

Vice-chairman Jiangning Xu Jinsong Ping

Dongyan Wei Jinling Wang

Naval University of Engineering, Hubei, China The National Astronomical Observatories of the Chinese Academy of Sciences, Beijing, China Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China The University of New South Wales, Sydney, Australia

Topic: S10: Policies, Standards and Intellectual Property Rights Chairman Junlin Yang

Beihang University, Beijing, China

Vice-chairman Miao Tian

China Satellite Navigation Office International Corporation Center, Beijing, China

Organization

Huiying Li

Yuxia Zhou

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Electronic Intellectual Property Center, Ministry of Industry and Information Technology, Beijing, China China Academy of Aerospace Standardization and Product Assurance, Beijing, China

Scientific Committee Senior Advisor: (By Surnames Stroke Order) Qingjun Bu Liheng Wang Yuzhu Wang

Guoxiang Ai Lehao Long Shuhua Ye Jiadong Sun Daren Lv Yongcai Liu Jingnan Liu Houze Xu Jinan Li Zuhong Li Guirong Min Rongjun Shen Chi Zhang Xixiang Zhang

China National Administration of GNSS and Applications, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Shanghai Astronomical Observatories, Chinese Academy of Sciences, Shanghai, China China Aerospace Science and Technology Corporation, Beijing, China The Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China Wuhan University, Hubei, China Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Hubei, China The Former Electronic Information Foundation Department of General Equipment Department China Academy of Space Technology, Beijing, China China Academy of Space Technology, Beijing, China China Satellite Navigation System Committee, Beijing, China The Former Electronic Information Foundation Department of General Equipment Department The 29th Research Institute of China Electronics Technology Group Corporation, Sichuang, China

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Lvqian Zhang Junyong Chen Benyao Fan Dongjin Luo Huilin Jiang Guohong Xia Peikang Huang Chong Cao Faren Qi Rongsheng Su Shusen Tan Ziqing Wei

Organization

China Aerospace Science and Technology Corporation, Beijing, China National Administration of Surveying, Mapping and Geo-information, Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China Changchun University of Science and Technology, Jilin, China China Aerospace Science and Industry Corporation, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China China Research Institute of Radio Wave Propagation (CETC 22), Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China Beijing Satellite Navigation Center, Beijing, China Xi’an Institute of Surveying and Mapping, Shaanxi, China

Chairman Changfeng Yang

China Satellite Navigation System Committee, Beijing, China

Vice-chairman Yuanxi Yang Shiwei Fan

China National Administration of GNSS and Applications, Beijing, China China Satellite Navigation Engineering Center, Beijing, China

Executive Chairman Jun Xie Lanbo Cai

China Academy of Space Technology, Beijing, China China Satellite Navigation Office, Beijing, China

Organization

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Committee Members: (By Surnames Stroke Order) Xiancheng Ding Qun Ding

Quan Yu Zhijian Yu Jian Wang Shafei Wang Wei Wang Lihong Wang Chengqi Ran Weimin Bao Yueguang Lv Zhaowen Zhuang Chong Sun Yadu Sun Tianchu Li Xianyu Li Minglin Li Hui Yang Longxu Xiao Yirong Wu Weiqi Wu Haitao Wu Manqing Wu Bin Wu Jun Zhang

China Electronics Technology Group Corporation, Beijing, China The 20th Research Institute of China Electronics Technology Group Corporation, Beijing, China Peng Cheng Laboratory, Shenzhen, China Taiyuan Satellite Launch Center of China’s Manned Space Project, Shanxi, China Alibaba Group, Zhejiang, China Academy of Military Sciences PLA China, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Legislative Affairs Bureau of the Central Military, Beijing, China China Satellite Navigation Office, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Science and Technology Commission of the CPC Central Military Commission National University of Defense Technology, Hunan, China Beijing Institute of Tracking and Communication Technology, Beijing, China Aerospace Engineering Research Institute of the PLA Strategic Support Force National Institute of Metrology, Beijing, China Research Institute of the PLA Rocket Force China Society for World Trade Organization Studies, Beijing, China China Academy of Space Technology, Beijing, China Research Institute of the PLA Rocket Force The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Xichang Satellite Launch Center, Sichuan, China Aerospace, Chinese Academy of Sciences, Beijing, China China Electronics Technology Group Corporation, Beijing, China Beijing Institute of Tracking and Communication Technology, Beijing, China Beijing Institute of Technology, Beijing, China

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Zhijie Chen Zhonggui Chen

Jinping Chen Baojun Lin

Zhixin Zhou Jianping Zhou Jianhua Zhou Jiancheng Fang Wenjun Zhao Jiang Hu Jie Jiang Shuren Guo Huikang Huang Xibin Cao Wenhai Jiao Yi Zeng Yi Cai

Organization

National Core Laboratory of Airspace Technology The 5th Research Institute of China Aerospace Science and Technology Corporation, Beijing, China Beijing Satellite Navigation Center, Beijing, China Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Space Engineering University, Beijing, China Chief Designer of China’s Manned Space Project Beijing Satellite Navigation Center, Beijing, China Beihang University, Beijing, China Beijing Satellite Navigation Center, Beijing, China BeiDou Application & Research Institute Co., Ltd. of Norinco Group, Beijing, China China Academy of Launch Vehicle Technology, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Ministry of Foreign Affairs of the People’s Republic of China, Beijing, China Harbin Institute of Technology, Heilongjiang, China China Satellite Navigation Engineering Center, Beijing, China China Electronics Corporation, Beijing, China BeiDou Ground-based Augmentation System Chief Engineer

Executive Members: (By Surnames Stroke Order) Jun Shen Dangwei Wang Rui Li Xiaogong Hu Aimin Zhang Xingqun Zhan

Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beihang University, Beijing, China Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China National Institute of Metrology, Beijing, China Shanghai Jiao Tong University, Shanghai, China

Organization

Xiaochun Lu Hong Li Zhongliang Deng Junlin Yang

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National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Tsinghua University, Beijing, China Beijing University of Posts and Telecommunications, Beijing, China Beihang University, Beijing, China

Organizing Committee Director Chengqi Ran

China Satellite Navigation Office, Beijing, China

Deputy Director Jun Yang Xiaohua Qu Yun Xiao

China Satellite Navigation Office, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China Nanchang Municipal People’s Government, Jiangxi, China

Secretary-General Haitao Wu

Satellite Navigation Headquarters, Chinese Academy of Sciences, Beijing, China

Deputy Secretary-General Weina Hao

Satellite Navigation Headquarters, Chinese Academy of Sciences, Beijing, China

Deputy Secretary Yao Wang Wenhai Jiao Mingquan Lu Jun Lu Weiquan Guo Bin Yang

Nanchang Municipal People’s Government, Jiangxi, China China Satellite Navigation Engineering Center, Beijing, China Tsinghua University, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China Nanchang Municipal Office of Civil-Military Integration, Jiangxi, China

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Organization

Committee Members: (By Surnames Stroke Order) Li Wang Ying Liu Guangfu Sun Di Xiao Caicong Wu Taosheng Wang Jun Shen Lu Chen Xiuwan Chen Junlin Yang Dongning Lin Baoming Zhou Jinjun Zheng Wenjun Zhao Qile Zhao Yamin Dang Min Shui Wei Xiong

International Cooperation Research Center, China Satellite Navigation Office, Beijing, China China Satellite Navigation Engineering Center, Beijing, China National University of Defense Technology, Hunan, China Beidou Union Technology Co., Ltd., Beijing, China China Agricultural University, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beijing Institute of Space Science and Technology Information, Beijing, China Peking University, Beijing, China BDS/GNSS Policy and Regulation Research Center, Beijing, China Beijing Shunyi District Economic and Information Commission, Beijing, China Nanchang Municipal Office of Civil-Military Integration, Jiangxi, China China Academy of Space Technology, Beijing, China Beijing Satellite Navigation Center, Beijing, China Wuhan University, Hubei, China Chinese Academy of Surveying and Mapping, Beijing, China The National Remote Sensing Center of China, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China

Contents

Time Frequencies and Precision Timing Research on the Method of Autonomous Establishing and Maintaining the Synthetic Atomic Time of Satellite Navigation Constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Lu, Richang Dong, Chengpan Tang, Yinan Meng, Gong Zhang, and Jianhua Shen A New Method to Suppress the AC-Stark Shift of Compact Cesium Beam Atomic Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shaohang Xu, Sifei Chen, Chang Liu, Yining Li, Jiale Wang, and Yanhui Wang A Compensation Method of Satellite Clock Day-Boundary Jumps Based on Epoch-Differenced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weiquan Huang, Menghao Li, Hui Li, Renlong Wang, Nan Li, and Liang Li Research on Integrity Monitoring Techniques for Atomic Clocks Based on DualKalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinming Huang, Zhiling Ren, Jing Peng, and Hang Gong The Beam Optics Analysis Based on Monte Carlo Simulation of the Magnetic State Selection and Optical Detection Cesium Beam Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sifei Chen, Shaohang Xu, Chang Liu, Yuanhao Li, and Yanhui Wang High Precision Time Synchronization of LEO Constellation Based on PPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Wang, MeiTing Yu, Hang Gong, Ming Ma, and GuangFu Sun

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Contents

A Rubidium Atomic Frequency Standard with Stability at 10 15 Level Operated Under Atmospheric Condition . . . . . . . . . . . . . . . . . . . Junyao Li, Gang Ming, Feng Zhao, Fang Wang, Pengfei Wang, and Ganghua Mei A Closed-Loop Calibration Method of the BeiDou Time Receiver . . . . . Guojun Li, Di Zhang, Yongxin Lin, and Jiawei Wang Feasibility Analysis for Evaluating On-Board Atomic Clocks by Inter-satellite Clock Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bin Yang, Yiwei Wu, Shichao Wang, Maolei Wang, Shenghong Xiao, and Yufei Yang Relativistic Effect in the Two-Way Time Comparison Between Navigation Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leyuan Sun, Shuaihe Gao, Jun Yang, Feng Xiao, Yuankun Fang, and Sen Feng

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Performance Evaluation and Analysis of BeiDou In-Orbit Satellite Atomic Clocks Based on Multiple Source Data . . . . . . . . . . . . . . . . . . . 105 Songtao Huangfu, Weisong Jia, Hui Yang, Jin Chang, Lifang Yuan, and Junwu Zhai Research Progress of Inter-satellite Precision Measurement and Time-Frequency Synchronization Technology Based on USO . . . . . 118 Xuan Liu, Xingwang Zhong, Dalei Xue, Pan Zhang, and Yifeng He Design and Fabrication of Thermostat for the Hydrogen Maser . . . . . . 128 Shuo Liu, He Yang, Weili Wang, Kai Huang, Yushan Lu, Yaxuan Liu, and Liang Wang Design of Low Additional Stability Multi-channel Digital Phase Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Kai Huang, Yanjun Chen, He Yang, Shuo Liu, Yushan Lu, Yaxuan Liu, and Liang Wang Monitoring Assessment and Impact Analysis of BeiDou and GNSS Time Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Shichao Wang, Ying Liu, Maolei Wang, Bin Yang, Lin Zhang, and Haibo Yuan A Satellite-Ground Precise Time Synchronization Method and Analysis on Time Delay Error Caused by Motion . . . . . . . . . . . . . . 158 Yanming Guo, Yan Bai, Shuaihe Gao, Zhibing Pan, Zibin Han, Yuping Gao, and Xiaochun Lu

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Ground Environment Test and In-Orbit Performance Verification of Spaceborne Cesium Atomic Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Jun Yang, Ning Zheng, Jingzhong Cui, Shiwei Wang, Wei Yang, Pei Ma, Zhidong Liu, Jiang Chen, Yinguang Ma, Yulong Zhao, Liangyu Huang, and Pengling Dong Analysis of In-Orbit Data of Domestic Space-Borne Cesium Atomic Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Pei Ma, Jun Xie, Jingzhong Cui, Zhidong Liu, Pengling Dong, Shiwei Wang, Jiang Chen, Wei Yang, Lu Wang, Ji Wang, Yinguang Ma, Jianxiang Wang, Jiqing Lian, Liangyu Huang, Jun Yang, Yulong Zhao, Ning Zheng, and Dongjun Wang GNSS Signal Processing Low Complexity Acquisition and Tracking Methods for CSK Modulated Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Tao Yan, Ying Wang, Tian Li, Ye Tian, Lang Bian, and Yansong Meng Reflection Objects Sensing and Localization with GNSS Multipath Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Xin Chen, Yilun Shao, Di He, and Wenxian Yu A High-Precision Doppler Frequency Estimation Algorithm for CDMA-TDMA Navigation Signal Structure . . . . . . . . . . . . . . . . . . . 215 Jiancheng Zhang, Lina Xu, and Mengting Zhang Research and GPU Parallel Implementation of the Compatibility Analysis Methodology Between FDMA and CDMA Navigation Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Weinan Zhang, Xia Ge, Zheng Yao, and Jiemin Shen A GNSS Loop Tracking Structure Based on Unscented Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Mingxing Gu, Yuan Hu, Minghui Mou, Shengzheng Wang, and Wei Liu A Vector Tracking Structure of FLL-Assisted PLL for GNSS Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Minghui Mou, Yuan Hu, Mingxing Gu, Shengzheng Wang, and Wei Liu Evaluation of Signal in Space Accuracy of New System Signal of BDS-3 Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Haichun Wang, Xiancai Tian, Longping Zhang, Wei Hu, Junwei Zhang, Shiming Gu, and Dezhi Zhang Interference Mitigation Based on Polarized Pattern Constrained Minimum Variance (PCMV) Using Dual-Polarized Array . . . . . . . . . . . 273 Ke Zhang, Lei Chen, Zengjun Liu, Jingyuan Li, Daping Hu, and Guangfu Sun

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Double Estimation Tracking Method Based on Chirp Delay Locked Loops for BOCC Modulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Xin Zhao, Xinming Huang, Xiaomei Tang, and Guangfu Sun An Improved GNSS Vertical Time Series Prediction Model Using EWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 Rui Tao, Tieding Lu, Yuanming Cheng, Xiaoxing He, and Xin Wang A Carrier Tracking Algorithm Based on Adaptive Unscented Kalman Filter Under Ionosphere Scintillation Conditions . . . . . . . . . . . 314 Pengyue Sun, Shengqiang Lou, Xiaomei Tang, and Yangbo Huang GNSS Spoofing Detection Based on Combined Monitoring of Acquisition Function and Automatic Gain Control . . . . . . . . . . . . . . . . 324 Tao Zhang, Xin Chen, Weihua Xie, Wenxian Yu, and Weimin Zhen LFM Interference Mitigation Method Based on Robust Statistics . . . . . 334 Yiming Wang, Qiongqiong Jia, and Renbiao Wu A Code Phase Pull-In Method Based on the Zero-Crossing Point of the S-Curve Under the Strong Multipath Environment . . . . . . . . . . . 344 Pengcheng Ma, Xiaomei Tang, Zhe Liu, Chunjiang Ma, and Gang Ou Anti-jamming Performance Evaluation Method of GNSS Receiver Based on Path Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Binbin Ren, Shaojie Ni, Feiqiang Chen, Zukun Lu, and Jian Wu Modeling and Evaluation of Pseudorange Deviation of Satellite Navigation Digital Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 Chunjiang Ma, Xiaomei Tang, Pengcheng Ma, Song Li, and Guangfu Sun Research on GNSS Time Series Noise Reduction Combining Principal Component Decomposition and Compound Evaluation Index . . . . . . . . 378 Xinrui Li, Shuangcheng Zhang, Zhiqiang Dong, Xinyu Dou, Yiming Xue, Lixia Wang, Chuhan Zhong, Yunqing Hao, Qintao Bai, and Pingli Li A Spoofing Detection Algorithm Based on Coprime Array for GNSS Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Yuqing Zhao, Feng Shen, and Dong Zhou Unambiguous Tracking Technique for Multicarrier Modulation Signals in the Framework of Cognitive Receivers . . . . . . . . . . . . . . . . . 397 Junjie Ma, Zheng Yao, and Mingquan Lu GNSS User Terminals Optimal Design of Multi-channel Correlator for the Same Code Signal and Its Application in Anti-jamming for GNSS . . . . . . . . . . . . . . 413 Rong Shi, Junhao Chen, and Jinchen Bao

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Impact Analysis of Meaconing Attack on Timing Receiver . . . . . . . . . . 423 Dong Fu, Jing Peng, Hang Gong, Ming Ma, and Gang Ou An Unambiguous Acquisition Algorithm for TC-OFDM Signals Based on BOC Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Jingrong Liu, Zhongliang Deng, Kai Luo, Shihao Tang, and Xiwen Deng Research on Carrier Tracking Algorithm of INS-Assisted TC-OFDM Receiver with Fuzzy Control . . . . . . . . . . . . . . . . . . . . . . . . 445 Guoshun Tang, Fuxing Yang, Zhongliang Deng, Xiwen Deng, and Shiwen Jiang DPCCRW: An Unambiguous Acquisition Technique for High-Order Binary Offset Carrier Modulated Signal . . . . . . . . . . . . . . . . . . . . . . . . 456 Xinming Huang, Zhang Ke, Jingyuan Li, Zengjun Liu, and Gang Ou Robust GNSS Position Estimation Using Graph Optimization Based Vector Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 Changhui Jiang, Yu Chen, Bohao Wang, Yuwei Chen, Shuai Chen, and Juha Hyyppä An Attitude Estimation Algorithm for Satellite Navigation Array Against Gross Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Jie Wang, Wenxiang Liu, Haibin Wang, Lu Zukun, and Ou Gang Self-supervised Calibration Method of Array Antenna for High-Precision GNSS Application . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Gang Liu, Kefan Wei, Xiaowei Cui, and Mingquan Lu An Evaluation Method for Anti-sEU Effects Design of SRAM-Based FPGA on Navigation Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 Xuhui Liu, Shaojie Ni, Shengqiang Lou, Pengyue Sun, and Yangbo Huang BeiDou Satellite Navigation Terminal Effectiveness Evaluation Based on Cloud Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Juan Wu, Xiaolin Jia, and Ting Zang An Algorithm for Satellite Power Anomaly Detection Based on Time Series Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 Yibo Si, Yuan Gao, and Huaang Chen Null Control Method Based on GNSS Array Anti-jamming Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Zhengwang Luo, Kejin Cao, Yinbing Zhu, and Bao Li W-Test Aided Quality Control Algorithm for GNSS/IMU Integrated Navigation in Urban Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 Ming Qiu and Rui Sun

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Carrier Phase Multipath Error Elimination Method for GNSS Signals Based on an APCRW Correlator . . . . . . . . . . . . . . . . . . . . . . . . 549 Chunjiang Ma, Xiaomei Tang, Zengjun Liu, Honglei Lin, and Guangfu Sun Fault Identification Method of GNSS/INS Integrated Navigation System Based on the Fusion of Chi-Square Test and Multiple Solution Separation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 Xin Li, Kun Fang, Xiao Li, Jichao Dong, and Zhipeng Wang Policies, Standards and Intellectual Property Rights Evaluation of Beidou Satellite Navigation Service Anti-jamming Capability Under International Standard Framework . . . . . . . . . . . . . . 573 Ying Chen, Yuan Liu, Jianhua Shen, Cheng Liu, Wei Wang, and Chengqian Lou Research on the Trademark Strategy of Beidou Industry . . . . . . . . . . . 582 Yuxuan Wang Research on Business Model Innovation of Beidou Satellite Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 Qingyi Gao, Jiachen Fan, Jinping Yu, and Wuxiang Zhu Insights and U.S. GPS International Cooperation Under Legal Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 Linlin Niu Study on the Legal Model of International Cooperation in the Field of Satellite Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 Xiaomeng Fan Study on the Security Protection System of Foreign Satellite Navigation System Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Wenqing Zhang and Chen Yu The Standardization Status and Standard Sets Construction of Beidou Satellite Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Kai Wang, Weijia Wang, Ying Liu, Ji Guo, Xiangyi Zhang, and Dongliang Liu Intellectual Property Risk and Prevention of BeiDou’s “Going-Out” Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 Lin Su, Jixuan Xiao, and Yuexuan Wang The Consideration of BDS International Standardization in Civil Aviation Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 Xin Jiang, Zhan Zhang, Zhe Fan, Tieshuai Li, and Boyuan Gong

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Preliminary Study on BDS Participation in ISO Standardization . . . . . 651 Yuxia Zhou, Qian Tan, Haofang Quan, Dengbang Kang, and Kanglian Zhao Research on Protocol Architecture and Standard System of Next Generation Navigation Integrated Space and Onboard Network . . . . . . 659 Xiongwen He, Mingwei Xu, Dong Yan, Zheng Qi, Hongcheng Yan, Lijun Yang, and Weisong Jia Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

Time Frequencies and Precision Timing

Research on the Method of Autonomous Establishing and Maintaining the Synthetic Atomic Time of Satellite Navigation Constellation Jun Lu1 , Richang Dong2(B) , Chengpan Tang3 , Yinan Meng1 , Gong Zhang4 , and Jianhua Shen5 1 Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China 2 Institute of Microsatellite Innovation, Chinese Academy of Sciences, Shanghai 200120, China

[email protected]

3 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China 4 Institute of Telecommunication and Navigation, CAST, Beijing 100094, China 5 The 54th Research Institute of CETC, Shijiazhuang 050031, China

Abstract. The autonomous establishment and maintenance of synthetic atomic time in satellite navigation constellations is increasingly becoming the development requirements of satellite navigation systems, this article systematically discusses the composition framework of synthetic atomic time in satellite navigation constellations. Inter-satellite/satellite-to-ground time-frequency comparison measurement technology, satellite navigation constellation synthetic atomic time distribution technology, and constellation dynamic clock group management technology have been modeled, using Beidou precision clock error data provided by IGS’s multi-GNSS experiment project (MGEX). The performance simulation of the synthetic atomic time of the satellite navigation constellation was carried out. Based on the synthetic atomic time established by six MEO satellites equipped with on-board hydrogen clocks in orbit, the astronomical stability has been increased from 5E−15/d for a single satellite (hydrogen clock) to 3.28E−15/d, with a 24-h forecast error increased from 14 cm for a single satellite (hydrogen clock) to 9 cm, which preliminarily proved the feasibility and effectiveness of the autonomous establishment and maintenance method for the synthetic atomic time. Keywords: Satellite navigation · Synthetic atomic time · Spaceborne atomic clock · Time-frequency transfer

1 Introduction In the process of satellite navigation, the user’s basic observation is the distance from the satellite to the user, and the distance is obtained by multiplying the propagation time of the measured signal by the speed of light. Therefore, the satellite navigation system must have a time reference with high accuracy and high stability as the basis [1]. The time bases of the world’s major satellite navigation systems are also traceable to achieve © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 3–16, 2021. https://doi.org/10.1007/978-981-16-3146-7_1

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unity with Coordinated Universal Time (UTC). The unification of the time base is also the basis for the coordinated provision of services by major navigation systems [2–4]. Benefiting from the advantages of global ground stations in the United States, the establishment and maintenance of the time reference of the GPS system constellation mainly relies on a large number of ground measurement and control systems to monitor the quality of signals broadcast by navigation satellites in real time, and to accurately measure and correct the clock errors of satellite atomic clocks. With the advancement of space-borne atomic clock technology, current navigation satellites no longer require long-term control by ground systems, and can maintain the time stability of the satellite clock for a certain period of time. The European Galileo system proposed a low-orbit constellation composed of 4– 6 low-orbit satellites [5], equipped with an iodine molecular optical clock, and highprecision measurement of mid- and high-orbit satellites through inter-satellite links. The characteristics of good performance have become the core of space-based autonomous punctuality, realizing the normal and autonomous operation of a joint ground station. In view of the limitation of the construction of ground stations outside my country, the Beidou satellite navigation system has innovatively designed a global inter-satellite link based on Ka phased array antenna [6–8]. Based on the inter-satellite link, the Beidou navigation constellation can realize inter-satellite two-way measurement and signal monitoring without ground station support. The inter-satellite link technology further enhances the autonomous time synchronization capability of the navigation constellation based on the improvement of the satellite clock timekeeping ability. Continuing the current system time reference construction system, on the one hand, it cannot maximize the performance of the entire network’s atomic clock, on the other hand, it is difficult to get rid of the strong dependence on ground stations. By carrying high-performance atomic clocks in the constellation and using the high-precision time-frequency transmission link between satellites to construct a comprehensive time-frequency reference for the constellation, it is the trend to realize the construction of the next-generation satellite navigation system. This article describes the basic framework of the future navigation constellation to achieve integrated atomic time reference, the integrated atomic time algorithm of the navigation constellation that adapts to different types of on-board atomic clocks, the high-precision inter-satellite/satellite-to-ground time-frequency comparison measurement technology, and the satellite navigation constellation integrated atomic time The distribution technology and the management technology of the constellation dynamic clock group have been model designed, and through simulation experiments, the feasibility and effectiveness of the independent establishment and maintenance method of the satellite navigation constellation integrated atomic time have been demonstrated.

2 Space-Based Time Base Composition Framework 2.1 Overall Framework Description The Beidou navigation system space constellation is a hybrid constellation composed of GEO/IGSO/MEO satellites. Considering that the LEO satellite constellation is an excellent carrier to realize the space-based observation of the navigation constellation, and the space-based observation is very small due to multipath, troposphere, and current

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layer, the observation accuracy is high, which will greatly improve the accuracy of the establishment and maintenance of the time reference [9, 10]. The low orbit (LEO) constellation will be further added in the future. Aiming at the Beidou hybrid constellation, the article proposes an integrated atomic time construction and distribution architecture for satellite navigation constellations based on high- and mid-orbit node satellites, as shown in Fig. 1. In this framework, the medium and high orbit satellites are used as the node satellites for the integrated atomic time calculation of the satellite navigation constellation, and constitute the core of the establishment and maintenance of the integrated atomic time of the satellite navigation constellation. The main components of the integrated atomic time of the satellite navigation constellation include three parts: on-board atomic clock, inter-satellite time and frequency signal transmission, and satellite-based time information processing. The inter-satellite time and frequency signal transmission includes two-way time synchronization links between medium and high orbit satellites. And the time signal monitoring link of low-orbit satellites. Medium-high orbit satellite

Two-way me synchronizaon and data transmission Low orbit monitoring Monitoring data return

Medium-high orbit satellite

Low orbit satellite

Low orbit satellite

Medium-high orbit satellite

Low orbit satellite

Low orbit satellite

Fig. 1. Schematic diagram of space-based time reference constellation composition.

According to the different division of time-based space-based tasks, the satellites in the mid-to-high orbit constellation are divided into time reference satellites, computing node satellites and ordinary satellites. Time reference satellites and computing node satellites also complete the same tasks as ordinary satellites. The division of labor for different satellites is as follows: (1) Time reference satellites are equipped with high-performance atomic clocks to participate in the establishment and maintenance of space-based time references. (2) The computing node satellite collects all high-precision inter-satellite link measurements in the constellation, completes the constellation time synchronization, completes the calculation of the space-based time reference, and distributes the spacebased time reference to ordinary satellites through the high-precision inter-satellite link. (3) Ordinary satellites receive the space-based time reference and inter-satellite link measurement distributed by the computing node satellite, calculate its own clock error, arrange it into a message, broadcast it to the user through the downlink navigation signal for positioning use, and use the downlink navigation signal to transmit the space-based time reference to the low orbit satellite. (4) The satellite-borne receiver of the low-orbit satellite completes the tracking measurement of the downlink navigation signal of the medium-high orbit satellite, and

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uses the space-based time reference information contained in the high, medium, low orbit satellite orbit and the medium-high orbit navigation message as known, and calculates the low The clock offset of the orbiting satellite receiver is used to transfer the space-based time reference to the low-orbit constellation. 2.2 On-Board Atomic Clock Configuration Among the current four major satellite navigation systems, the United States’ GPS navigation satellites use a combination of cesium atomic clocks and rubidium atomic clocks, the European Union’s Galileo satellites use a combination of rubidium atomic clocks and passive hydrogen atomic clocks, and Russia’s GLONASS-K third-generation navigation satellite A combination of rubidium atomic clock and passive hydrogen atomic clock will also be used. The Beidou-3 satellite navigation satellite uses a combination of rubidium atomic clock and passive hydrogen atomic clock [11]. In the Beidou-3 satellite-borne time-frequency system, based on the reliability, stability and drift rate of the system, the atomic clock group adopts the configuration scheme of “2 hydrogen clock + 2 rubidium clock” and “4 rubidium clock” [11]. The short-term, medium- and long-term stability and drift rate indicators achieved by the spaceborne high-precision rubidium atomic clock and hydrogen clock are shown in the following table (Table 1): Table 1. Achievement status of Beidou-3 satellite-borne atomic clock indicators. Project

High precision rubidium clock

High-precision hydrogen clock

Index requirements

Measured value

Index requirements

Measured value

Short-term stability

≤3 × 10–12 /1s

1.2 × 10–12 /1s

≤1 × 10–12 /1s

6.2 × 10–13 /1s

Long-term stability

≤2 × 10–14 /d

1.0 × 10–14 /d

≤7 × 10–15 /d

5.0 × 10–15 /d

Drift rate

≤1 × 10–13 /d

7.5 × 10–14 /d

≤1 × 10–14 /d

2.9 × 10–15 /d

The mid-to-long-term stability and drift rate of satellite clocks depend on the reference on-board atomic clock. The mid-to-long-term stability and drift rate of hydrogen clocks are better than those of rubidium clocks; the Beidou-3 time-frequency system introduces hydrogen clocks and uses hydrogen clocks as the main, Realizing the satellite clock’s long-term stability is better than 7E−15/d, and the drift rate is better than 1E−14/d. According to the current development of space-borne atomic clock technology at home and abroad, future navigation satellites can be equipped with laser-cooled atomic clocks [2–13], mercury ion microwave clocks [14] and other new types of spaceborne atomic clocks, whose stability is better than 1E−15/d, The drift rate is better than 1E−16/d, which is 1–2 orders of magnitude higher than the current stability level of space-borne atomic clocks. We recommend that this new type of high-performance atomic clock be configured on the high- and middle-orbit navigation satellites as the

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main working atomic clock, and the constellation integrated atomic clock is established through inter-satellite link measurement and data transmission. At the same time, traditional hydrogen clocks and rubidium clocks are configured as backup atomic clocks to ensure satellite clocks. Group operation reliability. In order to ensure the continuity of the satellite navigation signal and prevent the navigation service interruption caused by the abnormal operation of the on-board master clock, the navigation satellite has designed the on-board time-frequency processing system, adopting the technology of smooth switching between the main and standby atomic clocks or the minimum clock group (not less than 3 clocks).) Control technology, realize that when the master clock is abnormal, seamlessly switch to the backup clock to keep the satellite time frequency signal continuously and stably output. 2.3 Space-Borne Time-Frequency Transfer Link High-precision satellite-borne atomic clock signals need to go through a series of complex satellite-borne time-frequency transmission links such as multi-stage phase-locked loops, carrier up-conversion, signal spreading, etc., and are finally sent to the ground by high-power antennas and transmitted to ground users. Or send to other satellites through inter-satellite links to realize inter-satellite time-frequency signal measurement and transmission. Therefore, the performance level of the on-board time-frequency transmission link directly determines the performance and feasibility of the establishment and maintenance of the integrated atomic time of the satellite navigation constellation. The navigation satellite load usually includes the space-borne time-frequency load, the navigation signal generation load and the navigation signal amplification load, which are finally sent out by the RNSS antenna or transmitted to other satellites by the phased array antenna. The noise of the signal transmission link, especially random measurement noise and system periodic noise, is the main reason that affects the time-frequency transmission, and ultimately limits the accuracy of the constellation synthesis when the atom is established. The time-delay stability of time-frequency loads is mainly limited by temperature changes, while the temperature changes during satellite flight cycles. In order to reduce the influence of temperature fluctuations on the stability of the time-frequency load, on the one hand, the space-borne atomic clock with a smaller temperature coefficient is selected for the time-frequency load, and the temperature coefficient of the navigation time-frequency load can be controlled to be better than 1E−12/°C. When the temperature fluctuation is controlled to 10 °C, the time delay stability fluctuation caused by the satellite periodic temperature fluctuation on the time-frequency signal will be reduced to 0.01 ns. The navigation signal generation load mainly includes a baseband signal generation module, a digital-to-analog conversion module, an up-conversion module, etc. The main components are broadband devices, which are not sensitive to temperature. By further increasing the signal generation load digitization rate, the realized temperature coefficient is reduced to within 1E−12/°C, and by controlling the temperature fluctuation to 10 °C the time delay stability fluctuation caused by the navigation signal generation load is reduced to within 0.01 ns.

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The navigation signal amplification load includes a high-power amplification module and a band-pass filtering module. The temperature coefficient of this part is relatively large. Through technical optimization, the temperature coefficient will be reduced to within 3E−12/°C, and the signal will be amplified and filtered when the satellite temperature fluctuates at 10 °C. The time delay stability fluctuation caused by the load is less than 0.03 ns. The temperature coefficients of RNSS antennas, inter-satellite link antennas and cables are very small, and their contribution to the delay stability can be ignored (Table 2). Table 2. On-board time-frequency link delay stability. Temperature stability

Stability of time-delay

Time-frequency system

10 °C

0.01 ns

Signal generator

10 °C

0.01 ns

Launch subsystem

10 °C

0.03 ns

Total link delays

10 °C

0.033 ns

In summary, through new technologies such as load digitization, it is possible to effectively reduce the impact of hardware temperature fluctuations on the delay stability of the space-borne time-frequency transmission link, and realize that the 10 °C satellite temperature fluctuation contributes 0.033 ns to the time-frequency stability of the noise. The additional phase noise of the space-borne time-frequency link contributes better than 5E−16/d to the integrated atomic time-space stability.

3 Key Technologies for Establishing and Maintaining Space-Based Time Benchmarks 3.1 Space-Based Atomic Time Algorithm Adapted to Different Types of Space-Borne Atomic Clocks Different types of space-borne atomic clocks have different performance characteristics. The real-time construction technology of constellation integrated atomic time is studied, the inter-satellite link two-way measurement and comparison method is used to achieve inter-satellite time-frequency comparison of medium and high orbit satellites, combined with the space-based integrated atomic time realization algorithm, Giving full play to the advantages of different types of space-borne atomic clocks is a strong guarantee for the realization of space-based time standards. (1) Time-frequency comparison of medium and high orbit satellite constellations Use the high-performance atomic clock and high-precision inter-satellite link measurement carried by the medium and high orbit satellite constellation to independently establish a space-based time reference. Select some medium and high orbit satellites as computing node satellites in the constellation to collect all inter-satellite link measurement

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data in the constellation to achieve high-precision time synchronization of the entire constellation. The basic observation equation of the two-way one-way inter-satellite link between Star A and Star B is as follows [15]:  ⎧    AB ⎨ ρAB (t0 ) = R  A (t0 ) − R  B (t0 − t2 ) + c ∗ clkA (t0 ) − clkB (t0 ) + τ Send + τ Rcv + ρcor B A     BA ⎩ ρBA (t0 ) = R  B (t0 ) − R  A (t0 − t1 ) + c ∗ clkB (t0 ) − clkA (t0 ) + τ Send + τ Rcv + ρcor B A

(1)

Here, ρAB (t0 ) and ρBA (t0 ) indicates that the two satellites A and B received pseudor



ange observations from each other, R A and R B represents the three-dimensional position vector of star A and star B, clkA and clkB respectively represents the clock difference between star A and star B, c is the speed of light, t is the traveling time of light, τASend and τBSend is the launch time delay of A and B stars, τARcv and τBRcv is the reception AB and ρ BA respectively indicate the error correction time delay of A and B stars, ρcor cor items that can be accurately modeled by one-way observation of two satellites, including antenna phase center correction and relativistic periodic effect correction. The difference between the two two-way pseudoranges is directly, and the clock difference between the two satellites can be obtained, that is, the relative clock difference: CLKBA (t0 ) = clkB (t0 ) − clkA (t0 ) =

AB − ρ BA ) τ Send − τARcv τ Send − τBRcv ρAB (t0 ) − ρBA (t0 ) − (ρcor cor − A + B 2∗c 2 2

(2)

In the above formula, the equipment delay parameters and error correction terms can be accurately modeled and known. (2) Space-based time benchmark construction The real-time filtering algorithm is used to construct the constellation integrated atomic time that is the space-based time reference. However, the space-based time reference is generally not directly available, but is reflected by the time difference between it and the reference satellite. Select satellite A as the reference satellite, and its clock difference with reference to the space-based time datum is: N 

TA1(t0 ) − clkA (t0 ) =

i=1

0 (t ) ωi · CLKiA 0

N

(3)

In the above formula, N is the number of satellites equipped with high-performance atomic clocks, and i refers to the satellites equipped with high-performance atomic clocks. 3.2 High-Precision Satellite-Ground Time-Frequency Comparison Measurement Technology The satellite-to-ground time synchronization of the satellite navigation payload is realized by the pseudo-range measurement of the satellite-to-earth two-way link signal. The

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principle of satellite-to-ground two-way time synchronization is shown in Fig. 1. The accuracy of the pseudo-range measurement is directly related to the accuracy of the satellite-to-ground time synchronization. When the satellite is within the visible range of the ground operation control station of the ground test support system, the ground receives the satellite L-band downlink ranging signal and measures the corresponding pseudorange to obtain the delay value observation; at the same time, the satellite receiving ground station L-band uplink injection Signal, and measure the corresponding pseudorange value, obtain the time delay observation value on the satellite, and then transmit all the measured data back to the operation control station, and the operation control station calculates the clock difference between the satellite and the ground. The upwardly injected navigation message contains the clock error information obtained from the previous ground, and at the same time, the ground uses the obtained clock error value to inject a phase modulation and frequency modulation command to adjust the time frequency of the on-board time-frequency load (Fig. 2).

Fig. 2. Schematic diagram of the principle of two-way time synchronization between satellite and ground

Suppose the ground uplink pseudorange value measured by the satellite at time t is ρSG , the satellite downlink pseudorange value measured by the ground station is ρGS , the observation equation is as follows: ρSG = RSG + c ∗ (clkG − clkS ) + c ∗ τSG

(4)

ρGS = RGS + c ∗ (clkS − clkG ) + c ∗ τGS

(5)

Here, RSG (RGS ) represents the geometric distance from the satellite to the ground station at time t, (clkG − clkS ) indicates the clock difference between star and ground, τSG (τGS ) indicates the system delay deviation such as receiving test and transmitting time delay. The star-ground clock difference is obtained through the difference between the two formulas (1) and (2): CLKSG = clkS − clkG

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1 1 (ρGS − ρSG ) + (τSG − τGS ) 2c 2

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(6)

3.3 Space-Based Time Base Distribution Technology The space-based time reference is constructed by some node satellites in the constellation using the high-performance atomic clock onboard. In addition, the space-based time reference needs to be traced to the ground UTC regularly to ensure that the space-based time reference and the ground UTC remain within the agreed range of indicators and control the traceability accuracy. Therefore, it is necessary to build space-based time reference distribution and synchronization technology to realize real-time non-destructive distribution of space-based time reference to other satellites, low-orbit constellations and ground stations in the constellation, to meet the needs of navigation and positioning timing and precise single-point positioning services. The space-based time reference distribution technology includes the following parts: (1) Distribution to other satellites in the medium and high orbit constellations The space-based time reference is distributed to other satellites in the mid-to-high orbit constellation using high-precision inter-satellite link measurement. The clock difference TA1(t0 ) − clkA (t0 ) of the reference satellite A relative to the space-based time reference obtained in the previous step is compared with the clock difference CLKBA (t0 ) of the A satellite and the B star realized by the high-precision inter-satellite link measurement, obtaining the clock difference of the satellite B compared to the space-based time reference. The clock difference to realize the transfer of space-based time reference to satellite B: TA1(t0 ) − clkB (t0 ) = TA1(t0 ) − clkA (t0 ) − CLKBA (t0 )

(7)

(2) Distribution to LEO constellations and users Distribute the space-based time reference to the low-orbit constellation and users through the downlink navigation signal of the medium-high orbit satellite. The observation equation for the pseudorange phase measurement of the medium and high orbit satellites by the satellite receiver and user receiver of the low orbit satellite is as follows:     sat   − Rrcv  + c ∗ (trcvclk − tsatclk ) + Dphs + Drel + Dtrop P = R + DIon + Decc + Dgtide + Dplm + εc     sat   λϕ = R − Rrcv  + c ∗ (trcvclk − tsatclk ) + Dphs + Drel + Dtrop − DIon + Decc + Dgtide + Dplm + windup + λN + εP

(8)

 rcv are the  sat and R Here, λ is the wavelength corresponding to the phase data, R satellite and receiver position vectors respectively, trcvclk and tsatclk are the receiver clock error and satellite clock error respectively, Dphs is the deviation of the satellite

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antenna phase center, Drel is the delay caused by the relativistic effect, Dtrop is the tropospheric delay, DIon is the ionospheric delay, Decc is eccentric correction of the station, Dgtide is the tide correction at the station, Dplm is the ranging deviation caused by the displacement of the station, N is the phase data ambiguity, εc and εP are pseudorange and phase multipath and noise respectively. In the above formula, the medium and high orbit satellite clock error parameter tsatclk is selected as the satellite clock error obtained in step (3) with reference to the space-based time reference. By introducing the high-precision orbit parameters of medium and high orbit satellites, and calculating the clock difference through low-orbit satellites or ground user receivers through navigation and positioning timing or precise single-point positioning, the space-based time reference can be transmitted to users and low-orbit satellites. 3.4 Constellation Dynamic Clock Group Management Technology The establishment of the space-based time reference requires the use of multiple highperformance atomic clocks distributed in the constellation node stars to achieve star clock comparison through high-precision inter-satellite links, obtain the weight of the timekeeping atomic clock, and establish a comprehensive atomic time through a weighting algorithm. The goal of the integrated atomic time of the navigation constellation is to achieve long-term stability improvement. At the same time, in order to avoid the weight of a single satellite clock being too large, and the performance of the integrated atomic time will be seriously affected in the event of a failure, the weight of the star clock needs to be limited. The selection of the star clock weight is usually based on the star clock stability (Allan standard deviation), expressed as 1 σi (τ ) (9) ωi =  n i=1 1 σi (τ )

ωi ωmin ≤ ωi ≤ ωmax ωi = (10) ωmax ωi ≥ ωmax Here, ωmax = A N , N is the number of on-board clocks, A is the experience value; ωmin is the minimum value. The space-based integrated atomic time is realized by the weighting of multiple star clocks by formula (3). The working characteristics of different types of star clocks are slightly different. Usually, from the initial work to the mid-life, the performance of the star clock improves with the aging time, and the middle becomes stable. Operation period: In the later period of work, due to factors such as space single particles and star clock aging, the performance of the star clock will decrease with the running time and the failure rate will increase. The weight of the integrated atomic time will be dynamically adjusted according to the changes in the performance of the star clock. The high-stability star clock has a relatively large weight; at the same time, in order to avoid the failure of the high-weight star clock, resulting in excessive performance degradation of the integrated atomic time, the formula (9) Perform weight restriction.

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The constellation network star clock judges the function and performance status of the star clock according to the satellite’s autonomous fault diagnosis strategy through the intra-satellite time-frequency processing load and the inter-satellite link measurement comparison results. When the star clock is abnormal, the time and frequency of a single satellite is stable. The switch function automatically switches to the hot backup clock; on the other hand, through the weight restriction strategy, the failed star clock will be quickly removed from the integrated atomic time statistics process, without affecting the integrated atomic time performance; finally, after the hot backup clock is switched, pass Compare with the integrated atomic time, statistically evaluate the stability and accuracy of the hot standby clock, and re-weight the integrated atomic time to maintain the network based on the stability.

4 Space-Based Time Benchmark Establishment and Maintenance Simulation and Experimental Verification Use the precise clock offset of the Beidou-3 network satellite provided by the MGEX analysis center as input to establish and maintain the simulation of the integrated atomic time of the satellite navigation constellation, and conduct experimental verification. The Beidou-3 networking satellites are used to construct two independent integrated atomic time references. The frequency stability of the two is shown in the following figure (Fig. 3):

Fig. 3. Space-based time reference frequency stability.

Among them, the fluctuations in the stability curve are caused by the noise associated with the satellite orbital period [16]. When selecting some satellites with a hydrogen clock as the main clock to establish an integrated atomic clock, the statistics of the clock error prediction performance achieved by the integrated atomic time established by different satellite numbers are shown in the following table (Table 3):

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J. Lu et al. Table 3. Space-based time reference frequency stability and forecast error.

Number of satellites

2-h forecast error RMS/95% (m)

24-h forecast errorRMS/95% (m)

frequency stability@100s

frequency stability@1000s

frequency stability@10000s

Frequency stability@1d

3

0.06/0.11

0.13/0.26

3.07E−13

5.15E−14

2.54E−14

5.06E−15

4

0.043/0.09

0.11/0.23

2.61E−13

4.47E−13

2.19E−14

4.38E−15

5

0.039/0.08

0.10/0.22

2.40E−13

4.01E−14

1.96E−14

3.80E−15

6

0.034/0.08

0.09/0.20

2.08E−13

3.62E−14

1.66E−14

3.28E−15

It can be seen from the table that as the number of atomic clocks (satellites) that compose the integrated atomic time increases, the stability indicators of the integrated atomic time have been improved, and the accuracy of the clock error prediction has increased accordingly. Among them, when 6 satellites are used to construct the integrated atom of the navigation constellation, the 2-h forecast error RMS of the integrated atom of the navigation constellation is 4 cm, the 24-h forecast error is 9 cm, and the stability of 100 s, 1000 s, 10000 s, and 86400 s are 2.08E−13, 3.62E−14, 1.66E−14, 3.28E−15. Taking the space-based time as a reference, the prediction performance of Beidou-3 atomic clock offset is shown in the following table (Table 4): Table 4. Space-based time reference frequency stability and forecast error. PRN

Clock

Long-term fitting residual

24-h forecast error

2-h forecast error

39

Hydrogen maser

0.28

0.14

0.05

40

Hydrogen maser

0.21

0.13

0.05

26

Hydrogen maser

0.18

0.13

0.07

27

Hydrogen maser

0.30

0.14

0.05

28

Hydrogen maser

0.19

0.14

0.08

35

Hydrogen maser

0.10

0.13

0.05

43

Hydrogen maser

0.39

0.21

0.05

45

Hydrogen maser

0.13

0.12

0.05

19

Rubidium clock

0.68

0.47

0.13

20

Rubidium clock

1.31

0.55

0.13

21

Rubidium clock

1.50

0.75

0.13

22

Rubidium clock

1.61

0.65

0.12

23

Rubidium clock

0.31

0.35

0.23

24

Rubidium clock

3.14

0.46

0.10

32

Rubidium clock

3.03

0.44

0.10

33

Rubidium clock

0.95

0.69

0.09

34

Rubidium clock

1.01

0.55

0.10

36

Rubidium clock

0.81

0.26

0.10

41

Rubidium clock

0.50

0.42

0.09

42

Rubidium clock

3.01

0.44

0.09

44

Rubidium clock

0.88

0.86

0.13

39

Hydrogen maser

0.28

0.14

0.05

0.95

0.37

0.09

Mean

Research on the Method of Autonomous Establishing

15

5 Summary This paper systematically discusses the composition framework of the integrated atomic time of the satellite navigation system constellation, and focuses on the key technologies for the establishment and maintenance of the integrated atomic time of the satellite navigation system constellation, including space-based atomic time algorithms suitable for different types of space-borne atomic clocks, high-precision inter-satellite/satellite-toearth time-frequency comparison measurement technology, satellite navigation constellation integrated atomic time distribution technology, and dynamic clock group management technology. Relying on Beidou-3 satellite on-board atomic clock configuration and the precision clock offset data of the Beidou-3 network satellite provided by the MGEX analysis center, the simulated results show that based on the 6-satellite configuration in orbit The integrated atomic time-to-day stability established by the MEO satellite onboard the hydrogen clock has been increased from 5E−15/d for a single satellite to 3.28E−15/d, and the prediction accuracy of the 24-h clock difference has been increased from 14 cm for a single satellite (hydrogen clock) to 9 cm. The feasibility and effectiveness of the method of autonomous establishment and maintenance of the integrated atomic time of the satellite navigation constellation is preliminarily proved.

References 1. Tavella, P., Petit, G.: Precise time scales and navigation systems: mutual benefits of timekeeping and positioning. Satell. Navig. 1(1), 1–12 (2020). https://doi.org/10.1186/s43020020-00012-0 2. Cheng, P., Cheng, Y., Wang, X., Xu, Y.: Update China geodetic coordinate frame considering plate motion. Satell. Navig. 2(1), 1–12 (2021). https://doi.org/10.1186/s43020-020-00032-w 3. Yang, Y., Xu, Y., Li, J., Yang, C.: Progress and performance evaluation of BeiDou global navigation satellite system: data analysis based on BDS-3 demonstration system. Sci. China Earth Sci. 61, 614–624 (2018) 4. Lu, J., Yang, Q.: Study on GNSS Interoperability. Scientia Sinica (Physica, Mechanica & Astronomica) 5, 534–540 (2010) 5. Gunther, C.: Kepler-A Satellite Navigation System without Clocks and little Ground Infrastructure (2018) 6. Wu, Y.: Key technologies of GNSS time scale. Acta Geodaetica Et Cartographica Sinica 46, 533 (2017) 7. Wu, Y.: Key technologies of GNSS time scale. Acta Geodaetica Et Cartographica Sinica 46, 533 (2017). (in Chinese) 8. Yang, Y.: Progress, contribution and challenges of Compass/Beidou satellite navigation system. Acta Geodaetica Et Cartographica Sinica 39, 1–6 (2010). (in Chinese) 9. Yang, Y., Ren, X.: Maintenance of space datum for autonomous satellite navigation. Geomatics Inf. Sci. Wuhan Univ. 43, 1780–1787 (2018). (in Chinese) 10. Yi, H., Zhong, C.: Research on time keeping algorithm of the autonomous navigating of navigation constellation. J. Astronaut. Metrol. Measur. 32(5), 22–26 (2012). (in Chinese) 11. Guo, S., Cai, H., Meng, Y., et al.: BDS-3 RNSS technical characteristics and service performance. Acta Geodaetica Et Cartographica Sinica 48(7), 810–821 (2019). (in Chinese) 12. Wang, Y., et al.: Reaching a few 10–15 long-term stability of integrating sphere cold atom clock. J. Chin. Opt. Lett. 16(7), 070201 (2018)

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13. Tremine, S., Esnault, F.X., Guerandel, S., Holleville, D., Delporte, J., Dimarcq, N.: Estimation of the compact cold atom clock HORACE frequency stability. In: Proceedings of the 20th EFTF (2006) 14. Ely, T., Burt, E., Prestage, J., Seubert, J., Tjoelker, R.: Using the deep space atomic clock for navigation and science. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65(6), 950–961 (2018). https://doi.org/10.1109/TUFFC.2018.2808269 15. Yang, Y., et al.: BeiDou-3 broadcast clock estimation by integration of observations of regional tracking stations and inter-satellite links. GPS Solutions 25(2), 1–12 (2021). https://doi.org/ 10.1007/s10291-020-01067-x 16. Wang, B., Lou, Y., Liu, J., Zhao, Q., Su, X.: Analysis of BDS satellite clocks in orbit. GPS Solutions 20(4), 783–794 (2015). https://doi.org/10.1007/s10291-015-0488-7

A New Method to Suppress the AC-Stark Shift of Compact Cesium Beam Atomic Clocks Shaohang Xu, Sifei Chen, Chang Liu, Yining Li, Jiale Wang, and Yanhui Wang(B) State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, Peking University, Beijing 100871, China [email protected]

Abstract. Cesium beam atomic clocks are widely used as frequency standards in time-keeping, communication, navigation and positioning as primary frequency standards. Compared to cesium beam clocks with magnetic state selection, optical pumping clocks have several advantages like high utilization rate of cesium atoms, no Majorana transition, etc. However, they have an obvious drawback, the AC Stark effect, or the so-called light shift. In order to solve this problem, this paper presents a new method to suppress the light shift in cesium beam clocks. The clock used in experiment uses the optically detected magnetic-state-selection scheme. We demonstrate theoretically that the α and β coefficients can be strongly suppressed by introducing the detuned light into the detection light. In addition, we experiment this scheme and the α-coefficient is successfully reduced from 1.23E−12/mW to 8E−14/mW. We also test the long term frequency stability with additional laser intensity noise. It’s shown that the Allan deviation at 20000s is reduced from 2.0E−13 to 5.9E−14, which reveals the suppression of the light shift with our method. Although the scheme proposed in this paper is based on optically detected magnetic-state-selection scheme, this method can be easily applied to compact optical pumping Cs clocks. These results are relevant for improving the long-term frequency stability of compact cesium beam atomic clocks. Keywords: Cesium beam clock · Light shift · Double-pass

1 Introduction Magnetic-state-selection cesium atomic clocks are widely used in time-keeping, communication, navigation and positioning, for their outstanding accuracy and long-term stability. Compared to cesium beam clocks with magnetic state selection, optical pumping clocks have several advantages like high utilization rate of cesium atoms, no Majorana transition, etc. However, they have an obvious drawback, the AC Stark effect, or the so-called light shift (LS). The existence of the LS is a significant factor limiting the frequency stability of optical pumping cesium atomic clocks. Theoretically, the LS of compact Cs clocks cannot be eliminated completely. But the influence of the LS can be reduced by several schemes, such as choosing appropriate pumping laser intensity [1], stabilizing the power of the pumping and detection light © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 17–25, 2021. https://doi.org/10.1007/978-981-16-3146-7_2

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[2], etc. Here, we present a new method to suppress the LS in cesium beam clocks. This method compensates the LS by introducing a detuned laser into the detection light. The clock used in experiment uses the optically detected magnetic-state-selection scheme [3]. The feasibility of LS suppression is theoretically and experimentally demonstrated with properly chosen detuned light spectra.

2 Description of the Method Generally, the effect of the LS in the Cs clock is reflected by two coefficients, the sensitivity of the LS νhf to laser power (PL ) fluctuation α and to laser frequency (νL ) fluctuation β. α = ∂υhf /∂PL ,

β = ∂υhf /∂υL .

(1)

The physics package of the optically detected magnetic-state-selection cesium-beam atomic clock is shown in Fig. 1.

Fig. 1. Physics package of the optically detected magnetic-state-selection cesium-beam atomic clock

The LS induced by the detection light is caused by two parts, the stray light and the fluorescence light. In order to simplify the theoretical calculations, three simplified conditions are considered in the subsequent calculations: i)

In our Cs clock, the stray light is much larger than the fluorescence light (inferred from Fig. 5), so the subsequent calculations only consider the contribution of stray light. ii) The hole of the atom exiting the microwave cavity is small enough, so the stray light is incident in the opposite direction along the direction of the Cs beam. iii) The average of the LS at different positions in the microwave cavity can be equivalent to the average of the stray light. In the subsequent calculations, all stray light refers to the average stray light. For a non-degenerate ground state |g, when a moving atom interacts with a monochromatic co-propagating light of frequency ω, the LS of the |g state can be

A New Method to Suppress the AC-Stark Shift

19

written as [4]: Eg = 

  q 2 Veg  q,e

(ω − ω˜ eg − kυ) , (ω − ω˜ eg − kυ)2 + γe2

(2)

where the summation is for all laser polarizations (q = 0, ±1)  qand  all possible  dipole q transitions from the ground state |g to the excited state |e; Veg  = deg Eq / is the absolute value of the electric dipole interaction matrix element for a given polarization q q; deg and Eq are the spherical components of the dipole matrix element and the electric ∼

field amplitude, respectively; ωeg and γe correspond to the frequency and the halfwidth of the transition |e − |g; k = ω/c is the wavevector of the laser, and v is the velocity of the atom. Rewrite Eqs. (2) as following νF=g (υ) =

  q 2 ν − ν˜ eg + υ/λ Is deg  , 2π 2 cε0 2 q,e (ν − ν˜ eg + υ/λ)2 + (γe /2π )2

(3)

∼

where νF=g (υ) = Eg /h; Is is the stray light intensity; ν and ν eg are the frequencies of the laser and the transition |e − |g, respectively; λ is the wavelength of the laser. The LS in the Cs clock is the difference between the LSs of the ground state F = 4 and F=3 tot (υ) = νF=4 (υ) − νF=3 (υ). νLS

(4)

Neglecting other frequency shifts, the Ramsey resonance curve is expressed as     ∞ ρ(υ) 2 bl L tot sin 1 + cos 2π {νd − ν0 − νLs (5) y(νd ) = (υ)} d υ, 2 υ υ 0 where ρ(v) is the atomic velocity distribution after the magnetic state selection; ν0 is the unperturbed frequency of the clock transition; νd is the frequency of the microwave field; b is the Rabi frequency; L is the microwave-free distance and l is the effective length of each interaction region. Then we add a square wave modulation to the microwave, the error signal after demodulation is the difference between the two microwave modulated Ramsey signals yerr = y(νd + νm ) − y(νd − νm ).

(6)

When the servo loop is closed, the error signal is equal to 0. Solving Eqs. (6) we have [5]

 ∞

L 2 bl sin 2π ν L d υ tot mυ 0 νLs (υ) υ ρ(υ) sin υ νd

 (7) = ∞

L ν0 sin 2π ν d υ ν0 0 υL ρ(υ) sin2 bl m υ υ where νd = νd − ν0 is the equivalent light shift (ELS) of the cesium atomic clock measured in the laboratory. In our clock, L = 16 cm, l = 0.8 cm, νm = 180 Hz, the stray light is σ polarized. The stray light intensity is difficult to measure experimentally in our

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clock, so an empirical value Is = 2 × 10−6 mW/cm2 is used in the following theoretical calculations. In the experiment, we only focus on the relative change of the ELS, so it will not affect the result. The velocity distribution is calculated from the Fourier transforms of Ramsey lineshapes obtained from the experiment as sketched in Fig. 2 [6]. The blue line in Fig. 3 shows the fractional ELS νd /ν0 calculated from Eqs. (7). In normal operation, the ELS has a positive value and increases as the intensity of stray light increases. However, it’s possible to obtain negative ELS at certain laser detuning. Therefore, we consider introducing the detuned light into the detection laser to produce a negative ELS to compensate the ELS in the Cs clock. Beyond the usual detection laser, we introduce the detuned laser with the detuning νm (negative) and intensity rm I0 , where I0 is the detection laser intensity. Theoretically, α and β coefficients can be significantly reduced with the appropriate rm and νm . For example, the red line in Fig. 3 characterizes the fractional ELS νd /ν0 for optical detecting by a multi-frequency laser field with the detection component tuned around the 4–5 cycling transition of cesium D2 line. The effect of this scheme mainly depends on the control precision of the frequencies and intensities of the two beams in the experiment. In practical operation, it is easy to reduce the ELS by about one order of magnitude or more.

Fig. 2. The velocity distributions of the cesium beam. Blue solid line: the velocity distribution after the magnetic state selection; red dashed line: the velocity distribution before the magnetic state selection

A New Method to Suppress the AC-Stark Shift

21

Fig. 3. The fractional equivalent light shift νd /ν0 for optical detecting by a laser field with the detection component tuned around the 4–5 cycling transition of cesium D2 line. Blue: singlefrequency stray light; red: multi-frequency stray light, rm = 0.56, νm = 454 MHz

3 Results of the Experiment 3.1 ELS Suppression with Detuned Light A convenient way to introduce the detuned light into the detection laser is to use doublepass method with an acousto-optic modulator (AOM), as shown in Fig. 4. This setup contains three parts: part A is the saturated absorption spectroscopy for the laser frequency locking; part B is the double-pass configuration, the two lasers are combined in a single-mode fiber to enforce the same spatial mode; part C is used to introduce an intensity noise to the laser before entering the beam tube, which is described in detail in the next section. Here, the output beam contains a detection light with frequency ν0 and a detuned light with frequency shifted by νm (negative detuning), where νm = 2νRF is the laser detuning, νRF are the frequency of the RF source. rm = Idetun /Idetect is defined as the ratio of the detuned light intensity to the detection light. After emitting from Fig. 4, the multi-frequency laser enters the cesium beam tube in Fig. 1 for atomic detection. The frequency of the AOM’s driving signal ranges from 200 MHz–300 MHz, corresponding to a tunable range of 400 MHz–600 MHz for the laser detuning νm . In order to demonstrate the suppression effect of detuned light on the ELS, we remain rm = 1 unchanged and measure the fractional α-coefficient of the ELS at different laser detuning νm , as shown in Fig. 5. In the theoretical calculation of α-coefficient, the ratio of stray light to incident light is set to ensure that the theoretical and experimental results are equal when the detuning is 0. The experimental results are in good agreement with the theory in Fig. 5. Moreover, we manage to reduce the α-coefficient at rm = 1, νm = 560 MHz to 6.5% of that in the case of single-frequency light, as shown in Fig. 6 and Table 1. The suppression effect of our experiment on the ELS is mainly affected by the control precision of the light power of the two beams. Therefore, the experimental results can be further improved by introducing a control loop for the power of both lasers.

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Fig. 4. Optical schematic of the experimental set-up. L1, L2, L3: lens with foci of 150, 20 and 100 mm, respectively; M: mirror; BS: beam splitter; PBS: polarizing beam splitter; HWP: half wave plate; QWP: quarter wave plate; PD: photodiode; FC: fiber collimator; ISO: optical isolator; SMF: single-mode fiber; AOM: acousto-optic modulator; LCVR: liquid crystal variable retarder

Fig. 5. The fractional α-coefficient as a function of the laser detuning νm . Black cross: Experimental results of multi-frequency laser; red solid line: theoretical calculation results

A New Method to Suppress the AC-Stark Shift

23

Fig. 6. The fractional frequency shift for different detection light power under a) single-frequency (black); b) multi-frequency, rm = 1, νm = 560 MHz (red) Table 1. Linear fitting parameters in Fig. 6 Intercepts (10−11 ) Slope (/mW) Single-frequency −1.797 ± 0.004 Multi-frequency

−1.75 ± 0.01

(1.23 ± 0.03) × 10−12 (−8 ± 8) × 10−14

3.2 Frequency Stability Results This section we demonstrate the impact of our scheme on stability. Because the effect of the ELS on the stability of our clock will not appear within a month of measurement time, we introduce a noise to demonstrate the influence of the ELS caused by the laser power fluctuation on the stability. In part C of Fig. 4, we introduce a random walk noise to the liquid crystal variable retarder (LCVR), and the output laser power has a random walk noise fluctuating within ±50% of the total power. For the single-frequency incident laser with the initial power of 1mW and multi-frequency incident light with the initial power of 1mW + 1mW and detuning of 560 MHz, we introduce the same random walk noise and measure the Allan deviation, as sketched in Fig. 7 and Table 2. Because of the larger clock signal background due to the detuned laser, the shortterm stability of the multi-frequency case is slightly higher than that of the singlefrequency case. However, the former achieves a much better long-term stability through the suppression of ELS, as expected.

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Fig. 7. Fractional frequency stability for different detuning conditions with the same random walk noise. Black: Single-frequency incident laser with the initial power of 1mW; red: multi-frequency incident laser with the initial power of 1 mW + 1 mW, νm = 560 MHz Table 2. Fractional frequency stability results in Fig. 7 Allan deviation

100s

20000s

Single-frequency 8.5 × 10−13 2.0 × 10−13 Multi-frequency

1.2 × 10−12 5.9 × 10−14

4 Conclusion By introducing the detuned light, we strongly suppressed the ELS of the compact optically detected magnetic-state-selection cesium-beam atomic clock in theory and experiment. The α-coefficient is experimentally reduced from 1.23 × 10−12 /mW to 8 × 10−14 /mW. With additional laser intensity noise, the Allan deviation at 20000s is reduced from 2.0 × 10−13 to 5.9 × 10−14 . This method can be easily applied to optical pumping Cs clocks. And by introducing detuned light into the pumping light rather than in the detection light, the influence of the detuned light on the clock signal background can be dramatically reduced. We can expect a better stability in the optical pumping Cs clocks with this method. These results are relevant for improving the long-term frequency stability of compact cesium beam atomic clocks.

References 1. Shi, H., Ma, J., Li, X., Liu, J., Zhang, S.: Realization of single optical frequency laser system for optically pumped cesium beam frequency standards. Opt. Quant. Electron. 49(12), 1–11 (2017). https://doi.org/10.1007/s11082-017-1232-z 2. Chen, Z., Liu, C., Wang, S., Wang, Y.: A method on laser power stabilization in optical detection cesium atomic clock. In: Sun, J., Yang, C., Guo, S. (eds.) China Satellite Navigation Conference (CSNC) 2018 Proceedings, vol. 497, pp. 607–614. Springer, Singapore (2018). https://doi.org/ 10.1007/978-981-13-0005-9_49

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3. Liu, C., Shi, R.Y., Wang, Y.H., Liu, S.Q., Dong, T.Q.: An optically detected cesium beam frequency standard with magnetic state selection. In: 2014 European Frequency and Time Forum, pp. 175–177. IEEE (2014) 4. Jun, J.W., Lee, H.S., Kwon, T.Y., Minogin, V.G.: Light shift in an optically pumped caesiumbeam frequency standard. Metrologia 38(3), 221–227 (2001) 5. Ohshima, S., Nakadan, Y., Ikegami, T., Koga, Y.: Light shifts in an optically pumped Cs beam frequency standard. IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991) 6. Shirley, J.H.: Velocity distributions calculated from the Fourier transforms of Ramsey lineshapes. IEEE Trans. Instrum. Meas. 46(2), 117–121 (1997)

A Compensation Method of Satellite Clock Day-Boundary Jumps Based on Epoch-Differenced Weiquan Huang, Menghao Li, Hui Li(B) , Renlong Wang, Nan Li, and Liang Li College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China [email protected]

Abstract. The satellite clock products are essential for precise point positioning (PPP). They can be obtained from International GNSS Service (IGS) analysis centers for most users. However, the final clock products provided by IGS analysis centers have day-boundary jumps between two adjacent days. The traditional compensation method based on single-epoch may introduce satellite clock errors, and then leads to a poor accuracy of PPP at the day-boundary. In this paper, a compensation method based on epoch-differenced is proposed. The method makes full use of all the satellite clock data before and after the day-boundary. After averaging clock data based on epoch-differenced, the day-boundary compensation items are estimated accurately. The final satellite clock products provided by Center of Orbit Determination in Europe are used to verify the compensation effect of the method proposed in this paper. The results show that, compared with the traditional compensation method based on single-epoch, the RMS and STD of clock model fitting residuals are improved by 1.80% and 9.83%, respectively. In addition, the RMS and STD accuracy of PPP are improved by 47.73% and 55.64% within two hours after the day-boundary, respectively. Keywords: Satellite clock · Day-boundary jumps · Compensation · Single-epoch · Epoch-differenced

1 Introduction The satellite clock products are essential for precise point positioning (PPP) [1, 15]. Many International GNSS Service (IGS) analysis centers provide satellite clock products, including Center for Orbit Determination in Europe (CODE), Natural Resources Canada (EMR), European Space Agency (ESA), Geo-ForschungsZentrum (GFZ), Groupe de Recherche en Geodesie Spatiale (GRG), Jet Propulsion Labs (JPL), Massachusetts Institute of Technology (MIT), National Geodetic Survey (NGS) and Scripps Institute of Oceanography (SIO) [2]. Users who need to process cross-day data, such as satellite clock products preprocessing, geological exploration, and island surveying, have put forward higher requirements for the continuity of satellite clock products [3, 4]. The satellite clock products provided © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 26–36, 2021. https://doi.org/10.1007/978-981-16-3146-7_3

A Compensation Method of Satellite Clock Day-Boundary Jumps

27

by each analysis center are estimated by the batch least square estimation [5], which leads to nanosecond clock jumps at the day-boundary. This phenomenon is called the satellite clock day-boundary jumps [6]. Combining with the composition of satellite clock errors [7], timescale difference biases (TDBs) and initial clock biases (ICBs) are the main causes of the satellite clock day-boundary jumps. TDBs with an accuracy better than 10−6 s are absorbed by the receiver clock in PPP. TDBs in satellite clock do not affect the PPP accuracy, but affect the continuity of satellite clocks at the day-boundary. ICBs are absorbed by the ambiguity in PPP, which only affect pseudorange observations instead of carrier phase observations. This causes PPP fluctuation or even reconvergence [7]. The satellite clocks estimated by continuous observation data can effectively avoid the day-boundary jumps [8]. Meanwhile, the literature [9] proposed ambiguity superposition to reduce the data independence between adjacent days. But it is limited to the arc lengths of satellite clock solution not exceeding 8 days. Therefore, it is necessary to compensate the satellite clock day-boundary jumps without changing the estimation strategy. Combining with the broadcast ephemeris, the satellite clock day-boundary jumps can be effectively compensated caused by TDBs [10]. While limited by the satellite clock accuracy of broadcast ephemeris, ICBs cannot be compensated accurately. On the basis of TDBs and ICBs, the literature [11] proposed to extrapolate the next epoch through the satellite clock of the first day. The satellite clock day-boundary jumps can be estimated and bridged. The main error items of the satellite clock day-boundary jumps are fully considered through extrapolation. However, only extrapolating a single epoch to estimate the compensation items may introduce satellite clock errors, and cause a poor compensation accuracy. The aforementioned researches mostly focus on compensating satellite clock dayboundary jumps instead of improving the compensation accuracy. Therefore, it is necessary to improve the traditional compensation method on single-epoch (SE). Analyzing and accurately compensating the satellite clock day-boundary jumps are of great significance for improving the PPP accuracy and the continuity of satellite clock products. In this paper, the final satellite clock products provided by CODE are analyzed and verified. Subsequently, a compensation method based on epoch-differenced (ED) is proposed in this paper. Compared with the traditional SE method, the ED method on improving the continuity of clock products is verified. Finally, 7 IGS stations are selected for PPP, and the ED method on improving the PPP accuracy are further verified.

2 Method 2.1 Main Error Items of Satellite Clock Day-Boundary Jumps Due to the equivalence of three satellite clock estimation methods, including undifferenced, epoch-differenced, and mixed-differenced [12], the satellite clock can be modeled as [7], C sa = Oa + Osa + C s + ε

(1)

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where subscript a is analysis center, superscript s is satellite, C sa is satellite clock, Oa is TDB, Osa is ICB, C s is the theoretical value of satellite clock, and ε is satellite clock noise. TDBs are caused by the different strategies of selecting reference satellite clocks. TDBs with an accuracy better than 10−6 s are absorbed by the receiver clock in PPP, and do not affect the PPP accuracy. ICBs related to satellites are introduced by initial satellite clock and absorbed by the ambiguity in PPP. This causes PPP fluctuation or even reconvergence. In order to analyze the error items in Eq. (1), the satellite clock data between two satellites and two adjacent epochs are processed by satellite-epoch-differenced, 1 ,s2 ) (i, j) = O(s1 ,s2 ) (i, j) + C (s1 ,s2 ) (i, j) + ε (s1 ,s2 ) (i, j) ∇C (s a a

(2)

where ∇ denotes the operator of satellite-epoch-differenced, (s1 , s2 ) denotes the satellite-differenced between satellite s1 and s2 , and (i, j) denotes the epoch-differenced between epoch i and j. The satellite-independent TDBs are eliminated by the satellitedifferenced. The ICBs are constant in the continuous clock solution arc [7], so ICBs are eliminated by the epoch-differenced. The final satellite clock products provided by CODE on DOY 214-275 in 2020, a total of 62 days, are selected to analyze the TDBs and ICBs (data from http://cddis.nasa. gov/archive/gps/products/2020). The G01 satellite is selected as the reference satellite. The raw/epoch-differenced and satellite-differenced/satellite-epoch-differenced data are shown in Fig. 1. Other satellites have the similar characteristics as the G06 satellite. The figure in Fig. 1 (a) and (b) respectively show the raw and satellite-differenced data of the G06 satellite near 00:00 on DOY 257 in 2020. It can be seen from Fig. 1 (a) that the raw G06 satellite clock data has a linear trend, and it is difficult to clearly distinguish the phenomenon of nanosecond satellite clock day-boundary jumps. It can be seen from the figure in Fig. 1 (a) that the raw G06 satellite clock data have day-boundary jumps, resulting in a poor continuity. In order to more clearly show the common phenomenon of satellite clock day-boundary jumps, the raw G06 satellite clock data are processed by epoch-differenced. On the whole, the epoch-differenced data of G06 satellite clock at the day-boundary are significantly greater than non-day-boundary. While a few epochdifferenced data are overwhelmed by the satellite clock noise. Due to the different datum selected on different days, the satellite clock data have TDBs. In order to separate the TDBs and ICBs from the satellite clock data, the G06 satellite clock data can be processed by satellite-differenced to eliminate TDBs. It can be seen from Fig. 1 (b) that, after the TDBs of G06 satellite clock data are eliminated by satellite-differenced, the phenomenon of satellite day-boundary jumps is significantly reduced from the epoch differenced data compared to Fig. 1 (a). It further shows that the ICBs are approximately equal before and after the day-boundary. In other words, ICBs are overwhelmed by the clock noise after eliminating TDBs. While the G06 satellitedifferenced data still have obvious jumps on DOY 225, 226, 257, 272, and 275 in 2020. It is possible that the ICBs are changed before and after the day-boundary of these days, or the ICBs are difficult to be submerged by the clock noise. Although TDBs do not affect the PPP accuracy, the continuity of the satellite clock data could be reduced. In order to prevent the satellite clock day-boundary jumps caused by TDBs and ICBs from affecting the continuity of satellite clock data and the PPP

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Fig. 1. (a) G06 satellite clock raw and epoch-differenced data (b) G06 satellite clock satellitedifferenced and satellite-epoch-differenced data

accuracy, it is necessary to accurately compensate the satellite clock day-boundary jumps. In addition, it is difficult to accurately estimate the TDBs and ICBs of satellite clock day-boundary jumps without introducing satellite clock products of other analysis centers. Therefore, the overall estimation of the compensation items on satellite clock day-boundary jumps can be carried out. 2.2 Estimation Method of Compensation Items on Satellite Clock Day-Boundary Jumps On the basis of TDBs and ICBs, combining with the data quality and the model strength of satellite clocks, an ED compensation method is proposed. The schematic figure based on ED method is shown in Fig. 2. According to Eq. (1), the satellite clock data on the kth day in Fig. 2 can be expressed as, Lsk (i) = Ok (i) + Osk (i) + C sk (i) + ε sk (i)

(3)

where Lsk (i) denotes the clock data at the ith epoch on the kth day of satellite s. Taking the satellite clock data at a sampling interval of 5 min as the fitting data, the magnitude of the

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Fig. 2. Schematic diagram of satellite clock day-boundary jumps compensation method based on ED

clock drift fitted by the quadratic polynomial model is 10–26 . It means that the clock drift can be ignored in the short-term prediction [13]. In other words, the difference of satellite clock data between adjacent epochs are approximately equal. The epoch-differenced is performed on the satellite clock data at non-day-boundary on the kth day to eliminate the ICBs, Lsk (i + 1) − Lsk (i) = τ · f sk + ε sk (i, i + 1)

(4)

where f is the linear trend item of satellite clock data, and τ is the sampling interval of satellite clock data. The f on the kth and (k + 1)th day are approximately equal without satellite clocks switching and clock frequency jumping. Then the epoch-differenced data at the day-boundary can be expressed as, Lsk (ie ) − Lsk+1 (if ) = τ · f sj + ε sj

(5)

where ie is the end epoch on the kth day, if is the first epoch on the (k + 1)th day, and f sj is the linear trend item of the satellite clock data at the day-boundary. In order to reduce the fitting error of the clock model and avoid the satellite clock errors of the single epoch, the satellite clock epoch-differenced mean value of all epochs on the kth and (k + 1)th days are estimated as the satellite clock epoch-differenced value at the day-boundary,   M N 1 1  1  s s s ˆ Lk (i, i + 1) + Lk+1 (i, i + 1) (6) Lk,k+1 (ie , if ) = 2 M N i=1

i=1

where M is the total epochs of the satellite clock data on the kth day, N is the total epochs of the satellite clock data on the (k + 1)th day,  denotes the operator of epochs differenced, and Lˆ k,k+1 (ie , if ) is the estimation value of clock epoch-differenced at the day-boundary. The median method is applied to detect and eliminate the gross clock data on the kth day [14]. The estimation value of clock day-boundary jumps is obtained s by the difference between Lˆ k,k+1 (ie , if ) and the satellite clock epoch-differenced data in the last two epochs on the kth day, s s Cˆ j = Lˆ k,k+1 (ie , if ) − Lsk (ie − 1, ie )

(7)

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s

Combining Cˆ j in Eq. (7), the estimated compensation items of satellite clock dayboundary jumps, the satellite clock data before the day-boundary can be bridged. The satellite clock data after bridged on the kth day can be expressed as, s s Lˆ k (i) = Lsk (i) − Cˆ j

(8)

The ED method makes full use of all the satellite clock data before and after the dayboundary. By averaging the value of the epoch-differenced clock data on the kth and (k + 1) th days, the day-boundary jump compensation items are accurately estimated. The satellite clock data on the (k + 1) th day are regarded as a reference to bridge the satellite clock day-boundary jumps. Compared with the traditional SE method, the satellite clock errors in the satellite clock data of the first epoch on the (k + 1) th day can be effectively avoided based on ED method.

3 Experimental Analysis 3.1 Experiment of Satellite Clock Day-Boundary Jump Compensation The satellite clock products provided by CODE on DOY 256 and 257 in 2020 are selected in the experiment. The satellite clock day-boundary jumps with Unprocessed (UP), compensation method based on SE and ED are verified. The G06 satellite clock epochdifferenced data are shown in Fig. 3. Other satellites have the similar characteristics as the G06 satellite. 0.5 UP

SE

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Epoch Difference (ns)

0.4 0.3 0.2 0.1 0 -0.1 -0.2 0

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20 30 Time (h)

40

Fig. 3. G06 satellite clock epoch-differenced data

As can be seen from Fig. 3, the G06 satellite clock epoch-differenced data have an obvious day-boundary jump at 00:00 on DOY 257 in 2020. And the satellite clock dayboundary jump is difficult to be submerged by satellite clock noise. Although the satellite clock day-boundary jumps are effectively compensated by traditional SE method, the compensated satellite clock epoch-differenced data still have a jump at the day-boundary. It is possible that the frequency change or satellite clock errors of the satellite clock data before day-boundary affects the accuracy of the clock model fitting and extrapolation,

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resulting in a poor accuracy of satellite clock day-boundary jump compensation. While ED method makes full use of the satellite clock data of all epochs before and after the day-boundary. By averaging the value of epoch-differenced satellite clock data between two days before and after the day-boundary, the satellite clock day-boundary jump compensation items are accurately estimated. The possible satellite clock frequency changes and satellite clock errors effects are suppressed, and the compensation accuracy of satellite clock day-boundary jumps is improved. In order to quantitatively analyze the compensation accuracy on the continuity of satellite clock products based on SE and ED method, the RMS and STD of all satellite clock fitting residuals within one hour before and after the day-boundary are shown in Table 1. It can more accurately reflect the compensation accuracy of the satellite clock day-boundary jumps and the continuity of the satellite clock products. Table 1. RMS and STD of clock model fitting residuals in all satellites Method RMS/(ns) STD/(ns) UP

0.4516

0.3139

SE

0.3676

0.2086

ED

0.3610

0.1881

Synthesizing Fig. 3 and Table 1, it can be seen that the satellite clock day-boundary jumps can be effectively compensated based on SE and ED method. Compared with the traditional SE method, the RMS and STD of clock model fitting residuals based on ED method are improved by 1.80% and 9.83% within one hour before and after the day-boundary. In terms of the continuity of the satellite clock data, the satellite clock day-boundary jumps can be more accurately compensated based on ED method. 3.2 Experiment of PPP In order to further verify the advantages of ED method in PPP, the satellite clock products provided by CODE on DOY 256 and 257 in 2020 are selected in the experiment. The satellite clock products with Unprocessed (UP), compensation method based on SE and ED are verified in PPP. The station selection of PPP is shown in Fig. 4, and the solution strategy of PPP is shown in Table 2. Considering that neither TDBs nor ICBs affect the PPP accuracy after convergence, so PPP accuracy on the next day can more intuitively and effectively reflect the compensation accuracy of the satellite clock day-boundary jumps. The PPP accuracy of the BOAV station is shown in Fig. 5. The PPP accuracy of other stations has similar characteristics as the BOAV station. It can be seen from Fig. 5 that the PPP accuracy of satellite clock based on UP method fluctuate significantly within about 2 h after the day-boundary. Compared with UP method, the PPP accuracy of satellite clock based on SE method is not significantly improved in the horizontal direction. It has a more obvious improvement in the elevation

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Fig. 4. Station selection of PPP

Table 2. Solution strategy of PPP Name

Strategy

Satellite system

GPS

Frequency observations

L1/L2

Precise ephemeris

Final satellite and orbit products provided by CODE

Compensation of day-boundary jumps

Satellite clock: UP/SE/ED Satellite orbit: Unprocessed [8]

Reference of station position

IGS SINEX file

Elevation cutoff angle

15°

Ionospheric delays

Ionosphere-free combined

Zenith tropospheric delays

Estimated

Tidal effect, earth rotation, antenna phase winding

Corrected

direction, but it still has an obvious fluctuation. This may be caused by the insufficient compensation accuracy of satellite clock day-boundary jumps. While the PPP fluctuation based on ED method are significantly improved in the horizontal and elevation direction. In order to quantitatively analyze the compensation accuracy on PPP based on SE and ED methods, the RMS and STD of PPP within two hours after the day-boundary are shown in Fig. 6. It can more accurately reflect the compensation accuracy of the satellite clock data and the PPP accuracy. It can be seen from Fig. 6 that, for ABPO, BOAV, COTE and ZIMM stations, SE method is better than UP method in RMS and STD of PPP within two hours after the day-boundary. For the YAR3 station, SE method has a lower RMS of PPP than UP method, but the stability is improved. For the JFNG station, SE method may have an insufficient compensation accuracy. And the RMS and STD of PPP based on SE method are lower than those of UP method. ED method is better than UP and SE method in RMS and STD of PPP within two hours after the day-boundary for all stations.

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Fig. 6. (a) RMS of PPP before and after compensating satellite clock day-boundary jumps (b) STD of PPP before and after compensating satellite clock day-boundary jumps

In order to comprehensively analyze the PPP accuracy of all selected stations based on SE and ED methods, the RMS and STD of PPP are shown in Table 3. It can be seen from Table 3 that SE method reduces the PPP accuracy within 2 h after the day-boundary, but it improves the PPP fluctuation or even reconvergence. Compared with the traditional SE method, the RMS and STD of PPP based on ED method are improved by 47.73% and 55.64% within two hours after the day-boundary, respectively.

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Table 3. RMS and STD of PPP values of all stations Method RMS/(m) STD/(m) UP

0.3898

0.1851

SE

0.4588

0.1702

ED

0.2398

0.0755

In terms of PPP accuracy, ED method can more accurately compensate the satellite clock day-boundary jumps.

4 Conclusions This paper focuses on the analysis of satellite clock day-boundary jump compensation method for the GPS final satellite clock products provided by CODE. The satellite clock data on DOY 214-275 in 2020 are selected, a total of 62 days. The main error items of satellite clock day-boundary jumps are analyzed. The experimental results show that TDBs and ICBs are the main error items that cause the satellite clock day-boundary jumps. In order to prevent TDBs from affecting the continuity of satellite clock products, and prevent ICBs from affecting PPP accuracy, a compensation method of satellite clock day-boundary jump based on ED method is proposed. The method makes full use of all the satellite clock data before and after the day-boundary. After averaging clock data based on epoch-differenced, the day-boundary compensation term is estimated accurately. The final satellite clock products provided by Center of Orbit Determination in Europe are used to verify the compensation effect of the method proposed in this paper. The results show that, compared with the traditional compensation method based on SE, the RMS and STD of clock model fitting residual are improved by 1.80% and 9.83%, respectively. In addition, the RMS and STD accuracy of PPP are improved by 47.73% and 55.64% within two hours after the day-boundary, respectively. In terms of the continuity of the satellite clock data and the PPP positioning accuracy, the satellite clock day-boundary jumps can be more accurately compensated based on ED method. Acknowledgements. This research was jointly funded by the National Natural Science Foundation of China (No. 61773132, 61633008, and 61803115), the China Postdoctoral Science Foundation (No. 2020M681078), the Postdoctoral Innovation Project in Shandong Province (No. 202003050), the Postdoctoral Applied Research Project in Qingdao (No. QDBSHYYYJXM20200101), and the Outstanding Youth Research Science Foundation in Heilongjiang Province (No. JC2018019).

References 1. Chen, C., Chang, G.B.: PPPLib: an open-source software for precise point positioning using GPS, BeiDou, Galileo, GLONASS, and QZSS with multi-frequency observations. GPS Solutions 25(1) (2021)

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2. He, Y.X., Li, H.J., Zhou, J.: Comparatively analysis of PPP results for products of different IGS analysis centers. J. Navig. Positioning 8(1), 38–42 (2020) 3. Cheng, C., Zhao, Y.X., Li, L., et al.: Performance evaluation of real time and final precision ephemeris products of BDS. In: China Satellite Navigation Conference (2018) 4. Chen, L., Song, W., Yi, W., Shi, C., Lou, Y., Guo, H.: Research on a method of real-time combination of precise GPS clock corrections. GPS Solutions 21(1), 187–195 (2017). https:// doi.org/10.1007/s10291-016-0515-3 5. Liu, Y.Y., Ye, S.R., Jiang, P., et al.: Investigation to discontinuity in the IGS final ephemeris and corresponding treatment. Geomatics Inf. Sci. Wuhan Univ. 39(10), 1174–1178 (2014) 6. Yang, H., Xu, C., Gao, Y.: Analysis of GPS satellite clock prediction performance with different update intervals and application to real-time PPP. Surv. Rev. 51(364), 43–52 (2019). https://doi.org/10.1080/00396265.2017.1359473 7. Yao, Y., He, Y., Yi, W., Song, W., Cao, C., Chen, M.: Method for evaluating real-time GNSS satellite clock offset products. GPS Solutions 21(4), 1417–1425 (2017). https://doi.org/10. 1007/s10291-017-0619-4 8. Guo, X.X., Li, M.: Research of IGS precise clock offset day boundary effects and eliminating methods. In: China Satellite Navigation Conference (2014) 9. Dach, R., Schildknecht, T., Hugentobler, U., Bernier, Laurent-Guy., Dudle, G.: Continuous geodetic time-transfer analysis methods. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(7), 1250–1259 (2006). https://doi.org/10.1109/TUFFC.2006.1665073 10. Zhao, L., Dousa, J., Ye, S., Vaclavovic, P.: A flexible strategy for handling the datum and initial bias in real-time GNSS satellite clock estimation. J. Geodesy 94(1), 1–11 (2019). https://doi. org/10.1007/s00190-019-01328-9 11. Bock, H., Dach, R., Jäggi, A., Beutler, G.: High-rate GPS clock corrections from CODE: support of 1 Hz applications. J. Geodesy 83(11), 1083–1094 (2009). https://doi.org/10.1007/ s00190-009-0326-1 12. Ye, S., Zhao, L., Song, J., Chen, D., Jiang, W.: Analysis of estimated satellite clock biases and their effects on precise point positioning. GPS Solutions 22(1), 16 (2018). https://doi.org/10. 1007/s10291-017-0680-z 13. Wei, D.K.: Study on the Satellite Clock Bias Forecast Model. Chang’an University (2014) 14. Wang, Y.P., Zhang, S.L., Xu, J.F., et al.: Data preprocessing strategy for BDS satellite clock bias data based on an improved median absolute deviation method. Sci. Surv. Mapp. 44(02), 109–115+127 (2019) 15. Li, L., Liu, X.S., Jia, C., Li, J.X., Zhao, L.: Integrity monitoring of carrier phase-based ephemeris fault deteciton. GPS Solut. 24(2), 7–8 (2020). https://doi.org/10.1007/s10291020-0958-4

Research on Integrity Monitoring Techniques for Atomic Clocks Based on DualKalman Filter Xinming Huang1,2(B) , Zhiling Ren1,2 , Jing Peng1,2 , and Hang Gong1,2 1 College of Electronic Science and Technology, National University of Defense Technology,

Changsha, China 2 Tianjin Institute of Advanced Technology, Tianjin, China

Abstract. As the core component of time-frequency reference generation of satellite navigation system, atomic clock is the guarantee for high-precision navigation signal generation and reception. The integrity monitoring of atomic clocks is the basis for time reference generation and spatial high-precision measurement. This paper adopts the idea of Kalman filter prediction residuals for integrity monitoring, establishes an accurate Kalman filter model of the atomic clock, constructs the Kalman prediction residual vector, and performs two-level Kalman filtering to form a DualKalman filter to improve detection sensitivity. Using IGS data to analyze the calculation examples, the results show that the DualKalman filter integrity detection technology proposed in this paper has the characteristics of high-sensitivity detection and can be used as a GNSS ground/satellite clock integrity monitoring method. Keywords: Atomic clock · Integrity monitoring · Dualkalman filter

1 Introduction The core component of time-frequency reference generation for satellite navigation systems, atomic clocks are the basis for the generation and reception of high-precision navigation signals. The high-precision time-frequency reference can ensure that GNSS users obtain accurate position and time information [1]. Any clock abnormality will affect system performance and may cause a range error of several kilometers [2]. Therefore, the rapid detection of clock abnormalities is essential, especially for safety-critical applications, such as aircraft landing [1]. The current global positioning system (GNSS) itself cannot provide users with timely warnings against various integrity threats (especially abnormal clock events). In order to improve the integrity of GNSS, literature [3] proposed autonomous integrity monitoring of satellite clocks, using multiple atomic clocks running at the same time and comparing with each other to obtain the original measurement results, and then combining appropriate detection methods to monitor atomic clock abnormalities. In recent years, the modeling and integrity detection of the clock model have received key attention, and a series of methods have been proposed, including the moving average method, the GLRT method, the least square method and the dynamic Allan variance © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 37–43, 2021. https://doi.org/10.1007/978-981-16-3146-7_4

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method, etc., all of which can be summarized as the clock based on the estimated residual Abnormal monitoring methods [4–13]. The clock model based on the Kalman filter is a more accurate modeling method, which has a stronger ability to detect clock abnormalities and can effectively detect frequency jump abnormalities [14, 15]. These are not effective in detecting anomalies such as small frequency jumps of the order of 10–12 . In the literature [14, 15], the author of this article improved the Kalman filtering method, and proposed a frequency jump anomaly detection algorithm based on the Nstep extrapolation prediction residual, and performed Wiener filtering on the prediction residual to improve the detection sensitivity. The algorithm can detect frequency drift jumps, but the time required to detect them is inversely proportional to the growth rate of the frequency drift jumps, and because the noise level of the prediction residuals is larger, the sensitivity of the detector is low. In order to solve this problem, it is necessary to provide a new technical idea. This paper further analyzes the clock anomaly detection algorithm based on the Kalman filter, modifies the original frequency hopping detector algorithm, and provides a new algorithm, using real data analysis to determine the effectiveness of the detector for clock anomalies. The structure of this paper is as follows: In Sect. 2, the Kalman filter model of the clock will be established. In Sect. 3, the DualKalman filter algorithm is proposed and the detailed derivation process of the new algorithm is given. In Sect. 4, this method is applied to the real data of IGS to evaluate the detection effect.

2 The Kalman Filter Model The measurement frequency output of common time scales, such as atomic frequency scales, is usually modeled as the sum of measurement noise, frequency white noise, frequency random walk noise, and slowly changing frequency drift determination items. Therefore, the received clock frequency measurement value expression is expressed as [16, 17] y(k) = yRW (k) + d · k · T + yW (k) + w(k)

(1)

Where T is the measurement interval, d is the linear frequency drift, which is regarded as a constant value, y(w) is the frequency white noise, and w(k) is measurement noise with variance σw2 . yRW (k) is the frequency random walk noise, which can be expressed as yRW (k) = yRW (k − 1) + yRW (k − 1)

(2)

According to [12], yW (k) has zero mean and variance given by 2 σ12 = E[yW (k)]

(3)

yRW (k − 1) are statistically independent Gaussian random variables, with zero mean and variance given by 2 σ22 = E[yRW (k)]

(4)

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A Kalman filter model is used whose measurement model can be expressed as y(k) = hT · X(k) + yW (k) + w(k)

(5)

  1 where h = . 0 The system model is expressed as follows X(k + 1) = A · X(k) + B · V (k) (6)         0 yRW (k) 1T 01 where A = ,B= , and V (k) = . , X(k) = 00 00 d ·k yRW (k) Therefore, the Kalman filter model for clock anomaly detection is built.

3 The Dual-Kalman Filter Method 3.1 N-step Prediction Residuals According to [18], the nth-step prediction of X(k) can be expressed as 



X(n + k) = An · X(k)

(7)

The predicted frequency deviation measurement at the n + k sampling period can be given as 





y(n + k) = hT · X(n + k) = hT · An · X(k)

(8)

The frequency deviation measurement at the n + k sampling period can be expressed as follows when there is no anomaly. y(n + k) = hT X(n + k) + w(k) = hT (An X(k) +

n 

Ai−1 BV(k + i)) + w(k)

(9)

i=1

The n + k prediction frequency residue can be given as following. 

y(n + k) = y(n + k) − y(n + k) 

= hT An (X(k) − X(k)) + hT

n 

Ai−1 BV(k + i) + w(k)

(10)

i=1 

Where X(k) − X(k) ∼ N (0, M[k|k]), where M[k|k] represents the estimated error covariance matrix of Kalman filter. The nth-step prediction frequency deviation residue can be rewritten as y(n + k) = x(n + k) + w(k)

(11)

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x(n + k) is defined as the prediction state residual, which can be expressed as following. 

x(n + k) = hT X(n + k) − hT An X(k) = hT (An X(k) +

n 



Ai−1 BV(k + i) − An X(k))

i=1 

= hT A(An−1 X(k) − An−1 X(k)) + hT A

n−1 

Ai−1 BV(k + i + 1) + hT BV(k + 1)

i=1 

= x(n + k − 1) + (d − d ) · T + yRW (k − 1) ≈ x(n + k − 1) + yRW (n + k − 1)

(12)

The model for x(n + k) is a first-order Gauss-Markov process, and x(n + k) is independent of yRW (n + k − 1), whose variance is hT M[k|k]h. Therefore, the prediction residuals can be modeled as a first-order Gauss-Markov process polluted by frequency white noise. 3.2 The Dedicated Kalman Filter In order to detect the clock anomaly, the predicted error should be minimized in the mean square sense, Kalman filter is chosen as the dedicated filter. The measurement model can be expressed as y(k) = x(k) + w(n − k)

(13)

A Kalman filter model is used whose system model is achieved, which can be expressed as follows x(k) = x(k − 1) + yRW (k − 1)

(14)

The filtered residue of the Kalman filter is expressed as z(k) = x(k) − ˜x(k|k − 1 )

(15)

z(k) is Gaussian random variables, with zero mean and variance of the filtered error. In order to detect the anomaly, we choose the energy detector, which can be expressed as T (z) =

N −1 

z 2 (n) > γ

(16)

n=0

The proposed energy detector T (z) follows a central chi-square distribution with N degrees of freedom when there exists no clock anomaly, while it has a non-central chi-square distribution with N degrees of freedom when clock anomaly happens. Thus the detection performance can be determined as  ∞ √ 1 z N − 1 − z+λ Pd = Pr{z > γ ; H1 } = ( ) 4 2 e 2 I N −1 ( zλ)dz (17) 2 2 λ γ

Research on Integrity Monitoring Techniques for Atomic Clocks

41

where the noncentral parameter λ is determined by the clock anomaly , and γ is the detection threshold, which can be acquired by false alarm as following.  ∞ N N z N Pfa = Pr{z > γ ; H0 } = (2 2 ( ))−1 z 2 −1 e− 2 dz (18) 2 γ The detector computes the energy of observations and compares it to a threshold.

4 Performance Analysis In order to further verify the detection performance of the proposed method, the measured data of IGS is used for analysis and verification. The following figure shows the frequency difference measurement value of the original clock difference data of GPS 29 satellite obtained from the International GNSS Service Organization (IGS) database. The time is from August 29, 2010 to November 14, 2010, sampling interval For 15 min. Observing the original frequency difference measurement value, you can see that there are several abnormal frequency jumps (Fig. 1). -12

3.6

x 10

3.4

Frequency Measurements

3.2 3 2.8 2.6 2.4 2.2 2 1.8

0

1000

2000

3000 4000 5000 6000 Measurement Time/15 minutes

7000

8000

Fig. 1. Frequency deviation of GPS PRN 29 satellite clock, obtained from IGS data.

The above-mentioned IGS raw data is used to analyze the detection performance of the DualKalman filtering method proposed in this paper. First, in order to be able to determine the filter parameters and the detection threshold of the detector, it is necessary to determine the deterministic parameter of the clock and the noise parameter. We use the estimation method proposed in [18–20] to obtain the corresponding clock parameters, and use the first 1000 sampling points without anomalies to estimate the parameters. The estimated parameters obtained are as follows: ⎧ 2 σ = (2 × 10−13 )2 ⎪ ⎪ ⎨ 12 σ2 = (5.2 × 10−16 )2 ⎪ f0 ≈ 2.8 × 10−12 ⎪ ⎩ d ≈ 3 × 10−16 /s

(19)

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After obtaining the clock parameters, construct the detection statistics of the DualKalman filtering method, and construct the detection statistics of the Kalman filtering method in the literature [14] as a comparison. The corresponding calculated values are shown in the figure below. We define the detection statistic of the Kalman filter algorithm in [14] as the predictive filter residual vector integrity monitoring statistic (PFRV-CAIM), and define the detection statistic of the DualKalman filter algorithm proposed in this paper as the bi-predictive filter residual vector integrity Monitoring statistics (DPFRV-CAIM). It can be seen from the figure that when there is a frequency jump, the value of the corresponding detection statistics will increase, and the detection effect of DPFRV-CAIM is better than that of PFRV-CAIM (Fig. 2). 400 The Original Method The Improved Method The Detection Threshold

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Detection Results

300 250 200 150 100 50 0

0

1000

2000

3000 4000 5000 6000 Measurement Time/15 minutes

7000

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Fig. 2. Detection results of real data.

5 Conclusions The atomic clock integrity monitoring algorithm based on Kalman filter is an effective method that can accurately model and detect clock abnormalities. Aiming at the problem that the residual variance of the Kalman filtering algorithm is too large, the DualKalman filtering algorithm is proposed, which can effectively suppress the influence of noise in the prediction residual and effectively detect clock anomalies. IGS data of satellite clocks is used to verify the new algorithm, the results show that the DualKalman filtering algorithm proposed in this paper has good integrity monitoring performance, which can provide a certain reference for GNSS clock integrity monitoring strategies.

References 1. Lee, S., Kim, J., Lee, Y.: Protecting signal integrity against atomic clock anomalies on board GNSS satellites. IEEE Trans. Instrum. Meas. 60, 2738–2745 (2011) 2. Kaplan, E.D., Hegarty, C.J.: Understanding GPS: Principles and Applications, 2nd edn. Artech House Inc., Boston (2006)

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3. Rodríguez-Pérez, I., et al.: Inter-satellite links for satellite autonomous integrity monitoring. Adv. Space Res. 47, 197–212 (2011) 4. Du, Y., Wang, J., Rizos, C., El-Mowafy, A.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2(1), 1–22 (2021). https://doi.org/10.1186/s43020-020-00034-8 5. Riley, W.J.: Algorithms for frequency jump detection. Metrologia 45, S154–S161 (2008) 6. Nunzi, E., Carbone, P.: Monitoring signal integrity of atomic clocks by means of the GLRT. Metrologia 45, S103–S107 (2008) 7. Galleani, L.: Detection of changes in clock noise using the time–frequency spectrum. Metrologia 45(6), S143–S153 (2008). https://doi.org/10.1088/0026-1394/45/6/S20 8. Galleani, L., Tavella, P.: Detection and identification of atomic clock anomalies. Metrologia 45, S127–S133 (2008) 9. Nunzi, E., Galleani, L., Tavella, P., Carbone, P.: Detection of anomalies in the behavior of atomic clocks. IEEE Trans. Instrum. Meas. 56, 523–528 (2007) 10. Galleani, L., Tavella, P.: The dynamic Allan variance. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 450–464 (2009) 11. Galleani, L.: The dynamic Allan variance II: a fast computational algorithm. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 182–188 (2010) 12. Sesia, I., Galleani, L., Tavella, P.: Application of the dynamic Allan variance for the characterization of space clock behavior. IEEE Trans. Aerosp. Electron. Syst. 47, 884–895 (2011) 13. Galleani, L., Tavella, P.: Detection of atomic clock frequency jumps with Kalman filter. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 504–509 (2012) 14. Huang, X., Gong, H., Gang, O.: Detection of weak frequency jumps for GNSS on-board clocks. IEEE Trans. Ultra Ferroelectr. Freq. Control 51(1), 1374–1375 (2014) 15. Huang, X., Gong, H., Zhu, X., Gang, O.: Detection of atomic clock frequency anomaly with Kalman filter. Metrologia 51(1), 1374–1375 (2014) 16. Tavella, P.: Statistical and mathematical tools for atomic clocks. Metrologia 45, S183–S192 (2008) 17. Galleani, L.: A tutorial on the two-state model of the atomic clock noise. Metrologia 45, S175–S182 (2008) 18. Davis, J.A., Greenhall, C.A., Stacey, P.W.: A Kalman filter clock algorithm for use in the presence of flicker frequency modulation noise. Metrologia 42, S1–S10 (2005) 19. Harris, P.M., Davis, J.A., Cox, M.G., Shemar, S.L.: Least-squares analysis of time series data and its application to two-way satellite time and frequency transfer measurements. Metrologia 40, S342–S347 (2003) 20. Greenhall, C.A.: Linear invariant estimation of clock phase and trend from noisy phase data. Metrologia 46, 569–577 (2009)

The Beam Optics Analysis Based on Monte Carlo Simulation of the Magnetic State Selection and Optical Detection Cesium Beam Clock Sifei Chen1 , Shaohang Xu1 , Chang Liu2 , Yuanhao Li3 , and Yanhui Wang1(B) 1 State Key Laboratory of Advanced Optical Communication System and Networks,

Department of Electronics, Peking University, Beijing 100871, China [email protected] 2 Information Technology Institute (Tianjin Binhai), Peking University, Tianjin 300450, China 3 School of Physics, Peking University, Beijing 100871, China

Abstract. Compact cesium beam clocks are of great importance in navigation, time-keeping and precision measurements. In traditional cesium clocks, cesium atoms are deflected by strong inhomogeneous magnetic fields, whose velocity distribution and populations of different quantum states are altered. Normally, the distributions are hard to describe with analytical functions. An alternative solution is to apply the Monte Carlo simulation to sample the atoms and calculate the trajectories. We apply the method to cesium beam clocks based on the magnetic state selection and fluorescence detection scheme. The state distributions of the detectable atoms are obtained with Monte Carlo simulation inside the collimator and finite element simulation of the magnetic field. The performance of the cesium beam tube is also estimated via the sampled atoms, such as the signal amplitude and the signal-to-noise ratio (SNR) of atomic shot noise and laser frequency noise. The estimated SNR of the designed cesium beam tube is over 7000 in a 1 Hz detection bandwidth. The influence of the deflection angle of the collimator on the performance of the beam tube is analyzed. The method can be used to guide the design of the cesium beam tube and is easily applied to different cesium beam clocks. Keywords: Cesium beam atomic clocks · Beam optics · Monte Carlo simulation

1 Introduction Cesium beam clock is one of the most developed atomic clocks with a history of over 70 years [1]. Its high performance in accuracy and long-term frequency stability among all kinds of passive microwave atomic clocks makes it play an important role in fields such as navigation, time-keeping and positioning. The principle of passive frequency standards is selecting, manipulating and detecting the states of atomic systems [2]. Traditional cesium beam clocks use inhomogeneous magnetic field to deflect the atomic beam based on the Stern-Gerlach experiment. The

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 44–52, 2021. https://doi.org/10.1007/978-981-16-3146-7_5

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deviation of the distribution of the atoms from thermal equilibrium influences the performance of the atomic clock. In experiment, the angular distribution of the collimated atomic beam is determined by the temperature of the oven and the shape of the collimator. The gradient of the magnetic field is inhomogeneous in space. As a result, it is difficult to analytically express the state distribution of the detectable atoms. At present, the beam optics analysis for magnetic selection cesium beam tubes is mainly fulfilled with numerical calculation under certain approximations [3–5]. One method is to perform Monte Carlo simulation to estimate the distribution function with sampled atoms. The beam intensity and the velocity distribution can be obtained under approximations with the collimator and the magnetic field [4, 5]. However, these results do not directly reflect the performance of the cesium beam tube. For passive frequency standards, the short-term frequency stability is inversely proportional to the signal-to-noise ratio (SNR), which is strongly affected by the beam intensity and the efficiency of the state selection. Therefore, we extended the estimation theory based on the Monte Carlo simulation and applied to cesium beam clocks with the magnetic selection and optical detection scheme. Trajectories of the atoms are solved accurately with direct simulation of the motions inside the collimator and finite element modeling of the magnet. We also developed a method to estimate the signal amplitude as well as the SNR. The theoretical background of the magnetic selection and optical detection scheme and the estimation method is introduced in Sect. 2. In Sect. 3, we analyse the influence on the state distribution of the atoms and the clock performance of the angle of the collimator.

2 Theoretical Background

Fig. 1. Scheme of the magnetic selection and optical detection cesium beam tube. α is the deflection angle of the collimator. θ, φ are polar angle and azimuth angle corresponding to the exit plane of the collimator

The basic structure of the magnetic state selection and optical detection cesium beam tube is shown in Fig. 1. Cesium atoms are ejected from the collimator and deflected under the action of the two-wire magnet. Atoms with positive effective magnetic moments, namely the atoms in |F = 3 and |F = 4, mF = −4 states are selected to enter the microwave cavity. The selected atoms undergo Ramsey resonance with microwave field. We also introduce the C-field to remove the degeneracy of hyperfine energy levels. After

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reaching the detection zone, the atoms interact with whose frequency is aligned  the laser,  with the cyclic transition line from |F = 4 to F  = 5 . The fluorescence radiated by atoms in |F = 4 states is converged on a photo diode through spherical mirrors and converted into electrical signal, reflecting the information of the atomic states. In this section, we introduce the method to generate atomic samples and calculate the motion equation and transition probability. Then we emphasize the performance estimation theory. 2.1 Initial States of Atoms The distribution of cesium atoms obeys the Boltzmann distribution in thermal equilibrium. It can be approximated that the cesium atoms are evenly distributed in 16 magnetic sublevels. The motion state of cesium atoms has 6 degrees of freedom, including its threedimensional coordinates and velocity (x, y, z, x˙ , y˙ , z˙ )T . Most theoretical work about the angular distribution of the atoms ejected from the collimator assumes that the collimator is equivalent to a round tube [6, 7], namely the azimuth angle φ is considered to be uniformly distributed. In experiment, we use folded paralleled tubes instead for higher beam intensity. Instead of applying the analytical formula, we use the open source software Molflow+ to directly perform Monte Carlo simulation of the atoms inside the tubes. The distributions of the emitted atoms are shown in Fig. 2. The azimuth distribution is obviously different from the ideal uniform distribution. We denote in the following section the atom numbers as i = 1, 2, 3 . . . NS , where Ns is the sample size. The state of each atom can be described with a column vector pi = (xi , yi , zi , x˙ i , y˙ i , z˙i )T , and the initial energy level of each atom is labelled as ni = 1, 2, . . . , 16, which accordingly represents state |F = 3, mF = −3, . . . |F = 4, mF = −4.

Fig. 2. Simulated azimuth distribution (a) and angular distribution for unit solid angle (b) of atoms ejected from the collimator. The sample size is 2 × 107

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2.2 The Solution of the Trajectories of Atoms To calculate whether the atoms can reach the detection zone, we need to solve the motion equations,   Fix Fiy Fiz T d pi = x˙ i , y˙ i , z˙i , , , . dt M M M In the state selection zone, the force acting upon the atoms is expressed as Fi (ni (F, mF )) = μeff (ni (F, mF ))∇B, where μeff (ni (F, mF )) is the effective magnetic moment of the ith atom. Its analytical expression is shown in [8].

Fig. 3. Relative error between theoretical formula and finite element simulation of the gradient of the magnetic field along z-axis (gray: outside the passage of the selection zone)

The knowledge of the magnetic field and its gradients determines the accuracy of the solution of the trajectories. We simulate the magnetic field with a finite element analysis tool. The result is shown in Fig. 3. It is shown that the gradient of the magnetic field only coincides with the two-wire field at the center of the magnet. The gradient significantly differs from the approximated formula in the marginal area, which increases the detect rate of the unwanted atoms. The magnetic field zone is divided into a 50 × 50 grid and the magnitude as well as the gradient of the magnetic field at any position are obtained with the linear two-dimensional interpolation algorithm. The difference of the gradient along the beam axis is neglected, namely Fx = 0. The differential equations are solved with the optimized Runge-Kutta method. Atoms are excluded from the output results when hitting the internal mechanical structure of the cesium beam tube. Figure 4(a) shows the simulated state distribution of atoms reaching the detection zone. Due to the angular distribution and the velocity distribution of the initial atoms, there are always unwanted atoms in |F = 4 states entering the detection zone (see Fig. 4(a), ni > 8).

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Fig. 4. (a) Normalized quantum states population histogram (b) Normalized effective velocity distribution of the detectable atoms (black, solid) versus the modified Maxwell distribution (red, dashed). The deflection angle of the collimator is 1°

We can also estimate the velocity distribution of the detectable atoms. For cesium beam tubes, the effective velocity distribution f (v) is the weighted difference of the velocity distribution of atoms in |F = 3, mF = 0 and |F = 4, mF = 0, which is f (v) = N3 f3 (v) − N4 f4 (v), Where N3 and N4 are the number of atoms in state |F = 3 and |F = 4. The velocity distribution is then obtained with the kernel density estimation method. The result is shown in Fig. 4(b) in comparison with the modified Maxwell distribution. The difference shows the velocity selective property of the magnet. 2.3 Transition Probability Cesium atoms undergo two main interaction processes with electromagnetic fields. One is the Ramsey resonance when atoms pass through the U-shaped microwave cavity. Under the two-level assumption, the transition probability near resonance is [8]    (1) Pi (τi ) = 21 1 + cos i Ti + φphase sin2 bτi , where τi , Ti are the time for the ith atom to pass through the single arm of the cavity and to freely evolve, b is the Rabi frequency, and i =  − ωi is the detuning frequency of the microwave field relative to the atom. Each sampled atom has different velocity and eigenfrequency due to the external C field. φphase in (1) is the cavity phase difference, which is neglected in the following discussion. For atoms in |F = 4, mF = ±4, Pi equals to zero because we only consider σ transition. The second transition process occurs in the optical detection zone. Atoms in quantum state |F = 4 interact with the laser field and radiate fluorescence. In experiment, the laser frequency is stabilized to the cyclic transition line and the laser light intensity is of the order of 100 –101 mW/cm2 . Atoms in the detection zone reach the steady state

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within a short time interval in comparison with the total interaction time. We therefore neglect the transient process in the simulation. The expectation of photons emitted by each atom can be written as

, βi = Ki σi σ55vd i

(2)

where Ki = 1 means the atom is accessible to the detection area, otherwise Ki = 0, σ55  is the probability that the atom is in the excited state, d is the diameter of the laser beam, vi is the velocity of the atom, is the natural line width of the D2 line, and σi is the probability that the atom is in the |F = 4 quantum state when it enters the detection zone. Analytically,

Pi , |ϕi  = |F = 3 . (3) σi = 1 − Pi , |ϕi  = |F = 4

2.4 Estimation of Signal and Noise We can estimate the overall signal and noise properties with the knowledge of the states of sampled atoms with (1)–(3). Photons received by the photo diode per unit time are converted into current as I (, b) = ηq ηc e NNS

NS 

βi (, b),

(4)

i=1

where ηc is the collection efficiency of the fluorescence collector, ηq is the quantum efficiency of the photo diode, e is the unit charge, NS is the size of the sample including the undetectable atoms, N is the total beam intensity emitted by the collimator per unit time. and , b are the frequency of the microwave field and its Rabi frequency respectively. In the magnetic state selection and optical detection scheme, there are two major noise sources, the shot noise and laser frequency noise. We can estimate the power spectral density of each noise source and calculate the respective signal-to-noise-ratio (SNR). Both the two noise sources are white noise in a considerable frequency range. From (4), the power spectral density of the shot noise is Sshot (, b) =

2N NS

NS 2   βi2 (, b). ηq ηc e

(5)

i=1

With (4) and (5), the SNR of shot noise can be written as SNRshot =

I ( √max ,b)−I (min ,b) , B·Sshot (mod ,b)

(6)

where I (max , b), I (min , b) are the maximum and minimum values of the central peak of the Ramsey fringe at the corresponding frequency detuning max and min . To generate the error signal, we need to modulate the microwave signal with a square wave. The actual noise spectrum corresponds to a detuned frequency  = mod . B is the detection bandwidth, which is normally set as 1 Hz.

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The other noise source is the laser frequency noise. The power spectral density according to [9] is Slf (mod , b) = ζ

2I (mod ,b) 22L + ( +γL )

,

(7)

3 +γL

where 1

2 1

(3 + γL ) 2 ζ = √ L (3 + 4γL ) + ( + 2γL ) . 2 γL

In the above equations, L is the Rabi frequency of the laser interaction, and γL is the linewidth of the laser. Similar to Eq. (6), we can also calculate the SNR for laser frequency noise, SNRlf =

I (√max ,b)−I (min ,b) . B·Slf (mod ,b)

(8)

The SNRs correspond to other noise sources, including light detection noise, photon shot noise, quantum projection noise, are also predictable using similar method. In fact, these SNRs are usually greater than 20000, which are negligible comparing with the shot noise and the laser frequency noise. Since different noise sources are independent of each other, their power spectral density can be directly superimposed, and the total SNR is  − 1 2 −2 −2 SNR = SNR−2 + SNR + SNR . shot lf other

(9)

3 Beam Optics Simulation With the estimation model described above, we can evaluate the performance of a cesium beam tube. For our scheme, one important beam optics parameter is the deflection angle of the collimator. We align the collimator outlet at the center of the magnet and analyse the influence of the deflection angle on the performance of the cesium beam tube. 3.1 Experimental Setup For each collimator deflection angle α, we use an identical atom sample for simulation. The oven temperature is set to 118 °C. The size of the sample NS is 2 × 107 . The estimated total beam intensity N is 1 × 1014 . In the experiment, a DFB laser is used to detect the atoms. The linewidth is 2 MHz, and the laser intensity is 5 mW/cm2 . The fluorescence collection efficiency ηc is about 0.3, and the quantum efficiency of the photo diode ηq is 0.87.

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3.2 Simulation Results We calculated the motion trajectory of each atom to determine whether it can reach the detection zone. Figure 5(a) shows the detectable rate of atoms with different magnetic moments with different deflection angles. As α increases, the reaching ratio of atoms decreases accordingly, but atoms in |F = 4, mF = −4 are relatively less likely to reach the detection zone, which means the state selection effect is better for greater deflection angle.

Fig. 5. Estimation results at different deflection angles of the collimator. (a) Ratio of the detectable atoms over the sample size (red circle with dashed line: F = 3, blue triangle with dotted line: F = 4, and black square with solid line: the total amount of the detectable atoms). (b) Amplitude of the microwave resonance signal Is (left, black circle, solid line) and the background Ib (left, black square, solid line) as well as their ratio Is /Ib (right, red triangle, dashed line). (c) Estimated signal-to-noise ratio corresponding to different noise sources (red dashed line: atomic shot noise; blue dotted line: laser frequency noise; black solid line: all noise sources). The error bars represent the confidence interval at 95% confidence level

We also estimated the photocurrent of the background signal without microwave field Ib = I (0, 0) as well as the amplitude of the microwave resonance signal Is = I (max , b)−Ib . The results are shown in Fig. 5(b). The microwave power was adjusted to maximize the Ramsey fringe for each set of simulation. As the deflection angle increases, both the Ramsey signal and the background amplitude decrease. However, as the ratio of atoms in |F = 4 decreases, the ratio of the Ramsey signal and the background increases. The result also reflects the improvement of the state selecting effect. Finally, we estimated the SNR at different deflection angles with (6), (8) and (9). The results are shown in Fig. 5(c). The atomic shot noise has different characteristics with the laser frequency noise. The laser frequency noise is only related to the state selection effect, and it is not related to the total beam intensity. As the deflection angle

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increases, SNRlf becomes negligible. However, SNRat is relevant with both the state selection effect and the beam intensity. When the deflection angle is not large, SNRat increases with the improvement of the state selection effect. When the deflection angle is greater than 1.6°, however, SNRat is limited by the detectable beam intensity. Due to the different characteristics of two noise sources, the peak of the total SNR appears at 1.6°, which is greater than 7000.

4 Conclusion We presented a Monte-Carlo-simulation-based method for evaluating the performance of magnetic state selection and optical detection cesium beam tubes. The distribution, and the signal-to-noise ratio were estimated via numerical calculations of sampled atoms. We also discussed the influence of the deflection angle of the collimator on the cesium beam tube. When the deflection angle is 1.6°, the estimated SNR is over 7000. We will conduct further experiments on the above estimation results to verify the accuracy of the simulation results. This method is not limited to our scheme and can be easily adapted to other types of cesium beam clocks. The estimation method can theoretically guide the design of cesium beam tubes to obtain better frequency stability performance of cesium atomic clocks.

References 1. Vanier, J., Audoin, C.: The classical caesium beam frequency standard: fifty years later. Metrologia 42(3), 31–42 (2005) 2. Kitching, J., Knappe, S., Donley, E.A.: Atomic sensors – a review. IEEE Sens. J. 11(9), 1749– 1758 (2011) 3. Becker, G.: “Exclusive Flop-Out” beam optics for the new primary cesium clocks of the PTB. Metrologia 18(1), 17–21 (1982) 4. Jaduszliwer, B.: Atomic trajectories in compact cesium-beam clocks. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(3), 121–126 (1990) 5. Chen, J., Zhu, H., Ma, Y., et al.: Monte Carlo simulation of a cesium atom beam in a magnetic field. J. Appl. Phys. 117(9), 094902 (2015) 6. Giordmaine, J.A., Wang, T.C.: Molecular beam formation by long parallel tubes. J. Appl. Phys. 31(3), 463–471 (1960) 7. Jones, R.H.: Molecular beam sources fabricated from multichannel arrays. I. Angular distributions and peaking factors. J. Appl. Phys. 40(11), 4641–4649 (1969) 8. Vanier, J., Audoin, C.: The Quantum Physics of Atomic Frequency Standards. Adam Hilger, Bristol (1989). Chapter 5 9. Dimarcq, N., Giordano, V., Cerez, P.: Statistical properties of laser-induced fluorescence signals. Appl. Phys. B (Lasers Opt.) 59(2), 135–145 (1994)

High Precision Time Synchronization of LEO Constellation Based on PPP Wei Wang, MeiTing Yu(B) , Hang Gong, Ming Ma, and GuangFu Sun College of Electronic Science and Technology, National University of Defense Technology, Changsha, China [email protected]

Abstract. Low earth orbit (LEO) constellation has significant advantages in enhancing the accuracy and integrity of GNSS. Navigation enhancement using LEO satellites has become a hot topic in the field of satellite navigation. The success of self-height accuracy time synchronization is the key to realizing LEO navigation enhancement. The non-difference precise point positioning is applied to LEO navigation enhanced satellite system to achieve high-precision time synchronization of LEO constellation. In this paper, the “scale factor” method is used to model the ionosphere above the orbit altitude of LEO satellite, and other errors such as receiver clock offsets are modeled. The accuracy and convergence rate of time synchronization of LEO satellite with different orbit altitude are analyzed when the ionosphere is not modified or the dual frequency correction is adopted. The results show that the PPP convergence rate of LEO satellite can reach less than 10 min; the influence of ionosphere on the time synchronization accuracy of LEO satellite can be ignored when the orbit altitude is above 850 km; when the orbit altitude is below 850 km, the ionosphere needs to be modified by dual frequency, and the time synchronization accuracy of LEO satellite after correction can reach less than 1 ns. Keywords: LEO navigation enhancement · High precision time synchronization · Ionospheric delay · Time synchronization accuracy

1 Introduction With the development of science and technology in our country and the progress of society, the country and cities have an increasing demand for high-precision positioning and time synchronization. At present, the signal of the existing navigation system is susceptible to obscuration and interference, which makes the existing navigation system still have certain defects [1]. In recent years, the way of providing navigation enhancement services through loworbit satellites has received widespread attention, and there are more and more researches on the enhancement of low-orbit navigation. One of the prerequisites for realizing the enhancement of low-orbit navigation and providing high-precision time synchronization services is that the low-orbit satellites themselves achieve high-precision time synchronization. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 53–61, 2021. https://doi.org/10.1007/978-981-16-3146-7_6

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The time synchronization accuracy based on the pseudorange method is often tens of nanoseconds [2], which cannot meet the current low-orbit navigation enhancements for high-precision time synchronization requirements. Therefore, this paper adopts the PPP (Precise Point Positioning) method for low-orbit satellites, and calculates the loworbit satellite clock offset through precision ephemeris and low-orbit satellite GNSS observation data to achieve high-precision time synchronization of low-orbit satellites. And analyze the impact of ionospheric delay on the time synchronization accuracy of low-orbit satellites at different orbit altitudes.

2 Time Synchronization Accuracy Analysis of GNSS PPP The traditional precise point positioning method is to calculate the precise satellite orbit parameters and satellite clock offsets by using the data of several IGS tracking stations around the world, and then process the phase and pseudo range observations collected by a single receiver by using the obtained satellite orbit parameters and satellite clock offsets [3]. Due to a certain delay in the precision ephemeris after IGS, real-time results cannot be obtained, and the prediction error of IGS clock offset products will increase with the extension of time, which limits the improvement of real-time precise point positioning accuracy. Since 2007, IGS has started the IGS real-time pilot project (IGSRTPPP). The observation data of the global real-time tracking network is collected and transmitted to each analysis center, and then each analysis center estimates the precise satellite orbit and clock offset in real time, and broadcasts it to the world based on the RTCM network transmission protocol through the Internet [14]. When performing precision point positioning on low-orbit satellites, an onboard GNSS receiver is installed on the satellite to receive pseudorange and carrier phase observations directly from the GNSS satellite. The real-time precise ephemeris can be injected to LEO satellites on the ground, and the auxiliary information such as precise ephemeris can be broadcast to the whole constellation through inter-satellite link for PPP clock offset calculation. 2.1 Mathematical Model The orbit altitude of LEO satellite is generally between 200 km and 2000 km, while the ionosphere is concentrated in the atmospheric region of 60 km to 2000 km [4]. Therefore, LEO satellite is generally located in the ionosphere, which is only affected by the ionospheric delay above the orbit altitude. The influence of earth tide and sea tide on it can be ignored [6], and there is almost no influence of troposphere and multipath effect. Therefore, the observation model of pseudorange and carrier phase data is as follows.   (1) ρ = Rsr + c dtr − dt s + ILEO + ερ   φ = Rsr + c dtr − dt s − ILEO + λN + εφ

(2)

Where, ρ is the code pseudorange observation value, φ is the carrier phase observation value, Rsr is the real distance between the LEO satellite receiver and the Beidou

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satellite, c is the speed of light, dtr is the receiver clock offset, dt s is the Beidou satellite clock offset, and ILEO is the ionospheric delay, λ is the wavelength of carrier phase, N is the integer ambiguity, ερ and εφ are the random error of observation pseudorange and carrier phase effect. For dual frequency receivers, the ionospheric effect in pseudorange and phase observation data can be eliminated by dual frequency combination [5]. In this paper, ionosphere-free combination model is used for simulation. Satellite orbit error oi and satellite clock offset t i can be corrected by precise satellite ephemeris and clock offset products. Antenna phase center error [6], earth rotation effect, antenna phase winding and other errors can be corrected by model. The unknown parameters such as receiver position coordinates, receiver clock offset and ionospherefree combination ambiguity can be estimated by means of least square estimation and Kalman filtering [11, 12]. 2.2 Analysis of Main Error Sources The time service accuracy of GNSS PPP for high-precision time service is mainly affected by various error sources and GNSS satellite visibility. From the least square calculation results, the time service error of 1 σ can be expressed as the product of observation error and TDOP value. σT = σobs · TDOP

(3)

The main error sources of GNSS PPP are ephemeris error, antenna phase center error, ionospheric delay error, relativistic effect error and noise. The following are different error analysis. 1. Ephemeris errors In this paper, the clock offset of LEO satellite in PPP mode is calculated, so the realtime requirement of precise ephemeris is high. The accuracy of the traditional GNSS satellite real-time precision ephemeris cannot meet the high-precision requirements, so this paper uses the information mount point provided by CNEs (Centre National d’Etudes spaces) to carry out PPP solution for the IGS real-time data stream SSR (state space representation) correction information of CLK93. After analysis, the signal-in-space ranging error (SISRE) of CLK93 BeiDou satellite is 0.1 m [10]. Because the data stream is real-time estimation, the precise ephemeris delay is only the transmission delay of the earth station to satellite and inter-satellite links, so the real-time performance is high [15]. 2. Antenna phase center deviation Antenna phase center deviation refers to the deviation between antenna centroid and phase center. GNSS and LEO satellite both exist. The deviation is related to altitude angle and azimuth angle. The deviation will be corrected during positioning and orbit determination. After correction, the deviation can be ignored [6]. 3. Ionospheric delay deviation Using multi-frequency data, ionosphere-free combination can be constructed to eliminate the first-order ionospheric term deviation, and the remaining higher-order term

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deviation can be ignored [9]. When constructing ionosphere-free combination, the combination error will be amplified. The expression of variance of ionosphere-free combination error is as follows.  f4 f4 σion,free =  2 1 2  σ12 +  2 2 2  σ22 (4) f 1 − f2 f 1 − f2 Where, σ12 and σ22 are ionosphere delay errors at two frequency points respectively. Normally, σ1 ≈ σ2 , The above formula can be simplified as In this paper, the dual frequency ionosphere-free combination of BeiDou B1 and B3 is adopted. The error amplification factor is about 3.53 according to the above formula. 4. Relativistic effect bias The deviation of relativistic effect can be eliminated by the model. After the model correction, the deviation is in millimeter order and can be ignored [13]. 5. Noise The noise is in the millimeter level. Taking the carrier observation noise of 0.003 m as an example, combined with the error amplification factor without ionosphere combination, the carrier observation noise is about 0.01 m after ionosphere-free combination. 2.3 Time Synchronization Accuracy Based on the above-mentioned error analysis, the specific calculation of GNSS PPP timing accuracy is carried out below. Through STK simulation, it can be obtained that under the condition of 50 BeiDou satellites, the range of the TDOP value at an orbit altitude of 500 km is 0.6–1.9. According to the introduced orbit error of 0.1 m and the carrier observation noise of 0.01 m, the combined error of the dual-frequency ionospherefree can be calculated as 0.1 m. According to the above TDOP value, the range of GNSS PPP timing accuracy can be calculated as 0.2–0.63 ns. Combined with the above analysis, based on the carrier phase observation data of GNSS receiver, CLK93 product is used for PPP real-time calculation, and the PPP time service accuracy is within 1 ns.

3 Experimental Analysis 3.1 Establishing Error Model 3.1.1 Ionosphere Error Model In the study of the theory, method and application of ionosphere delay correction for GPS signals, it is generally assumed that all free electrons in the ionospheric region are concentrated in an infinitely thin sphere with height H and the center of the sphere is located at the center of mass of the earth. The ionospheric electron content above the ground can be calculated by the global ionospheric grid model [8]. For the ionospheric electron content above the orbit altitude of LEO satellite, a thin layer model is also

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established for the ionosphere above the orbit altitude of LEO satellite. However, the electron content above the orbit altitude of LEO satellite is relative to the electron content above the ground, which is related to the orbit altitude of the satellite. Oliver et al. mentioned the “ionosphere scale factor method” to build a thin layer model of the ionosphere above the orbit altitude of LEO satellite [7]. The basic idea of the method is as follows. Firstly, the height of the peak electron density is determined, and the height of the equivalent thin layer model of the ionosphere above the orbit and the percentage of the electron content above the orbit in the total electron content are calculated by using Chapman electron density profile function. Secondly, the puncture point of GNSS signal on the equivalent thin layer model and the zenith distance of the signal at the puncture point are calculated. Then, the ionosphere delay correction model is used to calculate the vertical total ionosphere delay at the puncture point. Finally, according to the calculated percentage, zenith distance and vertical total ionosphere delay, the ionosphere delay correction value in the propagation direction of GNSS signal can be obtained. Chapman electron density profile function can be expressed as Ne(h) = Ne0 · exp(1 − z − exp(−z))

(5)

z = (h − h0 )/H

(6)

Using Chapman electron density profile function to calculate the height of the ionosphere thin layer model above the orbit and the ionosphere scale factor after “correction” can be expressed as hIP = h0 − H ln(1 − ln((e + exp(1 − exp(−zs )))/2)) α=

e − exp(1 − exp(−zIP )) e − exp(1 − exp(h0 /H ))

(7) (8)

Where, Ne0 is the peak value of electron density, h0 is the peak height of electron density; H is the rate of change of electron density height, generally 100 km; e is a constant of 2.718282; exp is an exponential function of e; zs = (hs − h0 )/H ; hs is the orbit altitude of LEO satellite. Assuming that the residual electrons above the orbit altitude of LEO satellite are concentrated in the infinitely thin spherical layer with the altitude of hIP (hIP > hs ), the GNSS satellite signal is transmitted to the LEO satellite at rs and passes through the ionosphere at point P. The altitude angles of GNSS satellite relative to LEO satellite and puncture point P are Es and EIP respectively. The code pseudorange error caused by ionosphere delay can be expressed as follows. 40.28 · M (EIP ) · VTEC(rIP ) 2 fL1 40.28 = − 2 · M (EIP ) · α · VTEC(λIP , φIP , 0) fL1

ρ = −

(9)

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Where λIP and φIP are the longitude and latitude of point P, respectively, and α is the ratio of the electron content VTEC(λIP , φIP , hIP ) above the orbit altitude of LEO satellite to the total electron content VTEC(λIP , φIP , 0) above the ground. M (EIP ) is the projection function, which is used to realize the transformation between the electron content in the vertical direction and the electron content in the oblique path of the single-layer model. The expression is as follows. M (EIP ) =

− 1  1 2 = 1 − [cos(Es )rs /rIP ]2 sin(EIP )

(10)

Thus, the ionosphere delay obtained by LEO satellite can be simulated. 3.1.2 Other Error Models The ephemeris error of satellite is the ephemeris error in Sect. 2.2.2. In addition, the antenna phase center deviation, relativistic effect, hardware delay deviation and noise should be considered, and their respective effects should be modeled in the form of noise. 3.2 Analysis of Time Synchronization Results Due to the different orbit altitudes of different LEO satellites, the impact of ionosphere delay is also different. In this paper, referring to the orbit altitude of the existing Starlink LEO satellites and considering the height of the peak value of the ionosphere electron concentration, the simulation experiments selected low-orbit satellites with orbit altitudes of 1325 km, 1150 km, 850 km, 550 km, and 350 km respectively. Each LEO satellite at different orbital altitudes simulates 7200 epochs of data, and PPP time synchronization simulation experiments is carried out for LEO satellites at different orbit altitudes. The simulation experiments are carried out using BeiDou precision ephemeris, and the frequency points are B1 and B3 signals. The time synchronization accuracy and convergence time of PPP to LEO satellites with different orbit altitudes are simulated under the condition that the receiver does not correct the ionosphere and the receiver passes dual-frequency correction respectively. The convergence time is the moment when the orbit error is less than 0.1 m. Without correction of the ionosphere and dual-frequency elimination of the ionosphere, the average time synchronization accuracy, RMSE, and convergence time of each orbit altitude are listed in Table 1. The simulation results of time synchronization accuracy of 1325 km, 850 km and 350 km orbit altitudes under the condition of uncorrected ionosphere and corrected ionosphere are listed, as shown in Fig. 1. The simulation results of convergence time are taken as an example of 350 km orbit altitude, as shown in Fig. 2. It can be seen from the simulation results that under the condition of not correcting the ionosphere, the time synchronization accuracy of LEO satellites is about 54.5 ns and 0.3 ns when the orbit altitude is 350 km and 1325 km. The convergence time of all orbit altitude satellites is within 10 min. as the orbit altitude increases, the time synchronization accuracy is gradually improved, and the convergence time is gradually shortened, and when the orbit altitude is greater than 850 km, the time synchronization accuracy is

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Table 1. Time synchronization mean and RMSE of each orbit altitude before and after ionosphere elimination Orbit altitude

RMSE (ns) Before elimination

Mean (ns) After elimination

Before elimination

Convergence time (s) After elimination

Before elimination

After elimination

1325 km

0.2926

0.2823

−0.1707

−0.2023

260

285

1150 km

0.3293

0.3383

−0.2428

−0.2114

282

256

850 km

0.9551

0.3805

−0.9258

−0.3335

390

263

550 km

15.4473

0.4145

−15.4461

−0.3647

535

196

350 km

54.5002

0.4307

−54.4997

−0.2576

526

194

Fig. 1. Time synchronization accuracy of 1325, 850, 350 km orbit altitude with and without correction of ionosphere

better than 1 ns. Under the condition of dual-frequency elimination of the ionosphere, the time synchronization accuracy of each orbit altitude can reach within 1 ns. It can be seen that the convergence time of each orbit altitude of LEO satellite is within 10 min. When the orbit altitude is higher than 850 km, the influence of ionospheric delay on the time synchronization accuracy is small and almost negligible. The time synchronization accuracy is within 1 ns. It is not necessary to eliminate the ionospheric delay to achieve high-precision time synchronization. However, when the orbit altitude is below 850 km, the time synchronization accuracy is greatly affected by the ionospheric delay, and a dual-frequency receiver is required to eliminate the ionospheric delay.

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Fig. 2. Convergence characteristics of 350 km orbit altitude with and without correction of ionosphere

4 Conclusion In this paper, a high-precision time synchronization method for LEO constellation based on dynamic PPP is studied. According to Chapman model, the ionospheric delay of LEO satellite is modeled, and the influence of ionosphere on time synchronization of LEO satellite is analyzed. The simulation results show that the convergence time of PPP is less than 10 min, and the ionospheric delay can not be eliminated when the orbit altitude is above 850 km. But when the orbit altitude is below 850 km, the influence of ionospheric delay should be eliminated by dual-frequency receiver. Acknowledgments. This study is supported by the ‘National Ministries and Commissions Funded Project’ of China (2019-JCJQ-JJ-190).

References 1. Yang, Y.: Concepts of comprehensive PNT and related key technologies. Acta Geodaetica et Cartographica Sinica 45(5), 505–510 (2016) 2. Zhou, Z., Yi, J., Zhou, Q.: Principle and Application of GPS Satellite Survey. The Mapping Publishing Company, Beijing (2004) 3. Liu, J., Ye, S.: GPS precise point positioning using undifferenced phase observation. Geomatics Inf. Sci. Wuhan Univ. 27(3), 234–240 (2002) 4. Peng, D., Wu, B.: The application of GIM in precise orbit determination for LEO satellites with single-frequency GPS measurements. Acta Astronom. Sinica 53(1), 36–49 (2012) 5. Jin, S.G., Su, K.: PPP models and performances from single- to quad-frequency BDS observations. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-020-00014-y 6. Zhang, X., Cai, S., Li, X., Guo, F.: Accuracy analysis of time and frequency transfer based on precise point positioning. Geomatics Inf. Sci. Wuhan Univ. 35(3), 274–278 (2010)

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7. Montenbruck, O., Gill, E.: Ionospheric correction for GPS tracking of LEO satellites. J. Navig. 55, 293–304 (2002) 8. Tian, S., Xu, R., Yu, Y., et al.: The impacts of ionospheric delay on the frequency transfer utilizing LEO satellite. Acta Astronom. Sinica 55(06), 512–521 (2014) 9. Ray, J., Senior, K.: Geodetic techniques for time and frequency comparisons using GPS phase and code measurements. Metrologia 42(4), 215–232 (2005). https://doi.org/10.1088/ 0026-1394/42/4/005 10. Wang, L., Li, Z., Ge, M., et al.: Investigation of the performance of real-time BDS-only precise point positioning using the IGS real-time service. GPS Solut. 23, 66 (2019) 11. Chen, X.: Precision time transfer methods based on geodetic time and frequency transfer receivers. Geomatics Inf. Sci. Wuhan Univ. 33(3), 245–247 (2008) 12. Zhang, X., Liu, J., Forsberg, R.: Application of precise point positioning in airborne survey. Geomatics Inf. Sci. Wuhan Univ. 31(1), 19–22 (2006) 13. Li, Z., Huang, J.: GPS Measurement and Data Processing. Wuhan University Press, Wuhan (2005) 14. Dong, J., Xu, A., Gao, M., et al.: Accuracy and convergence analysis on GPS real time precise point positioning. J. Navig. Positioning 6(3), 92–97 (2018) 15. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9

A Rubidium Atomic Frequency Standard with Stability at 10−15 Level Operated Under Atmospheric Condition Junyao Li1 , Gang Ming2(B) , Feng Zhao2 , Fang Wang2 , Pengfei Wang2 , and Ganghua Mei2(B) 1 University of Chinese Academy of Sciences, Beijing 100049, China 2 Key Laboratory of Atomic Frequency Standards,

Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology Chinese Academy of Sciences, Wuhan 430071, China {ming,mei}@apm.ac.cn

Abstract. Among several kinds of traditional atomic clocks, rubidium atomic clock shows more extensive applications for its small size, low power and simple structure. In last 20 years, driven by the demands of satellite navigation and relevant fields, the Rb atomic clock has been greatly improved on its frequency stability. Now the long-term stability of satellite-borne Rb atomic clock is better than 5×10−15 at one day. However, when Rb clock runs under atmospheric condition, its long-term stability performance deteriorate seriously. There is a 10 to 100 times deterioration at 104 s and one day, which makes Rb clock impossible to reach 10−15 level. For solving these problems, to develop a high-stability, low-drift and compact-structure type of high performance Rb clock which could fit the atmospheric environment, we conducted a sufficient research on high-performance Rb clock’s environment adaptation. Finally, we developed a prototype whose stability √ reached 6.5 × 10−13 / τ , 7.0 × 10−15 at 104 s and 5.0 × 10−15 at one day. Keywords: High-performance rubidium atomic clock · Environment sensitivity · Long-term stability · Barometric effect

1 Introduction In the past 20 years, driven by satellite navigation and relevant fields, the vapor-cell rubidium atomic clock’s performance has been dramatically improved. The space-borne rubidium clock √ operated under the vacuum environment reaches short-term stability 5×10−13 / τ and long-term stability better than 5×10−15 at one day [1]. Unfortunately, there is severe deterioration of Rb clock performance under atmospheric conditions due to environmental influences such as temperature, atmospheric pressure, electromagnetic field. As a result, the vapor-cell Rb clock’s frequency stability has never reached the level of 10−15 before. We want to develop a high-performance Rb clock operated under the atmospheric condition to fulfil the demand, such as working in a secondary metering

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 62–73, 2021. https://doi.org/10.1007/978-981-16-3146-7_7

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station of timing system. There would be a broad application prospect with its highfrequency stability, small size, low power consumption, high reliability and low cost. Then we carried out a comprehensive study on Rb clock’s adaptability in the atmospheric condition. In this paper, we evaluated the stability performance of Rb clock in the atmospheric environment. Furthermore, we analyzed the instability contribution of several factors and carried out some critical design improving. Finally, the developed high-performance rubidium clock prototype shows a significant improvement on its long-term stability under atmospheric condition.

2 Performance Influence to Rb Clock of Atmospheric Environment 2.1 Structure and Principle of Rb Clock In this paper, the Rb clock is a lamp pumping rubidium vapor-cell clock. The schematic diagrams of physics and electronic are shown as Fig. 1 and Fig. 2:

Fig. 1. Physic package of the lamp pumping rubidium vapor-cell clock

The physical package consists of three vapor cells and two temperature zones. In this design, the rubidium spectrum lamp uses xenon gas as the starting gas. It adopts opticalisotope filtering technology to filter the useless components in the pump light, reducing the shot noise in photoelectric detection. The slotted-tube microwave cavity invented by our laboratory has the advantages of fantastic resonant mode, simple structure and small volume [2]. The filter cell and absorption cell with a diameter of 20 mm are settled in the microwave cavity, working in the same temperature zone. In the electronic package, the voltage controlled oscillator outputs a signal of 10 MHz. The 10 MHz signal multiplied 9 times in the multiplier enters into the modulator (modulation frequency 136 Hz) to get a small frequency modulation. The modulated signal goes through the SRD frequency multiplier to achieve 76 times multiply. After that, it mixes the 5.3125 MHz signal output from the synthesizer. Finally, we obtain the 6834.6875 MHz modulated microwave signal to interrogate the 87Rb clock transition.

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Fig. 2. Electronic parts of the lamp pumping rubidium vapor-cell clock

The physical’s signal output contains information of the polarized frequency deviation between the microwave signal and atomic clock transition. The information is then conversed into an oscillator signal, locking the frequency-locked loop. Finally, the local oscillator frequency tightly locks to the atomic transition frequency. The system output reaches the same frequency stability as the atomic transition, making it a dependable source of frequency standard. 2.2 Contrast Experiment and Result In order to test the stability under the atmospheric environment, we designed an environmental platform shown in Fig. 3 which can simulate the environment of vacuum test and atmospheric. The platform is able to quantitatively change the internal pressure that would be useful to test the sensitivity of pressure.

Fig. 3. Environmental platform

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We compare the Rb clock’s frequency stability performances in vacuum and test atmospheric environment. The results are shown in Fig. 4.

Fig. 4. Frequency stability contrast result of vacuum environment and atmospheric environment

Compared with the vacuum test environment, the Rb clock frequency performance under atmospheric condition shows more instability. Especially for long-term stability, the Rb clock frequency stability can reach 6.1 × 10−15 at 104 s and 2.5 × 10−15 at one day in vacuum, but only 5.5 × 10−14 at 104 s (about 10 times worse) and 2.5 × 10−13 at one day (about 40 times’ worse) in the atmospheric environment.

3 Analysis of the Effects on Stability In the atmospheric environment, due to the influences of temperature, atmospheric pressure, electromagnetic field, the working environment of Rb clock is worse than the satellite-borne environment which is vacuum and temperature-controlled. As a result, the performance of rubidium clock is seriously deteriorated. After measurement and evaluation, Neither the shot noise nor intermodulation effect is√the main factor that ruins √ the performance. The instability of each noise is 5 × 10−13 / τ and 4.5 × 10−13 / τ . And the influence on long-term is about 1 × 10−15 at one day. Therefore, environment sensitivity is the main source of instability in atmospheric environment, such as collision frequency shift, cavity-pulling effect, second-order Zeeman effect, light shift, microwave power frequency shift, etc. [3, 4]. The influence on output frequency of these physical

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processes can be quantified as sensitivity coefficients. These sensitivity coefficients will be different when it works in different system schemes and structures [5]. Under atmospheric condition, we monitor cell temperature, lamp temperature, light intensity, atmospheric pressure and other relevant parameters. Then we will analyze the influence of physical effects and estimate the instability contribution from each effect on Rb clock output frequency. 3.1 Barometric Effect The barometric effect is the collision frequency shift of the buffer gas [6, 7]. We can get the correlation between the pressure and the Rb clock output frequency by changing the internal pressure of the environmental platform, as shown in Fig. 5 and Fig. 6. There is a strong correlation between the changes in pressure and frequency. With linear fitting, we obtain that the pressure sensitivity coefficient is 1.17 × 10−13 /hPa.

Fig. 5. Pressure changing in environmental platform

Fig. 6. Frequency with pressure changing

3.2 Temperature Coefficients There are two temperature-controlled zones in physical package. One is the lamp cell in the lamp, and the other is absorption and filter cells in the microwave cavity. And the temperature coefficient of physical package is affected by the lamp and the microwave cavity (absorption cell and filter cell). Because the vapor cell containing the atoms and buffer gases is placed inside a microwave cavity. Microwave cavity temperature can also be written as ‘cell temperature’ in this paper for their equal values. Temperature fluctuations in the vapor cell impact the clock frequency through the temperature dependent buffer-gas pressure shift and via buffer-gas density changes in the cell. And the influence is determined by the gas material and internal pressure of each cell [8, 9]. According to the designed system parameters, the temperature coefficient of the buffer-gas is 2 × 10−11 /◦ C. And the temperature stability of microwave cavity is shown as Fig. 7.

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Fig. 7. Temperature stability of cell

Due to the cavity feedback on the atoms and because of detuning of the cavity from νRb , the cavity pulling effect arises. The cavity pulling shift can be calculated as Formula 1: α QL υ cav υ CP = υ0 1 + S Qa υ 0

(1)

The detuning between microwave resonance frequency and atomic transition frequency can be expressed as υcav . QL means the Q value of microwave cavity, and Qa means the Q value of microwave resonance transition line. α means closeness to the active oscillation threshold, and S is saturation factor. So, the slotted-tube cavity frequency shift coefficient of temperature is measured: TC = 51 kHz/◦ C. Slotted-tube microwave cavity’s Q value QL is about 400. And the linewidth of microwave resonance transition is about 750 Hz. Then the cell temperature coefficient of cavity-pulling effect is 1.1 × 10−12 /◦ C. By affecting atomic collisions, the variation of the spectral lamp temperature brings shape distortion of spectral line and light intensity fluctuation, then produces frequency shift. And the lamp temperature coefficient is 1 × 10−11 /◦ C. The stability of lamp temperature is shown as Fig. 8. 3.3 C Field The C field influence on the long-term stability is generally caused by the second-order Zeeman frequency shift. The magnetic field B includes the combination of contributions from the applied quantization magnetic field B0 , the residual field Br and the field related to the noise of the magnetic shields Bs . We measured the frequency shift is 2 Hz after the system applied C field. For B0 is 5.9μT , the coefficient of magnetic field is 9.9×10−5 /T, Br is the remained field after shielded the external fluctuations. It is about 10 pT in our experiment.

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Fig. 8. Stability of lamp temperature

3.4 Light Shift The light intensity fluctuation of the lamp output produces a light shift [10]. The measured result shows that every 10% changes will lead to 1 × 10−11 frequency shift. And the fluctuation of light intensity is 5.5 × 10−5 at one day, as shown in Fig. 9.

Fig. 9. Stability of light intensity

3.5 Microwave Power Shift Microwave power shift happens due to the fact that atoms are relatively motionless during the microwave interaction time so that spatial gradients can cause line inhomogeneity effects inside a microwave cavity. The inhomogeneity of light field, C field and microwave field causes the shift on the clock hyperfine frequency which will further affect the long-term stability of frequency [11].

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A special method for measuring intracavity microwave power for rubidium clock with the intracavity-frequency-multiplication method is proposed in the research [12]. The sensitivity of rubidium clock to microwave power is 2 × 10−12 /dB, and the average fluctuation of microwave power is 5 × 10−4 dB at one day. 3.6 Total Evaluation of Stability Under the atmospheric condition, Evaluation of long-term instability is shown as Table 1. Table 1. Contribution evaluation of relevant effects on long-term instability Effects

Fluctuation at one day

Sensitivity coefficient

Stability at one day

Barometric effect

2.1 hPa

1.2 × 10−13 /hPa

2.4 × 10−13

Cell temperature effect

2.5 × 10−3 °C

2.1 × 10−11 /◦ C

5.3 × 10−14

Lamp temperature effect

9.8 × 10−3 °C

1.0 × 10−11 /◦ C

9.8 × 10−14

C-field

10 pT

9.9 × 10−5 /T

9.9 × 10−16

Light shift

5.5 × 10−5

1.0 × 10−11 /10%

5.5 × 10−15

Microwave power frequency shift

5.0 × 10−4 dB

2.0 × 10−12 /dB

1.0 × 10−15

Shot noise

1.7 × 10−15

Intermodulation noise

1.5 × 10−15

Total

2.6 × 10−13

Measure result

2.1 × 10−13

According to above results, the total evaluation is basically equivalent to the measurement. And the main cause of long-term instability under atmospheric condition are pressure and temperature, whose sensitivity coefficients and parameter fluctuations will be optimized in following improvement.

4 Testing Result of High-Performance Prototype in Atmospheric Environment Based on above analyzing, we rebuild the system, optimized relevant parameters, designed an anti-atmospheric device to decrease the barometric sensitivity, improved the thermal property of the system. Finally, we succeed the development of highperformance Rb clock prototype working in atmospheric environment, and measured its stability.

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4.1 Improvement of Pressure Sensitivity We repeat the pressure changing experiment, verify the improvement of pressure sensitivity as Fig. 10 and Fig. 11. In Fig. 10, the pressure changes in environmental platform, and Fig. 11 shows the frequency shift. Analyzing the result, the prototype’s pressure coefficient is 2.45 × 10−15 /hPa, which has been improved by 50 times.

Fig. 10. Pressure changing in environmental platform

Fig. 11. Frequency with pressure changing

4.2 Improvement on Temperature We optimize the temperature sensitivity, measure the output frequency shift under different lamp and cell temperatures, as shown in Fig. 12:

Fig. 12. Frequency shift of different lamp and cell temperature

In different cell temperature points, the figure shows different curves with lamp temperature changing. We can find all the curves converge nearly on one point, and its X-axis (lamp temperature) is 110.8 °C. At the same time, curve of cell temperature

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66.3 °C is the smoothest. Therefore when the lamp temperature is 110.8 °C and the cell temperature is around 66.3 °C, there will be the temperature coefficient’s zero-point. We adjust the parameters of lamp and cell temperature to above value, optimize the cell temperature coefficient to 4.0 × 10−12 /◦ C, lamp temperature coefficient to 3.2 × 10−12 /◦ C. 4.3 Improvement of Stability Testing the frequency stability in atmospheric environment, we monitored the atmospheric pressure and physical package’s temperature. There is an average pressure fluctuation shows 1.3 hPa at one day, which estimates 3.1×10−15 instability at one day. And there is an average fluctuation of cell temperature shows 2.7 × 10−4 ◦ C at one day as Fig. 13, which estimates 1.1 × 10−15 instability at one day. At the same time, there is an average fluctuation of lamp temperature shows 2.6×10−4 ◦ C at one day as Fig. 14, which estimates 8.3 × 10−16 instability at one day. Both the barometric effect and temperature effect have been effectively improved, which means the long-term stability budget can reach the level of 10−15 at one day.

Fig. 13. Stability of cell temperature

Fig. 14. Stability of lamp temperature

Finally, under atmospheric condition, we measured the frequency stability of prototype as shown in Fig. 15. √ Form above. The short-term stability reached 6.5 × 10−13 / τ , and the long-term stability is 7.0 × 10−15 at 1 × 104 s and 5.0 × 10−15 at one day time scale.

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Fig. 15. The tested frequency stability of prototype under atmospheric condition (15 days’ frequency data)

5 Conclusion The high-performance rubidium atomic clock prototype operated under atmospheric √ condition has reached the stability of 6.5 × 10−13 / τ . The long-term stability performance is at the level of 10−15 for 7.0 × 10−15 at 1 × 104 s and 5.0 × 10−15 at one day. And there is a 10 times improvement at 1 × 104 s and 40 times improvement at one day. For the first time, the frequency stability of vapor-cell rubidium clock working in atmospheric environment reaches the level of 10−15 . And the performance of prototype still has the potential to be improved. Acknowledgement. This research is support by the National Natural Science Foundation of China (NSFC 11803073).

References 1. Mei, G., Zhong, D., An, S., et al.: IEEE 2016 European Frequency and Time Forum (EFTF)York, United Kingdom (2016.4.4–2016.4.7). 2016 European Frequency and Time Forum (EFTF)-Main features of space rubidium atomic Frequency standard for BeiDou Satellites, pp. 1–4 (2016)

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2. Wang, P., Wang, C., He, S., et al.: A slotted-tube microwave cavity for HIGN performance miniaturized rubble frequency standards. Chin. J. Magn. Reson. 33(3), 452–457 (2016) 3. Shen, Q., Lin, H., Deng, J., et al.: Pulsed optically pumped atomic clock with a medium- to long-term frequency stability of 10−15 . Rev. Sci. Instrum. 91(4), 045114 (2020). https://doi. org/10.1063/5.0006187 4. Almat, N., Gharavipour, M., Moreno, W., et al.: Long-term stability analysis towards n · MAD, big error can be found. There will be phase jump in the long-term operation of the satellite clock [2]. The construction mode of the inter-satellite link is many to many. If the master clock of a satellite is abnormal, the inter-satellite clock difference measured after the construction of the link will jump. Therefore, in the evaluation process, if the evaluation result of the inter-satellite clock difference between the satellite and other satellites decreases significantly, it can be judged that the satellite clock has a jump.

4 Evaluation Method Generally, frequency accuracy, frequency drift rate, ten thousand second stability and day stability are used to evaluate the performance of on orbit satellite clock. The frequency stability index can be evaluated by using inter-satellite clock difference data. The frequency stability of the satellite clock represents the random fluctuation of the output frequency of the frequency source. In order to improve the confidence of the calculation results, the overlapping Allan variance and overlapping Hadamard variance after deducting the drift are generally used to calculate the stability. for {xi }, number is N , N = M + 1. Data sampling interval is τ0 , Variance calculation average sampling interval is τ = m × τ0 , Allan is: σy2 (τ ) =

N −2m  2 1 xi+2m − 2xi+m + xi 2 2(N − 2m)τ

(4.1)

i=1

1 ≤ m ≤ int(M /2). σy (τ ) is frequency stability, ADEV . The clock error data of more than three satellites compared at the same time can be obtained by using the inter-satellite link, and the frequency stability of the on-board clock can be calculated by using the 3-triangle hat method or the polygon hat method. For the overlapping Allan of two relatively independent clocks in the interval, Eq. (4.2) can be obtained, where is the mathematical expectation.       (4.2) E σij2 = E σi2 + E σj2 When the number of clocks is 3, Eq. (4.3) is from Eq. (4.2). ⎧ 2 ⎪ σ = σi2 + σj2 ⎪ ⎨ ij σjk2 = σj2 + σk2 ⎪ ⎪ ⎩ 2 σik = σi2 + σk2

(4.3)

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The variance of each clock is shown in Eq. (4.4) ⎧  1 2 2 2 2 ⎪ σ σ = + σ − σ ⎪ i ij ik jk ⎪ ⎪ 2 ⎪ ⎨  1 2 σij + σjk2 − σik2 σj2 = ⎪ 2 ⎪ ⎪   ⎪ ⎪ ⎩σ2 = 1 σ2 + σ2 − σ2 ij k jk 2 ik When the number of clocks is more than 3, can get Eq. (4.5) [9]. ⎞ ⎛ ⎧ N  ⎪ 1 ⎪ 2 ⎪ ⎪ σij2 − B⎠ ⎪ σi = N − 2 ⎝ ⎪ ⎨ j=1 ⎛ ⎞ ⎪ N N ⎪   ⎪ 1 ⎪B = ⎝ ⎪ σkj2 ⎠ ⎪ ⎩ 2(N − 2) k=1

(4.4)

(4.5)

j=1

5 Simulation Result The overlapping Allan variance is calculated by using IGS precise clock error product GPS satellite in April 2017, and its frequency stability is shown in Fig. 2 (Table 1).

Fig. 2. GPS Overlapped Allan

The 1, 6, 10, 30, 15, 17, 29, 31 satellites are selected to simulate the inter-satellite clock error. Among them, the first four stars are IIF with the same performance, the last four stars are IIRM, and the first four stars are better than the last four stars in the stability. The fitting residual value (RMS) of the (1h) inter-satellite relative clock error of the link is between 0.03 ns and 0.22 ns, with an average value of 0.13ns. The residual value adopted is basically consistent with that of beidou-3 inter-satellite link [7] (Table 2).

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Table 1. Results of satellite on-board clock evaluated GPS type/clock type

10000 s frequency stability

Day frequency stability

GPSIIR, RM/Rb

3.4 × 10–14 to 8.4 × 10–14 3.0 × 10−14 to 4.6 × 10–14

1.1 × 10−14 to 5.0 × 10–14

GPSIIF/Rb

1.4 × 10−14 to 8.1 × 10–15

Table 2. RMS of inter-satellite 2-lever fitting error F PRN06

0.03

IIF PRN10

0.09

0.07

IIF PRN30

0.03

0.04

0.07

IIRM PRN15

0.12

0.12

0.14

0.13

IIRM PRN17

0.17

0.18

0.19

0.22

0.2

IIRM PRN29

0.13

0.13

0.14

0.13

0.16

0.2

IIRM PRN31

0.11

0.12

0.16

0.14

0.14

0.17

0.1

IIF PRN01

IIF PRN06

IIF PRN10

IIF PRN30

IIRM PRN15

IIRM PRN17

IIRM PRN29

The polygon hat method is used to calculate two types of satellite clocks in two groups. From Eq. (4.5) can get Eq. (5.1) (Tables 3 and 4): ⎧  1  1 2 2 2 2 2 2 ⎪ σ12 + σ13 σ23 − + σ14 + σ24 + σ34 ⎪ σ12 = ⎪ ⎪ 3 6 ⎪ ⎪   1  ⎪ 1 ⎪ 2 2 2 2 2 2 2 ⎪ σ12 + σ23 + σ24 − σ13 + σ14 + σ34 ⎨ σ2 = 3 6 (5.1)   1  1 ⎪ 2 2 2 2 2 2 2 ⎪ ⎪ σ + σ23 + σ34 − σ + σ14 + σ24 σ3 = ⎪ ⎪ 3 13 6 12 ⎪ ⎪     ⎪ ⎪ ⎩σ2 = 1 σ2 + σ2 + σ2 − 1 σ2 + σ2 + σ2 4 14 24 34 12 13 23 3 6 Through the simulation of inter-satellite clock error, the IIRM is stable between 4.1e-14 and 6.8e-14. IIF is stable between 1.9e-14 and 4.8e-14 in 10000 s. In addition, the simulated PRN29 satellite are abnormal, so the clocks connected with them all jump, so the clock difference between satellites can quickly locate the abnormal clocks. In reference 7, the precise clock error evaluation results of MEO satellite from December 2018 to February 2019 show that the ten thousand second stability of beidou3 rubidium clock is better than 5e-14, with an average of 3.4e-14, and the ten thousand

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IIF PRN06

4.1E-14

IIF PRN10

3.3E-14

IIF PRN30

4.4E-14

3.1E-14

3.2E-14

IIRM PRN15

4.2E-14

3.3E-14

3.6E-14

IIRM PRN17

3.7E-14

IIRM PRN29

5.1E-14

IIRM PRN31

4.2E-14

4.3E-14

3.0E-14

3.7E-14

4.2E-14

5.6E-14

5.7E-14

Satellite clock

IIF PRN01

IIF PRN06

IIF PRN10

IIF PRN30

IIRM PRN15

IIRM PRN17

IIRM PRN29

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

2.8E-14

5.6E-14 4.6E-14

5.2E-14 4.3E-14

3.0E-14 6.0E-14 5.3E-14

5.8E-14 6.0E-14

6.5E-14 —

Table 4. Day frequency stability by evaluating inter-satellite IIF PRN06

7.8E-15

IIF PRN10

6.8E-15

IIF PRN30

8.7E-15

IIRM PRN15

9.5E-15

IIRM PRN17

2.4E-14

IIRM PRN29

2.6E-14

2.4E-14

2.4E-14

2.4E-14

1.8E-14

2.3E-14

IIRM PRN31

2.3E-14

2.4E-14

2.1E-14

2.4E-14

1.6E-14

2.6E-14

2.3E-14

Satellite clock

IIF PRN01

IIF PRN06

IIF PRN10

IIF PRN30

IIRM PRN15

IIRM PRN17

IIRM PRN29

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

7.2E-15 4.4E-15 8.8E-15 2.5E-14

7.6E-15 9.9E-15 2.3E-14

1.1E-14 2.7E-14

1.7E-14

—

second stability of hydrogen clock is better than 5.0e-14, with an average of 1.8e-14. Rubidium clock is better than 2.0e-14 in day stability, with a mean value of 3.39e-14 in ten thousand seconds and 1.62e-14 in day stability, hydrogen clock is better than 7.0e-15

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Fig. 3. GPS overlap Allan

Table 5. Overlapped Allan and 2-level fitting error by evaluating inter-satellite the result table of frequency stability by polygon hat method Fisrt Group

10000s

Day

IIF PRN01

4.73E-14

6.28E-15

IIF PRN06

2.99E-14

3.76E-15

IIF PRN10

1.98E-14

5.10E-15

IIF PRN30

3.80E-14

4.93E-15

Second Group

10000s

Day

IIRM PRN15

4.81E-14

3.22E-15

IIRM PRN17

6.55E-14

1.78E-14

IIRM PRN29

6.78E-14

1.57E-14

IIRM PRN31

4.17E-14

1.71E-14

in ten thousand seconds and 1.78e-14 in ten thousand seconds, with a mean value of 5.2e-15 in day stability. All of them meet the design index of 2.0e-14 for rubidium clock and 7.0e-15 for hydrogen clock. The precise clock error evaluation results of September 2019 MEO satellite show that the day stability of the rubidium clock of beidou-3 is better than 3.4e-14, with an average of 1.7e-14, and the day stability of the hydrogen clock is better than 8.6e-15, with an average of 6.7e-15 [10]. The on-board phase comparison data can objectively reflect the performance of the on-board clock in real time, but it is difficult to obtain for a long time. It is difficult to distinguish the 10 000 s stability of E-15 level from the two-way link noise of satellite

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ground radio. The inter-satellite clock difference can meet the E-15 level evaluation of the ten thousand second stability of the on-board clock. Figures 3 and Table 5 show the analysis results of cat1.0 [11].

6 Summary To sum up, the inter-satellite link is an important part of the Beidou satellite navigation system. In the aspect of performance evaluation of on-board atomic clocks, although the data of inter-satellite link returned has delay, inter-satellite clock error can still be used as an important source for frequency stability evaluation. At present, ISL data is mainly used in autonomous navigation, clock error prediction and so on. The application of this data needs to be further explored, such as precise point positioning, clock life assessment, deep space exploration and so on.

References 1. Zhen, J., Lin, Y.: GPS crosslink technology and autonomous navigation algorithm analysis. Spacecraft Eng. 18(2), 28–35 (2009) 2. Yupu, W., et al.: The long-term performance analysis for on-board atomic clocks of BDS. Acta Geodaetica et Cartographica Sinica 46(2), 157–1693 (2017) 3. Sun, G., et al.: Performance evaluation of spaceborne atomic clock for BDS-3 basic system. In: China Satellite Navigation Conference (CSNC) 2020, Chendu, vol. 3, pp. 3–15 (2020) 4. Fen, C.: Analysis of correlation between clock offset and environmental temperatures of stations for TWSTFT. J. Time Freq. 36(3), 148–155 (2013) 5. Pan, J.: System error calibration for time division multiple access inter-satellite payload of new-generation Beidou satellites. Sci. China Press 62(23), 2671–2679 (2017) 6. Ruan, R., et al.: Integrated orbit determination and time synchronization for BDS-3 satellites with satellite-ground and inter-satellite one-way Ka-pseudoranges. Acta Geodaetica et Cartographica Sinica 49(3), 292–299 (2020) 7. Guo, S., Cai, H., et al.: BDS-3 RNSS technical characteristics and service performance. Acta Geodaetica et Cartographica Sinica 48(7), 810–821 (2019) 8. Zhou, S., et al.: Status of satellite orbit determination and time synchronization technology for global navigation satellites system. Acta Astronomica Sinica 60(4), 32-1–32-10 (2019) 9. Bai, S.-S., Dong, S.-W., et al.: Research on the method of performance monitoring and evaluation for active hydrogen maser. Acta Astronomica Sinica 10. Shen, L., et al.: Performance evaluation of spaceborne atomic clock for BDS-3 basic system. In: China Satellite Navigation Conference (CSNC) 2020, vol. 3, pp. 3–14 (2020) 11. Bin, Y., et al.: Software design and application of the high precision time frequency data analysis tool. In: China Satellite Navigation Conference (CSNC), Harbin (2018)

Relativistic Effect in the Two-Way Time Comparison Between Navigation Satellites Leyuan Sun1,3 , Shuaihe Gao2(B) , Jun Yang1 , Feng Xiao3 , Yuankun Fang3 , and Sen Feng4 1 National University of Defense Technology, Changsha 410073, China 2 National Time Service Center, Xi’an 710600, China

[email protected]

3 Xichang Satellite Launch Center, Xichang 615000, China 4 Beijing Institute of Remote Sensing Information, Beijing 100094, China

Abstract. Influenced by the high-speed of satellites and the gravitational field of the earth, the satellite-borne clock is affected by the effect of special and general relativity. The classic Newtonian theory in the earth space only achieves timetransfer accuracy within 1 × 10–8 , which is far from matching the performance of the current satellite-borne clock and satisfying inter-satellite time comparison accuracy. This paper has studied the inter-satellite two-way time comparison under the framework of relativity, and the real data of inter-satellite links is used to analyze the relativistic effect of the Beidou-3 inter-satellite two-way time comparison. The results have demonstrated that the gravitational delay of the inter-satellite measurement signal caused by the central gravity of the earth reaches the order of sub-nanosecond, but the asymmetry of gravitational delays in the two-way time comparison is only 0.01 ps which can be ignored with the sub-nanosecond time comparison accuracy; the amplitude of the periodic relativistic effect introduced by the central gravitational field of the earth is about ±1~ ±2 ns, which must be corrected as a systematic error; the periodic relativistic effect introduced by the gravitational J 2 perturbation of the earth reaches ±0.1 ns, which needs to be compensated with the time comparison accuracy of the sub-nanosecond order. In the currently released satellite precision clock products and broadcast ephemeris, only the relativistic effect correction caused by the central gravitational field of the earth is considered. With the continuous improvement of the performance and time transfer accuracy of the spaceborne atomic clock, further consideration of the relativistic effect modification from gravitational J 2 perturbation of the earth is required. Keyword: Inter-satellite Link · Two-way time comparison · Relativistic effect

1 Introduction For updating the ephemeris of Medium Earth Orbit (MEO) satellites periodically, BeiDou-3 satellites have been equipped with two-way inter-satellite links (ISLs). Combining two-way time comparison through satellite-ground links and ISLs, the clock errors © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 95–104, 2021. https://doi.org/10.1007/978-981-16-3146-7_10

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in arcs overseas have been measured and the prediction precision of the clock errors in re-entry arcs has been promoted significantly [1]. The precision of inter-satellite two-way time comparison through BeiDou-3 ISLs reaches sub-nanosecond and of the satelliteborne atomic clock reaches 1 × 10–11 [2]. The operation of satellite-borne atomic clocks is influenced by the special and general relativity because of high-speed motions and the gravitational field. The classic Newtonian theory in the earth space can only achieve time-transfer accuracy within 1 × 10–8 , which is far from matching the performance of the current satellite-borne clock and satisfying inter-satellite time comparison accuracy. Therefore, the time measurement and transmission of satellite clocks should be studied in the relativistic framework. Liu [3] and Petit [4] have studied the two-way time comparison with picosecond precision in the relativistic framework. The relativistic effect in the time reference establishment of the navigation constellation was researched by Liu [5]. Ren [6] has analyzed the general relativity of navigation satellites on post-Newtonian approximation theory. Kouba [7–9] has introduced the relativity correction models of satellite clocks influenced by the central and J2 gravitational potential of the earth and analyzed the relativistic effect of GPS and Galileo satellite clocks. Based on the work of [7–9], this paper has established inter-satellite two-way time comparison model in the relativistic framework, and analyzed the relativistic effect with ISL data. The International GNSS Service (IGS) clock product and navigation message only consider the relativistic effect of the earth’s central gravitational potential. According the conclusion, the relativistic effect of earth’s J 2 gravitational perturbation should be further corrected with the precision promotion of satellite-borne clocks and time transmission.

2 Relativistic Effect of Satellite-Borne Clocks There are proper time and coordinate time in the time-space measurement with the framework of general relativity. The proper time could be realized by an atomic clock according to the definition of the second, and used for local time measurement. The coordinate time is determined by the time-space metric of the overall coordinate system and used as a time-like coordinate. The general relativity was recommended as the theoretical basis of time-space reference frame and the SI second as the measurement unite of the coordinate by the International Astronomical Union (IAU) in 1991 [3]. The second interval of the Terrestral Time (TT) is definied as the SI second on the rotary geoidal surface. When TT is used as the coordinate time, according to the timesapce measurement metric with post-Newtonian asscuacy, the transformation between the proper of the satellite-brone normal atomic clock and the TT is     v2 c2 dTT (1) − W0 dτ = 1 − V + V + 2 Where, V and V are gravitational potential of the earth and tide potential of the external celestial body of the satellite-borne atomic clock. v is the velocity of the clock in the geocentric inertial coordinate system.

Relativistic Effect in the Two-Way Time Comparison

The gravitational potential of the earth is further described as [10]   n ∞    n

GM⊕ V = aE r · Pnm (sin φ)(Jnm cos mλ + Knm sin mλ) 1− r

97

(2)

n=2 m=0

Where, GM⊕ is the gravitational constant and aE is the equatorial radius of the earth. λ and φ are respectively the longitude and geodetic latitude. Pnm is the associative Legendre polynomial. Jnm and Knm are the gravitational potential coefficients. When the earth gravitational potential is divided into the central and disturbed terms, the former model is simplified as V =

GM⊕ −R r

(3)

R is the disturbed gravitational potential due to the non-spherical earth. With the time transformation accuracy in the order of sub-nanosecond, only the central gravitational potential of the earth is considered. According to the two-body motion, the relationship is obtained   2 1 − (4) v2 = GM⊕ r a a is the semi-major axis of the satellite orbit. Plug the relationship into (1) and integrate, we get     3 GM⊕ 2 TT = 1 − W0 − c2 (τ − τ0 ) + 2 aGM⊕ · e sin E (5) 2 a c Where, e is the orbital eccentricity and E is the eccentric anomaly. The first term of the above equation demonstrates the normal frequency of the satellite clock diverges from the TT because of the relativistic effect. The frequency deviation is compensated before launching. The second term is the Conventional Periodic Relativistic Correction (CPRC) of the satellite clock δ per = −

2 aGM⊕ · e sin E c2

(6)

The CPRC is corrected by the IGS clock product and navigation message, and the correction precision reached the level of 0.1 ns [8]. The CPRC also should be corrected in the inter-satellite two-way time comparison. Equivalent to (6), the CPRC model based on the position and velocity in the geocentric inertial coordinate system is δ per = −

2r · v c2

(7)

With the performance promotion of satellite clocks, time transformation with higher precision is required. In the transformation precision of picosecond, V + V is ignored except for the J 2 term   aE2 3 2 3 2 1 (8) R = GM⊕ 3 J2 − sin i cos 2u + sin i − r 4 4 2

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Where, i is the orbital inclination and u is the argument of latitude. Integrate (1) again, the transformation is obtained [9]     3 GM⊕ 2 c2 (τ − τ0 ) + 2 aGM⊕ · e sin E+ TT = 1 − W0 − 2 a c (9)     2  3 2 1 aE GM⊕ 2 3 1 − J GM a sin i sin 2u − 7 i sin − τ (τ 2 ⊕ 0) 2 a 2 c2 a 2 The frequency deviation of the satellite normal atomic clock caused by the J 2 term is   3 2 7 aE2 J2 GM⊕ 1 − sin i y(J2 ) = 2 a 3 c2 2

(10)

The above deviation is less than the level of 1 × 10–15 for BeiDou MEO satellites, far less than the inherent frequency deviation. Only the periodic relativistic correction caused by the J 2 term should be considered δ per (J2 ) = −

 3 aE2 J GM⊕ a sin2 i sin 2u 2 2 a 2 c2

(11)

3 Relativistic Effect of Two-Way Time Comparison 3.1 Realization of Two-Way Time Comparison With the inter-satellite link system of space division and time division, the dual oneway measurement of a satellite pair is completed in two contiguous half-timeslots as illustrated in Fig. 1. Satellite i sends out a measurement signal at tiSnd . Satellite j receives the signal at tjRev and then sends out another measurement signal at tjSnd which is received by satellite i at tiRev . The sending moments tiSnd , tjSnd and the receiving moments tiRev , tjRev are the local time of satellites. t S1 , t S2 , t R1 and t R2 are the corresponding system times. δ·Snd and δ·Rev are the hardware delay of transmitting and receiving channels. Completing the two-way measurement, two inter-satellite pseudorange functions are established





ρij = c t R1 − t S1 + cxj t R1 − cxi t S1 (12) ρji = c t R2 − t S2 + cxi t R2 − cxj t S2 The former two terms contain geometric transmission delay in vacuum and the systemic errors, e.g., hardware delays and atmosphere delays. The third and forth terms are the satellite clock errors. 3.2 Relativistic Correction of Two-Way Time Comparison When corrected with relativistic effect, the satellite normal atomic clock runs in the speed of TT. When the measurement signal is supposed to transmit in vacuum and TT is

Relativistic Effect in the Two-Way Time Comparison

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Fig. 1. Two-way measurement between satellites

used as the coordinate time, the time-space measurement metric in the geocentric inertial coordinate system with post-Newtonian asscuacy is   

2 ds2 = − 1 − 2U c2 1 + Lg c2 dTT 2     (13) + 1 + 2U c2 dr 2 + r 2 dθ 2 + r 2 sin2 θ dφ 2 Where, θ and φ are respectively the colatitude in the nonrotational geocen

and longitude tric coordinate system. The scaling factor 1 + Lg originates from the transformation from the Geocentric Coordinate Time (TCG) to TT. As to the light signal, let ds2 = 0, the transmitting delay is [4]      T= du c − Lg du c + ωe r 2 sin2 θ dφr c2  

 2  + 1 + r 2 sin2 θ dφr du ωe2 r 2 sin2 θ du 2c3   (14) +2U du c3 φr is the longitude in the rotational geocentric coordinate system, satisfying dφ = ωe dTT + dφr . du is the length increment along the transmission path. The former four terms in (14) is the geometric delay T s , and the last term is the gravity delay δ g , that is T = T s + δg

(15)

For the signal transmitted by satellite i and received by j, the geometric delay is 

 (1 − LG )rj t R1 − ri t S1  s (16) Tij = c rj and ri are the position vectors of the satellites in the geocentric inertial coordinate system. With the precision in the level of picosecond, only the gravity delay caused by earth’s central gravity is considered





 j  2GM⊕ ri t S1 + rj t R1 + d t S1 , t R1 g 3



2U du c = ln S1 (17) δij = c3 + rj t R1 − d t S1 , t R1 ri t i

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Where, d t S1 , t R1 = ri t S1 − rj t R1 . Taking into the periodic relativity of satellite clocks, other systemic errors, and measurement noise, the inter-satellite two-way time comparison function in the relativistic framework is established 





sys ρij = rj t R1 − ri t S1  + cxj t R1 − cxi t S1 + cδij + εij  R2

S2 

R2

S2 (18) sys − rj t  + cxi t − cxj t + cδji + εji ρji = ri t The goal of inter-satellite time comparison is correcting the systemic errors, filtering the random errors ε· , and calculating the relative clock errors xij = xi − xj [2]. The systemic errors are sys

g

per_r

per_ r

per_s

per_s

pco

δij = δjRev + δiSnd + δij + δj + δj − δi (J2 ) − δi (J2 ) + δijato + δij sys g per_r per_r per_s per_s pco δji = δiRev + δjSnd + δji + δi + δi (J2 ) − δj − δj (J2 ) + δjiato + δji (19) which could be corrected by models. The superscript “per_r” and “per_s” mean periodic relativistic corrections respectively for receiving satellites and transmitting satellites. According to the above functions, the relativistic effects in inter-satellite two-way time compassion include the two-way gravity delay term g

g

g

δISL = δij − δji

(20)

Two-way conventional periodic relativistic correction 

  per per_r per_s per_r per_s δISL = δj − δi 2 + δj + δi

(21)

And two-way J 2 periodic relativistic correction 

  per per_r per_s per_r per_s δISL (J2 ) = δj (J2 ) + δj 2 (J2 ) − δi (J2 ) + δi (J2 )

(22)

4 Assessment of Relativistic Effect The inter-satellite link and precise orbit determination data of BeiDou-3 MEO satellites in October, 2019 are collected for relativistic assessment.

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4.1 Gravity Delay The results of precise orbit determination are used for calculating the one-way gravity delay. Figure 2 demonstrates the signal gravity delay transmitted by the satellite C19, which reaches sub-nanosecond. While in the two-way time comparison, only the unsymmetrical gravity delay maters, which is shown in Fig. 3. The unsymmetrical value is in the level of 0.01 ps which could be ignored in the sub-nanosecond two-way time comparison.

Fig. 2. One-way gravity delay

Fig. 3. Two-way unsymmetrical gravity delay

4.2 Conventional Periodic Relativistic Effect For assessing the conventional periodic relativistic effect in the inter-satellite two-way time comparison, the measurement is corrected with systemic errors except for periodic relativistic effect and inter-satellite clock errors are calculated and daily detrended with second-order polynomials. The residual errors in Fig. 4 demonstrate the conventional periodic relativistic effect. The CPRC period is about 12 h, close to the orbital period and the magnitude is ±1~ ±2ns, which should be precise compensated.

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Fig. 4. Conventional periodic relativistic effect in the inter-satellite two-way time comparison. The theoretical values are calculated with (21)

4.3 J 2 Periodic Relativistic Effect For assessing the J 2 periodic relativistic correction (J 2 PRC) in the inter-satellite twoway time comparison, the measurement is corrected with systemic errors except for J 2 periodic relativistic effect and inter-satellite clock errors are calculated and daily detrended with second-order polynomials. The residual errors in Fig. 5 illustrate the J 2 periodic relativistic effect. The period is about 6 h, close to the orbital half-period and the magnitude reaches 0.1 ns.

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Fig. 5. J 2 periodic relativistic effect in the inter-satellite two-way time comparison. The theoretical values are calculated with (22)

5 Conclusion The classical Newtonian theory cannot satisfy the sub-nanosecond inter-satellite time comparison. The inter-satellite two-way measurement models in relativistic framework are established. The relativistic effect in inter-satellite two-way time comparison is further assessed with inter-satellite link data. The two-way gravity delay could be neutralized as common systemic errors depending on the symmetrical paths. The period of conventional periodic relativistic effect is about 12 h, and the magnitude is ±1~ ± 2 ns. The period of J 2 periodic relativistic effect is about 6 h and the magnitude reaches 0.1 ns. The J 2 periodic relativistic effect should be precisely compensated with the precision promotion of inter-satellite measurement and time comparison.

References 1. Pan, J.Y., Hu, X.G., Zhou, S.S., et al.: Time synchronization of new-generation BDS satellites using inter-satellite link measurements. Adv. Space Res. 61(1), 145–153 (2018) 2. Sun, L.Y., Gao, Y., Huang, W.D., et al.: Autonomous time synchronization using BeiDou inter-satellite link ranging. In: IEEE International Conference on Signal, Information and Data Processing (2019)

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3. Liu, L.: Relativistic theory of time transfer and techniques of clock synchronization. Information Engineering University (2004) 4. Petit, G., Wolf, P.: Relativistic theory for picosecond time transfer in the vicinity of the Earth. Astron. Astrophys. 286, 971–977 (1994) 5. Liu, L.L., Wang, Y.K., Chen, J.Y., et al.: Effects of relativity in autonomous time reference for navigation constellation. J. Astronaut. 36(4), 470–476 (2015) 6. Ren, H.F., Jia, X.L., Liu, X.G.: Effects of general relativity for navigation satellites on postNewtonian approximation theory. In: Chinese Satellite Navigation Conference (2010) 7. Kouba, J.: Relativistic time transformations in GPS. GPS Solut. 5(4), 1–9 (2002). https://doi. org/10.1007/PL00012907 8. Kouba, J.: Improved relativistic transformations in GPS. GPS Solut. 8(3), 170–180 (2004). https://doi.org/10.1007/s10291-004-0102-x 9. Kouba, J.: Relativity effects of Galileo passive hydrogen maser satellite clocks. GPS Solut. 23(4), 1–11 (2019). https://doi.org/10.1007/s10291-019-0910-7 10. Wang, J.S., Zhu, K.J., Hu, X.G., et al.: Satellite Orbits Model, Methods and Applications. National Defense Industry Press, Bejing (2012)

Performance Evaluation and Analysis of BeiDou In-Orbit Satellite Atomic Clocks Based on Multiple Source Data Songtao Huangfu(B) , Weisong Jia, Hui Yang, Jin Chang, Lifang Yuan, and Junwu Zhai Beijing Institute of Spacecraft System Engineering, Youyi Road, Haidian District, Beijing 100094, China

Abstract. As a key payload, the performance of the satellite-based atomic clock will have an important impact on the whole navigation system. At present, the on-orbit performance evaluation of satellite-based atomic clocks is mainly based on the precise clock bias products released by IGS MGEX, iGMAS, and other organizations. Due to the influence of space environment changes, equipment aging, and other factors, there are gross errors in the clock bias data. In this paper, we propose a method of using SAIM clock monitoring telemetry data to assist in the detection and rejection of gross errors in the precision clock products, and then select the typical satellites C19, C20, C36, C37, C41, and C42 of Beidou-3 with different life spans to evaluate and analyze the in-orbit performance of rubidium atomic clocks. The multi-source data of Beidou-3 satellites are from 2019-01-01 to 2020-11-21. On this basis, the in-orbit performance of the rubidium atomic clock is analyzed and evaluated in terms of satellite clock stability, frequency accuracy, frequency drift rate, and other indicators. The evaluation results show that the Beidou C19, C20, C36, C37, C41, C42 satellites 10,000 s frequency stability reached the order of 10−14 , frequency drift rate (days) overall in the order of 10−13 , frequency accuracy overall in the order of 10−11 . Keywords: BeiDou satellite · Multiple source · Atomic clocks performance · Evaluation and analysis

1 Introduction As the on-board time reference for navigation system ranging, the satellite-based atomic clock is a key payload of the satellite navigation system, and its performance directly determines the accuracy of navigation positioning and time-frequency transmission and is one of the hot spots for the on-orbit performance evaluation of BeiDou satellites. At present, the main evaluation methods of satellite-based atomic clocks are based on the precision clock bias products released by IGS MGEX, iGMAS, and other organizations, and the long-term characteristic change analysis and quality evaluation of GNSS satellite clocks from the perspective of frequency stability, frequency accuracy and frequency drift rate, etc. [1].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 105–117, 2021. https://doi.org/10.1007/978-981-16-3146-7_11

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During the long-term operation of atomic clocks, gross errors often occur and are reflected in the precision clock bias products. To use and analyze the clock bias data effectively, it is necessary to detect and reject the gross errors. There are studies on detection methods and rejection strategies in the literature [2, 3], but the above processing is based on the precision clock bias products themselves, and a single data source cannot guarantee the rationality of the aberration processing. In this paper, we collect the precision clock bias product data released by IGS MGEX, iGMAS, and other organizations and the telemetry data of satellite autonomous integrity monitoring (SAIM), carry out gross error detection and rejection using multi-source data, and select typical satellites of Beidou-3 with different life spans to evaluate and analyze the in-orbit performance of atomic clocks based on the above algorithm, and give evaluation conclusions.

2 Single-Source Data Gross Error Detection Method The median method (MAD) of literature [2] is used as an example for gross error detection of precision clock bias product data. If the frequency difference observation of  precision clock difference product data is Y = y1 , y2 , ..., yi , ... , then the median can be expressed as: MAD = Median{|yi − Median(Y)|/0.6745}

(1)

When the observation yi > Median(Y) + n · MAD (n is an integer), the observation is considered as a gross error and is eliminated. The method is a simple and effective method for gross error detection, but there exists an integer variable n. In the process, it is found that different evaluation results are obtained with different n selections. Taking BeiDou C19 satellite as an example, its precision clock bias product data from 2019-01-01 to 2021-01-11 is selected, and the overlapping Hadamard variance frequency stability data processing results are shown in Fig. 1 as n changes from 1 to 64 (n changes from small to large corresponding to Color bar changes from blue to red). From the above analysis, the MAD gross error detection method has some subjectivity and the analysis results will be different due to the presence of integer variable n. Other single-source data gross error detection methods also have similar problems and cannot guarantee the rationality and credibility of the gross error processing. For this reason, a satellite clock stochastic model needs to be established, based on which SAIM clock monitoring telemetry data is introduced to research multi-source data gross error detection methods.

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Fig. 1. Results of BeiDou C19 satellite frequency stability analysis after processing by MAD method (n changes from 1 to 64)

3 Satellite Clock Noise Modeling The satellite clock model can be divided into two parts: the deterministic time model and the stochastic model [4], in which the stochastic model reflects the noise of the atomic clock, and the model that conforms best to the experimental data is the powerlaw spectral noise model, which consists of five independent types of noise: FM random wandering noise, FM flicker noise, FM white noise, FM flicker noise, and FM white noise. The noise types of different kinds of satellite clocks are distinct, and the noise types of the same kind of satellite clocks are not the same, and there is a chance that the satellite clock noise types will change as the sampling time changes [5]. This paper covers both the gross error determination and the evaluation of satellite clock performance after error rejection. In order to simplify the research path and facilitate engineering applications, in this paper, the missing values of data sources are processed based on the deterministic time model for interpolation without changing the sampling time of the original data; in the case of clock difference prediction, the prediction results are used for the selection of gross error thresholds and data cleaning without changing the original data content, thus simplifying the atomic clock noise model to Gaussian white noise processing; and then introducing Kalman filtering and multisource fusion gross error detection algorithm. Then, the typical satellites of Beidou-3 with different lifetimes are selected for in-orbit performance evaluation and analysis, and the evaluation conclusions are given. The time difference between the atomic clock and the standard reference source is shown as follows [6]: 1 T (t) = a + bt + ct 2 + ξ (t) 2

(2)

Where a is the clock phase difference between the satellite atomic clock and the standard reference source; b is the frequency difference between the satellite atomic clock frequency and the standard reference frequency; c is the drift rate, which is determined by the change in the nature of the satellite atomic clock itself, ξ (t) is the noise component, and t is the time.

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For data sources, the iGMAS and the Wuhan University precision clock bias products [7, 8], as well as the SAIM clock monitoring telemetry data, are selected in this paper. The SAIM system of the BeiDou satellite includes the clock signal autonomous integrity monitoring module [9], which is like the Time Keeping System (TKS) of GPS [10, 11]. During the generation of the 10.23 MHz clock signal, a hot standby clock is used to provide an accurate reference signal, the two are compared with each other under each ephemeris. The results of phase measurement and anomaly detection are obtained with high accuracy and transmitted via telemetry. In order to ensure the smooth switching between the Primary and Backup clocks on satellite, both the working and hot standby clock signals of some BeiDou satellites’ SAIM system are generated based on the same type of atomic clock, this results in the 10.23 MHz phase measurement not truly reflecting the frequency drift rate. The processing found that the working clock and reference clock product characteristics of good consistency, resulting in SAIM BeiDou satellite frequency drift rate is much lower than the real drift rate. Therefore, this paper is mainly for precision clock bias product data processing, the SAIM clock monitoring telemetry data only to assist in completing the gross error detection and rejection.

4 Gross Error Detection Method Based on Multiple Source Data According to the analysis of the satellite clock noise model in Sect. 3, combined with the fact that the objective of this study is gross error detection rather than accurate prediction, the atomic clock noise model can be simplified to a Gaussian white noise treatment. The Kalman filtering algorithm is introduced for atomic clock parameter estimation and gross error detection. In Eq. 2, a is the clock phase difference between the atomic clock and the standard reference time source; b is the frequency difference between the atomic clock frequency and the standard reference frequency; c is the frequency drift rate. As a result, the expression of the ith sampled state vector xi is shown as Eq. 3. xi = [a(i), b(i), c(i)]T

(3)

The iterative expression for the state vector from the i-1st sample to the ith sample is shown as Eq. 4. xi = Axi−1 + qi−1

(4)

Where, A is the state transfer matrix, which is related to the sampling interval; qi−1 is the three-dimensional noise of clock phase difference, frequency difference, and frequency drift rate, which is only predicted as the threshold and not predicted precisely, so it is considered as three-dimensional zero-mean Gaussian white noise and is temporally uncorrelated with each other. The clock bias measurement for the ith sample is shown as Eq. 5. yi = Hxi + ri

(5)

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Where H is the measurement matrix, ri is the one-dimensional noise, and as above, ri can be considered as zero-mean Gaussian white noise in this case. The prior error variance array of the state vector xi after the ith sampling is shown as Eq. 6. − Pi−1 = APi−1 AT + Q

(6)

 Pi−1 is the posterior error variance array at the previous moment and Q =  Where E qi qiT is the variance array of state noise. The priori estimates of the state vector xi are shown in Eq. 7. − xˆ i− = Aˆxi−1 − Where xˆ i−1 is the Kalman optimal estimate at the previous moment. The estimated value of the state vector at the moment i is shown as follows:   xˆ i = xˆ i− + ki yi − yˆ i

(7)

(8)

yˆ i = Hxˆ i−

(9)

 −1 T ki = Pi− HT HP− H + R i

(10)

 R = E ri riT

(11)

Where yˆ i is the clock bias estimate, ki is the gain matrix, and R is the variance array of the measurement noise. After that, the error variance array Pi = (I − ki H)Pi− is updated for the next moment error variance array. Under a single-source of precision clock bias product data, if its phase difference, frequency difference, and drift rate three-dimensional noise matrix is qi−zc , then Eqs. (12) to (14) are substituted into (4) to (11) as the initial state, and the Kalman optimal estimation results are obtained by continuous iteration [6].  T Q = E qi−zc qi−zc (12) P1 = (I − k1 H)Q

(13)

 −1 k1 = QHT HQHT + R

(14)

In this paper, SAIM clock monitoring telemetry data is used to assist in completing the gross error detection and rejection. The SAIM main and backup clocks are taken as 10.23 MHz phase difference telemetry vectors and converted into 1PPS vectors according to Eq. 15. P1PPS = 10.23e6 × P10.23M

(15)

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The phase difference, frequency difference, and frequency drift rate of P1PPS are processed to obtain the three-dimensional noise matrix qi−SAIM , which replaces qi−zc in Eq. (12) to obtain Eq. (16).  T (16) Q = E qi−SAIM qi−SAIM After that, Eqs. (13), (14) and (16) are substituted into (4)–(11) as the initial states, and the Kalman optimal estimation results are obtained by continuous iteration, and the upper and lower envelopes are taken as the reference of the gross error rejection threshold. However, since both the working and reference clock signals of the Beidou SAIM system are generated based on the same type of atomic clock, the 10.23 MHz phase measurement results of the Beidou satellite do not truly reflect the frequency drift rate. During processing, it was found that the good consistency of the product characteristics of the working and reference clocks resulted in the SAIM 1PPS frequency drift rate is much lower than the real drift rate. Therefore, after replacing qi−zc with qi−SAIM , it was found that the gross error judgment threshold could not change with the frequency drift rate at a long observation time, resulting in the real data being filtered out. To this end, a segmentation filtering and threshold generation strategy is used to determine the segmentation time t1 and determine the gross error rejection threshold according to the atomic clock frequency daily drift rate indicator or the maximum value of the test packet, as follows. 1. Satellite clock frequency drift rate indicator c is used as a priori information (available through indicators or test packets). 2. The SAIM 1PPS frequency difference of P1PPS is processed and its uncertainty std_ bSAIM is obtained according to Eq. 17, where, τ0 is the sampling interval. std_bSAIM = std[diff(10.23e6 × P10.23M )/τ0 ]

(17)

t1

3. Solve for t1 according to Eq. 18. t1 =

2 × std_bSAIM  c

(18) 

4. Correct qi−SAIM according to Eq. 19 and Eq. 20 to obtain qi−SAIM , where qi−SAIM (:, 1) is the 1st column phase difference vector and qi−SAIM (:, 2) is the 2nd column frequency difference vector. 



qi−SAIM (:, 2) = qi−SAIM (:, 2) + c

(19)

1  qi−SAIM (:, 1) = qi−SAIM (:, 1) + c2 2

(20)

5. Replace qi−SAIM with qi−SAIM in Eq. 16 to obtain the Kalman filter result and its upper and lower envelope curves.

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6. The upper envelope of each Kalman filter result is repeated by the maximum value of the group, and the lower envelope is repeated by the minimum value of the group, multiplied by a constant integer (2 is chosen in this paper) as the gross error rejection threshold. 7. When the precision clock difference product data exceeds the gross error detection threshold, the value is suspected to be a wild value, and the moment of its occurrence T is recorded. After that, the SAIM integrity alarm data and maintenance records of T ± 0.1 h are searched for to determine whether the interruption is planned or not, and if there is no alarm or planned interruption, the value is considered to be a wild value and set to NaN (Not a Number). Otherwise, the value is considered not a wild value and is kept, and there is a possibility that the satellite clock is faulty. For the NaN after gross error rejection and the missing data points, the Kalman filtering algorithm is used to predict and interpolate them.

5 Gross Error Detection and Rejection Results Taking the C19 and C20 satellites, the earliest orbiting satellites of BDS-3, as an example (orbited on 2017-11-05 with a one-arrow-two-satellite launch and 1,162 days in orbit as of 2021-1-10 [12]). Selecting the data from 2019-01-01 to 2021-01-01, the results of the clock difference and frequency difference without excluding the gross error are shown in Fig. 2.

Fig. 2. Phase and frequency of BeiDou C19C20 satellite precision clock bias products

The precision clock bias products, the SAIM frequency difference measurement data, and the SAIM frequency stability processing results are shown in Fig. 3. According to the following figure, the C19 satellite SAIM 10,000 s frequency stability reaches 2.55e-15,

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and the C20 reaches 3.16e-15, which indicates that the Primary and the Backup clock have good consistency of product characteristics, but this cannot reflect the real state, so they are not involved in Fig. 5.

Fig. 3. Frequency comparison of Beidou C19C20 satellite precision clock bias products and SAIM clock measurement data & the SAIM frequency stability processing results

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The segment filtering and threshold generation are performed according to the algorithm in Sect. 4, and the results are shown in Fig. 4. From the figure, the algorithm in this paper can effectively eliminate the outliers and avoid the false rejection of useful data.

Fig. 4. Results of gross error detection threshold generation of BeiDou C19C20 satellites

In the MAD method, it can be seen from Fig. 1 that the smaller the n, the better performance of satellite clock frequency stability, but it can be seen from Fig. 4 that there is a false rejection of useful data when n = 1, so n = 2 is the most reasonable, and the MAD processing results under n = 2 are chosen here for comparison. Taking the ground test data as reference, the difference of frequency stability processing between this paper and the n = 2 MAD method is shown in Fig. 5. From Fig. 5, the frequency stability (especially the 10,000-s stability) processing results are closer to the ground test results under the gross error detection and rejection method in this paper, which further proves the effectiveness of the gross error detection and rejection method of multiple data sources in this paper.

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Fig. 5. Comparison of frequency stability processing between this paper and the traditional MAD method

6 In-Orbit Evaluation Results of BeiDou Satellite Atomic Clocks According to the gross error detection and threshold selection strategy in Sect. 5, C19 and C20 satellites with 1162 days in orbit (as of 2021-01-10, the same below), C36 and C37 satellites with 783 days in orbit, and C41 and C42 satellites with 391 days in orbit were selected, and the frequency stability, frequency accuracy, and frequency drift rate evaluation results were obtained after processing as shown in Fig. 6, Fig. 7 and Fig. 8.

Fig. 6. Results of frequency stability assessment of BeiDou satellite clocks (C19, C20, C36, C37, C41, C42)

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Fig. 7. Beidou satellite clock frequency accuracy assessment results (C19, C20, C36, C37, C41, C42)

Fig. 8. Results of frequency drift rate evaluation of BeiDou satellite clocks (C19, C20, C36, C37, C41, C42)

According to Fig. 6, with rubidium atomic clocks as working clocks, the frequency stability of Beidou C19, C20, C36, C37, C41, and C42 satellite clocks is consistent, and the frequency stability of 10,000 s has reached the order of 10−14 . According to Fig. 7, the C20, C36, and C37 satellites were maintained twice between 2019-01-01 and 2021-01-01, and each maintenance adjusted the satellite clock frequency accuracy to near 2e-11. The C19 satellite clock frequency drift rate was better than the other satellites, which were not maintained during the period, and the accuracy changed slowly near 1e-11. The C41 and C42 precision clock differential product data insufficient time, but from the trend, the maintenance frequency should be comparable to C20, C36, and C37 satellites. Satellite clock frequency accuracy maintained at the order of 10−11 overall. According to Fig. 8, the overall satellite clock frequency drift rate (days) is in the order of 10−13 , and the drift rates of C20, C36 and C37 have a trend of gradual convergence,

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so the subsequent maintenance frequency will gradually decrease, which is conducive to the stable operation of the system.

7 Conclusion In this paper, the Kalman filtering and multi-source fusion gross error detection algorithm is introduced to address the shortcomings of traditional single data source gross error detection method processing in terms of rationality and credibility. The following 3 main points are studied. 1. To address the complexity of the atomic clock noise model and to simplify the research path and facilitate engineering applications, the forecast results are considered only for the selection of gross error thresholds and data cleaning, without changing the original data content. In this way, the atomic clock noise model is simplified to a Gaussian white noise treatment as a prerequisite for the introduction of the Kalman filtering method. 2. Using SAIM telemetry data to assist in completing the gross error detection and rejection of precision clock bias products, replacing the SAIM phase difference telemetry vector noise matrix with the precision clock bias product noise matrix as a parameter for Kalman filtering. 3. For the characteristics that the observed frequency drift rate of the SAIM on some satellites (the Primary and Backup clocks are the same type) is much lower than the real drift rate, the satellite clock frequency drift rate which can be obtained through indicators or test packets is introduced as a priori information, and the segmentation filtering and threshold generation strategy is adopted to determine the segmentation time according to the maximum value of the atomic clock daily drift rate indicators or test packets, and the upper and lower envelopes of the Kalman filtering results of each segment are multiplied by a constant. The integer is used as the final gross error rejection threshold. Then, using the ground test data as a reference, we compare the differences between this paper and the traditional MAD method. The results show that the frequency stability (especially the 10,000-s stability) processing results are closer to the ground test results by using this paper’s gross error detection and rejection method. Finally, this paper selects typical satellites C19, C20, C36, C37, C41, and C42 of Beidou-3 with different life spans to carry out the evaluation and analysis of the in-orbit performance of the rubidium atomic clocks and gives the following three evaluation conclusions. 1. The frequency stability of Beidou C19, C20, C36, C37, C41, and C42 satellite clocks is consistent, and the frequency stability of 10,000 s has reached the order of 10−14 . 2. C19 frequency drift rate is an order of magnitude lower than other satellite clocks; C20, C36, and C37 frequency drift rate have a trend of gradual convergence, so the subsequent maintenance frequency will gradually decline, and the system service will be more stable; C41, C42 precision clock bias product data time shortage is not

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yet a visible trend. C20, C36, C37, C41, C42 drift rate is in the order of 10−13 , C19 drift rate in the order of 10−15 . 3. Between 2019-01-01 and 2021-01-01, C20, C36, and C37 satellites were maintained twice, and each maintenance adjusted the satellite clock frequency accuracy to near 2 × 10−11 ; C19 satellite clock frequency drift rate was better than other satellites, and no maintenance was performed during the period, and the frequency accuracy changed slowly around 1 × 10−11 ; C41 and C42 precision clock bias data time are insufficient, but from the trend, the maintenance frequency should be comparable to C20, C36, and C37 satellites. The satellite clock frequency accuracy is maintained in the order of 10−11 .

References 1. Huang, G., Zhang, Q., Li, H., et al.: Quality variation of GPS satellite clocks on-orbit using IGS clock products. Adv. Space Res. 51(6), 978–987 (2013) 2. Yang, Y., Song, L., Xu, T.: Robust estimator for correlated observations based on bifactor equivalent weights. J. Geodesy 76(6–7), 353–358 (2002) 3. Hongchun, L., Xiaochun, L.U., Jianfeng, W.U.: A two-step method for precise detection of satellite clock’s abnormal data. Geomatics Inf. Sci. Wuhan Univ. (2019) 4. Jones, R.J.: Time and frequency metrology. Proc Spie 70(6), 2567–2596 (2001) 5. Jiao, Y., Kou, Y.H.: Analysis, modeling and simulation of GPS satellite clock errors. Scientia Sinica 041(005), 596–601 (2011) 6. Sun G.: Rubidium atomic clock error modeling and forecasting based on parameter constrained Kalman filter. In: 48th Annual Precise Time and Time Interval Systems and Applications Meeting (2017) 7. International GNSS Monitoring & Assessment System Product/Data [EB/OL]. http://www. igmas.org/Product/Search/index/cate_id/38.html. Accessed 03 Jan 2021 8. IGS Data Center of WUHAN University [EB/OL]. http://www.igs.gnsswhu.cn/index.php/ home/dataproduct/mgex.html. Accessed 03 Jan 2021 9. Cao, Y., et al.: Initial analysis of the BDS satellite autonomous integrity monitoring capability. GPS Solut. 23(2), 35 (2019). https://doi.org/10.1007/s10291-019-0829-z 10. Weiss, M, Shome, P., Beard, R.: On-board GPS clock monitoring for signal integrity. In: 42nd Annual Precise Time and Time Interval ( PTTI) Meeting, Reston, USA, November 2010, pp. 15–18 (2010) 11. Wu, W.W., Guo, F., Zheng, J.Z.: Analysis of Galileo signal-in-space range error and positioning performance during 2015–2018. Satell. Navig. 1(1), 1–13 (2020) 12. Beidou Constellation Status [EB/OL]. https://glonass-iac.ru/en/BEIDOU/. Accessed 27 Jan 2021

Research Progress of Inter-satellite Precision Measurement and Time-Frequency Synchronization Technology Based on USO Xuan Liu(B) , Xingwang Zhong, Dalei Xue, Pan Zhang, and Yifeng He Xian National Civil Aerospace Industrial Base, No. 504 Chang’an Eastern Street, Xian 710100, People’s Republic of China

Abstract. Ultra-stable oscillator (USO) is a kind of OCXO with excellent short-term frequency stability performance. It has been gradually applied in the aerospace field such as high-precision measurement and time-frequency synchronization with very good results and exhibited huge application potential in China in recent years. Firstly, the paper outlines the characteristics of USO and the development status at home and abroad. The background of the first use of USO in China and the progress of localization is introduced. Secondly, for high-precision inter-satellite time synchronization requirements, we have achieved inter-satellite time synchronization performance with accuracy better than 0.1 ns using USO and low-orbit GPS receiver. Relevant performance evaluation method and actual measurement results are introduced. Finally, an inter-satellite ranging system combining USO and GPS precision orbit determination with actual measurement performance better than 5 um accuracy is achieved. The overall plan, evaluation mechanism, progress and results are given as well. The article gives the potential application direction of USO in the future, which has certain reference and reference significance for future gravity field detection, gravitational wave detection and load research in other scientific fields in China. Keywords: Ultra-stable oscillator · GPS · Inter-satellite measure · Time synchronization · Gravity field exploration

1 Introduction The precise measurement of the earth’s gravity field shows great application value in oceanography, hydrology, geophysical science and military aspects. Leo satellite tracking Leo satellite technology, referred to as SST-LL, is one of the most effective means of detection of gravitational field [1]. China’s first satellite-based earth gravitational field exploration mission is proceeding in depth. The ultra-stable crystal oscillator (USO) onboard is a key stand-alone product that provides time and frequency for the two core payloads of K-band range (KBR) and GPS receiver, thus its short-term frequency stability performance determines the accuracy of inter-satellite measurement and precise orbit determination. USO is an OCXO crystal oscillator with excellent short-term frequency stability performance. It can provide 10–13 order of frequency stability (Allan variance © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 118–127, 2021. https://doi.org/10.1007/978-981-16-3146-7_12

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index) within the time range of 1 s–1000 s, and has extremely low phase noise with huge application potential in the field of precision measurement and timing technology. There are only a handful of manufacturers that can develop aerospace-grade USO in the world, and the Applied Physics Laboratory (APL) of Hopkins University in the United States is a typical representative. APL’s products are widely used in NASA’s many low-orbit earth observation satellites, deep space exploration vehicles and other aerospace precision payloads, with superior performance. Based on the demand of China’s first-generation earth gravity field detection satellites, the Xi’an Branch of the Chinese Academy of Space Technology (CAST) began to track and study USO technology at the end of the “Eleventh Five-Year Plan”. For aerospace applications, CAST-USO has been continuously optimized and improved in terms of miniaturization, low power consumption and high stability. In 2017, CAST-USO with international advanced levels was successfully developed. Relevant payload applying this USO product has realized the micronlevel precision ranging capability and the centimeter-level precision level of precise orbit determination. The time synchronization and high-precision ranging technology involved in this article are all researches based on the low-orbit binary satellite gravity detection satellite mission (Fig. 1 and Table 1). Table 1. Allan variance comparison of APL-USO and CAST USO Technical index

APL-USO For GRACE [2]

APL-USO For GRAIL [3]

CAST-USO

Allan variance

2 × 10–13 (2s)

9 × 10–14 (1s)

1.2 × 10–13 (1s)

1.8 × 10–13 (10s)

8 × 10–14 (10s)

1.4 × 10–13 (10s)

1.8 × 10–13 (100s) 3.5 × 10–13 (1000s)

1.1 × 10–13 (100s) 2.7 × 10–13 (1000s)

2.8 × 10–13 (100s) 3.5 × 10–13 (1000s)

Fig. 1. USO product of CAST (left) and APL

2 GPS-Based Time Synchronization 2.1 Principle In order to meet the KBR micron-level ranging accuracy, for K-band signal, the phase measurement resolution is required to be 10–4 cycles [4]. For this reason, KBR uses a

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difference frequency phase measurement system, in which two K-band radio frequency signals are mixed to obtain an intermediate frequency signal witch the signal period greatly expanded. Based on the principle that mixing does not change the phase variation, measuring the phase of the intermediate frequency signal can represent the phase of K radio frequency. As a result, phase measurement accuracy is greatly improved. For a single satellite, the influence of the time scale error on the ranging is shown in formula (1.1) which is a linear relationship and can be expressed as: e = fbp × te

(1.1)

Among them, fbp = 502 KHz is the frequency of intermediate signal te = t1 − t2 is the time-tag error of KBR measurements of the two low obiters. To make  the phase measurement accuracy better than 10–4 cycle, time-tag error te ≤ e fbp . It  can be gotten that te ≤ 10−4 5 × 105 ≈ 0.15 ns. So, the synchronization accuracy of the time of KBR measurements should be better than 0.15 ns In order to obtain the phase measurement accuracy of 10–4 cycle (Fig. 2).

Fig. 2. General view of high-low track link between GRACE and GPS satellites

Refer to the design of GRACE, we can use GPS receiver with USO to obtain highprecision pseudo-range and carrier phase observations. The measured GPS carrier phase accuracy is better than 2 mm (1σ). Using post-event IGS precision ephemeris (orbit accuracy 2–3 cm, clock difference 0.2 ns) and precision carrier observations, and using the receiver clock error characteristics to establish a simple dynamic equation, and using Kalman filter to estimate the parameters of the observation value to detect gross errors and cycle slips and using damped LAMBDA to solve the whole cycle ambiguity, GPS post-processing can obtain extremely high-precision differential orbit information and inter-satellite time difference data by defining different weights between dynamic orbit determination and geometric orbit determination [5–7]. 2.2 Verification As shown in Fig. 3 below, a test verification system is independently developed and built in which a dual-frequency dual-channel GNSS simulator is used to simulate the GPS

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satellite signal in orbit and the receiver runs the GRACE satellite orbit. The integrated design of KBR and GPS receiver makes the K-band signal and GPS signal synchronized sampling (the alignment accuracy of the time tag is better than 30 ps) to ensure that the time difference obtained based on GPS POD processing can represent the sampling time of the dual-satellite K-band signal.

Fig. 3. The method of evaluating time difference precision based on USO and GPS POD

Firstly, the performance of GPS original observations is analyzed. As shown in Fig. 4, the accuracy of GPS-L1’s C/A code pseudorange is about 21 cm, and the carrier phase pseudorange accuracy is better than 1mm. Secondly, a time interval analyzer with 20 ps accuracy is used to measure the time difference of the falling edge of 1pps outputted from the AB satellite KBR-GPS integrated receiver as the truth value of time difference. We should note that the 1pps is the measurement sampling clock inside the integrated receiver. The time difference obtained from GPS precision orbit determination postprocess is considered as the actual value is obtained aligning and by second and the std is counted as shown in Fig. 5. We can see the accuracy is about 0.03 ns. The average value −62 ns shown in the figure is caused by the inconsistent channel delay of the AB receiver and the inconsistent radio frequency cable delay. Through calibration, the average value can be controlled within ±10 ns which does influence the subsequent high-precision ranging measurement.

Fig. 4. Precision test of C/A PN code and carrier phase based on USO

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Fig. 5. Test of time difference of dual satellites based on USO and POD

3 High-Precision Inter-satellite Ranging 3.1 Principle As showed in Fig. 6, satellite i and satellite j transmit Ka band signal to each other respectively and the difference of these signals is 502 kHz. The receiving terminals continuously monitor the phase changes of 502 kHz signal using phase locked loop to j obtain one way phase measurements ϕi and ϕji .

KBR-i Local MW signal 24GHz

KBR-j Input MW signal 24GHz+502KHz

+502KHz Phase measurement

Input MW signal 24GHz

Local MW signal 24GHz+502KHz

-502KHz Phase measurement

Fig. 6. KBR signal flow graph

The theoretical basis of KBR is DOWR(dual one way ranging) which can effectively suppress the common error caused by medium and long term frequency instability of USO, as showed in Fig. 7. At the specified nominal measuring time t, one way phase measurement of satellite i can be expressed as: j

j

ϕi (t + ti ) = ϕi (t + ti ) − ϕ j (t + ti ) + Ei i, j = 1, 2, i = j

(1.2)

Formula (1.2) is the phase difference between the received signal and the local reference signal, among which the phase of received signal in satellite i can be represented by the one of transmitted signal in satellite j. j

ϕ j (t + ti ) = ϕj (t + ti − τi )

(1.3)

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j

Where τi is the signal travel time from satellite j to i. So formula (1.3) can be written as: j

j

j

ϕi (t + ti ) = ϕi (t + ti ) − ϕj (t + ti − τi ) + Ei

(1.4)

ti called time-tag error is the difference of actual and nominal sampling time, j which needs to be corrected by GNSS measurement. Ei is the sum of measurement errors including integer ambiguity, ionosphere error and other phase measuring errors. Phase ϕi (t) can be decomposed into the reference phase ϕ i and phase errors caused by the oscillator δϕi ϕi (t) = ϕ i (t) + δϕi (t)

(1.5)

So formula (1.4) can be written as: j

j

j

j

ϕi (t + ti ) = ϕ i (t + ti ) + δϕi (t + ti ) − ϕ j (t + ti − τi ) − δϕj (t + ti − τi ) + Ei (1.6) Formula (1.6) can be arranged using Taylor polynomial method, in which phase change ϕ˙ i (t) is represented by constant standard frequency fi : ϕ i (t + ti ) ≈ ϕ i (t) + ϕ˙ i (t)ti ≈ ϕ i (t) + fi ti ϕ i (t + tj − τji ) ≈ ϕ i (t) + fi tj − fi τji δϕi (t + ti ) ≈ δϕi (t)+δfi (t)ti

(1.7)

δϕi (t + ti − τji ) ≈ δϕi (t)+δfi (t)ti − δfi (t)τji In that way, the result of DOWR is [8]: j

 ≡ ϕi (t + ti ) + ϕ ij (t + tj )

(1.8)

Because the frequencies of microwave signal in two satellites are designed differently, f1 represents the microwave signal in satellite i while f2 represents that in satellite j. If formula (1.7) is substituted into (1.6) and then formula (1.6) is substituted into (1.8), it can be got that: j

j

(t) ≈ (fi τji + fj τi ) + (δfi τji + δfj τi ) +(fi − fj )(ti − tj ) + (δfi − δfj )(ti − tj ) + E

(1.9)

Among them, the first item represents the instantaneous phase measurement item, which is the target measurement result. The second item represents the phase error caused by the oscillator, in which the error caused by the long-term drift of the oscillator has been suppressed. The third item represents the time difference error. When the accuracy is better than 0.15 ns, the residual error of this term is less than 1 um. The fourth term is the coupling term between the oscillator and the time scale error, and the impact on the accuracy can be ignored. Consequently, the biased distance measurement can be written as: R(t) = λ(t), λ = c/(fi + fj )

(1.10)

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Fig. 7. Schematic of dual one way phase measurement [8]

3.2 Time-Tag Correction DOWR As mentioned before that DOWR can effectively suppress the phase errors caused by medium and long term frequency instability of USO, a key prerequisite of ensuring noise suppression ratio is that measurement time consistency must reach a certain precision when two one way phase measurements are superimposed based on Eq. (1.8). GRACE requires that this time consistency is better than 0.1 ns. In practical projects, it can be ensured that the GNSS pseudorange measurements are tagged with KBR measuring time if the time-tag produced by local USO is used to sample GNSS and KBR measurements gnss at the same time. In this paper, GNSS and KBR measuring time are denoted by ti and ti respectively. t = ti − tj = (ti − tgnss ) − (tj − tgnss ) gnss

= (ti

gnss

− tgnss ) − (tj

gnss

− tgnss ) = ti

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As showed in Fig. 8, t is used to correct KBR measuring time and two one way phase measurements from satellite i and satellite j can be resampled at nearly the same time. In practice, it is chosen that measurement of satellite j is resampled at ti . After the time-tag is unified, two satellites’ KBR one-way measurements are superimposed and the dual one way distance measurement can be obtained. The speed measurement can be obtained through the difference and filter processing [9, 10].

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Fig. 8. Principle of time tag correction

4 Test and Verification 4.1 Testing System Refer to the KBR design plan of GRACE, two sets of KBR-GNSS equipment and ground test system ware developed as shown in Fig. 9. The system is mainly composed of K-band antenna, GPS antenna, microwave transceiver equipment, USO and integrated receiver. The receiver is used to obtain the one way phase measurement of the KBR system, and at the same time capture and track the GPS navigation signal to generate the pseudorange measurement. The measurements of KBR and GPS are packaged and sent to special test equipment. After data preprocessing, precise orbit determination, and two-way KBR comparison, the biased distance between satellites and the time-tag difference data are obtained respectively. The test was carried out in a dedicated shielded dark room, and the K-band signal free propagation distance is about 3.5 m. KBR-GNSS i K/Ka transceiver GNSS RF module

USO

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K/Ka transceiver

Integrated receiver

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Fig. 9. Experimental system of SST-LL KBR-GNSS

4.2 Testing Results Using the test system shown in Fig. 9, under constant temperature, constant humidity and vibration isolation environment, a large number of KBR and GPS observation data

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Fig. 10. KBR Range error time series (static, left picture)

Fig. 11. KBR Range error time series (dynamic, comparison of range measured and range got from XL-80 laser interferometer, right picture)

were obtained. The actual measurement results show that the accuracy of the satellites measurement time difference obtained by the post-processing of GPS data is better than 0.1ns. Using the time difference correction DOWR method, the KBR biased distance measurement is obtained as shown in Fig. 10, in which the distance measurement accuracy is 1.05um, and the speed measurement accuracy is 0.26um. Figure 11 shows the distance and velocity measurements curve when the distance between the AB satellites increases stepwise. In this result, the laser interferometer is used to provide the true value of the inter-satellite distance change, with which the performance of KBR under dynamic distance conditions is evaluated. The results show that the KBR measurement curve closely coincides with the interferometer’s curve, and the distance measurement accuracy of KBR is 1.15 um and the speed measurement accuracy is 0.32 um/s, which has reached the expected performance level.

5 Conclusion This paper focuses on the technical characteristics and development status of USO. Based on the low-orbit earth gravitational field detection project, the application of USO

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in high-precision GPS receiver, precise orbit determination, and high-precision intersatellite ranging is done in-depth research and analysis. A verification system was built based on the ongoing research project and related test results were given. The results showed that USO has superior performance and has shown great application value and potential in the field of precision measurement technology. The research results of this paper have certain reference significance for the inter-satellite ranging system of China’s first generation Earth’s gravity field detection satellite and gravitational wave detection project.

References 1. Wang, Z.T., Jiang W.P.: Theory and Method of Determining the Earth’s Gravitational Field Based on Satellite Tracking Satellite Technology, pp. 5–13. Wuhan University Press, Wuhan (2011) 2. Bertiger, W., Dunn, C.: Relative time and frequency alignment between two low earth orbiters. GRACR, Jet Propulsion Laboratory, California Institute of Technology 3. Weaver, G.L., Asmar, S.W.: GRAIL USOs: another in-flight quartz radiation experiment. Johns Hopkins University Applied Physics Laboratory. IEEE (2012) 4. Yang, S., Zhong, X.: A high-resolution phase difference measurement technique, Space Electron. Technol. 5(1) (2008) 5. Kroes, R., Bertiger, W.: Precise GRACE baseline determination using GPS. GPS Solut 9, 21–31 (2005). https://doi.org/10.1007/s10291-004-0123-5 6. Liu, G.Y.: Real-time positioning algorithm with single frequency GPS phase and pseudo-range and detection of cycly slip. Crustal Deform. Earthq. 21(3) (2001) 7. Wu, S.-C., Bar-Sever, Y.E.: Real-time sub-cm differential orbit determination of two low-earth orbiters with GPS bias fixing. Jet Propulsion Laboratory, California Institute of Technology 8. Liu, X., Wang, D.: Research on the effect of signal propagation delay between satellites on KBR’s measurement performance. In: Academic Conference Proceedings of China Aerospace Institute (2015) 9. Liu, X., Wang, D.: Research on the inversion method of USO frequency stability joining GPS and inter-satellite distance measurement. In: China Satellite Navigation Conference 2016 Proceedings, vol. III (2016) 10. Tavella, P., Petit, G.: Precise time scales and navigation systems: mutual benefits of timekeeping and positioning. Satell. Navig. 1(1), 1–12 (2020). https://doi.org/10.1186/s43020020-00012-0

Design and Fabrication of Thermostat for the Hydrogen Maser Shuo Liu1(B) , He Yang2(B) , Weili Wang1 , Kai Huang1 , Yushan Lu3(B) , Yaxuan Liu1 , and Liang Wang1 1 Beijing Institute of Radio Metrology and Measurement, No. 80 Yongding Road, Haidian District, Beijing 100854, China 2 China Center for Aerospace Science and Technology International Communication, No. 8 Fucheng Road, Haidian District, Beijing 100048, China 3 School of Microelectronics, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, China

Abstract. In this paper, a temperature thermostat used for the hydrogen maser is designed and fabricated based on the analysis of heat dissipation of the hydrogen maser. The high power and precise temperature control is realized by using the PID temperature control and semiconductor refrigeration techniques in the design and fabrication of thermostat. Under the condition of 300 W heat dissipation, the temperature fluctuation is within ±0.05 °C, better than the existing similar products in the worldwide. The thermostat could provide excellent temperature environment for a high performance hydrogen maser. Keyword: Hydrogen maser · Thermostat · Temperature stability

1 Introduction Due to its excellent medium and long-term stability, the proportion of hydrogen clocks in the time keeping clock group is increasing; currently, the weight of hydrogen clocks in large-scale timekeeping laboratories has reached more than 70% [1]. But the hydrogen masers are vulnerable to the temperature fluctuation of the environment. Although the environment can be controlled by the air conditioner (AC) whose ability of temperature control is within ±0.5 °C, the performance of hydrogen maser are still constrained by the fluctuations of the environment. To improve the stability of temperature controlled by the AC will face the dilemma of technique and cost. In this paper, a high temperature thermostat used for the hydrogen maser are designed and fabricated according to the analysis of heat dissipation of the hydrogen maser. That will provide excellent temperature environment for improving the high performance of the hydrogen maser. Based on the simulation of heat dissipation of the hydrogen maser, methods of the high power temperature control and the fine PID temperature control combining semiconductor refrigeration are used in the design and fabrication of thermostat. Under the condition of 300W heat dissipation, the temperature fluctuation is better than ±0.05 °C. That is

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 128–133, 2021. https://doi.org/10.1007/978-981-16-3146-7_13

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better than the products of the series of HM made in USA whose temperature fluctuation is ±0.1 °C and the series of HECR made in Japan whose temperature fluctuation is ±0.03 °C without thermal load [2]. The thermostat designed and fabricated in this paper will be used for the hydrogen maser or cesium maser, which will greatly promote the performance of clock group’s Time keeping and Time service.

2 Design of Thermostat 2.1 Thermo-Simulation of Hydrogen Maser The thermo-simulation is analyzed considering the typical dissipation 200 W of hydrogen maser, which will help understand the distribution of heat energy. We build a simple model constructed by 6 surfaces according to the cooling tubes arrangement. The chamber is built by 5 cm heat insulating layers, whose size is designed to contain the dimensions of mainly current hydrogen masers. The outside shell exchanges heat naturally with the environment and the heat of hydrogen maser radiates with the inner shells. The maximum dissipation power is 300 W. The heat simulation is shown in Fig. 1. When the temperature of cooling surface maintains 15 °C, the maximum temperature of hydrogen maser is 38.5 °C. The ordinary temperature control point of microwave cavity is 45 °C, so keeping the cooling surface at 15 °C will not influence the control of cavity in the maser and it will works well. 2.2 Construction of Thermostat According to the simulation analyzed above, the thermostat is designed. That is mainly contains chamber, cooling liquid system and temperature controlling system. As shown in Fig. 2. The chamber is constructed by bearing structure, door and cooling tubes etc. To avoid the influence of the environment, the chamber is protected by the insulating layers. The schematic diagram of chamber is shown in Fig. 3. Cooling liquid systems is constructed by refrigerant, cooling pack and circulating pump. Refrigerant can be deionized water or glycol. Circulating pump can pump the refrigerant along the tubes cooling the surface. Semiconductor refrigerant based on the effect of peltier is chosen as the cooling pack. When the current flows through the semiconductor refrigerant, one of the bottom will absorb the heat and another bottom of that will release the heat, so the cooling process is finished. Temperature controlling system is constructed by temperature sensors and PID modules. When the temperature value transfers to PID modules, the PID will judge the difference of set point and actual temperature, and then adjust the parameters to stabilize the set temperature. The schematic flow of temperature control is shown in Fig. 4 and Fig. 5.

3 Optimization of Temperature Stabilization The influence of parameters on temperature stabilization mainly includes flow of refrigerant, cooling pack and parameters of PID modules.

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Hydrogen maser

Tempera ture sensor

Cooling tube

cooling liquid system

Semiconductor refrigerant

Semiconductor refrigerant

Fig. 1. Thermo simulation of hydrogen maser

Fig. 2. Schematic diagram of thermostat

3.1 Temperature Rise vs. Flow of Refrigerant The simulations of temperature rise depend on the flow of refrigerant under the heat dissipation of 200 W, 300 W and 400 W is analyzed, as shown in Fig. 6. When the flow velocity is bigger, the temperature rise decreases with the increases of flow velocity. But bigger flow will increase the resistance of cooling system, while small flow will increase the temperature of chamber which will make the ability of heat dissipation and homogeneity worse. Choice of the trade off mentioned above is the flow of 4 L/min, which will consider the heat dissipation and the load of system. 3.2 Cooling Packs Semiconductor refrigerant is the solid components of current exchange energy which takes the advantage of high reliability, small volume, rapidly cooling and non-vibration

Fig. 3. Schematic diagram of chamber

Fig. 4. Schematic diagram of temperature control

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Fig. 5. Flow chart of temperature control

and non-noise. Consideration of the maximum 400 W cooling capacity, single semiconductor refrigerant with 100 W cooling capacity and biggest temperature 67 °C is chosen. Four single semiconductor refrigerants are integrated to one cooling pack. The pack will get the maximum cooling capacity of 400 W and mounted on the cooling plate, shown as Fig. 7.

Fig. 6. Variation of chamber’s temperature rise versus the velocity of refrigerant

Fig. 7. Module of refrigerant

3.3 Fuzzy Self-tuning Technique of PID Compared to traditional PID technique, the fuzzy self-tuning PID technique takes the advantage of quick response, small over-adjust and strong adaptability. In this paper, fuzzy PID is used in the controlling system [3, 4]. Consideration of the normal temperature fluctuation of 2 °C and the non-normal temperature fluctuation of 10 °C which represent the air conditioner works well and malfunctioned, the simulation of PID process is analyzed. As shown in Fig. 8, the former of control process has bigger fluctuations when the environment temperature is bigger, conversely still.

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Fig. 8. Simulation of PID temperature control

Fig. 9. Hydrogen thermostat.

4 Experimental Data The chamber of thermostat and the cooling liquid and temperature controlling system are shown in Fig. 9a and b. Figure 9 a is the cooling liquid and temperature controlling system, Fig. 9 b is the chamber. The sapphire active maser with 110W power made in BIRM is placed in the thermostat and is tested under the lab environment where has the fluctuations of 2 °C. The temperature fluctuation is shown in Fig. 10 a. Every point represents 100 s. The temperature fluctuates with 0.035 °C during the most time in one day. Considering the malfunction of air conditioner, the thermostat is placed in the corridor where the temperature fluctuation is about 6–8 °C and the 300 W heat source is loaded in the thermostat. The temperature fluctuation is shown in Fig. 10 b. The fluctuation is bigger than the thermostat works in the lab environment, but the temperature still be controlled in the range of ±0.05 °C.

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Fig. 10. Temperature fluctuation of thermostat under different environment and heat dissipation

5 Experimental Data In conclusion, the technique of high power and the PID technique is combing used to control the thermostat of the hydrogen maser. The temperature of the thermostat is controlled in ±0.05 °C with the 300 W heat dissipation. Bigger temperature difference will be considered in the future works to improving the adaptability of atomic clocks.

References 1. Dong, S.: Atomic clocks and their applications in time keeping. J. Electron. Measur. Instr. 41, 490–493 (2004) 2. https://www.smc.eu/ 3. Ang, K., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 13(4), 559–576 (2005) 4. Matsuo, T., Nakano, K.: Robust control of multivariable systems by PID+Q controller. In: Proceedings of American Control Conference, vol. 40, pp. 3674–3678 (1997)

Design of Low Additional Stability Multi-channel Digital Phase Comparator Kai Huang1(B) , Yanjun Chen1 , He Yang2(B) , Shuo Liu1 , Yushan Lu3(B) , Yaxuan Liu1 , and Liang Wang1 1 Beijing Institute of Radio Metrology and Measurement, No. 80 Yongding Road, Haidian District, Beijing 100854, China 2 China Center for Aerospace Science and Technology International Communication, No. 8 Fucheng Road, Haidian District, Beijing 100048, China 3 School of Microelectronics, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, China [email protected]

Abstract. In this paper, the multi-channel low additional stability phase comparator is designed and fabricated based on the technique of digital double mixing cascaded analog double mixing while noise suppression is used in the frequency doubling link. Compared to the single analog double mixing technique, the method presented in this paper is more advanced in the low additional stability. When the input frequency is 10 MHz, the additional stability reaches 1.7E−14@1s 2.7E−15@10s, 4.6E−16@100s, 1.37E−16@1000s, 4.4E−17@10000s. The multi-channel comparator designed in this paper will satisfy the requirement of high performance atomic clocks in the time keeping lab and novel frequency clocks and microwave sources. Keyword: Low additional stability format · Phase comparator · Multi-channel

1 Introduction In recent years, atomic clock technology has made rapid progress with the frequency accuracy and the frequency stability greatly improved. Commercially hydrogen masers have got the one second stability better than 1E−13. And new atomic clocks and microwave oscillators have reached the one second stability at the level of E15 [1]. While the comparator is still at the level of E−14, such as the British Quartzlock A7 series whose one second stability is 5E−14, Germany TimeTech’s PCO whose one second stability is 2.5E−14, Symmetricom’s 5125A has reached one second stability of 3E−15 with single-channel input port [2, 3]. The lagging development of comparator affects the measurement accuracy of high performance frequency standards and novel microwave sources to a certain extent. A multi-channel low additional stability phase comparator is designed and fabricated based on the technique of digital double mixing cascaded analog double mixing while noise suppression is used in the frequency doubling link is proposed in this paper. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 134–141, 2021. https://doi.org/10.1007/978-981-16-3146-7_14

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This method has lower additional frequency stability than a single analog dualmixing phase comparator due to the use of secondary digital mixing technology and link noise suppression technology, and the comparator have 12 input channels which can match the requirement of multiple frequency standards comparisons. When the input frequency is 10 MHz, the additional frequency stability is 1.7E−14 @ 1s, 2.7E−15 @ 10s, 4.6E−16 @ 100s, 1.3E−16 @ 1000s, 4.4E−17 @ 10000s. The stability of the multi-channel phase comparator proposed in this paper is better than that of A7 and other products mentioned above. It can meet the comparison between multiple high performance atomic frequency standards in the clock group and the novel atomic standard or microwave sources.

2 Design of the Multi-channel Comparator

Frequency Divider 5/10/100MHz Input

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Computer Management software

Fig. 1. Schematic diagram of multi-channel comparator

Multi-channel phase comparator is mainly composed of the frequency doubling module (FDM), the analog dual-mixing module (ADMM), the digital dual-mixing module (DDMM), the high stability common source module (HSCSM) and the time measurement module (TMM). The schematic diagram is shown in Fig. 1. The main function of the frequency doubling module is to multiply the input frequency from 5 MHz, 10 MHz to 100 MHz. If the input signal is 100 MHz, the 100 MHz will be used directly. The input signals after entering the ADMM are mixed with the HSCSM and the phase difference will be created. The phase differences after handling by the DDMM input to the time digital convertor (TDC) which will promote the precision of measurement. 2.1 Frequency Doubling Module Frequency doubling module is the key module of high-precision multi-channel phase comparator [4]. The noise level of the front-end frequency multiplier directly determines

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the noise floor of the whole system. The block diagram of the frequency doubling module is shown in Fig. 2. The reference signal or the measured 5 MHz, 10 MHz and 100 MHz signals are input and judged. The frequency doubling signal is filtered to obtain 100 MHz signal. Switch2 10MHz

5/10/100MHz Input

2x

2x

2x

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Filter

2x

Switch3 100MHz

100MHz

Fig. 2. Schematic diagram of frequency multiplier

2.2 Analog Dual-Mixing Module Analog dual-mixing technology is one of the key technologies for multi-channel phase comparator system to achieve high resolution [5]. The frequency standard frequency under test and the reference standard frequency are mixed in the HSCSM with the dual-balanced mixer. Other frequency components except the mixing frequency will be filtered after the signal pass through the low pass filter. The reference sinusoidal beat signal and the measured sinusoidal beat signal are obtained. The phase discrimination with the common source will lower the frequency which is equivalent to amplify the phase difference. That will promote the resolution of measurement. The additional phase noise introduced by common source can be eliminated by dual-balanced structure designed. Thus the precision of the system measurement is improved. The schematic diagram of the analog double mixing is shown in Fig. 3. The 5 MHz signals of maser under test and reference maser pass through the frequency doubling modules respectively and are mixed with the analog common source of 98.99990 MHz. After zero-crossing comparison, the intermediate frequency signal of 1.00010 MHz is generated, and the 100- fold frequency difference multiplication is obtained at the analog mixing. 2.3 Digital Dual-Mixing Module Digital dual-mixing time difference measurement technology is also one of the key technologies to achieve high resolution in multi-channel digital phase comparator. The

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ADMM Maser under test 5MHz

×20

Mixer 1

Zero1.00010MHz crossing comparison

Mixer 2

Zero1.00010MHz crossing comparison

HSCSM 98.99990MHz

Reference maser 5MHz

×20

Fig. 3. Schematic diagram of analog double mixing

method of digital dual mixer time difference phase detection is used in this paper, which can greatly reduce the number of analog devices. Every channel is controlled by correlation algorithm and program that makes it easier to enlarge the numbers of channels and improves the consistency of channels. In the traditional analog double mixing method, the low frequency beat signal is directly obtained by analog mixing and the time difference measurement is carried out after reshaping of zero crossing comparison. Due to the slow rising speed of low frequency beat signal near zero crossing, it is necessary to realize reshaping zero crossing comparison through multi-stage amplification which leads to large additional noise. In order to reduce the noise caused by amplification shaping, digital double mixing is cascaded after analog mixing. The schematic diagram is shown in Fig. 4. The signals of maser under test and reference maser are doubling and two-stage mixed respectively and 100 Hz beat signals are obtained. Two 100 Hz signals are used as the opening and closing signals of the time interval counter for time difference measurement. According to the principle of dual-mixing time difference measurement, the measurement resolution of dual-mixing is improved by f0 /fb times than that of direct measurement, where f0 is the nominal frequency of the measured signal and fb is the beat frequency. Considering the frequency doubling operation in Fig. 3 and the time difference measurement resolution of the time interval counter is 1ns, the time difference measurement resolution will be 1 ns × 100 Hz/100 MHz = 1 fs, which is the theoretical resolution of the double mixing time difference measurement. Considering the additional noise introduced by the process of amplification, reshape and common source in fact, the measurement resolution cannot reach this theoretical value. 2.4 High Stability Common Source Module The noise of the two signals provided by the common source can theoretically be offset by using the method of dual-mixing time difference to measure the frequency stability. While the measurement error caused by the common source is related to the sampling time t actually, the situation is more important in the high-precision frequency stability measurement. In order to further decrease the influence of additional phase noise, the common source should have high frequency stability. In this paper, the single side band

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Analog mixer intermediate frequency signal 2

Time interval measurement

Common source 10MHz

100Hz D-Triger 1

Digital common source1MHz

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Phase difference data

100Hz D-Triger 2

Fig. 4. Schematic diagram of digital double mixing

mixing method is used. When the phase is precisely controlled, the useless signal can almost be completely offset. So the requirements for the filter performance will be depressed. The principle block diagram is shown in Fig. 5. The first stage circuit realizes the down-conversion of 10 MHz signal to 9.99000 MHz signal. The second stage signal realizes the up-conversion of 9.99000 MHz signal to 9.99999 MHz signal. The third stage signal realizes the down-conversion of 9.99999 MHz signal to 9.89999 MHz signal. The 98.99990 MHz signal is obtained by inputting 9.89999 MHz to the multiplier, and then 100 Hz beat signal is generated by analog double mixing and digital double mixing. Considering the smoothing ability of the system to noise and the ability of data collection and transmission, the beat frequency 100 Hz is proper. Since the beat frequency is smaller, the lesser time difference data is collected in the unit cycle and the background noise of the system is worse. If the beat frequency is larger, the more time difference in a unit cycle will cause great pressure on data transmission. 2.5 Time Measurement Module The high-precision time interval measurement module used in this paper adopts the combination of coarse counter and fine counter. The coarse counter uses the direct counting method. The time clock pulse to be measured is filled in the gate signal composed of the time interval counter. The number of time clock pulses is obtained the counting circuit, and then the time interval cab be calculated. The method of digital interpolation and the transmission channel composed by the delay units cascaded in each other are used in the fine counter. The output of each delay unit is connected to the data input of the latch. The start signal of the measured time interval is used as the input signal of the delay chain, and the end signal is used as the sampling signal. The number of delay units passing through the delay chain is proportional to the measured time interval. The function of the counter is controlled by FPGA in this paper. The FPGA can not only simplify the circuit hardware structure, but also can improve the counting accuracy of the counter. The principle block diagram is shown in Fig. 6. The TDC used in this paper is based on the classical Nutt structure delay line method. The system consists of two delay lines

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Fig. 5. Schematic diagram of high stable common source

and a coarse counter. Two delay lines record the time intervals of positive jumps of the start/Stop and the subsequent clock signals respectively. The coarse counter records the clock cycles between positive jumps of the start and Stop signals. The function of a multiplexer is converting a 126 bit delay output structure into an 8 bit binary output.

Delay Line Start Multiplexer Delay Line Stop

Main Counter Clock

Fig. 6. Schematic diagram of TDC

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Fig. 7. Photo of Multi-channel comparator

3 Experimental Data A high-precision multi-channel phase comparator based on the five modules discussed above is proposed, the comparator is shown in Fig. 7. The additional stability at 10 MHz input is measured and the additional stability is 1.7E−14 @ 1s, 2.7E−15 @ 10s, 4.6E−16 @ 100s, 1.37E−16 @ 1000s, 4.4E−17 @ 10000s, as shown in the Fig. 8. The phase difference was measured, as shown in Fig. 9.

Fig. 8. Additional stability of Multi-channel comparator

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Fig. 9. Phase difference of Multi-channel comparator

4 Conclusion In this paper, a multi-channel phase comparator with 12 input channels and low additional stability is proposed. The technique of frequency difference multiplication method composed by digital dual-mixing cascaded by analog dual-mixing and the technique of link noise suppression are used in the comparator. The additional stability reaches the international advanced level.

References 1. 2. 3. 4. 5.

https://www.vremya-ch.com/ https://www.timetech.de/ https://www.microsemi.com/ Fienup, J.R.: Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982) Chong, C.P., Smith, K.C.: A high-resolution CMOS comparator. INT. J. Electronics 46, 409– 415 (1988)

Monitoring Assessment and Impact Analysis of BeiDou and GNSS Time Offset Shichao Wang1(B) , Ying Liu2 , Maolei Wang1 , Bin Yang1 , Lin Zhang1 , and Haibo Yuan3 1 Beijing Satellite Navigation Center, Beijing 100094, China 2 Beijing Institute of Tracking and Telecommunication Technology, Beijing, China 3 National Time Service Center, Chinese Academy of Sciences, Xi’an, China

Abstract. Global Navigation Satellite System (GNSS) time offset is one of the most important foundations for GNSS interoperability. BeiDou satellites broadcast BeiDou time and other GNSS time offset parameters (BGTO parameters) through navigation messages, ensuring that receivers can use multiple GNSS systems for integrated positioning. In this paper, the definition of the time offset error (BGTOE) are studied; the quantitative relationships between BGTOE and joint positioning result and accuracy are derived. Then the BGTOE is accessed based on the data of UTC(k) and BIPM Circular T. Evaluation results show that the fluctuation range of BGTOE is about 27 ns, and the standard deviation is about 10 ns. It will produce a position offset of 12.6 m and a time offset of 14.7 ns for joint positioning results. In a longer time scale, it will bring about a loss of position accuracy of about 10 m and a loss of time accuracy of about 20 ns, which can basically meet the needs of joint positioning, but there is still room for optimization from the prospect of improving the joint positioning performance. Keywords: BeiDou · Interoperability · BGTO parameters · Joint positioning · Time offset error · Monitoring and evaluation

1 Introduction With the BeiDou Global Navigation Satellite System launching its service on July 31, 2020, there are now four major global navigation satellite systems (GNSS) - GPS, GLONASS, Galileo and BeiDou - providing services worldwide. It has become an important researching trend and developing direction to realize interoperability among GNSS and make full use of the four constellations to provide users with higher-performance navigation and positioning services. Different satellite navigation systems have their own time systems: GPS time is GPST, GLONASS time is GLONASST, Galileo time is GST, and BeiDou time is BDT [1]. Each of these time scales differs from others, receivers must be able to obtain the relationship between them when performing joint positioning. Determining the interrelationships or deviations of the time scales mentioned above is GNSS time interoperability [2]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 142–157, 2021. https://doi.org/10.1007/978-981-16-3146-7_15

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There are three methods for users to obtain the time difference between GNSS systems. The first is calculating by themselves through solving the observation equations, in which the time difference between multiple GNSS systems is involved as an unknown quantity, like users’ position and time. This method does not rely on GNSS systems to provide additional information, which is less demanding on the system side, and the solved GNSS time difference is exactly that exhibited on the user side, leading to slightly better performance [2, 3], but it requires users to observe a larger number of different GNSS satellites (at least 5 satellites for dual-system joint positioning, and 6 satellites for three-system joint positioning, and so on). This is not friendly enough for applying GNSS interoperability in non-open environments such as urban environments with many tall buildings. Secondly, the time differences are generated on the system side and directly broadcasted to users. The earlier GPS and GLONASS systems do not reserve the interface of time difference parameters between GNSS systems in their messages, but the Galileo system has taken interoperability into consideration and designed the interface for broadcasting the time difference between Galileo and GPS. While the newly-built BeiDou system has fully considered the interoperability and broadcasts the time difference parameters between BeiDou and other three major systems in its navigation messages, i.e., BGTO (BeiDou and GNSS Time Offset) parameters [4]. Thirdly, the time differences are obtained by using UTC. All four GNSS systems broadcast the time difference between their respective times and UTC or UTC(k), so the time interoperability of GNSS systems can be achieved by using UTC or UTC(k) as a common reference. Currently, the International Bureau of Metrology (BIPM) is conducting extensive research on the topic of UTC and GNSS reciprocity [5], indicating that the use of UTC for GNSS time interoperability is an important direction, and the method has been mentioned in the literature [6–8]. However, this method requires a clear traceability of each GNSS system time to UTC, and the specific traceability of BDT to UTC has not been disclosed yet, so the time interoperability between BeiDou and other GNSS systems cannot be achieved using this method until it is disclosed. In this paper, we focus on the second method, which is to monitor and evaluate the BGTO parameters broadcasted by BeiDou and analyse its impact. In recent years, the UTC parameters of BeiDou have received attention [10], while there are few related literature about BGTO parameters. The literatures [2, 9–12] has conducted a comprehensive analysis on the monitoring of time difference between GNSS systems and the influence of different methods on joint positioning. On the base of them, the definition of BeiDou and other GNSS systems time offset error (BGTOE) is investigated and the quantitative relationships between BGTOE and joint positioning result and accuracy are derived in Sect. 2. In Sect. 3, the BGTOE evaluation methods based on UTC(k) and BIPM Circular T are proposed, and monitoring and evaluation results of BGTOE are given in Sect. 4.

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2 BeiDou and Other GNSS Time Offset Error (BGTOE) and Its Effect 2.1 Definition and Connotation of BGTOE The BGTO parameters are calculated by BeiDou system. According to the BeiDou system interface control documents, these parameters are published by both BeiDou-2 and BeiDou-3, and they are not broadcasted by BeiDou-2, while have been broadcast by BeiDou-3 [4, 13]. The physical meaning of BGTOE is the error of the time deviation between BeiDou and other GNSS system times that obtained by BGTO parameters. BGTOE characterizes the accuracy loss when users use BGTOE parameters to obtain the time deviation of the BeiDou time from other GNSS times. The definition formula is BGTOE = BGTOobtained by users − BGTOreal value

(1)

Since the BGTO needs to be broadcasted by satellites, users must use a forecast model to obtain other GNSS times, so the BGTOE is mainly synthesized of the forecast model error σt_pre and the measurement error σt_mea , which can be expressed as  2 2 + σt_mea (2) BGTOE = σt_pre where the forecast error is calculated by the residual between the forecast values obtained by BGTO parameters and the actual measured values, while the measurement error σt_mea are composed of various types of errors during the measurement conducted by BeiDou system. Considering that GNSS time is generally maintained by atomic clocks, thus having high stability, and the BGTO parameters are updated hourly, the forecast error is usually small. On the other hand, since there is no direct time comparison link between BeiDou and other GNSS systems, the measurement error can be large, and even systematic bias may exist. Therefore σt_mea is the main component of BGTOE. 2.2 Impact on Joint Positioning of BGTOE 2.2.1 Introducing Position Deviation In this section, the effect of BGTOE on joint positioning is quantitatively analysed for the least squares positioning solution. The observation equation for single-GNSS-system positioning is as follow     j ρk = X j − xk  + cd τk (3) j

where ρk is the pseudorange from receiver k to satellite j, which is measured by the receiver and corrected for errors of the ionosphere, troposphere, and satellite clock T  aberration. X j = X j , Y j , Z j is the position vector of the satellite j in the corresponding T  coordinate system, xk = xk , yk , zk is the position vector of the receiver k, d τk is the

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receiver clock error, and c is light speed. To solve the four unknowns of three-dimensional position and receiver’s clock error, at least four satellites need to be observed, i.e. j ≥ 4. When using the GNSS time offset parameters broadcasted by GNSS systems for joint positioning, assuming that the coordinate systems of different GNSS systems have been transformed, the observation equation becomes     j (4) ρk = X j − xk  + cd τk + cδtmn where δtmn is the time offset between the GNSS m and the GNSS n, obtained from the broadcasted GNSS time offset parameters, and δtmn = 0 when m = n. According to the common practice, to facilitate the solution, Taylor series expansion of the observation equation at an approximate location and neglecting second-orderhigher terms [14] are required. The linearized pseudorange localization error equation are as follow j

j

j

vk = I k xk − cd τk − Lk − cδtmn

(5)

j

where vk is the observation error of the receiver k, which generally consists of some slow j variations  and noises. I k is the unit vector pointing from the receiver k to the satellite k, X j −ˆxk Y j −ˆyk Z j −ˆzk , j , j j ρˆk ρˆ ρˆk k j  j  satellite j, ρˆk = X − xˆ k . j

Ik =

j

. ρˆk is the approximate distance from the receiver k to the j

j

j

j

Lk is a constant term, Lk = ρˆk − ρk . Considering the scenario of joint positioning using the four GNSS systems, and without losing generality assuming that the BDT is used as the time reference for solution, the BGTO parameters broadcast by BeiDou are used to determine δtmn , the following joint equations can be derived ⎫ vkBD,1 = I kBD,1 xk − cd τk − LkBD,1 ⎪ ⎪ ⎪ ⎪ .. ⎪ ⎪ ⎪ . ⎪ ⎪ BD,n1 BD,n1 BD,n1 ⎪ ⎪ vk = Ik xk − cd τk − Lk ⎪ ⎪ ⎪ GPS,1 GPS,1 GPS,1 ⎪ vk = Ik xk − cd τk − Lk − cδtGPS−BD ⎪ ⎪ ⎪ ⎪ .. ⎪ ⎪ ⎪ . ⎪ ⎪ ⎬ GPS,n2 GPS,n2 GPS,n2 = Ik xk − cd τk − Lk − cδtGPS−BD vk (6) GAL,1 GAL,1 GAL,1 vk = Ik xk − cd τk − Lk − cδtGAL−BD ⎪ ⎪ ⎪ ⎪ .. ⎪ ⎪ ⎪ . ⎪ ⎪ ⎪ GAL,n3 GAL,n3 GAL,n3 ⎪ = Ik xk − cd τk − Lk − cδtGAL−BD ⎪ vk ⎪ ⎪ ⎪ vkGLO,1 = I kGLO,1 xk − cd τk − LkGLO,1 − cδtGLO−BD ⎪ ⎪ ⎪ ⎪ ⎪ .. ⎪ ⎪ . ⎪ ⎪ ⎭ GLO,n4 GLO,n4 GLO,n4 = Ik xk − cd τk − Lk − cδtGLO−BD vk

where n1 , n2 , n3 and n4 represent the number of the observed BeiDou, GPS, Galileo, and GLONASS satellites respectively. Equation (6) can be written in the form of matrixs V = AX − L − cT BGTO

(7)

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where

⎡

⎤ I kBD,1 −1 ⎢ .. .. ⎥ ⎢ . . ⎥ ⎢ ⎥ ⎢ I BD,n1 −1 ⎥ ⎢ k ⎥ ⎢ GPS,1 ⎥ ⎢ Ik −1 ⎥ ⎢ .. .. ⎥ ⎢ ⎥ ⎢ . . ⎥ ⎢ GPS,n2 ⎥    T ⎢I  1 T −1 ⎥ n k ⎢ ⎥, X = xk , L = L1 L2 · · · Ln , V = vk , · · · , vk , A = ⎢ GAL,1 k k k cd τk −1 ⎥ ⎢ Ik ⎥ ⎢ ⎥ . . ⎢ .. .. ⎥ ⎢ ⎥ ⎢ GAL,n3 ⎥ ⎢ Ik −1 ⎥ ⎢ GLO,1 ⎥ ⎢ Ik −1 ⎥ ⎢ ⎥ ⎢ .. .. ⎥ ⎣ . . ⎦ GLO,n4 −1 Ik T  T BGTO = 01×n1 δtGPS−BD I 1×n2 δtGAL−BD I 1×n3 δtGLO−BD I 1×n4 . where n = n1 + n2 + n3 + n4 is the total number of GNSS satellites observed. Considering that the BGTO parameter used by the receiver is in fact Tˆ BGTO which is measured and calculated by BeiDou system, the least square solution of Eq. (7) can be expressed as  −1   AT L + cTˆ BGTO Xˆ = AT A

(8)

Thus the positioning error can be expressed as vXˆ = X − Xˆ   −1  = X − AT A AT L + cTˆ BGTO

(9)

The following equation can be derived with Eq. (7) and Eq. (9)   −1  vXˆ = X − AT A AT AX − V − cT BGTO + cTˆ BGTO  −1 = AT A AT (V + c · BGTOE)

(10)

where BGTOE = T BGTO − Tˆ BGTO is the matrix consisting of the BGTOEs. It can be shown by Eq. (10) that the joint position error is related to pseudorange observation error V and BGTOE, and there will be a position offset (as well as a time offset) in solutions. The offset caused by BGTOE is  −1 AT · BGTOE vXˆ = c AT A

(11)

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 −1 Let H = AT A , the offset can be further expressed in the form of chunking matrixes as ⎡

⎤T ⎡ ⎤ A1 BGTOE1 · 0n1 ×1 4  −1 ⎢ A ⎥ ⎢ BGTOE · I  ⎥ 2 n2 ×1 ⎥ ⎢ 2⎥ ⎢ vXˆ = c AT A = cH BGTOEj Aj I nj ×1 ⎣ A3 ⎦ ⎣ BGTOE3 · I n ×1 ⎦ 3 j=1 A4 BGTOE4 · I n4 ×1

(12)

where H is the geometric matrix related only to the constellation configuration of the observed satellites. A1 to A4 respectively represents the observation equation coefficient matrix of BeiDou, GPS, Galileo and GLONASS satellites, which is only related to the observed satellite constellation configuration of the corresponding GNSS systems. BGTOE1 to BGTOE4 represents the time offset error between BeiDou and BeiDou, GPS, Galileo, GLONASS time respectively and ⎫ BGTOE1 = 0 ⎪ ⎪ ⎪ ⎪ ˆ BGTOE2 = δtGPS−BD − δ tGPS−BD ⎬ BGTOE3 = δtGAL−BD − δ ˆtGAL−BD ⎪ ⎪ ⎪ ⎪ ⎭ ˆ BGTOE4 = δtGLO−BD − δ tGLO−BD The Eq. (12) is the quantitative relationship between BGTOE and the joint positioning result. 2.2.2 Causing Position Accuracy Loss It is assumed that the performance of the BGTO parameters obtained from BeiDou system is very good, i.e., the BGTOE is zero-mean and thus will not cause position offset in average. However, the various noises introduced during BGTO parameters’ measurement will also bring additional accuracy loss to joint positioning. Assuming that BGTOEj is zero-mean and uncorrelated with variances of σBGTOE, GPS , σBGTOE, GAL , σBGTOE, GLO , and that the receiver’s pseudorange measurement error for each satellite of each GNSS system during an observation are zero-mean and uncorrelated noise, and that the variances of measurement noise for different GNSS systems are σURE, BD , σURE, GPS , σURE, GAL , σURE, GLO , then E(V) = 0 E(BGTOE) =0 

⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬

E V • BGTOET = 0     ⎪ ⎪ 2 ⎪ E VV T = diag σURE, In ×n σ 2 In ×n σ 2 In ×n σ 2 In ×n ⎪ ⎪  BD 1  1 URE, GPS 2 2 URE, GAL 3 3 URE, GLO 4 4 ⎪  ⎪ ⎭ T 2 2 2 E BGTOE • BGTOE = diag 0n1 ×n1 σBGTOE, GPS In2 ×n2 σBGTOE, GAL In3 ×n3 σBGTOE, GLO In4 ×n4

(13)

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The variance of the position error can be derived from Eq. (10) and Eq. (13)    −1  −1 E vXˆ vTXˆ = AT A AT · E(V + c · BGTOE)(V + c · BGTOE)T · A AT A     −1    −1 = AT A AT · E VV T + c2 E BGTOE · BGTOET · A AT A (14)  −1 Let H = AT A , Eq. (14) can be expressed in the form of chunk matrixes as ⎡

⎡ ⎤ ⎤T A1 A1    ⎢ A ⎥     ⎢ ⎥ A 2 2⎥ T ⎥ + c2 E BGTOE · BGTOET · ⎢ E vXˆ vTXˆ = H ⎢ ⎣ A3 ⎦ · E VV ⎣ A3 ⎦H A4 =

4 

A4

  2 2 2 HATj Aj H σURE, + c σ j BGTOE, j

(15)

j=1

=

4 

  2 2 2 H j σURE, j + c σBGTOE, j

j=1

where H j = HATj Aj H is the geometric matrix related to the constellation configuration only. Equation (15) shows that the impact of positioning accuracy due to BGTOE when using BGTO parameters for least-squares joint positioning can be quantified as   E vXˆ vTXˆ

BGTOE

= c2

4 

2 H j σBGTOE, j

(16)

j=1

It can be seen that with the same number of total observation satellites, joint positioning will definitely bring additional accuracy loss. Therefore, the significance of joint positioning lies more in making full use of the multiple GNSS satellites and increasing the number of visible satellites. Referring to the definition of accuracy factor, the component influence factor of BGTOE on positioning accuracy can be derived as  ⎫ j j j j j ⎪ GDOPBGTOE, j = c h11 + h22 + h33 + h44 ⎪ ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ j j j j ⎪ PDOPBGTOE, j = c h11 + h22 + h33 ⎪ ⎪ ⎪ ⎬  j j j (17) HDOPBGTOE, j = c h11 + h22 ⎪ ⎪  ⎪ ⎪ ⎪ j j j ⎪ ⎪ VDOPBGTOE, j = c h11 + h22 ⎪ ⎪ ⎪  ⎪ ⎪ j j ⎭ TDOPBGTOE, j = h44

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j

where hrr (r = 1, 2, 3, 4) is the diagonal element of the matrix H j . The error of the BGTOE’s impact on positioning accuracy can be expressed by σBGTOE and the component  impact factors as. 2 4   j 2 Position accuracy, PDOPBGTOE, j σBGTOE, j j=1  2 4   j 2 HDOPBGTOE, j σBGTOE, Horizontal position accuracy, j. j=1  2 4   j 2 Vertical position accuracy, VDOPBGTOE, j σBGTOE, j. j=1  2 4   j 2 Time accuracy, c TDOPBGTOE, j σBGTOE, j. j=1

The expressions above are the quantitative relationships between BGTOE and the joint positioning accuracy (including timing accuracy). If only two GNSS systems are used for joint positioning, it can be simplified as. Position accuracy, PDOPBGTOE × σBGTOE . Horizontal accuracy error, HDOPBGTOE × σBGTOE . Vertical accuracy error, VDOPBGTOE × σBGTOE . Time accuracy, cTDOPBGTOE × σBGTOE . 2.2.3 Calculation Example Calculations of the position offset impact and component impact factor are carried out for two-system joint positioning. Two constellation configurations, better and worse, are used respectively, and the constellation configuration design is shown in Table 1. Table 1. Constellation configuration used in the example Satellite Azimuth (°) Pitch (°) GNSS 1

10

0

2

10

90

GNSS1

3

10

270

GNSS1

4

45

45

GNSS1

5

10

180

GNSS2

6

45

225

1

50

0

2

60

20

GNSS1

3

70

50

GNSS1

4

15

250

GNSS1

5

30

180

GNSS2

6

45

225

GNSS2

Constellation configuration

GNSS1 Better

GNSS2 GNSS1 Worse

The proportions of position deviation (m) and time deviation (ns) to BGTOE (ns) were calculated according to Eq. (12) and are shown in Table 2. The results show that

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the proportions of position and time deviations to BGTOE are about 0.2 for the better constellation, and about 0.5 for the worse constellation. Table 2. Proportion factor of position & time offsets to BGTOE Deviations

Better constellation configuration

Worse constellation configuration

Position deviation (m)/BGTOE(ns)

0.23

0.47

Horizontal deviation (m)/BGTOE(ns)

0.18

0.30

Vertical deviation (m)/BGTOE(ns)

0.14

0.36

Time deviation (ns)/BGTOE(ns)

0.17

0.55

The component impact factors of BGTOE are calculated according to Eq. (16) and Eq. (17), which are shown in Table 3, where the position error’s unit is meter and time error’s unit is nanosecond. It can be seen that for the better constellation, the proportions of positioning and timing accuracy to σBGTOE are about 0.3, while for the worse constellation the proportion of positioning accuracy to σBGTOE is about 1, and that of the timing error is about 2. If the impact of BGTOE on positioning error is controlled at 10 m, the σBGTOE needs to be controlled at 10 ns or so, and the time error caused by BGTOE is around 20 ns. Table 3. Component influence factors of positioning accuracy The component impact factors

Better constellation configuration

Worse constellation configuration

PDOPBGTOE

0.35

1.06

HDOPBGTOE

0.15

0.54

VDOPBGTOE

0.31

0.91

TDOPBGTOE

0.37

2.27

3 Monitoring and Evaluation Method of BGTOE 3.1 Method Based on UTC(k) The most fundamental method to evaluate the BGTOE should be establishing a direct high-precision time comparison link between GNSS systems, but at present BeiDou system does not have such a link. Another method is to use a receiver to solve the time of each GNSS system, and then obtain the BGTO’ by subtracting them from each other, and use the BGTO’ to evaluate the broadcasted BGTO parameters. Evaluation principle

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is shown in Fig. 1. This method needs to calibrate the receiver for each GNSS system. In this paper, the UTC(NTSC) is selected as the reference to measure and solve GNSS time. Unfortunately, the receiver used in this paper is only calibrated for BeiDou and GPS, therefore only BDT-GPST can be evaluated. BDT-GPST BDT

One-way monitoring

GPST

One-way monitoring UTC(k)

Fig. 1. Assessing method based on UTC(k)

In this method, data of UTC(NTSC)-GNSST are used for the evaluation reference in this paper, and the uncertainty budget is shown in Table 3. Table 4. Uncertainty of the assessing method based on UTC(k) Evaluation object

BDT-UTC(NTSC)

UTC(NTSC)-GPST

Total uncertainty

BDT-GPST

3.2 ns

1.4 ns

3.5 ns

3.2 Method Based on UTC(k) and BIPM Circular T In order to evaluate BGTOE parameters, a method based on UTC(k) and BIPM Circular T is also proposed. The basic idea is to establish a co-visual time comparison link between BDT and UTC(k) to obtain BDT-UTC(k), and then obtain the UTC-GPST and UTC-GLONASST in BIPM Circular T. Principle of this method is shown in Fig. 2. However, this method cannot evaluate BDT-GST owing that the UTC-GST has not been given in BIPM Circular T yet. Moreover, limited by the frequency of calculating UTC of every 5 days, the assessment results of this method will be sparse with a sampling interval of 5 days. In this method, data of UTC(NTSC) and UTC-GNSST given by BIPM Circular T are used, so the evaluation uncertainty is mainly related to these two values, the uncertainty budget is shown in Table 5.

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BDT

GPST

BDT-GPST

Co-visual

UTC(k)

GLONASST

BIPM circular T

BIPM circular T

BIPM circular T

UTC

Fig. 2. Assessing method based on UTC(k) and BIPM

Table 5. Uncertainty of the assessing method based on UTC(k) and BIPM Evaluation object BDT-UTC(NTSC) UTC(NTSC)-UTC UTC-GNSST Total uncertainty BDT-GPST BDT-GLNT

1.4 ns 1.4 ns

2.5 ns

10* ns

10.4 ns

2.5 ns

100* ns

100.0 ns

* Note: According to the description in BIPM Circular T, the global uncertainty is of the order of

10 ns for UTC-GPST and 100 ns for UTC-GLONASST. The corresponding class A uncertainties calculated in this paper using 100-day data is 3.2 ns and 1.8 ns.

4 Monitoring and Evaluation Results of BGTOE 4.1 Monitoring Results of BGTO The BGTO parameters broadcasted by BeiDou since July 2020 are shown in Fig. 3. Navigation messages are uploaded hourly in BeiDou system, so the sampling interval of the monitoring result is 1 h. The figure shows that GPST and GST are in good agreement, while there is a deviation of about 20 ns between GLONASST and GPST as well as GST. The three curves fluctuate in a similar trend, which is a reflection of the fluctuation of BDT. 4.2 Monitoring and Evaluation Results of BGTOE Based on UTC(k) The BDT-GPST broadcasted by BeiDou system and obtained using UTC(NTSC) are shown in Fig. 4, where the former has a sampling interval of 1 h and the latter has a sampling interval of 15 min. The difference between this two curves is BGTOE, which is shown in Fig. 5. It can be seen that the value of BGTOE fluctuates between 26.7 ns and 18.7 ns, and the standard deviation of BGTOE is σBGTOE, GPS = 10.4 ns.

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Fig. 3. Monitoring result of BGTO broadcast by BeiDou system

Fig. 4. Monitoring result of BGTO based on UTC(NTSC)

Fig. 5. Assessment result of BGTOE based on UTC(NTSC)

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4.3 Monitoring and Evaluation Results of BGTOE Based on UTC(k) and BIPM Circular T The BDT-GPST, BDT-GLONASST broadcasted by BeiDou system and obtained using UTC(NTSC) and BIPM Circular T are shown in Fig. 6. The former has a sampling interval of 1 day, while the latter has a sampling interval of 5 days limited by the UTC calculation frequency. In addition, limited by the co-viewing comparison data between UTC(NTSC) and BDT, only 2-month data are given in this paper. The BGTOE curves were obtained by doing the difference separately as shown in Fig. 7, and it can be seen that the value of BGTOE is between −24.9 ns~7.3 ns, and the standard deviation of BGTOE are σBGTOE, GPS = 8.8 ns, σBGTOE, GPS = 9.8 ns.

Fig. 6. Monitoring result of BGTO based on UTC(NTSC) and BIPM circular T

Fig. 7. Assessment result of BGTOE based on UTC(NTSC) and BIPM circular T

4.4 Results of the BGTOE’s Effect on Positioning From the results above, it can be seen that the BGTOE is not exactly zero-mean noise, but fluctuates with a range from −26.7 ns to 18.7 ns during the evaluation period.

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This fluctuation introduces position and time deviations in a joint positioning. Taking the maximum BGTOE of −26.7 ns, the position and time deviations generated by the BGTOE are calculated using the two constellation configurations in Sect. 2 and are shown in Table 6. Table 6. Effects of BGTOE on position and time offset Position Deviation

Better constellation Worse constellation configuration configuration

Position deviation (m)

6.1

12.6

Horizontal deviation (m) 4.8

8.0

Vertical deviation (m)

3.7

9.6

Time deviation (ns)

4.5

14.7

From the results above, it can be seen that the standard deviation of the BeiDou system BGTOE is about 10 ns during the evaluation period. Taking the worse value in the evaluation results as σBGTOE = 10.4 ns, and using the two constellation configurations in Sect. 2, the impact of BGTOE on positioning accuracy is calculated and shown in Table 7. Table 7. Effect of BGTOE on joint positioning accuracy Precision Loss

Better constellation Worse constellation configuration configuration

Position error (m)

3.6

11.0

Horizontal error (m) 1.5

5.6

Vertical error (m)

9.5

9.5

Time error (ns)

3.8

23.6

The analysis results above show that for short-term positioning or single positioning in the evaluation time period, the BGTO parameters broadcast by BeiDou system introduce a maximum position deviation of about 12.6 m and a time deviation of 14.7 ns. For a longer time scale, the BGTO parameters introduce a loss of position accuracy of about 11 m and a loss of time accuracy of about 23.6 ns in a statistical sense. Therefore, the BGTO parameters’ performance of BeiDou system can basically meet the requirements of joint positioning, but there is still room for optimizing from the perspective of improving joint positioning performance.

5 Conclusion In this paper, the BGTO and its deviation error BGTOE of BeiDou system are studied, and the quantitative impacts of BGTOE on joint positioning result and accuracy are

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derived. Then the BGTOE evaluation methods based on UTC(k) and BIPM circular T are proposed, and the monitoring evaluation and impact analysis of BGTOE are carried out. The main conclusions are (1) BGTOE will cause position and time deviation for joint positioning, and the impact coefficients are only related to the constellation configuration with the value around 0.5. (2) BGTOE will cause position and time accuracy loss for joint positioning, and the impact coefficients are only related to constellation configuration, which is around 1 and 2, respectively. (3) The BGTOE of BeiDou system fluctuates from −26.7 ns to 18.7 ns, and the σBGTOE is about 10 ns during the evaluation period in this paper. This performance introduces a maximum position deviation of about 12.6 m and a time deviation of 14.7 ns in a single position or short-time position. In a long-term statistical sense, it brings about a position accuracy loss of about 11 m and a time accuracy loss of about 23.6 ns. It can basically meet the requirements of joint positioning, but there is still room for optimization from the perspective of improving the joint positioning performance. It should be noted that the evaluation results of BGTOE in this paper only include BDT-GPST and BDT-GLONASST, and the evaluation period is not long enough. Therefore, the next work include: 1) evaluating and analyzing BGTOE on a longer time scale; 2) studying other BGTOE evaluation methods to cover the evaluation of BDT-GST, and using UTC parameters for evaluation is a possible direction; 3) conducting experimental validation for the impact of BGTOE on joint positioning.

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9. Wenhai, J., Huiqun, Z., Lin, Z., et al.: Evaluation method and analysis of GNSS broadcast coordinated universal time error. J. Surv. Mapping 49(7), 805–815 (2020) 10. Xue, Z.: Determination of time deviation of GNSS system and its influence on positioning results. Acta Temporalica Sinica 37(1), 57–64 (2014) 11. Chen, J., Wu, B., Hu, X., et al.: GPS/glonss time difference monitoring and its application in multi-mode positioning. In: Electronic Proceedings of the Third China Annual Conference on Satellite Navigation: S02 Satellite Navigation Signal System and its Compatibility and Interoperability (2012) 12. Zhang, H., Li, X., Xu, L.: GNSS time deviation monitoring and forecasting. In: China Satellite Navigation Academic Annual Meeting (2010) 13. China Satellite Navigation Office. BeiDou Navigation Satellite System Signal in Space Interface Control Documen. Open Service Signal B1I(Version 3.0) [Z/OL]. (2019–02). Accessed 30 Jan 2021. http://www.BeiDou.gov.cn/xt/gfxz/201902/P0201-90227592987952674.pdf 14. Zhao, L., Ding, J., Ma, X.: Principles and applications of satellite navigation. Northwestern Polytechnic University Press [et al.] (2011)

A Satellite-Ground Precise Time Synchronization Method and Analysis on Time Delay Error Caused by Motion Yanming Guo1,2,3(B) , Yan Bai1,3(B) , Shuaihe Gao1 , Zhibing Pan1 , Zibin Han1,2,3 , Yuping Gao1 , and Xiaochun Lu1,3 1 National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

[email protected]

2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of

Sciences, Xi’an 710600, China

Abstract. Currently for the accuracy of long-range time transfer can only reach up to 100 ps, limiting the wide application of high-precision time-frequency reference in space science. The study of the satellite-ground precise time synchronization method can provide an effective solution for developing long-range time transmission technology. In this paper, a satellite-ground time synchronization method based on two-way time difference measurement is studied. Simultaneously, we propose a method for correcting the time delay error caused by satellite and ground station motion, and the related analysis is carried out. The simulation results show that when we control the attitude error within 72 as (0.02°), the phase center calibration error is less than 1 mm, the precise orbit determination error is less than 10 cm (three axes), the satellite-ground time synchronization performance is better than 0.02 ps after correcting the time delay error caused by target motion based on the two-way time difference measurement without considering other error factors. With the other error impacts (ignore calibration error of atmospheric parameters), the satellite-ground synchronization performance can reach 0.45 ps. The research of satellite-ground precise time synchronization and error correction can provide an inevitable technical accumulation and reference for high-precision time-frequency transmission technology in space. Keyword: Satellite-ground time synchronization · Two-way time difference measurement · Time delay caused by motion · Error correction · Performance

1 Introduction In the middle of the 20th century, the invention of atomic clocks such as cesium clocks and hydrogen clocks based on quantum transition opened a new era for time measurement., with inaccuacies improving from 10 ms (ms) per day in 1967 to 100 ps (ps) per day for the primary cesium atomic clocks using laser-cooled atomic fountains. The best atomic fountains approach ten ps error per day, i.e., frequency stability of 1E-16@1day. The © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 158–171, 2021. https://doi.org/10.1007/978-981-16-3146-7_16

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frequency stability of an optical atomic clock using laser cooling and other advanced technologies can be better than 1E-17@1day [2], and it will be able to obtain better time-frequency performance in a microgravity environment [3]. The rapid development of space atomic clock technology makes the long-distance transfer of high-precision time and frequency [4] has become a current research hotspot. High-precision time and frequency transfer technology are vastly used in necessary physical testing, geophysical measurement, relativity verification, satellite navigation, in-depth space exploration, etc. It is also an effective means to achieve high-precision atomic clock performance evaluation in space. Atomic Clock Ensemble in Space (ACES) is a European Space Agency (ESA) project [5], aims to operate a new generation of atomic clocks in the microgravity environment of the International Space Station (ISS) and build high-precision time and frequency transfer links with ultra-stable clocks on the ground. Simultaneously, a multi-frequency twoway micro-wave link (MWL) time synchronization algorithm was developed. Therefore, this method can achieve a satellite-to-ground time synchronization accuracy better than 10 ps [6]. To further improve the accuracy of time and frequency transmission, ESA plans to launch another time and frequency reference project (EGE) to enhance the accuracy based on the ESA-ACES project and achieve stability or uncertainty E-18 space timefrequency reference. On this basis, the use of MWL and carrier phase measurement methods can achieve ps-level satellite-ground time synchronization accuracy [7]. China is currently deploying and constructing a high-precision time-frequency system for the space station, which requires higher measurement accuracy for MWL [8, 9], while the traditional two-way time comparison accuracy is sub-ns [10], which cannot meet the corresponding demand. In order to obtain higher time comparison accuracy, it’s necessary to develop high-precision time measurement links and data processing algorithms. In this paper, we study the requirements for error compatible with the operation of the next generation space clocks under the time synchronization application scenario of low-orbit spacecraft and ground station. Through research based on two-way time difference measuring of precise time synchronization method, the paper introduces a high-speed relative motion of the spacecraft and the ground station in space, analyzing the time delay error caused by target motion. In Sects. 1.1 and 1.2, we briefly describe the satellite-ground precise time synchronization method and motion error theory. We explicitly derive the effect of several errors on the time synchronization in Sect. 1.3. Up to this point, our results are entirely general (within the specified approximations). Our main results are calculating the effect of these errors on the determination of the relative motion and the time transfer (MWL). 1.1 Satellite-Ground Precise Time Synchronization 1.1.1 Two-Way Time Difference Measurement Principle The two-way time difference measurement technique is an effective means of longdistance time transmission [11]. Assuming that the low-orbit spacecraft and the ground station receive or transmit signals with frequencies of F1 and F2 simultaneously, the

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Fig. 1. The principle of two-way time synchronization.

principle of two-way time synchronization is shown in Fig. 1. In the earth centered inertial coordinate frame, we established a two-way measurement between the spacecraft and ground station:          ⎧  Snd Rcv Rcv Snd  Rcv + cδSSnd ⎪  + cxG tGRcv − cxS tSSnd + cδG ⎪ ρSG (tS , tG ) = RG tG − RS tS ⎪ ⎪ ⎪           ⎪ ⎪ ion tro ⎪ RS tSSnd , RG tGRcv + δKG RS tSSnd , RG tGRcv + δSG ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ g ⎨ + (δ rel (t Rcv ) − δ rel (t Snd )) − δ OF + δ + εSG G G S S SG SG           ⎪ Snd Rcv Rcv Snd  Snd ⎪ t − R t ρ (t , t ) =  + cxS tSRcv − cxG tGSnd + cδSRcv + cδG R ⎪ GS G S S G G S ⎪ ⎪ ⎪           ⎪ ⎪ ⎪ + δ ion R t Snd , R t Rcv + δ tro R t Snd , R t Rcv ⎪ ⎪ G G S S G G S S GS GS ⎪ ⎪ ⎪ ⎩ g rel Rcv rel Snd OF + (δS (tS ) − δG (tG )) − δGS + δGS + εGS

(1)

Where c is the speed of light in vacuum; ρSG and ρGS are downlink pseudo-range and uplink pseudo-range respectively; RS and RG are the position vectors of the low-orbit spacecraft and the ground station in ECI, respectively; xS and xG are the clock difference of the spacecraft and the ground station.; δ Snd and δ Rcv are the hardware transmission delays of the signal transmitting channel and receiving channel; δ rel is the equivalent delay of relativistic periodic effect; δ ion is the equivalent time delay of ionosphere effect; δ tro is the equivalent time delay of troposphere effect; δ OF is the equivalent delay of phase center offset (PCO); δ g is the signal transmission delay caused by the gravitational field of the earth; and ε is ranging noise.

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Due to the space transmission delay of the signal and the spacecraft’s high-speed motion, the satellite-ground two-way measurement data contain the satellite position and clock difference information at different coordinate times. For the two-way ranging at the same receiving time t0 , Eq. (1) can be modified as: ⎧ ⎪ ρSG (tSSnd , tGRcv ) = |RG (t0 ) − RS (t0 )| + dSG + cxG (t0 ) − c[xS (t0 ) + dxS (tSSnd , t0 )] ⎪ ⎪         ⎪ ⎪ ⎪ Rcv Snd ion Snd tro Snd ⎪ + cδ R t , R R t , R + cδ + δ + δ (t ) (t ) S G 0 S G 0 ⎪ G S SG S KG S ⎪ ⎪ ⎪ ⎪ ⎨ + (δ rel (t Rcv ) − δ rel (t Snd )) − δ OF + δ g + εSG G G S S SG SG Snd Rcv ⎪ ρGS (tG , tS ) = |RS (t0 ) − RG (t0 )| + dGS + cxS (t0 ) − c[xG (t0 ) + dxG (tGSnd , t0 )] ⎪ ⎪ ⎪         ⎪ ⎪ Snd ion tro ⎪ ⎪ + cδSRcv + cδG RG tGSnd , RS (t0 ) + δGS RG tGSnd , RS (t0 ) + δGS ⎪ ⎪ ⎪ ⎪ ⎩ g rel Snd OF (tG )) − δGS + δGS + εGS + (δSrel (tSRcv ) − δG (2) Where d is the correction of spatial distance error, dx(t, t0 ) is the correction of clock difference between spacecraft clocks and ground clocks. In the time comparison between the low-orbit spacecraft and the ground station, it’s important to correct the system error during signal transmission. Then, the clock difference x between the satellite and ground station can be calculated by making the difference between the two-way measurement equation. xGS (t0 ) =xS (t0 ) − xG (t0 )   Snd , t Rcv ) − ρ (t Snd , t Rcv ) + (d Snd Snd = ρGS (tG SG S SG − dGS ) + c(dxG (tG , t0 ) − dxS (tS , t0 )) S G     

     Rcv − δ Snd − c δ Rcv − δ Snd + δ ion R t Snd , R (t ) − δ ion R (t Snd ), R (t ) + c δG G 0 S 0 G S S SG S S GS G G      

tro R t Snd , R (t ) − δ tro R (t Snd ), R (t ) + δSG S S G 0 S 0 GS G G rel (t ) + δ rel (t Snd ) − δ rel (t Snd ) − δ rel (t )) + δ OF − δ OF + δ g − δ g +ε + (δG 0 SG − εGS 2c G G S S S 0 SG GS SG GS

(3)

The proposed method is similar to the time synchronization method used in the intersatellite link (ISL) of the Beidou-3 system (BDS-3). However, the time synchronization performance of BDS-3 can only achieve sub-ns. When the conditions are available to achieve higher transmission accuracy, more accurate error processing methods are also needed. 1.1.2 Error Handling Strategy In the context of the high-precision (ps level) atomic clock set carried on the high -speed low-orbit spacecraft, to achieve the ps level time transfer accuracy, it is necessary to analyze and correct the error term generated in the process of two-way time synchronization. The specific errors and their processing strategies are shown in Table 1: Under the premise that the hardware capability is up to standard, we can achieve higher time/frequency comparison accuracy (ps level). Hence, we should deeply consider the effect of the errors mentioned above and use the corresponding methods to eliminate the errors to satisfy the link stability. Simultaneously, the rapid movement of low-orbit satellites will cause more significant delay errors, which has a more significant impact

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Method

Channel time delay

Closed-loop self-calibration

Time delay caused by motion Ephemeris + Model ionosphere

Multi-frequency model

troposphere

Model

Periodic relativistic effect

Higher-order model

Gravity delay Phase center offset

Model Model or Two-way elimination

on the satellite-ground time synchronization performance, and the correction method can reduce the impact of motion delay errors [12]. 1.2 Delay Error Caused by Motion and Its Correction Method 1.2.1 Spatial Distance Error Correction Method

Fig. 2. Spatial distance error between satellite and ground in two-way ranging. (Spatial distance error caused by the asymmetry path, dSG and dGS show the asymmetry part)

In Eq. (3), the spatial distance error correction amount in the two-way ranging can be expressed as: dis = (dSG − dGS )/2c

(4)

As shown in Fig. 2, the Spatial distance error term is caused by the high-speed relative motion between the spacecraft and the ground station. Due to the fast action of the spacecraft, this error term is of high magnitude. It needs to be accurately corrected based

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on the high-precision orbit information (sp3 doc.) provided afterward. The calculation formulas are given by  dSG = |RG (t0 ) − RS (tSSnd )| − |RG (t0 ) − RS (t0 )| (5) dGS = |RS (t0 ) − RG (tGSnd )| − |RS (t0 ) − RG (t0 )| When the uplink and downlink pseudo-range data are known, the above Eq. (5) can be rewritten as: ⎧ ρSG (tSSnd , tGRcv ) ⎪ ⎪ )| − |RG (t0 ) − RS (t0 )| ⎨ dSG = |RG (t0 ) − RS (t0 − c (6) Snd Rcv ⎪ ⎪ ⎩ dGS = |RS (t0 ) − RG (t0 − ρGS (tG , tS ) )| − |RS (t0 ) − RG (t0 )| c Therefore, the spatial distance error can be accurately corrected using the following Eq. (7): dis = (dSG − dGS )/2c 

ρSG (tSSnd , tGRcv ) )| c  ρGS (tGSnd , tSRcv ) − |RS (t0 ) − RG (t0 − )| / 2c c =

|RG (t0 ) − RS (t0 −

(7)

Here, ρGS is uplink pseudo-range and ρSG is downlink pseudo-range, the ECI orbital coordinate RG of the ground station is known, RS is the result of post precise orbit determination (POD) of the spacecraft. In this expression (7) can be interpreted as the compensation of spatial distance error, it is shown that the final time synchronization accuracy is mainly affected by the orbit accuracy of spacecraft and ground station in the ECI coordinate. However, the orbit accuracy is affected by the attitude error, phase center calibration error, and POD error. 1.2.2 Clock Error Correction Method Similarly, combining the previous Eq. (3) with the same expressed in clock error correction clk , we obtain clk = (dxG (tGSnd , t0 ) − dxS (tSSnd , t0 ))/2

(8)

To simplify Eq. (8), we use the uplink and downlink pseudo-range data to calculate signal transmission time. Thus, the Eq. (8) can be rewritten as:  clk = (xG (t0 −

ρGS (tGSnd , tSRcv ) ) − xS (t0 )) − (xG (t0 ) − xS (t0 )) c

+ (xS (t0 ) − xG (t0 )) − (xS (t0 −

 ρSG (tSSnd , tGRcv ) ) − xG (t0 )) /2 c

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 ρSG (tSSnd , tGRcv ) ρGS (tGSnd , tSRcv ) )) −(xG (t0 ) − xG (t0 − )) /2 c c

(9)

Where xG is the clock error of the ground station, it can be accurately measured, and xS is the precise clock error of spacecraft. 1.3 Simulation Results and Analysis

Fig. 3. MWL data simulation system

To verify the correctness of the satellite-ground precise time synchronization algorithm and analyze the delay error caused by spacecraft’s motion. We assume that a high-precision optical frequency clock on a low Earth-orbiting spacecraft (≈450 km altitude), the clock’s frequency stability in a microgravity environment is around E-18. The ground station is located in Xi’an, and the ground station clock is used as a time reference. We also assume that there is no error in the calibration of atmospheric parameters, and the equipment delay and other measurement errors caused by the equipment are ignored. Based on the above time synchronization theory and error correction strategy, the time synchronization between the simulated low-orbit spacecraft and the ground station was realized based on the two-way time difference measurement, the distance and clock difference caused by the relative motion were corrected. MWL data simulation system is shown in Fig. 3, the box on the left represents the input parameters, the grey box represents the algorithm model to be used, the red section shows the final product that the simulation software can obtain (include the two-way pseudo- range observation data, relative clock difference and geometric distance between the spacecraft and the ground station). 1.3.1 Observation Data The MWL is characterized by its continuous emission. It measures the time offsets between the locally generated and received signals. It provides three or more measurements (or observables) of the code (one on the spacecraft, two or more on the ground)

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and three or more measurements of the phase of the carrier frequency at a sampling rate of one Hertz. When the cut-off height Angle is set to 20°, the MWL data simulation system is used to generate the satellite-ground two-way pseudo-range observation data of one day (0~86400 s), and a total of four continuous arc observations data are obtained. One of the arcs with more continuous data was selected for the experiment, with a total data of about 300 s and a time interval of 1 s, as shown in Fig. 4.

Fig. 4. Pseudo-range data obtained by simulation

1.3.2 Error Correction and Performance Analysis Clock Difference Error The pseudo-range observation data of the simulation above is used to obtain the clock difference non-simultaneous error correction amount of the two-way MWL by using Eq. 9. The result is shown in Fig. 5.

Fig. 5. The error of clock difference caused by the motion of satellite and ground station

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As shown in Fig. 5, when the spacecraft is carrying an atomic clock of E-18 magnitude, the clock difference error caused by its high-speed motion is no more than E-14 ps, which is almost negligible compared to the time synchronization accuracy requirement of 1 ps. Therefore, in this case, the error of clock difference caused by motion does not to be corrected. Spatial Distance Error Similarly, we use the above observation data to calculate the two-way Link space distance error, and the result is shown in Fig. 6.

Fig. 6. The error of spatial distance caused by the motion of satellite and ground station

Figure 6 shows that the spatial distance error reaches tens of nanoseconds in the twoway system proposed in this paper, which greatly influences the time synchronization accuracy of ps-level, and we can use the precise orbit data obtained after processing to correct this error accurately [13]. Precise orbit determination (POD) data is associated with the center of mass of GPS receiver. Two-way pseudo-range is obtained by time-frequency equipment, the time-frequency equipment antenna and GPS receiver antenna phase center is not in the same location. The spacecraft attitude or orbit uncertainty leads to the ephemeris orbit data is inconsistent with the actual orbit data, which affects the time synchronization performance. Therefore, we considered the impact of antenna phase center calibration error, attitude error and POD error. The phase center calibration is done on the ground. Therefore, the calibration error can be controlled within 5 mm. Figure 7 and Table 2 show the residual and uncertainty of the residual after correcting the spatial distance error for different phase center calibration errors. As shown in Fig. 7, in the case of only phase center calibration error, the uncertainty (Equivalent to Root Mean Square) of the spatial distance correction residual increases with the increase of phase center calibration error. The residual after correcting the spatial distance error is less than 0.12 ps, and the uncertainty of residual is better than 0.03 ps, which does not have a significant impact on the ps-level accuracy of links.

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Table 2. The uncertainty of residual (After correcting the spatial distance error for different phase center calibration errors). Phase center calibration error (mm)

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Fig. 7. Residual after spatial distance correction (Different color lines show the results of different phase center calibration errors)

Fig. 8. Residual after spatial distance correction (Different color lines show the results of calibration errors of different satellite attitude error) Table 3. The uncertainty of residual (After correcting the spatial distance error for different attitude errors). Attitude error (as)

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Figure 8 and Table 3 show results of spatial distance correction in different attitude angles. It can be seen that the uncertainty of spatial distance correction residual is better than 0.01 ps when the attitude is within 80 arc seconds (as). The accuracy of precise orbit determination can reach within 10 cm afterward. Under different orbit determination errors, the spatial distance correction residual and its uncertainty are shown in Fig. 9 and Table 4. When the POD error is less than 10 cm, the residual after correcting the spatial distance error is not more than 0.06 ps, and the uncertainty of residual is not more than 0.015 ps.

Fig. 9. Residual after spatial distance correction (Different color lines show the results of different satellite POD error)

Table 4. The uncertainty of residual (After correcting the spatial distance error for different POD errors). POD error (cm) 10 Uncertainty of residual (ps)

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After integrating the influence of various error factors on the spatial distance correction, combined with the existing technical indexes, the effect of multiple factors on the spatial distance correction is shown in Table 5: Table 5. The influence of comprehensive error factors Attitude error

phase center calibration error

POD error

Uncertainty of residual

1, the M correlation peaks can be distinguished. When δ > 1, no matter which shifted code is transmitted, the correlation peak can be obtained by correlating with the local reference code. Moreover, when the code delay is 0, that is, when the local reference signal is aligned with the received signal, there will always be a correlation main peak, which is the basis of the proposed method for acquisition and tracking. The correlation functions of different code periods are coherently accumulated. Considering that the message is random, the different CSK symbols are broadcasted with equal probability. Only the correlation peak with 0 delay is accumulated and enhanced all the time, and the final correlation function is equivalent to the sum of the above correlation functions. Therefore, in the acquisition stage, after multi code period coherent accumulation, the equivalent correlation function is as follows: Racquisition (τ ) =

M −1 

Rm,ref (τ )

m=0

=



(M − |a|) · 1 −

|τ +a·δ·Tc | Tc

  , |τ + a · δ · Tc | ≤ Tc , a = 1 − M , . . . , M − 1

0, otherwise (5)

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The final acquisition result is to find the maximum correlation peak, similar to the traditional BPSK signal. It is noted that there are multiple peaks in the correlation function, and the ambiguity problem may occur. However, different from BOC Signal, each peak is separated by δ chips, which can be effectively suppressed by applying acquisition search strategy. The simulation conditions are consistent with the previous one. The results are shown in Fig. 3. The code phase delay is set to 100T c . The results show that the method is effective. 9 X: 100.1 Y: 8.996

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Fig. 3. The proposed acquisition method with 40 period coherent accumulations

It should been noted that the proposed method increases the implement complexity. On the one hand, the local reference code signal is changed from 1-bit quantization to U + 1 bits quantization. In order to simplify, the received signal can be correlated with M shifted code sequences respectively, and then added to obtain the resulting correlation function. Each shifted code is 1-bit quantization, which reduces the computational complexity. On the other hand, the required number of coherent accumulation increases. In practical application, when the C/N0 is high, it only needs to accumulate a small number of code periods to distinguish the main peak from the side peak.

4 Low Complexity Tracking Method for CSK Signal The traditional tracking method for BPSK signal cannot be directly applied to CSK signal, because the transmitted CSK symbol is unknown. 4.1 The Proposed Tracking Scheme The tracking loop structure applied in this paper is similar to that of the traditional tracking loop, but the main difference is the local reference signal cref (t). The received signal correlated with the Early, Prompt, Late versions of cref (t). The correlation values of I-branch and Q-branch are IE, IP, IL, QE, QP,QL. The DLL is used for code tracking and the pure PLL is used for carrier tracking (CSK has no 180 degree phase reversal, so pure PLL can be used).

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Assuming that the IF carrier frequency has been correctly acquired, i.e. f˜IF ≈ fIF . The correlator output is as follows:

√ d jθ e IE + jQE = 2C Rˆ m,ref τ − + nIE + jnQE 2 √ IP + jQP = 2C Rˆ m,ref (τ )ejθ + nIP + jnQP

√ d jθ ˆ IL + jQL = 2C Rm,ref τ + + nIL + jnQL (6) e 2 Where C is the signal power. Rˆ m,ref (τ ) is the correlation function under the band∞ limited condition, i.e. Gm,ref (f ) = −∞ Rm,ref (τ )e−j2π f τ d τ and Rˆ m,ref (τ ) = ∞ j2π f τ df . n , n , n , n , n , n IE QE IP QP IL QL are noise terms. d is −∞ Gm,ref (f )H (f )e correlator spacing. For the carrier tracking loop, the carrier loop discriminator function can be as follows: Dcarrier = atan2(QP, IP)

(7)

These correlation values can be obtained by one code period accumulation or multiple code period coherent accumulation. In fact, when CSK is demodulated, each shifted code sequence is generated to obtain the corresponding correlation value. In this case, the maximum correlation value can be used to calculate the carrier loop discriminator output, and the carrier tracking accuracy is equivalent to that of the traditional BPSK. The key is the code tracking method. The code loop discriminator function can be written as: 



(8) Dcode = IE 2 + QE 2 − IL2 + QL2 Figure 4 shows the code discriminator curve at the main peak, which can be used to track the code delay. 2 1.5

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Fig. 4. GNSS security augmentation method based on LEO satellite

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4.2 Code Tracking Error The correlation values satisfy the following joint Gaussian distribution at τ ≈ 0, i.e. (IE, IL, QE, QL)T ∼ N (μ, )

(9)

Where μ and  are √

T        2C Rˆ m,ref −d 2 Rˆ m,ref d 2 0 0 ⎤ ⎡ ˆ 0 0 Rref ,ref (0) Rˆ ref ,ref (d ) ⎥ ˆ ˆ N0 ⎢ 0 0 ⎥ ⎢ Rref ,ref (−d ) Rref ,ref (0) = 0 0 Rˆ ref ,ref (0) Rˆ ref ,ref (d ) ⎦ TP ⎣ 0 0 Rˆ ref ,ref (−d ) Rˆ ref ,ref (0) μ=

(10)

respectively. Where Rˆ ref ,ref (τ ) is the auto-correlation function of cref (t) under ∞ bandwidth limitation. Considering that Gref ,ref (f ) = −∞ Rref ,ref (τ )e−j2π f τ d τ , ∞ Rˆ ref ,ref (τ ) = −∞ Gref ,ref (f )H (f )ej2π f τ df , we have Gref ,ref (f )=Tc sinc2 (π fTc )

 (M − |a|)ej2π faNTc

a=1−M

 = Tc sinc (π fTc ) M + 2

M −1 

M −1 



((M − a)2 cos(2π faNTc ))

(11)

a=1 M −1 We can see that Rm,ref (τ ) = Rref ,ref (τ ). Therefore, for the main peak, m=0     we have E Rm,ref (τ ) = Rref ,ref (τ ) M . So, Rˆ m,ref (τ ) ≈ Rˆ ref ,ref (τ ) M . As shown in Fig. 5.

Fig. 5. The correlation function at the main peak after filtering

The code tracking error variance is expressed as: σ2 =

2BL (1 − 0.5BL TP )TP σV2 KV2

(12)

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Where BL is the code loop noise bandwidth unit in Hz. σV is the discriminator output standard deviation, and K V is the discrimination curve gain. Similar to the derivation process of reference [16], the gain of discrimination curve is derived as follows:  ∞

 ∞ 16π C H (f )Gref ,ref (f ) cos(π fd )df · H (f )fGref ,ref (f ) sin(π fd )df KV = M2 −∞ −∞ (13) The variance of discriminator output is as follows: 

16C ˆ 2 d 2 2 2 σ4 + 8 1 − ρ R − ρ)σ σV ≈ (1 2 M2 2

(14)

Where σ 2 = TNP0 Rˆ ref ,ref (0), ρσ 2 = TNP0 Rˆ ref ,ref (d ).

5 Performance Analysis

fa

The detection probability with a false alarm probability P =10-3

In this section, the acquisition and tracking performance of the proposed method are simulated and analyzed. The parameters are as following: The signal is CSK(3,1) modulated signal. The code rate is 2.046 Mcps, and the chip waveform is rectangle. The code length is 2046. One code period is 1 ms. The signal bandwidth is 6.138 MHz. Figure 6 shows the detection probability of the proposed method when the false alarm probability is 0.001. It can be seen that the detection probability can be equivalent to the corresponding BPSK signal by coherent accumulation of M = 8 code periods. By increasing the number of coherent accumulation, the detection probability can be further improved. 1 BPSK,Tp=1ms

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Fig. 6. The detection probability with a fixed false alarm probability 0.001

The result of code tracking error is shown in Fig. 7. BL = 1 Hz, d = T c . It can be seen that compared with BPSK signal with the same code rate, the tracking performance of CSK signal with the proposed method would be degraded when the coherent integration time is the same. However, CSK modulated signals can be accumulated coherently in multiple periods, and BPSK data components usually adopt non-coherent accumulation due to the influence of data sign. In this way, for low C/N 0 , the performance difference between the two kinds of signals will be reduced.

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6 Conclusions CSK modulated signal is gradually applied in GNSS signal because of its flexible high data rate capability. However, it is not suitable for independent ranging, and needs the assistance of other signal components. On the basis of extending the definition of CSK signal, this paper proposes a method of independent acquisition and tracking of CSK signal. Compared with BPSK signal with the same code rate, the performance of CSK signal acquisition and tracking with this proposed method would suffer some degradation, but it can be compensated by increasing the time of coherent integration. More importantly, the significance of the proposed method is increases the independence of CSK signal, which provides the basis for the further application of CSK signal in GNSS.

References 1. Cabinet Office. Quasi-Zenith Satellite System Interface Specification Centimeter Level Augmentation Service (IS-QZSS-L6–001), Draft Edition, 31 August 2018 2. Chatre, E., Benedicto, J.: Galileo programme update. In: ION GNSS+ 2020, pp. 950–977 (2020) 3. Shen, J., Geng, C.: Update on the BeiDou navigation satellite system (BDS). In: ION GNSS+ 2020, pp. 978–1015 (2020) 4. Garcia-Peña, A.J., Paimblanc, P., Julien, O., Ries, L., Grelier, T.: Analysis of different CSK configurations in an urban environment when using non-coherent demodulation. In: Navitec 2014, 7th ESA Workshop on Satellite Navigation Technologies, December 2014, Noordwijk, Netherlands (2014) 5. Peña, A.G., Ries, L., Boucheret, M.L., Corazza, S., Macabiau, C., Escher, A.C., Damidaux, J.L.: Implementation of Code Shift Keying signaling technique in GALILEO E1 signal. In: NAVITEC 2010, 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals, December 2010, Noordwijk, Netherlands, pp. 1–8 (2010) 6. Garcia-pena, A.J., Aubault-Roudier, M., Ries, L., Boucheret, M.L., Poulliat, C., Julien, O.: Code Shift Keying prospects for improving GNSS signal designs. In: InsideGNSS, November/December 2015, pp. 52–62 (2015) 7. Garcia-Pena, A., Julien, O., Anghileri, M., Floch, J.J., Paonni, M.: Multi-purpose TDM component for GNSS. In: ION GNSS+ 2018, pp. 943–962 (2018) 8. Garcia-Pena, A., Salos, D., Julien, O., Ries, L., Grelier, T.: Analysis of the use of CSK for future GNSS signals. In: ION GNSS+ 2013, pp. 1461–1479(2013)

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9. Anghileri, M., Floch, J.J., Margaria, D., Motella, B., Garcia-Peña, A., Julien, O., Macabiau, C., Chauvat, R., Paonni, M.: FUNTIMES: future navigation and timing evolved signals. In: ION GNSS+ 2018, pp. 876–912 (2018) 10. Andreotti, R., Emmanuele, A., Fontanella, D., Zanier, F., Luise, M.: Code-Shift-Keying (CSK) with advanced FEC coding for GNSS applications in satellite multipath channel. In: ION/IEEE PLANS (2014) 11. Aubault-Roudier, M., Ries, L., Poulliat, C., Boucheret, M.-L., Garcia-Pena, A., Julien, O., Kubrak, D.: LDPC Channel code optimization for a GNSS CSK-modulated signal. In: ION GNSS+ 2015, pp. 1888–1901 (2015) 12. Roudier, M.: Analysis and Improvement of GNSS Navigation Message Demodulation Performance in Urban Environments. Signal and Image Processing. INP Toulouse, 2015. English (2015) 13. Chen, Y., Wang, D., Chen, S., Ma, W., Li, D., Dong, Q.: Research on receiving method of Code Shift Keying (CSK) signal. In: China Satellite Navigation Conference (CSNC) 2020 Proceedingd: Volume III, pp. 298–309 (2020) 14. Nakakuki, K., Hirokawa, R.: An efficient acquisition method for the CSK signal of QZSS LEX. In: ION GNSS+ 2013, pp. 340–347 (2013) 15. Zhang, H.: An Optimized acquisition scheme with half interleaving code patterns in a QZSS LEX single frequency receiver. In: ION GNSS+ 2016, pp. 417–426 (2016) 16. Yan, T., Wei, J., Tang, Z., Qu, B., Zhou, Z.: Unambiguous combined correlation functions for sine-BOC signal tracking. GPS Solut. 19(4), 623–638 (2014). https://doi.org/10.1007/s10 291-014-0420-6

Reflection Objects Sensing and Localization with GNSS Multipath Signals Xin Chen(B) , Yilun Shao, Di He, and Wenxian Yu Shanghai Key Laboratory of Navigation and Location Based Services, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China [email protected]

Abstract. In urban canyon environments, the reception of GNSS multipath signals will cause the degradation of positioning precision of a GNSS receiver, and sometimes will lead to hundreds of meters positioning error. However, multipath signals, which are generated by reflections of the satellite line-of-sight signal, contain information about positions and velocities of the reflection objects. Therefore, they give means for a receiver to sense surrounding objects and environments. In this paper, an algorithm for he reflection object sensing and localization with GNSS multipath signals is proposed. The results of experiments show that this algorithm is able to estimate the distance, azimuth, and elevation of the reflection object with respect to the receiver with a root mean squared error of 10 m, 10°, and 5°, respectively. This method enables a GNSS receiver with the capability of environment sensing, avoidance of obstacles, and even positioning augmentation apart from its original positioning and navigation ability. Keywords: GNSS multipath signal · Reflection object sensing · Reflection object localization

1 Introduction In urban canyon environments, GNSS signals are highly possibly reflected by surrounding buildings or objects and incident into receivers. These reflected signals are known as GNSS multipath. Multipath signals can cause the deterioration of receiver positioning accuracy. The position errors caused by multipath may reach hundreds of meters in some severe urban scenarios. Usually, multipath signals are taken as interferences to receivers and need to be eliminated or suppressed as much as possible. In the past decades, researchers have proposed different algorithms to mitigate the effects of multipath signals, including baseband signal multipath processing, multipath error suppression in position computation, multipath prediction with three dimensional (3D) city maps, etc. [1–4]. Since the GNSS multipath signal is generated by the reflection or scattering mechanism on the surface of a reflection object, it contains the information about the position and velocity of the reflection object. Thus, it provides a means for a receiver to sense the state of the reflection object and even the surrounding environment. The idea of utilizing © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 203–214, 2021. https://doi.org/10.1007/978-981-16-3146-7_20

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multipath signals was firstly proposed in wireless indoor positioning research, in there the incident angle and delay of a broadband wireless multipath signal are measured by a receiver with an antenna array. A double layer particle filter named as Rao-Blackwellized filter was designed to estimate the positions of the virtual signal emission sources, and then the receiver own position accuracy was augmented with the assistance of these estimated information [5–7]. However, the research about utilizing GNSS multipath in urban environments for position accuracy augmentation or environment perception has not been seen in publications. The challenges of using GNSS multipath signal are manifold: First, the weak power of GNSS multipath makes not easy the accurate estimation for multipath delay, carrier phase and Doppler frequency. Second, different from the static wireless signal emission sources in [5–7], GNSS satellites are fast moving, and so are the positions of the virtual multipath emission satellite. This inevitably increases the estimation difficulty for the virtual emission sources. Third, there are not only regular buildings in urban environments, but also lots of irregular objecting such as trees, traffic signs, pedestrians, vehicles, etc. Those irregular objects can produce a large amount of short lifetime and time-variant scattering multipath, which are difficult to make use of. In this paper, an algorithm is proposed that can localize the GNSS reflection objects by only using multipath signals. First, assuming that the positions and velocities of GNSS satellites, the receiver, and the reflection object are known, a signal reflection propagation model is able to be established and the formulas for the multipath signal parameters like delay and Doppler fading frequency can be derived as well. Then, a multipath parameter estimation method is proposed to extract and estimate multipath parameters from the received signals. Last, based on the constructed propagation model and the estimated multipath parameters, a particle filter is designed to properly estimate the localization and orientation of the reflection object. The experiment results show that the estimation root mean squared errors for the azimuth, elevation, and distance of the reflection object with respect to the receiver are less than 10◦ , 5◦ , and 10 m, respectively. The method proposed in this paper enables a GNSS receiver to sense the surrounding objects to a certain extent and even augment the positioning performance.

2 Multipath Signal Observation Model in Urban Scenario 2.1 Multipath Signal Geometric Propagation Model In urban environments, specular reflection and scattering reflection are the two most common multipath generation types. Specular reflection multipath usually occurs on the surface of a building and its propagation obeys the principle of specular reflection model. Scattering multipath is usually generated by reflection on pedestrians, vehicles, traffic signs, and other irregular objects in the city. Its propagation principle can be modeled by a point scattering source. Figure 1 shows the propagation paths of these two types of multipath signal. In this model, the local east-north-up (ENU) coordinate system is adopted and O represents the origin of the local coordinate system. s = [se , sn , su ]T represents the real position of the satellite, u = [ue , un , uu ]T represents the position T T   of the receiver, vs = vse , vsn , vsu and vr = vre , vrn , vru , respectively, represent the velocities of the satellite and the receiver.

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However, in a GNSS receiver, the satellite and receiver positions are normally computed in the earth-centered-earth-fixed (ECEF) coordinate system. If the ECEF coordinates of the origin O of the local ENU coordinate system is known, the satellite position s and the receiver position u can be converted between the ECEF system and the ENU system without any difficulties. The conversion method can be found in many literatures like [8, 9]. Assuming there is a reflection plan A and a smaller reflection object B around the receiver, and the corresponding reflection multipath lm and the scattering multipath lb are generated by the plan A and the object B. The purpose of this research is to estimate the position of A or B by proper processing the multipath signals. According to previous research findings [10, 11], the reflection multipath is generally produced by the large glass walls of the buildings in urban. The signal power of this type of multipath is strong and stable, thus making it easy to be detected and estimated. However, the power of the scattered multipath is weak and unstable, making the estimation for the multipath parameters unreliable. Therefore, we mainly focuses on the detection of the reflection multipath and the estimation of the reflection plane in this research. Assume that the vertical distance from the origin O to the reflection plane A is da , and the azimuth and elevation of A are denoted as αa and θa respectively. Then, the position of the reflection plane can be uniquely determined by the vector x = [da , αa , θa ]T . If we use na to denote the unit normal vector of the reflecting surface, it can be computed as: na = [cosθa sinαa , cosθa cosαa , sinθa ]T

(1)

Given the satellite position s and velocity vs , the satellite mirror image position sm and velocity vm relative to the reflection plane A can be computed by the following equation [12]: sm = −2da na − (I 3 + (na ×)(na ×))s

(2)

vm = −(I 3 + (na ×)(na ×))vs

(3)

where I 3 is a 3x3 unit matrix, (na ×) is the antisymmetric matrix of the normal vector na , whose expression is: ⎤ ⎡ 0 −sinθa cosθa cosαa (4) (na ×) = ⎣ sinθa 0 −cosθa sinαa ⎦ −cosθa cosαa cosθa sinαa 0 In a receiver, the code phase delay τ (in unit of meter) and the Doppler fading frequency fdδ (in unit of Hz) of the multipath signal with respect to the LOS signal can be estimated. Hence, we need further to develop the relationship between the delay τ and the fading frequency fdδ with the positions and velocities of the satellite and the receiver. τ = |sm − u| − |s − u| fdδ

 −1 sm − u s−u = − (vs − vr ) • (vm − vr ) • |sm − u| |s − u| λ

(5) (6)

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where | | is the vector modular operation, • is the vector dot product operation, and λ is the carrier wavelength. Since s, vs , u and vr are all known, Eqs. (5) and (6) actually establish the relationship between the receiver observation parameters τ and fdδ and the unknown reflection plane position vector x.

Fig. 1. Multipath signal geometric propagation model Fig. 2. Algorithm workflow for the estimation of multipath delay and Doppler fading frequency.

2.2 Estimation Method for the Multipath Delay and Doppler Fading Frequency In the urban canyon, a receiver often receives not only the satellite LOS signal but also a few delayed replica multipath signals at the same time. The overall incident signal expression can be written as:  

L−1 (7) s(t) = αl (t)c(t − τl (t))cos 2π f0 + flD (t) t + n(t) l=0

where αl (t) denotes the signal amplitude, c(t) is the pseudo-random code sequence of the satellite signal, τl (t) is the multipath delay, f0 is the nominal carrier frequency, and flD (t) is the Doppler frequency. The subscript l represents the l-th multipath signal and l = 0 denotes the component of the LOS signal. n(t) is the noise signal. Multipath Doppler fading frequency is defined as fdδ,l = flD (t) − f0D (t). The receiver is assumed to be in a dynamic environment, so all the multipath signal parameters are time-varying functions of time t. According to Eq. (7), we need to estimate the multipath parameters τl (t) and fdδ,l from s(t). Wireless signal channel parameter estimation algorithms, such as SAGE[13], MEDLL[14], CADLL[15], etc., can be used for multipath signal parameter estimation. However, these methods can only estimate the amplitude αl (t), delay τl (t) and carrier phase of the multipath signal, but cannot estimate the Doppler fading frequency fdδ,l .

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Furthermore, these methods are designed to estimate the channel parameters at a single snapshot, but cannot track the variations of these multipath parameters in a continuous way. According to [11, 16], a Kalman filter can be designed to estimate and track the multipath parameters accurately. We define a multipath state vector that needs to be T  estimated in the receiver: ϑ l = τ, τ˙ , α I , α˙ I , α Q , α˙ Q , ϕ, fdδ , where τ˙ is the change rate of the delay τ , α I and α Q are the amplitude values of the I and Q branches in the baseband tracking loop, α˙ I and α˙ Q are the change rate of the amplitudes, ϕ is the carrier phase difference between the multipath and the LOS, fdδ can be considered as the derivative of ϕ. Next, the following state update equation can established: ϑ l k = ϑ l k−1 + wk

(8)

where ϑ l k is the state vector at the time moment k, ϑ l k−1 is the state vector at the previous time moment, wk is the system noise,  is the state transition matrix: ⎡

A2x2 ⎢ 02x2 =⎢ ⎣ 02x2 02x2

02x2 A2x2 02x2 02x2

02x2 02x2 A2x2 02x2

⎤ 02x2 02x2 ⎥ ⎥ 02x2 ⎦ A2x2

(9)



1T and T is the update period. 01 The observation equation of the Kalman filter is:

where A2x2 =

(10)

∼

∼I

∼Q

∼

In Eq. (10), yl k is the observation vector at time moment k, τ k , α k , α k and ϕ k , respectively, represent the estimation of multipath delay, amplitudes of the I and Q branches, and the multipath carrier phase based on the channel parameter estimation algorithm (SAGE /MEDLL/CADLL). In this research, the CADLL algorithm is used  to  estimate the channel parameters. H represents the observation matrix, B1x2 = 1 0 . r4x1 is the observation noise matrix. Figure 2 shows the algorithm workflow that simultaneously estimates and tracks multipath delay and Doppler fading frequency based on the channel parameter estimation method and Kalman filter designed according to Eqs. (8), (9), and (10). The number L of the multipaths can be determined by minimum description distance of information algorithm presented in [17].

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3 Reflection Plane Localization Based on Particle Filter According to the description of the multipath propagation and measurement models in last Section, we want to localize the reflection plane A according to the measurements τ and fdδ . By observing Eq. (1) to (6), it is found that the reflection plane position has a strong nonlinear relationship with the multipath parameters, so we will adopt particle filtering algorithm to achieve this task. Particle filtering uses the Bayesian principle and implements the estimation of the unknown state through two steps: prediction and update [18]. First, we define the position vector of the reflection plane at time tk as x(tk ), and assume that the state parameter follows the first-order Markov progressive model: p(x(t k )|x(t k−1 )) = δ(x(t k ) − x(t k−1 ))

(11)

Since the reflection plane is usually the surface of a building on the sides of a street, it can be considered as static. Therefore in (11), we use the δ(•) function to characterize this feature.   



T

δ

Let define the measurement vector at time tk as z(tk ) = τ (tk ), f d (tk ) . Because 

the estimated delay τ (tk ) comes from the correlation function of the pseudo-random 

δ

code sequence c(t) and the estimated Doppler fading frequency f d (tk ) is the result of the estimation for the carrier Doppler frequency, it can be approximately considered that the two measured quantities are independent of each other and the estimation errors approximately have the Gaussian distribution. Therefore, the prior probability density of z(tk ) is: 

− 1 e p(z(t k )|x(t k )) = 2πσ τ σ f



τ (tk )−τ (tk |x(tk )) 2σ τ 2

⎛

2

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⎞2

δ

f d (tk )−f δd (tk |x(tk ))⎠

−

2σ f 2

(12)

where τ (tk |x(tk )) and fdδ (tk |x(tk )) are the predicted delay and Doppler fading frequency computed by formulas (5) and (6), στ and σf are the measurement noise standard deviations of multipath delay and fading frequency, respectively. Let set the number of particles in the particle filter to Ns . According to the principle of particle sampling, the posterior probability density of the reflection surface position vector x(tk ) can be expressed as: 

N s ω(j) (t k )δ x(t k ) − x(j) (t k ) p(x(t k )|z(t k )) ≈ (13) j=1

where ω(j) (tk ) represents the weight of the j-th particle at time tk , and the update equation is: ω(j) (t k ) = ω(j) (t k−1 )p(z(t k )|x(t k−1 ))

(14)

In order to prevent particle degradation, the particle weight normalization operation is required before each state update, and the particles need to be resampled after the state

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update. The normalization operation for the particle weights is as follows:

Ns ω(j) (tk ) = ω(j) (tk )/ ω(j) (tk ) j=1

(15)

The particle resampling operation can be carried out according to the method given in [18]. All the particles need to be assigned initial values at time 0. The initialization rule is as follows: First, assume that the distance parameter da is initially uniformly partitioned   at Mda grid points in the range of 10m, 2τ (t0 ) , where τ (t0 ) is the first-time estimate of the multipath delay provided by CADLL method. The azimuth parameter αa is initially  ◦ ◦ uniformly partitioned at Mαa grid points in the range of αsat − 90 , αsat + 90 , where parameter θa is uniformly partitioned at Mθa αsat is azimuth of the satellite.  The◦ elevation ◦ grid points in the range of −10 , +10 . These initial ranges are developed partially according to the geometric propagation model shown in Fig. 1 and partially obtained by empirical experience. Then, the total number of particles of the particle filter is equal to Ns = Mda Mαa Mθa . The weight of each particle can be initialized with the principle of equal value ω(j) (t0 ) = 1/Ns . 



4 Algorithm Performance Verification 4.1 Static Scenario Test at the SJTU Microelectronics Building Firstly, we chose a patio at the Microelectronics Building of Minhang Campus of Shanghai Jiao Tong University to test the estimation accuracy for the reflection plane position at static scenario. In this scenario, the north and west sides of the patio are buildings, on the surface of which there are glass curtains which are likely to produce significant reflected multipath signals. The GNSS antenna was placed at the southeast corner of the patio. A high-precision RTK receiver was utilized to survey the accurate positions of the patio, the surrounding buildings, and the antenna. Hence, the 3D map for this test scenario was obtained, as shown in Fig. 6, for the next accuracy verification. Next, a software receiver was used to process the GNSS signal and estimate the multipath signal parameters with the algorithm introduced in Sect. 2.2. Upon getting these measured multipath parameters, the reflection plane localization was performed with the particle filter presented in Sect. 2.3. The results show that a multipath signal belonging to Beidou PRN 20 satellite with a duration of about 120 s was successfully detected. The satellite’s elevation angle is only 16.8 ◦ and the azimuth angle is 61.1 ◦ , so its multipath is likely to be produced by the west side building of the patio (Figs. 3, 4 and 5). As soon as the reflection plane is localized, the reflection point of the signal occurring at the plane can be further computed. This is done by that the intersection point of the connection line starting from the image satellite position sm to the receiver position u with the reflection plane determined by the estimated vector x can be derived according to the mirror reflection law. Although the actual size of the reflection plane cannot be known, it is able to be approximated by assuming that the reflecting surface is a plane with both width and height being 5 m and centered around the reflection point. As shown 

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in Fig. 6, the pink plane is the estimated reflection plane and the light-yellow plane is the true position of the building surface on the west side of the patio. It can be seen that the estimated distance and orientation of the reflection plane are very close to the real building surface (Fig. 7).

BDS PRN20

Up

North East

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Fig. 3. SJTU microelectronics building terrace environment photo, a multipath signal from Beidou PRN20 satellite (elevation 16.8°, azimuth 61.1°) is detected.

Fig. 4. The multipath signal delay τ and Doppler fading frequency fd δ of Beidou PRN20 satellite are estimated by the multipath parameter estimation algorithm with a duration of about 120 s. The estimated mean value of multipath delay is 122.4 m, and the standard deviation is 5.16 m, the mean value of Doppler fading frequency is −0.0052 Hz, and the standard deviation is 8.56 × 10-4 Hz

4.2 Pedestrian Dynamic Scenario at Shanghai Lujiazui Area In the second experiment, we chose the Shanghai Lujiazui area as a typical urban environment to test proposed algorithm’s performance. A pedestrian GNSS signal recording platform, as shown in Fig. 7, was built by the researcher group, on which is equipped with a GNSS IF signal recorder, an IMU device, and a portable computer. The experiment route was on a circular pedestrian overpass as shown in Fig. 8. The choice of this place was to mitigate the blocking effects by trees or buildings. The data collection last about 8 min.

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Fig. 5. Using particle filter algorithm to Fig. 6. 3D display of reflection plane estimation estimate the position of multipath signal and reflection point estimation results. reflection plane, the estimated RMSE errors of distance da , azimuth αa and elevation angle θa are 0.99 m, 5.4° and 0.3°, respectively.

Figure 8 shows the estimated positions of the multipath signal reflection points on the Google earth 3D map. Since a large number of weak power multipath signals were received in this experiment, the variances of these estimated multipath delays and Doppler fading frequencies were quite large, which resulted in large errors in the estimated reflection plane positions. For this reason we only kept those multipath whose carrier-to-noise ratios were greater than 28 dB/Hz, and there were 11 effective multipaths kept at last (shown as red marked points in Fig. 8). The yellow track was the walking route during the data collection. It can be observed from Fig. 8 that most of the strong reflection multipaths are caused by the reflection on the glass curtain walls of the two tall buildings that are close to the southeast side of the ring-shaped overpass. These reflection points are distributed at different positions on the surface of the building, which helps to outline the building. It can be predicted that if the data collection time is lengthened, more multipath signals can be obtained, so as the reflection points. It can be expected that a clearer reflection building skeleton can be obtained.

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Because the exact 3D maps of the buildings in the Lujiazui area in this experiment cannot be obtained, the estimation accuracy for the localization of these reflection planes cannot be assessed either. However, the correctness of the results can be roughly verified by the following method. We select the reflector position estimated by a multipath signal of Beidou PRN9 satellite and the reflector position estimated by a multipath signal of Beidou PRN23 satellite, which are shown in Figs. 9 and 10. In addition, the coordinates of the reflection points can be calculated according to the location of the receiver and the orientations of the satellites with respect to the two reflection planes, which are shown in Fig. 11. It can be seen in the figures that the estimated reflector positions have high reliability.

Fig. 7. Pedestrian navigation data Fig. 8. Walking trajectory (yellow line) and estimation acquisition platform. result of multipath reflection point position.

Fig. 9. Estimation of reflection plane position of Beidou PRN9 satellite.

Fig. 10. Estimation of reflection plane position of Beidou PRN23 satellite.

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Fig. 11. Experimental results of reflection plane position estimation of walking movement scene in Lujiazui area.

5 Conclusions In this paper, an algorithm based on the GNSS multipath channel parameter estimation and a particle filter algorithm is proposed to localize the reflection plane and reflection point of a multipath signal. The correctness and accuracy of the algorithm are verified by experiments in a static environment and a dynamic environment. In the future, the algorithm will be expanded from the current Beidou B1I signal to other Beidou frequency signals. The methods to simplify estimation complexity or improve estimation accuracy will be studied as well. Acknowledgments. Acknowledgments The research work in this paper is supported by the National Key Research and Development Program (2018YFB0505103) and the Science and Technology Project of State Grid Corporation of China (SGSHJX00KXJS1901531).

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10. Chen, X.: Statistical multipath model comparative analysis of different GNSS orbits in static urban canyon environment. Adv. Space Res. 62(5), 1034–1048 (2018) 11. Chen, X., He, D., Pei, L.: BDS B1I multipath channel statistical model comparison between static and dynamic scenarios in dense urban canyon environment. Satellite Navigation 1(1), 1–16 (2020). https://doi.org/10.1186/s43020-020-00027-7 (2014) 12. 13. Fleury, B.H., Tschudin, M., Heddergoot, R., Dahlhaus, D., Pedersen, K.I.: Channel parameter estimation in mobile radio environments using the SAGE algorithm. IEEE J. Sel. Areas Commun. 17(3), 434–450 (1999) 14. Van Nee, R.D.J.: The multipath estimating delay lock loop. In: Proceedings of the IEEE 2nd International Symposium on Spread Spectrum Techniques and Applications, Yokohama, Japan, November 1992. 15. Chen, X., Dovis, F., Peng, S., Morton, Y.: Comparative studies of GPS multipath mitigation methods performance. IEEE Trans. Aerosp. Electron. Syst. 39(3), 1555–1568 (2013) 16. Chen, X., Morton, J., Yu, W., Truong, T.-K.: GPS L1CA/BDS B1I multipath channel measurements and modeling for dynamic land vehicle in Shanghai dense urban area. IEEE Trans. Veh. Technol. https://doi.org/10.1109/TVT.2020.3038646. 17. Was, M., Ziskind, I.: Detection of the number of coherent signals by the MDL principle. IEEE Trans. Acoust. Speech Signal Process. 37(8), 1190–1196 (1989) 18. Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174– 188 (2002)

A High-Precision Doppler Frequency Estimation Algorithm for CDMA-TDMA Navigation Signal Structure Jiancheng Zhang(B) , Lina Xu, and Mengting Zhang AVIC Xi’an Flight Automatic Control Reseach Institute, Xi’an, China

Abstract. In the pseudolite-based area navigation system, the code division multiple access (CDMA) and time division multiple access (TDMA) signals are usually jointly applied to solve the near-far effect. However, the effective integration time during acquisition is shortened due to the characteristic of TDMA signal, and the accuracy of Doppler frequency estimation is then reduced, which does not meet the requirement of carrier tracking loop. To solve this problem, this paper proposes a high-precision Doppler frequency estimation algorithm. In this algorithm, the low-precision estimation of Doppler frequency is obtained during acquisition. Thereafter, the medium-precision estimation is realized by non-coherent integration and quadratic interpolation. Finally, Prolonging the effective coherent integration time via data code searching, high-precision Doppler frequency estimation is obtained. Experiments are carried out with the measured data, and the results show that the accuracy of Doppler frequency estimation is greatly improved, and meets the requirement of carrier tracking loop. Keywords: Area navigation · Pseudolite navigation · CDMA · TDMA · Frequency estimation

1 Introduction Global navigation satellite system (GNSS) is a prominent topic in recent years [1, 2], since it has the advantages of high-precision positioning, available all-weather and all-day, and wide-coverage. Nevertheless, when the navigation signal is obstructed or jammed in complex environments such as indoor, gorge, and so on, the precision of positioning will decrease even invalid. The advantages of GNSS and its limitations in some fields give birth of the pseudolite navigation technique [3]. Pseudolite navigation adopts the similar signal structure and positioning principle as the GNSS, which can augment GNSS performance [4], even autonomous positioning via deploying multiple transmitters. Locata is a typical landbased pseudolite navigation system [5–7], which is developed by the Locata company in Australia. In 2011, the U.S. air force carried out flight test at White Sands Missile Range in New Mexico, and got sub-meter localization precision [8]. Code division multiple access (CDMA) is usually employed by the GNSS, the isolation between different codes of CDMA is low, for the C/A code of GPS L1 band, the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 215–223, 2021. https://doi.org/10.1007/978-981-16-3146-7_21

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isolation is about 20 dB. For the pseudolite-based area navigation, the distance between receiver and transmitter varies greatly, if the CDMA is employed, the auto-correlation peak of weak signal is easily submerged by the cross-correlation of strong signal, that is the near-far effect [9]. The near-far effect is the key problem that should be considered for the pseudolite navigation. As far as signal structure, employing the CDMA and time division multiple access (TDMA) signal structure is an effect method to solve this problem [5, 10]. Locata also applies this type of signal structure, which obtains high isolation by sacrificing the time resource substantially. We study pseudolite receiver signal processing under the CDMA and TDMA signal structures in this paper, aiming at the Doppler frequency estimation is not accuracy enough to meet the requirement of carrier tracking loop, a new algorithm which obtains high-precision Doppler frequency estimation via three-level precision (low-precision, medium-precision, and high-precision) estimations is presented. Theoretical analyses and experimental results show that the proposed method can obtain high precision Doppler frequency estimation and meet the requirement of carrier tracking loop. The layout of the remainder is organised as follows. The problem formulation is introduced in Sect. 2. In Sect. 3, the principle of the proposed method is analysed in detail. Experiments are carried out in Sect. 4 to validate the proposed method. Finally, we draw the conclusions in Sect. 5.

2 Problem Formulation The signal structure of CDMA and TDMA is shown in Fig. 1. It is composed of multiple continuous time frames, each time frame is divided into ten time slots, the durations of each time frame and time slot are 1 ms and 0.1 ms, respectively. Different transmitters occupy different time slots during the transmitting period, while remain silent in other time slots, e.g., transmitter 0 transmits signals in the time slot 0, while remains silent in time slots 1~9.

Fig. 1. Signal structure of TDMA and CDMA

For area navigation, the propagation time from transmitter to receiver is short, the received signals from different transmitters do not overlap or overlap very litter in the time domain. Additionally, protection interval can be set between different time slots to ensure that the signals received from different transmitters are not overlapped.

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Besides, each transmitter still adopts CDMA signal structure with the C/A code rate of 10.23 MHz, one time slot contains a complete C/A code period. In acquisition, the searching interval of Doppler frequency is set to 5,000 Hz, so the maximum Doppler frequency estimation error is 2,500 Hz. The maximum theoretical SNR loss caused by the frequency estimation error is:    sin π T fd ,a  , (1) sinc T fd ,a = π T fd ,a where T denotes the C/A code period, fd ,a represents Doppler frequency estimation error, According to (1), the SNR loss caused by the frequency estimation error of 2500 Hz is about 0.9 dB. Phase locked loop (PLL) aided by the frequency locked loop (FLL) is adopted for the carrier tracking loop, and the discriminator of FLL is [2] ωe (n) =

Pcro sign(Pdot ) , t(n) − t(n − 1)

(2)

where 

Pdot = IP (n − 1)IP (n) + QP (n − 1)QP (n) . Pcro = IP (n − 1)QP (n) − QP (n − 1)IP (n)

(3)

This discriminator is insensitive to the 180° phase shifts in case of data code bit transition, and it requires the frequency estimation error is in the scope of (−1/4T, 1/4T ), where T is effective integration time. Since the TDMA signal is adopted, the effective integration time is 1/10 of the tracking interval. If the tracking interval is 1 ms (one time frame), the effective integration time is 0.1 ms, so the Doppler frequency estimation error should be in the scope of − 250 Hz~250 Hz. Unfortunately, the Doppler frequency estimation error can be reached to 2500 Hz during acquisition, which does not meet the requirement of FLL. Therefore, it is necessary to further improve the Doppler frequency estimation accuracy.

3 Principle of the Proposed Method Estimating signal frequency via the peak’s location of its spectrum is a popular frequency estimation method for the frequency modulated (FM) signal. The frequency estimation accuracy of this method is mainly affected by the signal duration, SNR, and the interval of discrete spectrum. The signal duration determines the physical frequency resolution, the SNR determines spectrum perturbation caused by the noise, and the interval of discrete spectrum determines the resolution of frequency estimation. According to the above analyses, we improve the Doppler frequency estimation accuracy from the following three aspects: decreasing the interval of discrete spectrum, improving the SNR and physical resolution. The details are as follows: (1) Obtain low-precision Doppler frequency estimation during acquisition;

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(2) Obtain medium-precision Doppler frequency estimation by decreasing the interval of discrete spectrum, and improving the SNR, while decreasing the interval of discrete spectrum is achieved by Chirp-Z transform (CZT), and the SNR improving is realized by non-coherent integration; (3) Obtain high-precision Doppler frequency estimation via improving the physical frequency resolution, which is achieved by data code searching. 3.1 Low-Precision Estimation The received intermediate frequency (IF) signal in digital form can be expressed as:   (4) S(n) = A × Rk (n)C(n)D(n) cos 2π (fi + fd )nTs + ϕ0 , k = 0, 1, · · · 9 where

 Rk (n) =

mT

+kTslot

frame 1, Fs 0, else

> 1/T, the spreading code is independent of the chirp subcarrier, the autocorrelation function of the BOCC signal is expressed as:   ⎤ ⎡ T    fd T   4 ∞   |τ | 2 (2l−1)2 sin c π fd + (2l − 1)Kτ 2 cos π (2 − l)(2f0 + β)τ + 2 π ⎦ejπ fd T ⎣   ∗ ABOCC−c τ, fd = 1 −     f T Tc + sin c π fd − (2l − 1)Kτ T2 cos π (2 − l)(2f0 + β)τ − d2 l=1

(3) When f d = 0, the autocorrelation function is:       ∞ |τ | 8 β ∗ R(τ ) = 1 − sin c(π (2l − 1)βτ ) cos 2π (f0 ) + (2l − 1)τ Tc 2 (2l − 1)2 l=1

(4) When τ = 0, the Doppler resolution expression is: A(0, fd ) = sin c(π fd T )ejπ fd T

(5)

Using the Wiener-Sinchin theorem, the Fourier transform of autocorrelation function is the power spectral density for a stable signal. Then the power spectral density of BOCC modulation is:

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⎤ ⎡      ∞  ∞  |τ | 8 β ⎣ 1− ∗ P(f ) = sin c(π (2l − 1)βτ ) cos 2π f0 + (2l − 1)τ ⎦e−j2π f τ d τ Tc 2 (2l − 1)2 l=1 −∞

=

  ⎞  ⎞⎞ ⎛ ⎛ ⎛ ∞ f − (2l − 1) f0 + β2 f + (2l − 1) f0 + β2  4 ⎝rect ⎝ ⎠ + rect ⎝ ⎠⎠ ⊗ (2l − 1)β (2l − 1)β Tc (π f )2 (2l − 1)2 l=1

sin2 (π fTc )

(6)

Where ⊗ is the convolution symbol, and rect() is the unit rectangular function. It can be seen from the above expressions that the correlation function of the chirp subcarrier directly acts on the traditional BPSK autocorrelation function. Correspondingly, the power spectral density (PSD) of BOCC is shaped by the rectangular PSD with convolution. By designing the initial frequency f 0 and frequency bandwidth β of the binary chirp subcarrier, the non-split spectrum and split spectrum signals corresponding to GNSS signal can be obtained. In order to directly show the characteristics of the BOCC signal and verify the theoretical derivation, the correlation function and PSD of the BOCC signal are simulated in the part. Assuming that the sampling rate is 100 MHz, and the correlation function and PSDs of BOCC(0,1.5,1,1 ms), BOCC(0.5,1.5,1,1 ms), BPSK(2), BOC(1,1), MSK-BPSK(2) and MSK-BOC(1,1) are shown in the Figs. 4, 5, 6 and 7. From the three-dimensional curves in Figs. 4 and 5, it can be seen that the theoretical curve of the BOCC correlation function is basically the same as the simulation result, which verifies the theoretical derivation. And there are sharp main peaks and crossed side-peaks, which are different from the chirp signal. The main peak does not have the coupling characteristics of Doppler and time delay, or the inclined characteristics in the time-frequency domain. It is clear that the shape of the correlation function is similar to that of the traditional GNSS signal when f d < 1/2/T. When f d increases, the correlation function appears two side-peaks, which affects the signal reception. Therefore, the Doppler deviation for BOCC signal should be less than 1/2/T. In Fig. 6, through the autocorrelation function of the low-order BOCC signal, it is clear that the BOCC signal has a sharper main peak than the traditional BOCs, MSK and BPSK signals, and a better reception performance potential. At the same time, BOCC signal has other side peaks in the autocorrelation functions, which may bring the tracking ambiguity problem. However, the corresponding side-peaks have smaller amplitude and a lower probability of false lock compared with BOC signal. From the power spectral densities (Fig. 7), the PSD of the BOCC signal differs greatly from that of t.

3 Dual Estimation Tracking Method Based on Chirp Delay Locked Loops 3.1 Program Description BOCC modulation has better signal performance and anti-interference potential. However, there is little receiving research. This part focuses on the tracking method of BOCC signal. Considering that the autocorrelation function of BOCC signal has other sidepeaks, referring to the traditional receiving method of GNSS signal, a double estimation

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Fig. 4. Theoretical correlation function of BOCC(0,2,1,1 ms)

Fig. 6. Autocorrelation function of different BOCC signal

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Fig. 5. Simulated correlation function of BOCC(0,2,1,1 ms)

Fig. 7. Power spectral density of different BOCC signal

tracking scheme based on chirp delay locked loop (CDLL) is proposed to solve the tracking ambiguity problem of BOCC signal maintaining superior tracking performance. The double estimation tracking structure based on CDLL is shown in Fig. 8. As can be seen from Fig. 8, compared with the double estimation scheme of the traditional GNSS signal, the difference lies in the subcarrier loop. a periodic binary chirp subcarrier delay locked loop is used in the part. Assuming that the received BOCC signal is a real signal, the signal within the period T is:  ⎛ ⎞⎤ 

 2β 2 ⎟⎥ ⎢ ⎜ π T (t − τ ) − 2π β + f0 ∗ u(t − τ ) − u t − T 2 − τ   ⎟⎥ ⎢ ⎜ rBOCC (t) = c(t − τ )sign⎢cos⎜  ⎟⎥ cos 2π fi + fd t + ϕ0 ⎣ ⎝

2



  ⎠⎦ 2β t − T 2 − τ + 2π f0 t − T 2 − τ ∗ u t − T 2 − τ − u(t − T − τ ) + π T ⎡

(7) Where f i is the radio frequency, f d is the Doppler frequency, τ is the signal delay, and ϕ0 is the initial phase of the carrier.

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Fig. 8. Diagram of the double estimation tracking scheme based on CDLL

Taking into account the high dynamics of the LEO enhanced GNSS, the code Doppler cannot be ignored. Therefore, the baseband signal after frequency conversion by the local carriers (I and Q) can be expressed as:       fsd fcd t t − τ schrip 1 + t − τ ej2π fd +jϕ (8) r1 (t) = c 1 + c β Where f cd is the spreading code Doppler, f sd is the Doppler frequency of the binary chirp subcarrier, schirp is the periodic binary chirp subcarrier, f d is the Doppler deviation between the signal Doppler and the local carrier. According to the double estimation tracking method, the CDLL and DLL loops respectively generate three local spreading codes, which are early, prompt and late codes for correlation with the baseband signal. According to the correlation function derivation of the BOCC signal in the second part, the total correlation results of RCE , RCL , RDE , RDL , RP are:    ⎤  ⎡ fd T 4 T cos π (2l − 1)(2f0 + β)(τc + dc ) + sin c π(fd + (2l − 1)K(τc + dc )) ⎢  ∞ 2 ⎥ 2 2 2 − 1) π (2l |τ | ⎢ ⎥ jπ fd T +jϕ RCE ≈ 1 − ⎥e ⎢      ⎦ Tc ⎣ fd T l=1 + sin c π(f − (2l − 1)K(τ + d )) T cos π (2l − 1)(2f0 + β)(τc + dc ) − c c d 2 2    ⎤  ⎡ fd T 4 T cos π (2l − 1)(2f0 + β)(τc + dc ) + sin c π(fd + (2l − 1)K(τc + dc ))  ⎢  ∞ ⎥ 2 2 π 2 (2l − 1)2 |τ | ⎢ ⎥ jπ fd T +jϕ RCL ≈ 1 − ⎥e ⎢       ⎦ Tc ⎣ fd T l=1 + sin c π(f − (2l − 1)K(τ + d )) T cos π − 1)(2f + β) τ − (2l c c 0 c d 2 2    ⎤  ⎡ fd T 4 T cos π (2l − 1)(2f0 + β)(τc + dc ) − sin c π(fd + (2l − 1)Kτc )    ∞ ⎥ 2 2 π 2 (2l − 1)2 |τ + d | ⎢ ⎥ jπ fd T +jϕ ⎢ RDE ≈ 1 − ⎥e ⎢       ⎦ ⎣ Tc fd T l=1 + sin c π(f − (2l − 1)K(τ + d )) T cos π (2l − 1)(2f0 + β) τc − c c d 2 2    ⎤   ⎡ fd T 4 T cos π (2l − 1)(2f0 + β)(τc + dc ) + sin c π(fd + (2l − 1)K(τc + dc ))    ∞ ⎥ 2 (2l − 1)2 2 2 π |τ − d | ⎢ ⎥ ⎢ RDL ≈ 1 − ⎥ejπ fd T +jϕ ⎢      ⎦ ⎣ Tc fd T l=1 + sin c π(f − (2l − 1)Kτ ) T cos π (2l − 1)(2f0 + β)(τc + dc ) − c d 2 2    ⎤  ⎡ T fd T 4 cos π (2l − 1)(2f0 + β)(τc + dc ) + sin c π(fd + (2l − 1)K(τc + dc ))    ∞ ⎥ 2 2 π 2 (2l − 1)2 τ ⎢ ⎥ jπ fd T +jϕ ⎢ RP ≈ 1 − ⎥e ⎢       ⎦ Tc ⎣ T T f d l=1 + sin c π(f + (2l − 1)Kτ ) cos π (2l − 1)(2f0 + β) τc − c d 2 2 

(9)

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Where f d is the deviation between the local carrier frequency and the Doppler of the signal, ϕ is the residual phase, 2*d is the relative interval between the early and late code in DLL, and 2*d c is the relative interval between early and late binary chirp signals in CDLL, the code delay deviation is τ, chirp subcarrier delay deviation is τc . A twoquadrant arctangent phase discriminator is used in PLL, and the phase discrimination function is: φe =

image(RP ) = π fd T + ϕ real(RP )

(10)

A non-coherent early minus late power discriminator is used in CDLL and DLL use, and the phase discrimination function is: δCDLL = |RCE |2 − |RCL |2

δDLL = |RDE |2 − |RDL |2

(11)

It can be seen from the expressions that Doppler will affect the amplitude of the correlation results while the signal delay does not affect the phase of coherent integration results, which makes the correlation results of BOCC signal similar with GNSS signals. The symmetrical frequency in binary chirp subcarrier mitigates non-stationary characteristics of traditional chirp signal. 3.2 Theoretical Performance Analysis From the theoretical expressions, it can be known that the correlation results are related to three factors: code delay deviation, CDLL delay deviation and PLL Doppler deviation. The controlled variable method is adopted to show the influence of different factors in a two-dimensional curve. In order to directly show the characteristics of the correlation function and the discrimination results of the BOCC signal under different delay and Doppler deviation conditions, BOCC (0,1.5,1,1 ms) is used as an example, and the sampling rate is 10 MHz. The Doppler frequency deviation is 0,100 and 200 Hz respectively, the DLL delay deviation is 0,0.2 and 0.4 chips (1chip = 1/1.023 MHz), the CDLL delay deviation is 0,0.15 and 0.3chips (1chip = 1/β). And the coherence interval in CDLL is normalized by 1/β. Then, the simulated autocorrelation function and the phase discrimination results of different loops are presented in Fig. 9, 10, 11 and 12. By controlling the value of the Doppler and code delay deviation in DLL, the correlation function (Fig. 9), carrier phase (Fig. 10) and chirp phase discrimination curves (Fig. 11) of CDLL can be obtained. From the simulation results in Fig. 9, it can be seen that different Doppler deviations do not affect the peak position of the correlation function in CDLL, but affect the peak amplitude, which means the stable zero-crossing point in chirp phase discrimination. At the same time, in Fig. 10, the carrier phases of the correlation results are basically the same for different CDLL delay deviations, showing a linear change with the Doppler frequency. Therefore, The CDLL delay does not affect the carrier phase of the correlation result. In addition, from the chirp phase discrimination curves of CDLL loop (Fig. 11), it can be found that the binary chirp phase discrimination gain is reduced as Doppler frequency derivation increases. And there are the only stable zero-crossing points which means that the tracking of CDLL is and unbiased. It is an advantage of the binary offset chirp carrier signals comparing with

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BOC signals. Controlling the Doppler and delay of CDLL, the code phase discrimination results can be obtained in Fig. 12. It is clear that different Doppler frequency deviations will not affect the position of the main peak in DLL, and the zero-crossing point in the final phase detection is stable and unbiased. However, the phase discrimination gain is slightly reduced with more and more Doppler frequency derivations. By comparing with Figs. 11 and 12, it is worth noting that the binary chirp phase discrimination gain of CDLL is higher than the corresponding code phase discrimination gain in DLL, which means that the CDLL has more potential for tracking performance.

Fig. 9. ACFs in CDLL under different Doppler derivations (τ = 0.2)

Fig. 10. Carrier phase in PLL under different binary chirp delays (τ = 0.2)

Fig. 11. Discrimination result in CDLL(τ = Fig. 12. Discrimination result in DLL (τc = 0.3, d = 0.2) 0.2, dc = 0.3)

When the tracking is stable, the carrier phase and delay deviation of PLL and DLL are close to 0. From the simulation curve in Fig. 9, the autocorrelation function of BOCC signal in CDLL is symmetrical, and the main peak is a triangular peak. Referring to the tracking accuracy theory of GNSS signals [15], the CDLL tracking accuracy with the non-coherent power discrimination scheme is:  ⎛ ⎞



 βr 2 βr 2   2 2 ⎜ ⎟ Gc (f ) sin (2π fdc )df ⎜ Gc (f ) cos (2π fdc )df  BL (1 − 0.5BL T ) ⎟



 ⎜ ⎟  −βr 2 −βr 2 ⎜ ⎟ σCDLL =  ∗ 1 + ⎜ ⎟ ⎛ ⎛ ⎞ ⎞



 2 ⎜ 2⎟  βr 2 βr 2 ⎜ ⎟  ⎝ ⎠ 2 ⎝ ⎝ ⎠ ⎠  (2π ) Cs /N0 fGc (f ) sin(2π fdc )df TCs /N0 Gc (f ) cos(2π fdc )df

−βr 2

−βr 2

(12)

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Where Gc (f ) is the power spectral density of the binary chirp subcarrier, and the power spectral density can be expressed as: Gc (f )binary−chirp =

⎛

∞ 

4

l=1

π 2 (2l − 1)3 β

⎛

⎝rect ⎝

 ⎞  ⎞⎞  ⎛ f − (2l − 1) f0 + β2 f + (2l − 1) f0 + β2 ⎠ + rect ⎝ ⎠⎠ (2l − 1)β (2l − 1)β

(13)

And the Cramer-Rao lower bound (CRLB) of tracking accuracy in CDLL can be obtained as:   BL (1 − 0.5BL T )  σdouble−estimation =  (14) βr   C  (2π )2 s f 2 Gc (f )df N0 −βr

At the same time, the correlation result in DLL of the BOCC signal is similar to that of the traditional BPSK signal. The code Doppler can be eliminated by the high-order DLL or the assistance of PLL. The final tracking accuracy of DLL is:  ⎞ ⎛   βr/2  βr/2  ⎟ GBPSK (f ) cos2 (2π fd )df GBPSK (f ) sin2 (2π fd )df ⎜  BL 1 − 0.5BL T ⎟ ⎜  ⎟ ⎜ −βr /2 −βr /2  ⎟ ⎜ σdouble−estimation−DLL =  ∗ ⎜1 + ⎟ ⎛ ⎞

⎛ ⎞ 2 ⎜ 2⎟  β /2 β 2  ⎟ ⎜ r r  ⎝ TCs /N0 ⎝ GBPSK (f ) cos(2π fd )df ⎠ ⎠  (2π )2 Cs /N0 ⎝ GBPSK (f ) sin(2π fd )df ⎠ −βr /2 −βr /2

(15) Where GBPSK (f ) is the power spectral density of the corresponding BPSK signal. Finally, the carrier phase tracking error with the arctangent phase discrimination scheme in PLL is:    1 BL 1+ (16) σPLL = Cs /No 2TCs /N0

4 Simulation and Analysis In order to further verify the tracking performance of the BOCC signal based on double estimation method, the tracking simulation is carried out in this part. Assuming that the sampling rate is 20 MHz, the filter bandwidth is 16 MHz, BOCC(0,1.5,1,1 ms), BOCC(0.5,1,1,1 ms), BOCC(0,2,1,1 ms), BPSK(2) and BOC(1,1) (The performance of MSK-BOC(1,1) with the wide filter bandwidth is not as good as the BOC signal, so it is not investigated here.) are investigated. And the radio frequency is 1575.42 MHz. Due to the high dynamics of the LEO satellites in enhanced GNSS, the Doppler frequency is 35 kHz and the Doppler frequency change rate is 210 Hz/s. In the meantime, the signal carrier-to-noise ratio is 44 dBHz, and the Doppler and code delay deviations obtained in the acquisition are 30 Hz and 0.2chips respectively. The loop bandwidth of DLL and CDLL is 2 Hz. In addition, the correlator space of DLL is 1/5chips (1chip = 1/f c ), and the correlator space of CDLL is 1/5chips (1chip = 1/β). 2nd order frequency locked loop (FLL) assists 3rd order phase locked loop (PLL), and the loop bandwidths are 20 Hz and

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50 Hz, respectively. The length of signal data is 8000 ms. The double estimation and match schemes are adopted for receiving BOCC and BOC signals. And the receiving conditions include non-interference, narrow-band interference and matched correlation interference. (1) non-interference reception Under the non-interference condition, the tracking error results of the BOCC signal are presented in Figs. 13 and 14. It is clear that BOCC(0,1.5,1,1 ms) and BOCC(0.5,1,1,1 ms) can be successfully tracked by using the double estimation method based on CDLL, and the code and carrier tracking performance is slightly better than that of BOC(1,1), where BOCC(0.5,1,1,1 ms) has the best tracking performance. Therefore, the double estimation scheme based on CDLL for BOCC signal in the paper is feasible.

Fig. 13. Code tracking error of different BOCC signals (44 dBHz)

Fig. 14. Carrier phase tracking error of different BOCC signals (44 dBHz)

(2) Narrowband interference (J/S = 20 dB, narrowband interference bandwidth is 200 kHz) At the same time, assuming that the ratio of narrowband interference to signal is 20 dB, and the interference bandwidth is 200 kHz, it can be seen from Figs. 15 and 16 that BOCC (0,2,1,1 ms) and BOC(1,1) can be tracked normally. However, the signal tracking performance is worse than that without interference. Moreover, it is worth noting that the tracking performance of the BOCC signal is significantly better than the corresponding BOC signal, which corresponds to the superior anti-interference performance of the BOCC signal. (3) Matched correlation interference (J/S = 20 dB) In addition, Assuming that the ratio of a matched interference to signal is 20 dB, it is clear from Figs. 17 and 18 that BOCC(0,2,1,1 ms) and BOC(1,1) can be tracked stably, and the tracking performance of BOCC signals is more excellent than the corresponding BOC signal. Under the simulation condition, the code-tracking accuracy of BOCC

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Fig. 15. Code tracking error with the narrowband interference (CN0 = 44 dBHz)

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Fig. 16. Carrier phase tracking error with narrowband interference (CN0 = 44 dBHz)

Fig. 17. Curve: code tracking error of different Fig. 18. Curve: carrier tracking error of BOCC signal with the correlation interference different BOCC signals with the correlation (CN0 = 44 dBHz) interference (CN0 = 44 dBHz)

(0,2,1,1 ms) is 20% higher than that of BOC(1,1), and carrier phase tracking accuracy is 29% higher, which verifies the superior tracking performance of BOCC signals with jamming.

5 Conclusions As the global navigation satellite systems develop, the LEO enhanced GNSS has received widespread attention. BOCC modulation becomes the focus in the paper because of its better receiving performance and anti-interference ability. The BOCC signal model and time-frequency domain characteristics have been analyzed in this paper, and a double estimation scheme based on chirp delay locked loop for receiving BOCC signal has been proposed. Finally, the simulation results verify the feasibility of the double estimation method and superior tracking performance with interference.

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Through the analysis of the double estimation scheme based on CDLL, it can be seen that the correlation function and carrier phase of the BOCC signal are similar to the traditional GNSS signal, which lays the foundation for the feasibility of the tracking method. In addition, the theoretical tracking performance is given in the paper. At the same time, the feasibility of the tracking method is verified by simulation and analysis, and the superior anti-jamming performance of BOCC signal is proved by comparing with BOC signal. The double estimation tracking method based on CDLL can offer a new choice for the application of BOCC signals in the future LEO enhanced GNSS. Acknowledgments. This work is supported by National Science Foundation of China (U20A0193, 62003354).

References 1. Li, X., Ge, M., Dai, X., Ren, X., Fritsche, M., Wickert, J., Schuh, H.: Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J. Geodesy 89(6), 607–635 (2015) 2. Yang, Y.X.: concepts of comprehensive PNT and related key technologies. Acta Geodaetica et Cartographica Sinica 45(5), 505–510 (2016) 3. Reid, T.G.R., Neish, A.M., Walter, T.F., Enge, P.K.: Leveraging commercial broadband LEO constellations for navigation. In: ION GNSS+2016, Portland, Oregon, September 2016, pp. 2300–2314 (2016) 4. Reid, T.G.R., Neish, A.M., Walter, T., et al.: Broadband LEO constellations for navigation. Navigation 65(2), 205–220 (2018) 5. Enge, P., Ferrell, B., Bennet, J., Whelan, D., Gutt, G., Lawrence, D.: Orbital diversity for satellite navigation. In: ION GNSS 2012, Nashville, TN, pp. 3834–3846 (2012) 6. Iridium boss reflects as final NEXT satellite constellation launches. http://www.decodesys tems.com/iridium.html. Accessed 11 Jan 2019 7. Meng, Y.S., Bian, L., Han, L., Lei, W., Yan, T., He, M., et al.: A global navigation augmentation system based on LEO communication constellation, pp. 65–71 (2018) 8. Wang, L., Chen, R.Z., Li, D.R., et al.: Initial assessment of the LEO based navigation signal augmentation system from Luojia-1A satellite. Sensors 18(11), 3919–3928 (2018) 9. Richards, M.A.: Fundamentals of Radar Signal Processing, 2nd edn. McGraw-Hill Press, New York (2005) 10. Kowatsch, M., Seifert, F., Lafferl, J.: Comments on transmission system using pseudo-noise modulation of linear chirps. IEEE Trans. Aerosp. Electron. Syst. 17(2), 300–303 (2007) 11. Qian, Y., Ma, L., Liang, X.: Symmetry chirp spread spectrum modulation used in LEO satellite internet of things. IEEE Commun. Lett. 22(11), 2230–2233 (2018) 12. Qian, Y., Ma, L., Liang, X.: The performance of chirp signal used in LEO satellite internet of things. IEEE Commun. Lett. 23(8), 1319–1322 (2020)

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13. Zhao, X., Huang, X.M., Sun, G.F.: BOCC: A new modulation based on chirp subcarriers for future BeiDou navigation-augmented signal. Electron. Lett. 57(1), 36–38 (2021) 14. Feng, C., Wang, T., Zhi, X., Huan, H.: An effective tracking loop for chirp spread spectrum communication systems. In: ICSP 2016, Chengdu, China, pp. 1196–1201 (2016) 15. Betz, J.W., Kolodziejski, K.R.: Generalized theory of code tracking with an early-late discriminator part II: noncoherent processing and numerical results. IEEE Trans. Aerosp. Electron. Syst. 45(4), 1557–1564 (2009)

An Improved GNSS Vertical Time Series Prediction Model Using EWT Rui Tao1(B) , Tieding Lu1 , Yuanming Cheng2 , Xiaoxing He3 , and Xin Wang4 1 Faculty of Geomatics, East China University of Technology, Nanchang, China 2 Nanchang Urban Planning and Design Institute, Nanchang, China 3 School of Civil Engineer and Architecture, East China Jiao Tong University, Nanchang, China 4 Fuzhou Investigation and Surveying Institute, Fuzhou, China

Abstract. GNSS vertical time series are non-stationary, non-linear, noisy, etc. Based on the in-depth study of the Prophet prediction model and Empirical wavelet transform (EWT), Aiming at the poor effect of the decomposed trend item and the single cycle item in the Prophet prediction process, an improved Prophet prediction method using EWT is proposed. First, the original time series is decomposed by EWT. Then, prophet prediction is performed on every component and the predicted time series signal is reconstructed. Finally, the accuracy and reliability of the prediction result are verified. This paper uses the measured GNSS vertical time series data from BJFS, WUHN and URUM stations provided by China Earthquake Administration to conduct four short-term prediction experiments with different time spans. The results show that the improved model can better represent the change trend of the original time series. Compared with the single model, its prediction effect is increased by 31.5%, 35.03%, 19.32%, 10.76% in the root mean square error, respectively. The average percentage error increased by 32.76%, 43.61%, 29.28%, 14%, respectively. It shows that the improved model has better short-term prediction effect and better applicability. Keywords: GNSS vertical time series · Prophet · Empirical wavelet transform · Short-term prediction · Improved model

1 Introduction The continuous development and improvement of GNSS observation technology and data processing methods, IGS (International GNSS Service) has accumulated basic geodesy data for more than 20 years, These data contribute to the continuous development of geodesy and geodynamics, and also provide an important data source for the research and analysis of GNSS coordinate time series (Jiang et al. 2018). Accurate prediction of GNSS coordinate time series is significant to research fields such as building deformation monitoring, crustal plate movement, and geometeorology (Ming et al. 2016). Existing studies have pointed out that the GNSS coordinate time series has obvious trend variation and periodic change in the three directions of N, E, and U, especially in the U direction, showing very obvious periodic change (Zhang et al. 2019). Various © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 298–313, 2021. https://doi.org/10.1007/978-981-16-3146-7_28

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types of “signals” and “noise” are superimposed on the GNSS coordinate time series (Ming et al. 2016), and the noise improvement in the U direction is more complicated (Su et al. 2014; He et al. 2017). Thus, it is difficult to establish a high-precision vertical time series prediction model. Nowadays, many scholars have conducted extensive research in the field of GNSS coordinate time series prediction. Zhang et al. (2019) used the polynomial periodic model and the ARMA model to predict and compare and analyze the vertical time series. The results showed that the ARMA model had a better prediction effect than the polynomial periodic model. Dong et al. (2016) used an improved fractal-gray improved prediction model to research vertical time series, which not only improved the model’s prediction accuracy, but also enhanced its applicability. Li et al. (2020) used the hybrid prediction model based on LSTM neural network for GNSS vertical time series prediction, which effectively improved the reliability of prediction and possessed certain generalization ability. However, in time series prediction research, there are still the following problems: a single prediction model cannot achieve a good prediction effect in a complex noise environment; the prediction model has high requirements on the original data, and the prediction accuracy is susceptible to gross errors, noise, and abnormalities. Problems such as missing values and data. Although the traditional gray-scale prediction model is widely used, its applicability is poor. Although artificial neural networks have high prediction accuracy, there are problems such as difficulties in selecting prediction parameters (Rajat et al. 2010). In response to the above problems, this paper proposes an improved Prophet prediction method using EWT, which is used for GNSS vertical time series prediction. The Prophet model is a new model of adaptive decomposition and prediction. Compared with the ARMA model, it has better adaptability to the original data. It is flexible in use and does not need to interpolate missing items, and does not require any prior conditions. The fitting process speed is faster, however, there are problems in the decomposition process that the decomposition trend item cannot better reflect the change of the signal trend, and the single decomposition of the periodic item. EWT is an adaptive signal decomposition method based on wavelet theory, which can decompose the original signal into many wavelet components with modal characteristics. Compared with Empirical Mode Decomposition (EMD), EWT has stronger theoretical support and does not generate modal mixing and pseudo mode function. This paper introduces the empirical wavelet transform method to improve the incomplete decomposition of the original vertical time series by Prophet, and proposes a new method of “decomposition- prediction- reconstruction” for GNSS vertical time series prediction. In this paper, 4 GNSS vertical time series with different time spans are selected for short-term prediction, and the results are statistically analyzed to explore the effect and applicability of the improved model.

2 Principles and Methods 2.1 EWT Gilles et al. (2013) proposed a new adaptive signal decomposition method-Empirical wavelet transform (EWT) in 2013. This is a new method with a small amount of calculation and strong robustness. The core idea is based on the spectral characteristics of

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the original signal, After adaptive segmentation, an orthogonal wavelet filter bank based on Fourier support is constructed, Extract different AM-FM (amplitude modulationfrequency modulation) parts with tightly supported Fourier spectrum (Wang et al. 2018; Daubechies 1992; Wang 2017; Sun et al. 2018). The specific process (Daubechies 1992; Wang 2017) is: 1) Perform Fourier transform on the signal to obtain the Fourier spectrum F(ω) of the support interval (0, π ); 2) Adaptively segment the Fourier spectrum F(ω), According to the Shannon criterion, the spectrum is decomposed into N frequency bands and N −1 boundary frequencies. Figure 1 is a schematic diagram of Fourier spectrum division; 3) Construct an empirical wavelet ϕ(ω) according to each boundary frequency, and determine the empirical scale function and empirical wavelet function; 4) Perform inverse Fourier transform on F(ω) ∗ ϕ(ω) to obtain different modal components. In Fig. 1, First, suppose that the Fourier support interval (0, π ) is divided into N frequency bands, There can be N − 1 dividing frequencies, and ωn is the boundary of adjacent frequency bands, ω0 = 0, ωN = π . All divided frequency bands can be expressed as n = [ωn−1 , ωn ], then ∪N n−1 n = [0, π ]. Set ωN as center, can define a transition zone with a width of Tn = 2τn , As shown in the shaded part in the picture:

Fig. 1. Fourier spectrum segmentation diagram

When n is determined, the empirical wavelet is defined as a band-pass filter on each n (Sun et al. 2018), and the empirical scale function and empirical wavelet function are determined according to the Meyer (Wang et al. 2018) wavelet to construct the empirical wavelet (Daubechies 1992), respectively, as Eqs. (1) and (2) are as follows: ⎧ ⎪ ⎨1   |ω| ≤ ωn − τn π 1 φn (ω) = cos 2 β 2τn (|ω| − ωn + τn ) ωn − τn ≤ |ω| ≤ ωn + τ (1) ⎪ ⎩ 0 other 

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⎧ 1   ⎪ ⎪ ωn + τn ≤ |ω| ≤ ωn+1 − τn+1 ⎪ ⎪ ⎨ cos π β 1 (|ω| − ωn+1 + τn+1 ) ωn+1 − τn+1 ≤ |ω| ≤ ωn+1 + τn+1  2  2τn+1

n (ω) = π 1 ⎪ sin β (|ω| − ω + τ ) ωn − τn ≤ |ω| ≤ ωn + τn ⎪ n n ⎪ 2 2τn ⎪ ⎩ 0 other (2) 

Among them: τn and β(x) are: (3)  β(x) = x4 35 − 84x + 70x2 − 20x3

(4)

f (t) is reconstructed as: f (t) = Wfε (0, t) ∗ φ1 (t) +

N

Wfε (n, t) ∗ n (t)

(5)

n=1

Among them: ∗ is the convolution operator, Wfε (0, t) is the Fourier transform approximation coefficient, Wfε (n, t) is the Fourier transform detail coefficient. The original signal F(t) is decomposed into 1 + N AM − FM components by EWT transformation, It contains an empirical scale component f0 that represents the overall trend change of the signal, And N empirical wavelet components fk representing different frequency domain characteristics in the signal. F(t) = f0 +

N

fk

(6)

k=1

2.2 Prophet Taylor et al. (2017) proposed the Prophet model and released a homologous open source software package to promote the application and implementation of the algorithm. Prophet model has been widely used in power system (Niu et al. 2020), market flow (Ge et al. 2019), economics and finance (Li et al. 2019), environmental protection (Zhang et al. 2019) and other fields, and has achieved good application effects. Prophet uses a generalized additive model to fit smoothing and prediction functions, and its decomposition framework is as follows: y(t) = g(t) + s(t) + h(t) + εt

(7)

The Prophet model adaptively decomposes the time series signal into 4 parts: Simulate the original sequence trend item g(t), Period term, s(t), Special mutation h(t) and Noise term εt .

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The trend item of Prophet decomposition is g(t), The change function of the (nonperiodic term) part of the nonlinear growth of the time series. Because the original signal is nonlinear and complex in the vertical time series, the trend term is generally expressed by the logistic regression function (Taylor et al. 2017) as: c (8) g(t) = 1 + e[−k(t−m)] Among them: k is the growth rate, m is the displacement, c is the upper limit of the trend value. As time t increases, g(t) approaches c. However, in the face of complex vertical time series, the growth rate k changes dynamically. At this time, it is necessary to introduce adaptive adjustment offset γ and growth rate change δ ∈ R. Equation 8 can be changed to: c     (9) g(t) = T T 1 + e− k+α(t) δ t− m+α(t) γ The fitting function of the periodic term A of Prophet decomposition is constructed by the Fourier series of the time series:     N 

2π nt 2π nt an cos + bn sin (10) s(t) = T T n=1

T is the time series period, T = 7, N = 3; If the annual cycle is T = 365.25, N = 10, 2n represents the expected number of cycles in the model. A is usually a holiday mutation, However, in the GNSS coordinate time series, there is no sudden and irregular influence caused by holidays or special dates, so its influence on the prediction of GNSS time coordinate series is not considered. εt is the residual term, And it obeys normal distribution, which can be expressed as predicted random noise or trend. 2.3 Improved Prophet Method Using EWT Figure 2 shows the algorithm flow chart of the improved model. This improved method first performs EWT decomposition and denoising of the original time series, and decomposes the original signal into 1 empirical scale component f0 and k empirical wavelet components fk , and Prophet prediction for each component, The obtained prediction components are equally weighted and reconstructed into the final prediction sequence signal. This method combines the advantages of EWT with strong theory, good adaptive ability, thorough modal decomposition, and the advantages of Prophet’s fast fitting prediction speed and high prediction accuracy to construct an improved EWT-Prophet prediction model. The specific steps are: 1) Use EWT to effectively decompose the original time series signal f (t): f (t) = f0 (t) +

n

fk (t)

(11)

k=1

f0 (t) is the empirical scale component, fk (t) is the decomposed empirical wavelet components, k is the number of empirical wavelets.

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Fig. 2. Flow chart of EWT-Prophet method

2) Prophet prediction is performed on all effective decomposition vectors of EWT, and the predicted time series are superimposed and reconstructed with equal weight to obtain the final improved model prediction time series, which is compared with the actual measured value released by Crustal Movement Observation Network of China (CMONC) to verify its prediction effect.

3 Experiment and Analysis The experimental data selected in this article are all from the GNSS data product service platform of China Earthquake Administration (http://www.cgps.ac.cn/), the data sampling frequency provided by the data service platform is 1/365.25 Hz, the sampling interval is 1/365.25 years. In this paper, the vertical time series data of three stations (BJFS, WUHN, URUM) were used for experimental analysis, Using four different span time series data to carry out short-term prediction experiments, The prediction result is compared with the real value(provided by China Earthquake Administration), and the prediction effect of the model is verified. The experiments with four spans are as follows: 8 groups short term (20 day sample prediction 10 days) 4 groups of medium and short term (150 day sample prediction 30 days) 3 groups of medium term (30 days for the 335-day sample) 2 groups of long term (30 days for a 700-day sample). The 17 groups of time series signals with different spans were decomposed by EWT, Each experiment can obtained One empirical scale component and n empirical wavelet component; Prophet modeling was carried out for each component, and the prediction results of each component were reconstructed to get the final prediction results, and compared with the measured values. In order to verify the prediction effect of the improved model, root mean square error (RMSE) and mean percentage error (MAPE) are used as the prediction effectiveness indicators in this paper, which can be expressed as:   n 1  2 xi − xi RMSE =  (12) n 

i=1

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 n  100%  xi − xi  MAPE =  x  n i 

(13)

i=1



x is the actual value, x is the predicted value.RMSE ∈ (0 + ∞], When the predicted value is exactly the same as the measured value, it is equal to 0, which is a perfect model; The greater the error, the larger the value. MAPE ∈ (0 + ∞], When MAPE is 0%, it means a perfect model, MAPE more than 100% indicates inferior model, The closer its value is to 0, the better the model. In order to more intuitively reflect the prediction accuracy improvement effect of the improved model, the prediction accuracy improvement ratio is introduced, and its expression is:   αEWT+Pr ophet % (14) δ = 1− αPr ophet Where δ is the percentage lift value,α is a different predictive validity metric. A negative value of δ indicates that the improved model prediction is not applicable. In order to verify the superiority of EWT decomposition method, In this paper, the pre-processed GNSS vertical time series were respectively decomposed by Prophet and EWT. Figure 3 is an exploded view of GNSS data at BJFS station. As can be seen from the figure, Prophet decomposes the original signal into 1 trend component (trend ), 1 year component (yearly) and 1 periodic component (weekly), EWT decomposes the original signal into 1 empirical scale component f0 and 5 empirical wavelet components f1 − f5 . The results show that Prophet decomposes the original signal in modules, and the decomposed trend item and period item cannot better present the detailed changes of the complex GNSS vertical time series signal, EWT decomposes the original signal from low frequency to high frequency modally, and better shows the trend item signal characteristics of the original data and the periodic item signal characteristics of different frequencies, which can effectively and thoroughly decompose the original signal (Fig. 4).

Fig. 3. Schematic diagram of Prophet decomposition

Fig. 4. Schematic diagram of EWT decomposition

Figure 5 is a schematic diagram of Prophet method prediction. It can be seen from this that only a few observation points near the extreme value and partial separation group

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value points are not within the confidence interval of the fitting, Most of the observation points are within the 80% confidence interval, and the points in the confidence interval are more evenly distributed around the fitted signal, It can be seen that the Prophet model has a good fitting effect for nonlinear, non-stationary, and noisy GNSS vertical time series signals. Most of the sample data is in the prediction confidence interval, The better fitting ability of the Prophet model can effectively reflect the overall trend movement characteristics and periodic changes of the original data. It has a certain degree of resistance to errors and outliers, and it has a certain degree of robustness.

Fig. 5. Schematic diagram of Prophet prediction

In Fig. 5: the black dots are the original measured data, the blue solid line is the prophet fitting and prediction sequence, and the blue area is the 80% prediction confidence interval. 3.1 Analysis of Experimental Results in Different Time Spans Select the vertical time series of different time spans of BJFS station for experiment: 1) In the short-term experiment, use 20-day continuous observation data to predict the 10-day plan, and 4 sets of data are used for experiments, and the predicted data is compared with the published data. In order to reduce the impact of contingency and seasonality of sample data on the prediction effect, this paper uses four sets of data from the BJFS station in 2012 to conduct experiments, which are the actual continuous observational data in January, April, July, and November of 2012. Due to the limited length of the article, only one set of short-term predictions of experiments is shown in the article, and the remaining experimental results are shown in tables. Figure 6 is a decomposition and comparison diagram of the two methods. It can be seen from the figure that, in terms of trend components, the EWT method has a more staged trend than the Prophet method, and can describe the local trend of the original data in more detail; It can be seen from the period term that the decomposition period term of Prophet is not dynamic, and the period and amplitude of its sliding window remain roughly unchanged. The EWT method is better than the Prophet method in this respect, and it has the ability to better reflect the sudden change of the signal.

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Fig. 6. Exploded comparison chart (left)

Fig. 7. BJFS station (January 2012) prediction results and prediction components comparison chart (right)

Figure 7 shows the short-term experiment decomposition and prediction of BJFS station in January 2012. It can be seen from the figure that the trend term of the time series in this experiment has obvious characteristics, and the periodicity of the noise signal is simple. EWT adaptively decomposes the sample signal into an empirical scale component f0 and an empirical wavelet component f1 . The result shows that the prediction effect of f0 is better than that of f1 , and its prediction data fits the original signal more closely, and it reflects the trend of the original sequence. The predicted f0 and f1 components are reconstructed into the final time series data, and finally they are compared with the directly predicted experimental data. Figure 6 shows that in the fitting part of the first 20 days, there is little difference between the fitting results of the improved model and the single model. This is because the Prophet model has a better fitting effect on the linear trend, but the prediction part in the next 10 days In EWT, the result of prediction after decomposition is better than the result of direct prediction, especially in the vicinity of extreme points and local trends, which can show that the improved model has better prediction effects. Table 1 is the accuracy analysis table of the short-term experimental results of the 4 groups of BJFS stations. From the results, it can be seen that the prediction effect of the improved model is better than that of the single model. In terms of the root mean square error, the errors of the two models are 4.86 and 2.80 respectively, which are improved on average 42.39%. In terms of the average percentage error, the errors of the two models were 42.99% and 23.00% respectively, an average increase of 46.50%, which proved that the short-term prediction improved model effect is better in the short-term time span. 2) In the short-medium term experiments, a 150-day continuous observation data prediction for 30 days is used, and two sets of data are used for experiments. The data are taken from the 2012 data of BJFS Station, and the predicted data is compared with the published data. In order to compare the prediction effect of the improved model, the absolute value residual is introduced as the test standard, and its expression is:   (15)  = xi − xi  



xi is the measured value, xi is the predicted value.

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Table 1. Accuracy analysis table of short-term experimental results of BJFS Model

RMSE MAPE

BJFS 2012.1

Prophet

1.61

EWT-Prophet 1.30

14.49%

BJFS 2012.4

Prophet

5.45

31.22%

EWT-Prophet 3.95

21.11%

Prophet

BJFS 2012.7 BJFS 2012.11

21.73%

8.62

86.40%

EWT-Prophet 3.44

29.36%

Prophet

32.60%

3.76

EWT-Prophet 2.50 Average of the 4 experiments Prophet

27.04%

4.86

42.99%

EWT-Prophet 2.80

23.00%

The prediction results are shown in Fig. 8. Figure a is a prediction comparison diagram, and Figure b is a residual comparison diagram of the two models.

Fig. 8. Prediction comparison chart, residual absolute value comparison chart

It can be seen from the residual error of the prediction results in Figure b that the improved model is better than the single model. Statistics show that the average absolute residual of the prediction results of a single model is −2.94, and the average absolute residual of the improved model is −0.08. It can be observed from figure a that because the same prediction model is used, the prediction graphs of the two models are roughly the same, but the prediction accuracy of the single model is poor, which is mainly due to the poor decomposition of the trend term of Prophet decomposition and the difference the decomposition of the periodic term. Thus, decompose the original data of the first 150 days. The decomposition is shown in Fig. 9 as the trend item decomposition diagram and the original signal diagram. It is shown in Fig. 9 that the empirical scale component (trend component) of EWT decomposition can better show the overall and local trend of the original signal. Compared with the trend term decomposed by Prophet, the local trend variation characteristics

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Fig. 9. Comparison chart of decomposed trend items

of the original signal can be better reflected. The short-medium term experimental results also show that the introduction of EWT into Prophet decomposition can decompose the original signal into modal components of different frequencies, which can more effectively reflect the overall trend and local changes of the original signal, and improve the prediction effect. Table 2 shows the short- medium-term experimental accuracy analysis tables of two groups of BJFS stations. From the results, it can be seen that the prediction effect of the improved model is better than that of the single model as a whole. In terms of the root mean square error index, the errors of the two models are 4.205 and 2.385, respectively, with an average increase of 43.28%. In terms of the average percentage error index, the errors of the two models are 53.51% and 23.56%, with an average increase of 55.97%, which proves that the is better in the short-medium term time span. Table 2. Accuracy analysis table of medium and short-term experimental results of BJFS station

BJFS 2012.6 BJFS 2012.11

Model

RMSE MAPE

Prophet

4.21

30.02%

EWT-Prophet 2.56

14.31%

Prophet

4.20

77.00%

EWT-Prophet 2.21

32.81%

Average of the 2 experiments Prophet

4.205

53.51%

EWT-Prophet 2.385

23.56%

3) In the medium-term experiment, 335 days continuous observation data were used to predict 30 days. Two groups of data were taken for experiments. The data were taken from BJFS station in 2011 and 2014, and the predicted data were compared with the measured data. Figure 10 is the comparison chart of residual absolute value of two methods in mid-span experiment of BJFS station in 2014. The statistics show that the average residual absolute value of the single model is 3.07, and the average residual absolute value of the improved model is 2.08.

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Fig. 10. Comparison of absolute residual values

Table 3 shows the accuracy analysis table of the medium-term experiments of two groups of BJFS stations. The results show that the prediction effect of the improved model is better than that of the single model as a whole. In terms of the root mean square error index, the errors of the two models are 2.79 and 2.155, respectively, with an average increase of 22.76%. In terms of the average percentage error index, the errors of the two models are 30.355% and 21.01%, with an average increase of 30.79%, which proves that the short-term prediction of the improved model is better in the medium-term time span. Table 3. Accuracy analysis table of mid-term experimental results of BJFS station

BJFS 2011 BJFS 2014

Model

RMSE MAPE

Prophet

1.96

36.11%

EWT-Prophet 1.82

24.57%

Prophet

3.62

24.60%

EWT-Prophet 2.49

17.45%

Average of the 2 experiments Prophet

2.79

EWT-Prophet 2.155

30.355% 21.01%

4) In the long-term experiment, the scheme of using 700-day continuous observation data to predict 30 days is adopted, and one group of data is taken for the experiment. The data are taken from BJFS Station in Beijing from 2012 to 2013, and the predicted data are compared with the measured data. Figure 11 is the absolute residual contrast figure. According to statistics, the average residual absolute value of single model is 3.18, and the average residual absolute value of improved model is 2.85. Table 4 shows the long-term experimental accuracy analysis table of a group of BJFS stations. The results show that the prediction effect of the improved model is better than that of the single model as a whole. In terms of the root mean square error index, the errors of the two models are 4.10 and 4.68, respectively, increasing by 12.39%. In terms of the average percentage error index, the errors of the two models are 33.92% and

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Fig. 11. Comparison of absolute residual values

38.27%, increasing by 11.37%, which proves that the short-term prediction model is better in the medium-term time span. Table 4. Analysis of long-term accuracy test results of BJFS station

BJFS 2012–2014

Model

RMSE

MAPE

Prophet

4.68

38.27%

EWT-Prophet

4.10

33.92%

In the short-term prediction results of long-span time series, it can be found that the accuracy of the improved model is improved compared with the single model, but the effect is not as obvious as the short-term and medium-term experiments in all time span samples. This is because in GNSS time series, there are obvious annual and semiannual periodic changes, which makes Prophet decomposition can effectively capture the characteristics of this type of periodic signal changes, so that the prediction effect can be effectively improved that Prophet model is more suitable for long-span time series prediction. 3.2 Verification Experiments and Results In order to verify the validity and universality of the improved model, different time span vertical time series signal prediction experiments are carried out on different stations. Table 5 is the accuracy analysis table of verification experiment. The verification data are selected from the measured vertical time series of WUHN and URUM stations. In the short-span experiment, in order to avoid the influence of the contingency and seasonality of historical data on the results, the data are taken from the actual continuous observation data of WUHN station in January, April, July and November 2012. the prediction results of Table 5, the root mean square error index of prediction results in four different time spans increased by 30.37%, 18.10%, 19.21%, 9% on average; The average percentage error increased by 32.46%, 34.80%, 26.83%, 16.60%. The prediction results show that the improved Prophet prediction method based on EWT can achieve better experimental results and has good applicability.

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Table 5. Accuracy analysis table of experiment Span

Model

RMSE

MAPE

WUHN 2012.1

Short

Prophet

3.31

32.47%

EWT-Prophet

2.46

26.57%

WUHN 2012.4

Short

Prophet

6.90

60.01%

EWT-Prophet

4.76

35.16%

WUHN 2012.7

Short

WUHN 2012.11

Short

Average of the 4 experiments WUHN 2010 URUM 2010

WUHN 2010

7.26

39.87%

EWT-Prophet

4.61

29.20%

Prophet

3.34

42.76%

EWT-Prophet

2.66

31.23%

Prophet

5.2025

43.7775%

EWT-Prophet

3.6225

30.54%

Medium -short

Prophet

5.31

36.91%

EWT-Prophet

4.63

28.04%

Medium -short

Prophet

6.75

67.55%

EWT-Prophet

4.01

40.06%

Prophet

5.69

52.23%

Average of the 2 experiments WUHN 2014

Prophet

Medium Long

EWT-Prophet

4.66

34.05%

Prophet

3.80

37.46%

EWT-Prophet

3.07

27.41%

Prophet

3.76

41.10%

EWT-Prophet

3.42

34.28%

4 Conclusion In view of the incomplete decomposition problem of Prophet model, this paper constructs an improved prediction method using EWT to apply to the short-term prediction of GNSS vertical time series. Four GNSS vertical time series with different time spans are selected for short-term prediction experiments. The results are statistically analyzed and the following conclusions are drawn: (1) Compared prediction results of the improved model with different time spans are compared with those of the single model. It can be seen from the prediction results that the improved model is better than the single model as a whole. The RMSE of the prediction results of the four different time spans are increased by 31.5%, 35.03%, 19.32% and 10.76%, respectively, and the MAPE are increased by 32.76%, 43.61%, 29.28% and 14%, respectively. From the decomposition effect, it can also be found that the trend term decomposed by EWT can reflect the overall trend and local trend characteristics of the original signal. EWT can decompose many empirical wavelets

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with different frequencies to describe complex, nonlinear and nonstationary GNSS vertical time series signals. The results show that the improved model has greatly improved the overall prediction accuracy and is more versatile. (2) The experimental results show that the improved Prophet prediction model has good prediction effect in the short-term, medium-term and short-term time series prediction. Compared with the long-span prediction, the prediction accuracy is significantly improved, and its prediction accuracy is better than that of the single Prophet prediction. The improved prediction method also strengthens the prediction effect of Prophet model in short-term time series. In this paper, empirical wavelet transform (EWT) is used to deal with nonlinear, non-stationary and noisy GNSS vertical coordinate time series signals. Combined with Prophet prediction method, we construct a new decomposition- predictionreconstruction prediction method. However, using this method to decompose the original time series by EWT increases some workload, and the Prophet method for vertical time series prediction has certain limitations. In addition, GNSS coordinate time series signal contains many noise combination characteristics, and its noise change also brings some obstacles to the prediction modeling. In order to establish a high precision and adaptive prediction model, further research is needed.

References Chang, T., Guo, Z., Xu, L., et al.: Scale prediction of AQI based on Prophet-random forest optimization model. Environ. Pollut. Control 41(07), 758–761+766 (2019) Daubechies, I.: Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia (1992) Dong, Y.: The error processing and trend prediction of GNSS deformation monitoring coordinate time series in strong interference environment. Wuhan University of Technology (2016) Gilles, J.: Empirical wavelet transform. IEEE Trans. Sig. Process. 61(16), 3999–4010 (2013) Ge, N., Sun, L., Shi, X., et al.: Research on sales prediction of Prophet-LSTM combination model. Comput. Sci. 46(S1), 446–451 (2019) He, X., Hua, X., Lu, T., et al.: Effect of time span on GPS time series noise model and velocity estimation. J. Natl. Univ. Defense Technol. 39(06), 12–18 (2017) Jiang, W., Wang, K., Li, Z., et al.: Prospect and theory of GNSS coordinate time series analysis. Geomat. Inf. Sci. Wuhan Univ. 43(12), 2112–2123 (2018) Li, S., Sun, X., Yin, L., et al.: A GPS height time series prediction method based on chaos theory and LSTM. J. Navig. Position. 8(1), 65–73 (2020). https://doi.org/10.16547/j.cnki.10-1096.202 00112 Li, L., Duan, G., Wang, J.: Reserve prediction of bank outlets based on prophet framework. J. Cent. South Univ. (Sci. Technol.) 50(01), 75–82 (2019) Ming, F., Yang, Y., Zeng, A., Jing, Y.: Analysis of seasonal signals and long-term trends in the height time series of IGS sites in China. Sci. China Earth Sci. 59(6), 1283–1291 (2016). https:// doi.org/10.1007/s11430-016-5285-9 Kai, N., Fanghua, H., Dong, F., et al.: Research on predictioning method of electric power material demand based on prophet algorithm. Sci. Technol. Innov. 33, 163–164 (2020) Acharya, R., Roy, B., Sivaraman, M.R., Dasgupta, A.: Prediction of ionospheric total electron content using adaptive neural network with in-situ learning algorithm. Adv. Space Res. 47(1), 115–123 (2010)

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Sun, G., Liang, Z., Yu, N., et al.: Short-term wind power probability density predictioning based on EWT and quantile regression forest. Electric Power Autom. Equip. 38(08), 158–165 (2018) Su, L., Ding, X., Zhang, Y., et al.: Study on coordinate time series of Shaanxi continuous GPS reference stations. J. Geodesy Geodyn. 34(05), 106–109+113 (2014) Taylor, S.J., Letham, B.: Predictioning at scale. Am. Stat. 72(1), 100–108 (2017) Wang, X., Li, Q., Zheng, S.: Short-term wind power prediction based on EWT-ESN. Acta Energiae Solaris Sinica 39(03), 633–642 (2018) Wang, Y.: Research on adaptive filter denoising method based on component decomposition. Harbin Institute of Technology (2017) Zhang, H., Lu, D., Wen, H., et al.: Analysis method of IGS station height time series based on CEEMD. Remote Sens. Inf. 34(06), 1–5 (2019) Zhang, M., Liu, P., Zhou, H., et al.: Comparison and analysis of the accuracy of two vertical coordinate predictioning models. Eng. Surv. Mapp. 28(04), 13–18 (2019)

A Carrier Tracking Algorithm Based on Adaptive Unscented Kalman Filter Under Ionosphere Scintillation Conditions Pengyue Sun, Shengqiang Lou, Xiaomei Tang, and Yangbo Huang(B) College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China

Abstract. The rapid change in the phase and amplitude of GNSS signals can cause the strong nonlinearity of carrier tracking under scintillation conditions. Moreover, the noise caused by ionospheric scintillation is non-Gaussian, resulting in difficult determination of the covariance of measurement noise. These would degrade the accuracy and robustness of conventional phase lock loop and extended Kalman filter (EKF)-based carrier tracking algorithms. This work proposes an adaptive unscented Kalman filter (UKF)-based carrier tracking algorithm to mitigate the adverse impacts of ionospheric scintillation. For one thing, the unscented transformation can effectively mitigate the linearization error of strong nonlinear cause by ionospheric scintillation, For another, we employ the phase lock indicator (PLI) to estimate the covariance of the measurement noise adaptively according to different scintillation scenarios. Through the adaptive UKF-based algorithm, the performance of carrier tracking under ionospheric scintillation can be improved, and the probability of divergence can be decreased. Simulation results demonstrate the validity of the analysis and the proposed method. Keywords: Ionospheric scintillation · Strong nonlinearity · Non-Gaussian noise · Adaptive unscented Kalman filter · Probability of loss-of-lock

1 Introduction Under ionospheric scintillation conditions, the integration of the in-phase and quadrature branches of the satellite navigation signal carrier tracking loop will not only present nonstationary and non-Gaussian characteristics, but also present strong nonlinearity in the estimation of carrier frequency, phase and other parameters due to the rapid fluctuation of amplitude and phase [1–3]. This makes the performance of the conventional phase locked loop (CPLL) based on the linear approximation of the discriminator degraded significantly [2, 4]. To avoid the linear approximation problem of phase discriminator in scintillation conditions, researchers proposed an anti-ionospheric scintillation carrier tracking algorithm based on EKF [5–7]. However, the algorithm also need to linearize the observation model with Taylor series expansion since its observation model of carrier tracking is a nonlinear transformation. Moreover, under strong scintillations, the measurement model © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 314–323, 2021. https://doi.org/10.1007/978-981-16-3146-7_29

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of the EKF-based algorithm has strong nonlinearity, and the linear approximation of the observation model will produce large errors, resulting in a decline in filtering performance. In addition, EKF needs to calculate the Jacobian matrix of the nonlinear function, which makes the implementation more complex and requires a large amount of computation. Although the Particle Filter (PF) algorithm can better adapt to nonlinear and non-Gaussian problems, its high complexity and large computation cannot meet the realtime requirements of navigation signal carrier tracking [8], and the problem of particle degradation of PF will greatly reduce the performance of the algorithm [9], which is a major bottleneck in its engineering application. The UKF is a method to approach nonlinear transformation through sampling strategy [10]. Compared with PF, it does not have particle degradation problem. Moreover, the UKF-based algorithm operates much fast as it needs much less sampling points than PF, which is equalling to EKF, and its estimation accuracy is significantly improved. However, although the application of UKF in high-dynamic environments can effectively improve carrier tracking performance [11–13], the UKF algorithm has important limitations under ionospheric scintillation conditions. In fact, the UKF algorithm is still a Kalman filtering (KF)-based algorithm. The statistic characteristics of measurement noise will seriously affect the performance of the algorithm, and even cause the divergence of filtering [14, 15]. Moreover, the noise introduced by ionospheric scintillation is non-Gaussian, and its noise covariance is difficult to determine. In view of this, this paper proposes a novel carrier tracking algorithm for scintillation mitigation based on adaptive UKF estimator. By employing the phase locking indicator (PLI), which can be the indicator of ionospheric scintillation intensity, the proposed algorithm can determine the covariance of measurement noise of UKF in presence of ionospheric scintillation adaptively.

2 Limitations of EKF Carrier Tracking Under Ionospheric Scintillation Conditions Ionospheric scintillation will cause rapid fluctuations in the amplitude and phase of the GNSS signal, and the signal received by the receiver can be modeled as [16]: r(t) = A0 δAC(t − τd )D(t − τd ) cos(ωt + φ0 + δφ) + n(t)

(1.1)

Where A0 is the signal amplitude, C(t) is the spreading code, D(t) is the message sequence, τ d is the pseudo code delay, ω is the frequency of carrier, φ 0 is the initial phase, n(t) is the additive white Gaussian noise, δA and δφ are the amplitude and phase fluctuations caused by ionospheric scintillation. This paper mainly studies the influence of ionospheric scintillation on carrier tracking. Therefore, assuming that the receiver has completed signal acquisition and the pseudo-code phase has been fully synchronized, the coherent integration results of the I and Q branches can be calculated as [17, 18]: IPk = A0 δADk cos(ϕR,k + ϕS ) + nI ,k = AS,k cos ϕR,k + nSI ,k + nI ,k QPk = A0 δADk sin(ϕR,k + ϕS ) + nQ,k = AS,k sin ϕR,k + nSQ,k + nQ,k

(1.2)

Where AS,k = A0 δAk Dk cosϕ S is defined as the integral envelop under the influence of scintillation, ϕ S is the phase discrimination error introduced by ionospheric scintillation,

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ϕ R is the true phase error, nI,k and nQ,k are the zero mean values of two orthogonal channels Gaussian white noise, nSI,k = −Ak sinϕ R,k sinϕ S and nSQ,k = Ak cosϕ R,k sinϕ S are defined as additive nonGaussian noise introduced by ionospheric scintillation. EKF-PLL (EKF-based PLL) takes the I and Q branch correlation values as observation data to estimate the carrier phase difference, and its observation equation can be modeled as:         nI ,k −Ak sinϕR,k sinϕS AS,k cos(Lsk ) AS,k cos(Lsk ) + xk = + nT ,k = + Ak cosϕR,k sinϕS nQ,k AS,k cos(Lsk ) AS,k cos(Lsk ) (1.3) Where sk = [ϕ R,k ω0,k ω1,k ω2,k ]T is the state vector of EKF-PLL, and the ω0,k , ω1,k , ω2,k are the first, second and third derivative of ϕ R,k respectively. L = [1 0 0 0], nT,k is the total noise term under ionospheric scintillations, and its covariance is Rk . It is difficult to estimate the covariance of the non-Gaussian noise terms nSI,k , and nSQ,k , nT,k due to the ionospheric scintillation. EKF-PLL linearizes the nonlinear observation equation of formula (1.3) through Taylor series expansion, and then recursively estimates the carrier phase difference through Kalman filtering. The recursive equation of EKF carrier phase difference estimation can be found in reference [17]. However, with the continuous enhancement of ionospheric scintillation, the approximate error of the above linearization will increase sharply, which will seriously affect the tracking performance of EKF-PLL. Especially under the ionospheric scintillation conditions, the mean value of the nonlinear observation vector shown in Eq. (1.3) can be accurately calculated as   2  e−0.5σS E cos(ϕR,k ) xk = E[h(sk )] = A0 Dk E[δAk ] −0.5σ 2  (1.4)  S E sin(ϕR,k ) e The mean value after EKF-PLL linear approximation is     cos(E ϕR,k  ) EKF xk = h(E[sk ]) = A0 Dk E[δAk ] sin(E ϕR,k )

(1.5)

Where E[δAk ] is the mean value of the amplitude scintillation sequence, and σs2 is the variance of ϕ S , which reflects the intensity of phase scintillation. Comparing the calculation results of Eqs. (1.4) and (1.5), the approximate error of EKF-PLL increases with the increase of the scintillation intensity. When the system is seriously nonlinear, the linearization of EKF-PLL will lead to obvious approximation error, resulting in the decline of EKF state estimation accuracy, and even lead to the filtering divergence problem.

3 Adaptive UKF Carrier Tracking Algorithm for Ionospheric Scintillation Conditions Similar to the EKF algorithms, the UKF-based carrier tracking algorithm also takes the correlation values of the I and Q branches as the measurement vector. The algorithm

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can directly follow the state vector and measurement equation of EKF-based algorithm shown in Eq. (1.3) [3]. The state model is essentially modeled by Taylor series expansion, sk+1 =  · sk + ζk

(6)

Where  is the state transition matrix, and ζk = [ζ 1,k ζ 2,k ζ 3,k ζ 4,k ]T is the state noise. First of all, by using proportional symmetric sampling strategy [6], The 2n + 1 canonical Sigma points {χ i } of UKF-PLL can be chosen. After that, the time update equation can be used to propagate the state estimates and covariance from one measurement time to the next, (i)

(i)

ξk|k−1 =  · χk−1

(1.7)

Then, using the mean and covariance weights to estimate the covariance of prior state estimation and estimation error, which is sˆk|k−1 = Pk|k−1 =

2n  i=0 2n 

(i)

Wm(i) ξk|k−1



T (i) (i) Wc(i) ξk|k−1 − sˆk|k−1 ξk|k−1 − sˆk|k−1 + Q

(1.8)

i=0 (i)

(i)

Where Wm is the mean weight, Wc is the covariance weight, and Q is the covariance of the state noise ζk . After the time update is completed, the measurement update can be performed. Finally, calculate the UKF filter gain, and update the state vector and covariance.   −1 Kk = Pxs Pxs , sˆk = sˆk|k−1 + Kk xk − xˆ k|k−1 Pk = Pk|k−1 − Kk Pxx KkT

(1.9)

Where Pxs is the cross-covariance of the state vector and the measurement vector, Pxx is the covariance of the predicted measurements. It can be seen that the main difference between UKF and EKF is that the state transfer of UKF is achieved through a series of nonlinear transformations of Sigma points, rather than the linear approximation by Taylor series expansion, which is more accurate in strong nonlinear models. It means that the nonlinear approximation error caused by ionospheric scintillation can be mitigated. Moreover, since the UKF does not need to be linearized, it does not need to calculate the Jacobian matrix of the nonlinear transformation h(·), and the amount of calculation is also reduced. For the UKF-based carrier tracking algorithm, for one thing, the ionospheric scintillation will cause strong nonlinear approximation error, for another, the difficulty of determination of the measurement noise covariance will also significantly affect the tracking performance and robustness. In view of this, this paper proposes the following measurement noise estimation algorithm. According to the definition of innovation, the innovation can be regarded as the prediction error of the measurement vector predicted by the system state vector. Therefore, its covariance is equivalent to the covariance of the measurement vector prediction,

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namely ˆ k = Pˆ xx = C

2n 





T ˆk ˆ k|k−1 η(i) ˆ k|k−1 + R Wc(i) η(i) k|k−1 − x k|k−1 − x

(1.10)

i=0

Thus, the real-time estimation of the noise covariance of the UKF carrier tracking algorithm can be obtained ˆ k = (xk − R

2n 

(i)

Wm(i) ηk|k−1 )(xk −

i=0

−

2n 

2n 

(i)

Wm(i) ηk|k−1 )T

i=0





T (i) (i) Wc(i) ηk|k−1 − xˆ k|k−1 ηk|k−1 − xˆ k|k−1

(1.11)

i=0

Formula (1.11) shows that the measurement noise covariance of the UKF algorithm can be estimated in real time through measurement vectors. However, with the increasing of scintillation intensity, the complex envelope of the I and Q branches will fluctuate much stronger, and the non-Gaussian noise introduced by scintillation will also become much larger. In order to solve this problem, we propose a phase-locked indicator (PLI)-based adaptive measurement vector estimation algorithm, which can adjust the measurement vector adaptively with different scintillation scenarios. The PLI can better reflect the intensity of ionospheric scintillation. Thus it can be used as a control variable for adaptive adjustment of measurement vectors. This paper designs the following adaptive measurement vector x˜ k = PLIk × xk + [1 − PLIk ] × zk

(1.12)

Where zk is the modification of the measurement vector, zk = x˜ k−1 + ˆxk

(1.13)

ˆxk = xˆ k|k−1 − xˆ k−1|k−2 is the prediction of the variation of the measurement vector. Through the above design, UKF-based carrier tracking algorithm can adaptively adjust the measurement vector through the PLI value under different ionospheric scintillation conditions. Substituting formula (1.12) into formula (1.11), the adaptive measurement noise covariance of UKF under ionospheric scintillation conditions can be obtained ˆ k = (˜xPLI ,k − R

2n  i=0

−

2n 

(i)

Wm(i) ηk|k−1 )(˜xPLI ,k −

2n 

(i)

Wm(i) ηk|k−1 )T

i=0





T (i) (i) Wc(i) ηk|k−1 − xˆ k|k−1 ηk|k−1 − xˆ k|k−1

(1.14)

i=0

Aiming at the above PLI-based adaptive UKF algorithm, the architecture of carrier tracking loop is shown in Fig. 1.

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Fig. 1. The architecture of AEKF-based PLL

Compared with EKF-PLL, the above tracking loop does not need to linearize the measurement equation of carrier tracking, which can better solve the strong nonlinear approximation error of the measurement model under strong scintillation conditions. Moreover, the real-time measurement noise covariance estimation is conducive to improve the accuracy and robustness of the carrier tracking loop under ionosphere conditions.

4 Simulation Verification In this section, the phase jitter, the probability of loss-of-lock and cycle slip of PLIUKF under different ionospheric scintillation conditions are simulated and analyzed. The CSM (Cornell Scintillation Model) model developed by Cornell University is used to generate ionospheric scintillation signals, and its input parameters are amplitude scintillation index S 4 and decorrelation time τ 0 . The simulation generates 5 different scintillation scenarios, with intensity gradually increased, and the specific parameters are shown in Table 1. Taking Beidou system B1I signal as an example, the C/N 0 is 40 dB-Hz, and the intermediate frequency is 9.548 MHz. The tracking performance of PLI-UKF is analyzed with the BeiDou system ionospheric scintillation software receiver (BDS-ISSR) developed at NUDT. For all the subsequent simulation results in this paper, the parameter settings of the software receiver are shown in Table 2. First, the standard deviation of the phase discrimination error under different ionospheric scintillation conditions is analyzed. The standard deviation of the carrier tracking loop can be calculated as  N 1    ϕE (k) − ϕE 2 (1.15) STD(ϕE ) = N k=1

Where {ϕ E (i), i = 1, …, N} is the phase discrimination error sequence of the tracking loop, ϕE is the average value of the sequence, and N = 120000 is the data length of phase error series in each scintillation scenario. Then the phase jitter of the four different tracking algorithms is shown in Fig. 2.

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P. Sun et al. Table 1. The fluctuation of amplitude and phase of BeiDou signal

Time [min]

Scintillation intensity

Amplitude fluctuation [dB]

Phase fluctuation [rad]

0–2

Weak: S 4 = 0.2, τ 0 = 1.4

[−0.8, 0.9]

[−0.52, 0.47]

2–4

Weak: S 4 = 0.4, τ 0 = 0.8

[−2.34, 2.6]

[−0.2, 0.23]

4–6

Moderate: S 4 = 0.5, σ ϕ = 0.5

[−4.7, 4.5]

[−0.54, 0.71]

6–8

Strong: S 4 = 0.7, σ ϕ = 0.3

[−7.1, 5.5]

[−1.1, 1.2]

8–10

Severe: S 4 = 0.9, σ ϕ = 0.1

[−10.3, 7.1]

[−1.83, 1.75]

Table 2. The settings of software receiver Tracking algorithm

Discriminator

Bn (Hz)

Tcoh (ms)

CPLL

ATAN

15

5

Adaptive

5

Adaptive

5

Adaptive

5

EKF — UKF — PLI-UKF —

Fig. 2. Comparison of the phase jitter under different scintillation conditions

It can be seen that the phase jitter of the proposed PLI-UKF algorithm outperforms other algorithms under different scintillation scenarios, and the stronger the scintillation, the more obviously the performance is improved. Under weak and moderate scintillation, the CPLL phase detector and the EKF measurement model are both in the linear region, and the performance of the four tracking algorithms is equivalent. Under strong

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scintillation, the phase jitter of EKF is not significantly improved compared to CPLL. However, the PLI-UKF and UKF reduce 4.5° (23.9%) and 2.63° (14.3%) respectively. Under severe scintillation conditions, its phase jitter of PLI-UKF was reduced by 6.37° (23.2%) and 3.99° (16%), respectively compared with CPLL and UKF. Secondly, the probability of loss-of-lock of four tracking loops under different ionospheric scintillation scenarios is analyzed. Supposing the tracking threshold C T /N 0 is 35 dB-Hz, then the probability of loss-of-lock can be calculated as [17]      (1.16) Ploss = P C N0 < CT N0 = P(IPk2 QPk2 < 13.56) Where IPk2 and QPk2 are the average power of the I and Q respectively, and T coh is the integration time. In different ionospheric scintillation scenarios, the probability of loss-of-lock of the four tracking loops is shown in Fig. 3.

Fig. 3. Comparison of the probability of loss-of-lock under different scintillation conditions

It can be seen that the PLI-UKF has the lowest probability of loss-of-lock under different scintillation conditions. Especially under strong scintillation, the PLI-UKF and UKF decreases about 52.6% and 28% respectively compared with CPLL, while the result of EKF is almost same as CPLL, which demonstrates the advantage of the unscented transformation in nonlinear approximation. Under severe scintillation, the probability of loss-of-lock of CPLL, EKF and UKF reached more than 90%, while the result of PLI-UKF was about 78%, which proves the robustness of PLI-UKF in carrier tracking under severe scintillation conditions. Finally, the cycle slip of four carrier tracking algorithms under different ionospheric scintillation scenarios is analyzed, as shown in Fig. 4. It can be seen that only CPLL occurs 1 cycle slip under weak and moderate scintillations (0–6 min). Under strong scintillation, due to the linear approximation error of phase detector, the CPLL and EKF occurs 21 times and 18 times cycle slips respectively, while UKF occurs 12 times cycle slips and PLI-UKF only occurs 7 times cycle slips, which decreased by 66.7% compared with CPLL. Under severe scintillation, cycle slip of CPLL increases sharply, and the loop can not work properly, the EKF and UKF occurs 48 times and 40 times cycle slips respectively. However, the PLI-UKF appears only 20 times cycle slips, and it is

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reduced about 50% compared with UKF. This is because that the PLI-UKF can estimate the non-Gaussian noise covariance introduced by ionospheric scintillation, which can effectively reduce the approximation error of the measurement model.

Fig. 4. The probability of loss-of-lock of the three loops under different scintillation conditions

5 Conclusions Ionospheric scintillation will cause rapid and random fluctuations in the amplitude and phase of the integration of the I and Q branches. It not only affects the performance of CPLL, but also degrades the accuracy and robustness of EKF-based carrier tracking loop. In this paper, we propose a carrier tracking algorithm for scintillation mitigation based on adaptive UKF, which can adaptively estimate the covariance of measurement noise in real-time. The proposed algorithm can effectively reduce the approximation error of the carrier tracking measurement model under strong scintillation conditions, and improve the accuracy and robustness of carrier tracking. However, both CPLL and KF-based carrier tracking algorithms employ closed-loop recursion architecture to realize real-time estimation of carrier parameters. Once the system state model occurs errors, the carrier tracking with closed-loop architecture will be affected continuously. In the future, the open-loop parameter estimation-based carrier tracking technology for ionospheric scintillation mitigation will be studied to fundamentally solve the problem of loop divergence under severe ionospheric scintillation conditions.

References 1. Robert, S.C., Bakry El-Arini, M., Christopher, J.H., et al.: Modeling the effects of ionospheric scintillation on GPS/satellite-based augmentation system availability. Radio Sci. 38(1), 1001 (2003)

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2. Kintner, P.M., Ledvina, B.M., de Paula, E.R.: GPS and ionospheric scintillations. Space Weather 5, S09003 (2007) 3. Pengyue, S., Xiaomei, T., Yangbo, H., Guangfu, S.: Wavelet de-noising Kalman filter-based global navigation satellite system carrier tracking in the presence of ionospheric scintillation. IET Radar Sonar Navig. 11(2), 226–234 (2017) 4. Ghafoori, F., Skone, S.: GPS scintillation modeling and receiver design strategies for lowlatitude regions. ION GNSS+ 2014, Session E3, Tampa, FL, 8–12 September 2014 (2014) 5. Vilà-Valls, J., Closas, P., Fernández-Prades, C.: Advanced KF-based methods for GNSS carrier tracking and ionospheric scintillation mitigation. In: IEEE Aerospace Conference, March 2015 (submitted) 6. Zhang, L., Morton, Y.T.: Tracking GPS signals under ionosphere scintillation conditions. In: ION GNSS 2009, Savannah, GA, 22–25 September 2009, pp. 227–234 (2009) 7. Macabiauetal, C.: Kalman filter based robust GNSS signal tracking algorithm in presence of ionospheric scintillations. In: Proceeding of the ION GNSS, September 2012, pp. 3420–3434 (2012) 8. Julier, S.: Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches. Wiley, Hoboken (2006) 9. Chen, Y.-H., Juang, J.-C., Kao, T.-L.: Robust GNSS signal tracking against scintillation effects: a particle filter based software receiver approach. In: ION 2010 International Technical Meeting, 25–27 January 2010, San Diego, CA, pp. 627–635 (2010) 10. Julier, S., Uhlmann, J., Durrant-Whyte, H.F.: A new method for the nonlinear transformation of means and covariances in filters and estimator. IEEE Trans. Autom. Control 45(3), 477–482 (2000). https://doi.org/10.1109/9.847726 11. Jwo, D., Lai, C.: Unscented Kalman filter with nonlinear dynamic process modeling for GPS navigation. GPS Solutions 12, 249–260 (2008) 12. Chen, X., Wang, W., Meng, W., Zhang, Z.: High dynamic GPS signal tracking based on UKF and carrier aiding technology. In: International Conference on Communications and Mobile Computing (CMC), pp. 476–480 (2010) 13. Liu, J., Lu, M.: An adaptive UKF filtering algorithm for GPS position estimation. In: 5th International Conference on Wireless Communications, Networking and Mobile Computing, pp. 1–4 (2010) 14. Vilà-Valls, J., Closas, P., Fernández-Prades, C.: On the identifiability of noise statistics and adaptive KF design for robust GNSS carrier tracking. In: Proceedings of the IEEE Aerospace Conference, March 2015 (2015) 15. Won, J.H., Pany, T., Eissfeller, B.: Characteristics of Kalman filter approach for signal tracking loop of GNSS receiver. IEEE Trans. Aerosp. Electron. Syst. 48(4), 3671–3681 (2012) 16. Kaplan, E.D., Hegarty, C.J.: Understanding GPS: Principles and Applications, 2nd edn. Artech House, Norwood (2006) 17. Sun, P., Tang, X., Chen, H., Sun, G.: Adaptive extended Kalman filter carrier tracking algorithm for BDS signals under ionosphere scintillation conditions. J. Natl. Univ. Def. Technol. 38(3), 25–31 (2016) 18. Hofmann-Wellenhof, B.: GPS Theory and Practice, p. 248. Springer, Wien (2001). https:// doi.org/10.1007/978-3-7091-6199-9

GNSS Spoofing Detection Based on Combined Monitoring of Acquisition Function and Automatic Gain Control Tao Zhang1 , Xin Chen1(B) , Weihua Xie2 , Wenxian Yu1 , and Weimin Zhen3 1 Shanghai Key Laboratory of Navigation and Location Based Services, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China [email protected] 2 Beijing Satellite Navigation Center, Beijing 100094, China 3 China Research Institute of Radiowave Propagation, Qingdao 266107, China

Abstract. Due to long-distance transmission from satellite to Earth, the received power of GNSS signals is extremely weak, causing that receivers are vulnerable to spoofing attack. Monitoring multiple correlation peaks in the acquisition function and abnormal deviation in the AGC values are two common methods to detect the presence of spoofing. However, it is found that the combination mode of these two methods and the corresponding combined performance have not been fully analyzed and verified. In this paper, the detection performances of these two methods are first analyzed. Next, a combined monitoring based on these two methods is proposed, and its combined performance is analyzed. Finally, a set of experiments are conducted to verify the correctness of theoretical analysis and test the combined detection performance. Keywords: Combined spoofing detection · Acquisition function · Automatic gain control

1 Introduction Relying on the precise ability of positioning, navigation and timing, GNSS is widely used in various fields of both national security and social economy. However, due to long-distance transmission from satellite to Earth, the received power of GNSS signals is extremely weak, causing that receivers are vulnerable to spoofing attack [1]. If the victim receiver misinterprets spoofing signals as authentic ones, it might deduce a false position fix, a false clock offset, or both [2]. Therefore, spoofing attack will pose a serious threat to the navigation security. Several anti-spoofing methods have been proposed in open literature, and they can be divided into two broad categories: spoofing detection and spoofing mitigation [3]. Spoofing detection aims at detecting the presence of spoofing signals and delivering a warning to victim receivers, while spoofing mitigation mainly concentrates on retrieving the positioning and navigation abilities of receivers [4]. Acquisition function refers to a two-dimensional function about the code phase and Doppler frequency, that is obtained © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 324–333, 2021. https://doi.org/10.1007/978-981-16-3146-7_30

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by correlating received signals with local replicas. When spoofing signals and authentic signals are both present, there will be two correlation peaks in acquisition function. This metric can be used to detect the spoofing presence. However, as the power of spoofing signals increases, the elevation of noise floor will obscure the authentic correlation peaks [5]. AGC is widely used in the RF front-end circuit to optimize the gain such that the amplitude of the incoming signal can utilize the entire range of the analog-to-digital converter (ADC). Since the power of received authentic GNSS signals on Earth is below that of the ambient thermal noise, when the power of spoofing signals is weak, AGC is driven mostly by the power of ambient thermal noise [6], leading to no significant change in AGC gains. When the power of spoofing signals is significantly stronger than that of authentic signals, AGC gains will deviate from the normal values. Although the spoofing detection methods based on acquisition function or AGC have been discussed in literatures [6–8], it is found that the combination mode of these two methods and the corresponding combined performance have not been fully analyzed and verified. In this paper, the detection performances of these two methods are first analyzed. Next, a combined monitoring based on these two methods is proposed, and its combined performance is analyzed. Finally, a set of experiments are conducted to verify the correctness of theoretical analysis and test the combined detection performance. The following sections are organized as follows. The performance analyses of acquisition function monitoring and AGC monitoring are respectively introduced in Sect. 2 and Sect. 3. The combined monitoring method and its theoretical detection performance are described in Sect. 4. Experimental results are analyzed and summarized in Sect. 5. Finally, conclusions are drawn in Sect. 6.

2 Performance Analysis of Acquisition Function Monitoring 2.1 Signal Model After being down-converted and filtered by the RF front-end circuit in a GNSS receiver, the received signals under spoofing attack can be modeled as:        i i i C i t − τ i Di t − τ i 2Pau r(t) = au au cos 2π(fIF + fd ,au )t + ϕau i∈AU

+



      j j j j j 2Psp C j t − τsp Dj t − τsp cos 2π(fIF + fd ,sp )t + ϕsp + η(t) (1)

j∈SP

where AU and SP represent visible satellite numbers, respectively, in authentic signals and spoofing signals. au and sp indicate the authentic signal and spoofing signal respectively. C(t) is the spreading code sequence. D(t) is the navigation message. τ, fIF , fd , ϕ denote, respectively, the code delay, receiver intermediate frequency, Doppler frequency and initial carrier phase. η(t) is assumed to be Additive White Gaussian Noise with power spectral density of N0 /2.

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Next, the signal acquisition is followed. For the k-th coherent integration period, the coherent integration outputs on the in-phase and quadrature branches are given by:     1  1  j (j,l) 1 l cos ϕ l i ψ (i,l) + + Ik = 2Pau 2P 2Psp ψc + ηI (t) (2) au au c 2 2 2 i∈AU i=l

j∈SP

i∈AU i=l

j∈SP

    1  1  j (j,l) 1 l (i,l) l i 2Pau sin ϕau + 2Pau ψs + 2Psp ψs + ηQ (t) Qk = 2 2 2

(3)

where T coh is the coherent integration time. τl and fdl are, respectively, the code phase and Doppler frequency of the local replica. ηI (t) and ηQ (t) are the uncorrelated Gaussian noise components at the in-phase and quadrature branches, respectively. The Gaussian noise components are both zero mean and have the variances of σn2 , the variance is given by σn2 = N0 /(2Tcoh ) [9]. (∗,l) (∗,l) ψc and ψs are the cross-correlation interferences between received signal and local replica, respectively, on the in-phase and quadrature branches. They are given as follows:       (∗,l) (∗,l) (4) ψc(∗,l) = Rc τ (∗,l) sin c π fd Tcoh cos π fd Tcoh + ϕ ∗       (∗,l) (∗,l) ψs(∗,l) = Rc τ (∗,l) sin c π fd Tcoh sin π fd Tcoh + ϕ ∗

(5)

 where Rc τ (∗,l) is the cross-correlation function of the spreading code. τ (∗,l) and fd(∗,l) are, respectively, the code phase difference and Doppler frequency difference between received signal and local replica. After coherent integration and non-coherent accumulation, the acquisition function can be expressed as: K      Ik2 + Qk2 Y τ l , fdl =

(6)

k=1

where K is the number of non-coherent accumulation. Each (τl , fdl ) point defines a searching cell in the acquisition function. 2.2 Hypothesis Testing Model According to the presence or absence of the target acquiring signal, the following hypotheses can be established. For each hypothesis, the expressions of the in-phase and quadrature components are given with their probability distributions: • H0 : signal is absent or not correctly aligned with local replica     Ik ∼ N 0, σ 2 ;Qk ∼ N 0, σ 2

(7)

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Z τ

l

, fdl



 K  Y τ l , fdl 1  2 2 2 = I = + Q k k ∼ χ (2K) σ2 σ2

327

(8)

k=1

• H1 : signal is present, only authentic signal is correctly aligned with local replica  



     1 1 l 2 l 2 l l (9) Ik ∼ N 2Pau cos ϕau , σa ;Qk ∼ N 2Pau sin ϕau , σa 2 2

K   Y τ l , f l  l K 1  2 Pau d l l 2 2 Z τ , fd = Ik + Qk ∼ χ 2K, = 2 (10) σa2 σa 2σa2 k=1

• H2 : signal is present, only spoofing signal is correctly aligned with local replica  



     1 1 l 2 l 2 l l (11) Ik ∼ N 2Psp cos ϕsp , σs ;Qk ∼ N 2Psp sin ϕsp , σs 2 2

K l K   Y τ l , f l  Psp 1  2 d l l 2 2 Z τ , fd = Ik + Qk ∼ χ 2K, = 2 (12) σs2 σs 2σs2 k=1

where χ2 (a, b) denotes chi-square distribution. a is the degree of freedom. b is the non-central parameter. According to the statistical analysis of the cross-correlation interferences, the variances of these hypotheses are given by: ⎛ ⎞  1  1  j (j,l) i ψ (i,l) + 2Pau 2Psp ψc ⎠ (13) σa2 ≈ σs2 ≈ σ 2 = σn2 + Var ⎝ c 2 2 i∈AU

j∈SP

2.3 Detection Threshold and Theoretical Detection Performance The false alarm probability on a searching cell and the overall false alarm probability in acquisition function are defined as [9]:  ∞     N  f Z τ l , fdl |H0 dZ; Pfa = 1 − 1 − Pfa−cell c (14) Pfa−cell = Zth

where Zth is the detection threshold for normalized amplitude of acquisition function. Nc is the total number of searching cells in acquisition function. Based on Eq. (8) and (14), the detection threshold for normalized amplitude of acquisition function is given by:   (15) Zth = Yth /σ 2 = F −1 2K, (1 − Pfa )1/Nc

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 where F −1 2K, (1 − Pfa )1/Nc is the inverse cumulative distribution function of the chisquare distribution with 2K degrees of freedom and evaluated at the probability value in (1 − Pfa )1/Nc . When authentic peak and the spoofing peak are simultaneously detected, the presence of spoofing signals will be determined. Therefore, the detection probability of spoofing presence in acquisition function monitoring can be expressed by:



     ∞   ∞   l l l l (16) f Z τ , fd |H1 dZ • f Z τ , fd |H2 dZ PD = Zth

Zth

Simulation test is conducted to analyze the theoretical detection performance. It is assumed that the received signals include 10 authentic signals with the power of −128 dBm for each (typical received power for authentic GPS signals), and 10 spoofing signals with equal powers. The overall false alarm probability is set to 0.001, and the total number of searching cells is 21 * 50000. As is shown in Fig. 1, the spoofing to authentic power ratio is defined as the power ratio between single spoofing signal and single authentic signal. It can be observed that as the number of non-coherent accumulation increases, the detection range of spoofing signal power is extended, and the detection probability is improved.

Fig. 1. Theoretical detection performance of acquisition function monitoring

3 Performance Analysis of AGC Monitoring Null hypothesis significance testing (NHST) is a method of statistical inference [10], where P-value is an important concept that refers to the probability of occurrence for the observation sample if the null hypothesis were true. A low P-value indicates that the sample result would be unlikely present if the null hypothesis were true, leading to the rejection of the null hypothesis. This method is extremely suitable for detecting abnormal AGC gains under high power spoofing attack. Assuming that GA denotes the AGC gains obtained from the RF front-end circuit when no spoofing signal is present, GAi (i = 1, 2, ..., m) are random samples of size m

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in GA , G A and SA2 denote the sample mean and sample variance respectively; while GE denotes the AGC gains obtained from the RF front-end circuit under unknown conditions, GEi (i = 1, 2, ..., n) are random samples of size n in GE , G E and SE2 denote the sample mean and sample variance respectively. Since the samples in GA and GE are independent of each other, when m and n are large (both m > 40 and n > 40), the test static as follows is approximately standard normal distributed according to Central Limit Theorem [10]: V =

G E − G A − (μE − μA )  ∼ N (0, 1) SA2 SE2 + n m

(17)

where μA and μE are, respectively, the population mean of GA and GE . Therefore, the test statistic value and corresponding P-value can be expressed by: GE − GA v= 2 ; P-value = SA2 SE + n m



v −∞

f (V )dV

(18)

where the lower the P-value, the higher the probability of spoofing presence. Typical P-value threshold can be set to 10−4 .

4 Combined Monitoring of Acquisition Function and AGC Based on the preceding analyses, a combined monitoring based on acquisition function and AGC is proposed, and its block diagram is shown in Fig. 2.

Fig. 2. Block diagram of combined monitoring

First, the digital intermediate frequency (IF) data of received signals and the corresponding AGC gains are recorded. Second, parallel code phase search is conducted to the digital IF data to obtain acquisition function, the coherent integration time is set to 1 ms, and the number of non-coherent accumulation is set to 10. And then the normalized maximum peak and secondary peak are calculated. Besides, sliding window is

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used to process the AGC gain samples, the window length L is set to 50 to ensure that it satisfies the Central Limit Theorem. The P-value of each sliding window is calculated by the NHST method. Finally, if the normalized maximum peak and secondary peak are both above the detection threshold, or the P-value of current sliding window is below the P-value threshold (10−4 ), the presence of spoofing signals will be determined. Simulation test is conducted to analyze the theoretical detection performance of the combined monitoring, which is shown in Fig. 4. It can be observed that the combination of acquisition function monitoring and NHST based AGC monitoring can compensate for each other’s limitations, which can not only extend the detection range of spoofing signal power, but also improve the detection probability.

5 Experimental Tests 5.1 Experimental Validation for Theoretical Analysis In order to verify the correctness of theoretical analysis, a simulator test is conducted, which is shown in Fig. 3. Two simulators are used to generate authentic signals and spoofing signals respectively, and the GNSS signal record system is used to record the digital intermediate frequency (IF) data of mixed signals and the corresponding AGC gains.

Fig. 3. Experimental setup of the simulator test

Next, acquisition function monitoring and AGC monitoring are applied to the recorded digital IF data and AGC gains. For acquisition function monitoring, the coherent integration time is 1 ms, the number of non-coherent accumulation is 10, the overall false alarm probability is 0.001, the total number of searching cells is 21 * 50000. For AGC monitoring, the length of sliding window is 50 and the P-value threshold is set to 10−4 . The comparison of experimental results and theoretical analysis is shown in Fig. 4. It can be observed that for acquisition function monitoring, AGC monitoring and combined monitoring, experimental results show high consistence with the theoretical analysis, the average errors of detection probability are all less than 0.03, which verifies the correctness of theoretical analysis.

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Fig. 4. Comparison of experimental results and theoretical analysis

5.2 Performance Test of Combined Monitoring for Static Receivers To test the detection performance of the combined monitoring method for static receivers, as is shown in Fig. 5, a receiving antenna on the roof is used to receive authentic satellite signals, and then spoofing signals are generated by applying certain time delays and Doppler variations to the authentic signals through the spoofer. Finally, the spoofing signals are broadcast to the static receiving antenna.

Fig. 5. Experimental setup of the static in-car test

Three different spoofing power settings are configured: low power spoofing, matching power spoofing and high power spoofing, the corresponding spoofing to authentic power ratios are −5 dB, 3 dB and 10 dB respectively. Next, the proposed combined monitoring method is applied to the recorded digital IF data and AGC gains, and the experimental detection results are shown in Fig. 6. Under low power spoofing or matching power spoofing, since the spoofing signals and authentic signals are closely aligned in both code phase and Doppler frequency at the beginning of spoofing attack, it takes a period of time to detect the multiple peaks in the acquisition function. Under high power spoofing, the performance of combined monitoring mainly depends on the AGC monitoring, hence it is not affected by the

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Fig. 6. Experimental detection results of the combined monitoring method

alignment between spoofing signals and authentic signals, and the spoofing presence can be detected throughout the spoofing attack.

6 Conclusion In this paper, a combined monitoring based on acquisition function and AGC is proposed, its detection performance is analyzed and tested. The average errors of detection probability between experimental results and theoretical analysis are less than 0.03, which verifies the correctness of theoretical analysis. Besides, the proposed combined monitoring can effectively detect the spoofing presence even though the power of spoofing signals is 5 dB lower than that of authentic signals. Acknowledgements. The research work was funded by the National Key Research and Development Program of China (No: 2018YFB0505103); Science and Technology Project of State Grid Corporation of China (No. SGSHJX00KXJS1901531).

References 1. Ioannides, R.T., Pany, T., Gibbons, G.: Known vulnerabilities of global navigation satellite systems, status, and potential mitigation techniques. Proc. IEEE 104(6), 1174–1194 (2016) 2. Psiaki, M.L., Humphreys, T.E.: GNSS spoofing and detection. Proc. IEEE 104(6), 1258–1270 (2016) 3. Wang, F., Hu, C., Wu, S., Tao, Y., Xu, Y.: Research on BeiDou anti-spoofing technology based on comprehensive radio determination satellite service. Satell. Navig. 1(1), 1–9 (2020). https:// doi.org/10.1186/s43020-019-0004-2 4. Jafarnia-Jahromi, A., Broumandan, A., Nielsen, J., Lachapelle, G.: GPS vulnerability to spoofing threats and a review of antispoofing techniques. Int. J. Navig. Obs. 2012, 1–16 (2012) 5. Jafarnia Jahromi, A., Broumandan, A., Nielsen, J., Lachapelle, G.: GPS spoofer countermeasure effectiveness based on signal strength, noise power, and C/N0 measurements. Int. J. Satell. Commun. Netw. 30(4), 181–191 (2012)

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6. Akos, D.M.: Who’s afraid of the spoofer? GPS/GNSS spoofing detection via automatic gain control (AGC). Navig. J. Inst. Navig. 59(4), 281–290 (2012) 7. Hegarty, C., Odeh, A., Shallberg, K., Wesson, K., Walter, T., Alexander, K.: Spoofing detection for airborne GNSS equipment. In: Proceedings of the 31st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2018), pp. 1350–1368, September 2018 8. Hegarty, C., O’Hanlon, B., Odeh, A., Shallberg, K., Flake, J.: Spoofing detection in GNSS receivers through cross-ambiguity function monitoring. In: Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), 20 September 2019, pp. 920–942 (2019) 9. Borio, D.: A statistical theory for GNSS signal acquisition. Ph.D. dissertation, Polytecnico di Torino (2008) 10. Devore, J.L.: Probability and Statistics for Engineering and the Sciences. Duxbury Press, Belmont (2008)

LFM Interference Mitigation Method Based on Robust Statistics Yiming Wang, Qiongqiong Jia, and Renbiao Wu(B) School of Electronic Information and Automation, Civil Aviation University of China, Tianjin, China

Abstract. Global Navigation Satellite System (GNSS) signal interruptions can degrade the quality of service of GNSS-based applications. In order to solve the problem of the Linear Frequency Modulation (LFM) jamming on GNSS signal, this study applies a robust analysis method based on Joint Time-Frequency Analysis (JTFA) to improve the performance of GNSS receiver. The design of robust estimator in the Time-Frequency (TF) domain is realized through the Zero-Memory Non-Linearity (ZMNL) transformation, which is derived from considering the signal as conforming to two-dimensional Laplace distribution. In addition, Monte Carlo experiments are designed for verification of the effectiveness of the robust method. Although this method has a 0.325 dB Loss of Efficiency (LoE) in output Carrier to Noise Ratio (CNR) of the tracking loop compared with the traditional receiver under the jamming-free condition, its performance is better than that of the traditional JTFA method under the condition of LFM interference: under the condition of high jamming to noise ratio, the carrier to noise ratio of the tracking loop is increased by 7 dB. In high sweep rate and multiple LFM interference occasion, the jamming to noise signal ratio is increased by 20 dB under the condition of the receiver loop losing lock limit unchanged. Keywords: GNSS signal anti-jamming · LFM interference · Joint time-frequency analysis · Robust statistics signal processing

1 Introduction In recent years, jammers have frequently interfered with GNSS based applications and caused performance degradation. The distance between GNSS satellites and the receiver is 20,000 or even 30,000 kms, and the transmitting power of the satellites is usually only dozens of watts, so the power of the satellite signal is very weak, and facile for jammers to interfere when it reaches the ground [1]. A jammer can transmit an undesired signal with a certain bandwidth to form intentional interference, of which Linear Frequency Modulation (LFM) interference is a common way of jamming. It is widely used among GNSS jammers due to its characteristics of simple implementation and low production cost. LFM signal is a continuous wave and can cover the entire bandwidth of GNSS receiver, so the mitigation is generally achieved through TF domain processing or adaptive filter [2]. Different scholars have implemented TF analysis and blanking of GNSS © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 334–343, 2021. https://doi.org/10.1007/978-981-16-3146-7_31

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received signals through different TF joint functions [3–5]. However, the method of using TF blanking will cause the loss of the signal in the original received data, the performance may deteriorate sharply under harsh conditions. This study proposes a method of LFM interference mitigation by applying the robust statistics theory into TF domain. The TFD of the received data is modularized as the two-dimensional Laplace distribution which is a heavy-tailed distribution, as a result, the nonlinear complex signum function is used as the Zero-Memory Non-Linearity (ZMNL) transformation to process the TF domain data, so as to reduce its influence on satellite signals while realizing jamming mitigation.

2 Signal Model and Problem Description This chapter introduces the model of GNSS signal under interference and two widely used interference suppression methods: adaptive notch filter (ANF) method and TF blanking method. Simple analysis of the advantages and disadvantages of the two methods is also mentioned in this chapter. 2.1 Signal Model Let s(n) represent the satellite signal, which has the following form,  s(n) = Ps · c(nTs − τ0 )d (nTs − τ )ej(2π fd nTs +ϕ0 )

(1)

Where n is a discrete time variable, Ps represents the power of the signal, c(·) is a pseudo random code sequence, d (·) is a navigation message, τ0 , fd and ϕ0 respectively represent the propagation delay, Doppler frequency shift and carrier phase of GNSS signal. Ts is the sampling interval of the Analog-to-Digital Converter (ADC). Let j(n) represent LFM interference, which has the following form,    j(n) = 2Pj exp{j2π nTs fj0 + F(n) + jϕc } Bw F(n) = f∧ (fc (nTs − τc )) (2) 2 In Eq. (2), Pj represents the power of LFM interference signal, fj0 represents the center frequency of LFM after down-conversion, Bw is LFM bandwidth, fc is LFM sweep frequency, sweep period Tc = 1/fc , initial phase of LFM is ϕc , time delay is τc . f∧ (x) = 2 · mod(x, 1) represents the sawtooth wave function. The function mod(x, y) is the remainder of x divided by y. Then the signal received by the receiver can be expressed as y(n) = s(n) + ε(n) + j(n) where ε(n) is the Additive White Gaussian Noise (AWGN).

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2.2 ANF Method ANF is a digital filter which can automatically adjust the performance of digital signal processing according to the input signal. The adaptive process involves an algorithm that uses the cost function to determine how to change the filter coefficients to reduce the cost of the next iteration process. The ANF method has the most prominent advantage of outstanding real-time performance. 2.3 TF Blanking In this study, STFT is used to transform the signal from time domain to TF domain. For simplicity, it is assumed that the point of the windowed Fourier Transform LF is equal to the window width LW , i.e., LF = LW = L and the window function is a rectangular window. L  fs /fc to ensure the resolution of JTFA. For jamming j(n), At a certain moment t0 = n0 Ts , define the short-time segment of interference signal  T j(n0 ) = j(n0 ), j(n0 + 1), . . . , j(n0 + L − 1) with starting time t0 , sampling interval Ts and length L, (·)T stands for the transpose operator. Then, the frequency response J(n0 ) of j(n0 ) in time domain can be expressed as J(n0 ) = F{j(n0 )} where F{·} is the discrete Fourier transform. The frequency domain response JTFD corresponding to j(n) on the sampling interval n = 0, . . . , N −1 is merged into a matrix according to columns. JTFD ∈ CL×N is the TFD of j(n) under STFT transformation.

Fig. 1. The TFD before and after interference mitigation by the blanking method

In Fig. 1(a) is a TFD containing LFM interference signals, whose spectral lines are approximately jagged. Since LFM interference is sparse in the instantaneous frequency domain, interference detection on this slice can effectively blank the jamming, as shown in the Fig. 1(b). The processed signal after mitigation can be obtained through TF synthesize. However, when the sweep rate increases or there are multiple LFM jamming, the signal loss rate will increase and the receiver may lose the lock.

3 Principles of Robust Statistical Theory In this chapter, we introduce a method of applying robust statistical theory to satellite signal parameter estimation to reduce the performance loss of MLE in the presence of interference.

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Under the normal condition of jamming-free, the parameters are obtained by the Maximum Likelihood Estimate (MLE). If the received  signal is defined as y = {y(0), y(1), · · · , y(N − 1)}T ; The local replica sτl ,fdl = Ac(nTs − τl )ej2π fdl nTs , whose delay is τl , Doppler shift is fdl , and amplitude is A, is also a column vector, and the residual r = y − sτl ,fdl ejϕl , where ϕl is the carrier phase, and the cost function J (τl , fdl , ϕl ) of MLE is the 2 norm of the residual r, and its compact form can be expressed as J (τl , fdl , ϕl ) = rH r [6]. · means taking the magnitude of the vector. To simplify the calculation, the Cross-Ambiguity Function (CAF) is defined as follows [7]: C(τl , fdl ) =

N −1

y(n)c(nTs − τl )e−j2π fdl nTs

(3)

n=0

MLE of parameters τ0 , fd , ϕ0 is realized through, ˆ = arg min J (τl , fdl , ϕl ) {τˆ , fˆd , ϕ} τl ,fdl ,ϕl

(4)

(ˆ·) represents the estimation of the parameter, and Eq. (4) is equivalent to the estimate of the maximum value of the CAF function. Thus, τl , fdl and ϕl can be separated and obtained by: {τˆ , fˆd } = arg maxC(τl , fdl ) ; ϕˆ =  C(τl , fdl ) τl ,fdl

(5)

MLE has been proved to be the optimal estimator for parameters under the normal condition without jamming. But in the presence of jamming, it has been proved that the undesired signals more obey the heavy-tailed distribution [8, 9]. GNSS signal parameter estimator under MLE may no longer be optimal [10]. If the Probability Density Function (PDF) of signal is defined as f (z) (z is a complex number to denote an analytic signal), and f (z) obeys the heavy-tailed distribution. ρ(·) is used to represent the cost function of robust method and to replace the quadratic cost function in MLE. Thus, the parameter estimation process can be expressed as, Jρ (τl , fdl , ϕl ) =

N −1

ρ(y(n) − Ac(nTs − τl )ej(2π fdl nTs +ϕl ) )

n=0

{τˆ , fˆd , ϕ} ˆ = arg minτl ,fdl ,ϕl Jρ (τl , fdl , ϕl )

(6)

the likelihood function is widely used to represent ρ(z) [11], ρ(z) = − log f (z)

(7)

ρ(·) changes as the form of f (z) obeying the heavy-tailed distribution changes.

4 Robust Processing in TF Domain In this chapter the robust estimation in TF domain will be discussed by one-dimensional orthogonal transformation on the time slice of the signal. A robust method diagram based on JTFA is presented at the end of this chapter.

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At the time t0 = n0 Ts , the section of y with the length of L is y(n0 ), and the sτl ,fdl section is sτl ,fdl (n0 ). The compact form of MLE cost function J (n0 , τl , fdl , ϕl ) at this moment is:

2

2







(8) J (n0 , τl , fdl , ϕl ) = y(n0 ) − sτl ,fdl (n0 )ejϕl = Y(n0 ) − Sτl ,fdl (n0 )ejϕl

Y(n0 ) = {Y(n0 , k)} = F{y(n0 )} (k = 0, 1, · · · , L − 1) is the expression of y(n0 ) in  the frequency domain, Sτl ,fdl (n0 ) = Sτl ,fdl (n0 , k) = F sτl ,fdl (n0 ) is the frequency domain expression for s(n0 , τl , fdl ). According to Eq. (6), the cost function Jρ (n0 , τl , fdl , ϕl ) of Robust method in the frequency domain at this moment is defined as: L−1  Jρ (n0 , τl , fdl , ϕl ) = ρ Y (n0 , k) − Sτl ,fdl (n0 , k)ejϕl

(9)

k=0

Since the amplitude of term Sτl ,fdl (n0 , k)ejϕl is negligible compared with Y (n0 , k), two-dimensional first-order Taylor expansion of the cost function ρ(·) is carried out and the Eq. (9) can be approximately expressed as: Jρ (n0 , τl , fdl , ϕl ) ≈

L−1

ρ(Y (n0 , k)) − A{CρFD (n0 , τl , fdl )e−jϕ }

(10)

k=0

Where, CρFD (n0 , τl , fdl ) =

L−1

k=0

ρz (Y (n0 , k))Sτ∗l ,fdl (n0 , k)) is the CAF function in the fre-

quency domain at that moment. The cost function JρTFD (τl , fdl , ϕl ) of the robust method in the TF domain can be expressed as the sum of the cost functions of all time slices, JρTFD (τl , fdl , ϕl ) =

N −1

JρFD (n, τl , fdl , ϕl )

(11)

n=0

The CAF function CρTFD (τl , fdl ) in the TF domain is expressed as, CρTFD (τl , fdl )

=

N −1 L−1

ρz (Y (n0 , k))Sτ∗l ,fdl (n0 , k))

(12)

n=0 k=0

For the robust estimation of the received signal parameters τ0 , fd and ϕ0 , that is:     {τˆ , fˆd } = arg maxτ,fd CρTFD (τl , fdl ), ϕˆ =  CρTFD (τl , fdl )

(13)

As shown in Fig. 1(a), the instantaneous frequency domain distribution of LFM jamming is similar to a pulse, while that of AWGN still obeys Gaussian distribution. Literature [12] assumed that the distribution of undesired signals containing pulses and AWGN was subject to a heavy-tailed distribution. If z ∈ C subject to two-dimensional Laplace distribution, ρz−Lap (z) could be written as follows [12]:  z z = 0 ρz−Lap (z) ≈ sign(z) = z (14) 0 z=0

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ρz−Lap (z) is a ZMNL transformation named as complex signum function. By replacing the cost function, MLE is changed to robust estimation, which enhances the performance of the estimator in the presence of outliers. The TFD of the received signal y obtained through STFT is a matrix that is pieced together by Fourier transform results of several time slices in time sequence, denoted as Y = {Y (n, k)} , (n = 0, 1, ..., N − 1 , k = 0, 1, ..., L − 1). The method of robust processing is used for each TFD points, and then the processed frequency domain data are arranged into TF domain matrix in time order to obtain the TFD Yρ after robust processing, i.e., Yρ = {ρz (Y (n, k))}. By TF synthesis, the time-domain data yρJTFA (n) of robust processing based on the JTFA can be obtained. The robust Estimation diagram is shown in Fig. 2.

Fig. 2. Diagram of robust method

5 The Simulation Results In this chapter, the first part compares the performance of three kinds of interference suppression methods when they deal with different interference power, sweep frequency rate and mixed signal number. Secondly, the Loss of Efficiency (LoE) of robust interference mitigation method without jamming is tested. In the simulation experiment, satellite signals are set through simulation parameters as shown in Table 1. Table 1. Settings of simulator GPS Bandwidth of front end

2 MHz

Sampling frequency

5.714 MHz

20 MHz

Sampling frequency

60 MHz

BDS Bandwidth of front end

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5.1 Performance Under LFM Interference During the acquisition of the GNSS receiver, once the satellite is captured, a correlation peak is found in the search space. The influence of jamming on the acquisition  stage can be evaluated by the correlation peak-to-noise base ratio αmean = 20 log10 xp /Ei [13], xp is the correlation peak at the acquisition stage and Ei is the average of i off-peak correlation points in the acquisition search space. The αmean of the output results is taken as the correlation quality. The quality curves are shown in Fig. 3. The performance of the robust method is better than that of the TF blanking in the harsh environment. The ANF method has good real-time processing performance, but there is a gap of effectiveness compared with the robust method, and it is difficult to compare the performance due to the difference in its principle. Therefore, only the robust method and the TF blanking method will be compared in the following experiments.

Fig. 3. A cross-correlation function comparison of the two methods

In order to test the influence of LFM sweep rate on the performance of 2 methods. LFM jamming set in with different sweep rates (from 1 to 10 kHz, step 250 kHz) was added to GPS data. Signals respectively processed with the TF blanking and robust method, the number of captured satellites and the robust method’s CNR data of the satellite which is closest to the zenith direction is shown in Fig. 4.

Fig. 4. Different sweep rate experiment

The output CNR deteriorate as the sweep rate increase and the limit frequency of the TF blanking method is 2.25 kHz and that of the robust method is 8.75 kHz. To test the influence of the number of LFM interference on the performance of the method. GNSS data as set in Table 1 is still selected, and the number of LFM interference

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Fig. 5. Comparison of the two methods’ performance under three LFM interference

is constantly changed (LFM parameters are the same as Table 1). In the case of only different starting frequencies, the number of sweep signals is continuously increased to test the performance of the robust jamming mitigation method. The relationship between the number of interference and time is shown in Fig. 5(a). When multiple LFM interference is added, the data processed by the TF blanking method immediately loses the lock, so it is meaningless to add its curve to Fig. 5. Figure 5(b) describes the output CNR of the tracking loop after noise mitigation by the robust method with the increasing number of interferences. It can be seen that the robust method can effectively mitigate the complex signals formed by multiple LFM interference despite the declining of the output CN0 . 5.2 Performance Without Interference In the jamming-free environment, the signal CNR increases from 31 dB to 40 dB. This data is sent to the receiver without processing and after robust method, respectively. It can be seen from the figure that, the signal processed by the robust method has a certain output noise ratio loss compared with the signal without processing. The Monte Carlo experiment verified that the difference of the output CNR (LoE) between nonprocessing and robust method was 0.325 dB when the experiment was repeated for 200 times (Fig. 6).

Fig. 6. Simulation results without interference

6 Conclusion and Analysis When single LFM interfere, the TF blanking method will lose all the amplitude and phase information outlier’s point, while the robust method based on JTFA retains the phase

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information and controls the amplitude value. In this way, part of the information in the original GNSS signal is preserved. When the interference power increases and the sweep rate remains constant, the blanking range of the hard threshold method becomes larger due to the constant threshold, thus leading to a larger GNSS signal loss rate. Therefore, in the case of single high-power LFM interference, the performance of robust processing method is better. When the sweep rate increase and the power is constant, the TFD of LFM signal will become wider in the TF domain plane due to the constant sampling rate of the receiver. The wider the spectral line is, the more information will be lost when the TF blanking method is applied, lead to the rise of GNSS signal’s loss when blanking, and robust method due to keep the phase information is less affected by this. This is also the reason for the experimental situation under multi-LFM interference. In the jamming-free case, the robust method based on JTFA has a LoE of about 0.325 dB. This indicates that there will be a certain amplitude of information loss under the condition of no outliers. From the points above, it can be seen that although there is about 0.325 dB LoE in the absence of interference case, this method has significant advantages in harsh environments. It can be applied to the frontend signal processing of GNSS software receiver as a way of mitigating LFM interference. Acknowledgments. This study was supported by the Natural Science Foundation of Tianjin (19JCQNJC01000).

References 1. Wu, R.: Adaptive Interference Mitigation in GNSS. Science Press, Beijing (2015) 2. Amin, M.G., Borio, D., Zhang, Y.D., et al.: Time-frequency analysis for GNSSs: from interference mitigation to system monitoring. IEEE Signal Process. Mag. 34(5), 85–95 (2017) 3. Borio, D., Camoriano, L., Savasta, S., Lo Presti, L.: Time-frequency excision for GNSS applications. IEEE Syst. J. 2(1), 27–37 (2008) 4. Savasta, S., Presti, L., Rao, M.: Interference mitigation in GNSS receivers by a time-frequency approach. IEEE Trans. Aerosp. Electron. Syst. 49(1), 415–438 (2013) 5. Fadaei, N., Jafarnia-Jahromi, A., Broumandan, A., Lachapelle, G.: Detection, characterization and mitigation of GNSS jammers using windowed-HHT. In: Proceedings of the International Technical Meeting of the Satellite Division Institute of Navigation, Tampa, FL, September 2015, pp. 1625–1633 (2015) 6. Huber, P.J., Ronchetti, E.M.: Robust Statistics. Wiley probability and Statistics, 2nd edn. Wiley, Hoboken (2009) 7. Gang, X.: GPS Principle and Receiver Design. Electronics Industry Press, Beijing (2009) 8. Blankenship, T.K., Kriztman, D., Rappaport, T.S.: Measurements and simulation of radio frequency impulsive noise in hospitals and clinics. In: Proceedings of the 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion, Phoenix, AZ, USA, 4–7 May 1997, vol. 3, pp. 1942–1946 (1997) 9. Middleton, D.: Non-Gaussian noise models in signal processing for telecommunications: new methods an results for class A and class B noise models. IEEE Trans. Inf. Theory 45, 1129–1149 (1999)

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10. Medina, D., Li, H., Vilà-Valls, J., Closas, P.: Robust statistics for GNSS positioning under harsh conditions: a useful tool? Sensors 19(24), 5402 (2019) 11. Zoubir, A.M., Koivunen, V., Chakhchoukh, Y., Muma, M.: Robust estimation in signal processing: a tutorial-style treatment of fundamental concepts. IEEE Signal Process. Mag. 29, 61–80 (2012) 12. Borio, D., Pau, C.: Complex signum non-linearity for robust GNSS interference mitigation. IET Radar Sonar Navig. 12(8), 900–909 (2018) 13. Qin, W., Dovis, F., Gamba, M.T., Falletti, E.: A comparison of optimized mitigation techniques for swept-frequency jammers. In: Proceedings of the 2019 International Technical Meeting of the Institute of Navigation, Reston, Virginia, January 2019, pp. 233–247 (2019)

A Code Phase Pull-In Method Based on the Zero-Crossing Point of the S-Curve Under the Strong Multipath Environment Pengcheng Ma, Xiaomei Tang(B) , Zhe Liu, Chunjiang Ma, and Gang Ou College of Electronic Science and Technology, National University of Defense Technology, Changsha, People’s Republic of China

Abstract. The pull-in or traction module in the Global Navigation Satellite System (GNSS) receiver is an important bridge between the acquisition and tracking process, which can compress the code phase and carrier frequency estimation error introduced by the coarse acquisition stage. The method commonly used in the pull-in process of code phase fine-estimation is the interpolation based on multi-correlators, which has a better ability when the power of the multipath signal is lower than that of the direct signal. However, when there are strong multipath signals with higher power than direct signals or spoofing with small delay about one chip, both of them will cause large distortion of correlation peak. As a result, the code phase interpolation method directly leads to a large code phase estimation deviation. In this paper, a traction method based on the first zero crossing of the phase discrimination function is proposed. The S-curve is fitted by the code phase discrimination function based on the code correlation reference waveform (CCRW). Then the code phase value of the first zero crossing of the fitted S-curve is taken as the estimation result. The simulation results show that the code phase traction method proposed in this paper can work well in different multipath scenarios, and can mitigate the code phase estimation deviation introduced by the traditional interpolation method under strong multipath environments. Keywords: GNSS receiver · Pull-in of the code phase · Discriminator · Code correlation reference waveform

1 Introduction GNSS has played an important role in daily navigation, precision surveying and mapping, electric power, finance, agriculture and fishery, unmanned equipment, and so on. It is providing accurate space-time service information for various human activities. However, as a kind of radio signal, satellite navigation signal is inevitably affected by multipath effect. Moreover, due to the low power of the signals, they are easily affected by all kinds of electromagnetic interference, especially the repeater spoofing which is similar to multipath signals and has always been one of the threats to all kinds of satellite navigation users.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 344–355, 2021. https://doi.org/10.1007/978-981-16-3146-7_32

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In the face of complicated scenes such as multipath or spoofing, abundant researches have been obtained, which are mainly focused on antenna design technology [1], polarization difference [2], tracking loop [3–5] and measurements processing [6, 7]. Less attention has been paid to the traction or pull-in model that can connect the acquisition and tracking stages and compress the uncertainty of acquisition results. The current traction methods can meet the application requirements when the power of multipath signal is lower than that of the direct signal, which is also the main signal scenario and important premise in the field of multipath research. In addition, the current research on the traction model is mainly focused on the precise estimation of carrier frequency [8–10], and less attention has been paid to the precise estimation of pseudo code phase. This is mainly because the code phase uncertainty of the acquisition result under the assumption of multipath scenario mentioned earlier can usually meet the requirements of the traction range of the code tracking loop. However, in the special multipath environment where the direct signal is attenuated and the reflected signal is strong, or when there is repeater spoofing interference, the assumption that the power of the multipath signal mentioned above is less than the direct signal cannot always be maintained. In the face of more challenging signal scenarios such as strong multipath environment, the current research results are mainly focused on signal quality monitoring [11] or integrity monitoring [12], including multipath detection [13] or spoofing detection [14]. However, there are relatively few studies on how to overcome the challenging signal conditions such as the multipath signal power is larger than the direct signal, and still output the measurements that meet the users’ requirements. This paper starts with the traction or pull-in model, aiming at the strong multipath environment, that is, when the power of the reflected or retransmitted signal is higher than that of the direct signal, a code loop traction method based on the zero-crossing point of the code phase discrimination function is proposed, and the code phase estimation deviation introduced by the traditional interpolation method is avoided. The structure of this paper is as follows. The second part introduces the signal scene and the corresponding signal model, which leads to the mathematical problem to be solved in this paper; the third part introduces the principle of the traction method based on the first zero-crossing point of the S-curve generated by the code correlation reference waveform, and then carries on the simulation analysis to its performance. Finally, the conclusion of this paper is given.

2 Signal Model In order to unify the expression, the scene in which the power of the multipath signal is greater than the direct signal is referred to as the strong multipath signal scenario. This section mainly introduces the strong multipath signal model and its influence on code phase estimation.

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2.1 Signal Model in Strong Multipath Environment The received signal model at the receiving antenna in the strong multipath environment is shown as follows. x(t) =

N 

Ai c(t − τi )D(t − τi ) cos(2π (f0 + fi )t + θi ) + n(t)

(1.1)

i=0

Among them, i = 0 represents the direct signal. i ≥ 1 represents the multipath signal. N represents the total number of signal paths, Ai is the amplitude of the received signal from different directions, c(t) represents the pseudo code sequence, and the width of the chip is Tc . τi indicates the signal delay of different paths, D(t) represents the navigation message, f0 represents the carrier reference frequency, fi is the Doppler frequency of different path signals, θi indicates the initial phase of the carrier, and n(t) is the thermal noise of the receiver. In this paper, in order to facilitate the analysis, the model constraints for strong multipath signals are as follows: the number of multipath is 1, the ratio of multipath power to direct signal power is [−3 dB, 10 dB], and the multipath signal delay is more than one chip, that is τi − τ0 ≥ Tc . After receiving the signal, the correlation values are obtained by the processing of the GNSS receiver. Assuming that the message symbol remains the same during the coherent integration time, the correlation values are shown as follows [15]. I (k) =

1 

Q(k) =

Ai R(εi ) sin c(fei Tcoh ) cos[ϕi (k)] + nI (k)

i=0 1 

(1.2) Ai R(εi ) sin c(fei Tcoh ) sin[ϕi (k)] + nQ (k)

i=0

where ϕi (k) represents the phase error between the received signal and the local reference signal. The frequency difference between the local reference frequency source and the signal is written as fei , and the code phase difference between the different path signal and the local code is εi . The coherent integration time is Tcoh . The correlation value of the noise channel correlation is shown as follows. nI (k) = nQ (k)=

1

(k+1)T  coh

n(t)c(t)dt

Tcoh

(1.3)

kTcoh

R(τ ) is the autocorrelation function of pseudo code, which can be expressed as     Tτc |τ | ≤ Tc R(τ ) = (1.4) 0 else

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2.2 Traction Deviation Introduced by Strong Multipath Assuming that the code phase of the acquisition output is τacq , the traditional code phase interpolation estimation method based on multi-correlator takes the acquisition initial phase τacq as the center, and takes d τacq as the step length, and the step range is ±1 code chip, and obtains the correlation value sequences:           R τacq − Tc , · · · , R τacq − d τacq , R τacq , R τacq + d τacq , · · · , R τacq + Tc (1.5) Then the index τpeak with maximum value in the envelope of these correlation values is searched as the center point of the interpolation. Finally, the code phase is estimated according to the correlation values on the left and right sides of the center point, and the captured code phase is modified according to the estimated results:     R τpeak + d τacq − R τpeak − d τacq     (1.6) τacq = τpeak +  R τpeak + d τacq + R τpeak − d τacq When the power ratio of the multipath signal to the direct signal is −3 dB, the delay of the multipath is one chip and the Doppler frequency difference between the multipath and direct signal is 0 Hz, the correlation peaks after superposition when the carrier phase of the multipath is in-phase or inverse-phase with the direct signal are shown in Fig. 1(a).

(a) MDR: -3dB

(b) MDR:3dB

Fig. 1. Correlation peak under multipath environment with different MDR

As can be seen from Fig. 1(a), when the power of the multipath signal is lower than that of the direct signal, the code phase of the direct signal can be represented at the maximum envelope of the correlation values. Therefore, the traditional code phase interpolation estimation method can output the correct code phase result. However, when the power of the multipath signal is higher than that of the direct signal, the shape of the correlation peak will be distorted greatly. When the power of the strong multipath signal is higher than that of the direct signal 3 dB, the correlation peak after superposition is shown in Fig. 1(b). As can be seen from Fig. 1(b), due to the existence of strong multipath, the code phase of the direct signal cannot be represented at the maximum of the correlation peak,

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so the code phase deviation will be introduced, which will lead to the receiver unable to track the direct signal normally and output the wrong measurement results.

3 Code Phase Pull-In Method Based on Zero-Crossing Point of Code Discrimination Function As can be seen from the previous analysis, when the power of the multipath signal is stronger than that of the direct signal, the traditional pull-in method is easy to output the wrong traction results. Therefore, when faced with challenging signal scenarios such as strong multipath or repeater spoofing with small delay, the pull-in strategy needs to be updated. Based on the accepted assumption that the multipath signal always lags behind the direct signal, a code phase pull-in method based on the zero-crossing point of the code discrimination function is proposed here. By searching and estimating the code phase value at the first zero crossing point of the code discrimination function, the code phase can be estimated properly under strong multipath environment. 3.1 Code Phase Discrimination Function The code phase discrimination function is an important module in the receiver. It outputs the code phase error between the signal generated locally and the received signal according to the correlation values. In addition to the commonly used early mines late correlation methods [15], the discrimination functions are also based on code correlation reference waveform [4, 5] and so on. The early mines late method is inevitable to introduce code phase estimation deviation under the strong multipath scenes. In order to solve the deformation caused by strong multipath, the code phase discrimination method based on code correlation reference waveform is adopted in this paper. There are many types of code correlation reference waveforms, among which W1, W2, W3 and W4 are commonly used [4, 5]. 3.2 Algorithm Model The block diagram of the code phase pull-in method proposed here is shown in Fig. 2. The expression of code discrimination function based on CCRW is as follows. d (ε) = IW (ε) × sign(I (ε)) + QW (ε) × sign(Q(ε))

(1.7)

where sign represents the symbol function. IW (ε) and QW (ε) represent the coherent integration result of the CCRW and they are shown as follows. IW (ε) =

Tcoh 1

sI (t − τi )w(t − τi + ε)dt

i=0

QW (ε) =

0 Tcoh 1 0

i=0

(1.8) sQ (t − τi )w(t − τi + ε)dt

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Fig. 2. Algorithm block diagram of code phase pull-in method based on the zero-crossing point of the discrimination function

where w(t) represents the result of XOR between the CCRW and the local code. The data fitting method is used in this paper. Data fitting is a classical mathematical problem, and different methods have different performance. This paper does not take it as the research focus. The third-order polynomial fitting method is selected based on the tradeoff between the ease of use, inherent shape and fitting performance of S-curve. When the code phase estimation deviation of the acquisition module for the direct signal is −0.2 chip and 0.2 chip respectively, the effect of the fitting method proposed in this paper is shown in Fig. 3.

Fig. 3. Data fitting of the code phase discrimination function

As can be seen from Fig. 3, the code phase results of the direct signal are all at the zero-crossing point where the slope of the fitted curve is positive. It is difficult to

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evaluate the performance of the algorithm mainly through formula derivation, and the performance is mainly carried out by simulations.

4 Performance Evaluation by Simulation In order to evaluate the performance of the proposed method under different scene parameters, this paper focuses on the impact of key parameters such as CCRW type, the power and delay of the strong multipath signal and accumulation time on the performance of the algorithm. The simulation parameters are set as follows. The signal used in the simulation is GPS L1CA with the PRN1, and the sampling rate is 10 MHz. The carrierto-noise ratio of the direct signal is 45 dBHz. The searching step is 1/32 chip and the searching range is ±0.25 chips. The Monte Carlo times is 1000. 4.1 Types of CCRW When there is no multipath signal, the code phase estimation accuracy of this algorithm is shown in Fig. 4.

Fig. 4. Code phase estimation accuracy without multipath

The signal length used in Fig. 4 is 2 ms. It can be seen from Fig. 4 that the code phase estimation accuracy decreases than the traditional interpolation method when there is no strong multipath, and there is little difference between the estimation accuracy of the four types of CCRW. When there is a strong multipath signal, assuming that the power of the multipath signal is higher than that of the direct signal 10 dB, the time delay is 1 chip, the estimated code phase deviation is shown in Fig. 5. It can be seen from Fig. 5 that there is a large deviation in the code phase estimated by the traditional traction method when there is a strong multipath signal. In the method proposed in this paper, the estimation deviation of W2, W3 and W4 waveform is about zero, while the W1 waveform has a certain estimation deviation when there is strong multipath, so the W2, W3 or W4 waveform can be selected as the local reference waveform. The standard deviation of their code phase estimation is shown in Fig. 6.

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Fig. 5. Code phase estimation deviation with strong multipath

Fig. 6. Code phase estimation accuracy with strong multipath

As can be seen from Fig. 6, the estimation accuracy is higher when the estimated delay error of the direct signals is about zero, which is due to the lack of data at two sides when the code phase error is large. Moreover, considering the in-phase and inverse-phase cases of multipath signal, the performance of reference waveform W3 is the best. 4.2 The Power of Multipath When the delay of the multipath signal is 1 chip, the influence of the multipath signal power on the code phase measurement deviation is shown in Fig. 7. As can be seen from Fig. 7, with the increase of the power of the multipath signal, the deviation of the traditional method increases gradually until it is estimated to the code phase of the multipath signal, while the method proposed in this paper does not produce the code phase estimation deviation with the change of the power of the multipath signal. When the code phase measurement is unbiased, the accuracy of the method proposed under the influence of different power of multipath signal is shown in Fig. 8. As can be seen from Fig. 8, with the increase of multipath signal power, the estimation accuracy of reference waveform W2, W3 and W4 is all near 0.05 chip, which meets the

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Fig. 7. Effect of different multipath signal power on code phase estimation deviation

Fig. 8. Effect of different multipath signal power on code phase estimation accuracy

traction requirement of code tracking loop. Moreover, the estimation accuracy of the W3 is the highest compared with the other two. 4.3 The Delay of Multipath When the power of the multipath signal is higher than that of the direct signal 10 dB, the effect of the multipath signal delay on the code phase measurement deviation is shown in Fig. 9. It can be seen from Fig. 9 that the multipath with the delay less than 1.8 chip will cause code phase deviation for the traditional method, and when the multipath delay is large, it has little effect on the traditional interpolation method, but the method proposed in this paper is not affected by the multipath delay with W2, W3 and W4. The effect of multipath signal delay on the code phase accuracy is shown in Fig. 10. As can be seen from Fig. 10, with the increase of multipath signal delay, the estimation accuracy of W2, W3 and W4 are all less than 0.1 chip, which meets the requirements of the code discrimination range.

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Fig. 9. Effect of different multipath signal delay on code phase estimation deviation

Fig. 10. Effect of different multipath signal delay on code phase estimation accuracy

4.4 The Signal Accumulation Length When the power of the multipath signal is higher than that of the direct signal 10 dB and the delay is 1 chip, the code phase deviations are shown in Fig. 18 with the increase of the estimated signal time. As can be seen from Fig. 11, the signal length used does not affect the measurement deviation in different algorithms. The effect of signal accumulation length on the accuracy is shown in Fig. 12. As can be seen from Fig. 12, with the increase of the signal accumulation length, the accuracy of code phase estimation is gradually improved. Therefore, the performance of this algorithm can be improved by improving the signal integration time.

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Fig. 11. Effect of different signal length on code phase estimation deviation

Fig. 12. Effect of different signal length on code phase estimation accuracy

5 Conclusion When there is strong multipath or small delay spoofing signal, the traditional pull-in method introduces code phase estimation deviation, and the loop cannot track the direct signal correctly. In this paper, a pull-in method based on the zero-crossing point of the CCRW discrimination function is proposed, and the code phase acquisition result is modified according to the code phase estimation result of the first zero-crossing point of the CCRW discrimination function. It avoids the code phase deviation introduced by the traditional traction method. In this paper, the effects of key parameters such as the type of CCRW, the power and delay of strong multipath signal and the signal accumulation time on the performance of the algorithm are simulated and analyzed. The following conclusions can be drawn: in different strong multipath signal scenarios, the W2, W3 and W4 reference waveforms have little difference in tracking accuracy and tracking deviation, but in a comprehensive comparison, the W3 reference waveform has better performance. The signal estimation length has a direct impact on the performance of the algorithm, and the longer signal estimation time can obtain higher code phase estimation accuracy. In the next step, the

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influence of fitting methods, signal dynamics and other factors on the performance of the algorithm need to be studied.

References 1. Du, L.: Research on the high-precision antenna and its multipath mitigation techniques in satellite navigation systems. Changsha, National University of Defense Technology (2017) 2. Zhang, K., Li, B., Zhu, X., Chen, H., Sun, G.: Multipath detection based on single orthogonal dual linear polarized GNSS antenna. GPS Solut. 21(3), 1203–1211 (2017). https://doi.org/ 10.1007/s10291-017-0603-z 3. Li, T.: Unambiguous synchronization method of BOC signals based on reference waveform design. Wuhan, Huazhong University of Science and Technology (2019) 4. Liu, Z.: Multipath mitigation based on strobe pulse design for modern global navigation satellite systems. National University of Defense Technology, Changsha (2015) 5. Ma, C.: High-precision error model and mitigation technique for GNSS receiver in multipath environment. National University of Defense Technology, Changsha (2020) 6. Teunissen, P.J.G., Montenbruck, O. (eds.): Handbook of Global Navigation Satellite Systems. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-42928-1 7. Xu, H., Angrisano, A., Gaglione, S., Hsu, L.-T.: Machine learning based LOS/NLOS classifier and robust estimator for GNSS shadow matching. Satell. Navig. 1(1), 1–12 (2020). https:// doi.org/10.1186/s43020-020-00016-w 8. Shen, J., Cui, X., Mingquan, L.: Initial frequency refining algorithm for pull-in process with an auxiliary DLL in pseudolite receiver. Electron. Lett. 52(14), 1257–1259 (2016). https:// doi.org/10.1049/el.2016.1504 9. Wang, K., Jiang, R., Li, Y., Zhang, N.: A new algorithm for fine acquisition of GPS carrier frequency. GPS Solut. 18(4), 581–592 (2013). https://doi.org/10.1007/s10291-013-0356-2 10. Tamazin, M., Noureldin, A., Korenberg, M.J., Massoud, A.: Robust fine acquisition algorithm for GPS receiver with limited resources. GPS Solut. 20(1), 77–88 (2015). https://doi.org/10. 1007/s10291-015-0463-3 11. He, C.: Research on evaluation methods of GNSS signal quality and the influence of GNSS signal on ranging performance. National Time Service Center, Chinese Academy of Sciences, Xi’an (2013) 12. Ren, Y.: The research on GNSS integrity monitoring under multi-scenarios. National Time Service Center, Chinese Academy of Sciences, Xi’an (2015) 13. Ali, P.: Receiver-level signal and measurement quality monitoring for reliable GNSS-based navigation. University of Calgary, Calgary (2019) 14. Psiaki, M.L., Humphreys, T.E.: GNSS spoofing and detection. Proc. IEEE 104(6), 1258–1270 (2016). https://doi.org/10.1007/10.1109/jproc.2016.2526658 15. Holmes, J.K.: Spread Spectrum Systems for GNSS and Wireless Communications. Publishing House of Electronic Industry, Beijing (2013)

Anti-jamming Performance Evaluation Method of GNSS Receiver Based on Path Selection Binbin Ren(B) , Shaojie Ni, Feiqiang Chen, Zukun Lu, and Jian Wu College of Electronic Science and Engineering Changsha, National University of Defense Technology, Changsha 410000, China

Abstract. At present, the electromagnetic environment of navigation signals is complex, the anti-jamming performance of GNSS receiver needs to meet higher requirements. At present, there is no systematic method to measure the antijamming performance of the receiver, and the dynamic performance is not taken into account. This paper mainly studies the measurement method of anti-jamming performance of GNSS receiver, and analyzes that the anti-jamming performance of GNSS receiver fluctuates with the change of the arrival angle of jamming signal. In view of this, a method of moving vehicle is proposed, that is, the receiver is placed on the vehicle and moves on the closed path with interference source, so that the azimuth angle and elevation angle of the interference signal entering the receiver are wide. In order to quantitatively measure the DOA range of the receiver on different closed paths, the directional coverage index is proposed in this paper. Finally, the three paths of the example are simulated and verified. Keywords: GNSS receiver · Anti-jamming performance · DOA · Mobile vehicle · Directional coverage

1 Introduction The growing dependency on the GNSS has raised concerns about its vulnerability to radio frequency interference (RFI) [1]. In navigation system, signals emitted by the satellites are very weak when it reaches the ground, usually 30 dB lower than the thermal noise, and thus can be easily jammed by unintentional interference or antagonistic jamming [2]. Interference could cause errors in navigation, positioning and timing. Therefore, it is very necessary to take measures to mitigate the interference. In satellite navigation, there are various ways to resist interference, jamming is usually suppressed in the time, frequency, and spatial domain, or in a domain of joint variables (e. g. time-frequency or spatial-time) [3, 4]. The interference mitigation methods in spatial domain are mainly realized by the adaptive nulling antenna. This is considered to be one of the most effective tools for interference mitigation [5]. The specific implementation algorithm of the adaptive nulling antenna usually uses the Power Inversion algorithm (PI) [6]. PI algorithm is attractive for suppression of interference. The principle of PI algorithm is to minimize the array output power [7].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 356–365, 2021. https://doi.org/10.1007/978-981-16-3146-7_33

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We found that as the incident angle changes, the anti-jamming performance of the receiver will change accordingly. In order to measure the interference mitigation performance of the receiver more objectively, the commonly used method is to fix the receiver on the turntable and rotate it in a microwave anechoic chamber, so that the receiver can receive the same interference signal at different incident angles and obtain the measurement results [8]. However, this method has obvious shortcomings of having no dynamic changes, and the results obtained are not true, which is not conducive to test the anti-jamming performance of the receiver. Based on this, a solution is proposed that mounts the receiver on a vehicle and move it along a fixed path in the test area with electromagnetic protection. The result obtained in this way is more realistic and dynamic. This allows the incident angle and azimuth angle of the same interference signal received by the receiver to be distributed as widely as possible to improve the reliability of receiver anti-jamming test results, and three paths were simulated to obtain the changes in azimuth and elevation angles. The ensuing question is how to measure the pros and cons of a given path. For this problem, this paper draws on the concept of joint entropy and designs the index of direction entropy, and combination number. By weighting these two indicators, the final indicator which is defined as directional coverage is obtained, thus realizing the measurement of any given path. The rest of this paper proceeds as follows. Section 2 introduces the PI algorithm, and simulates its anti-jamming performance changes with the change of the interference arrival angle. Section 3 proposes the mobile receiver scheme, and Sect. 4 gives the measurement indicators. Finally, Sect. 5 concludes this paper.

2 Power-Inversion (PI) Algorithm The basic principle of the power inversion algorithm is as follows. The output of a certain array element is used as a reference signal to ensure that the weighting coefficient of the output power of this signal is constant, and the array values of other channels are adjusted to minimize the power of the array output signal. The output signal after spatial filtering becomes: Y = WH · X

(1)

where xk (n) is the signal received by the k-th element, the array input signal is X = [x1 (n), x2 (n), . . . , xN (n)]T , the array weighting vector is W = [w1 , w2 , . . . , wN ]T , the superscript H represents the conjugate transpose of the matrix. At this time, a constraint is introduced that W T S = 1, where S = [1, 0, ...0]T , and S is a N × 1 column vector which means that the first column of signals is allowed to pass completely, this can avoid meaningless solutions [9]. The power of the output signal is:     H  2 H H = WRX W H p = E |Y | = E W X W X (2)

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The optimal weight vector is: W opt =

R−1 X S

ST R−1 X S

= αR−1 X S

(3)

Considering a 4-element area array, the array elements are arranged as shown in the Fig. 1: y

0.5m 60° 0.5m

X

0.5m

Fig. 1. Array element distribution

We set the azimuth and elevation angle of the useful signal to (100°, 30°), and the power is −135 dBm. The DOA of three interference sources are (0°, 30°), (20°, 50°), (40°, 70°), and the three signal powers are all set to −60 dBm. The noise power is − 100 dBm. Using the above antenna array, the PI criterion is used to weight the array. Through simulation, we observe the directional pattern under the PI criterion, analyse the performance, and the following results are obtained in Fig. 2 [10].

Fig. 2. The radiation pattern of PI algorithm

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The pitch angle is chosen as 30° to slice the three-dimensional image, and the results are depicted in Fig. 3

Fig. 3. Sectional view of the beam pattern when the pitch angle is 30°

The azimuth angle is chosen as 120° to slice the three-dimensional image, and the results are shown in Fig. 4:

Fig. 4. Sectional view of the beam pattern when the azimuth angle is 120°

The results show that the PI algorithm has formed a null in the direction of interference with strong power, thereby achieving a suppression effect. It can be seen that the PI algorithm has strong ability of restraining jamming. Afterwards, by fixing the relative positions of three interferences (that is, the azimuth angle is always 20° apart, and the pitch angle remains unchanged), the azimuth angle of jammer 1 was traversed from 0 to 360°. By measuring the jamming to noise ratio (JNR), we observed the changes in the interference mitigation performance, and obtained the following results (see Fig. 5).

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Fig. 5. The anti-interference performance varies with the incident angle

3 Mobile Receiver Solution According to the analysis in the previous section, the difference in the incident direction of the interference will cause the difference in the anti-jamming performance of the receiver. In order to test the receiver performance more objectively, this article proposes a scheme that placing the receiver on a carrier, and setting the carrier to move at a constant speed according to a fixed path in the test area with electromagnetic protection. Firstly, three paths of circle, ellipse, and square are considered, and the main lobe width of the interference source antenna is constrained, The experimental scene is set as follows. The entire experimental site is in the electromagnetic protection net, the center area is the preset path to be taken by the vehicle, and up to four interference sources are set around in Fig. 6.

Fig. 6. Simulated scene

The preset paths are circle, ellipse, and rectangle. The total length of the control path is the same, both are 80 m, and the geometric center is at the origin. The vehicle travels counterclockwise at a constant speed along the route. As shown below (Fig. 7):

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Fig. 7. Path selection. (a) circle path (b) ellipes path (c) rectangle path

In addition, we set the main lobe width of the interference source antenna to 2α, and the interference source may cover the position on the path partially or all of it. The schematic diagram is as follows (Fig. 8):

2

Antenna beam

Path

Fig. 8. Schematic diagram of interference signal coverage on the path

The specific coverage derivation results are listed in Table 1, where A refers to the azimuth angle. Table 1. Coverage derivation The quadrant of the interference source

Lower limit of azimuth

Higher limit of azimuth

I

A−α A < α : 0/360 + A − α

A+α A < α : A + α/360

II

180 − A − α

180 − A + α

III

180 + A − α

180 + A + α

IV

360 − A − α A < α : 0/360 − A − α

360 − A + α A < α : α − A/360

Perform simulation calculations. Set simulation parameters: the path is set as above, the main lobe width of the interference source antenna is set to 2α = 25◦ , the wavelength is 0.19 m, and the receiver antenna array is the same as the previous section.

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Following which is the simulation of four interference sources, and the positions of the four jammer are listed respectively: (25, 25, 13) m, (−10, 50, 52) m, (−20, −60, 60) m, (30, −50, 16) m. We get the following result in Fig. 9 and Fig. 10.

Fig. 9. Azimuth distribution under four interference signals

Fig. 10. Pitch distribution under four interference signals

In this way, when multiple interference arrived, the jamming interference incidence angle received by the receiver has a wider distribution. Contrast with this method, the method of testing the turntable in a microwave anechoic chamber does not consider the real motion scene of the carrier, and cannot obtain the dynamic characteristics of the anti-jamming receiver. The test results of the method proposed in this article are more realistic, this method raises the confidence level of the final forecasted results and makes result more reasonable and objective. It is of great significance to the interference mitigation test in engineering.

4 Directional Coverage In order to quantitatively describe the distribution, this article proposes the index of “directional coverage”, which can be used to measure the distribution span of the incident

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angle of the interference signal received by the receiver on different paths, and then quantitatively measure the advantages and disadvantages of different paths. The definition of joint entropy is adopted, and the formula is as follows [11, 12]: H (X , Y ) = H (X ) + H (Y | X )   =− p(x) log p(x) − p(x, y) log p(y | x)

(4)

where H (X ) represents the information entropy of X, Conditional entropy H (Y |X ) represents the uncertainty of random variable Y under the condition of known random variable X.  H (X ) = − p(x) log p(x) (5) H (Y | X ) = −



p(x, y) log p(y | x)

(6)

Among them, the azimuth angle, the elevation angle correspond to X and Y respectively, and the combined information amount of the azimuth angle and the elevation angle above the path can be obtained to judge the quality of the path. In addition, another way is used to measure. The combination of the distributed azimuth and elevation angles corresponds to a small unit of an imaginary ball with an area of 1, and the overall area is all possible combinations of azimuth and elevation angles to find the path Percentage of the total area, and then quantitatively measure the pros and cons of the path. The problem is that the value is too small, so remove the denominator, only solve the number of combinations on the path, divide by a constant, so that the value is proportionally expanded, and the result comparison will not change. The formula is as follows: Y = N /100

(7)

where N is the number of incident angle combinations. In order to solve the problem of the inconsistency of the path measurement results by the above two calculation methods, we have adopted a weighted treatment for the above two indicators. The weighting algorithm selects the analytic hierarchy process (AHP), and finally obtains the comprehensive evaluation index, which is recorded as the direction coverage (Dc). The process is as follows: Construct a judgment matrix [13]   1 4 B= (8) 1/4 1 Find the largest characteristic root: λmax = 2, the weight vector is w = [0.8, 0.2]T , the final direction coverage is Dc = wT × [H , Y ]T

(9)

where H stands for the joint entropy. We measured the directional coverage of the above four interference sources on three different paths, and listed the results in Table 2: It can be concluded from the above table that, in the given three paths, the circular path has the best square coverage and the square path the worst.

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Path

Index Path entropy (H)

Combination block

Directional coverage

Circle

10.245535

59.85

20.166428

Ellipse

9.303806

44.91

16.425045

Rectangle

8.782723

33.78

13.782179

5 Conclusion This article first introduces the PI algorithm commonly used in navigation anti-jamming, and uses this algorithm to traverse all possible DOA of three interferences. Through this, it is found that as the direction of the interference incident changes, the anti-jamming performance of the receiver section fluctuates. In order to test the antijamming performance of GNSS receivers, a solution is proposed that move the receiver on the carrier according to a fixed path, so that the incident angle and azimuth angle of the same jammer received by the receiver have as wide a distribution as possible to examine the anti-jamming performance of the receiver. Finally, an index of directional coverage is proposed. By weighting the two calculation results, an accurate index can be obtained. Any given path can be quantitatively measured, so as to judge the directional coverage of the path, which has great engineering application value in anti-jamming testing.

References 1. Thomas, M., Norton, J, Jones, A., et al.: The royal academy of engineering. In: Global Navigation Space Systems: Reliance and Vulnerabilities (2011) 2. Chen, F., Nie, J., Zhu, X., et al.: Impact of reference element selection on performance of power inversion adaptive arrays. In: 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), Savannah, GA, pp. 638–644 (2016) 3. Wang, X., Amin, M., Ahmad, F., et al.: Interference DOA estimation and suppression for GNSS receivers using fully augmentable arrays. IET Radar Sonar Navig. 11(3), 474–480 (2017) 4. Amin, M., Sun, W.: A novel interference suppression scheme for global navigation satellite systems using antenna array. IEEE J. Sel. Areas Commun. 23(5), 999–1012 (2005) 5. Liu, Y., Zhang, S., Shi, D., et al.: Anti-Jamming space-time processor with digital beamformer for satellite navigation. In: Proceedings of the Seventh Asia-Pacific Conference on Environmental Electromagnetics (CEEM 2015), Hangzhou, China, pp. 50–54 (2015) 6. Capozza, P.T., Holland, B.J., Hopkinson, T.Ml.: A single-chip narrow-band frequency domain excisor for a global positioning system receiver. IEEE J. Solidstate Circ. 35(3), 401–410 (2000) 7. Zhang, L., Liu, W., Langley, R.J.: A class of constrained adaptive beamforming algorithms based on uniform linear arrays. IEEE Trans. Signal Process. 58(7), 3916–3922 (2010) 8. Amin, M., Wang, X., Zhang, Y., et al.: Sparse arrays and sampling for interference mitigation and DOA estimation in GNSS. Proc. IEEE 104(6), 1302–1317 (2016)

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9. Xu, H., Cui, X., Lu, M.: Effects of power inversion spatial only adaptive array on GNSS receiver measurements. Tsinghua Sci. Technol. 23(2), 172–183 (2018) 10. Meng, D.W., Feng, Z.M., Lu, M.Q.: Anti-jamming with adaptive arrays utilizing power inversion algorithm. TsingHua Sci. Technol. 13(6), 796–799 (2008) 11. Du, Y., Wang, J., Rizos, C., El-Mowafy, A.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2(1), 1–22 (2021). https://doi.org/10.1186/s43020-020-00034-8 12. Wu, J., Zhang, M., Xie, X., Shi, G., et al.: Joint entropy degradation based blind image quality assessment. In: 2018 IEEE Fourth International Conference on Multimedia Big Data (BigMM), Xi’an, pp. 1–6 (2018) 13. Yaraghi, N., Tabesh, P., Guan, P., et al.: Comparison of AHP and Monte Carlo AHP under different levels of uncertainty. IEEE Trans. Eng. Manage. 62(1), 122–132 (2015)

Modeling and Evaluation of Pseudorange Deviation of Satellite Navigation Digital Receiver Chunjiang Ma, Xiaomei Tang(B) , Pengcheng Ma, Song Li, and Guangfu Sun College of Electronic Science, National University of Defense Technology, Changsha, Hunan, People’s Republic of China

Abstract. In GNSS, the pseudo-range deviation of the receiver reduces the positioning and timing accuracy of the user, which significantly affects the service performance of the system. In this paper, the pseudo-range deviation introduced by baseband digital signal processing has been studied. This error is related to the satellite and the receiver, and it is difficult to eliminate it even with differential technology. A digital code phase pseudo-range deviation signal model is established, and it is proposed that the deviation can be decomposed into resolution error and zero-bias error. Combining the characteristics of the error, the applicability error evaluation method is proposed, and the theoretical evaluation result is given. The simulation results show that the error model and evaluation method proposed in the article have the applicability of bandwidth limited effect and Doppler effect, which is helpful to guide the parameter design of satellite navigation receiver. Keywords: GNSS · DSSS · Resolution error · Zero-bias error

1 Introduction In the Global Navigation Satellite System (GNSS), Direct Sequence Spread Spectrum (DSSS) signals are widely used. By modulating the pseudo-random sequence and spreading the spectrum bandwidth, the application requirements of weak signal reception are met. At the same time, by estimating the initial code phase of the spread spectrum signal, the unambiguous time delay observation can be obtained, which can provide support for navigation and positioning timing services [1]. In the spread spectrum signal receiver, the code phase discriminator uses the characteristic that the ideal autocorrelation is a trigonometric function and is axisymmetric about the zero phase delay. However, when the signal involved in the correlation operation is distorted, the estimated pseudo-range may be biased. The pseudo-range deviation of the satellite is related to the distortion of the transmitted signal [2]. The multipath pseudo-range deviation is related to the multipath components mixed into the signal transmission [3]. This article mainly studies the pseudo-range deviation introduced by the receiver during digital signal processing, and assumes that the received signal is relatively ideal. The research on the introduction of pseudo-range deviation to the digital code phase discriminator mainly focuses on the discriminator resolution error [4]. As early as 1995, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 366–377, 2021. https://doi.org/10.1007/978-981-16-3146-7_34

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Sami et al. analyzed the performance of the digital code phase tracking loop [4]. In 2006, Akos et al. found that when the sampling frequency is a multiple of the code rate, the digital code correlation curve has serious distortion [5]. In the same year, Quirk et al. first proposed the concept of commensurate sampling and non-commensurate sampling, and pointed out that the code phase resolution can be improved by designing the sampling frequency [6]. If the receiver baseband signal processing clock is not restricted, the noncommensurate sampling method can significantly suppress the pseudo-range resolution error, but it cannot suppress the pseudo-range zero-bias error. In 2017, Jin found that under non-equal sampling conditions, there is still a pseudorange deviation that is significantly larger than the resolution error, and it is defined as a zero-bias error [7]. Jin suppresses the zero offset error from the perspective of error estimation and sampling frequency design. Yang analyzed the zero-bias error model of the digital discriminator and found that the zero-bias error is closely related to the relative interval of the discriminator [8]. On this basis, Ma uses statistical methods to study the zero-bias error, and analyzes the optimal parameter design to suppress the zero-bias error [9]. However, these are still independent studies on resolution errors or zero-bias errors, ignoring the close relationship between the two types of errors. When Ma studied the bias error, it was assumed that non-equal sampling was used, and the impact of resolution error was ignored. Affected by the spread spectrum code, Quirk did not give an accurate definition and theoretical formula when studying the resolution error. This article focuses on the deficiencies of the above-mentioned research. First, the signal model of the digital code phase discriminator is studied, and the resolution error and zero offset error are defined. Then, combined with the characteristics of the error, an error evaluation method is proposed, and the evaluation result of the error theory is deduced. Secondly, a simulation experiment was designed to verify the applicability of the pseudo-range deviation analysis model and evaluation method under the bandwidthlimited effect and the Doppler effect. Finally, the work of this paper is summarized.

2 Signal Models The DSSS signal is the physical carrier for the satellite navigation system to transmit time and space information. By modulating the pseudo-random sequence, the receiving gain can be significantly improved to meet the application of weak satellite navigation signals. In addition, by estimating the phase of the pseudo-random code of the spread spectrum signal, an unambiguous time delay observation result can also be obtained. In the time domain, the direct sequence spread spectrum signal s(t) can be expressed as: +∞ cn p(t − nTc − τ0 ) (1) s(t) = n=−∞

Among them, p(t) represents a rectangular wave signal with a time length of Tc ; cn represents the n-th spreading code sequence; τ0 represents the code phase delay.

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Define the autocorrelation function R(τ ) of spread spectrum signal as: R(τ ) =

1 Tcoh

t=T  coh

s(t)s(t + τ )dt

(2)

t=0

Among them, Tcoh represents the coherent integration time of the correlator. For an ideal random code spread spectrum signal, the theoretical autocorrelation function R0 (t) is a trigonometric function, which can be expressed as:     1 − τ Tc , |τ | ≤ Tc (3) R0 (τ ) = 0, |τ | > Tc In the code phase discriminator, two sets of correlators with early phase and later phase are used. By comparing the correlation values, the time delay difference between the local replicated signal and the received signal is estimated. In the satellite navigation receiver, the discrimination function D(ε) of the early minus late code phase discriminator can be expressed as: D(ε) = k0 [R(ε − d0 ) − R(ε + d0 )], ε ∈ [−d0 , d0 ]

(4)

Among them, k0 represents the normalization coefficient of the discriminator; ε represents the code phase deviation between the local replica signal and the received signal; d0 represents the early and late code phases; D0 (= 2d0 ) is also called the discriminator correlation interval. For a spread spectrum signal modulating an ideal random sequence, the theoretical value of the early minus late code phase discrimination function D0 (ε) is: D0 (ε) =

1 [R0 (ε − d0 ) − R0 (ε + d0 )]=ε, ε ∈ [−d0 , d0 ] 2

(5)

Among them, when the phase delay is within the linear range [−d0 , d0 ], the output of the discriminator is equal to the code phase ε to be estimated.

3 Pseudo-range Bias Introduced by Discretization At present, most satellite navigation receivers use baseband digital signal processing technology. The digitization of the receiver significantly improves the performance of navigation signal processing and also brings new problems. The digital baseband received signal can be expressed as: s(n) = ck (=(fc +fcd )nTs −τ0 ) , n = 1, 2, 3 · · ·

(6)    Among them, n represents the serial number of the discrete signal; fc = 1 Tc represents the code rate; fcd represents the code Doppler frequency. The digital code phase correlation function r(τ ) can be expressed as: r(τ ) =

N −1 1  ck (=(fc +fcd )nTs ) ck (=(fc +fcd )nTs −τ ) N n=0

(7)

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The corresponding digital code phase discrimination function d (ε) can be expressed as: d (ε) =

1 [r(ε − d0 ) − r(ε + d0 )], ε ∈ [−d0 , d0 ] 2

(8)

As shown in Fig. 1, the ideal code phase discrimination curve is a straight line with a slope of 1 and passing through the zero point. However, the actual digital code phase discrimination curve may be a broken line and deviate from the zero point.

Fig. 1. Schematic diagram of code phase discrimination curve (ideal curve and distortion curve)

Define the resolution P(ε) of the digital code phase discriminator as the width of a step on the discriminating curve, namely:



P(ε) = MAX τ |d (τ )=d (ε) − MIN τ |d (τ )=d (ε) (9) Among them, MAX{·} represents the maximum value; MIN{·} represents the minimum value. When the resolution P(ε) of the discrimination curve is large, the phase discrimination function d (ε) jumps with the code phase delay ε, which makes the code tracking loop difficult to converge. In addition, even if the code phase tracking successfully converges, the stepwise variation of the discrimination curve may cause the pseudo-range deviation to be blurred or deviated. In the code phase tracking loop, when the code phase converges from the negative half axis of the phase delay, the pseudo-range resolution error dedown (0) of the digital discriminator can be expressed as:

dedown = MIN τ |d (τ )=0 (10) When the code phase converges from the positive half axis of the phase delay, the up pseudo-range resolution error de (0) of the digital discriminator can be expressed as:

up de = MAX τ |d (τ )=0 (11)

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Under the condition of non-equal sampling [6], if the sampling frequency is large enough, the resolution of the code phase can be small enough. However, since the pseudorandom spreading code sequence is not truly random, the formula (3) is generally not satisfied for satellite navigation signals. When the phase delay is greater than 1 chip, the value of the signal autocorrelation function R(τ ) is not necessarily equal to zero. When the phase delay is −Tc and Tc , the value of the autocorrelation function is not necessarily equal. At this time, the autocorrelation function is asymmetric about the zero phase delay, causing the code phase discrimination curve to deviate from the zero point. At this time, the pseudo-range zero-bias error of the digital discriminator can be defined as:



(12) S = MAX τ |d (τ )=0 or MIN τ |d (τ )=0 In the satellite navigation digital receiver, the resolution error and the zero-bias error take effect at the same time. The resolution error has nothing to do with spread spectrum code modulation. When the resolution error is negligible, the zero-bias error is mainly caused by the pseudo-random characteristics of the spread spectrum code.

4 Error Modeling and Evaluation Method The following is to model and evaluate the resolution error and zero-bias error of the pseudo-range. 4.1 Resolution Error The phase resolution P(ε) of the code phase discriminator is related to the code phase delay ε and the correlation interval of the discriminator. In addition, the calculation of the phase resolution will be affected by the pseudo-random sequence. In order to eliminate this influence, the following analysis is based on the rectangular wave signal. The periodic code sequence C 0 that defines the level polarity continuously inverted is: C 0 = {+1, −1}2

(13)

Among them, {·}2 indicates that the period of the code sequence is 2. For the digital autocorrelation function rC0 (τ ) of the periodic code sequence C 0 , if it is assumed that the number of signal sampling points and the number of spreading  codes  within the coherent integration time Tcoh are integers, and they are Ns = Tcoh Ts and   Nc = fc Tcoh + fcd Tcoh respectively. At this time, the code phase resolution of the autocorrelation curve is constant, which can be expressed as [6]: p0 =

Tcoh LCM(Ns , Nc )

Among them, LCM(·) represents the least common multiple.

(14)

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Define the residual factor of the discriminator correlation interval D0 relative to the phase resolution p0 of the correlation curve as α:    (15) α = D0 p0 − D0 p0 Among them, · means  rounding down; the value range of α is [0, 1). When the ratio D0 p0 of the correlation interval D0 to the phase resolution p0 is an integer,  the residual factor α is the smallest and is equal to zero in value; when the ratio D0 p0 is 0 or infinitely close to 1, the residual factor α is the largest and equal to 1 in value. When the residual factor α is the largest or the smallest, the steps of the digital code phase discrimination curve are uniformly distributed, and the corresponding code phase resolution is constant p0 or 0.5 p0 . When the residual factor A takes other values, the corresponding code phase resolution has two cases, αp0 and (1 − α)p0 , and the corresponding occurrence probabilities are α and 1 − α respectively. In order to eliminate the influence of the code phase delay on the resolution evaluation of the discriminator, the average resolution MEAN(P) is defined as: MEAN(P) = MEAN{P(ε), ε ∈ [0, Ts ]}

(16)

Among them, MEAN{·} represents the average value. According to the above analysis, the average code phase resolution MEAN(P) of the digital discriminator based on the rectangular wave signal is:

 MEAN(P) = 2(α − 0.5)2 + 0.5 p0 (17) Among them, when the residual factor is α = 0, the maximum value of the average resolution error is p0 ; when the residual factor is α = 0.5, the minimum value of the average resolution error of the discriminator is 0.5 p0 . Therefore, in order to improve the code phase resolution of the discriminator, it can be achieved by increasing the resolution p0 of the corresponding correlator and at the same time by designing the residual factor α = 0.5. 4.2 Zero-Bias Error The following analyzes the pseudo-range bias error caused by the pseudo-random spread spectrum code, and ignores the pseudo-range resolution error. The article [9] proposed an equivalent code reference waveform method to analyze the zero-bias error. Modification of the code phase discrimination function d (ε) of formula (8), we can get: d (ε) =

N −1 1  c k (=(fc +fcd )nTs −τ0 )·  2N ck (=(fc +fcd )nTs −ε+d0 ) − ck (=(fc +fcd )nTs −ε−d0 ) n=0

(18)

Define the rectangular wave reference signal w(t) as the early phase signal s(t + d0 ) minus the late phase signal s(t − d0 ), namely: w(t) = 0.5(s(t + d0 ) − s(t − d0 ))

(19)

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Therefore, the early minus late code phase discrimination function can be equivalent to the cross-correlation function d  (ε) of the received signal s(t) and the local code reference signal w(t), which can be expressed as: d  (ε) =

N −1 1  ck (=(fc +fcd )nTs −τ0 ) wk (=(fc +fcd )nTs −τ0 ) 2N

(20)

n=0

Define the non-zero part of the reference signal w(t) as the effective reference waveform. In the code sequence, if the level polarity of the adjacent code sequence is continuously reversed, the effective reference waveform appears continuously, and the period is Ts . At this time, define the average sampling point cs of the effective reference waveform as: cs = 2d0 fs

(21)

When the average number of sampling points cs is close to an odd number, the zero offset error S introduced by the spreading code may increase; conversely, when the average number of sampling points cs is close to an even number, the zero-bias error S will decrease [9]. For the situation where the level polarity of adjacent code sequences is continuously reversed, when the average number of sampling points cs is equal to an even number, the zero-bias error S takes the minimum value of zero; when the average number of sampling points cs is equal to an odd number, the zero-bias error S takes the maximum value for [9]: MAX(S) =

fc (1 + 2d0 )fs

(22)

In order to eliminate the influence of specific spreading code sequences on the evaluation of zero offset error, the set A composed of spreading code sequences is defined as: A = {C 1 , C 2 , C 3 , · · · , C k , · · ·}

(23)

Among them, C k represents the k-th group of code sequences, and the zero-bias error corresponding to this group of code sequences is Sk . Based on the set A, define the average phase bias error MEAN(S) and the phase bias error standard deviation STD(S) as: MEAN(S) = MEAN{S1 , S2 , S3 , · · · , Sk , · · ·}

(24)

STD(S) = STD{S1 , S2 , S3 , · · · , Sk , · · ·}

(25)

When there are enough samples in set A, the theoretical values of average phase bias error MEAN(S) and phase bias error standard deviation STD(S) can be obtained [9]: MEAN(S) = 0

(26)

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STD(S) ==

     Fc Tcoh · cs − 2 · round cs 2  2Fs Tcoh

373

(27)

Therefore, in order to reduce the influence of the spreading code sequence on the pseudo-range measurement and reduce the zero-bias error of the pseudo-range, there are two processing methods: 1) Design the average number of sampling points to make it as close to an even number as possible; 2) The use of long-period spreading code sequences makes the zero-bias errors in different periods independent of each other, and can reduce the impact through smooth filtering.

5 Simulation and Analysis In the previous analysis, the bandwidth limitation effect and Doppler frequency shift effect of the received signal were ignored. The following uses simulation to analyze the impact of these two effects on the error model and evaluation method proposed in this article. 5.1 Applicability to Bandwidth Limited Effects

0.05

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Fig. 2. Digital code phase discrimination curve under different bandwidth conditions

In a bandwidth-limited system, the energy of the high-frequency part of the ideal spread spectrum signal will be lost, resulting in distortion of the discriminator. Compared with the code phase discrimination curve of the infinite bandwidth signal, the discrimination curve of the band-limited signal is relatively smooth. In the digital code phase discriminator, if the local signal is a digital signal with infinite bandwidth, the phase resolution of the discriminating curve is not affected by the receiving bandwidth.

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Figure 2 shows the simulation results of the digital code phase discrimination curve under different bandwidth conditions. The simulation uses the L1 C/A code of the Global Positioning System (GPS), the code length is 1023 chips, the code number is 1, and the code rate is 1.023 MHz. Set the sampling frequency to 20 MHz, the coherent integration time to 1 ms, and the correlation interval to 1 chip. The simulation results show that the bandwidth limitation effect will slightly affect the slope at the zero-crossing point of the discrimination curve, but it will hardly affect the phase resolution. 0.12 B=4M B=6M B=8M

0.1

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STD of zero-bias [m]

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0 10

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Fig. 3. STD of zero-bias under different bandwidth conditions

In order to calculate the statistical value of the bias error, the GPS long-period P code is used as the sample of the pseudo-random spreading code sequence set A to carry out the simulation experiment. Figure 3 shows the simulation results of the zero deviation standard deviation under different bandwidth conditions. Set the spreading code rate to 1.023 MHz, and the corresponding signal bandwidth is 2.046 MHz. Four scenarios with receiving bandwidths of 4 MHz, 6 MHz, 8 MHz, and 10 MHz are selected, and the sampling frequency of 10 MHz to 20 MHz is traversed. The simulation results show that the bandwidth limitation effect will affect the size of the zero-bias error to a certain extent, but it will not change the law of the zero-bias error with the sampling frequency. 5.2 Applicability to the Doppler Effect When the receiving terminal and the transmitting terminal move relative to each other in the radial direction, the received signal will be affected by the Doppler effect. For satellite navigation systems, since the navigation satellites always revolve around the earth, the Doppler effect needs to be considered when receiving navigation signals. First, analyze the influence of the Doppler effect on the pseudo-range bias error. For the code phase discriminator, the code Doppler effect can be simply equivalent to adding the code Doppler frequency to the standard spreading code frequency.

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If thecode Doppler is directly superimposed on the code rate, the standard deviation STD S d of the pseudo-range zero-bias error with Doppler can be expressed as:  

      Fc + Fcd Tcoh · cds − 2 · round cds 2 

 STD S d == (28) 2Fs Tcoh   Among them, cds = 2d0 Fs Fc Fc + Fcd represents the average number of sampling points with Doppler. Then analyze the influence of the code Doppler frequency on the pseudo-range resolution error. In order to eliminate the influence of the pseudo-range bias error, the following simulation experiments are carried out based on the periodic code sequence C0. 0.25

Digital code phase discrimination [m]

0.2 Dop=0 m/s Dop=100 m/s Dop=200 m/s Dop=500 m/s

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.25

-0.2

-0.15

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-0.05 0 0.05 Code phase delay [m]

0.1

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Fig. 4. Digital code phase discrimination curve under different code Doppler frequency conditions

Figure 4 shows the simulation results of the digital code phase discrimination curve under different code Doppler frequency conditions. Set the code rate to 1.023 MHz, the coherent integration time to 1 ms, the sampling frequency to 5 MHz, and the correlation interval to 0.4092 chips. At this time, the phase resolution of the digital code phase correlator is 0.059 m. The simulation selected four cases where the code Doppler is 0 m/s, 100 m/s, 200 m/s and 500 m/s. The results show that when the code Doppler frequency is relatively large, it will have a significant impact on the resolution of the discrimination curve. In order to further analyze the influence of code Doppler on the resolution error, the code Doppler in the range of 0–1000 m/s is simulated below. Set the code Doppler resolution to 1 m/s,  the local code phase calculation range of the average code phase resolution error is −5p0 , 5p0 , and the local code phase resolution is 0.01p0 , where p0 is 0.059 m. Figure 5 shows the simulation results of the average code phase resolution error versus code Doppler frequency. The simulation results show that, in most cases, the average resolution error of the digital code phase changes continuously with Doppler.

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Average code phase resolution error [m]

0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0

100

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400 500 600 Code doppler [m/s]

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Fig. 5. Average code phase resolution error variation curve

However, there are some frequency points, and the average resolution error has a large jump. To analyze the reason, the code phase resolution formula (14) of the autocorrelation curve is not a continuous function for the independent variable Nc .

6 Conclusions This paper studies the pseudo-range deviation introduced by the discretization of the code phase discriminator. Starting from the signal model, the mechanism of the pseudorange deviation of the digital code phase discriminator is studied. According to different causes of error, the pseudo-range deviation is divided into two types: resolution error and zero-bias error, and the corresponding evaluation methods and theoretical results are given. The results of simulation experiments show that the pseudo-range error model and evaluation method of the digital receiver proposed in this paper are applicable even when the bandwidth limitation effect and code Doppler effect of the received signal are considered. Acknowledgments. This work was supported by the National Natural Science Foundation of China under grant No. U20A0193 and 62003354.

References 1. Borre, K., Akos, D.: A Software-Defined GPS and Galileo Receiver: Single-Frequency Approach. Birkhäuser, Boston (2007) 2. He, C.Y., Lu, X.C., Guo, J., et al.: Initial analysis for characterizing and mitigating the pseudorange biases of BeiDou navigation satellite system. Satell. Navig. 1, 3 (2020) 3. Van Dierendonck, A.J., Fenton, P., Ford, T.: Theory and performance of narrow correlator spacing in a GPS receiver. Navigation 39(3), 265–283 (1992)

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4. Mileant, A., Million, S.: The performance of the all-digital data transition tracking loop using nonlinear analysis. IEEE Trans. Commun. 43(2), 1202–1215 (1995) 5. Akos, D.M., Pini, M.: Effect of sampling frequency on GNSS receiver performance. Navigation 53(2), 85–95 (2006) 6. Quirk, K.J., Srinivasan, M.: PN code tracking using noncommensurate sampling. IEEE Trans. Commun. 54, 1845–1856 (2006) 7. Jin, X., Zhang, N., Yang, K., et al.: PN ranging based on noncommensurate sampling: zero-bias mitigation methods. IEEE Trans. Aerosp. Electron. Syst. 53, 926–940 (2017) 8. Yang, J., Yang, T.K., Li, J.S., Li, H.N., Yang, T.S.: Analysis of noncommensurate sampling effects on the performance of PN code tracking loops. Sci. China (Technol. Sci) 61(6), 107– 119 (2018) 9. Ma, C.J., Ni, S.J., Tang, X.M., Xiao, Z.B., Sun, G.F.: Zero-bias elimination with selective noncommensurate sampling for pseudo-noise code tracking. IET Radar Sonar Navig. 14(3), 349–355 (2020) 10. Ma, C.J., Lv, Z.C., Tang, X.M., Xiao, Z.B., Sun, G.F.: Zero-bias mitigation method based on optimal correlation interval for digital code phase discriminator. Electron. Lett. 55(11), 667–668 (2019) 11. Ma, C.J., Tang, X.M., Lv, Z.C., Xiao, Z.B., Sun, G.F.: High-precision pseudo-noise ranging based on BOC signal: zero-bias mitigation methods. Appl. Sci. Basel 9(15), 1–18 (2019)

Research on GNSS Time Series Noise Reduction Combining Principal Component Decomposition and Compound Evaluation Index Xinrui Li1,2 , Shuangcheng Zhang1,2(B) , Zhiqiang Dong1 , Xinyu Dou1 , Yiming Xue1 , Lixia Wang1 , Chuhan Zhong3 , Yunqing Hao4 , Qintao Bai4 , and Pingli Li5 1 School of Geological Engineering and Geomatics, Chang’an University, Xi’an 710054, China 2 State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China 3 Sinopec Petroleum Engineering Corporation, Dong’ying 257026, China 4 Shaanxi Water Conservancy and Electric Power Survey and Design

Institute, Xi’an 710001, China 5 The 20th Research Institute of CETC, Xi’an 710068, China

Abstract. As a tool of adaptive signal decomposition, SSA can decompose GNSS time series into several SSA components, and select meaningful components to reconstruct, so as to reduce noise. In view of the fact that there is no general method to objectively determine the number of reconstruction layers, an adaptive SSA noise reduction method combining principal component decomposition and composite evaluation indicators is proposed: by combining the root mean square error and smoothness of the denoising signal Negatively correlated indicators are normalized, and then the coefficient of variation is used to determine the weight, and the two indicators are linearly combined to obtain the composite evaluation indicator T; then based on the principle component decomposition idea, the indicator T is combined to determine the number of reconstruction layers, T The smaller the value, the better the denoising effect and the better the number of corresponding reconstruction layers, so that the SSA method has adaptive denoising ability. This method no longer uses qualitative analysis, but uses quantitative analysis to accurately determine the optimal number of reconstruction layers. Through the analysis of simulation data and measured GNSS time series data, it is concluded that adaptive SSA can achieve the best ratio of the two negatively correlated indicators of noise reduction results in detail information and approximation information, and can be applied to GNSS time series under complex noise background. Keywords: Principal component decomposition · Composite evaluation index · Self-adaption · SSA · GNSS time series

1 Introduction GNSS deformation monitoring has the characteristics of high monitoring accuracy and small accumulated displacement. Its monitoring sequence includes real displacement and observation noise, etc. It is often difficult to distinguish deformation and trend items © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 378–386, 2021. https://doi.org/10.1007/978-981-16-3146-7_35

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if the original time sequence is directly analyzed. Zhang Qin [1], Liu Jingnan and others [2] applied wavelet transform analysis to deformation monitoring and obtained real deformation signals; Dai Hailiang and others [3] combined wavelet multi-scale decomposition and SSA to analyze the time series of GNSS station coordinates, Effectively extracted useful information such as trend items and periods in the time series; Zhang Shuangcheng et al. [4] used the EMD method to reduce the noise of the IGS station time series, and reasonably separated the signal and noise in the GNSS time series; Lu Tieding et al. [5] proposed a deformation monitoring data processing method using variational modal decomposition combined with sample entropy; Ma Jun et al. [6] used wavelet packet coefficient information entropy to effectively eliminate colored noise in the residual sequence. As a tool for adaptive signal decomposition, SSA can decompose the signal into several SSA components, and select several meaningful components for reconstruction, thereby reducing noise [7]. The key step to achieve SSA noise reduction is to determine the effective rank of the Hankel matrix, that is, the number of effective singular values. Dai Haomin et al. [8] select the number of singular values according to the matrix rank minimization theory; Wang R et al. [9] divide the cumulative value of eigenvalues by the sum of all eigenvalues by pre-setting a percentage threshold and compare and judge with the threshold; Qian Zhengwen [10] used the number of dominant frequencies in the fast Fourier transform results to determine the order of the effective rank; Wang Yiyan [11] proposed a signal denoising algorithm based on the mean value of eigenvalues; Kang Chunyu et al. [12] proposed a A principal component decomposition method determines the number of effective singular values. The above methods have achieved good results in practical applications, but there are also certain limitations. According to the GNSS timing characteristics, this paper makes further improvements on the basis of the principal component decomposition method [12], and introduces a composite evaluation index T [13] to obtain an adaptive SSA method, which no longer adopts a qualitative analysis method, but the method of quantitative analysis is used to accurately determine the optimal reconstruction layer number, so that SSA has the ability of adaptive noise reduction.

2 SSA Principle SSA is gradually developed on the basis of classical Karhunen Loeve spectral decomposition [14] and embedding theory. SSA includes embedding, singular value decomposition, grouping and reconstruction. Let the length of one-dimensional discrete time series signal x(n) be n, the signal vector be x = [x1 , X2 , …, xn ]T , and T be transpose operator. The specific steps [15] are as follows: ➀ Embedding (constructing the trajectory matrix): The signal vector is overlapped and evenly divided into several parts. Define the length of these segments (called window length) as L, where L satisfies 1 < L ≤ L/2. Then the trajectory matrix X (trajectory

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matrix) can be defined as X = [x1 ,…, xN−L+1 ], namely: ⎡ ⎤ x1 x2 · · · xN −L+1 ⎢ x2 x3 · · · xN −L+2 ⎥ ⎢ ⎥ X =⎢ . . . ⎥ .. .. ⎣ .. .. ⎦ . xL xL+1 · · ·

(1)

xN

It can be seen that the matrix X is the Hankel Matrix. ➁ Singular value decomposition: Perform singular value decomposition on the trajectory matrix X to obtain: X =

L 

λi Ui ViT

(2)

i=1

Among them, λi is the singular value arranged in descending order, with λ1 ≥ λ2 ≥ … ≥ λL ≥ 0. Ui and Vi are the left and right singular vectors of X respectively. ➂ Grouping: If noise reduction is performed on the original sequence, the grouping operation is to express the trajectory matrix X constructed by the original sequence x(n) as the sum of the useful signal S and the noise E, that is, X = S + E. In this way, the grouping operation is to determine the appropriate value to achieve signal-to-noise separation. ➃ Reconstruction: The purpose of reconstruction is to transform the matrix obtained by the above grouping into a required sequence of length N. Let x∗u,p be the u-th element of the p-th one-dimensional SSA component. Let xa, b, p be the ath row and b column elements of the p-th trajectory matrix Xp after singular value decomposition. Then the grouping matrix is reconstructed and it can be converted back to a one-dimensional signal. The reconstruction formula is: ⎧ u 1 ⎪ xm,u−m+1,p 1≤u ≤L−1 ⎪ ⎪ u ⎪ ⎪ m=1 ⎪ ⎨ L 1 xm,u−m+1,p L≤u≤K (3) x∗u,p = L ⎪ m=1 ⎪ ⎪ ⎪ L

⎪ ⎪ 1 ⎩ N −u+1 xm,u−m+1,p K + 1 ≤ u ≤ N m=1

Among them, K is the total number of segments, K = N − L + 1; u = 1, …, N; p = 1, …, L.

3 Adaptive SSA Combining Principal Component Decomposition and Compound Evaluation Index From the above SSA principle, it can be seen that the key step to achieve noise reduction is how to determine the effective rank of the Hankel matrix, that is, the number of effective singular values q. In this paper, the composite evaluation index T is obtained by linearly combining the root mean square error and smoothness of the denoising signal. Based on

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the principal component decomposition idea, the joint index T can directly determine the number of effective singular values q, which makes the SSA method have adaptive denoising ability. The calculation formula of root mean square error (RMSE) and smoothness (r) [16] is:   N 1   [s(n) − x(n)]2 (4) RMSE = N n=1

N −1

r=

n=1 N −1

[s(n + 1) − s(n)]2 (5) [x(n + 1) − x(n)]2

n=1

Among them, s(n) is the signal after denoising, and x(n) is the original signal. Normalize the RMSE and r indicators: PRMSE =

RMSE − min(RMSE) max(RMSE) − min(RMSE)

Pr =

r − min(r) max(r) − min(r)

(6) (7)

Use the coefficient of variation method to determine the weight of the normalized PRMSE and Pr: σPRMSE CVPRMSE = (8) μPRMSE σPr CVPr = (9) μPr WPRMSE = WPr =

CVPRMSE CVPRMSE + CVPr

CVPr CVPRMSE + CVPr

(10) (11)

Among them, σ and μ are the standard deviation operation and the mean operation respectively, CV represents the coefficient of variation, and W is the weight based on the coefficient of variation. Then the composite evaluation index T can be expressed as: T = WPRMSE × PRMSE + WPr × Pr

(12)

The smaller T is, the better the denoising effect is and the better the number of reconstruction layers is. According to the SSA principle, as long as the original signal x(n) contains useful signals, the reconstructed component (RC) RC1 corresponding to the first singular value

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λ1 decomposed by the trajectory matrix X must be the useful signal. Therefore, the useful signal RC1 in x(n) can be extracted first, the remaining signal components can be obtained, and the composite evaluation index T1 of RC1 can be calculated. Regarding the remaining signal components as a new noisy signal, and repeating the above process, the useful signal in the original signal can be extracted in turn, and a set of composite evaluation indicators T1 , …, Tk can be obtained. The number of reconstruction layers q can be directly determined according to the index T. The specific steps of the adaptive SSA algorithm are as follows: ➀ According to the above SSA principle, the original time sequence x(n) is embedded and singular value decomposition is performed to obtain a set of singular values λ1 , …, λL arranged from large to small. ➁ Determine that the maximum singular number k of the termination cycle is equal to twice the corresponding number of singular value mean method [11], and calculate the reconstruction components RC1 , …, RCk corresponding to the first k singular values. i

RCj . ➂ Definition: Si = j=1

Among them, 1 ≤ i ≤ k, calculate the composite evaluation index T1, …,Tk corresponding to S1 , …, Sk , and determine Tq = min(T1 , …, Tk ) (1 ≤ q ≤ k). ➃ The Sq corresponding to Tq is the useful signal S after the final noise reduction.

4 Analysis of Self-adaption SSA Noise Reduction Calculation Examples 4.1 Simulation Data Noise Reduction Analysis GNSS time series generally consist of three parts: period, trend and noise. Construct 5 sets of simulation data models, which are mainly composed of two periodic signals, and add a Gaussian white noise and a low-frequency trend item, the sampling rate is 1s, and a total of 2000 sampling points are set. The expression is: y(t) = 3 sin(

2π t 4π t 4π t 2π t ) + 2 cos( ) + sin( ) + 2 cos( ) + at + wgn(t) 360 360 360 360

(13)

Among them, wgn(t) is Gaussian white noise, and a is the low-frequency trend term parameter. The simulation data I, II, III, and V add Gaussian white noise with signal-to-noise ratios of 6 dB, −6 dB, and 10 dB respectively, and set a = 0.0005; the simulation data IV adds 15 impulse noises randomly on the basis of the simulation data I; simulation Data V adds Gaussian white noise with a signal-to-noise ratio of 6 dB, and sets a = 0.001. In order to verify the reliability of the adaptive method in this paper, traditional evaluation indicators such as signal-to-noise ratio (SNR), root mean square error (RMSE), and smoothness (r) are used to quantify the effect of denoising, and compared with the literature [10, 11] method for comparison. If the signal-to-noise ratio index of the signal after noise reduction is higher, the root mean square error and smoothness index are smaller, indicating that the noise reduction effect is better.

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Figure 1 (a) and (b) from top to bottom are the analog data I and IV: the original signal, the noise-stained signal, the denoising results of the adaptive method, the mean method [11], and the FFT (Fast Fourier Transform) method [10] are compared with The original signal comparison chart. For reasons of space, only the comparison chart of denoising results of simulated data I and IV is given. It can be seen that the three methods can effectively remove noise, but the average method does not eliminate the noise completely. The FFT method fails to effectively retain the low-frequency trend term, and there is excessive denoising, which causes the increase in sampling points. The original unnoise signal has a large deviation. The denoising effect of the adaptive method in this paper is obvious, and the clean signal can be restored almost completely, and the original signal characteristics are preserved to the greatest extent. Table 1 shows the results of quantitative analysis of five groups of simulation data by three methods. In the five groups of data, when the signal-to-noise ratio is reduced, the mean method is not thorough; the adaptive method makes the best proportion allocation between RMSE and R value, and the SNR value obtained by the adaptive method is higher than that of the FFT method, which indicates that the adaptive method can better retain the original signal characteristics.

a Simulation data Ⅰ

c

Simulation data Ⅳ

Fig. 1. Comparison of denoising results of simulated data among self-adaption method, averaging method and FFT method

Figure 2 shows the result of using the adaptive method to calculate the composite evaluation index T corresponding to the number of reconstruction layers of the simulated data I. It can be found that when the number of reconstruction layers is 5, the T value is the smallest, that is, the optimal number of reconstruction layers is 5. 4.2 GNSS Elevation Sequence Noise Reduction Analysis Compared with analog data, the components of GNSS time series are often more complicated. Simulation data alone is not enough to explain the pros and cons of each method. This paper uses the single-day solution time series of BJFS provided by SOPAC for comparative analysis. Among them, prior to the time sequence analysis, the individual gross errors in the BJFS station time sequence were eliminated and de-trending items were processed. Figure 3 shows the BJFS station from top to bottom: the original time sequence, the denoising results obtained by the adaptive method, FFT method, and the average method are compared with the original time sequence, and the composite evaluation

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Table 1. Quantitative analysis of the denoising results of simulated data from three methods Analog data

Method

I

Self-adaption Mean FFT

II

III

IV

V

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RMSE

r

6.310

1.972

0.000623

5.782

1.868

0.134

5.001

2.044

0.000622

Self-adaption

15.870

0.499

0.009233

Mean

15.850

0.501

0.009229

FFT

12.398

0.745

0.009210

Self-adaption

3.162

3.104

0.00360

Mean

5.692

2.320

0.453

FFT

2.996

3.164

0.00261

Self-adaption

4.066

2.446

0.000382

Mean

5.554

2.069

0.266

FFT

3.909

2.501

0.000381

Self-adaption

5.889

1.907

0.00686

Mean

6.141

1.851

0.0423

FFT

4.836

2.152

0.00676

Fig. 2. The composite evaluation index T corresponding to each reconstruction layer of the simulation data I

index T value corresponding to each reconstruction layer of the adaptive method. Among them, when the FFT method is applied to the BJFS station sequence, there are only two main frequencies in the fast Fourier transform result, and the reconstruction result has excessive denoising phenomenon and seriously deviates from the true value, so the method is invalid. Table 2 shows the RMSE and r values of the denoising results of the BJFS station obtained by the adaptive method and the average method in this paper. It can be seen that the adaptive method makes the best proportional distribution between the RMSE and the r value, and the denoising results are more reliable.

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Table 2. Quantitative analysis of GNSS elevation time series denoising results by two methods Site

Method

SNR

RMSE

r

BJFS Self-adaption 7.270 0.00631 0.0004 Mean

7.928 0.00634 0.0003

Fig. 3. Comparison of denoising results of BJFS station with adaptive method, FFT method and average method

5 Conclusion In this paper, the principal component decomposition method is further improved, and combined with the composite evaluation index t to determine the number of reconstruction layers, so that the SSA method has the ability of adaptive de-noising. The experimental analysis shows that the adaptive SSA method has the following two characteristics: first, it does not use qualitative analysis method, but uses quantitative analysis method to accurately determine the optimal number of reconstruction layers; second, it can make the noise reduction results reach the best proportion in the two negative correlation indexes of detail information and approximation information. However, this paper only uses five groups of simulation data and one GNSS elevation time series to verify the adaptive SSA method, which has some limitations. In the next step, we need to study and analyze the time series data of more GNSS stations. Acknowledgement. This work has been supported by State Key Laboratory of Geo-Information Engineering (SKLGIE2019-Z-2-1); National Key R&D Program of China (2020YFC1512000, 2019YFC1509802, 2018YFC1505102); Natural Science Foundation of China projects (NSFC) (42074041,41731066); ZFS (ZFS19001D-ZTYJ08, Y9E0151M26) and CETC Industrial development fund project “BDSBAS International Standards Research” (20201121);Shaanxi Natural Science Research Program (2020JM-227); Fundamental Research Funds for the Central Universities (No. 300102269201, 300102299206). The authors gratefully acknowledge UNAVCO for providing experimental data; Kristine Larson, Carolyn Roesler, Berkay Bahadur, and many others who have provided open access to MATLAB code. Three anonymous reviewers are thanked for their constructive review of this manuscript.

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References 1. Zhang, Q., Jiang, Y., Wang, X.: Research on application of wavelet transform in deformation monitoring. Eng. Surv. Mapp. 14(1), 8–10 (2005) 2. Huang, S., Liu, J.: An effective method to eliminate noise in GPS deformation monitoring system. Acta Geodaetica et Cartographica Sinica (02), 104–107 (2002) 3. Dai, H., Sun, F., Xiao, K., et al.: Application of wavelet multi-scale decomposition and singular spectrum analysis in GNSS station coordinate time series analysis. Geomatics Inf. Sci. Wuhan Univ. 1–11 (2019) 4. Zhang, S., He, Y., Li, Z., et al.: EMD is used for GPS time series noise reduction analysis. J. Geodesy Geodyn. 37(12), 1248–1252 (2017) 5. Lu, T., Xie, J.: De-noising of deformation monitoring data based on variational modal decomposition and sample entropy. J. Geodesy Geodyn. 41(01), 1–6 (2021) 6. Ma, J., Cao, C., Jiang, W., et al.: Using wavelet packet coefficient information entropy to remove colored noise of GNSS station coordinate time series. Geomatics Inf. Sci. Wuhan Univ. 1–119 (2020) 7. Wang, J., Lian, L., Shen, Y.: Application of singular spectrum analysis in GPS station coordinate monitoring sequence analysis. J. Tongji Univ. (Nat. Sci.) 41(02), 282–288 (2013) 8. Dai, H., Xu, A., Sun, W.: Signal denoising method based on improved singular spectrum analysis. Trans. Beijing Inst. Technol. 36(07), 727–732 (2016) 9. Wang, R., Ma, H., Liu, G., et al.: Selection of window length for singular spectrum analysis. J. Franklin Inst. 352(4), 1541–1560 (2015) 10. Qian, Z., Cheng, L., Li, Y.: Signal denoising method by means of SVD. J. Vib. Meas. Diagn. 31(4), 459–463 (2011) 11. Wang, Y.Y.: Mean value of eigenvalue-based SVD signal denoising algorithm. Comput. Appl. Softw. 29(05), 121–123 (2012) 12. Kang, C., Zhang, X.: An adaptive noise reduction method based on singular value decomposition. Tech. Acoust. 27(3), 455–458 (2008) 13. Zhu, J., Zhang, Z., Kuang, C., et al.: A reliable quality evaluation index for wavelet denoising. Geomatics Inf. Sci. Wuhan Univ. 40(5), 688–694 (2015) 14. Johnstone, I.M.: On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat. 2(29), 295–372 (2001) 15. Kuang, W.: Adaptive Decomposition of Signal and its Application in Non-parametric Denoising. Guangdong University of Technology (2018) 16. Tao, K., Zhu, J.: Comparative study on evaluation methods of wavelet denoising quality. J. Geodesy Geodyn. 32(02), 128–133 (2012)

A Spoofing Detection Algorithm Based on Coprime Array for GNSS Receiver Yuqing Zhao1(B) , Feng Shen1(B) , and Dong Zhou2 1 School of Instrumentation Science and Engineering,

Harbin Institute of Technology, Harbin 150001, China {zhaoyuqing,fshen}@hit.edu.cn 2 School of Aeronautics, Harbin Institute of Technology, Harbin 150001, China [email protected]

Abstract. Spoofing is a deliberate attack that can coerce global navigation satellite system (GNSS) receivers into generating false position/time solutions. The characteristics of spoofing are very similar to authentic GNSS signals, therefore, it is difficult to discriminate their presence. In this paper, we propose a spoofing detection technique based on coprime array before the de-spreading of GNSS receivers. The direction of arrival (DOA) estimation and cross-correlation peaks monitoring are combined to provide a reliable spoofing separation and detection method, in which the coprime array instead of the conventional uniform linear array (ULA) is adopted to DOA estimation so that the proposed technique is effective when the number of signals (include spoofing and satellite signals) is higher than array elements. It is worth noting that all the processes are performed on the raw digital base-band signal samples without de-spreading GNSS signals. The simulation results demonstrate the effectiveness of the proposed spoofing detection technique. Furthermore, the estimated DOA is helpful for spoofing mitigation and location in some applications. Keywords: Global navigation satellite system (GNSS) · Spoofing detection · DOA estimation · Coprime array · Cross-correlation

1 Introduction GNSS dependent timing and positioning systems are widespread in both military and civilian fields. However, GNSS receivers are vulnerable to interference, especially the spoofing signals, which bring about much more dangerous than the jamming [1]. Consequently, to improve the security of GNSS, effective spoofing detection technique is an indispensable component.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 387–396, 2021. https://doi.org/10.1007/978-981-16-3146-7_36

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In recent years, many contributions have been made towards the development of spoofing countermeasure techniques, such as encryption-based defences [2], abnormal feature monitoring [3–6] and aided equipment verification [7]. It is worth noting that most of the methods mentioned above operate after the acquisition and tracking of the GNSS receiver. More specifically, acquiring and tracking all authentic and spoofing signals will cause a higher computational burden. Considering the fact that the signal received by the array antenna contains the spatial characteristics of the incident signal from different directions, it is robust and effective to detect spoofing with spatial processing instead of complex acquisition and tracking [8–10]. However, the degrees of freedom (DOF) of the conventional spoofing detection algorithm based on ULA is limited by the number of sensors. In addition, the existing countermeasures mostly use the DOA obtained by array signal processing only and ignore other signatures of the incident signals. In this paper, we propose a novel robust and efficient GNSS spoofing detection scheme by using raw signal before signal acquisition, tracking and position solution, where the coprime array DOA estimation and cross-correlation monitoring are combined. On the one hand, we formulate the DOA estimation by using the coprime array because of its sparse sensor deployment, which can achieve a better parameter estimation performance and detect more spoofing sources with less sensors. On the other hand, the time-domain cross-correlation is performed on the signals of each spatial channel based on the estimated DOAs to provide a sufficiently reliable detection system for the GNSS receivers. Finally, two simulation scenarios are performed to verify the performance of the proposed method.

2 Signal Model of Coprime Array In this paper, we assume the multiple counterfeit pseudo random noise (PRN) signals are transmitted by a single antenna. Without loss of the generality, the received baseband sampled signal that comprises M A authentic signals, M S spoofing signals and the noise can be expressed by A

x(nTS ) =

M  p=1

S

apA spA (nTS ) +

M 

aqS sqS (nTS )+n(nTS )

(1)

q=1

in which T S is the sampling interval and n(nT S ) is complex additive white Gaussian noise vector with diagonal matrix σv2 I. Here σv2 denotes the power of noise. spA (nTS ) and sqS (nTS ) represent the pth authentic signal, the qth spoofing respectively, and spA (nTS ) = sqS (nTS ) =

 

PpA DpA (nTS − τpA )CpA (nTS − τpA )ej2π(fIF +fp )nTS +jφp A

A

PqS DqS (nTS − τqS )CqS (nTS − τqS )ej2π(fIF +fq )nTS +jφq S

S

(2)

where the superscripts A and S represent authentic signals and spoofing signals, respectively. f IF means the intermediate frequency, the parameters ϕ, P, f , τ, denote the phase, power, Doppler frequency and code delay of each signal. In generally, PpA /PqS < 1. D is the ±1 valued navigation data code and C is the ±1 valued PRN code.

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In Eq. (1), apA and aqS are the steering vectors of the authentic signal and spoofing respectively, which describe the carrier phase difference of signals received from different antenna elements in a certain direction. Figure 1 shows the coprime array antenna geometry generated by a pair of ULAs.

Fig. 1. Sparse ULAs of the coprime array

We assume there are M A authentic signals and M S spoofing signals imping on the coprime array antenna from the directions θ = [θ1 , θ2 , . . . , θK ], then the steering vector of the coprime array can be expressed as a(θ ) = [1, · · · , e−j

2π λ di

sin θ

, · · · , e−j

2π λ d2M +N −1 sin θ

]T

(3)

It is worth noting that M S spoofing transmit counterfeit PRN signals from the same direction, thus K = M A + 1, and the received signal model in Eq. (1) can be rewritten as A

x(nTS ) =

M 

S

apA spA (nTS ) + aqS

p=1

M 

sqS (nTS )+n(nTS )

(4)

q=1

3 Proposed Technique 3.1 Covariance Matrix Construction The genuine GNSS signals and spoofing are both typical weak signal whose power is below the noise level, hence it is very challenging for the GNSS receiver to detect and separate multiple spoofing signals of its received raw signal. To overcome this problem, the characteristics of GNSS signals are fully exploited in this paper. It is well known that counterfeit GNSS signals also have periodic structures similar to the authentic ones. In addition, their chip rate samples, which are separated by integer multiples of spreading gain, have strong self-coherence. Taking GPS as an example, the cyclic correlation matrix can be expressed as   (G) = E x(nTs )xH (nTs − Tc/a ) = ARPRNs AH (5) Rxx where A = [a(θ1 ), a(θ2 ), · · · , a(θK )] is the steering matrix of coprime array. Tc/a denotes the C/A code period. RPRNs represents the covariance matrix of PRN signals. It can be seen from Eq. (5) that the noise component has been removed from cyclic correlation matrix.

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Considering that covariance matrix cannot be obtained accurately in practice, it is usually replaced by the sample covariance matrix, which can be estimated by a sampled data block XN and its reference data block XNref : 1 (G) H ˆ xx R ≈ XN XNref N

(6)

where XN = [x(k).....x(k − (N − 1))], XNref = [x(k − L).....x(k − (N − 1) − L)], N is the length of the data block and L denotes the number of samples in one code period. In order to improve the accuracy of estimation and reduce the degradation of estimation performance caused by bit hopping, time averaging can be performed for multiple data blocks and their corresponding reference data blocks. (G) ˆ xx is vectorized to increase the number After that, the sample covariance matrix R of DOFs provided by coprime array, which can be modeled as

(G) ˆ xx z = vec(R ) = Bp

(7)

T    in which B = a∗ (θ1 ) ⊗ a(θ1 ) · · · a∗ (θk ) ⊗ a(θK ) and p = σ12 σ22 · · · σK2 represents the incident signal power. The vector z can be regarded as the equivalent received signal of the virtual array with the corresponding signal source p and steering matrix B. In this interpretation, the rank of the covariance matrix calculated by the received signal z of the equivalent virtual array will be reduced to one. The following rank-one covariance matrix can be denoted as Rs = zzH

(8)

To address this problem and exploit the increased DOFs, the Modified MUSIC (MMUSIC) is a good candidate, based on which the full rank covariance matrix corresponding to virtual array can be obtained by Rs = Rs + Jq (Rs )∗ Jq = ARPRNs AH

(9)

where Rs and RPRNs represent the modified Rs and RPRNs respectively, Jq is ⎤ 0 ··· 0 1 ⎢ .. . . . . ⎥ ⎢ . . . 0⎥ ⎥ Jq = ⎢ ⎢ .⎥ ⎣ 0 1 . . . .. ⎦ 1 0 ··· 0 ⎡

(10)

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3.2 GNSS Spoofing Detection We first perform eigen-decomposition to Rs :   H   2 0  UA R s = UA UO H 0 0 UO

(11) 2

where UA and UO denote the signal subspace and zero subspace respectively, and is the diagonal matrix formed by the nonzero eigenvalues in R s . Then, we devise a new DOA estimator for coprime array source estimation. The resulting DOA estimation algorithm is developed by a linear algebraic connection between the zero subspace and the signal subspace of Rs . And then, the improved MUSIC algorithm, termed signal-plus-zero subspace MUSIC, seeks the spectrum peak of +

f (θ ) = H

+

−2

aH (θ )RA a(θ ) aH (θ )PO a(θ )

(12)

H

where PO = UO UO and RA = UA UA . Remarkably, the proposed DOA estimator exploits more structure of Rs , which is more robust to the effects of subspace mismatches due to correlated signals, finite sample sizes, or low SNR. The DOA and the corresponding spatial spectrum response can be obtained by Eq. (12). In generally, to be more effective, a spoofer might transmit several PRN signals with consistent features. Therefore, the presence of multiple spoofing signals can considerably increase the power content in the direction of the spoofer, based on which, we devise a spoofing detection technique that makes full use of the orthogonality of satellite navigation PRN codes. Specifically, the oblique subspace projection technique is applied to separate each spatial signals. Defining the oblique projection matrix EX Y :  −1 ⊥ ⊥ H EX Y = X H X PY X X PY

(13)

⊥ repwhere X  and Y  denote the range space and zero space, respectively. P Y resents the orthogonal projection matrix whose range space is perpendicular to Y . Then, the spatial signal with direction θi can be denoted as

z(n) = Ea(θi )(A∼a(θi )) x(nTs )

(14)

in which θi (i = 1, 2, · · · K) and a(θi ) denotes the steering vector of the i-th spatial signal. A ∼ a(θi ) represents the steering matrix of the co-prime array, which excepts the steering vector a(θi ). Then the highest spatial spectrum response corresponds to the spatial signal is selected to perform cross-correlation calculation with other spatial signals, which can be expressed as ∗     (15) Rcross = IFFT FFT (zmax ) • FFT zother where zmax and zother are data vectors corresponding to the highest spatial spectrum response and other spatial signals, respectively. Although the accuracy of the DOA

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estimation of the spoofing signal will be affected by the weak sources and strong correlation, there must be cross-correlation peaks between the highest spatial spectrum response corresponds to the spatial signal and other signals when the spoofing exists. On the contrary, if there is no spoofing, there will be no significant difference in the spatial spectrum response of each spatial signal, and due to the orthogonality of the PRN code, there will be no correlation peak in the cross-correlation results. Therefore, spatial spectrum response comparison combined with cross-correlation peak monitoring provides an effective method for GNSS spoofing detection.

4 Simulation Results In this section, the proposed spoofing detection method will be verified in different scenarios. In our simulations, we consider a coprime array consisting of a pair of sparse uniform linear sub-arrays with 2M = 2 × 3 = 6 and N = 5 sensors, respectively. Hence, the coprime array antenna that consists of 2M + N − 1 = 10 sensors. The additive noise is considered as a zero mean white Gaussian random process. The number of samples in C/A code chip is 37 and the length of the data block is 37000. The SNR of the authentic signal at the receiver is −20 dB. • Scenario 1: In the first example, we consider a scenario that includes five authentic satellite signals, the PRN and DOA information of these signals are shown in the following Table 1. We assume that there is no spoofing signal in this simulation. According to the proposed method, the spatial power spectrum is first obtained by the proposed DOA estimation algorithm, and the result is shown in Fig. 2. Table 1. Simulation parameters of the signal sources in scenario 1. Sat1 PRN 3

Sat2

Sat3 Sat4 Sat5

5

9

DOA −50° −30° 0°

18

25

10°

50°

It can be seen from the Fig. 2 that the proposed DOA estimation algorithm can effectively estimate the direction of all signal sources and the signal comes from 0°direction has the highest spatial spectrum response. And then we separate the received signals by Eq. (14) for cross-correlation calculation. The cross-correlation results between the signal with the highest spatial spectrum response and other spatial signals are shown in Fig. 3.

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Fig. 2. The estimated spatial spectrum based on co-prime array.

Fig. 3. The cross-correlation results in scenario 1.

As Fig. 3 shows there is no correlation peak in the correlation results between the signal with the highest spatial spectrum response and other spatial signals, which means the PRN codes of the signal in 0° direction and the remaining signals are orthogonal. In addition, there is not much difference in spatial spectrum response between the signals. Therefore, the simulation results show that five spatial signals are all genuine satellite signals, which are consistent with the simulation scenario settings. • Scenario 2 In this scenario, we assume ten authentic signals and one spoofing signal, which means the number of incident signals is more than the number of antenna sensors. The code phase differences between the spoofing signals and the corresponding satellite signals are aligned within 0.5 chips. The power of each spoofing signal is −17 dB. And other the simulation parameters of incident signals is shown in Table 2.

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Sa2

Sa3

Sa4

Sa5

Sa6

Sa7

Sa8

Sa9

Sa10

SP

PRN

1

3

6

8

11

16

19

21

22

26

[1 3 6 8]

DOA

−50°

−40°

−30°

−20°

0°

10°

20°

30°

40°

50°

−10°

According to the framework of the proposed algorithm, we first obtain the spatial spectrum and estimate the DOA of all the signals, as shown in Fig. 4. Figure 4 shows the DOAs of the incident signals can be accurately estimated even in the case of more sources than sensors. And the spatial spectrum response in −10° direction is significantly higher than the other DOAs, thus the cross-correlation results between it and other sources are shown in Fig. 5. It can be seen from Fig. 5 that there are four correlation peaks between the spatial channels in the -10° direction and −50°, −40°, −30°, −20° direction. Therefore, it is obvious that the spatial signal in the −10° direction has the same PRN code as other four spatial channels, which means that there is spoofing in the received signals, and the DOA of the spoofing is −10°.

Fig. 4. The estimated spatial spectrum based on co-prime array.

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Fig. 5. The cross-correlation results scenario 2.

5 Conclusions This paper proposes a GNSS spoofing detection technique based on co-prime antenna arrays which can be divided into two stages. In the first stage, we propose a DOA estimation method based on co-prime array for GNSS signals, where a novel pre-processing algorithm is proposed to solve the problem of signal model mismatch caused by low power and strong correlation. In the second stage, the estimated DOA is used to divide the space channel of the received signal and the cross-correlation operation is performed on the signal with highest spatial spectrum response and other signals. Simulation results in Sect. 4 demonstrate that the proposed spoofing detection technique is robust and still reliable when the number of incident source signals is more than array elements. Acknowledgments. This research was funded by National Natural Science Foundation of China, grant number 61673128 and 61573117.

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References 1. Wesson, K., Shepard, D.: Straight talk on anti-spoofing. GPS World 23(1), 32–39 (2012) 2. Humphreys, T.E.: Detection strategy for cryptographic GNSS anti-spoofing. IEEE Trans. Aerosp. Electron. Syst. 49(2), 1073–1090 (2013) 3. Akos, D.M.: Who’s afraid of the spoofer? GPS/GNSS spoofing detection via automatic gain control (AGC). Navigation 59(4), 281–290 (2012) 4. Jafarnia-Jahromi, A., Broumandan, A., Nielsen, J., Lachapelle, G.: GPS spoofer countermeasure effectiveness based on signal strength, noise power and C/N0 observables. Int. J. Satell. Commun. Netw. 30(4), 181–191 (2012) 5. Dovis, F., Chen, X., Cavaleri, A., Ali, K., Pini, M.: Detection of spoofing threats by means of signal parameters estimation. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), pp. 416–421 (2011) 6. Wang, F., Hu, C., Wu, S., Tao, Y., Xu, Y.: Research on BeiDou anti-spoofing technology based on comprehensive radio determination satellite service. Satell. Navigat. 1(1), 1–9 (2020). https://doi.org/10.1186/s43020-019-0004-2 7. Jiang, W., Li, Y., Rizos, C.: Optimal data fusion algorithm for navigation using triple integration of PPP-GNSS, INS, and terrestrial ranging system. IEEE Sens. J. 15(10), 5634–5644 (2015) 8. Daneshmand, S., Jafarnia-Jahromi, A., Broumandan, A., Lachapelle, G.: Low-complexity spoofing mitigation. GPS World 22(12), 44–46 (2012) 9. Shi, W., Zhu, H., Cai, P.: The GPS deception jamming identification technology of based on the DOA of received signal. Ship Sci. Technol. 35(4), 111–116 (2013) 10. Broumandan, A., Jafarnia-Jahromi, A.: Overview of spatial processing approaches for GNSS structural interference detection and mitigation. Proc. IEEE 104(6), 1246–1257 (2016)

Unambiguous Tracking Technique for Multicarrier Modulation Signals in the Framework of Cognitive Receivers Junjie Ma, Zheng Yao(B) , and Mingquan Lu Department of Electronic Engineering, Tsinghua University, Beijing 100084, China [email protected]

Abstract. With the continuous construction and improvement of global navigation satellite systems (GNSSs), the number of navigation signals broadcast by GNSSs has increased significantly, and the spectrum resources are becoming increasingly scarce. In order to solve the contradiction between limited spectrum resources and the growing demand for positioning, navigation and timing services, some scholars have proposed a multicarrier modulation scheme which multiplexes narrow-band signals in several adjacent spectrum slots into a composite wide-band signal. On the one hand, multicarrier modulation signals can make full use of the spectrum resources, and on the other hand such signals can provide diversified processing strategies. Based on the idea of cognitive receivers and the inherent characteristics of multicarrier signals, we propose two different unambiguous tracking techniques named energy aggregation method and multidimensional loop tracking method respectively. In the first method, the energy of different signal components is aggregated, which can improve the positioning performance while maintaining the unimodal characteristic of the correlation function. In the second method, the potential high-precision ranging performance of high-frequency subcarriers in the multicarrier signal is further exploited. By introducing additional subcarrier loop, the one-dimensional correlation function is extended to two-dimensional. In the dimension of subcarrier, the correlation function is sharper and still has the characteristic of multiple correlation peaks, but in the dimension of pseudo-random noise (PRN) code, the correlation function presents the unimodal characteristic, so it can assist the subcarrier loop to eliminate ambiguity. The proposed tracking methods can be embedded in the architecture of cognitive receivers, where GNSS receivers can flexibly configure the receiving parameters according to the internal and external environment, and select proper receiving strategy. For example, in scenarios where the requirement in positioning precision is moderate, the system could select single-component receiving and processing strategy. In scenarios with high requirement for positioning performance, the system will choose multicomponent receiving mode. Simulation results show that in the above two methods, multicomponent wideband reception can improve the ranging accuracy successfully. Besides, the ranging accuracy of the second method is much better than that of the first method. Keywords: Multicarrier modulation · Multicomponent reception · Unambiguous tracking · Cognitive receivers

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 397–410, 2021. https://doi.org/10.1007/978-981-16-3146-7_37

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1 Introduction The contradiction among the scarce spectrum resources, limited transmission power and the growing demand for positioning, navigation and timing is becoming more and more severe in the modernized global navigation satellite systems (GNSSs). In order to solve this contradiction, some scholars have proposed multicarrier constant envelope multiplexing as a solution in recent years [1, 2]. Multicarrier constant envelope multiplexing technique can combine the navigation signals at several adjacent frequency points into a composite signal while maintaining the constant envelope characteristics of the composite signal. The constant envelope characteristic can make the high power amplifiers (HPAs) on satellites work in the near saturation region, so as to improve the amplification efficiency. The multicarrier characteristic of the composite signal can provide diversified navigation services while making full use of the scarce spectrum resources. With the continuous improvement of GNSSs, the number of navigation signals has grown rapidly. According to the literature, there are more than 400 satellite navigation signals in the upper L band [3]. Consequently, the continuous vacant spectrum is unavailable. Under this circumstance, the multicarrier signal can make full use of the unoccupied spectrum slots and broadcast narrowband signals in these slots. Multicarrier multiplexing techniques combine these narrowband signal components into a wideband signal, thereby providing more flexible and diverse receiving modes. For example, in the scenarios with high signal-to-noise ratio or moderate positioning accuracy requirements, receivers can choose the single-component receiving mode, whereas in scenarios with weak signal strength or high positioning accuracy requirements, receivers will select multicomponent wideband receiving mode. The above mentioned advantages of multicarrier signals can be better presented in the framework of cognitive receivers [4]. In the multicarrier signal discussed in this paper, each signal component has the same code rate and adopts the BPSK modulation. Therefore, when a signal component is received separately, the correlation function presents the triangular unimodal structure, and there is no ambiguity in tracking, but when adopting multicomponent wideband receiving mode, it is necessary to avoid the ambiguity in tracking. Traditional unambiguous tracking methods such as Bump-jump [5], ASPeCT [6], and Dual Estimation Technique (DET) [7] are designed for binary offset carrier (BOC) signals, and the research on unambiguous tracking for multicarrier signals is still insufficient. Therefore, in this paper we propose two unambiguous tracking techniques for multicarrier signals, which are named as energy aggregation method and multi-dimensional loop tracking method. The main idea of the energy aggregation method is to move the signal components at different frequency points to a unified frequency point to achieve energy aggregation, thereby improving the ranging accuracy through increasing the signal power during multicomponent reception. Since each signal component adopts BPSK modulation, the correlation function can still maintain the unimodal characteristic. Multi-dimensional tracking loop method further exploits the ranging performance of the high-frequency subcarriers. The idea of this method is inspired by DET, which expands the one-dimensional correlation function to two-dimensional by introducing an additional subcarrier loop. In the dimension of subcarrier, the correlation function is sharper and still has multiple peaks, but the correlation function presents the single-peak characteristic in the dimension of the pseudo-range noise (PRN) code. Therefore, it can

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assist the subcarrier loop to eliminate ambiguity. The multi-dimensional loop tracking method not only aggregates the energy of different signal components, but also extracts the high-precision ranging results of the high-frequency subcarriers, so it is better than the energy aggregation method in ranging accuracy. Both unambiguous tracking methods can be embedded in the framework of cognitive receivers, where the system can flexibly configure the receiving parameters and select the receiving scheme according to the internal and external environment.

2 Model and Characteristics of Multicarrier Signals 2.1 Mathematical Model of Multicarrier Signals Consider the multicarrier signal consisting of N independent signal components, in which the power, initial phase, and the carrier frequency of the i th component are denoted as Pi , φi , and fi respectively. The composite multicarrier signal s(t) is defined as s(t) =

N  

Pi exp[j(2π fi t + φi )]si (t)

(1)

i=1

where si (t) is the baseband signal of the i th component, which is expressed as si (t) =

+∞ 

(−1)ci [k] di (t)pi (t − kTc(i) )

(2)

k=−∞

where ci [k], di (t), pi (t) are the spreading code with chip rate 1/Tc(i) , navigation data, and chip waveform of the spreading code. For signals adopting BPSK modulation, the definition of pi (t) is given in (3).  (i) 1, 0 ≤ t < Tc , (3) pi (t)= 0, otherwise Based on previous definitions, the multicarrier signal s(t) can also be expressed as s(t)= s0 (t) exp(j2π f0 t)   N  Pi exp(jφi )si (t) exp(j2π fsi t) exp(j2π f0 t) =

(4)

i=1

in which s0 (t) is the baseband composite multicarrier signal, and f0 is the central frequency of the radio frequency carrier. fsi is the subcarrier frequency of the i th component, which satisfies fsi + f0 = fi . Considering the nonlinear feature of HPAs, auxiliary signals are usually added to s0 (t) to make the whole signal achieve lower peak-toaverage power ratio [2]. For the simplicity of discussion, we do not expand on this topic. Besides, the sinusoidal subcarrier exp(j2π fsi t) can be substituted with step-shape

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subcarrier sci (t) =

+∞  l=−∞



Ni π

sin

−1 π Ni

1 exp(j 2π Ni (l + 2 ))ψTl (t − lTl ), where Tl is the

duration of per step, and the absolute value of Ni = 1/(fsi Tl ) is the number of steps in one subcarrier period. ψTl (t) is the unit pulse whose value takes one when t ∈ [0, Tl ), and takes zero otherwise. 2.2 Main Characteristics of Multicarrier Signals The analysis in this section and subsequent sections will be based on a five-component multicarrier signal proposed in [1]. In this multicarrier signal, all signal components have the same power and are all located in the in-phase path. Besides, all components adopt BPSK (0.5) as the modulation scheme. The subcarrier frequency of the i th signal component is fsi = (i − 3) × 2.046 MHz. In this multicarrier signal, different PRN codes are selected for different signal components to reduce the mutual interference among the components. The power spectral density of the above baseband multicarrier signal is shown in the figure below (Fig. 1).

Fig. 1. Power spectral density of the multicarrier signal

Three usual receiving modes for the above multicarrier signal are listed in [1], which are single-component reception, partial-component reception and full-component reception. In the single-component receiving mode, the receiver only processes the component located at the central frequency point. In the partial-component receiving mode, the receiver will jointly receive s2 (t), s3 (t) and s4 (t). In the full-component receiving mode, the receiver will process all the five components. Figure 2 shows the correlation functions corresponding to the above three receiving modes. It can be seen that as the number of received components increases, the correlation function becomes sharper and the signal energy increases significantly, which means higher ranging accuracy. Although multicomponent reception can improve the ranging accuracy, it also leads to tracking ambiguity because of the side peaks in the correlation function. In the next section we will propose two unambiguous tracking methods to solve this problem.

Unambiguous Tracking Technique for Multicarrier Modulation Signals 8

10 5 Single-component reception Three-component reception Five-component reception

6

Correlation Value

401

4

2

0

-2

-1

-0.5

0

0.5

1

PRN Code Chips

Fig. 2. Correlation functions in different receiving modes

3 Unambiguous Tracking Technique for Multicarrier Signals in the Framework of Cognitive Receivers 3.1 Cognitive Receivers The concept of cognitive GNSS receivers has been proposed in [4]. There are two main differences between cognitive receivers and traditional GNSS receivers. One is that the cognition layer is added to enable traditional GNSS receivers to perceive the internal and external environment of the system and then make decisions. The other one is that the components of the receivers can be flexibly reconfigured. In the framework of cognitive receivers, the advantages of multicarrier signals can be better presented. Cognitive receivers play a variety of roles in the reception of multicarrier signals: 1. Energy consumption monitoring: When the cognition layer detects that the available battery power is insufficient, it will prompt the receiver to work in single-component reception mode. If the cognition layer detects that the current energy resources are sufficient, it can switch to the multicomponent receiving mode. On this basis, the cognition layer configures corresponding parameters such as the sampling rate, the bandwidth of the filter, and the early-late separation in the GNSS receiver. 2. Interference monitoring: When the cognition layer detects intentional or unintentional interference at a certain frequency band, it will prevent the receiver from receiving such signal components in that frequency band. 3. Noise monitoring: If the cognition layer judges that the noise in the current environment is intense, it should adopt the multicomponent reception mode. For example, Fig. 3 and Fig. 4 are the acquisition results of the above-mentioned five-component multicarrier signal under low signal-to noise ratio (SNR) environment. The results in the figures show that it may be difficult to acquire the signal in the single-component receiving mode under low SNR. In this case, multicomponent receiving mode should be selected.

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Fig. 3. Acquisition in the single-component receiving mode

Fig. 4. Acquisition in the full-component receiving mode

3.2 Energy Aggregation Unambiguous Tracking Technique for Multicarrier Signals As mentioned above, the reception of multicarrier signals faces the problem of tracking ambiguity. To solve this problem, this section proposes an energy aggregation unambiguous tracking method for the reception of multicarrier signals. The core idea of this method is to use local subcarriers to shift the spectrum of the received signal so that all signal components are located at the same frequency point. At the same time, the correlation values of the above signal components need to be combined after coherent

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integration. The modulation method of each signal component is BPSK, whose corresponding correlation function is unimodal, therefore there is no problem of tracking ambiguity. More concretely, assuming that the baseband multicarrier signal is s0 (t − τ ), where τ represents the time delay corresponding to the code phase. The prompt (P), early (E), and late (L) branches of the local signal are pi (t) = ci (t − τˆ ) exp(j2π fˆsi (t − τˆ )) ei (t) = ci (t +  − τˆ ) exp(j2π fˆsi (t − τˆ )) li (t) = ci (t −  − τˆ ) exp(j2π fˆsi (t − τˆ ))

(5)

where ci (t) is the PRN code which equals to the value of si (t)di (t) in (2).  is half of the early-late separation, and τˆ , fˆsi are the estimations of τ and fsi obtained from the code delay lock loop. Suppose the received signal deprived of the carrier are multiplied by the conjugate of the above-mentioned signals, and the results after coherent integration are denoted by Pi , Ei and Li respectively. Let I denotes the set of subscript indexes of the signal components to be received, then the input E and L signals of the code phase discriminator are  E= |Ei | i∈I

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where sgn(·) is the sign function and Re(·) means the real part of the variable. In the above scheme, the selection of I and the early-late separation are determined by the cognition layer. The schematic representation of the proposed energy aggregation unambiguous tracking technique is shown in Fig. 5. In this schematic diagram, Subcarrier_c and PRN Code_c represent the subcarrier and PRN code corresponding to the reference signal whose subcarrier is constant. In this diagram, complex numbers are used to replace the I and Q branches, and all multipliers mean conjugate multiplication. It should be pointed out that the above method and the corresponding schematic diagram consider the situation where different signal components carry different data. If the same data is used for different signal components, the gray modules in this diagram can all be replaced by ordinary summation. Figure 6 shows the correlation functions derived from this method in the three receiving modes mentioned in Sect. 2.2. It can be seen that the correlation functions present the single-peak characteristic. Therefore, there is no tracking ambiguity problem. Besides, the signal energy is effectively aggregated during multicomponent reception. Figure 7 plots the code tracking error of the three receiving modes under different carrier-to-noise ratios (2000 independent experiments). The filter one-sided bandwidth is set to 6 MHz.

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Fig. 5. The schematic representation of the proposed energy aggregation unambiguous tracking technique

The code loop bandwidth is set to 1 Hz, and the coherent integration time is 2 ms. The early-late separation is set to 0.8 × Tc , and the code loop phase discriminator is δ = k()

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in which k() represents the reciprocal of the slope of the E−L E+L − (τˆ − τ ) curve when the estimation is relatively accurate. The results in Fig. 7 demonstrate that the code tracking error decreases with the increase of the carrier-to-noise ratio. Besides, the multi-component receiving mode can improve the ranging accuracy. This improvement mainly comes from the increase of signal energy. 3.3 Unambiguous Tracking Technique Based on Multi-dimensional Tracking Loops The energy aggregation unambiguous tracking method proposed in the previous section can avoid the problem of peak mislock and improve the ranging accuracy when adopting multicomponent receiving mode, but it does not fully exploit the ranging performance of high-frequency subcarrier. This section proposes a multicarrier signal unambiguous receiving method based on a multi-dimensional loop structure, which can make full use of the ranging capability of high-frequency subcarriers.

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The main idea of this method is to introduce additional subcarrier loop to decouple the subcarrier and PRN code to some extent. The phase information extracted from the subcarrier tracking loop has much higher ranging accuracy, while the phase information extracted from the code loop can assist the subcarrier loop to eliminate ambiguity. The schematic representation of the proposed unambiguous tracking technique based on multi-dimensional tracking loops is shown in Fig. 8. The main difference between this method and the method proposed in the previous section is the introduction of a subcarrier

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numerically controlled oscillator (NCO) and a subcarrier tracking loop, which makes the generation and adjustment of subcarriers independent of the PRN code tracking loop. Similar to the previous section, this schematic diagram considers the case of different signal components carrying different messages. If different signal components use the same message, the gray modules in the figure below can all be replaced with ordinary summation modules.

Fig. 8. The schematic representation of the proposed unambiguous tracking technique based on multi-dimensional tracking loops

Next, we will describe this method in detail. We still assume that the baseband multicarrier signal is s0 (t − τ ), where τ represents the time delay corresponding to the code phase. The prompt (P), early (E), and late (L) branches of the local signals derived from the PRN code loop are cpi (t) = ci (t − τˆc ) exp(j2π fˆsi (t − τˆs )) cei (t) = ci (t + c − τˆc ) exp(j2π fˆsi (t − τˆs )) cli (t) = ci (t − c − τˆc ) exp(j2π fˆsi (t − τˆs ))

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loop. Suppose the received signal deprived of the carrier are multiplied by the conjugate of the above-mentioned signals, and the results after coherent integration are denoted by CPi , CEi and CLi respectively. Let I denotes the set of subscript indexes of the signal components to be received, then the input E and L signals of the code phase discriminator are  CE = |CEi | i∈I

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where s is half of the early-late separation. Suppose the received signal deprived of the carrier are multiplied by the conjugate of the above-mentioned signals, and the results after coherent integration are denoted by SEi and SLi respectively, then the input E and L signals of the subcarrier phase discriminator are  SE = sgn[Re(CPi )]Re(SEi ) i∈I

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where Ts is the least common multiple of the subcarrier periods and round (·) is the rounding function. We utilize this method to receive the multicarrier signal described in Sect. 2.2. Figure 9 is a two-dimensional correlation function when receiving all the components. It can be seen that the correlation function is sharper in the subcarrier dimension but there exists whole-cycle ambiguity. Besides, the correlation peak in the PRN code dimension is relatively flat and there is no ambiguity. Figure 10 shows the correlation function in the subcarrier dimension when the estimation from the code tracking loop is accurate. The results demonstrate that the subcarrier correlation peak is steeper when adopting five-component reception. Besides, the correlation value is larger.

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Fig. 9. Correlation function in the five-component receiving mode

Fig. 10. Correlation functions in the subcarrier dimension

Figure 11 plots the subcarrier tracking error of different receiving modes under a series of carrier-to-noise ratios. The results show that compared with the energy aggregation method, this method can significantly improve the ranging accuracy, and the code tracking error of the five-component reception is smaller than that of the three-component reception.

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Fig. 11. Subcarrier tracking error standard deviation with respect to carrier-to-noise ratio in the multi-dimensional loop tracking method

4 Conclusions In this paper, we propose two unambiguous tracking techniques named energy aggregation method and multi-dimensional loop tracking method in the framework of cognitive receivers. In the energy aggregation method, signal components located at different frequency points but with the same modulation method are moved to the same frequency point through subcarriers for energy aggregation. Since the single-peak characteristic of the BPSK signal itself is maintained, tracking ambiguity does not exist. Because the signal energy is aggregated, the accuracy of ranging in multicomponent reception is higher than that in single-component reception. The multi-dimensional loop tracking method further exploits the ranging performance of the high-frequency subcarriers inherent in the multicarrier signal. By additionally introducing a subcarrier loop, the PRN codes and the sub-carriers are decoupled to some extent, and the one-dimensional correlation function is extended to two-dimensional. This method combines the advantages in the PRN code tracking loop and the subcarrier tracking loop. The correlation peak in the subcarrier dimension is steeper, while the correlation function in the dimension of the PRN code maintains the single-peak characteristic. Therefore, it is possible to extract the high-precision estimation result from subcarrier loop while using the result from the code loop to assist the subcarrier loop in ambiguity elimination. Acknowledgment. This research was supported by National Natural Science Foundation of China (Grant No. 61771272), and Young Innovation Foundation of Beijing National Research Center for Information Science and Technology (Grant No. BNR2021RC01015).

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References 1. Yao, Z., Ma, J., Zhang, J., Lu, M.: Multicarrier constant envelope composite signal – a solution to the next generation satellite navigation signals. In: Proceedings of the 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 1520–1533 (2017) 2. Yao, Z., Guo, F., Ma, J., Lu, M.: Orthogonality-based generalized multicarrier constant envelope multiplexing for DSSS signals. IEEE Trans. Aerosp. Electron. Syst. 53(4), 1685–1698 (2017) 3. Betz, J.W.: Signal structures for satellite-based navigation: past, present, and future. In: Proceedings of the ION 2013 Pacific PNT Meeting, Honolulu, Hawaii, April 2013, pp. 131–137 (2013) 4. Shivaramaiah, N.C., Dempster, A.G.: Cognitive GNSS receiver design: concepts and challenges. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 2782–2789 (2011) 5. Fine, P., Wilson, W.: Tracking algorithm for GPS offset carrier signals. In: Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1999, pp. 671–676 (1999) 6. Julien, O., Macabiau, C., Cannon, M., Lachapelle, G.: ASPeCT: Unambiguous sine-BOC(n, n) acquisition/tracking technique for navigation applications. IEEE Trans. Aerosp. Electron. Syst. 43(1), 150–162 (2007) 7. Hodgart, M.S., Blunt, P.D.: Dual estimate receiver of binary offset carrier modulated signals for global navigation satellite systems. Electron. Lett. 43(16), 877–878 (2007)

GNSS User Terminals

Optimal Design of Multi-channel Correlator for the Same Code Signal and Its Application in Anti-jamming for GNSS Rong Shi(B) , Junhao Chen, and Jinchen Bao Science and Technology on Electronic Information Control Laboratory, Chengdu, China [email protected]

Abstract. With the increasing complexity of electromagnetic environment, the appearance of multipath interference in urban canyon and man-made intentional sliding code correlation jamming makes the performance of the traditional satellite navigation receiver, which has the same code acquisition and tracking loop with three channels: early, present, late complex correlators, greatly reduced or even failed. In order to solve this problem, it is pointed that the multiplication and integration of PN code and signals can be realized by using a simple logic operation and a digital adder in the receiver. Based on this idea, a multi-channel correlation operation for the same code is proposed to get the correlation curve for a duration window in real time, so as to discriminate the artificial sliding code correlation jamming. The detection, identification and discrimination on the process about multi correlation peaks meeting, merging and separation caused by the jamming signal ensure the receiver to track the real signal correlation peak continuously and stably. It effectively avoids the situation that the delay locking loop in the traditional navigation receiver is wrong or out of locking. The simulation results verify the effectiveness and correctness of this method. It provides an important reference for the architecture design and anti-jamming application for the next generation satellite digital navigation receiver. Keywords: Multi-channel correlator for the same code signal · Correlation curve · Multi-path signal processing · Sliding code correlation jamming · Anti-jamming · Anti deception

1 Introduction In the traditional satellite navigation receiver, only three complex correlators, early, present and late, are usually used to complete the correlation operation in the receiving channel for the same pseudo-random code signal, so as to realize acquisition and tracking on the code [1, 2]. Although this design is simple, its anti-jamming ability is not strong. As the electromagnetic environment in application scenarios becomes more and more complicated, especially the multipath propagation effect in urban canyons is increasingly strong, the traditional pseudo code tracking loop design can’t achieve high-precision ranging [3, 4]. On the other hand, since the parameters and PN code sequences of civil © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 413–422, 2021. https://doi.org/10.1007/978-981-16-3146-7_38

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satellite navigation signals are fully open for the public, with the widespread use of artificially sliding code correlation jamming, the probability of code loop unlock for the satellite navigation receiver becomes more and more large [5, 6]. Although signal integrity detection, positioning data validity analysis and other means can be used to assist the receiver in finding abnormal signals [7, 8], this does not fundamentally change the situation about weak anti-jamming ability of PN code tracking loop. In order to solve above problem, the working mechanism of PN code acquisition and tracking loop for the traditional satellite navigation receiver is briefly reviewed in this paper, then it is pointed out that the multiplication and integration of PN code and signals in the correlator of a traditional receiver can be realized by using simple logic processing and a digital adder in digital receiver, which means that according to the current developing level of digital chip integration technology, multi-channel correlation operation for the same code signal can be realized. It is possible to display the correlation curve continuously and in real time for the digital navigation receiver. Therefore, the multi-channel correlator for the same code is used to effectively identify the artificial sliding code correlation jamming signal. The whole process of meeting, merging and separating of two correlation peaks can be discovered in real time in the observation window. Finally, two different peaks can be distinguished and tracked continuously by means of bimodal location in image processing, which can effectively avoid the unlock and wrong lock of DLL (delay lock loop) in the traditional navigation receiver. The details are as follows.

2 PN Code Acquisition and Tracking Loop of a Traditional Satellite Navigation Receiver In a traditional satellite navigation receiver, DLL is usually used to acquire and track PN code signals. It usually has three complex correlators, which are Early correlator (denoted by E), Present correlator (denoted by P) and Late correlator (denoted by L). The time delay between E and L usually is one chip in code phase, while that between E and P, or P and L is half a chip. The IF digital signal sampled by the receiver is converted to baseband through I/Q orthogonal down convertor. After the carrier is stripped off, the correlation peak offset estimation can be obtained through the correlation operation of the above three complex correlators. Then, according to the estimated value, the correlation peak can be captured and tracked by loop control, and finally the measurement value of pseudo range can be obtained. The block diagram of PN code tracking loop for a PN signal in a traditional satellite navigation receiver is shown in Fig. 1. It can be seen that each complex correlator performs correlation operation on the signals of in-phase I branch and orthogonal Q-branch respectively. Therefore, the output R(ta , tb ) of the correlator in time period [ta , tb ] is expressed as follows.  tb R(ta , tb ) = c(t) · s(t)dt (1) ta

Where c(t) is the locally recovered pseudo code signal and s(t) is the baseband received signal after stripping off the carrier. Since each group of signals has I/Q two

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branches, there are six multipliers and six integrators in the traditional DLL. For each correlator, the final correlation value RA of I/Q two branches, respectively denoted by RI and RQ , can be obtained as follows.  RA = R2I + R2Q (2) The tracking error is formed by three final correlation values, RA,E , RA,P and RA,L , which are output by Early, Present and Late correlator, through the discriminator of DLL. After the code loop filter, the local code generator is controlled to adjust the code phase to compensate the error. Finally the purpose of continuous tracking and locking the pseudo code signal is achieved.

3 Digital Implementation and Optimal Design of the Same Code Multiple Correlators Only six correlators in DLL are used in Fig. 1, because the multiplier and integrator occupy a large amount of resources in the traditional hardware. A satellite navigation receiver generally needs to acquire and track 8–12 navigation satellite signals, so the hardware cost of the receiver is relatively high. However, with the continuous progress of chip integration technology in digital receiver, the scale of digital logic circuit becomes larger and larger, which is no longer restriction for the satellite navigation receiver design. On the other hand, the local PN code cb,i , where subscript i represents the sampling serial number, is a binary signal with the value of {+1, −1}. In digital logic circuit design, the baseband signal is generally represented by the signed binary complement code sb,i . When the value of local PN code cb,i is +1, the multiplier in Fig. 1 is through directly. When its value is −1, the multiplier in Fig. 1 is to get the opposite number, which can be realized to add 1 after all bit logical negation for the signed binary sequence, denoted by sb,i . Thus, the binary sequence of the multiplier output mb,i is as follows.  sb,i if cb,i = +1 mb,i = (3) sb,i + 1 if cb,i = −1

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It can be seen that the multiplier in the satellite navigation receiver can be completed by logic operation and an adder, and the occupied hardware resource is very small. Moreover, the integrator in the digital logic circuit can be implemented by an accumulator, and its integral value Ib,i is as follows. Ib,i = Ib,i−1 + mb,i

(4)

In fact, the accumulator in formula (4) can also be combined with the adder in formula (3), because the addition 1 operation in the second conditional branch in formula (3) can be realized by the carry input branch of the adder. Therefore, the multiplication and accumulation operations in the whole correlator can be completed by one digital adder in the digital logic circuit.  Ib,i−1 + sb,i if cb,i = +1 (5) Ib,i = Ib,i−1 + sb,i + 1 if cb,i = −1 It can be seen that in the digital logic circuit of the satellite navigation receiver, the function of formula (1) can be realized by an adder with conditional judgment. On the other hand, the final output value of each correlator group in Fig. 1 needs the square root operation shown in formula (2). If CORDIC (Coordinate Rotation Digital Compute) algorithm is directly used, the hardware resource cost is also very high. Therefore, in engineering application, the JPL approximation method is generally utilized for calculation as follows.  x + y/8 if x ≥ 3y (6) RA = x − x/8 + y/2 otherwise       Where x = max |RI |, RQ  , y = min |RI |, RQ  . In fact, since all coefficients in formula (6) are integer powers of 2, it can be realized by an adder with shift operation in digital circuit with less hardware resources. Moreover, as the operation for formula (6) is implemented after a period of time accumulation for formula (5), the optimal design method can be used to achieve the time sharing of the calculation module. The function of formula (6) in the digital circuit needs several clock cycles. The accumulated time in formula (5) is generally in the range from 1/10 to 1 about a navigation message data symbol cycle, which is far longer than the operation time in formula (6). Therefore, in the digital circuit module design, a complete function for formula (6) can provide time sharing for many correlators, and only more register resources are needed. In summary, the traditional design constraint, in which correlators occupy a lot of hardware resources, is no longer the handicap for the current satellite navigation receiver. The widely used correlators in formula (5) will become an important way to improve the performance of digital navigation receiver. With this optimized design basis, it is feasible to display the correlation curve continuously in real time for the digital navigation receiver, and the block diagram of PN code tracking loop with multi correlators for the same code is shown in Fig. 2.

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4 Correlation Curve Formation and Recognition on the Sliding Code Correlation Jamming The multi-channel correlators for the same code in the above simplified digital logic circuit can calculate the correlation value in a continuous time period with 1/4 spread spectrum code chip time as the sampling interval. It forms a continuous correlation curve in the observation window in real time, as shown in Fig. 3, in which 33 correlators are utilized to sample 8 code chip time tc intervals, corresponding to 33 sampling points. The correlation peaks in Fig. 3 are not sharp, which is actually caused by multipath interference. In the traditional method, a continuous correlation curve is mainly produced by Fourier transform, in which the hardware resource consumption is still large. Therefore the above multi-channel correlators for the same code have greater advantages than the traditional one. Continuous correlation curve

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Because the PN code phase corresponding to the correlation peak in the correlation curve is the original data for the pseudo range measurement at this moment, the peak formed by the correlation between the locally reproduced PN code sequence and the actual received navigation signal is an important reference point in the satellite navigation and location. The nominal PN code rate in GNSS is denoted by CrC . If the PN code at 1575.42 MHz of GPS L1 frequency is considered as an example, its PN code rate is 1.023Mcps. The PN code rate of local reproduction in the navigation receiver is denoted by CrR . In general, CrC and CrR satisfy the following relation. VS − VR = (CrR −CrC ) · c CrC (7) Where VS and VR are the velocity components of navigation satellite and receiver respectively along their connection line, c = 3×108 m/s is the velocity of electromagnetic wave. If Eq. (7) is integrated along the time axis, the distance variation L during the integration period [t1 , t2 ] between the navigation satellite and the receiver can be obtained, which also corresponds to the variation of the pseudo range measurement value in the receiver.  t2   L = (8) (VS − VR )dt = CrR CrC −1 · c(t2 − t1 ) t1

It can be deduced from Eq. (8): (1) When CrR = CrC , the PN code rate in local reproduction for the navigation receiver is equal to the nominal PN code rate in GNSS, L = 0, which means that the distance between the navigation satellite and the receiver remains unchanged; (2) When CrR > CrC , the PN code rate in local reproduction is larger than that in GNSS, L > 0, which means that the distance between the navigation satellite and the receiver is increasing; (3) When CrR < CrC , the PN code rate in local reproduction is less than that in GNSS, L < 0, which means that the distance between the navigation satellite and the receiver is decreasing; The distance change completely reflects the pseudo range variation, so the above three cases also correspond to the pseudo range variation actually measured by the receiver. If the jammer produces the jamming signal by using the same PN code sequence and simulating the signal generation mode of the navigation satellite, and the PN code rate of the jamming signal is denoted by CrJ , the jamming signal will also generate correlation peak with the locally reproduced PN code signal in the navigation receiver. Reference to the same cases as above, the distance variation relationship between jammer virtual position and navigation receiver can also be obtained under different CrJ and CrC as follows: (1) When CrJ = CrC , the pseudo range generated by the jamming signal remains unchanged; (2) When CrJ > CrC , the pseudo range for the jamming signal increases; (3) When CrJ < CrC , the pseudo range for the jamming signal decreases;

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Since CrJ is actively controlled by the jammer, it means that the distance variation rule between the jammer virtual position and the navigation receiver derived from the pseudo range measurement principle can be fully controlled by the jammer. Therefore, there will be a different value LJS between the pseudo range generated by the jamming signal and that of the real navigation satellite. When LJS changes continuously, the correlation peak of the jamming signal will slide relatively to the real one. When CrJ meets the following conditions through the jammer controls, different sliding effects will occur as shown in Fig. 4, in which the real correlation peak is taken as a reference point on the time axis. (1) When CrJ > CrR , the correlation peak generated by the jamming signal will slide from left to right on the time axis; (2) When CrJ < CrR , the correlation peak generated by the jamming signal will slide from right to left on the time axis.

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Since the intensity of jamming signal is generally greater than that of normal navigation satellite signal, the correlation peak of jamming signal is also greater than that of normal one. According to the correlation peak sliding process shown in Fig. 4, when the two correlation peaks are overlapped and then separated, the PN code tracking loop in the receiver with DLL will track the correlation peak of jamming signal with larger amplitude, and it will lose locking on correlation peak of the normal signal. Because DLL has only three correlators, it can’t completely reproduce and effectively distinguish the above situations. For the multi-channel correlators for the same code in this paper, due to the parallel multi-channel correlation operation, a section of correlation curve in an observation window as shown in Fig. 3 can be obtained, so the whole process about two correlation peaks meeting, merging and separating can be monitored in real time. By the double peak positioning method in image processing to distinguish and track the two different level correlation peaks in the navigation receiver, it can avoid the code loop unlocking or wrong locking, and ensure that the satellite navigation receiver always tracks the real correlation peak.

5 Simulations The civil navigation satellite signal with PRN = 1 on the L1 frequency of GPS is considered as an example. Its spread spectrum pseudo code is a gold sequence with the

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period of 1023, its code rate is 1.023 Mcps, and code period is 1ms. For the data rate of satellite navigation message is 50bps, in order to avoid the performance degradation caused by the data symbol integration with opposite values, the maximum time for integral clearing in DLL tracking loop of the traditional satellite navigation receiver is 20 ms. Because all parameters and specification of the civil code are public, the jamming signal can be produce as same as the real signal of the navigation satellite with PRN = 1, which has been demonstrated by the commercial programmable satellite navigation simulator in real application. The jammer can accurately control the pseudo code phase of the jamming signal by adjusting the pseudo code rate, so that the correlation peak of the jamming signal will slide relative to that of the normal signal. The relative sliding rate is set as 0.25 chip/s. Since the duration time in one PN code for GPS is approximately 1us, it is equivalent to that the distance change between the pseudo satellite produced by the jammer and the navigation receiver is faster than that between the real satellite and the receiver by 0.25 us/s × 3 × 108 m/s = 75 m/s. For the navigation receiver with traditional DLL, the jamming signal intensity is about 3–6 dB higher than the normal one, so that the sliding code correlation jamming will make the lock position of the DLL gradually shift from the normal signal correlation peak to the jamming signal correlation peak, as shown in Fig. 5. The yellow, blue and green dots respectively represent the correlation output values of Early (E), Present (P) and Late (L) correlators in the traditional DLL. The whole evolution process of three correlators in traditional DLL from real signal to sliding code correlation jamming signal are shown in detail, and it also reveals the disadvantages of traditional receiver design.

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In order to solve these problems, the 33 channel multi correlators for the same code designed in this paper can produce the correlation curve shown in Fig. 5 on 33 consecutive

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（d）T1+20

Fig. 6. Tracking on two correlation peaks in the observation time window

Compared with Fig. 6 and Fig. 5, a section of correlation curve in the observation time window can be obtained in real time through the multi-channel correlators for the same code, which eliminates the disadvantage that the traditional three correlators can’t identify the sliding code correlation jamming, and effectively avoids the code loop wrong locking on the jamming signal. In this way, it can keep the continuous locking and tracking on the correlation peak of the real signal, and finally use the correlation peak position of the real signal to carry out pseudo range measurement and positioning calculation, which greatly improves the anti-jamming and anti-deception ability for the satellite navigation receiver.

6 Conclusions For the problem that the anti-jamming ability of PN code tracking loop in traditional satellite navigation receiver is inadequate when multiple correlation peaks occur at the same time, based on the analysis that digital correlation operation can be realized by the simple logic operation and adder, the design scheme of pseudo-random code tracking loop of multi-channel correlators for the same code signal is proposed in this paper. It realizes the real time continuous present of correlation curve in the observation window. We analyze its advantages to the traditional receiver in the application of anti sliding

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code correlation jamming. Finally, the validity and correctness of the theoretical analysis are verified by simulations. It provides an important reference for the architecture design and anti-jamming application of the next generation satellite digital navigation receiver.

References 1. Teunissen, P., Montenbruck, O.: Handbook of Global Navigation Satellite Systems. Springer, Germany (2017). https://doi.org/10.1007/978-3-319-42928-1 2. Kaplan, E.D., Hegarty, C.J.: Understanding GPS Principle and Applications, 2nd edn. Artech House Inc., Boston (2006) 3. Phan, Q., Tan, S., Mcloughlin, I.V., et al.: A unified framework for GPS code and carrier-phase multipath mitigation using support vector regression. Adv. Artif. Neural Syst. 4, 1–14 (2013) 4. Yozevitch, R., Moshe, B.B., Weissman, A.: A robust GNSS LOS/NLOS signal classifier. Navigation 63(4), 429–442 (2016) 5. Adamy, D.L.: EW 104: EW Against a New Generation of Threats. Artech House Inc., Boston (2015) 6. Liu, Q.: The jamming technology of DSSS communication system based on sequence jitter. Harbin Engineering University, Harbin, China (2018) 7. Hsu, L.T., Tokura, H., Kubo, N., et al.: Multiple faulty GNSS measurement exclusion based on consistency check in urban canyons. IEEE Sens. J. 17(6), 1909–1917 (2017) 8. Groves, P.D., Jiang, Z.: Height aiding C/N0 weighting and consistency checking for GNSS NLOS and multipath mitigation in urban areas. J. Navig. 66(5), 653–669 (2013)

Impact Analysis of Meaconing Attack on Timing Receiver Dong Fu, Jing Peng, Hang Gong, Ming Ma(B) , and Gang Ou National University of Defense Technology, 410073 Changsha, Hunan, China [email protected]

Abstract. GNSS timing receivers are widely used in power distribution systems and cellular towers to provide precise timing service, the vulnerability of GNSS makes users face the threat of spoofing. Meaconing brings challenges to time security since it can attack receivers that use military signal. This paper analyzes the impact of two kinds of common meaconing attack on the timing receiver. Aiming at the abnormal step of the receiver clock bias after being attacked, a spoofing detection method based on RFFLS clock bias prediction is proposed. The main factors affecting the detection probability of the method are analyzed, and the conditions that need to be met for the detection probability to reach 99% or more under different clock types are given. The results show that the higher the frequency stability of the clock, the farther the distance between the meaconer and the receiver, and the sooner the detection time from the last time correction, the higher the probability of spoofing detection. High quality TCXO or a clock with higher frequency stability can make the timing receiver have effective spoofing detection capability in short term. Keywords: GNSS · Timing · Clock bias prediction · Spoofing detection

1 Introduction As a way of timing service, Global Navigation Satellite System (GNSS) has become the key time service method for major infrastructure such as power system, cellular towers and financial trading institutions with its advantages of high precision, all-weather, and wide coverage [1]. However, GNSS receivers are facing various kinds of interference in the complex electromagnetic environment, especially spoofing. Among all kinds of spoofing, meaconing has the ability to spoof the receiver using military and civil signal, so it is a great threat to the timing service users. In order to protect the security of GNSS timing, deep research on the impact of meaconing on timing receivers is essential. At present, scholars have conducted research on GNSS receiver spoofing and antispoofing technology. Humphrey and Huang, etc. systematically analyzed the implementation principles of various spoofing technologies, and summarized the detection and mitigation technologies [2–4]. In the aspect of timing spoofing, Huang proposed meaconing technology to attack timing receivers [5]. Liu briefly analyzed the ability of chip scale atomic clock (CSAC) to detect spoofing based on clock bias prediction [6]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 423–434, 2021. https://doi.org/10.1007/978-981-16-3146-7_39

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Zhu summarized the security reinforcement technology of timing receiver from different aspects [7]. However, the features of the impact of meaconing on timing receivers and the influencing factors of the performance of detection algorithms based on clock bias prediction are still unclear. Hence, we research the mechanism of meaconing and propose a clock bias prediction spoofing detection method based on recursive forgetting factor least square (RFFLS), the relationship between the detection ability and the key influencing factors are analyzed.

2 Timing Spoofing and Detection Model 2.1 Principle of Timing Spoofing When a meaconer attacks a receiver, it usually interferes first. After the receiver tracks the spoofing signal, the meaconer adds the same channel delay to each satellite signal on the basis of the original delay [5]. The pseudorange positioning equation is established as:     ρi = (xi − xu )2 + (yi − yu )2 + (zi − zu )2 + ctu = ρi + ρ = Ri + c tuu + tch (1) where i: number of satellite; tu : user clock bias calculated by the spoofing signal; tuu : true clock bias between the receiver and GNSS;  ρi : pseudorange measurement; Ri : geometric distance from the satellite to the receiver; tch : additional channel delay; ρ: pseudorange increment corresponding to tch ; (xi , yi , zi ): satellite position in earth centered earth fixed coordinates (ECEF); (xu , yu , zu ): user position calculated by the spoofing signal in ECEF; Equation (1) shows that the common part of the pseudorange error caused by spoofing signal only affects the clock bias. Since the real-time clock (RTC) module of the timing receiver adjusts the output frequency signal with the clock bias at regular intervals [5], spoofing the clock bias is equivalent to spoofing time synchronization. 2.2 The Effect of Meaconing on Receiver Clock Bias The common kinds of meaconing in this paper are simple and sophisticated meaconing. Meaconer enhances the received satellite signal and transmits it from the antenna without any other parameter modification in simple meaconing condition [8]. Assuming that the receiving and transmitting antenna coordinates of the meaconer are the same, the principle of simple meaconing is shown in Fig. 1.

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Fig. 1. Principle of simple meaconing attack

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Fig. 2. Principle of sophisticated meaconing attack

where R is the real position of receiver, J is the position of meaconer, tproc is the processing delay of meaconer and S i is the position of satellite. A pseudorange positioning equation is established as:  ρi = (xi − xu )2 + (yi − yu )2 + (zi − zu )2 + ctu = Rsi J + ctproc + ctJR + ctuu (2) where Rsi J : true distance from the satellite to the meaconer; tJR : propagation path delay from the meaconer to the receiver; The relationship between satellite position and the propagation path delay between the meaconer and the receiver (xJ , yJ , zJ ) is:  (3) Rsi J = (xi − xJ )2 + (yi − yJ )2 + (zi − zJ )2 According to Eq. (2), (3), the solution is:  xu = xJ , yu = yJ , zu = zJ tu = tuu + tproc + tJR

(4)

Equation (4) shows that after simple meaconing attacked, the receiver position is on the meaconer position, and the clock bias is the accumulation of the path delay tJR and the processing delay tproc . Regardless of whether the sophisticated meaconing uses multiple devices or single device, different time delays are added to each satellite signal, so that the target receiver position is set at the purpose position. The principle of sophisticated meaconing is shown in Fig. 2.

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The transmission time of the user receiving the retransmission signal of the same satellite at a certain moment is earlier than the transmission time of the direct signal, where S i is the position of the when the direct signal was launched. Sei is the satellite position when the retransmission signal was transmitted. If the receiver is to be spoofed from the real position R to the false position F, the following equation needs to be satisfied:   i + tproc + tJR + ctuu = Rsi F + ctu (5) Rsi J + c tctrl e

e

where ctJR is the distance from the meaconer to the receiver; Rsi F is the distance from e the retransmitted satellite to the spoofing location. Then the controllable delay of each satellite signal can be expressed as:   i tctrl = Rsi F /c − Rsi J /c − tJR + tproc + tu − tuu (6) e

e

In this case, if the receiver clock is not spoofed: tu − tuu = 0

(7)

Since the meaconer must be physically achievable, it needs to meet: i tctrl ≥0

(8)

Timing receivers usually have location integrity check. When the sophisticated meaconing needs to avoid the detection in position domain, R and F coincide.  i < 0 is Rsi J , c tproc + tJR and Rsi F constitute a triangle geometrically, and tctrl e e substituted into Eq. (6) and meaconer cannot perform physically. Hence, the delay caused by physical realization must be added to both sides of Eq. (6) so that the meaconer can spoof receiver:   i , i = 1, 2, . . . (9) tphy = −min tctrl From the Eq. (1), tphy is only added to the clock bias. So, the receiver’s clock bias is: tu = tuu + tphy

(10)

tphy is the minimum amplitude of the clock bias step caused by the spoofing timing under the condition that the meaconer does not change the position of the receiver. The amplitude depends on the position of the retransmission satellite, meaconer and receiver. Since satellite signals are incident from all directions, considering Eq. (6), (9) and Fig. 2 is easy to know that tphy is usually greater than the distance ctJR from the meaconer to the receiver, which means that under the condition of retransmission the same satellite signal, the clock bias step caused by sophisticated meaconing is usually greater than that of simple meaconing. Once the meaconer controls the receiver, it can modify the pseudorange delay slowly to change the clock bias. It is difficult to detect by conventional methods such as RIAM. Hence, we consider to detect abnormal clock bias step.

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2.3 Spoofing Detection Method Based on Clock Bias Prediction The method we proposed predicts the clock bias by fitting the clock source parameters based on the historical data. The polynomial model of the clock bias is: X = Ha + e

(11)

where a = [a0 , a1 , a2 ]T : a0 is clock bias at reference time t0 , a1 is clock drift, a2 is clock drift rate; e: n-dimensional error vector; H: relation matrix; X: n-dimensional clock bias observation vector; ⎡ T⎤ ⎡ ⎤ h1 1 t1 − t0 (t1 − t0 )2 ⎢ hT ⎥ ⎢ 1 t2 − t0 (t2 − t0 )2 ⎥ ⎢ 2⎥ ⎢ ⎥ H =⎢ . ⎥=⎢. (12) ⎥ .. .. ⎣ .. ⎦ ⎣ .. ⎦ . . hTn

1 tn − t0 (tn − t0 )2

The least square solution of a is:  −1 aˆ = H T H HTX

(13)

In order to prevent the increase of observational data from causing data saturation and reducing the performance of parameter estimation, while considering the prediction accuracy and computational complexity, this work uses RFFLS to predict the clock bias [9, 10], and the detailed flow of RFFLS is: 1) Use m data (m ≥ 3) to calculate the fitting parameters aˆ m and T m : ⎧  −1 ⎪ ⎨ aˆ m = H T WH H T WX   ⎪ ⎩ T = H T WH −1 m

(14)

where T m is extracted weight vector matrix for subsequent calculations, W is forgetting factor matrix, which aims to enhance the contribution of new data to the forecast model and weaken the influence of old data, which expressed as:   (15) W = diag λn−1 , λn−2 , · · · , λ0 , 0 < λ ≤ 1 2) Iteratively calculate aˆ k and T k at time tk :   ⎧ T k−1 hk hTk T k−1 1 ⎪ ⎪ ⎨ Tk = T k−1 − λ λ + hTk T k−1 hk   ⎪ ⎪ ⎩ aˆ = aˆ T ˆ k−1 k k−1 + T k hk xtk − hk a

(16)

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3) Calculate the predicted clock bias at time tk ˆtu = hTk · aˆ k

(17)

In essence, RFFLS algorithm only fits the deterministic component of the clock source bias, the random component also affects the clock bias too. It is known that the random component is composed of five kinds of random noise, and the frequency stability is characterized by Allan variance in time domain [11]. It is generally believed that the clock source noise obeys a zero mean Gaussian distribution [12], its variance σc2 is: σc2 = σy2 (T ) · T 2

(18)

where σy2 is Allan variance, which is related to the properties of the clock itself, T is the time since previous RTC correction. The clock bias prediction error δtu is defined as the difference between calculated clock bias and predicted clock bias: δtu = tu − ˆtu

(19)

In the normal scenario, RFFLS performs single-step prediction, and correct the parameter estimation error each step, so the mean of δtu is zero. In the spoofing scenario, there is no available clock bias solution after the receiver is jammed, and RFFLS performs multi-step prediction. So the mean of δtu is non-zero. The statistical hypothesis testing is: assume H0 (authentic signal) and H1 (spoofing signal), then:   H0 : δtu ∼ N 0, σ 2   H1 : δtu ∼ N t, σ 2 (20) where t is tproc + tJR and tphy in simple and sophisticated meaconing scenarios respectively, and the variance σ 2 is: σ 2 = σ02 + σc2

(21)

where σ02 = TDOP 2 · σρ2 is the variance of the last single-step prediction error, and σρ2 is the variance of the pseudorange measurement noise. σ02 can be calculated in real time during the prediction process [13, 14], and it doesn’t change much when observing the satellite stably. Assuming that constant false alarm detection is used, according to 3 σ criterion, if the false alarm probability PFA = 0.15%, the detection threshold γ is:  γ = 3 σ02 + σc2 (22) Combining Eq. (18), (20)–(22), the detection probability PD is:  ∞ 1 2 2 PD = √ e−(x−t) /2σ dx σ 2π γ

(23)

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In conclusion, the spoofing detection threshold γ and detection probability PD are affected by the frequency stability σy2 , the time T from the previous correction and single-step prediction error σ0 . In addition, PD is also affected by the clock bias step amplitude t, which is mainly determined by ctJR .

3 Simulation and Analysis 3.1 Simulation Setup The receivers use BDS-B3I signal with the time synchronization. The authentic signal and spoofing signal needed are generated by the simulation of intermediate frequency signal [15, 16]. The scheme includes normal and sophisticated meaconing scenario. The simulation parameters are shown in Table 1. Table 1. Simulation parameter setup Type

Parameter

Satellite position

2020/08/25 broadcast ephemeris [17]

Start time

UTC: 07:00:01:00

Simulation period

120 s

Spoofer position

37.9530°, 102.6502°, 1486.0 m

Statistical user position 37.9552°, 102.6502°, 1482.8 m

The receiver starts to output the navigation solution after 1 s of tracking, and the solution update interval is 1 s, the power of spoofing signal is 5 dB higher than that of authentic signal, the processing delay of the meaconer tproc is ignored [5]. The common clock types of timing receiver are temperature compensate crystal oscillator (TCXO), oven controlled crystal oscillator (OCXO) and CSAC. We simulate clock bias and random noise data of corresponding clock according to typical h-parameters [18–21], then the frequency stability Allan deviation curve as shown in Fig. 3, where TCXO1 and TCXO2 are low-quality and high-quality TCXO respectively. The simulation starts from the last clock bias correction time, and assume that the receiver will not be corrected later. 3.2 Spoofing Detection and Performance Analysis Before the tracking loop of timing receiver loses locking (1–60 s), the single-step prediction error of the clock bias under different clock types are shown in Fig. 4. The single-step prediction error of the first 10 s is not calculated since the clock bias data is used to fit the initial RFFLS parameters. It can be seen from Fig. 4 that the better frequency stability of clock, the smaller single-step prediction error of clock bias, and the more accurate RFFLS fits the parameters.

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Fig. 3. Curve: allan deviation of clock source

Fig. 4. Curve: single-step prediction deviation of clock bias before losing lock

After the tracking loop of timing receiver loses locking (61–120 s), the multi-step prediction error and the corresponding detection thresholds in the scenario of normal and sophisticated meaconing are shown in Fig. 5. The detection threshold of TCXO1 with poor stability is at the microsecond level, which is higher than the clock bias step amplitude, and the spoofing cannot be detected. The detection thresholds of better TCXO2, OCXO and CSAC are at the hundreds of

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Fig. 5. Curve: multi-step prediction deviation of clock bias after losing lock

nanoseconds level, ten nanoseconds and nanoseconds, respectively. It is lower than the clock bias step amplitude and the spoofing will be detected. According to the conclusion of Sect. 2.2, tJR is used as the minimum value of t in sophisticated meaconing scenario, and the relationship between T , ctJR and detection probability PD is analyzed. The results are shown in Fig. 6. Because the longterm stability of the crystal oscillator is poor, and the distance between the meaconer and receiver is too far will limit the ranging accuracy and affect the spoofing success, hence PD in the short-term range is discussed (T ≤ 1000 s, ctJR ≤ 1000 m). It can be seen from Fig. 6 that the farther distance between meaconer and receiver, the sooner time from previous correction, and the better frequency stability of clock, the higher detection probability. Furthermore, if PD of meaconing is required to be higher than 99%, then the areas that T and ctJR satisfied are shown in Fig. 7. Because TCXO1 with poor stability, only T < 70 s can achieve a required detection probability, which is impossible in actual scenario, while for TCXO2 with better frequency stability, T is not more than 300 s. For OCXO, ctJR < 160 m and T are long enough to reduce the detection probability, and PD is much higher than TCXO. Because meaconer cannot be too close to receiver in the actual scenario, it is believed that OCXO can effectively detect meaconing in the short term. However, PD of CSAC is almost more than 99% within the discussion scope. In addition, corresponding to the conditions of 60 < T < 120 and ctJR = 244 m in the simulation to Fig. 6 and Fig. 7, it can be verified that only TCXO1 cannot detect spoofing effectively, which is consistent with the result of Fig. 5.

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Fig. 6. The relationship between detection probability and influencing factors

Fig. 7. Over 99% detection probability area (white)

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4 Conclusion This paper analyzes the influence of meaconing attack on timing receivers, proposes a spoofing detection method based on RFFLS clock bias prediction, and analyzes the factors that affect the detection probability. The results show that the better frequency stability of clock, the farther distance between meaconer and receiver, and the sooner detection time from last clock bias correction, the higher probability of spoofing detection. If the timing receiver users need a detection probability of more than 99% in a short term (in 1000 s), the time from last clock bias correction cannot exceed 70 s for low-quality TCXO, it cannot exceed 300 s for high-quality TCXO, the distance between meaconer and receiver cannot be less than 160 m for OCXO and there is almost no limit for CSAC. Acknowledgements. This paper is funded by the National Natural Science Foundation of China under grant nos. 62003354 and the National Ministry and Commission Project under grant no. 2019-JCJQ-JJ-190.

References 1. Wu, H., Li, B., Wu, J.: Beidou Timing Technology and Its Application. Publishing House of Electronics Industry (2016) 2. Wang, F., Hu, C., Wu, S., Tao, Y., Xu, Y.: Research on BeiDou anti-spoofing technology based on comprehensive radio determination satellite service. Satell. Navig. 1(1), 1–9 (2020). https:// doi.org/10.1186/s43020-019-0004-2 3. Huang, L., Tang, X., Wang, F.: Anti-spoofing techniques for GNSS Receiver. Geomat. Inf. Sci. Wuhan Univ. 36(11), 1344–1347 (2011) 4. Psiaki, M.L., Humphreys, T.E.: GNSS spoofing and detection. Proc. IEEE 104(6), 1258–1270 (2016) 5. Huang, L., Gong, H., Zhu, X., Wang, F.: Research of re-radiating spoofing technique to GNSS timing receiver. J. Natl. Univ. Defense Technol. 35(04), 93–96 (2013) 6. Liu, Y., Li, S., Fu, Q., Zhou, Q.: Chip-scale atomic clock aided INS/GNSS integrated navigation system spoofing detection method. J. Chin. Inert. Technol. 27(5), 654–660 (2019) 7. Zhu, X., Wu, Y., Gong, H., et al.: GNSS timing receiver toughen technique in complicated jamming environments. J. Natl. Univ. Defense Technol. 37(03), 1–9 (2015) 8. Becker, G.T., Lo, S., De Lorenzo, D., et al.: Efficient authentication mechanisms for navigation systems - a radio-navigation case study. In: Proceedings of the Institute of Navigation National Technical. Meeting. Institute of Navigation (2009) 9. Song, C., Wang, F., Zhuang, Z.: A method for GPS receiver clock offset prediction based on the forgetting factor least squares. Sci. Surv. Mapp. 59(A1), 41–43 (2008) 10. Yu, H., Hao, J., Liu, W., et al.: A real-time anomaly monitoring algorithm for satellite clock. Geomat. Inf. Sci. Wuhan Univ. 41(1), 106–110 (2016) 11. Dong, S.: Study on several important technical issues in time-keeping. National Time Service Center. Chinese Academy of Sciences (2007) 12. Tavella, P.: Statistical and mathematical tools for atomic clocks. Metrologia 45(6), S183 (2008) 13. Sturza, M.A.: GPS navigation using three satellites and a precise clock. Navigation 30(2), 146–156 (1983)

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14. Ramlall, R. Streeter, J., Schnecker, J.F.: Three satellite navigation in an urban canyon using a chip-scale atomic clock. In: Proceedings of the Institute of Navigation National Technical. Meeting. Institute of Navigation (2011) 15. Li, Y.: Research on the technology of SINS/GPS ultra-tight integration navigation system. Beihang University (2012) 16. Ba, X. Luo, S., Chen, J.: A method for producing digital IF data of GPS/BDS satellite. Institute of Microelectronics of the Chinese Academy of Sciences (2016) 17. Test and Assessment Research Center of China Satellite Navigation Office. Data download. http://www.csno-tarc.cn/support/downloads. Accessed 22 May 2021 18. Kasdin, N.J.: Discrete simulation of colored noise and stochastic processes and 1/fα power law noise generation. Proc. IEEE 83(5), 802–827 (1995) 19. Curran, J.T., Lachapelle, G., Murphy, C.C.: Digital GNSS PLL design conditioned on thermal and oscillator phase noise. IEEE Trans. Aerosp. Electron. Syst. 48(1), 180–196 (2013) 20. Kou, Y., Zhang, Q.: A method for simulating the crystal oscillator errors in GPS receiver. J. Electron. Inf. Technol. 8, 1319–1324 (2004) 21. Bruggemann, T.S., Greer, D.G., Walker, R.: Chip scale atomic clocks: benefits to airborne GNSS navigation performance (2006)

An Unambiguous Acquisition Algorithm for TC-OFDM Signals Based on BOC Modulation Jingrong Liu(B) , Zhongliang Deng, Kai Luo, Shihao Tang, and Xiwen Deng Beijing University of Posts and Telecommunications, 10th Xitucheng Road, Beijing, China [email protected]

Abstract. The utilization of binary offset carrier (BOC)-modulated signal in communication and navigation fusion system is promising, which can share the communication and navigation frequency band as well as improve the positioning accuracy. In this paper, BOC modulation is introduced into the time and code division orthogonal frequency division multiplexing (TC-OFDM) system, leading to multiple peaks of autocorrelation function (ACF), which will absolutely result in acquisition ambiguity in the traditional BPSK signal receiver. An unambiguous acquisition method based on reconstruction of side peak suppression (RSPS) is proposed. By constraining the non-linear combination of local waveform and received signal without side peak, the local waveform unambiguous waveform set is obtained, and the autocorrelation function is reconstructed. Theoretical analysis and simulation results show that under a good condition of SNR, the unambiguous acquisition algorithm RSPS proposed in this paper can compress the correlation peak width of the BOC (14, 2) modulated communication and navigation fusion signal by more than 80% under the same detection probability as the traditional acquisition method. Keywords: Communication and navigation fusion system · TC-OFDM · BOC · Unambiguous acquisition

1 Introduction With the application and popularization of “BeiDou +5G”, communication navigation fusion system has become a hot research topic. In the common-band system of communication and navigation fusion system, communication signals and navigation signals share the frequency band, positioning signals can assist communication signals to access rapidly, and the wide bandwidth of communication signals can provide reliable data transmission for positioning. The TC-OFDM system realizes wide-area and highprecision indoor and outdoor seamless positioning, making up for the lack of accurate positioning of GPS in the city due to the shelter of buildings and weak indoor signal [1]. The introduction of binary offset carrier (BOC) modulation in TC-OFDM system can use frequency band resources more efficiently and solve the problem of spectrum congestion caused by the continuous expansion and upgrading of the communication © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 435–444, 2021. https://doi.org/10.1007/978-981-16-3146-7_40

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and navigation integrated system. At the same time, the spectrum splitting characteristics can improve the accuracy of positioning. However, the multi-peak characteristic of the autocorrelation function of BOC modulated signal will lead to the problem of fuzziness in the acquisition and tracking process. In order to solve the deterioration of receiver performance caused by BOC modulation, unambiguous acquisition technology was proposed and widely studied by scholars at home and abroad [2–5]. The representative unambiguous acquisition methods are BPSK like method and various derivative edge peak elimination methods. Generalized removing ambiguity via side-peak suppression (GRASS) algorithm is a kind of general BOC signal unambiguous acquisition algorithm, which can realize the unambiguous acquisition very well [6–8], but the loss of high-order BOC signal acquisition is large. In order to solve the problem of the acquisition ambiguity caused by multiple peaks of autocorrelation function in BOC-modulated TC-OFDM signals, this paper proposes a new unambiguous acquisition method based on reconstitution of side peak suppression (RSPS), and realizes the unambiguous acquisition which bring great performance improvement to the communication and navigation fusion positioning system.

2 An Unambiguous Acquisition Algorithm Based on Reconstruction of Side Peak Suppression 2.1 BOC Modulated Communication and Navigation Fusion Signal Model In TC-OFDM system positioning signal and communication signal are fused by co-band transmission. The frequency bands occupied by communication signal and positioning signal are overlapped, and different signals can be distinguished by different transmission power. PN code modulation is used to modulate baseband signal to generate spread spectrum signal and the baseband spread spectrum signal is modulated by the subcarrier square wave to generate BOC baseband signal and finally, the BOC modulated signal is modulated to the carrier. The generation principle is shown in Fig. 1

Fig. 1. Schematic diagram of the generation of BOC modulation communication and navigation fusion signal

We assume that the waveform of local code is √ rCN (t) = 2PD(t − τ (t))s(t − τ (t))exp{j[2π(fIF + fd )(t − τ (t)) + θIF ]} + n(t) (1)

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P is the power of the receive signal, D is the data code, S is the PN code, fIF is the intermediate frequency, fd is the doppler frequency, τ (t) is the propagation delay of signal, θIF is initial carrier phase, n(t) is additive Gaussian white noise with mean 0 and variance σn2 . After the complex signal is converted by A/D, the discrete digital IF signal which can be processed by the receiver baseband is obtained. The signal can be expressed as: √ i(n) = 2PD(n − τ )s(n − τ )sin(2π(fIF + fd )t(n) + θIF ) + ni (n) (2) q(n) =

√  2PD(n − τ )s(n − τ )cos(2π(fIF + fd )t(n) + θIF ) + nq (n

The received BOC modulation signal can be simply expressed as: √ rBOC = 2PD(n − τ )s(n − τ )sc(t)cos(ωt + θ) + n(t)

(3)

(4)

ω is the carrier frequency, τ is the propagation delay of signal, θ is initial carrier phase, sc(t) is the subcarrier. According to the subcarrier phase, the BOC signal is divided into sinusoidal BOC signal and cosine BOC signal, and the BOC signal is referred to as sinusoidal BOC signal later.  sgn(sin(2π fsc )t) sine − modulation sc(t) (5) sgn(cos(2π fsc )t) cosine − modulation The subcarrier frequency fsc = m × 1.023 MHz, spread-spectrum code rate fs = n × 1.023 MHz, BOC signal can be simply expressed as BOC (m, n), modulation order is defined as M = 2 m/n. 2.2 Characteristics of BOC Modulation Conduction Fusion Signal 2.2.1 Power Spectral Density BOC modulation leads to the spectrum splitting of communication and navigation fusion signals, its normalized power spectral density can be expressed as ⎧  2 f ⎪ sin( 2fπsc )sin( πfsf ) ⎪ ⎪ M is an even number ⎨ fs πf cos( π f ) 2fsc GBOC−CN (f ) (6)  2 f ⎪ sin( 2fπsc )cos( πfsf ) ⎪ ⎪ f M is an odd number ⎩ s πf πf cos( 2fsc )

Figure 2 shows the spectrum comparison of BPSK, BOC (1, 1) and BOC (14, 2) modulated TC-OFDM signals. It can be seen from the diagram that the spectrum of TCOFDM signal modulated by BOC is obviously split compared with BPSK modulation, and the higher the modulation order M, the greater the spectral peak spacing. Inspired by this, subsequent studies can consider using BOC with different modulation orders to modulate communication signals and navigation signals, so as to realize the fusion of communication and navigation signals.

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Fig. 2. The power spectrum of the BPSK modulated and BOC modulated communication and navigation fusion signal

2.2.2 Autocorrelation Function The expression of the BOC modulated communication and navigation fusion baseband signal is rBOC−CN (t) = s(t)

M −1 k=0

(−1)k ϕk (t)

M is the order of BOC modulation signal, ϕk (t) is pulse function.  c (k+1)Tc ] 1 t[ kT M , M ϕk (t) = 0 others

(7)

(8)

The autocorrelation function of BOC modulated communication and navigation fusion signal can be expressed as    2 (−1)k+1 − 2k M−2k + 2k − 1 − (2M − 2k + 1)|τ | |τ | ≤ Tc (9) Rτ = 0 others Among them, k = M |τ |, · represents an upward integer. Figure 3 shows the normalized autocorrelation function curve of BPSK, BOC (1, 1) and BOC (14, 2) fusion signals. It can be seen from the Fig. 3 that compared with the autocorrelation function of BPSK signal, the autocorrelation function of BOC modulation signal has multiple subpeaks in addition to the main peak, and the number of side-peaks increases with the increase of modulation index. The main peak of the autocorrelation function of the BOC modulated communication and navigation fusion signal has a larger slope and a smaller width, which will bring higher code tracking accuracy and stronger multipath resolution to the communication and navigation fusion signal. However, the multi-peak property of autocorrelation function will lead to the possibility of capturing or tracking its side-peak in the acquisition and tracking process of communication and navigation fusion signal, which is the ambiguity of BOC signal.

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Fig. 3. The autocorrelation function of the BOC modulated communication and navigation fusion signal

2.3 The Principle of the Reconstitution of Side Peak Suppression Algorithm In order to eliminate the influence of the side peak in the autocorrelation function on the acquisition of the communication and navigation fusion signal, it is necessary to eliminate the edge peak of the BOC communication and navigation fusion signal. By restricting the nonlinear combination waveform of the local waveform and the synthetic waveform of the received signal, there is no positive edge peak, and the local waveform without fuzzy waveform set is obtained, and the local waveform is selected. Figure 4 gives the schematic diagram of edge peak elimination reconstruction algorithm.

Fig. 4. The schematic diagram of the RSPS algorithm

We suppose the waveform of local code is s(t) =

M −1 k=0

sk ϕk (t)

(10)

sk is the value of each chip for local code waveform, its value is multilevel, k = 0, 1, · · · , M − 1. The RSPS algorithm needs to use the cross-correlation function of the local code and BOC communication and navigation fusion signal of to construct a new waveform.

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The correlation function of local code and BOC signal is

 ⎧ (k+1)Tc τM c ⎪ r + − k (rk+1 − rk ), kT ⎪ k Tc  M ≤τ ≤ M ⎨

RB/L (τ ) = rk−M + τ M − k + M (rk−M +1 − rk−M ), (k−M )Tc ≤ τ ≤ Tc M ⎪ ⎪ ⎩ 0, |τ | > Tc

(k−M +1)Tc M

(11) Among them rk is values at each point of cross-correlation function of the local code and BOC communication and navigation fusion signal ⎧ 1 M −1−k (−1)i si+k , 0 ≤ k ≤ M − 1 ⎨ M i=0 M −1−k rk = M1 (12) (−1)i−k si , 1 − M ≤ k < 0 i=0 ⎩ 0, |k| ≥ M The core idea of the RSPS algorithm is to keep the main peak of autocorrelation function and suppress the side peak, therefore, to obtain the unambiguous waveform set, the cross-correlation function between the local code and the BOC signal should satisfy: τ = 0 the value is 0, with respect to τ = 0 symmetry and high matching with BOC autocorrelation function waveform, which can be expressed as ⎧ r0 = 0 ⎪ ⎪ ⎨ ri = −ri (13) ⎪ rr < 0, i > 0 ⎪ ⎩ i i+1 ri ri−1 < 0, i < 0 From Eq. 12 and Eq. 13, it can be obtained that RSPS algorithm’s constraint condition of local code is ⎧ M −1 2 d =M ⎨ k i=0 i i (14) i=0 (−1) d i > 0 ⎩ di = dM −i−1 , i = 1, 2, · · · , M2 − 1 Reconstituting of the correlation signal  2 R(τ) = |RB (τ )|2 − xRB/L (τ )

(15)

Among them x is reconstituting coefficient. The problem of finding the local optimal matching waveform is essentially an optimization problem. The constraint condition is formula 14. The objective of optimization is to eliminate the edge peaks. The value of reconstruction coefficient is related to the noise introduced, so the minimum value should be selected. x = 2M − 3 The optimal local waveform is  d0 = dM −1 = di = dM −i−1 =

(−1)i−1 √ ,i 2M −3

√M −1 2M −3

= 1, 2, · · · , M2 − 1

(16)

(17)

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For BOC (14, 2) signal, the local waveform corresponding to M = 14 is ⎧ d0 = d13 = 13 ⎨ 5 d1 = d3 = d5 = d8 = d10 = d 12 = 15 ⎩ d2 = d4 = d6 = d7 = d9 = d 11 = − 15

441

(18)

3 Performance Analysis In order to analyze the performance of RSPS unambiguous algorithm for BOC modulated TC-OFDM signal acquisition in this paper, in this section, the theoretical analysis of the algorithm performance in this paper is completed by calculating the detection probability Pd of the RSPS edge peak reconstruction elimination algorithm under the fixed false alarm rate Pfa . Assuming that the noise is Gaussian white noise, let Pn (x) be a noise power spectral density function with zero mean value. When there is no useful signal in the received signal, x obeys the central χ 2 distribution with degree of freedom 2, and its probability density distribution function is Pn (x) =

1 e 2σ12

− 2σx



(19)

1

False alarm rate Pfa can be expressed as  ∞ Pfa = Pn (x)dx

(20)

TH

Detection probability can be expressed as  Pd = PT (V > VT |The signal exists) =

∞

Ps (x)dx

(21)

VT

When there is TC-OFDM signal in the received signal, x obeys the non-central χ 2 distribution with degree of freedom of 2. Let Ps (x) be the power spectral density function of communication and navigation fusion signal and noise superposition. √ L−1 √  2 x xλ 1 − x+λ2 2σ ,x > 0 ) e ( IL−1 Ps (x) = 2σn2 λ σ2

(22)

IL−1 (x) is the modified Bessel function for the first kind. λ = L · CNR · T (R2B/L1 + R2B/L2 ) δ12 = 2L · CNR · T δ22 = 2L · CNR · T

R2B/L1 (ε) R2L2 (ε) R2B/L1 (ε) R2L2 (ε)

(23)

(24)

(25)

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T is the coherent integration time, ε is the phase estimation deviation of local reconstruction code, RB/L1 and RB/L2 are the cross-correlation functions between the leading and lagging codes and the BOC signal. Using Q function [9] to approximate the detection probability of capture results.   TH − μ (26) Pd (TH ) ≈ Q  δ1 2 + δ1 2 Among them Q(x) is Gaussian Q function, μ is the mean value of the test standard, and TH is the threshold value set by acquisition. The main purpose of RSPS algorithm is to eliminate the acquisition ambiguity in signal synchronization, but it will also bring some performance loss. Compared with the traditional algorithm, incoherent accumulation brings additional multiplicative additional noise. In the case of small Doppler effect estimation error, RSPS non-ambiguity acquisition algorithm is more suitable for coherent integration time unrestricted pilot channel.

4 Analysis of Simulation Results In order to verify the above proposed RSPS unambiguous acquisition algorithm of communication and navigation fusion signal based on BOC modulation, this section simulates and compares the autocorrelation function reconstructed by BOC (14, 2) autocorrelation function and RSPS algorithm in MATLAB, and finally obtains the results shown in Fig. 5. In the figure, only the envelope near the main peak position is selected, and the negative half axis of the y axis of the BOC (14, 2) autocorrelation function is not concerned.

Fig. 5. The autocorrelation function reconstructed by the RSPS

It can be seen from Fig. 5 that the RSPS algorithm improves the autocorrelation function of the BOC (14, 2) modulated communication and navigation fusion signal

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obviously, only the main peak is retained, and the width of the main peak is basically unchanged. At the same time, all the side peaks are matched and eliminated by using the local reconstructed waveform, which completely eliminates the side peaks and significantly improves the acquisition accuracy of the communication and navigation fusion signal. Compared with the traditional BPSK modulation method in TC-OFDM system, the correlation peak width is reduced by 80%, what’s more the increase of the slope of the correlation peak will also enhance the anti-interference ability of the communication and navigation fusion system and the ranging accuracy in complex indoor scenes will also be greatly improved.

Fig. 6. Acquisition detection probability of the traditional and RSPS algorithm

From Fig. 6, it can be seen that the acquisition and detection probability of BOC (14, 2) modulation channel fusion signal based on RSPS algorithm is significantly lower than that of traditional BPSK modulation channel fusion signal when the SNR condition is poor. However, when the SNR condition is good (above −19 dB), the acquisition detection probabilities of the two modulation schemes are both above 90%.

5 Conclusion This paper introduces the characteristics of TC-OFDM system, signal model and BOC modulation signal, and verifies the theoretical derivation and simulation experiment. The acquisition algorithm of BOC (14, 2) modulation and communication and navigation fusion signal without ambiguity based on the reconstruction of Side Peak Suppression (RSPS) is proposed. By restricting the non-linear combination waveform of the local waveform and the synthesized waveform of the received signal without positive side peaks, the local waveform without ambiguity waveform set is obtained, and the local waveform is optimized, and the correlation function without ambiguity is reconstructed. Finally, the simulation verifies the effectiveness and excellent performance of the algorithm in this paper. The results show that the introduction of BOC (14, 2) modulated

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communication and navigation fusion signal with the adoption of the RSPS unambiguous acquisition algorithm proposed in this paper has a certain practical value for reducing the probability of false acquisition and improving the positioning accuracy of the communication and navigation fusion signal receiver. Acknowledgments. This work was financially supported by the National Key Research & Development Program under Grant No. 2017YFC08220 and No. 2018YFC0809702

References 1. Research on the Key Technologies of TC-OFDM Indoor Positioning Receiver Baseband Signal Processing. Beijing University of Posts and Telecommunications (2013) 2. Martin, N., Leblond, V.: BOC(x, y) signal acquisition techniques and performances. In: Proceedings of ION GPS/GNSS 2003, Portland, OR, pp. 188–198 (2003) 3. Ries, L., Lestarquit, L., et al.: A software simulation tool for GNSS2 BOC signals analysis.. In: Proceedings of U.S. Institute of Navigation GPS Conference, Portland, OR, pp. 2225–2239 (2002) 4. Heiries, V., Roviras, D., et al.: Analysis of non- ambiguous BOC signal acquisition performance. In: Proceedings of ION GNSS, Long Beach, CA, pp. 2611–2622 (2004) 5. Avellone, G., Frazzetto, M., Messina, E.: On the acquisition ambiguity for Galileo BOC(n, n) modulated signals. In: Proceedings of IEEE ICC, pp. 4438–4443 (2007) 6. Zhou, Y., Hu, X., Ke, T., Tang, Z.: Ambiguity mitigating technique for cosine-phased binary offset carrier signal. IEEE Trans. Wirel. Commun. 11(6), 1981–1984 (2012) 7. Yao, Z., Lu, M., Feng, Z.: Unambiguous sine-phased binary offset carrier modulated signal acquisition technique. IEEE Trans. Wirel. Commun. 9(2), 577–580 (2010) 8. Julien, O., Macabiau, C., Bertrand, E.: Analysis of Galileo E1 OS unbiased BOC/CBOC tracking techniques for mass market applications. In: 2010 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (N AVITEC), pp. 1–8 (2010) 9. Simon, M.K.: The nuttall Q function—its relation to the marcum Q function and its application in digital communication performance evaluation. IEEE Trans. Commun. 50, 1712–1715 (2002)

Research on Carrier Tracking Algorithm of INS-Assisted TC-OFDM Receiver with Fuzzy Control Guoshun Tang(B) , Fuxing Yang, Zhongliang Deng, Xiwen Deng, and Shiwen Jiang Beijing University of Posts and Telecommunications, Beijing, China [email protected]

Abstract. The Time and Code Division-Orthogonal Frequency Division Multiplexing (TC-OFDM) system multiplexes the resources of mobile communication network and has an indoor distributed system, which can achieve indoor and outdoor wide-area coverage of positioning signal. Considering the indoor complex environment, dynamic stress or occlusion will cause a large fluctuation of positioning signal. In order to prevent the sudden change of carrier to noise ratio (CNR) and the loss-of-lock, this paper proposes an INS-assisted receiver carrier tracking algorithm. Through the introduction of fuzzy control, the observation output by the TC-OFDM receiver loop and INS are judged, the fusion switching of INS aided TC-OFDM receiver carrier tracking loop state is controlled, so as to improve the indoor environmental adaptability of the receiver and ensure the robustness of the deeply integrated system in a complex environment. The simulation results show that the algorithm can effectively prevent the loss-of-lock and the divergence of deeply integrated navigation system caused by the sudden change of CNR, and improve the dynamic performance of the receiver. Keywords: INS · TC-OFDM · Integrated navigation · Fuzzy control

1 Introduction With the advent of 5G and the Internet of Everything, location information technology has been paid more and more attention [1]. The traditional wide-area coverage positioning system, such as the Global Navigation Satellite System (GNSS), can provide good location services outdoors. However, when the user is in the indoor environment, it is difficult to provide the same high-precision indoor location services because the signal is vulnerable to occlusion. At the same time, the Time and Code Division-Orthogonal Frequency Division Multiplexing (TC-OFDM) system can realize wide-area broadcasting of positioning signals by being mounted on communication base stations, and can also provide indoor location users with enhanced TC-OFDM positioning signals that meet predetermined indicators through the indoor distributed system, And a highly sensitive positioning receiving terminal is designed, which can effectively solve the problem of indoor positioning difficulty. However, due to the blocking and interference of indoor

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 445–455, 2021. https://doi.org/10.1007/978-981-16-3146-7_41

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positioning signals caused by non-line-of-sight propagation, and the positioning accuracy of a receiver is damaged. The Inertial Navigation System (INS) can operate independently without any external information [2, 3]. It can provide high-precision motion measurement at a certain time after initial alignment. Therefore, the TC-OFDM receiver and INS can complement each other well in indoor positioning. Some scholars have consideried the use of integrated navigation to improve the positioning performance and anti-interference ability of the indoor receiver, and did not in-depth study the INS-assisted TC-OFDM receiver loop switching method and criteria. Taking into account the complexity and variability of the indoor environment, the carrier is subject to dynamic stress and other conditions, which can easily lead to the sudden change of carrier-to-noise ratio (CNR), leading to the receiver loop losing lock and the system divergence. This paper proposes a carrier tracking algorithm for the INS-assisted TC-OFDM receiver loop with fuzzy control, which can adaptively adjust the on-off and related assistant parameters of the INS-assisted TC-OFDM receiving carrier loop switch according to external conditions. The algorithm can track the positioning signal stably even if the CNR changes suddenly or the environment changes dynamically, which improves the robustness of the entire combined system.

2 The Traditional Carrier Tracking Algorithm Because the TC-OFDM base station transmits a positioning signal that shares the same frequency band with the communication signal, the wavelength of a corresponding carrier is much shorter than the length of a Weil code, the loop band-width of the carrier loop is also much larger than the loop bandwidth of the code loop, the carrier loop is subject to greater dynamic stress than the code loop, the carrier loop is the weak link of the TC-OFDM receiver. From this level, as long as the problem of dynamic stress can be solved from the carrier tracking, it can alleviate to a certain extent the loss-of-loop to the receiver. In the carrier tracking loop, although the phase-locked loop (PLL) has larger noise bandwidth and worse tolerance to dynamic stress than the frequency-locked loop (FLL), it can achieve better carrier phase tracking accuracy [4]. After a trade-off, the general TCOFDM receiver chooses the commonly used second-order FLL to assist the third-order PLL to achieve stable tracking of the carrier phase. The two subsystems of the traditional TC-OFDM/INS tightly integrated navigation system are generally combined in the ranging fields of pseudorange, carrier phase, and Doppler shift. Since the output of the observation by the INS have not entered the tracking loop of the receiver, the carrier tracking algorithm of the integrated navigation system is generally a second-order FLL assisted third-order PLL. Although the tightly integrated navigation system has been able to effectively combine the advantages of both sides to a certain extent, it does not improve the tracking performance of the TC-OFDM receiver in essence. In order to further improve the anti-interference ability and positioning performance of the positioning receiver, the observations obtained by the IMU sensor can be fed back to the tracking loop of the TC-OFDM receiver. Compared with the tightly integrated navigation system mentioned above, although the TC-OFDM/INS deep integrated navigation system puts forward higher requirements on the loop structure of the receiver,

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at the same time, the receiver tracking loop can effectively reduce the loop filter bandwidth according to the movement of the carrier, thereby achieving an improvement in the signal-to-noise ratio. As mentioned before, INS can be used to replace the second-order FLL to assist the PLL to complete the carrier tracking of the receiver, which not only avoids the influence caused by the dynamic stress that is limited by the loop bandwidth, but also avoids the interference caused by various environmental factors. When the receiver is indoors and in a static state, the INS has no output of velocity and acceleration, and the carrier tracking loop of the receiver degenerates to the thirdorder PLL. When the receiver is in the dynamic scene, the INS can calculate the velocity and acceleration information according to the motion of the carrier and feed it back to the carrier loop of the receiver, so that the loop can quickly adjust the internal numerical control oscillator (NCO), the receiver still has the best tracking performance. This design can make full use of the applicability of the INS to the dynamic scene, reduce the noise bandwidth of the PLL and maintain high tracking accuracy.

3 INS-Assisted TC-OFDM Carrier Tracking Algorithm with Fuzzy Control 3.1 The Whole Frame In the previous section, the traditional INS-assisted third-order phase-locked loop structure of the TC-OFDM receiver was introduced. Due to the direct connection between the two for combination, there is no effective isolation between each other, and it is impossible to determine under what circumstances the INS is required for assistant output. In this case, INS failure will lead to the direct coupling tracking loop losing lock, even the whole integrated navigation system diverging. In order to improve the robustness of the integrated navigation system, this paper applies the fuzzy control to the carrier tracking algorithm of the traditional INS-assisted TC-OFDM receiver loop introduced in the previous section. The structure of the carrier tracking algorithm of the deeply integrated navigation system is shown in Fig. 1. This figure reflects the main components of the carrier tracking algorithm for deep combined systems proposed in this article. The algorithm consists of four parts: TC-OFDM receiver carrier loop unit, INS unit, fuzzy estimation unit, and INS-assisted loop switch unit. The traditional second-order FLL assisted third-order PLL, the FLL with larger noise bandwidth is used to quickly pull in and firmly track the weak positioning signal, and then the PLL accurately measures the carrier frequency and phase of the tracking signal. The switching between the two is achieved by real-time comparison of a preset CNR threshold, but the threshold is generally an empirical value based on environmental measurements. Because PLL has better tracking ac-curacy and flexibility, the algorithm proposed in this paper still uses the third-order PLL as the main structure of carrier tracking loop, and INS is used to improve the dynamic performance of the loop, the fuzzy control is used to realize the fusion switching of second-order FLL and INS. The specific switching criteria of the structure are as follows: in the case of receiver cold start or loop loss lock, the receiver loop uses second-order FLL to assist third-order

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Positioning /Fixed speed calculation

Carrier frequency auxiliary unit

INS auxiliary loop switch unit

INS module Integrator /Zeroer Carrier loop phase detector

Pseudo code stripping

Integrator /Zeroer

...

Fuzzy estimation

Loop filter CNR calculation

Voltage-controlled oscillator

Phase detection error

Fig. 1. Introduce fuzzy control deep combination tracking algorithm block diagram

PLL to fast traction and accurately track the signal; in the harsh environment of high dynamic or low CNR, the INS-assisted third-order PLL can be used to work; when the integrated navigation system is in the condition of low dynamic or high CNR, the loop degenerates into a third-order PLL to output high-precision carrier phase measurement. The filter parameters corresponding to each loop state are the optimal invariant values obtained from the actual measurement simulation. 3.2 Fuzzy Estimation Unit and Fusion Switching Coefficient As mentioned above, CNR can measure and help determine whether the receiver is tracking the TC-OFDM positioning signal well. At the same time, the change rate of CNR (DCNR) is also used as the input of the fuzzy controller, and DCNR takes the change value of CNR at a time interval of 2 s. The above two inputs calculate the fusion switching coefficient β, which together affect the fusion state of INS and receiver carrier loop. The coefficient value β represents the weight value input to the loop filter occupied by the FLL and the PLL loop discriminator, and can dynamically reflect the loop state of the carrier tracking loop at this time. In order to maintain the adaptability and tracking performance of the receiver in various environments, the initial value of the fusion switching coefficient β is set to 0.5, at this time, the weights of the second-order FLL and the third-order PLL are the same, the carrier loop of the receiver is the second-order FLL-assisted third-order PLL; Then according to the change of CNR of the received signal for a period of time, the corresponding DCNR value is obtained, and the β value in this state is calculated. When the CNR calculated by the receiver loop increases, the value of β will be increased to switch the loop to the PLL so as to suppress the noise error caused by the introduction of FLL; When the CNR calculated by the receiver loop decreases, β will be reduced and the INS unit will be introduced to assist the receiver loop to enhance the dynamic

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performance of the tracking loop and ensure the carrier tracking accuracy as far as possible. Both the fuzzy estimation unit in this section and the INS-assisted loop switch unit mentioned in the next section are realized by the fuzzy controller, which is the core part of the fuzzy estimation unit. According to the above fuzzy control input and output variables, the corresponding fuzzy controller can be designed. According to the fuzzy control theory, the fuzzy controller is mainly composed of four parts: fuzzify, knowledge base, fuzzy reasoning, and defuzzify [5, 6]. Due to the mixed-signal and noise components in the received positioning signal, the TC-OFDM receiver’s CNR measurement method uses the difference of signal plus noise power in different noise bandwidths to deduces the value of CNR. The calculation formula is shown in the following Eq. (1). 1 μp − 1 C = N0 Tcoh M − μp

(1)

Among them, Tcoh is the correlation integration time, M is the number of epochs, and μp  is the average ratio of the broadband power with bandwidth 1 T to the narrowband coh  power with a bandwidth of 1 MTcoh . It is necessary to determine the universe of input and output variables for fuzzy reasoning [6]. By collecting a large number of TC-OFDM positioning signals in various indoor environments, and processing the received data. it is found that the CNR variation range of TC-OFDM signals can be characterized from 25 dB/Hz to 45 dB/Hz in most cases. The domain of CNR is expressed by CNR → X1 = { 25 28 32 37 45 }

(2)

From the above formula and the definition of DCNR, it can be concluded that the range of DCNR is −10 to 10, and the domain of DCNR is expressed by DCNR → X2 = { −10 −5 0 5 10 }

(3)

According to the Monte Carlo theory [7], and the range of the fusion switching coefficient is defined as 0 to 1, so the domain of is expressed by   β → X3 = 0 0.2 0.5 0.8 1 (4) The fuzzy controller in this paper is based on the reasoning mechanism of the Mamdani algorithm [8]. And the input and output fuzzy variables are expressed as negative big (NB), negative small (NS), zero (Z), positive small (PS), and positive big (PB) in fuzzification language. The membership function is a triangular-shaped function, as shown in Fig. 2. The fuzzy control rules as shown in the following formula, in which the relation word adopts IF-and-Then:       j j j (5) IF X1 = Y1 and X2 = Y2 Then X3 = Y3 j = 1, 2, · · · , 25

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Fig. 2. Membership function graph j

j

j

In the above formula, Y1 , Y2 and Y3 are fuzzy sets of the membership function. Since two input variables have seven input states, 25 fuzzy rules are needed to express the whole fuzzy controller, and the fuzzy rule Table 1 is established. Defuzzification should also be carried out based on the Mamdani algorithm [7]. In order to make the output smoother, the center of the area algorithm is used to defuzzify. As shown in the following formula. nj

β=

 βj μ βj

j nj  μ βj

(6)

j

Where nj is the total number offuzzy outputs, βj is the specific output value of the jth membership function, and μ βj is the degree of membership corresponding to βj . 3.3 INS-Assisted Loop Switching Unit and Switching Criterion When the PLL is in a locked state, the carrier phase difference between the local carrier and the received signal carrier is close to 0 in theory. However, due to the phase jitter and dynamic stress, the phase detector has a measurement error (denote as θ ). In order to achieve effective isolation between the INS and the receiver loop, and to avoid the receiver loop loss caused by sudden CNR or dynamic stress enhancement. When the receiver loop is separated from the INS module, avoid using the output of the observation by the INS to determine whether the receiver loop needs the assistance of INS. In this case, the phase discrimination error output by the receiver carrier loop can

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Table 1. Fuzzy control rule table DCNR CNR NB

NS Z

PS PB

NB

NB

NB NB NB NS

NS

NB

NS NS NS PS

Z

NB

NS Z

Z

PS

NB

NS Z

PS PB

PB

NB

NS Z

PS PB

PS

be selected as the decision control quantity to reduce the false decision rate of the entire system. Moreover, when the INS-assisted receiver loop works together, the influence of the INS on the system should be considered at this time, and the jerk calculated by the INS can well reflect the movement status of the entire integrated navigation system. In summary, the θ and jerk can be used as inputs to determine whether the INS and receiver loops need to be separated or fused at the same time. If the tracking loop is in the working state of a third-order PLL or a second-order FLL-assisted third-order PLL under INS separation. When the jerk in-creases or the phase discrimination error increases, the INS-assisted loop switching can be closed to switch the loop to INS-assisted third-order PLL, and the loop bandwidth can be adjusted appropriately to improve the dynamic performance. If the receiver is cold started or the tracking loop loses lock, the INS-assisted switch can be disconnected to separate the receiver carrier tracking loop from the INS, so that the receiver loop can quickly capture and pull into the steady-state tracking state. Through the simulation test of a large amount of data, the Fuzzy control rule table of the INS-assisted loop switching unit can be obtained as shown in Table 2, where 0 and 1 represent the switch on-off respectively. Table 2. Fuzzy control rule table of INS-assisted loop switching unit Jerk

Phase detection error θ 0

Pi/32

3Pi/32

Pi/8

5Pi/32

Pi/4

5Pi/16

3Pi/8

0

0

0

0

0

1

1

1

1

5

0

0

1

1

1

1

1

1

10

1

1

1

1

1

1

1

1

When the INS assists the TC-OFDM receiver carrier tracking loop to track the positioning signal stably, the INS unit can replace the FLL to complete the real-time tracking of the carrier frequency. At this time, the carrier loop o will not retain and continuously output the carrier frequency offset. If the INS-assisted switch is directly disconnected, the carrier frequency offset may increase sharply, leading to loss-of-lock

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or even false tracking. Therefore, when the ins and the receiver loop are coupled with each other, the switch cannot be turned off directly; Similarly, when the ins and receiver loop are separated from each other, the switch cannot be closed directly. In order to avoid the sharp change of carrier frequency offset caused by the direct on-off of the switch, This paper introduces the variables fˆdI and facc , which are the carrier doppler frequency estimator of INS and the TC-OFDM receiver tracking loop output frequency accumulated latch respectively, to update the carrier frequency and output it in real-time. Among them, the value of the switch K is still 1 or 0, which respectively indicate onoff. frec is the increased variable to express the output carrier frequency of the tracking loop at the moment, and the loop auxiliary value fAUX is sent to the loop, in order to help the loop determine the carrier frequency offset to adjust the carrier loop NCO. The calculation expression is shown in the following formula. fAUX = (fˆdI − frec ) · K + facc

(7)

When the auxiliary decision control gives an instruction to close the switch K, the value of K is set to 1, and the observation value of frec is received to help update the value of fAUX in real-time. When the auxiliary decision control gives the switch K off instruction, the value of K is set to 0, and the value of fAUX calculated by fˆdI , frec and facc at the previous moment is output to the receiver loop to minimize the risk of loop jitter.

4 Simulation Analysis 4.1 Carrier Tracking Algorithm Comparison Simulation In order to ensure the best tracking performance of the receiver in practical engineering, the loop update time is set to be the same as the coherent integration time [8]. In the simulation, it is necessary to realize the continuous tracking of the carrier signal in the loop. Once the loop losses lock, it should be able to re-track the loop immediately. And the loop parameters of the receiver are as follows: the noise bandwidths of the secondorder FLL and the third-order PLL in the receiver are 2 Hz and 10 Hz respectively, the coherent integration time is 100 ms. And the residual carrier frequency of the signal is 1060 Hz, the code rate of the Weil code is 10.23 MHz. The tracking performance of INS assisteded TC-OFDM receiver carrier tracking algorithm with fuzzy control is compared with the traditional carrier tracking algorithm of the integrated navigation system (Including second-order FLL, third-order PLL, second-order FLL-assisted third-order PLL, and INS-assisted third-order PLL). The Fig. 3a shows the dynamic performance simulation of five carrier tracking methods, in which the 30 s to 50 s of the simulation time, the carrier is placed in a dynamic environment, and when the values of acceleration is g, the values of jerk is 5 g. It can be seen from the Fig. 3a that the carrier tracking loop of the TC-OFDM receiver alone has a poor endurance to dynamic stress. The frequency and phase tracking errors of the carrier fluctuate greatly from 30 s to 50 s. The INS-assisted carrier tracking loop and the algorithm mentioned in this article can significantly improve the receiver loop’s carrier tracking ability to withstand dynamic stress.

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(a)Dynamic performance simulation

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(b) Under the of sudden CNR’s condition

Fig. 3. Comparison simulation chart of each carrier tracking algorithm

When the five carrier tracking methods encounter a sudden change in the CNR of the received signal at the 10 s, the change process of the carrier tracking phase error and the residual carrier frequency is shown in Fig. 3b. It can be seen from the figure that the third-order PLL has the worst resistance to signal fluctuations. When the CNR changes suddenly, the carrier phase error and the carrier frequency error both increase sharply. However, the third-order PLL assisted by INS with fuzzy control introduced in this paper has good stability, which can obviously prevent the increase of tracking error caused by signal fluctuation, and the algorithm proposed in this paper is the best among the five carrier tracking methods. 4.2 On-Off Simulation of INS-Assisted Loop Switch Unit In order to verify the correctness and reliability of the INS-assisted loop switch and switching criteria, this paper makes a comparative simulation, the results are shown in Fig. 4. Among them, figure a is the direct coupling switch without the assistant output of carrier frequency, and the switch is directly turned off in the 4 s, the carrier frequency cannot be tracked stably in that epoch, the frequency tracking error increases linearly, and the loop will jitter sharply and lose lock, which will lead to the divergence of the whole deep integrated navigation system. The Fig. 4b introduces the loop switching unit with the assistant carrier frequency output, so there is no sharp increase in carrier frequency tracking error. Whether the assistant switching unit is turned off at 4 s or turned on at 8 s, the carrier frequency can be tracked stably. Through this simulation, it is verified that the introduction of assistant carrier frequency output to the switching unit, it can significantly increase the stability and robustness of the entire integrated navigation system.

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a. Without the assistant output of carrier frequency

b. Introducing the assistant output of carrier frequency

Fig. 4. The comparative simulation of INS-assisted loop switch unit

5 Conclusion Based on the INS/TC-OFDM deep combined system, this paper introduces a fuzzy control algorithm to realize the fusion and switching of the INS-assisted TC-OFDM receiver carrier tracking loop, a large amount of data is collected in indoor environment, and simulation verification is carried out. The experimental results show that: Comparing the carrier tracking algorithm of the deeply integrated navigation system without fuzzy control and the carrier tracking algorithm relying solely on the TC-OFDM receiver, this algorithm can effectively prevent the receiver loop from losing lock due to the fluctuation of TC-OFDM positioning signal, improve the tolerance of receiver to dynamic stress, and ensure the carrier tracking accuracy of TC-OFDM receiver in indoor environment. Within a certain dynamic range, compared with the existing deep combination system carrier tracking method, the method proposed in this paper can effectively avoid the divergence caused by the sudden change of the environment and improve the robustness of the entire system. Acknowledgments. This work is financially supported by Nation Key Research & Development Program under Grand No. 2016YFB0502001 and No. 2018YFC0809702.

References 1. Xu, R., Chen, W., Xu, Y., Ji, S.: A new indoor positioning system architecture using GPS signals. Sensors 15(5), 10074–10087 (2015) 2. Alban, S., Akos, D.M., Rock, S.M.: Performance analysis and architectures for INS-aided GPS tracking loops. In: Proceedings of the Institute of Navigation National Technical Meeting (1998) 3. Babu, R., Wang, J.: Ultra-tight GPS/INS/PL integration: a system concept and performance analysis. GPS Solut. 13(1), 75–82 (2009)

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4. Liu, W., Bian, X., Deng, Z., Mo, J., Jia, B.: A novel carrier loop algorithm based on maximum likelihood estimation (MLE) and Kalman filter (KF) for weak TCOFDM signals. Sensors 18(7), 2256 (2018) 5. Qin, H., Sun, X., Cong, L.: Using fuzzy logic control for the robust carrier tracking loop in a global positioning system/inertial navigation system tightly integrated system. Trans. Inst. Meas. Control. 36(3), 354–366 (2014) 6. Kamel, A., Renaudin, V., Nielsen, J., Lachapelle, G.: INS assisted fuzzy tracking loop for GPS-guided missiles and vehicular applications. Int. J. Navigat. Observ. 2013, 1–17 (2013) 7. Mo, J., Deng, Z., Jia, B., Jiang, H., Bian, X.: A novel FLL-assisted PLL with fuzzy control for TC-OFDM carrier signal tracking. IEEE Access 6, 52447–52459 (2018). https://doi.org/ 10.1109/ACCESS.2018.2870908 8. O’Driscoll, C., Petovello, M., Lachapelle, G.: Choosing the coherent integration time for kalman filter-based carrier-phase tracking of GNSS signals. GPS Solut. 15(4), 345–356 (2011)

DPCCRW: An Unambiguous Acquisition Technique for High-Order Binary Offset Carrier Modulated Signal Xinming Huang1,2(B) , Zhang Ke1,2 , Jingyuan Li1,2 , Zengjun Liu1,2 , and Gang Ou1,2 1 College of Electronic Science and Technology, National University of Defense Technology,

Changsha, China 2 Tianjin Institute of Advanced Technology, Tianjin, China

Abstract. Binary offset carrier (BOC) modulation has been widely adopted in modern global navigation satellite system (GNSS) not only for its characteristic of spectrum-split, but also for its high measuring precision and good multipath mitigation ability. BOC modulation brings the ambiguity problem due to its multiple peak auto-correlation function (ACF). Especially for high-order BOC modulated signal, the ambiguity problem is more serious as its ACF is more complicated. In the paper, an unambiguous acquisition technique with side-peak cancelation method is proposed for high-order BOC modulated signals. By constructing a new local auxiliary signal, and with the help of the traditional Bump-Jump technique, the risk of false lock has been completely removed. Performance analysis results show that the proposed technique has a significant performance improvement compared with the existing methods. Keywords: Global navigation satellite system · High-order · Binary offset carrier · Unambiguous acquisition

1 Introduction Binary offset carrier (BOC) modulation has been widely adopted in modern global navigation satellite system (GNSS) not only for its characteristic of spectrum-split, but also for its high measuring precision and good multipath mitigation ability [1, 2]. BOC modulation brings perfect characteristics, while it also brings big challenge for new signal receiving as the auto-correlation function (ACF) is of multiple peaks, which might lead to false peak acquisition [3]. Especially for cosine-phased BOC modulated signal, the ambiguity problem is more serious as its ACF is more complicated [4]. In order to guarantee the unambiguous acquisition of BOC signals, several methods are proposed, the bump jump (BJ) technique and the BPSK-like technique are two traditional methods. The BJ technique adopts two auxiliary branches, the very early (VE) and very late (VL) branches to guarantee avoid false peak acquisition, but the performance of the BJ technique depends on the Carrier-Noise-Ratio (CNR) and the amplitude differences between the ACF peaks of receiving BOC signals [5]. Thus the BJ technique © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 456–465, 2021. https://doi.org/10.1007/978-981-16-3146-7_42

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is not suitable for high-order BOC signal. The BPSK-like technique adopts filters to acquire energy of two main sidebands and change the BOC signal into a BPSK signal [6]. It avoids the ambiguous problem confronted, while might need more complicated pull-in process from acquisition to tracking and extra filter resources. The side peak suppression technique achieves unambiguous test criterion by constructing special local reference signals. Several methods based on the side peak suppression technique are proposed. ASPeCT, a typical side peak suppression technique, is proposed to realize unambiguous acquisition and tracking of BOC signals. However, the method can be only used to sine-phased BOC(n, n) signal [7]. The authors in [8] proposed a general unambiguous technique named general removing ambiguity via side peak suppression (GRASS) for all sin-phased BOC signals. By employing a local auxiliary signal, and subtracting the cross-correlation function between the local signal and the received signal from the ACF of the BOC modulated signal, GRASS technique achieves the target of all the positive peaks. The methods proposed in [9, 10] and [11] also achieve unambiguous acquisition for sin-BOC(m, n) signals. While the method in [9] achieves better performance only for high-order BOC signals, and the method in [10] and [11] is of much higher complexity due to its use of time-division switch. Moreover, almost all these techniques are not suitable for both cosine and sine high-order BOC(m, n) signals. The authors in [4] proposed an acquisition technique for cosine-BOC(m, n) signals based on the GRASS technique. By introducing a new special local auxiliary signal, the final correlation function has only two small positive side peaks which are rectified by combing with the classical bump jump (BJ) technique [5]. However, the sensitivity degradation of the proposed method is more severe with the increase of modulation order and non-coherent number of summation. The authors in [12] and [13] achieve unambiguous receiving for BOC(m, n) signals by constructing new local reference signals. The two methods do not need auxiliary branches while confront the problem of heavy performance degradation, especially for high-order BOC signal. In the paper, we propose the unambiguous acquisition technique for high-order BOC signals by introducing a new special local auxiliary signal. The final correlation function has only two positive side peak, which are rectified by combing with the classical bump jump (BJ) technique. The new technique achieves better performance than traditional methods.

2 The Proposed Unambiguous Technique 2.1 BOC Modulation The BOC modulated signal can be expressed as: s(t) = c(t)sign(sin(2π fs t + φ)

(2.1)

Where c(t) is the pseudo random noise (PRN) code, sign(sin(2π fs t +φ) is the square wave, in which f s is the sampling frequency, φ is the initial phase, with values of 0 or 90°. If φ equals to 0°, the signal is a sine-phased BOC modulated signal, otherwise, it is a cosine-phased one.

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In the paper, BOC modulated signal is defined as BOC(m, n), where m is the ratio of the square wave frequency f s to 1.023 MHz, and n is the ratio of the PRN code rate Rc to 1.023 MHz. Sine-phased BOC(m, n) signal can be expressed as:  s(t) = cl (−1)l ϕl (t − lTc ) (2.2) l



c (i+1)Tc 1 t ∈ [ iT M , M ]. 0 others T c is the symbol duration, which is divided into M segments. In the paper, we define cosine-phased BOC(m, n) signal as BOCs (m, n). Cosine-phased BOC(m, n) signal can be expressed as:  s(t) = cl (−1)l ϕl (t − lTc ) (2.3)

Where ϕi (t) is basic pulse wave, which is defined as ϕi (t) =

l

⎧ (i+1)T iT ⎨ 1 t ∈ [ 2Mc , 2M c ] c (i+2)Tc , T is the symbol duration, which is Where ϕi (t) = −1 t ∈ [ (i+1)T c 2M , 2M ] ⎩ 0 others divided into M segments. In the paper, we define cosine-phased BOC(m, n) signal as BOCc (m, n). BOCs (m, n) and BOCc (m, n) have the same expression, except the basic pulse wave, the ACF of these BOC signals has one main peak and multiple side-peaks. These side-peaks cause the ambiguity problem. 2.2 Local Auxiliary Signal for High-Order BOC Signal Our objective is to keep the main peak of high-order BOC ACF while remove all the positive side peaks. In order to remove all the positive side peaks, we first define the basic pulse symbol for sine-BOC signal and cosine-BOC signal as following respectively. ⎧√ ⎪ M /2, 0 ≤ |t| < Ts /2 ⎪ √ ⎪ ⎪ ⎪ ⎨ −√M /2, Ts /2 ≤ |t| < Ts (2.4) d (t) = − M /2, 0 ≤ |t − Tc | < Ts /2 √ ⎪ ⎪ ⎪ | |t M /2, Ts /2 ≤ − Tc < T ⎪ ⎪ ⎩ 0, others ⎧√ ⎪ M /2, −2Ts ≤ t < −Ts , 0 ≤ t < Ts ⎪ ⎪ ⎪ ⎪ Tc − Ts ≤ t < Tc , Tc + Ts ≤ t < Tc + 2T ⎨ √ d (t) = − M /2, −Ts ≤ t < 0, Ts ≤ t < Ts ⎪ ⎪ ⎪ Tc − 2Ts ≤ t < Tc − Ts , Tc ≤ t < Tc + Ts ⎪ ⎪ ⎩ 0, others

where T s is the subcarrier period, which equals to

Tc 2M

.

(2.5)

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With the basic pulse symbol, the local auxiliary signal is achieved as following  L(t) = cl d (t − lTc ) (2.6) l

Figure 1 and Fig. 2 show the local auxiliary signals for BOCs (14, 2) and BOCc (15, 2.5) signals. As can be seen, it looks like the traditional narrow correlation pulse waveform except for the basic pulse symbol.

Fig. 1. The local code for sine-BOC(14, 2)

Fig. 2. The local code for cosine-BOC(15, 2.5)

The target is to keep the main peak of BOC ACF while remove the positive side peaks. In order to improve the acquisition performance, we choose the dot product combining method as following R(τ ) = RB (τ ) · RB/L (τ )

(2.7)

where RB (τ ) is the ACF of cosine-BOC signals, RB/L (τ ) is the CCF of cosine-BOC signals and the local auxiliary signal. Applying the new local auxiliary signals, we achieve the final test criterion of BOCs (14, 2) and BOCc (15, 2.5) signals, the high-order BOC modulated signals adopted by Beidou and Galileo systems, as Fig. 3 and Fig. 4. We also give the ACF of BOCs (14, 2) and BOCc (15, 2.5) signals. As can be seen, the new test criterion could eliminate almost all the side peaks except for the two positive side peaks. There are two major side peaks existed, which might lead to false lock. The traditional BJ technique is chosen to rectify the false lock. As the magnitude between the side peak and the main peak is 0.45 for BOCs (14, 2) and 0.12 for BOCs (14, 2), the BJ technique will easily guarantee no false lock.

3 Acquisition Performance Analysis The proposed acquisition scheme for high-order BOC signal is shown in Fig. 5. The in-phase and quadra-phase channel outputs of auto-correlation correlators and crosscorrelation correlators can be expressed as ⎧  ⎪ IB/B,k = Tp C/N0 sin c(π fTp )RB (τ ) cos(ϕ) + nIB/B,k ⎪ ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ ⎨ QB/B,k = Tp C/N0 sin c(π fTp )RB (τ ) sin(ϕ) + nQB/B,k (3.1)  ⎪ ⎪ ⎪ IB/L,k = Tp C/N0 sin c(π fTp )RB/L (τ ) cos(ϕ) + nIB/L,k ⎪ ⎪ ⎪  ⎪ ⎪ ⎩Q B/L,k = Tp C/N0 sin c(π fTp )RB/L (τ ) sin(ϕ) + nQB/L,k

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Fig. 3. The envelops of the final test criterions Fig. 4. The envelops of the final test criterions of the sine-BOC(14, 2) of the cosine-BOC(15, 2.5)

Fig. 5. The proposed acquisition scheme for high-order BOC signal

Where, C/N0 is the carrier-noise-ratio, T p is the coherent integration time, f is the carrier Doppler residual, τ is the code delay residual, ϕ is the carrier phase residual, and nIB/B,k , nQB/B,k , nIB/L,k , nQB/L,k are noise of each channels. The test criterion proposed can be expressed =

L−1 

IB/L1 ,k · IB/L2 ,k + QB/L1 ,k · QB/L2 ,k k=0

C sin c2 (π fTp )R2 (τ ) N0 L−1   + nIB/L1 ,k nIB/L2 ,k + nQB/L1 ,k nQB/L2 ,k = LTp

(3.2)

k=0

where L is the non-coherent number of summations. nIB/B,k , nQB/B,k , nIB/L,k , nQB/L,k are uncorrelated and can be regarded as Gaussian noises, which the following distribution  nIB/L1 ,k , nIB/L2 ,k , nQB/L1 ,k , nQB/L2 ,k ∼ N (0, S ) (3.3)

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RB/L (0) ⎢ RB/L (0) 1 S = ⎢ ⎣ 1

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⎤ ⎥ ⎥ 1 RB/L (0) ⎦ RB/L (0) 1

(3.4)

In this paper, the variances of nIB/B,k , nQB/B,k , nIB/L,k , nQB/L,k are normalized. When there is only noise present, the probability of false alarm can be achieved by the following expression ⎛ ⎞ ⎧ (L + i − 1)! ⎪ γ ⎪ L−1 L−i−1 ⎪ ⎟ L+i ⎪ (1 − ρ)L e 1−ρ   ⎜ ⎪ ⎜ 2 (i)!(L − 1 − i − j)! ⎟ ⎪ ⎪ 1 − ⎜  L−1−i−j ⎟, γ < 0 ⎪ ⎪ ⎝ ⎠ − 1)! (L γ ⎪ ⎪ i=0 j=0 ⎪ ×(1 + ρ)i − ⎨ 1−ρ ⎛ ⎞ PFA = ⎪ (L + i − 1)! ⎪ ⎪ ⎪ L−1 L−i−1 ⎟ L ⎪ γ   ⎜ 2L+i (i)!(L − 1 − i − j)! ⎪ ⎜ ⎟ ⎪ (1 + ρ) e− 1+ρ ⎪ ⎜   ⎪ L−1−i−j ⎟, γ ≥ 0 ⎪ ⎝ ⎠ ⎪ (L − 1)! γ ⎪ i=0 j=0 ⎩ ×(1 − ρ)i 1+ρ (3.5) where γ is the detection threshold, ρ equals to RB/L (0). Given the probability of false alarm, the detection threshold γ can be acquired by the above expression. The detection probability can be confirmed by   γ −μ (3.6) PD ≈ Q σ Where QM ,N (α, β) is Nuttall Marcum Q-function [14], and γ equals to LTp NC0 sin c2 (π fTp )R2B (τ ) 

μ = L(μ1 μ2 + 2ρ) σ 2 = L((μ21 + μ22 + 2ρμ1 μ2 ) + 2(1 + ρ 2 ))

(3.7)

 Where μ1 and μ2 are mean values of the correlators, which equal to LTp NC0 sin c2 (π fTp )RB/B (τ ) and LTp NC0 sin c2 (π fTp )RB/L (τ ) respectively.

4 Performance Analysis Given the probability of false alarm PFA , the detection performance is related to the non-coherent number of summations L, the coherent integration time T p . In this paper, the probability of false alarm is constant with value of 10–6 . We achieve the detection performance via simulations under circumstances with different L and T p . Theoretical values of the probability of detection for BOCs (14, 2) and BOCc (15, 2.5) signals with different values of L and T p are also calculated.

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4.1 Results for BOCs (14, 2) Signal The detection performances of BOCs (14, 2) signal are shown in Fig. 6 and Fig. 7. The values of the probability of detection for traditional ambiguous acquisition method, the acquisition technique proposed in [13] and the acquisition technique proposed in [4] with the assumption of no false side peaks acquisition are also provided for comparison. The values of the methods have been obtained by Monte Carlo (MC) simulation with 1000 runs. As seen from the simulation results, the performance of the proposed technique in this paper is slightly worse than the ambiguous acquisition method when L = 1. This is because of the extra noise introduced by the new local auxiliary signal, which is the price for unambiguous acquisition. Meanwhile, the performance of the proposed technique achieves slightly better performance than the traditional ambiguous acquisition method when L = 5. Thus it can be concluded that larger non-coherent summation is more helpful for the proposed technique. This is because there is no square operation in the new technique, which decreases the square loss. Compared with improved GRASS, the performance of the proposed technique in this paper achieves slightly better performance when L = 1. And larger non-coherent number of summations would make the performance gap between improved GRASS and the proposed one wider, while longer coherent integration time would not. Thus the new technology is more suitable for the acquisition structure with larger non-coherent number of summations. Compared with the technique in [13], the performance of the proposed technique is much better, especially for small value of L. Thus the new technique is more suitable for high-order cosine-phased BOC signal acquisition. 1 0.9

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 20

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Fig. 7. The detection probabilities for BOCs(14, 2) signal, L = 5, Tp = 1 ms

4.2 Results for BOCc (15, 2.5) Signal As seen from the simulation results, the performance of the proposed technique in this paper is slightly worse than the ambiguous acquisition method when L = 1. This is because of the extra noise introduced by the new local auxiliary signal, which is the price for unambiguous acquisition. Meanwhile, the performance of the proposed technique achieves slightly better performance than the traditional ambiguous acquisition method when L = 5. Thus it can be concluded that larger non-coherent summation is more helpful for the proposed technique. This is because there is no square operation in the new technique, which decreases the square loss. Compared with improved GRASS, the performance of the proposed technique in this paper achieves slightly better performance when L = 1. And larger non-coherent number of summations would make the performance gap between improved GRASS and the proposed one wider, while longer coherent integration time would not. Thus the new technology is more suitable for the acquisition structure with larger non-coherent number of summations. Compared with the technique in [13], the performance of the proposed technique is much better, especially for small value of L. Thus the new technique is more suitable for high-order cosine-phased BOC signal acquisition (Figs. 8 and 9).

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5 Conclusions The existing unambiguous acquisition methods are mainly designed for low-order BOC signals, and the acquisition sensitivities will obviously degrade when they are applied to high-order BOC signal, the acquisition sensitivity obviously degrades. In this letter, a new local auxiliary signal is constructed for high-order cosine-phased BOC modulated signals, with which only two positive side peaks exist. Combined with the classical bump jump (BJ) technique, the chance of false peak acquisition could be eliminated. The performance of the new technique is analyzed via theory and simulation, and results show that it achieves better performance than existing techniques.

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References 1. Betz, J.W.: The offset carrier modulation for GPS modernization. In: Proceedings of ION GPS, pp. 639–648 (1999) 2. Avila-RodÁvila-Rodríguez, J.A.: On generalized signal waveforms for satellite navigation. Ph.D. thesis, Faculty of Aerospace Engineering, University FAF Munich, Munich, Germany (2008) 3. Martin, N., Leblond, V., Guillotel, G., Heiries, V.: BOC(x, y) signal acquisition techniques and performances. In: Proceedings of 2003 ION-GPS/GNSS, pp. 188–198 (2003) 4. Zhou, Y., Hu, X., Ke, T., Tang, Z.: Ambiguity mitigating technique for cosine-phased binary offset carrier signal acquisiton. IEEE Trans. Wirel. Commun. 11(6), 1981–1984 (2012) 5. Lohan, E.S., Burian, A., Renfors, M.: Low-complexity unambiguous acquisition methods for BOC-modulated CDMA signals. Int. J. Commun. Syst. Netw. 26, 503–522 (2008) 6. Fine, P., Wilson, W.: Tracking algorithm for GPS offset carrier signals. In: Proceedings of 1999 ION NTM (1999) 7. Julien, O., Macabiau, C., Cannon, E., Lachapelle, G.: ASPeCT: unambiguous sine-BOC(n, n) acquisition/tracking technique for navigation applications. IEEE Trans. Aero. Electron. Syst. 43, 150–162 (2007) 8. Yao, Z., Lu, M., Feng, Z.: Unambiguous sine-phased binary offset carrier modulated signal acquisiton technique. IEEE Trans. Wirel. Commun. 9(2), 577–580 (2010) 9. Yan, T., Wei, J., Tang, Z., Qu, B., Zhou, Z.: Unambiguous acquisition/tracking technique for high-order sine-phased binary offset carrier modulated signal. IEEE Trans. Wirel. Commun. 84, 2835–2857 (2015) 10. Chae, K., Lee, S., Liu, P., Yoon, S.: An unambiguous correlation function for generic sinephased binary offset carrier signal tracking. Comput. Electr. Eng. 49, 161–172 (2015) 11. Lee, Y., Chong, D., Song, I.: Cancellation of correlation side-peaks for unambiguous BOC signal tracking. IEEE Commun. Lett. 16(5), 569–572 (2012) 12. Qi, J., Chen, J., Li, Z., Zhang, D.: Unambiguous BOC modulated signals synchronization technique. IEEE Commun. Lett. 16(7), 986–989 (2012) 13. Shen, F., Xu, G., Xu, D.: Unambiguous acquisition technique for cosine-phased binary offset carrier signal. IEEE Commun. Lett. 18(10), 1751–1754 (2014) 14. Nuttall, A.H.: Some integrals involving the Q function. Naval Underwater Systems Center, New London Lab., New London, CT, 4297 (1972)

Robust GNSS Position Estimation Using Graph Optimization Based Vector Tracking Changhui Jiang, Yu Chen, Bohao Wang, Yuwei Chen(B) , Shuai Chen(B) , and Juha Hyyppä 02430 Masala, Finland [email protected], [email protected]

Abstract. Vector tracking (VT) is proposed and demonstrated as a superior method to obtain more robust navigation solutions. In VT, instead of individually tracking the signals, VT accomplishes signal tracking and navigation solutions estimation through a central navigation filter, mutual aiding between the channels is realized in this manner. Commonly, a Kalman Filter (KF) is employed as the center navigation filter to estimate the navigation solutions, the estimated navigation solutions are then fed back to calculate the signal tracking parameters. However, KF works in a recursive manner, relationships between the current state and all the past states are ignored, which might degrade the estimation of the navigation solutions. In this paper, we proposed a Graph Optimization (GO) based on VT. GO optimized the state estimation utilizing all the past information instead of KF, the state transformation, and measurement model were all added to the GO as the constraints to optimize the state estimation. An experiment was carried out for assessing the proposed GO-VT, statistical analysis of the navigation solutions and the corresponding comparisons demonstrated the superiority of the proposed GO-VT method. Keywords: GNSS · Vector tracking · Graph optimization

1 Introduction Global Navigation Satellite System (GNSS) represented by Global Position System (GPS), BeiDou Navigation System (BDS), Galileo Satellite Navigation etc., is popular and widely employed to generate Position, Navigation and Timing (PNT) information for various vehicles [1, 2]. Users with a GNSS receiver generate the PNT information with receiving the satellites signals. While there are at least four satellites are in-view and well-tracked, precise navigation solutions are extracted based on the signal tracking results [3, 4]. In the conventional scalar-tracking based GNSS receiver, Phase Lock Loop (PLL) and Delay Lock Loop are designed to accomplish the carrier tracking and code tracking for generating Doppler frequency measurements and code phase measurements [5, 6]. Then, the velocity and position are obtained through the extracted Doppler frequency measurements and code phase measurements. In Scalar-tracking method, each channel works independently, no information is exchanged between these channels and no information is fed back to signal tracking [7–13]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 466–472, 2021. https://doi.org/10.1007/978-981-16-3146-7_43

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Vector Tracking (VT) is a new signal tracking method, which combines the signal tracking and navigation solutions estimation together into a single navigation filter [7–9]. Kalman Filter (KF) is usually employed as the navigation filter to estimate the navigation solutions with the signal tracking results as the measurements. In VT architecture, mutual aiding between channels are realized. In the KF-VT, the navigation solutions are fed back to calculate the signal tracking parameters. Therefore, state vectors of the navigation filter are highly related, this characteristic is ignored. With the aim to improve the VT performance, in this paper, we proposed a Graph Optimization (GO) based vector tracking method. GO was employed to substitute the KF as the VT navigation filter to accomplish the navigation solutions estimation. Compared with KF, GO method has following characteristics: (1) GO method optimized past and current state vectors together, and the state propagation and measurement model were regarded as the constraints; (2) An iterative process was included in the GO method for obtaining more optimized results, and the iterative process could also alleviate the negative influence on the navigation results. Reminder of the paper was organized as: (1) Sect. 2 presented the Kalman filter based Vector Tracking including the equations, state model and measurement model of the navigation filter; (2) Sect. 3 presented the proposed GO-VT method. Then, the experimental results were presented for assessing the performance of the proposed method.

2 Kalman Filter Based Vector Tracking Figure 1 presents the vector tracking based on Vector Code Lock Loop (VDLL) and Vector Frequency Lock Loop (VFLL). As illustrated, navigation solutions are fed back to calculate the signal tracking parameters (code phase and Doppler frequency), and Numerically Controlled Oscillators (NCO) are driven to generate a local signal replica. The differences between the local signal and the received signals are extracted using code and frequency discriminators. Specifically, the VFLL accomplishes the carrier tracking and generates frequency tracking errors; the VDLL tracks the pseudo code and generates code phase errors. The extracted frequency and code tracking errors are employed in the navigation filter as the measurements to update the navigation solutions estimation. The benefit of this approach is that a central navigation filter estimating navigation solutions brings about mutual aiding between channels. In other words, “good” satellites contribute to the position, velocity, and clock error determination; then, the navigation solutions are fed back to set signal parameters for tracking the “bad” satellites, which helps to reduce the tracking errors of the “bad” signals. The core of the vector tracking is the navigation filter; commonly, it is a Kaman filter. In the Kalam filter vector tracking, position errors, velocity errors, clock bias, and drift errors are employed as the state variables, defining the state vector δX as [8–13]: δX = [δpos,δvel, δtb , δtd ]T

(1)

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where, the vector δpos denotes the three-axis errors in ECEF coordinates, the vector δvel denotes the three-axis velocity in ECEF (Earth Centered Earth Fixed) navigation frame, δtb denotes the time bias error, and δtd denotes the time drift error. The measurement model is constructed based on the relationship between the navigation solutions and the signal tracking parameters; specifically, the code phase error is related to the position error, and the frequency tracking error is related to the velocity error. Assuming the carrier discriminators output is zρ˙ , then, the pseudo-range rate measurement equation is written as [8–13]: δzρ˙ = Hρ˙ · δvel+δtd +vρ˙

(2)

where, δtd demotes the velocity error caused by the clock drift, vρ˙ denotes the noise vector, Hρ˙ denotes the Line-Of-Sight (LOS) vector projecting the velocity measurements to the LOS vector. Assuming the pseudo-range measurement vector is δzρ , the relationship between the state variables and the measurement is written as [8–13]: δzρ = Hρ · δpos+δtb +vρ

(3)

where, the vector Hρ denotes the LOS vector projecting the position n errors to the LOS direction. δtb denotes the positioning errors caused by the clock bias, vρ denotes the pseudo range noise. Therefore, the measurement vector can be written as:     δzρ vρ =H · δX + (4) δZ = vρ˙ δzρ˙ Kalman filter works recursively, results from the previous epoch affect the estimation of the current state. In vector tracking, the measurements are generated from the signal tracking results, obviously, adjacent state vectors are correlated. In Kalman filter, the only state from the last epoch and measurements from the current epoch are utilized for current state vector estimation. Uncertainty contained in the previous state estimation will pose a negative effect on the current estimation. Historical measurements and the state propagation model are ignored. Optimizing the estimation of the past states and current state helps to alleviate the negative effect of the uncertainty on current state estimation. In addition, the vector tracking measurement is constructed with first-order linearized, which might also degrade the performance of the Kalman filter based navigation filter. The question is how to find the optimal estimation of the current utilizing all the available measurement and state propagation model. This is the logical flow of the graph optimization vector tracking.

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Fig. 1. The architecture of the vector tracking.

3 Vector Tracking Using Graph Optimization Unlike the Kalman filter vector tracking (KF-VT), the measurement and state propagation model are regarded as constraints in the graph optimization vector tracking (GO-VT). The cost function for finding the optimal estimation of the state is constructed based on the state and measurement model. The formula is written as:  T  T S M −1 M e ek Errork = ekS Q−1 +e R (5) k k k k where ekS = δXk − Fk−1,k · δXk−1

(6)

ekM = δZk − Hk · δXk

(7)

Qk and Rk denote the variance of the state processing and measurement noise at the k th epoch, ekS denotes the error obtained from the state propagation model, ekM denotes the error obtained from the measurement model. If there are SA past state vectors, then the cost function is re-written as: Error =

k  k−SA+1

Errori =

k 

k  T  T  S M −1 M e ei eiS Q−1 + e R i i i i

k−SA+1

k−SA+1

(8)

In Eq. (8), all states are treated as variables which are optimized through finding the minimum value of the cost function. The relationship between the cost function errors and states are presented in Fig. 2. The circles denote the state vector to be estimated through optimizing the cost function. The rectangles refer to the measurement constraints from the different satellites. Here, we assume that there are N in-view satellites available here. The rectangles with yellow background mean the state vector transformation between adjacent states.

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Compared with Kalman filter, it can be observed that the GO method optimally estimates all the states together through the cost function. Usually, the Levenberg-Marquart (LM) method with an iterative process is utilized to solve for the cost function. More details of the LM method solving for the cost function is presented in the additional sources. In the GO-VT, much more past information is employed in optimizing the estimation of these states instead of the recursive manner in Kalman filter. In VT, the states are time-correlated; therefore, utilizing more historical information can alleviate the uncertainties of the current state estimation. Also, the iterative process in the LM method can alleviate the negative effect of the measurement model nonlinearity [6]. Figure 3 presents an experimental results comparison between KF-VT and GO-VT. GOVT obtains a better estimation of the navigation solutions, here, the SA value (Eq. (8)) is set to 10 considering the computation load.

...

X k -1

Fk -1,k

e kSV-11 ... e kSV-1i ... e kSV-1N

Xk

Fk ,k +1

e kSV1 ... e kSVi ... e kSVN

X k +1

...

e kSV+11 ... e kSV+1i ... e kSV+1N

Fig. 2. Graph of the state and measurement constraints

4 Experiments For testing and comparing the performance of the proposed method, here, a GPS L1 intermediate frequency (IF) dataset was generated with a signal simulator. A GPS L1 signal collector was employed to collect the IF dataset, which was then processed by the Vector Tracking (VT) Software Defined Receiver (SDR) implemented in MATLAB. A dynamic trajectory was employed to test and assess the performance of the proposed method. Nine satellites were employed in the navigation solutions estimation. Figure 3 and Fig. 4 presented the horizontal positioning errors. After statistical analysis, the mean values decreased by 13.2%, and the Standard Deviation (STD) decreased by 29.2%. Figure 4 presented the Cumulative Distribution of the Horizontal position errors and it also demonstrated better performance of the GO-VT.

5 Summary and Future Prospective GO-VT is implemented and preliminarily demonstrated better than KF-VT. The superiority is brought from substituting the KF with GO. The ideal way is to find the optimal

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Fig. 3. Horizontal position errors

Fig. 4. Cumulative distribution of the horizontal position errors

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estimation of the state vectors using all the past state and measurement constraints. However, a more efficient method to solve for the cost function is expected to be developed, LM method is time-consuming. Moreover, it is interesting to investigate GO-VT to detect and mitigate the multipath and None-Line-Of-Sight (NLOS) signals in urban areas. Also, the GO-VT is a more flexible framework to develop multi-sensor integration system based on the GO-VT. Acknowledgement. This research was financially supported by Academy of Finland projects “Ultrafast Data Production with Broadband Photodetectors for Active Hyperspectral Space Imaging (336145)”, Forest-Human-Machine Interplay - Building Resilience, Redefining Value Networks and Enabling Meaningful Experiences (UNITE), (337656) and Strategic Research Council project “Competence-Based Growth Through Integrated Disruptive Technologies of 3D Digitalization, Robotics, Geospatial Information and Image Processing/Computing – Point Cloud Ecosystem (314312). Additionally, Chinese Academy of Science (181811KYSB20160113, XDA22030202), Beijing Municipal Science and Technology Commission (Z181100001018036), Shanghai Science and Technology Foundations (18590712600) and Jihua lab (X190211TE190) and Huawei (9424877) are acknowledged.

References 1. Groves, P.D.: Principles of GNSS, inertial, and multisensory integrated navigation systems, [Book review]. IEEE Aerosp. Electron. Syst. Mag. 30(2), 26–27 (2015) 2. Jiang, C., Chen, S., Chen, Y., Shen, J., Liu, D., Bo, Y.: Superior position estimation based on optimization in GNSS. IEEE Commun. Lett. (2020) . 48(12), 3. 1507 (2019) 4. Jiang, C., Chen, S., Chen, Y., Bo, Y., Wang, C., Tao, W.: Performance analysis of GNSS vector tracking loop based GNSS/CSAC integrated navigation system. J. Aeronautics Astronautics Aviation 49(4), 289–297 (2017) . 39(1), 1–6 (2010) 5. 6. Petovello, M., Lachapelle, G.: GNSS solutions: what are vector tracking loops and what are their benefits and drawbacks. Inside GNSS 4(3), 16–21 (2009) 7. He, Z.: Receiver architecture: what is a maximum likelihood vector tracking receiver? Inside GNSS 8(4), 27–30 (2013) 8. Lashley, M., Bevly, D.M., Hung, J.Y.: A valid comparison of vector and scalar tracking loops. In: IEEE/ION Position, Location and Navigation Symposium, pp. 464–474, May 2010 9. Zhao, S., Akos, D.: An open source GPS/GNSS vector tracking loop-implementation, filter tuning, and results. In: Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, pp. 1293–1305, January 2011 10. Jiang, C., Chen, S., Chen, Y., Bo, Y.: Research on a chip scale atomic clock aided vector tracking loop. IET Radar Sonar Navig. 13(7), 1101–1106 (2019) 11. Jiang, C., Chen, S., Chen, Y., Bo, Y.: Research on a chip scale atomic clock driven GNSS/SINS deeply coupled navigation system for augmented performance. IET Radar Sonar Navig. 13(2), 326–331 (2018) 12. Jiang, C., Xu, B., Hsu, L.-T.: Probabilistic approach to detect and correct GNSS NLOS signals using an augmented state vector in the extended Kalman filter. GPS Solutions 25(2), 1–14 (2021). https://doi.org/10.1007/s10291-021-01101-6 13. Jiang, C., Chen, S., Chen, Y., Liu, D., Bo, Y.: A GNSS vector tracking method using graph optimization. Express Briefs IEEE Trans. Circ. Syst. II (2020)

An Attitude Estimation Algorithm for Satellite Navigation Array Against Gross Error Jie Wang1,2(B) , Wenxiang Liu1 , Haibin Wang2 , Lu Zukun1 , and Ou Gang1 1 College of Electronic Science, National University of Defence Technology,

Changsha 410073, China [email protected] 2 College of Electronic Engineering, National University of Defence Technology, Hefei 230031, China

Abstract. Based on the assumption that the signal waveform of satellites is known, the DOA of each satellite signal can be estimated by using the maximum likelihood estimation method, and then the antenna array attitude can be estimated by using the DOA of two satellites. Under the jamming condition, the accuracy of DOA estimation of different satellites is different, even wrong estimation may happen, which leads to the failure of attitude estimation. In this paper, according to the accuracy analysis of the maximum likelihood estimation method and the attitude determination error analysis conclusion, the RANSAC based attitude estimation method against gross error is proposed in the process of the antenna array attitude determination, so as to improve the estimation accuracy and fault tolerance. Finally, the simulation results show the effectiveness of the proposed method. Keywords: Antenna array · Anti-jamming · DOA · Attitude estimation

1 Introduction GNSS based attitude determination has a wide range of applications [1–3]. Most of the existing research focuses on multi antennas attitude determination in non-interference environment [4, 5]. In order to improve the anti-jamming performance of navigation receiver, the antenna array based anti-jamming receivers are more and more used. It is of great significance to study the attitude determination method based on antenna array receiver, which can not only provide attitude information for the carrier, but also improve the robustness of anti-jamming processing. Papers [6, 7] study the antenna array attitude determination based on maximum likelihood estimation in the presence of interference. Using the characteristics that the GNSS signal waveform is known, the maximum likelihood theory is used to estimate the signal DOA or attitude of the array [8, 9]. To estimate the attitude, two different methods are used in papers [6, 7]. One is to use the large sample decoupling maximum likelihood (DEML) method to calculate the DOA of each satellite signal, and then use the principle of multi vector attitude determination to obtain the antenna array attitude. The other is to take the attitude of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 473–482, 2021. https://doi.org/10.1007/978-981-16-3146-7_44

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the antenna array as the estimator and convert the DOA estimation of all satellites into the attitude estimation. In the jamming condition, when the DOA of the satellite signal and the DOA of the jamming are almost the same, the SNR will still have a large loss after the anti-jamming processing, which leads to DOA estimated by the DEML method has the larger error or even is wrong, leading to larger estimation error of the above two kinds of attitude determination method at last. In this paper, after the DOA of each satellite signal is estimated by using the DEML, the wrong or large error satellite signal propagation vectors are eliminated by consistency detection, and then the filtered satellite observation vectors are used for multi vector attitude determination to improve the accuracy of attitude estimation.

2 Principle of Attitude Determination for Antenna Array Navigation Receiver 2.1 Signal Model It is assumed that the antenna array is composed of M ideal omnidirectional elements, and the mutual coupling among the elements is not considered. Assumed that a satellite navigation signal and K independent interference signals in the far field are incident as a plane wave. The signal received by antenna array is expressed as complex baseband, which can be written as x(t) =

L  l=1

al sl (t) +

K 

ak jk (t) + n(t) = y(t) + j(t) + n(t)

(1)

k=1

where x(t) = [ x1 (t) x2 (t) . . . xN (t) ]T is the input signal vector, and each row corresponds to an antenna element. s(t) is the satellite signal received by the reference antenna element, a0 is the steering vector of the satellite signal, jk (t) is the kth interference signal received by the reference antenna element, ak is the corresponding steering vector. n(t) is a dimension additive Gaussian white noise vector with mean value of zero, and it is assumed that each noise component is independently and identically distributed with a variance of σ2 . Steering vector contains all the spatial information of the incident signal, which is determined by the array element distribution and the incident angle of the signal. Assume that the arrival Angle of the satellite signal is θ l = [αl φl ] , where, αl and φl are respectively the pitch angle and azimuth angle of the signal, then the expression of its steering vector is:  ⎤ ⎡ T expj 2π λ p1 e(θ l ) ⎢ exp j 2π pT e(θ l ) ⎥ ⎥ ⎢ λ 2 al = ⎢ (2) ⎥, l = 0, 1, . . . , L .. ⎦ ⎣ .   T exp j 2π λ pM e(θ l )

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where λ is the wavelength of the incident signal, pn is the three-dimensional coordinates of the nth array elements, and e(θ l ) is the unit propagation vector of the plane wave, whose calculation formula is as follows: e(θ l ) = [cos αl cos φl cos αl sin φl sin αl ]T

(3)

The lth satellite signal is expressed as: yl (tn ) = γl βl (tn )sl (tn ), n = 1, . . . , N

(4)

Where γl is the amplitude of the satellite signal and βl is the information code of the satellite signal. Since the period of the information code is long, we assume that it is a constant. sl is the carrier modulated by the pseudo-code. The parameters are the pseudo-code sequence and the carrier doppler. sl (tn ) = dl (tn )ejωd tn n = 1, . . . , N

(5)

According to the above assumptions, the lth satellite signal received by the antenna array is: yl (tn ) = γl βl (tn )a(θl )sl (tn )

(6)

Ignore βl , then the signal received by the antenna array is: x(tn ) =

L 

γ a(θ l )sl (tn ) + j(tn ) + n(tn )

l=1

(7)

= A( )Γ s(tn ) + j(tn ) + n(tn ) n = 1, . . . , N where: Θ = [θ 1 , θ 2 , . . . , θ L ], A(Θ) = [a(θ 1 ), a(θ 2 ), . . . , a(θ L )], Γ  diag γ1 , γ2 , . . . , γL , s(tn ) = [s1 (tn ), s2 (tn ), . . . , sL (tn )]T .

=

2.2 DOA Estimation Principle of Signal with Known Waveform If the signal waveform is known, the negative logarithmic likelihood of the array output vector is:

 N  1 L(Θ, γ, Q) = ln |Q| + tr Q−1 [x(tn ) − By(tn )][x(tn ) − By(tn )]H (8) N n=1

where B = A(Θ), When solving the likelihood function, Q is estimated by: 

Q=

N  H 1  x(tn ) − By(tn ) x(tn ) − By(tn ) N 



(9)

n=1

Assuming that the satellite signals are tracked according to the received signal, and the phase parameters of the doppler and pseudo-code of the satellite signals are obtained, the satellite signals can be constructed as follows: yˆ l (tn ) = βl (tn )sl (tn ), n = 1, . . . , N

(10)

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If the constant term in Eq. (9) is ignored, the likelihood function of the arrival angle estimation of a single satellite signal can be written: LLR1 =

N    H x(tn ) − a(θ l )γl yˆ l (tn ) Q−1 x(tn ) − a(θ l )γl yˆ l (tn ) l

(11)

tn =1

In the process of solving, the following formula can be used to estimate Ql : −1 ˆ ˆ l = Rˆ xx − Rˆ H Q yx Ryy Ryx

(12)

N 1  Rˆ yx = yˆ l (tn )xH (tn ) N

(13)

N 1  1 Rˆ xx = x(tn )xH (tn ) N 2

(14)

where:

n=1

n=1

The definition of Rˆ yy is similar as Rˆ xx . According to the above likelihood function and the conclusion of paper [9], for the estimation of the DOA of a single satellite, we rearranged the sampled data into an M*N dimensional array, and projected the estimated satellite signal into the sampled data space: ul =

X yˆ H l εl

(15)

 yˆ l = yˆ l (t1 ), yˆ l (t2 ), . . . , yˆ l (tN )

(16)

X = [x(t1 ), x(t2 ), . . . , x(tN )]

(17)

εl = yˆ l yˆ H l =

N 

yˆ l (tn )ˆyH l (tn )

(18)

n=1

Then the estimated value of signal amplitude is as follows:   −1 ˆ l ul aH θˆ l Q   −1   l = 1, . . . , L γˆl = ˆ l a θˆ l aH θˆ l Q

(19)

The estimated value of θ l is: θˆ l = arg max θl

 2  H  ˆ −1 a (θ l )Q l ul  ˆ −1 aH (θ l )Q l a(θ l )

l = 1, . . . , L

(20)

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2.3 Two Methods of Antenna Array Attitude Determination There are two ways of attitude determination using maximum likelihood estimation based on known signal waveform for antenna array receiver. First, the DOA of each satellite signal is estimated separately, and then the attitude of the antenna array is obtained by using the solutions of Wahba’s problem. Second, the antenna array attitude is directly taken as the estimator to be estimated, and the DOA estimation of all satellites is converted into the attitude estimation. Method 1: After the DOA is obtained, the signal propagation vector eˆ (θˆ l ) of the lth satellite can be calculated according to Eq. (4). The calculated propagation vector is the representation of the signal propagation vector in the antenna array frame (The frame is centered at the antenna reference array element, called b frame), we remark the propagation vector as eˆ b (θˆ l ). Under the assumption that the antenna array position and ephemeris information are known, the expression of the satellite propagation vector in the navigation frame (The navigation (n-) frame is centered at the array and aligned with the east, north, and up directions. The n-frame serves as a reference frame for the attitude of the vehicle) can be calculated as en (θ l ). Because the distance between the satellite and the receiver is far greater than the positioning error of the satellite and the receiver, the estimation error of en (θ l ) can be ignored. The attitude of the antenna array is expressed by the direction cosine matrix C bn , then: eˆ b (θˆ l ) = C bn en (θ l )

(21)

When the DOA of two or more satellites is calculated, the attitude can be solved according to the solutions of Wahba’s problem [10]. Method 2: The attitude angle of the antenna array is directly taken as the estimator, the likelihood function with the DOA of a single satellite signal is converted into the likelihood function with the attitude angle of the antenna array, and the likelihood function composed of all satellite signals is summed to form the likelihood ratio of the attitude angle of the antenna array, which is denoted as:  H N L  x(tn ) − a(C bn , en (θ l ))γl yˆ l (tn )  LLR2 =   −1 x(tn ) − a(C bn , en (θ l ))γl yˆ l (tn ) l=1 n=1 Ql Compared with Method 1, Method 2 takes antenna array attitude as the estimator. Although the multi-vector attitude determination process is reduced in the solution process, the likelihood function solution is a 3d variable estimation process, and the computational complexity is obviously increased. The satellite DOA in Method 1 and antenna array attitude angle in Method 2 are respectively solved by global search method throughout the rest of this article.

3 Attitude Estimation Algorithm Against Gross Error 3.1 Performance Analysis of Attitude Determination Based on Simulation In order to analyze the performance of antenna array pose determination algorithm, signal simulation experiments are carried out in different scenes. The simulation system

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includes array satellite signal generation module, array interference signal generation module, signal acquisition and tracking module, and attitude solving module [11]. In the simulation, a central circle array of four arrays, 12 satellite signals, and a carrier to noise ratio of 45 dB are used. The simulation scenes include non-interference scenes and single-suppressed interference scenes. The receiver attitude angle: pitch angle, roll angle and azimuth angle, is denoted as att = [θ η ϕ]T , and the estimation error is denoted as  = [δθ δη δϕ]. The first kind scenario is a non-interference scenario. During the simulation, the antenna array attitude is fixed, and the satellite signal DOA is random. Methods 1 and 2 are used to estimate the receiver attitude, and the simulation is repeated for 100 times. The results show that the estimation error of the two methods is small in the non-interference scenario. The estimation error variance of method 1 is [1.5°, 1.3°, 1.8°], and that of method 2 is [0.9°, 0.9°, 1.3°]. Scenario 1 is set for further analysis as: the antenna array attitude is [10°, 3° 60°], the actual angle of arrival of each satellite is shown in Fig. 1 (a) marked as X, and the interference signal power is 0. The simulation results show that the estimation errors of Method 1 and Method 2 are [−1.9°, −2.0°, −1.2°], [−1.5°, −1.0°, −1.0°] respectively, and their estimation accuracy is close. Figure 1 (a) shows the DOA of the real satellite signal and the DOA estimated by method 1. Figure 1 (b) shows the optimal objective function (Eq. (21)) values corresponding to different DOAs of Method 1 of PRN 12 navigation satellite signal. Figure 1 (c) shows the different satellites DOA estimation errors of level angle and azimuth angle in Scenario 1. Figure 1 (d) shows the likelihood ratios (Eq. (23)) corresponding to different attitude angles in Method 2. In the second kind scenario, a suppressed jamming with 85dB interference to signal ratio is added, and the angle of arrival of the jamming signal is fixed at [15° and 120°]. After 100 times of simulation, the variance of attitude estimation error in method 1 is [9.9°, 9.2°, 44.4°], the mean absolute error is [6.8°, 5.8° and 17.8°], and the variance of attitude estimation error in method 2 is [2.3°, 1.9° and 2.9°], the mean absolute error is [1.8°, 1.6° and 1.96°]. Compared with the Method 2, the estimation accuracy of Method 1 decreases significantly. Scenario 2 is set for further analysis as: the antenna array attitude and the angle of arrival of satellite signal are the same as Scenario 1, and the interference with the interference signal ratio of 85 dB is added, and the angle of arrival is [15° 120°]. The simulation results are shown in Fig. 2. At this time, the estimation errors of Method 1 and Method 2 increase significantly, which are [4.0°, 8.6°, 2.2°], [−4°, −1°, 0°], respectively. Comparing with Fig. 1(d) and Fig. 2(d), it is not difficult to find that the reason why the estimation accuracy of Method 1 decreases significantly is that the DOA estimation error of some satellite signals increases in the interference environment, but the traditional multi vector attitude determination method can not effectively eliminate the influence of DOAs estimation errors. Although the estimation error of Method 2 is less than that of Method 1 in large interference environment, Method 2 needs 3D search in the process of attitude estimation, which requires a large amount of computation and is difficult to be applied in some scenes. In order to improve the accuracy of attitude estimation in interference environment, we propose an anti-gross error antenna array attitude estimation method based on Method 1.

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Fig. 1. Simulation result of Scenario 1

3.2 An Anti-gross Error Algorithm for Antenna Array Attitude Determination The loss function of multi vector attitude determination estimation is as follows: L(C bn ) =

L  2    al eˆ b (θˆ l ) − C bn en (θ l )

(23)

l=1

Because the estimation accuracy of each satellite propagation vector eˆ b (θˆ l ) is b unknown, it should be set al = 1 in the estimation. Cˆ n can be estimated after the multi vector attitude determination method is used, for each satellite, record:  2 b   (24) Ll = eˆ b (θˆ l ) − Cˆ n en (θ l ) Ll represents the matching degree between the DOA estimation results and the attitude estimation results. If Ll is too large, it can be considered that there is a matching

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Fig. 2. Simulation result of Scenario 2

error. The analysis of simulation results in Sect. 3.1 shows that in the interference environment, the angle of arrival estimation error of some satellites is too large or completely wrong, which leads to the increase of antenna array attitude estimation error. In order to eliminate the influence of these gross errors and improve the estimation accuracy, this paper uses the random sample consensus algorithm to eliminate the error matching. The RANSAC algorithm can estimate the parameters of the mathematical model iteratively from a set of observation data sets with mismatched points. In the antenna array attitude estimation, due to the status of the number of visible satellites and tracking, there are few pairs of observation data. We optimize the parameters of RANSAC algorithm by preprocessing. The number of observations is determined by the number of captured stars, and the matching error threshold is determined by the loss function value obtained by conventional calculation.

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This algorithm can effectively judge the accuracy of satellite arrival Angle estimation, has strong robustness, and can eliminate the problem of increasing arrival Angle estimation error caused by interference. Taking Scenario 2 as an example, after using this method, the number of satellites participating in pose determination is 6, and the final pose determination error drops to [-2.6°, 3.9°, -2.5°], which proves that this algorithm has a good performance. After 100 simulation experiments, the estimation accuracy of the anti-gross error algorithm based on Method 1 was improved from the estimation error variance [9.9°, 9.2°, 44.4°] and the mean absolute error [6.8°, 5.8°, 17.8°] to the estimation error variance [5.3°, 5.3°, 5.7°] and the mean absolute error [4.2°, 4.2°, 4.4°] when single interference was 85 dB. The estimation accuracy of this method is equivalent to that of Method 2, but the computational complexity is much less than that of Method 2.

4 Conclusions The traditional antenna array attitude determination method in the interference scene has insufficient robustness, and the attitude estimation accuracy is affected by the low signal-to-noise ratio or low DOA estimation accuracy of some satellite signals. In this paper, an anti-gross error antenna array attitude estimation method is proposed, which can greatly improve the attitude estimation accuracy in the interference environment by using low computational complexity. Theoretical analysis and simulation results show that this method has significant advantages and can be applied to antenna array receiver attitude determination in complex electromagnetic environment. Obviously, in the case of a priori information, this method can also effectively identify and eliminate the influence of deception signal in theory. The application of the algorithm in the scene with deception signal will be studied in the future.

References 1. Chiang, K., Psiaki, M., Powell, S., Miceli, R., O’Hanlon, B.: GPS-based attitude determination for a spinning rocket. IEEE Trans. Aerosp. Electron. Syst. 50(4), 2654–2663 (2014) 2. Meurer, M., Konovaltsev, A., Cuntz, M., Hättich, C.: Robust joint multi-antenna spoofing detection and attitude estimation using direction assisted multiple hypotheses RAIM. In: Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), pp. 3007–3016, September 2012 3. Raskaliyev, A., Patel, S.H., Sobh, T.M., Ibrayev, A.: GNSS-based attitude determination techniques—a comprehensive literature survey. IEEE Access 8, 24873–24886 (2020) 4. Tsikin, I., Shcherbinina, E.: GNSS attitude determination based on antenna array space-time signal processing. In: Internet of Things, Smart Spaces, and Next Generation Networks and Systems, pp. 573–583. Springer, Cham (2016) 5. Zhen, D.: Toolbox for attitude determination with a multiple-antenna system using GPS. Center for Sensor Systems (ZESS), University of Siegen, Germany (2008) 6. Markel, M., Sutton, E., Zmuda, H.: An antenna array-based approach to attitude determination in a jammed environment. In: Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), pp. 2914–2926, September 2001

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7. Markel, M.D.: Interference mitigation for GPS based attitude determination (2003) 8. Li, J., Compton, R.T.: Maximum likelihood angle estimation for signals with known waveforms. IEEE Trans. Sig. Process. 41(9), 2850–2862 (1993) 9. Li, J., Halder, B., Stoica, P., Viberg, M.: Computationally efficient angle estimation for signals with known waveforms. IEEE Trans. Signal Process. 43(9), 2154–2163 (1995) 10. Markley, F.L.: 30 years of Wahba’s problem (1999) 11. Lu, Z., Nie, J., Chen, F., Chen, H., Ou, G.: Adaptive time taps of STAP under channel mismatch for GNSS antenna arrays. IEEE Trans. Instrum. Meas. 66(11), 2813–2824 (2017)

Self-supervised Calibration Method of Array Antenna for High-Precision GNSS Application Gang Liu, Kefan Wei, Xiaowei Cui(B) , and Mingquan Lu Tsinghua University, Haidian District, Beijing 100084, China [email protected]

Abstract. GNSS array antenna have been widely used for single-tone, narrowband, wide-band interference mitigation in satellite navigation application, however, this induces biases to code phase and carrier phase measurement, which will restrict its usage in high-precision application. Biases could be compensated based on calibration of array pattern in Microwave Anechoic Chamber, which is complicated and could not handle platform influence. Towards this issue, this paper proposed a self-supervised calibration method of array antenna phase center for high-precision GNSS application cooperated with inertial technology. Firstly, high-precision GNSS receiver is designed for amplitude and carrier phase measurement of multi-antennas simultaneously. Secondly, we use a single axis servo turntable to speed up the calibration process by rotation scheme optimization, satellite direction vectors are projected to array coordinate system based on platform attitude measured by an inertial north finder. Finally, data smoothing and local interpolation are utilized for measurement pattern fitting. Open-sky test is carried out, thus validating the effectiveness of this method. Keywords: Global navigation satellite system (GNSS) · Inertial north finder · Array antenna calibration · Anti-jamming · High-precision application

1 Introduction Global navigation satellite system (GNSS) is providing multi-scale positioning and timing services through the world. However, GNSS receivers are susceptible to intentional or unintentional interference, because GNSS use Direct Sequence Spread Spectrum (DSSS) modulation method and the signal power density at the receiver is below the thermal noise, this threaten most of life safety related applications, such as automatic driving and aviation. GNSS array antenna consists of a number of distributed antennas, signals from each antenna element are processed in space, time or frequency domain separately, or as a combination of them, such as Spatial Adaptive Processing (SAP), Spatial Frequency Adaptive Processing (SFAP) and Spatial Temporal Adaptive Processing (STAP) [1–3]. Coherent processing of signals from all the antenna elements can mitigate the electromagnetic interference by changing the receive pattern adaptively to form a Controlled Reception Pattern Antenna (CPRA) system [4, 5]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 483–495, 2021. https://doi.org/10.1007/978-981-16-3146-7_45

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High-precision application requires the array antenna to measure pseudo-range and carrier phase at a fixed phase center. Basically, high accuracy measurement is unreachable for the following reasons. Firstly, antenna elements are distributed with different phase center which need to be projected together. Secondly, non-ideal array antenna suffers from uncertainties such as uneven cable lengths, coupling between elements, antenna gain and phase variations, time varying mismatches between RF channels. Thirdly, the frequency response of each antenna elements varies with satellite directions and frequency bins, so adaptive filtering technique will introduce extra distortion in the GNSS measurements. However, array antenna calibration could be carried out to handle those non-ideal factors for High-precision application. Biases mainly come from two sources, RF frontends and array antenna, which could be handled separately [16, 17]. Kim [6] proposed to use equalization filters to calibrate RF front-ends distortion, this scheme has obviously effect but with low efficiency of implementation. Lorenzo [7] realized a space-time adaptive algorithms to reject radio frequency interference, then fixed the weight and tried to estimate the pseudo-range and carrier-phase bias, finally the bias was used to compensate the receiver measurements, cm level carrier-phase bias residuals after compensation was reported, but this method was inapplicable for dynamic scene. O’Brien [8] estimated the biases of the measurements based on phase discriminant curve and then compensate them in the tracking loop, this modified the receiver structure and is hard to realize on a hardware platform. Authors from university of Calgary [9–11] used a projection methodology for the calibration of antenna arrays using baseband discriminator output, but this method was computationally costly and omitted the RF front-ends bias. Wang [12] established a phase center compensation model for anti-jamming antenna array, then use this model for measurement compensation. But error induced by phase center offset cannot be compensated using fixed lookup table, while must corrected by the anti-jamming calculation result in real time, this was un-suitable for hardware implementation. Xu [13] and Tian [14] used a two-step carrier phase bias calibration technique for array antenna beamforming using software receiver realized on GPU, ambiguity of carrier phase was fixed with RTKLIB, but the calibration and beamforming were based on the saved dataset with post processing, total pattern calibration and test were not carried out, nor on a hardware platform in real time. Niestroj [15] used spherical harmonic functions to estimate antenna array manifolds based on sparse measurements, this was an excellent interpolation candidate. It can be seen that centimetre scale positioning is realized based on well calibrated array antenna [13, 14], but the existing research is not accomplished in practice sufficiently, nor realized on hardware platform. Moreover, antenna coordinate system was undefined relative to the world frame for most of the research. This paper proposes a hardware implementation of bias calibration for SFAP beamforming scheme cooperated with inertial technology. Firstly, coordinate system of array antenna is measured by inertial north finder. Secondly, a special receiver is designed for amplitude and phase pattern calibration. Thirdly, a single axis servo turntable is used to improve the calibration speed and accuracy. Finally, calibration results are used to calculate steering vector and weight vector for adaptive beamforming algorithm.

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The remainder of this paper is organized as follows. Section 2 proposes the selfsupervised calibration scheme and implementation. Section 3 gives the test results, while Sect. 4 concludes this paper.

2 Self-supervised Calibration This paper intend to use a post-installation calibration scheme with open-sky satellite signals, which is easy to perform and more accurate considering the platform influence, as shown in Fig. 1.

Fig. 1. Calibration system for array antenna amplitude and phase pattern

Constructing the look up table (LUT) and some correct coefficient is the specific purpose of array calibration. Measuring frequency response in the array antenna coordinate system is the feasible approach for array pattern calibration. Based on the above analysis, inertial measurement unit (IMU) is involved to sense the attitude of array antenna in the world coordinate system, satellite incident direction is calculated by the receiver in the world coordinate system, so satellite steering vector could be projected to the array antenna coordinate system. We can choose antenna 1 as the reference, then all the calibration could be carried out to construct the LUT. This is the basic principle of array pattern calibration. We use GNSS signals for antenna pattern calibration, cooperated with a single axis servo turntable to speed up the calibration process, the calibration system is shown in Fig. 2. The whole system consist of array antenna, GNSS calibration receiver, inertial north finder, IMU and single axis servo turntable, a 4-elements Y shape array antenna is used for demonstration. There are five coordinate systems: (1) n − xn yn zn (north-east-down) is the navigation coordinate system.

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Single axis servo turntable

xn

ya Receiver

2

1 za

zf

zn

xf

yn

3 1 4

North Finder

Holder

xa

IMU

yb Array xb antenna zIMU b 4 yf North Finder

Receiver

3

Fig. 2. Calibration system architecture

(2) b − xb yb zb (right-front-up) is the body coordinate system fix on the IMU. (3) a − xa ya za (right-front-up) is the array coordinate system with same orientations as body coordinate system. (4) r − xr yr zr (right-front-up) is the turntable coordinate system. (5) f − xf yf zf (right-front-up) is the north finder coordinate system. We suppose the transition matrix between b, a, r and f are well known, actually, the a and b are treated as the save coordinate system in this paper. Satellite azimuth az s,enu and elevation el s,enu are calculated by the receiver in n, then the incident direction vector is expressed as: T  es,n = cos(az s,enu ) cos(el s,enu ) sin(az s,enu ) cos(el s,enu ) − sin(el s,enu )

(1)

Rotation matrix from n to a is: ⎡ ⎤ − cos φ sin ψ + sin φ sin θ cos ψ cos φ cos ψ + sin φ sin θ sin ψ sin φ cos θ Rna = ⎣ cos θ cos ψ cos θ sin ψ − sin θ ⎦ − sin φ sin ψ − cos φ sin θ cos ψ sin φ cos ψ − cos φ sin θ sin ψ − cos φ cos θ (2) Where (φ, θ, ψ) are the roll, pitch, yaw angle of the array antenna, which are measured by the inertial north finder. Thus, satellite incident direction vector in a is: T  (3) es,a = xs ys z s = Rna es,n In array coordinate system, satellite azimuth and elevation are:   az s,a = atan2 xs , ys , el s,a = asin z s

(4)

Thus, we transform the satellite measurement in n to a, and the antenna pattern calibration is performed in a.

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2.1 Multi-antenna GNSS Receiver A multi-antenna double frequency GNSS receiver is designed for array antenna calibration, the structure of which is shown in Fig. 3.

Fig. 3. Structure of calibration GNSS receiver

Where L is the number of array antennas. Acquisition engine is shared within multi antennas, measurement of pseudo-range, carrier phase, power are extracted in the PVT module, which is more accurate than baseband discriminator. Measurements of each antenna output in self-defined protocol or in RTCM protocol. The calibration receiver is realized on a Xilinx FPGA platform in real time, which is designed to uses the same hardware as the beamforming receiver, so one can change the firmware to switch between the two modes. 2.2 Inertial North Finder High precision gyroscopes are used to find the north direction and determine the orientation by detecting the earth‘s rotation rate and gravity vector. The inertial north finder this paper used consist of a single MEMS gyroscope and three accelerometers, the gyroscope is designed by Tsinghua University with 0.1 degree/h bias stability, the accelerometer from ADI named ADXL354. A 4-position north finder algorithm is used [18], in each position, 1 min of gyroscope samples are record, and the algorithm output the roll, pitch, yaw angle within 5 min. We fix the north finder on a marble table, six tests are carried out. The measured yaw angles are shown in Table 1. Table 1. North finding results of six tests Yaw measurement index Angle [degree]

1

2

3

4

5

6

Mean [degree]

Variance [degree]

285.14

286.01

285.92

285.53

285.61

285.62

285.64

0.31

North finding error peak-peak is within 1°, this is accurate enough for GNSS beamforming application.

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2.3 Method for Speeding up Calibration Measuring array antenna pattern with live signals is cost-effective compared to calibration in microwave anechoic chamber, moreover, the actual electromagnetic environment is considered as one can calibrate the array after its installation. However, the traditional calibration method is time-consuming and imprecise due to some GNSS satellite limits. Firstly, the satellite sky-plot changes slowly, one spends a lot of time for full pattern coverage. Secondly, although satellites appear in most parts of the sky, there are two ‘holes’ in the sky where no satellites ever appear, this is due to the fact that satellite orbital planes are inclined at 55° for GPS and BDS with respect to the equator, Fig. 4 shows the GPS satellite motion coverage over 24 h at latitude 40.0° and longitude 116.0°.

Fig. 4. GPS satellite motion coverage over 24 h

This paper uses a single axis servo turntable to speed up the calibration process with the following steps. (1) The array pattern is divided into 5◦ × 5◦ grid along azimuth and elevation, we set the satellite cutoff angle to 10◦ , the higher the elevation is, the less grids the receiver measures, we have 71, 70, 68, 66, 63, 59, 56, 51, 47, 42, 37, 31, 25, 19, 13, 7, 1 grids to process for 10◦ , 15◦ , 20◦ , L, 90◦ elevation. (2) The turntable only rotates with 5◦ a step along the azimuth axis, for each positon, one minute of correlation power and carrier phase are recorded, then the turntable shift to the next position, the shift time is 30 s, so 90 s are needs for one position calibration. (3) We predict the satellite azimuth and elevation over a period of time based on ephemeris or almanac. Make sure there is enough candidates for each elevation pattern, for example, the total time of satellite with elevation within 10◦ and 15◦ must longer than 71 × 90 s, it is the same for other elevations. However, we can use a fix length of time simply, such as two hours. (4) We search the correct rotation angle of the turntable from higher to lower elevation to cover the whole array pattern, thus generates the sequential pairs of turntable shift angle and the exact time-stamp, which is sorted by time-stamp. (5) The turntable rotates according to the shift angle table and records the data.

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(6) Linear interpolation is performed for those uncovered pattern region. 2.4 Calibration Data Process Figure 5 shows the position of each antenna element and the satellite incident direction. Suppose the reference antenna at the origin, the other antennas are distributed in x-y plane on a circle with an interval of 120°.

Fig. 5. Array antenna coordinate system

In the array coordinate system, the position of fore antenna elements are:  

√

√ 3 r 3 r 3 = −  4 = (0, −r, 0)  1 = (0, 0, 0), p 2 = r, , 0 , p r, , 0 , p p 2 2 2 2

(5)

α and β denote the azimuth and elevation of the satellite incident vector, then the unit vector of satellite incident direction is: k = (cos β sin α, − cos β cos α, − sin β) Geometric phase delay relative to the reference antenna is: √ r 3 r cos β sin α − cos β cos α)/λ φ2,c = ( 2√ 2 r 3 φ3,c = (− r cos β sin α − cos β cos α)/λ 2 2 φ4,c = (r cos β cos α)/λ

(6)

(7)

φms denotes carrier phase measurement extracted by receiver, thus, measured phase delay relative to the reference antenna is: φ2s = φ1s − φ2s , φ3s = φ1s − φ3s , φ4s = φ1s − φ4s

(8)

Non-ideal phase bias is calculated by removing the geometric phase delay from measured phase delay: s s s = φ2s + φ2,c , φ3,c = φ3s + φ3,c , φ4,c = φ4s + φ4,c φ2,c

LUT is generated by Eq. (9) for different azimuth and elevation.

(9)

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3 Experimental Tests and Results An experiment is carried out to verify the proposed scheme in the real environment using GPS L1 C/A, GPS L5, BDS B1C and BDS B2a signals. The experiment is performed on the roof of Weiqing Building, Tsinghua University, Beijing, China. Figure 6 shows the experiment equipment consist of jamming device, 4 element beamforming array antenna and traditional antenna without anti-jamming capability. The array antenna used in this paper consist of 4 antenna elements, antenna 1 is selected as reference to establish the coordinate system in Fig. 7.

Fig. 6. Experiment equipment

Fig. 7. Antenna elements layout

The test consists of three processes. Firstly, the calibration process is performed to get the whole pattern carrier phase LUT using open sky signals. Secondly, an eight hours beamforming using the LUT is performed to test the stability of high-precision localization when the beam changed with time. Thirdly, beamforming under wide-band interference is performed for high-precision anti-jamming applications. A modified RTKLIB software [19] is used for high-precision test. 3.1 Array Pattern Calibration Test The calibration test last for more than six hours, the north finder senses roll, pitch, yaw angle of the array, then the turntable rotates according to the shift table and records the carrier phase measurement, after compensation of the geometric phase bias, non-ideal phase bias relative to the reference antenna could be calculated, as shown in Fig. 8 with legend of elevation. Remember that the antennas are distributed in x-y plane on a circle with an interval of 120°, we observe the 120° phase shift from the calibrated array pattern. The non-ideal phase bias is used to form a LUT for carrier phase compensation. We use the LUT to compensate other sampled carrier phase data, the phase bias after compensation is shown in Fig. 9. The phase bias is limited within 0.05 circle after compensation, the same result is observed for L5 frequency.

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Fig. 8. Non-ideal phase bias with legend of elevation for L1 frequency

Fig. 9. Phase bias after compensation for L1 frequency

3.2 Beamforming Test Without Interference Based on the LUT generated by calibration process, the beamforming process experiment is conducted. Roll, pitch and yaw angle of the array antenna are calculated by the north finder, then the LUT could be used to calibrate steering vector for each satellite, thus, the weight vectors for SFAP are calculated with steering vector constraint.A sinoGNSS K803 receiver is used as base station, the SFAP beamforming receiver is used as rover, and the RTCMv3 output of them are processed by a modified RTKLIB software. The beamforming test lasts for more than eight hours to test whether the phase bias shift with the satellite incident direction changing. Figure 10 shows the east and north position error over 8 h, the standard deviation of east position error is 2.6 mm, north is 2.4 mm, up is 7.7 mm. The residuals of double-differenced carrier phase are calculated based on the fixed integer ambiguity, as shown in Fig. 11 for BDS B1C signal. Actually, the residuals of double-differenced carrier phase are within 0.25 carrier cycle, which is satisfied with high-precision application.

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Fig. 10. East and north position error over 8 h with beamforming

Fig. 11. Residuals of double-differenced carrier phase for beamforming test without interference

The test results verify the SFAP scheme introduced in this paper, after the full coverage calibration of array pattern, phase center of the array is fixed at the reference antenna for arbitrary satellite with different steering vector. 3.3 Beamforming Test with Interference An oppressive wide-band interference is generated by signal generator, with interferenceto-noise ratio (INR) of 60dB, a Septentrio Mosaic X5 receiver connected to the traditional antenna is used to make a comparison. The test is performed with the following steps: (1) System initialization. (2) Interference from azimuth 0◦ , last about two minutes. (3) Interference stopped for two minutes; (4) Interference from azimuth 90◦ , last about two minutes. (5) Interference stopped for two minutes, then close the test. Figure 12 shows the east and north position error, the standard deviation of east position error is 1.9 mm, north is 3.9 mm, up is 6.3 mm. The residuals of double-differenced carrier phase are calculated based on the fixed integer ambiguity, as shown in Fig. 13 for BDS B1C signal. The C/N0 of each receiver under different circumstances are listed in Table 2. The results show that the beamforming method keeps carrier phase ambiguity fix under different wide-band interference while Mosaic X5 receiver failed to tracking the signal. Meanwhile, beamforming method has 3–7 dB enhancement in C/N0 compared to Nulling method, thus verifies the effectiveness of the calibration scheme in this paper.

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Fig. 12. East and north position error under interference with beamforming

Fig. 13. Residuals of double-differenced carrier phase for beamforming test with interference

Table 2. C/N0 of each receiver under different circumstances L1C/A and B1C PRN

C22 C30 C36

C40

C45

C46

G04 G16 G26 G27

None Mosaic X5 interference Nulling

37.5 45.3 46.94 ------ ------ ------ 44.7 44.6 45.2 46.1 40.0 43.0 45.0

42.0

42.0

42.0

42.0 42.0 46.0 44.0

Beamforming 46.0 50.0 51.0

49.0

43.0

47.0

49.0 49.0 51.0 49.0

0° Mosaic X5 interference Nulling

0

0

0

0

28.0 42.0 36.0

36.0

37.0

38.0

38.0 37.0 41.0 37.0

Beamforming 41.0 48.0 47.0

42.0

43.0

43.0

42.0 44.0 45.0 37.0

90° Mosaic X5 interference Nulling

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

34.0 37.0 43.0

43.0

42.0

28.0

40.0 38.0 40.0 42.0

0

Beamforming 40.0 45.0 47.0

47.0

43.0

34.0

46.0 42.0 43.0 45.0

4 Conclusion This paper proposed a self-supervised calibration method for beamforming SFAP algorithm. This method uses open-sky satellite signals to calculate the carrier phase bias LUT aided by an inertial north finder, thus we get the exact frequency response of SFAP algorithm. A single axis servo turntable and an acceleration method are introduced to improve the calibration speed and accuracy. The non-ideal carrier phase bias are compensate in

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the frequency domain using transfer function of SFAP. Experiment results show that the phase center of the array antenna is fixed at the reference antenna center, which satisfies the requirements of high-precision application. The beamforming receiver keeps carrier phase ambiguity fix under different wide-band interference, besides, 3–7 dB C/N0 enhancement is observed compared to nulling method.

References 1. Fante, R.L., Vaccaro, J.J.: Wideband cancellation of interference in a GPS receive array. IEEE Trans. Aerosp. Electron. Syst. 36(2), 549–564 (2000) 2. Trees, V.: Optimum Array Processing: Part IV of Detection, Estimation and Modulation Theory. Wiley, New York (2002) 3. Moore, T.: Analytic study of space-time and space-frequency adaptive processing for radio frequency interference suppression. Ph.D. thesis, Ohio State University, USA (2002) 4. Motella, B., Savasta, S.: Method for assessing the interference impact on GNSS receivers. IEEE Trans. Aerosp. Electron. Syst. 47(2), 1416–1432 (2011) 5. Gao, G.X., Sgammini, M., Lu, M., Kubo, N.: Protecting GNSS receivers from jamming and interference. Proc. IEEE 104(6), 1327–1338 (2016) 6. Kim, U.S.: Mitigation of signal biases introduced by controlled reception pattern antennas in a high integrity carrier phase differential GPS system. Ph.D. thesis, Stanford University, San Francisco, USA (2007) 7. Lorenzo, D.S.D., Lo, S.C., Enge, P.K.: Calibrating adaptive antenna arrays for highintegrity GPS. GPS Solution 16(2), 221–230 (2012) 8. O’Brien, A.J., Gupta, I.J.: Mitigation of adaptive antenna induced bias errors in GNSS receivers. IEEE Trans. Aerosp. Electron. Syst. 47(1), 524–538 (2011) 9. Anantharamu, P.B., Borio, D., Lachapelle, G.: Self-contained GNSS-based Antenna Array Calibration. ION ITM 2011, Session C5, San Diego, CA (2011) 10. Vagle, N., Broumandan, A., Jafarnia, A., Lachapelle, G.: Characterization of GNSS Measurement Distortions Due to Antenna Array Processing in the Presence of Interference Signals. UPINLBS 2014, Corpus Christi, Texas, pp. 71–80 (2014) 11. Daneshmand, S., Sokhandan, N., Zaeri-Amirani, M., Lachapelle, G.: Precise calibration of a GNSS antenna array for adaptive beamforming applications. Sensors 2014(14), 9669–9691 (2014) 12. Wang, D.W., Li, J.Q., Zhou, X.P.: Phase center correction for GNSS adaptive anti-jamming antenna array. Trans. Beijing Inst. Technol. 37(3), 325–330 (2017) 13. Xu, H., Cui, X., Shen, J., Lu, M.: A Two-step beam-forming method based on carrier phases for GNSS adaptive array anti-jamming. In: ION ITM 2016, Monterey, California, pp. 793–804 (2016) 14. Tian, Z., Chang, X., Cui, X., Lu, M.: Carrier phase bias calibration technique for array antenna receiver. In: CSNC 2020, Chengdu, China, pp. 336–350 (2020) 15. Niestroj, M., Brachvogel, M., Zorn, S., Meurer, M.: Estimation of antenna array manifolds based on sparse measurements. In: ION GNSS 2018, Miami, Florida, pp. 4004–4011 (2018) 16. Hailong, X., Cui, X., Mingquan, L.: Data oriented calibration method to reduce measurement bias in SFAP based GNSS receivers. Electron. Lett. 54(9), 591–593 (2017) 17. Gupta, I.J., Moore, T.D.: Space-frequency adaptive processing (SFAP) for radio frequency interference mitigation in spread-spectrum receivers. IEEE Trans. Antennas Propag. 52(6), 1611–1616 (2004)

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18. Zhang, Y., Zhang, R., Zhou, B., Zhang, X., Song, M., Mi, L.: Detection methods of earth’s rotation rate with a MEMS gyroscope. In: ICEMI2015. Qingdao, China, pp. 1552–1557 (2015) 19. Li, W., Cui, X., Lu, M.: Urban RTK using adaptive point mass filter with wide-lane measurements. In: ION ITM 2016, Monterey, California, pp. 846–857 (2016)

An Evaluation Method for Anti-sEU Effects Design of SRAM-Based FPGA on Navigation Satellites Xuhui Liu, Shaojie Ni, Shengqiang Lou, Pengyue Sun(B) , and Yangbo Huang College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China

Abstract. In the space application of electronic equipment on navigation satellites, static random access memory (SRAM)-based field programmable gate array (FPGA) circuits will encounter single event effects (SEEs) in space radiation environment, which may lead to functional abnormalities. The mainstream measures often apply hardening technologies such as triple modular redundancy and refreshing error correction to the anti-SEU effects protection designs of FPGA circuits on navigation satellite. Since not all single event upsets (SEUs) will lead to system function failure, in order to comprehensively evaluate the validity of the protection design methods, based on FPGA resource characteristics, this paper firstly proposes an index called classified configuration data abnormal rate. On this basis, according to the effects of single event upsets in different configuration areas on the circuit function, the failure rate and curves of reliability change of different configuration structures are obtained. And through bit-by-bit upset fault injection tests based on the internal configuration access port (ICAP) circuits to verify these evaluation indicators, the experimental results prove the validity of the evaluation method. Keywords: Anti-SEU effects protection design · SRAM-based FPGA on navigation satellites · Internal configuration access port · Classified configuration data abnormal rate · The curves of reliability change

1 Introduction SRAM-based FPGA has the characteristics of low power consumption, low cost, high performance, high integration density and repeatable programming [1]. It is widely used in electronic equipment in the space segment of satellite navigation systems. High energy particles in space may cause single event effects when hitting the sensitive parts of electronic devices, which changes the logical state of the storage unit and leads to failure of the device [2]. Therefore, it is necessary to take effective hardening measures for the FPGA circuits on navigation satellites. Currently, common design hardening methods include Triple Modular Redundancy (TMR) and refreshing error correction [3]. In order to measure the reliability of SRAM-based FPGA circuits in space radiation environment, it is necessary to evaluate the ability of anti-single event upset effects. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 496–504, 2021. https://doi.org/10.1007/978-981-16-3146-7_46

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At present, the main index used in its reliability evaluation is the upset cross section [4, 5]. But for any FPGA-based design, not all Single Event Upset (SEU) will cause failure of system function, and some SEUs may not affect system function. There are two main reasons for this phenomenon: firstly, the design resources are limited, and the control bits corresponding to those programmable logic resources that are not occupied generally have no effect on the system function. The second reason is that the circuit may have adopted triple modular redundancy hardening designs. Although SEU occurred in some locations, it will not appear at the outputs of the system after passing through the majority voters. The existence of this special phenomenon makes the evaluation index called upset cross section unable to comprehensively and accurately evaluate the reliability of hardening designs of SRAM-based FPGA on navigation satellites. This paper proposes an evaluation method for anti-single event upset designs of SRAM-based FPGA on navigation satellites. The method firstly classifies according to the impact of different abnormalities on system functions, and proposes the index called classified configuration data abnormal rate. On this basis, the failure rate and curves of reliability change under different abnormal conditions are calculated, solving the quantitative evaluation problems when SEU has different effects on configuration memory. It provides a new solution accurately and comprehensively evaluate anti-SEU designs of SRAM-based FPGA on navigation satellites.

2 The Reliability Evaluation Method Based on Bit-By-Bit Upset Fault Injection Tests The SEE fault modes of SRAM-based FPGA on navigation satellites are mainly classified into two categories. One type is caused by SEUs in configuration memory, user triggers, etc., and the other is the failure caused by single event function interruption and single event transient pulse in power-on reset state machine and configuration state machine [6]. Among them, the first type is the most important manifestation, and SEUs in configuration memory accounts for more than 90% of them in SRAM-based FPGA [7]. Through program loading and fault injection, the configuration data of FPGA can be directly modified. At the same time, fault injection tests can be implemented on FPGAs to simulate SEE in space. The flow chart of the entire evaluation process is shown in Fig. 1, which mainly includes the following steps. 1) Selecting the locations of configuration memory and through implementing fault injection tests, counting the addresses of faults and the number of abnormal bits; 2) According to the impact of different abnormalities on system functions, we can divide it into three parts. If the system function interruption can be restored by readback refreshing, it belongs to the first type of abnormal situation. If the interruption of systematic function cannot be restored by readback refreshing, but restored by software reset, it belongs to the second type of abnormal situation. If it can only be recovered by power-on and reset, it belongs to the third type of abnormal situation. 3) Evaluating these situations respectively.

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Initialization

Through the fault injection tests, counting the error addresses and the number of abnormal bits Classification according to the impact of different abnormalities on system functions Calculating classified configuration data abnormal rate and finding upset rate of the FPGA in a specific scenario

Calculating circuit failure rate and reliability

End Fig.1. The flow chart of evaluation process

After the number of abnormal bits has obtained statistically through fault injection tests, the configuration data abnormal rate pij of the internal configuration structure j in the i-th type of FPGA abnormal situation can be calculated: pij =

bij × 100% btotal

(1)

Where bij is the number of abnormal bits of internal configuration structure j in the i-th abnormal situation. Since BRAM is mainly designed for hardening protection through internal self-refreshing, the probability of occurrence of abnormal bits in this part is low, so btotal is the total number of configuration bits of this type of FPGA except BRAM. This article applies XQR2V3000 FPGA, and btotal can be calculated as 7543040 by referring to Table 1 [8]. Looking up upset rate of the FPGA in a specific scenario in the FPGA data sheet, and calculating failure rate λi in the i-th abnormal situation: 1 λi =  ej j

pij

(2)

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Table 1. Virtex-II frame number per column Column type

IOB

IOI

CLB

Device

Columns per device

Frames per column

Columns per device

Frames per column

Columns per device

Frames per column

XQR2V1000

2

4

2

22

32

22

XQR2V3000

2

4

2

22

56

22

XQR2V6000

2

4

2

22

88

22

Column Type

BRAM Interconnect

device

Columns per device

Frames per column

Columns per device

Frames per column

XQR2V1000

4

22

1

4

XQR2V3000

6

22

1

4

XQR2V6000

6

22

1

4

GCLK

Where ej is the turnover rate of internal configuration structure j of the FPGA in a specific scenario, whose unit is h/(device · upset). λi is the failure rate of the i-th abnormal rate, whose unit is 1/year. Defining the failure rate function as: Number of failures per unit time Number of components facing failure Increment of failure probability per unit time = Original system reliability 1 Qi (t + t) − Qi (t) · = lim t→0 t Ri (t) dRi (t) 1 · =− Ri (t) dt λi (t) =

(3)

The formula for reliability of the i-th abnormal situation is: Ri = e−

t 0

λi (t)dt

= e−λi t

(4)

Where Qi (t) represents failure probability of the i-th abnormal situation, Ri (t) represents reliability of the i-th abnormal situation, and t represents time.

3 Bit-by-Bit Upset Fault Injection Tests 3.1 The Structure of Fault Injection System The designed schematic block diagram of fault injection system in this paper is shown in Fig. 2. The system is a stand-alone device that mainly contains 4 FPGAs and 1 DSP.

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Specifically, FPGA1 is responsible for running hardening configuration items to simulate TMR application scenarios. FPGA2 is responsible for running single modular configuration items and providing reference functions. FPGA3 is responsible for comparing the functional differences between FPGA1 and FPGA2. FPGA4 implements logic loading of the first three FPGAs, implementing partial refreshing and fault injection of FPGA1. The main functions of the DSP are as follows: ➀Controlling and configuring the normal functions of FPGA1 and FPGA2; ➁Controlling process of refreshing and fault injection; ➂Judging whether the function comparison is consistent. Then, taking down the discrepancies and taking measures to restore function before fault injection again.

DSP Address,data and clock

FPGA1

Interface signal

FPGA2

Interface signal

Controlling signal

Controlling signal

FPGA3 Controlling signal

FPGA4 Fig. 2. The schematic block diagram of TMR fault injection test platform

Among them, FPGA1 adopts a design scheme that combines TMR and feedback refreshing. The TMR design ensures detection and fault tolerance of SEU, and feedback refreshing can correct SEU errors in memory units. The traditional TMR design can ensure that after SEU occurs in any module of the triple modular design, the output getting through majority voters is still correct. Therefore, this design strengthens the FPGA’s ability to resist SEU to a certain extent. However, if faults continue to accumulate and cause SEUs to occur in any two modules of the triple modular design, the TMR design will produce wrong output at this time. It can be seen that traditional TMR structure design cannot prevent accumulation of SEU faults. In view of this, we adopted the TMR design scheme with a feedback refreshing mechanism as shown in Fig. 3. This scheme can still have correct output after SEU occurs in any module of the triple modular design. Because after the clock arrives, the module with SEU will correct the wrong data, which effectively prevents accumulation of SEU faults and improves reliability of FPGA1. 3.2 The Process of Fault Injection Tests The flow chart of the entire experiment test is shown in Fig. 4. It can be seen that FPGA2 runs single modular FPGA program and produces correct outputs. As the object of bit-by-bit upset fault injection tests. FPGA1 is mainly responsible for running FPGA triple modular hardening program. FPGA3 is responsible for comparing the functional differences between FPGA1 and FPGA2. Once the function is unusual due to fault injection, if the function comparison results are still inconsistent after waiting for a certain period of time, the DSP outputs abnormal interrupted function. At this time, the faults are considered unrecoverable and the fault injection takes effect. If the function

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A

D

Q

D

Q B

D

Q

Majority voter 0

Output TR0

Majority voter 1

Output TR1

Majority voter 2

Output TR2

Clock signal T0

Clock signal T1

C

Clock signal T2

Fig. 3. Implementation of TMR design with feedback refreshing mechanism

comparison results are consistent, then the faults are considered to be recoverable and the fault injection does not take effect at this time. FPGA4 is a loading FPGA chip, which mainly responsible for controlling the Slave SelectMap interface to load FPGA1 ~ 3 globally. In addition, it also implements the local dynamic refreshing and fault injection of FPGA1 with TMR designs. It is worth noting that faults can also be injected through the Joint Test Action Group (JTAG) interface [9, 10], but it has a defect of slow access speed. Therefore, it is the SelectMap interface that have been used for fault injection for FPGA1 with TMR designs. DSP controls the start and stop of functions of FPGA1 and FPGA2, comparing results and debugging information through the outputs from serial ports. Besides, it controls the start of dynamic refreshing of FPGA1 through FPGA4, traversing automatic fault injection tests except BRAM resources. Once the DSP detects unusual interruption of functions, it stops the process of function comparison, locking the current frame address of automatic fault injection and assigning start frame address to automatic faults injection. Besides, refreshing FPGA1 globally before the next fault injection, and injecting configuration frame data into all resources correctly except BRAM. Then restarting from the address where the fault was reported last time, and repeating the cycle until all resources have been traversed except BRAM.

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FPGA1

2

FPGA3

Initialization

FPGA4 Loading logic of FPGA1 3

Waiting to be ready Consistent function

1 3

Initializing FPGA1 3 4

8

Waiting for abnormal interruption 6

Handling abnormal function

FPGA1 runs TMR program, and FPGA2 runs single modular program

Functional comparison

2

Inconsistent function

5

Stopping functional comparison

7

Waiting for partial refreshing signal of FPGA1

Partial refreshing FPGA1

Reloading FPGA1

Fig. 4. The flow chart of tests

4 The Analysis of Test Results This article is based on Xilinx XQR2V3000 FPGA (applicable to other FPGAs). Specifically, FPGA1 implements TMR hardening designs. FPGA2 implements single modular functions and implementing bit-by-bit fault injections in configuration memory of FPGA1 with TMR hardening designs. At the same time, comparing the functions of the two FPGAs to determine whether an abnormality occurs after fault injection tests. The statistical results of the fault injection tests are shown in Table 2: Table 2. The statistical results of bit-by-bit upset fault injection tests Type

Classification according to abnormality

Number of abnormal bits

CLB

The first type

104

BRAM interconnect

The second type

29

IOB

The second type

3

GCLK

The third type

4

Referring to Xilinx Virtex-II series FPGA data sheet [11], we can see that when XQR2V6000 FPGA works in a geosynchronous orbit scenario, upset rates of its configuration memory and block memory are 1.8 h/(device ·upset) and 11.8 h/(device ·upset), respectively. According to the results of fault injection tests, the reliability parameters of the circuits with hardening protection designs obtained by formulas (1) and (2) are shown in Table 3. It can be seen from Table 3 that after the FPGA adopts anti-irradiation hardening protection designs, when working in geosynchronous orbits, its CLB is most prone to SEU, and 1-bit upset in this part occurs approximately every 34.2 years. However, 1bit upset occurs in BRAM interconnection and GCLK approximately every 503.2 years

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and every 609 years, respectively. Furthermore, IOB is relatively stable, with 1-bit upset approximately every 761.3 years. Table 3. The reliability parameters of circuit designs Type

Configuration data abnormal rate

Failure rate/(1/year)

CLB

0.0014%

1/34.2

BRAM interconnect

0.0004%

1/503.2

IOB

0.00004%

1/761.3

GCLK

0.00005%

1/609

From formula (4), the curves of reliability change of each configuration structure are shown in Fig. 5.

Fig. 5. The curves of reliability change of each configuration structure

5 Conclusions This paper proposes a reliability evaluation method for different abnormalities of SRAMbased FPGA on navigation satellites. Through implementing bit-by-bit upset fault injection tests and based on FPGA resource characteristics, different types of abnormalities can be classified and evaluated, which can be applied as a supplement method to evaluate reliability of software of FPGA on navigation satellites against SEU. Furthermore, through classification and evaluation of software design of Xilinx XQR2V3000

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FPGA, the failure rate and curves of reliability change of each configuration structure are obtained, which verifies validity and reliability of the evaluation method and provides a new solution for accurately and comprehensively evaluate reliability of the software-based anti-radiation hardening design methods. However, in the complex space irradiation environment, SRAM-based FPGAs still have the possibility of multiple bits upset failure, and the reliability evaluation of multiple bits upset needs to be studied in the future, so as to further improve the evaluation system of anti-SEU hardening design for SRAM-based FPGAs. Acknowledgments. This work is supported by the National Nature Science Foundation of China under Grant No. U20A0193, No. 62003354.

References 1. Carstenschmid, F.L., Carlo, L., Rice, R., et al.: Fault-Tolerant Technology of SRAM-Based FPGA. China Aerospace Publishing House, Beijing (2009) 2. Biwei, L.: Modeling and Hardening of Single Event Effect in Integrate Circuit. National University of Defense Technology, Changsha (2009) 3. Michel, H., Belger, A., Lange, T., et al.: Read back scrubbing for SRAM FPGAs in a data processing unit for space instruments. Adaptive Hardware & Systems 1–8 (2015) 4. Ningfang, S., Jiaomei, Q., Xiong, P., et al.: Evaluating SEU effects in SRAM-based FPGA with bit-by-bit upset fault injection. J. Beijing Univ. Aeronautics Astronautics 38(10), 1285–1289 (2012) 5. Xiong, P., Wei, D., Zhengguo, Y., et al.: Simulation and evaluation of SEU effects in SRAMbased FPGA with random fault injection. Microelectron. Comput. 35(7), 23–27 (2018) 6. Zhongming, W.: Techniques for Evaluating Single Event Effect in SRAM-based FPGAs, pp. 3–5. Tsinghua University, Beijing (2011) 7. Xilinx Inc. Device reliability report. UG116(v10.8) (2017) 8. Xilinx UG156(v3.1.2). Xilinx TMRTool User Guide. Xilinx User Guide (2017) 9. Sterpone, L., Violante, M.: A new partial reconfiguration-based fault-injection system to evaluate SEU effects in SRAM-based FPGAs. IEEE Trans. Nucl. Sci. 54(4), 965–970 (2007) 10. Herrera-Alzu, I., López-Vallejo, M.: Design techniques for Xilinx Virtex FPGA configuration memory scrubbers. IEEE Trans. Nucl. Sci. 60(1), 376–385 (2013) 11. Xilinx Corp. Virtex II platform FPGA user guider. http://www.xilinx.com/support/docume ntation/data_sheets/ds031.pdf. 2007-11-5/2010-11-8

BeiDou Satellite Navigation Terminal Effectiveness Evaluation Based on Cloud Theory Juan Wu(B) , Xiaolin Jia, and Ting Zang Xi’an Research Institute of Surveying and Mapping, Xi’an, China

Abstract. With the continuous development of the Beidou satellite navigation system, the Beidou satellite navigation terminal has been transformed from “bus slot + board card” to modularized and chip-based. Its functions, performance and practicability have been continuously improved, and it has been more and more widely used in military and civil fields. The effectiveness evaluation of the Beidou navigation terminal can accurately grasp the capabilities of the equipment in the process of use, and can provide an important basis for the design demonstration, appraisal and finalization of Beidou navigation terminal equipment. Effectiveness evaluation indicator system for BeiDou equipment is constructed based on the function of the equipment, and index weights are calculated through AHP method. Considering the randomness and uncertainty of the BeiDou equipment effectiveness evaluation, an integrated evaluation method which feasibility is studied by an example, is given using backward cloud and integrated cloud. The evaluation example and result analysis show that this method combining qualitative and quantitative analysis, is not only reduces the subjective factors in the evaluation, but also gets overall and visualized evaluation results, which provides a new way for effectiveness evaluation of BeiDou user equipment. Keywords: Cloud theory · Effectiveness evaluation · BeiDou satellite navigation terminal · Analytic hierarchy process (AHP) · Indicator system

1 Introduction With the rapid development of Beidou satellite navigation system, all kinds of Beidou terminal equipment, such as hand-held type, vehicle type, command type, timing type and so on, have played an important role in the military field. How to effectively evaluate the effectiveness of Beidou user machine is an important basis for fully understanding its application capability, clear positioning development level, and carrying out equipment design demonstration, equipment appraisal and finalization and military application. Effectiveness evaluation is a process of constructing effectiveness measurement index to qualitatively and quantitatively analyze and evaluate the capability and effectiveness of weapons under given conditions [1]. At present, the effectiveness evaluation of Beidou navigation terminal mainly adopts the combination of expert scoring and index weighted average. The advantage of this method is that the evaluation is simple and easy to operate, and the disadvantage is that the subjective factors have a great influence on © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 505–517, 2021. https://doi.org/10.1007/978-981-16-3146-7_47

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the results. Because there is no normalization of the index data of different dimensions, it is easy to lead to the weak role of some indicators, which leads to the deviation of the evaluation results. The evaluation method based on cloud model belongs to multi-index comprehensive evaluation method, which has been widely used in information systems and all kinds of weapons and equipment effectiveness evaluation. Wang Qinglong [2] constructed a comprehensive effectiveness evaluation function based on cloud model and applied it to the effectiveness evaluation of C4ISR system. Liu Wei [3] gave a calculation method for evaluating hierarchical cloud model. Guo Jiao [4, 5] and others discussed the problems existing in effectiveness evaluation of shipborne navigation equipment from the aspects of effectiveness evaluation object, effectiveness evaluation index system and effectiveness evaluation method. Based on ADC model, the comprehensive effectiveness evaluation index system of shipborne navigation equipment was established, and tried to use cloud model for effectiveness evaluation. In order to solve the problem of quantification of underlying index and index weight in cloud comprehensive operation in cloud model evaluation, based on the analysis of the characteristics of Beidou navigation satellite terminal effectiveness evaluation index, the quantitative models of neutral index and interval index are given. considering that the correlation of each index is weak, this paper proposes an improved floating cloud algorithm for cloud integration calculation, and the feasibility of the method is verified by numerical simulation.

2 Overview of Cloud Model Based on the combination of probability theory and fuzzy mathematics theory, the cloud model uniformly describes the randomness, fuzziness and relevance of the concept by giving random certainty to the sample points [6]. The definition and digital characteristics of cloud model are discussed in detail in references [7] and[8], which will not be repeated here. Through three digital features: expectation, entropy and super-entropy, different algorithms can be designed to generate cloud droplets and certainty, and different cloud models can be obtained, thus different clouds can be constructed. According to the central limit theorem, if the factors that determine the result of a random variable are not completely independent, or the magnitude of the factor action is not exactly the same, the random variable obeys the pan-normal distribution [9]. For the performance data of Beidou navigation terminal, the function of each performance index is not exactly the same, so the evaluation result obeys the pan-normal distribution. The normal cloud model belongs to pan-normal distribution, which can theoretically describe the efficiency of Beidou satellite navigation terminal. 2.1 Forward Cloud Generator The quantitative value is generated by the digital featureC(Ex , En , He ) of the cloud, which is called the forward cloud generator (forward cloud generator). Take the most commonly used second-order forward normal cloud generator as an example, the specific algorithm is as follows [10, 11]. Input: digital features Ex , En , He , and the number of cloud droplets generated n.

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Output: n cloud droplets Xi and their certainty μ(Xi ) (i = 1,2, …, n) algorithm steps: (1) Generate a normal random number Yi = RN (En , He ),He with En as expected value and He2 as variance. (2) Generate a normal random number Xi = RN (Ex , Yi ), with Ex as expected value and Yi 2 as variance.   (Xi −Ex )2 ; (3) Calculate μ(Xi ) = exp − 2Y2 i

(4) Xi with certainty μ(Xi ) becomes a cloud drop in the number field. (5) Repeat steps (1) to (4) until the required n cloud droplets are generated. 2.2 Reverse Cloud Generator Given the cloud droplets, the three eigenvalues of the cloud model Ex , En , He , are the reverse cloud generator (backward cloud generator). The existing algorithms of inverse cloud generator can be divided into the algorithm of inverse cloud generator based on certainty and the algorithm of inverse cloud generator without certainty. Because it is difficult to obtain samples with certainty in practical application, the algorithm has some limitations. The uncertain inverse cloud generator algorithm usually uses each order moment of the sample to directly estimate the digital features of the qualitative concept from a given data sample. The following is a specific algorithm of a commonly used reverse cloud generator [12, 13]. Input: the quantitative value of N cloud droplets in the number field space X1 and X2, …., Xn; Output: estimators of expected values Ex , Entropy En and Super Entropy He of a ˆ e. qualitative concept Eˆ x , Eˆ n , H Algorithm step: (1) Calculate the sample X1 , X2 , …, Xn., the sample mean, sample variance and absolute central moment of the first order sample of Xn, namely: X= S2 =

1 n-1

1 n

n 

Xi

i=1

n  2  Xi − X

n n    1    M Xi − X n - 1 Xi n

(1)

 − X

(2) Using the mathematical properties of the second-order normal cloud X, namely: ⎧ EX = Ex ⎪ ⎨ (2) E|X − EX | = π2 En ⎪ ⎩ 2 2 DX == He + En (3) By using the method of moment estimation, the system of equations can be obtained: ⎧ EX = ⎪ ⎨ Ex = X  (3) E|X − EX | = π2 En = M X − X ⎪ ⎩ 2 2 2 DX = He + En = S

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(4) From the above equation, the estimators of the parameters are as follows: ˆ =X Ex

 n     Xi − X ˆ =2 1 En πn Hˆ e =



(4)

i=1

ˆ 2 S 2 − EN

ˆ estimate is the unbiased estimate ofEx, From the reference [8], it is known that Ex ˆ ˆ are asymptotic normal unbiased estimators of En and He, respectively. while Enand He With the increase of En /He , the sum of squares of the errors of the three eigenvalues decreases exponentially [8].

3 Establishment of Index System 3.1 Index Hierarchy The premise of effectiveness evaluation is the establishment of effectiveness evaluation index system, and the evaluation result is directly related to the choice of index system. The efficiency index mainly includes performance index, quality index and so on. Each index should be independent of each other as far as possible, and the index data should be easy to collect, measure and calculate [14]. According to the above principles, taking into account the core competencies such as positioning, speed measurement, timing and communication of Beidou satellite navigation terminal, the supporting capability of general hardware platform and basic software application, as well as the applicable ability of users, the effectiveness evaluation index system of Beidou satellite navigation terminal is established as shown in Table 1 [15, 16, 17, 18]. The index system is composed of nine performance factor layers and corresponding indicators. In the effectiveness evaluation, the index system can be appropriately refined, added or deleted according to the different types of specific user computers and the specific requirements of the evaluation. 3.2 Index Weight The commonly used weight determination methods are expert evaluation method, grey correlation method, entropy method, analytic hierarchy process and so on. Among them, Analytic hierarchy process (AHP) is one of the most effective methods to construct statistical weights, which is widely used, and satisfactory results have been obtained in the application. There is no interdependent relationship among the internal elements of the index system established in this paper. therefore, this paper uses the combination of qualitative and quantitative analytic hierarchy process to determine the weight of each index. Firstly, the judgment matrix is obtained by comparing the relative importance of each index, and then the consistency of the judgment matrix is tested. if it does not meet the consistency requirements, the judgment matrix is revised. Finally, the maximum eigenvalue λmax of the judgment matrix A and the corresponding eigenvector W are

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Table 1. Effectiveness evaluation index system of Beidou satellite navigation terminal Number

Ability layer

Index layer

1

PVT capability C1

Positioning accuracy C11 Speed measurement accuracy C12 Timing accuracy C13

2

Signal receiving ability C2

Receiving sensitivity C21 Signal dynamic range C22 Signal acquisition time C23

3

Anti-interference ability C3

4

Communication ability C4

Anti-interference sensitivity C31 Interference suppression system C32 Communication frequency C41 Single communication information capacity C42

5

Hardware supporting capacity C5

CPU Performance C51 GPU Performance C52 RAM Performance C53 Display performance C54 Endurance time C55

6

Software support capability C6

Navigation performance C61 System management ability C62 Data management capability C63

7

Intact sexual ability C7

Fault detection rate C71 Fault identification rate C72 Availability rate C73

8

Safety protection capability C8

Environmental adaptability C81 System security C82 Data security C83

9

Dynamic adaptability C9

Maximum speed C91 Maximum acceleration C92

normalized as the weight of the index. In this paper, the formulas for calculating the maximum eigenvalues and Eigenvectors of the matrix by the square root method[19]are given. W = (w1 , w2 , L,wm )T

(5)

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m 

1

m

aij

j=1

wi =



m  i=1

m 

 1 , (i = 1, 2, L,m)

(6)

m

aij

j=1

λmax =

m  (AW )i i=1

mwi

(7)

4 Effectiveness Evaluation Calculation Method Based on Cloud Model After the establishment of the index system, the efficiency data are collected, such as positioning accuracy, speed measurement accuracy, signal reception sensitivity, navigation planning performance anti-interference ability, etc., and then, the single performance cloud model of the lowest index is obtained by using the reverse cloud algorithm; thirdly, the comprehensive performance attribute cloud model is obtained by combining the single performance cloud using the integrated cloud algorithm. Finally, by comparing the correlation with the evaluation standard cloud, the effectiveness evaluation result is obtained, and the cloud map of the evaluation result is obtained by using the forward cloud. 4.1 Evaluation Standard Cloud Considering the general cognition of comments, taking the percentile system as an example, less than 60 points are unqualified, 80 to 90 points are good, and more than 90 points are excellent. Therefore, this paper uses four evaluation grades: “excellent”, “good”, “qualified” and “unqualified”. In order to directly display the membership degree of cloud droplets on the cloud map, the evaluation result is between [0,1]. According to the “3 σ” principle of normal cloud [20], the calculation results are listed in Table 2. Figure 1 shows four evaluation criteria, in which the horizontal axis is the efficiency value and the vertical axis is the membership degree of the efficiency value. Table 2. Evaluation standard cloud model Evaluation grade

Score interval

Cloud model parameters (Ex,En,He) qualified

Unqualified

[0,0.6)

(0.30,0.100,0.030)

Qualified

[0.6,0.8)

(0.70,0.033,0.009)

Good

[0.8,0.9)

(0.85,0.017,0.002)

Excellent

[0.9,1]

(1.00,0.033,0.003)

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Fig. 1. Evaluation Standard Cloud Model

4.2 Underlying Indicator Cloud Model 4.2.1 Quantitative Processing Model of Index (1) Normalization of quantitative Indexes As the dimensions and orders of magnitude of the quantitative indicators are different, the indicators must be dimensionless before the effectiveness evaluation. The quantitative index of Beidou navigation user is mainly neutral index and interval index. The neutral index is the maximum or minimum value of the known index, and the interval index is the optimal interval and the maximum tolerance interval of the known index. The quantitative publicity of neutral index and interval index is shown in formula (8) and (9) [21].

(8) ⎧ g1 −xi ⎪ i < g1 ⎨ 1 − g1 −a , a TD ) = √ e 2σ 2 dx = σ √ e 2σ 2 d == σ √ e 2 dy = σ J (TD ) σ 2π TD 2π TD 2π TD

(18)

Where ξ is the measurement noise, x is a random variable, J is the probability density function of standard Gaussian distribution, and σ represents the standard deviation of the Kalman covariance matrix. The threshold TD can be solved by Eq. (18), where Pfd (GNSSfault) takes the value of 4 × 10–8 /h in Fig. 3 in Sect. 4.1, and n represents the number of fault hypotheses.   Pfd (GNSSfault) TD = σ J −1 Pfd , Pfd = n

(19)

In the case of a satellite with faulty measurements, if the sign of the noise is opposite to the true measurement, the presence of noise may reduce the magnitude of the fault,

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that is, a missed detection event has occurred. Therefore, the faulty measurement can be modeled as a Gaussian variable, so that the threshold is calculated based on the value of the probability of missed detection. 2  ∞  ∞ − 1 x2 − 1x 1 x 1 Pmd = P(F > an , F + ξ < an ) = √ e 2σ 2 dx = σ  √ e 2σ 2 d  = σ  J (an ) σ 2π an 2π an

(20)

Among them, F is the fault vector and Pmd is the probability of missed detection whose value is 1 × 10–8 /h in Fig. 4. an = σ  J −1 (Pmd )

(21)

Only when an is less than TD , false alarm and missed detection events will not cross. In the simulation analysis later, TD will be chosen as the threshold for MSS monitoring to ensure the continuity of the system.

5 Simulation and Analysis In the previous sections, the χ2 -MSS algorithm was analyzed theoretically. In this section, the algorithm will be simulated and analyzed to verify the performance of the algorithm. 5.1 Simulation Conditions In the simulation, the mask angle was 10° , and the constellation contains 30 satellites, of which 8 satellites are available. The predicted pseudo range of the jth satellite is expanded by a certain multiple to simulate the satellite fault. The probabilities of false alarm and missed detection are set to 4 × 10–8 /h and 1 × 10–8 /h respectively, the threshold for the first chi-square test, MSS fault identification and exclusion test are set to 50 m, 40 m and 52 m. Since the χ2 -MSS algorithm is aimed at satellite faults, the influence of INS error accumulation on the fault identification results is negligible. 5.2 Fault Identification Inject GNSS fault into satellites within 200 s–220 s. Figure 5(a) shows the simulation result of the gray box in Fig. 2. It can be seen from the figure that the chi-square test has judged the existence of the fault, but the specific faulty satellite cannot be identified. Figure 6 shows the simulation result of the red box in Fig. 2. Figure 6(a) shows the simulation result under a single fault condition, the blue line represents the solution separation p between the subset solution that has not removed the faulty satellite and the all-in-view solution, and the orange line represents the solution separation q between the subset solution that has removed the faulty satellite and the all-in-view solution. It can be seen from the comparison of the two lines that q exceeds the threshold and is much greater than p . Figure 6(b) shows the simulation results in the case of double faults. The lines in different colors represent the solution separation composed of different subsets. It can be seen from the Fig. 6(b) that for multiple satellites failing at the same time,

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(a)

(b)

Fig. 5. Chi-square test results: (a) FD, (b) exclusion test

(a)

(b)

Fig. 6. Simulation diagram of MSS FI: (a) single fault, (b) double faults

multiple test statistics may exceed the threshold, but the solution separation test statistic that does not include faulty satellites is still the largest, and it is the only one that can pass the exclusion test under the premise of no excessive exclusion. Figure 5(b) shows the simulation result of the green box in Fig. 2. After removing the faulty satellites identified in Fig. 6, the exclusion test passes. Compared with Fig. 5(a), it shows that the faulty satellites are correctly identified. 5.3 Performance Evaluation The blue line is the state error obtained by using the χ2 -MSS FI algorithm, the fault was captured at 209s, after which the state error showed a clear downward trend; the yellow line is obtained by using the chi-square test for fault detection and exclusion (FDE), that is, all GNSS observations within the failure time are discarded directly, although the growth rate of the state error has decreased, it will still increase significantly due to the accumulation of INS errors; the orange line is obtained by using the chi-square test for FD without any fault handling method, the state error does not rise until the fault ends (Fig. 7).

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Ending time

Capture time

Fig. 7. Comparison results of state errors using three methods

Figure 8(a) shows the peak position errors of the three methods when a 20s GNSS failure occurs. It can be seen that the χ2 -MSS method has the smallest peak position errors and can better ensure the accuracy of positioning results. Compared with not using any fault handling method, the error peaks in the three directions are reduced by 42%, 45%, and 43% respectively. In addition, since the failure time is short at this time, it is also effective to discard all GNSS observations during the failure time directly. However, when the failure time is longer, as shown in Fig. 8(b), due to the long-term accumulation of INS error, the result of this method will be very poor. At this time, compared with this method, χ2 -MSS method has reduced the error peaks of 53%, 66% and 63% in the three directions respectively.

(a)

(b)

Fig. 8. Peak position errors of three methods: (a) 20s GNSS fault, (b) 70s GNSS fault

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Next, compare the simulation trajectories of the above-mentioned methods when a 70s GNSS failure occurs, as shown in Fig. 9. Where the blue trajectory is the original trajectory, the motion trajectory obtained by using the χ2 -MSS method for FI has the highest similarity to it, and discarding the GNSS measurements directly will cause a serious deviation of the motion trajectory. As shown in Fig. 10, where the number 1 represents the use of the MSS algorithm, and 0 represents the use of the chi-square test. It can be seen that for this study, it is only necessary to start the MSS algorithm on demand during the failure period. This is a measure to reduce the algorithm complexity at the application level. As mentioned in Sect. 3, the χ2 -MSS algorithm also reduces the algorithm complexity from the theoretical level by reducing the number of subsets.

Fig. 9. Comparison results of simulation trajectories

Fig. 10. χ2 -MSS algorithm complexity

6 Conclusions This paper proposes an efficient FI algorithm for GNSS/INS integrated navigation, aiming to make a better balance between algorithm complexity and performance. Based on the propagation process of GNSS faults in KF, this paper designs chi-square and MSS test statistics; on the basis of the above research, an FI algorithm fusing chi-square and MSS is proposed; in order to calculate the threshold of the FI algorithm, the integrity risk and continuity risk are allocated. Simulation results show that this method can identify faulty satellites accurately and efficiently, avoid the occurrence of wrong or excessive exclusion. Compared with simple fault handling methods, this method has an accurate and efficient FI function: in the scenario of 20s short-term failure, compared with only using chi-square test for FD, the peak position errors in the north, east, and up directions are reduced by 42%, 45% and 43%; in the scenario of 70s long-term failure, compared with the use of chi-square test for FDE, the peak position errors of the three directions are reduced by 53%., 66% and 63%; compared with the (m − 1) method, this method is also effective in the case of multiple faults. Compared with the MSS algorithm with superior performance but high complexity, this method has the following advantages: in the fault detection step, MSS can be started on demand; in the exclusion test step, the

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number of subsets is reduced by CN1 × CN1 −1 × . . . CN1 −m . Therefore, the computational complexity is reduced while ensuring the efficient FI function. Acknowledgments. The authors would like to thank many people at the National Key Laboratory of CNS/ATM for their advice and interest. The work was carried out with financial support from the National Natural Science Foundation of China (grant nos. 61871012, 62022012, U1833125 and U2033215), the National Key Research and Development Program of China (grant nos. 2020YFB0505602 and 2018YFB0505105), Open Fund Project of Intelligent Operation Key Laboratory of Civil Aviation Airport Group (grant no. KLAGIO20180405), and the Beijing Nova Program of Science and Technology (grant no. Z191100001119134).

References 1. Bhatti, U.I.: An improved sensor level integrity algorithm for GPS/INS integrated system. In: ION GNSS, Fort Worth, TX, pp. 3012–3023 (2006) 2. Tanil, C.: Optimal INS/GNSS coupling for autonomous car positioning integrity. In: ION GNSS+ 2019, Miami, FL (2019) 3. Groves, P.: Principles of GNSS, Inertial and Multi-Sensor Integrated Navigation Systems, 2nd edn. Artech House, London (2013) 4. Tariq, A.: Building a robust integrity monitoring algorithm for a low-cost GPS-aided-INS system. Int. J. Control Autom. Syst. 8(5), 1108–1122 (2010) 5. Yongchao, W.: Research on autonomous integrity detection technology of satellite navigation aided by external equipment. Beijing University of Aeronautics and Astronautics, Beijing, China (2005) 6. Juan, B., Todd, W.: Advanced RAIM user algorithm description: integrity support message processing, fault detection, exclusion, and protection level calculation. In: ION GNSS 2012, Nashville, Tennessee (2012) 7. Clark, B.J.: GPS/INS integration with fault detection and exclusion in shadowed environments. In: IEEE/ION Position, Location and Navigation Symposium, Monterey, USA (2008) 8. Xin, H.: GNSS/IMU tightly coupled scheme with weighting and FDE for rail applications. In: ION ITM 2020, San Diego, California, pp. 570–583 (2020) 9. Shizhuang, W., Xingqun, Z.: Fault detection and exclusion for tightly coupled GNSS/INS system considering fault in state prediction. Sensors 20(3), 590 (2020) 10. Gongmin, Y.: Lecture notes on strapdown inertial navigation algorithms and integrated navigation principles. North-Western Polytechnical University, Xi’an, China (2016) 11. Bhatti, U.I.: Integrity of an integrated GPS/INS system in the presence of slowly growing errors part I: a critical review. GPS Solut. 11, 173–181 (2007) 12. Jinsil, L., Minchan, K.: Integrity algorithm to protect against sensor faults in tightly-coupled KF state prediction. In: ION GNSS 2019, Miami, Florida (2019) 13. Mathieu, J.: Fault detection and exclusion using solution separation and chi-squared ARAIM. IEEE Trans. Aerosp. Electr. Syst. 52(2), 726–742 (2016) 14. Blanch, W.: Baseline advanced RAIM user algorithm and possible improvements. IEEE Trans. Aerosp. Electr. Syst. 51(1), 713–732 (2015) 15. ICAO Annex 10: Aeronautical Telecommunications, Volume 1 (Radio Navigation Aids) (2016) 16. Wei, L., Dan, S.: Error bounds of the GNSS/INS integrated system against GNSS fault for integrity monitoring. In: ION ITM 2020, San Diego, California, pp. 557–569 (2020)

Policies, Standards and Intellectual Property Rights

Evaluation of Beidou Satellite Navigation Service Anti-jamming Capability Under International Standard Framework Ying Chen, Yuan Liu, Jianhua Shen(B) , Cheng Liu, Wei Wang, and Chengqian Lou The 54th Research Institute of CETC, Shijiazhuang 050031, China

Abstract. Anti-jamming capability is an important index of satellite navigation service. The anti-jamming capability is standardized in relevant standard documents such as International Civil Aviation Organization (ICAO), Radio Technical Commission for Aeronautics (RTCA), Aeronautical Radio, Incorporated (ARINC) and American Federal Aviation Administration (FAA). According to the basic framework of the international standard mentioned above, this paper carries out test and test on the anti-jamming ability of Beidou B1C signal, and carries out the baseline test on the pseudo-range tracking accuracy of the receiver of Beidou B1C signal in the aviation electromagnetic environment, and obtains relevant test data. On standardized test framework, Beidou B1C signal in limited bandwidth white noise interference tolerance, continuous wave interference tolerance and tolerance of the pulse interference and so on various types of interference tolerance under receiver capture signal carrier to noise ratio remained above 31 dB-Hz, the tracking error is lower than 0.5 m (1 sigma) of support the Beidou draft standards and recommended measures to develop and validate, which laid a foundation for the Beidou satellite navigation system to join the international standard system. Keywords: Anti-jamming capability · Beidou satellite navigation service · ICAO · Radio technical commission for aeronautical

1 Introduction The Beidou Navigation Satellite System is a Global Navigation Satellite System (GNSS) independently built and operated by China and compatible with other Satellite Navigation systems in the world. It can provide all kinds of users with high-precision, highly reliable positioning, Navigation and timing services all day and all day around the world. Going abroad and entering the international market is the inevitable development of the application of Beidou system, an important symbol of Beidou’s status as one of the four major GNSS core suppliers, and an important embodiment of China as a responsible major country. In numerous applications in the field of GNSS, the international civil aviation, the international maritime, international mobile communications, such as search and rescue is an important application field of GNSS, the typical industries to demonstrate the application effect, with release here Beidouinternational standards in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 573–581, 2021. https://doi.org/10.1007/978-981-16-3146-7_53

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the field of industry, is to obtain Beidouapplication in the field of relevant international trade passes, and expand the Beidouconstruction and application benefits, accelerate the industrialization and internationalization of Beidouinevitable choice. Since 2010, China has started to join the International Civil Aviation Organization (ICAO), and promote the formulation of Beidou international standards in international civil aviation. In ICAO standard, the anti-jamming description of GPS and GLONASS is as follows: in a specific aviation electromagnetic interference environment, GPS pseudo range tracking accuracy is 0.36 m, and GLONASS pseudo range tracking accuracy is 0.8 m (only affected by receiver loop noise, receiver clock and dynamics). The aviation EMI environment specified here is mainly non-hostile interference, which is derived from other existing airborne equipment (VHF, HF, DME, XPDR, SAT, etc.). Comparing the interference tolerance limits of GPS and GLONASS, it is found that the interference tolerance limits of both are completely the same in the part outside the band, but according to the difference in the central frequency points and working bandwidth of GPS and GLONASS, the corresponding tolerance adjustment is made in the band, and it is ensured that the on-board noise ratio of the receiver meets the specified index in the case of the interference tolerance after adjustment. The signal anti-jamming performance test of Beidou B1C mainly refers to the relevant standard documents of International Civil Aviation Organization (ICAO), Radio Technical Commission for Aeronautics (RTCA), Aeronautical Radio, Incorporated (ARINC) and Federal Aviation Administration (FAA). ICAO Standards And Recommended Practices (SARPs) puts forward requirements for GNSS system’s service performance, signal characteristics, messages, etc., as well as general requirements for the functions of airborne receivers. The requirements for the receiver include the elimination of satellites marked as unhealthy, tracking satellites, solving ephemeris and meeting certain anti-jamming requirements [1]. According to ICAO’s requirements, RTCA puts forward more specific technical requirements, refines the indicators according to different application backgrounds, and gives relevant implementation suggestions [2–7]. ARinc puts forward specific industrial application standards, and avionics manufacturers carry out product design, such as shape design, interface design, interface standard, etc., according to the specific standards [8–12]. The FAA Technical Standard Orders (TSO) provide a comprehensive description of the relevant RTCA standards, and only after meeting the FAA TSO certification can the navigation equipment be finally installed on the aircraft [13–20]. The standards of different organizations can be classified from an equipment perspective, including antenna standards, air-based Augmentation System (ABAS), ground-based Augmentation System (GBAS), and satellity-based Augmentation System (SBAS). For the anti-interference test of Beidou B1C and B2A receivers, there are many standards mentioned above and these standards echo each other.

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2 International Standard Requirements for Anti-jamming Capability of Satellite Navigation Services 2.1 Continuous Wave Interference (CWI) After the receiver enters the steady-state navigation state, it shall meet the CWI continuous wave interference tolerance performance as shown in Table 1. This interference level is defined at the antenna port, and the satellite signal level at the antenna port is −166.5 dBW (refer to the Beidou B1C ICD file). Table 1. CWI interference tolerance standards for B1C in steady-state. Interference frequency: fi

Interference tolerance limitation in steady-state

fi ≤ 1315 MHz

−4.5 dBW

1315 MHz < fi ≤ 1500 MHz

From −4.5 dBW to −38 dBW linearly

1500 MHz < fi ≤ 1525 MHz

From −38 dBW to −42 dBW linearly

1525 MHz < fi ≤ 1 565.42 MHz

From −42 dBW to −150.5 dBW linearly

1565.42 MHz < fi ≤ 1585.42 MHz

−150.5 dBW

1585.42 MHz < fi ≤ 1610 MHz

From −150.5 dBW to −60 dBW linearly

1610 MHz < fi ≤ 1618 MHz

From −60 dBW to −42 dBW linearly

1618 MHz < fi ≤ 2000 MHz

From –42 dBW to −8.5 dBW linearly

1610 MHz < fi ≤ 1626.5 MHz

From −60 dBW to −22 dBW linearly

1626.5 MHz < fi ≤ 2000 MHz

From −22 dBW to −8.5 dBW linearly

fi > 2000 MHz

−8.5 dBW

2.2 Additive White Gaussian Noise (AWGN) After entering the steady state of the navigation receiver, it should satisfy Table 2 with limited bandwidth white noise tolerance performance goals, and the limited range of 1575.42 MHz ± Bwi/2 bandwidth white noise interference plus or minus (Bwi) is the equivalent noise jamming signal bandwidth, the antenna ports of the satellite signal level is 166.5 dBW (−161–5.5 dBW) (refer to beidou B1C ICD files). 2.3 Pulse Interference After the receiver enters the steady-state navigation state, it shall meet the pulse interference tolerance performance objective in Table 3.

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Interference frequency Bwi

Interference tolerance limitation in steady-state

0 Hz < Bwi ≤ 700 Hz

−150.5 dBW

700 Hz < Bwi ≤ 10 kHz

From −150.5 to −143.5 dBW linearly

10 kHz < Bwi ≤ 100 kHz

From −143.5 to −140.5 dBW linearly

100 kHz < Bwi ≤ 1 MHz

−140.5 dBW

1 MHz < Bwi ≤ 20 MHz

From −140.5 to −127.5 dBW linearly

20 MHz < Bwi ≤ 30 MHz

From −127.5 to −121.1 dBW linearly

30 MHz < Bwi ≤ 40 MHz

From −121.1 to −119.5 dBW linearly

40 MHz < Bwi

−119.5 dBW

Table 3. Pulse interference tolerance standards for B1C in steady-state. BDS B1C Frequency

1 575.42 MHz ± 20 MHz

Near band or in band interference threshold (pulse peak power)

−20 dBW

pulse width

≤125 µs

Pulse duty cycle

≤1%

jamming signal band width

≥1 MHz

3 Beidou B1C Signal Airborne Electromagnetic Environment Interference Test Framework Based on two typical products of standard receivers, Novatel OEM7 Series and domestic receivers, ComNav Technology Ltd. K708 Series, the anti-interference test of Beidou B1C signals is carried out, and the acquisition threshold and pseudo range tracking accuracy of B1C signals are measured under given sweep interference, limited bandwidth noise interference and pulse modulated interference. It should be noted that the pseudo range tracking accuracy test does not include errors caused by signal propagation such as multipath errors, tropospheric and ionospheric errors, as well as spatial and control segment errors such as ephemeris errors and star clock errors. The basic form of interference testing framework is shown in Fig. 1.

4 Beidou B1C Signal Test Results 4.1 CWI Signal Interference Based on the test framework shown in Fig. 1 and the CWI interference standard requirements shown in and Table 1, the anti-CWI interference performance of Beidou B1C signals was evaluated by using both foreign and domestic receivers.

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Special interference source

Amplfier

Navigaon signal simulator

Clock source

Combiner and switch matrix

Foreign receivers

Program controlled DC supply

Domesc receiver

Program controlled DC supply

Power divider

signal source

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Signal analyzer

gateway

Auto calibraon module

Switch

Test control unit

acquision unit of test data

post processing module

Fig. 1. The basic form of interference testing framework for B1C.

Under the condition of CWI interference, the SNR data output of standard receivers captured B1C signals is shown in Fig. 2. As can be seen from Fig. 2, under the interference of CWI, the on-board noise ratio output of receivers is basically stable, which remains above 29 dB-Hz, and the average is around 33 dB-Hz.

Fig. 2. The SNR data output of standard receivers captured B1C signals.

Under the condition of CWI interference, the data output of the standard deviation of pseudo distance tracking error of captured B1C signals by standard receivers is shown in Fig. 3. As can be seen from Fig. 3, the pseudo-range tracking error of foreign B1C receivers is better than 0.4 m (1 sigma) under the interference of CWI.

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Fig. 3. The data output of the standard deviation of pseudo distance tracking error of captured B1C signals by standard receivers.

4.2 White Noise Interference with Limited Bandwidth Based on the test framework shown in Fig. 1 and AWGN interference standard requirements shown in Table 2, the anti-AWGN interference performance of Beidou B1C signals was evaluated by using standard receivers and domestic receivers. Under the condition of AWGN interference, the data output of the B1C signal’s load-noise ratio captured by standard receivers is shown in Fig. 4. As can be seen from Fig. 4, after the addition of AWGN interference, the on-board noise ratio of standard receivers deteriorated somewhat, and the on-board noise ratio basically remained above 29 dB-Hz, and the average is around 31 dB-Hz.

Fig. 4. The data output of the B1C signal’s load-noise ratio captured by standard receivers.

Under the condition of AWGN interference, the data output of the standard deviation of the pseudo distance tracking error of the captured B1C signal by standard receivers is

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shown in Fig. 5. As can be seen from Fig. 5, under AWGN interference, the pseudo-range tracking error of foreign B1C receivers is better than 0.3 m (1 sigma).

Fig. 5. The data output of the standard deviation of the pseudo distance tracking error of the captured B1C signal by standard receivers

4.3 Pulse Interference Based on the test framework shown in Fig. 1 and pulse jamming standard requirements shown in Table 3, the anti-pulse jamming performance of Beidou B1C signals was evaluated by using both standard receivers and domestic receivers. Under the condition of pulse interference, the output of the SNR data captured by standard receivers for B1C signals is shown in Fig. 6. As can be seen from Fig. 6, after the addition of pulse interference, the on-board noise ratio output of standard receivers

Fig. 6. The output of the SNR data captured by standard receivers for B1C signals.

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is basically stable, and its on-board noise ratio is basically kept above 31 dB-Hz, and the average is around 33 dB-Hz. In the condition of pulse interference, the data output of the standard deviation of pseudo distance tracking error of captured B1C signal by standard receivers is shown in Fig. 7. As can be seen from Fig. 7, the pseudo-range tracking error of foreign B1C receiver is better than 0.45 m (1 sigma) under pulse interference.

Fig. 7. The data output of the standard deviation of pseudo distance tracking error of captured B1C signal by standard receivers.

5 Conclusion Under the framework of international standards, the performance of Beidou Global System B1C signals under various types of interference conditions is tested, and the test results are summarized as follows: (1) In the case of B1C limited bandwidth white noise tolerance interference, the B1C signal load-noise ratio of receivers is kept above 31 dB-Hz, and the receiver tracking error is better than 0.3 m (1 sigma). (2) In the case of B1C CWI, the B1C signal load-noise ratio of receivers is kept above 33 dB-Hz, and the receiver tracking error is better than 0.4 m (1 sigma). (3) In the case of B1C pulse tolerance interference, the B1C signal load-noise ratio of receivers is kept above 33 dB-Hz, and the tracking error of the receiver is better than 0.45 m (1 sigma). In summary, empirical evidence, The signal design of Beidou Global System B1C conforms to the requirements of ICAO, Radio Technical Commission for Aeronautics (RTCA), Aeronautical Radio, Incorporated, ARINC and the Federal Aviation Administration (FAA). It has the basic conditions for incorporation into the international standard system.

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Acknowledgments. Under the support of Air traffic management bureau of China civilaviation administration and China Satellite Navigation Office, the Beidou ICAO standardization work team was organized with Beihang National Key Laboratory of ATM/CNS, TianJin 712 Communication & Broadcasting Co., Ltd. and other industry, education, research organizations. The work team has completed all the technical validation in ICAO and has achieved a major breakthrough in the past 10 years. The author would like to express sincere thanks to the Beidou ICAO standardization work team for their important work in the early stage.

References 1. ICAO: Convention on International Civil Aviation 2. RTCA: DO-208, Minimum Operational Performance Standards for Airborne Supplemental Navigation Equipment Using Global Positioning System (GPS) 3. RTCA: DO-228, Minimum Operational Performance Standards for Global Navigation Satellite Systems (GNSS) Airborne Antenna Equipment 4. RTCA: DO-301, Minimum Operational Performance Standards for Global Navigation Satellite System (GNSS) Airborne Active Antenna Equipment for the L1 Frequency Band 5. RTCA: DO-253C, Minimum Operational Performance Standards for GPS Local Area Augmentation System Airborne Equipment 6. RTCA: DO-229D, Minimum Operational Performance Standards for Global Positioning System/Wide Area Augmentation System Airborne Equipment 7. RTCA: DO-235B, Assessment of Radio Frequency Interference Relevant to the GNSS L1 Frequency Band 8. ARINC: Characteristic 743, Airborne Global Positioning System Receiver 9. ARINC: Characteristic 743A, GNSS Sensor 10. ARINC: Characteristic 743B, Global Navigation Satellite System (GNSS) Landing System Sensor Unit (GLSSU) 11. ARINC: Characteristic 755-4, Multi-Mode Receiver (MMR)-Digital 12. ARINC: Characteristic 756-3, GNSS Navigation and Landing Unit (GNLU) 13. FAA: TSO-C190, Active Airborne Global Navigation Satellite System (GNSS) Antenna 14. FAA: TSO-C144a, Passive Airborne Global Navigation Satellite System (GNSS) Antenna 15. FAA: TSO-C145d, Airborne Navigation Sensors Using The Global Positioning System Augmented By The Satellite Based Augmentation System (SBAS) 16. FAA: TSO-C146d, Stand-Alone Airborne Navigation Equipment Using The Global Positioning System Augmented By The Satellite Based Augmentation System 17. FAA: TSO-C196a, Airborne Supplemental Navigation Sensors for Global Positioning System Equipment using Aircraft-Based Augmentation 18. FAA: TSO-C161a, Ground Based Augmentation Sys 19. Interference Mask and Anti-Interference Testing for BDS B1C and B2a signals, JWGs/5, Montreal, 15–24 October 2019 20. Wang, P., Shi, X., Wang, T., Wang, Z.: Civil avionic EMI surrounding impact assessment and testing on the performance of Beidou B1I signal. In: Sun, J., Liu, J., Yang, Y., Fan, S., Yu, W. (eds.) CSNC 2017. LNEE, vol. 437, pp. 645–657. Springer, Singapore (2017). https://doi. org/10.1007/978-981-10-4588-2_55

Research on the Trademark Strategy of Beidou Industry Yuxuan Wang(B) China Industrial Control Systems Cyber Emergency Response Team (Electronic First Research Institute, Ministry of Industry and Information Technology), Beijing, China

Abstract. The Beidou-3 global satellite navigation system has been opened, the innovation entities of China attach great importance to the patent layout of Beidourelated technologies and the cultivation of high-value patents. At the same time, the trademark protection of the Beidou industry and key innovation entities is slightly weak. To this end, this article starts from the aspect of theory and practice, analyzes the current status of Beidou trademark applications and trademark litigation cases, studies the trademark strategy of Beidou industry. In order to improve the intellectual property protection performance of China’s satellite navigation industry, this paper puts forward the mechanism and path from the perspective of improving the awareness of trademark protection, increasing the operation model of collective trademarks and certification trademarks, strengthening research on the trademark system of the targeted Belt and Road countries, exploring the protection of well-known trademarks and strengthening the training of intellectual property rights. Keywords: Beidou industry · Trademarks · Application · Operation · Protection

The Beidou-III Global navigation satellite System was officially launched on July 31, 2020. At present, the BDS is in a critical period of popularizing the application of BDS. The innovation subjects in Beidou industry attach great importance to the patent layout of core technologies and products. In trademark field, however, the current application, use and protection situation of Beidou official logo associated with Beidou enterprises trademark is uneven.

1 Status Quo of Protection for Beidou Related Marks 1.1 Status Quo of the Protection of Beidou Official Symbols In the similar trademark query page on the website of the Trademark Office in China, “Beidou Navigation Satellite System” was used as the keyword to search in category 9. As of December 25, 2020, there were 26 relevant trademark application information. The retrieval result of the first item with the highest relevance is: the official logo of “Beidou Navigation Satellite System” applied by Beijing Institute of Space Science and Technology Information, it was applied on October 20, 2010, and approved for registration on March 7, 2014. If Beijing Institute of Space Science and Technology Information was © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 582–587, 2021. https://doi.org/10.1007/978-981-16-3146-7_54

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searched as the subject of the application, it can be found that it has 70 registered trademarks. In addition to its application in category 9, it also applied trademarks “beidou ) in category 19-building materials supplies, 3-daily satellite navigation system” ( chemicals, 32-beer beverage, 11-air conditioning of lamps and lanterns, 36-financial management, 06-metal materials, 42-web services, 01 chemical raw material, etc. 1.2 Status Quo of Trademark Protection for Key Enterprises in Beidou Industry In order to investigate the status quo of trademark protection in enterprises of different sizes, 9 enterprises are selected to be studied of their efforts in trademark application and other intellectual property rights protection. It was found that Beijing BDStar Navigation Co., Ltd. (BDStar Navigation) currently has 89 registered trademarks, including BDStar Smart Network, BDStar Smart Network„ Beidou Zhilian, etc., which are registered in the 9th, 12th, and 42nd categories. Beijing Unistrong Science & Technology Co., Ltd. (hereinafter referred to as “Unistrong”) now , Unistrong, RINO TRACK, Beidou has 167 registered trademark, including Plus, etc., registered in 9th, 38th, 35th categories. Hwa Create Corporation (hereinafter referred to as “Hwa Create”) has 93 registered trademarks, including the trademarks , etc., which are registered in categories 9, 38, etc. Guangzhou of HWAIC, Haige Communications Group Incorporated (hereinafter referred to as “Haige Communications”) has registered 13 trademarks, including Tiantong Partner, Haige Tiantong Partner, Haige Communications, SAT Haige, etc., which are registered in category 9, 38, etc. Taidou Microelectronics Technology Co., LTD. (hereinafter referred to as “Taidou Microelectronics”) owns 45 trademarks such as Taitou, Location Geek and TECHTOP, which are registered in categories 9, 12 and 38. Several small and medium-sized enterprises in Beidou satellite navigation industry were selected for trademark strategy analysis. Sichuan Beidou Xinghe Technology Co., Ltd. has no registered trademarks. Xiamen Beidou Information Technology Co., Ltd. has a similar situation, Guangdong Qiaoxing Aerospace Technology Co., Ltd. once applied for a trademark named “Beidou SOS”, which has been invalid now [1].

2 Typical Trademark Litigation in Beidou Industry 2.1 Trademark Reverse Confusion Case In Beidou industry, the case of “Renwo You” of Unistrong is a typical trademark litigation case. The plaintiff, Zhang Chunlong, applied for registration of the trademark “Renyi You” on August 15, 2003. The trademark was approved to be registered on April 14, 2005, which approved the use of navigation equipment such as network communication. Zhang subsequently licensed Beijing Lakeway to use the trademark. On June 6, 2008, Unistrong was approved to register the trademark “Renwo You”. The plaintiff sued that it is found that consumers confuse the source of communication products of “Renyi you” and navigation products of “Renwo You”, affect the normal sales of its products. After hearing the case, the court held that the products of network communication equipment and the products of vehicle navigation equipment did not constitute similar commodities

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from the perspective of different functions, uses and consumption objects. Moreover, even if the plaintiff did not use the registered trademark in a standardized way, even if the relevant public generated reverse confusion, the plaintiff was also held responsible. The court ruled that the plaintiff lost the case. 2.2 Trademark Rejection Review Cases Take a trademark rejection review case between Taidou Microelectronics and THE State Intellectual Property Office [2] as an example. On the ground that the trademark in dispute constitutes the situation referred to in Article 30 of the Trademark Law, the Trademark Review and Adjudication Board rejected the application for the registration of the trademark in dispute on the commodities under review. TAIDOU Microelectronics claimed that the trademark in dispute can be distinguished from the trademark No. 8573191 of “TAIDOU” (referred to as cited trademark II) of Henan TAIDOU Three-star cable Co., LTD. And the revocation procedure of the cited trademark II has been initiated because the trademark has not been used for three consecutive years. After hearing the case, the court held that the holder of the cited trademark II had been dissolved and cancelled, and his qualification as a legal subject had been lost, and there was no evidence to show that he had dealt with the rights of the cited trademark II. Therefore, the cited trademark II has lost the function of distinguishing the source of goods, and is no longer constitutes an obstacle to the application for trademark registration and has a material impact on the outcome of the trial of this case. Therefore, the defendant should re-examine the case after this judgment takes effect.

3 Problems in Beidou Industry Trademark Protection 3.1 The Trademark Protection Awareness of Relevant Enterprises is Not Strong Enough In Beidou industry, a large number of small and medium-sized enterprises pay little attention to trademark protection except that a few listed enterprises or large enterprises have relatively clear trademark strategies. For Beidou listed companies view in the international market, international trademark registration of products is extremely important. At present, the international registration of trademarks of Beidou industry situation is not optimistic, without increase awareness of trademark protection, and international application by the Madrid agreement, we may lose the initiative in the international market. 3.2 Lack of Experience in Trademark Operation Trademark is one of the most important intangible assets of an enterprise, and it is also an important guarantee for its market competition. Most of the enterprises put the trademark on the shelf after the completion of trademark registration and have no intention to make further use of the trademark. Currently, there are no operating cases related to trademark transfer or licensing found in Beidou enterprises.

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3.3 Few Competitive Trademarks In the Beidou industry, there are few well-known trademarks and brands, so it is difficult for the public to hear them well, which is not commensurate with the status of the Beidou industry. After the market regulatory authorities stopped recognizing well-known trademarks and adopted the principle of recognizing famous trademarks on demand, through which way to operate Beidou related enterprises’ trademarks and improve their brand competitiveness is also a big problem. It is also very necessary to implement Beidou industry trademark development strategy.

4 Suggestions and Strategies for Beidou Industry Trademark Development 4.1 Enhance the Awareness of Trademark Protection and Make a Good Plan for Brand Protection First of all, in the development process of state major projects, the concept should be changed. We should prepare trademark layout in advance, well-organize the trademark applications and grasp the opportunity to lead behind. In the meanwhile, other individuals or enterprises should be prevented from rushing to register with the intention of free-riding. In major national projects such as Beidou, independent and distinct brand concepts and core brand values should be adopted. It is necessary to establish a classification management system for trademarks, apply for registration and protection of secondary trademarks other than major trademarks, and provide all-round protection for Beidou and other projects. Enterprises in Beidou industry should strengthen the awareness of trademark registration, use, management and protection, and make the best strategic planning for brand protection. When making development plans, enterprises should study the trademark policies of the countries and regions that may be involved in the product in advance, investigate the relevant provisions of the local trademark registration protection, and determine the local trademark protection strategies. If an enterprise suffers losses due to improper use of its trademark, it should take the initiative to study the trademark protection rules at home and abroad, strengthen the crackdown on illegal acts, and protect its own legitimate rights and interests. Through the three-dimensional protection of the trademark to establish a complete trademark protection network, and maintain the integrity of the brand in the international market. 4.2 Increase the Operating Model of Collective Trademarks and Certification Trademarks to Enhance Protection At present, China’s Beidou-related enterprises can only use registered product trademarks or service trademarks in publicity. However, due to the huge differences in trademarks between enterprises, it is difficult to form a large-scale publicity effect in the industry. It is recommended to establish an intellectual property association or alliance in the Beidou industry to apply for the registration of a collective trademark or certification mark with this identity. Through the common and shared characteristics of collective

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trademarks, the joint members can strengthen their strength, promote intensive operation and expand product promotion. 4.3 Strengthen Research on the Trademark System of the Targeted Belt and Road Countries At present, Beidou basic products have been exported to more than 120 countries and regions, including more than 30 “Belt and Road” countries. This is also the international market that many Beidou companies focus on. Before going abroad, trademark layout should be carried out in advance, and the trademark system of the destination country should be studied. At present, China’s “Beidou” has been accurately applied in different scenarios in many countries such as Thailand warehousing and logistics, Indonesia, as well as Kuwait, Uganda, Myanmar, Maldives, Cambodia, Pakistan and many other countries. Therefore, companies need to formulate specific trademark strategies for these countries before going abroad. There are four main ways for companies to register trademarks abroad, namely, country-by-country registration, EU registration, African Intellectual Property Organization registration, and Madrid trademark international registration. Taking the aforementioned countries as examples, Uganda, Myanmar, Pakistan, Maldives, and Kuwait have adopted the method of country-by-country registration; Cambodia, Thailand, Indonesia, and the Philippines can register international trademarks through Madrid. In addition, although most countries adopt a trademark registration protecting system, there are still major differences from China in terms of specific systems, procedures, and details. Enterprises need to pay more attention and formulate scientific and effective protection plans for the target country. Many countries have trademark authorities and trademark laws, and have relatively complete trademark registration protection systems. However, take the Maldives, where the Beidou products already sold, as an example, it has no trademark law or trademark registration system. It can only show the public its ownership of a certain trademark by publishing a warning notice in the local newspaper. In countries such as Cambodia and Philippines, applicants are required to actively submit trademark use evidence or use oath to the trademark authority within a specified time. 4.4 Improve the Protection of Official Logos and Names and Explore Ways to Protect Well-Known Trademarks On the one hand, we can learn from the protection of the Olympic logo and other ways to strengthen the protection of Beidou official logo [3]. On the other hand, the Beidou industry should strengthen the brand consciousness, building famous brand and well-known trademarks. At present, China implements the principle of recognizing wellknown trademarks on demand, and Beidou related enterprises can take the initiative to use the rules to identify well-known trademarks if there is a need, so as to improve their brand competitiveness.

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4.5 Strengthen Intellectual Property Training and Improve the Ability to Deal with Trademark Infringement To further improve the planning and layout of Beidou brand and trademark protection, the Beidou industry needs to strengthen intellectual property training for all kinds of enterprises, especially training in trademark management, application and protection. It is suggested to adopt the following measures: demonstrate the application for trademark is not similar to the cited trademark, apply for revocation of the cited trademark that has not been used for three consecutive years, file argument of objections, reach the agreement of trademark coexistence with the prior right owner and other legal means.It is important to promote the healthy development of Beidou industry through continuous improvement of trademark strategy and accumulation of protection experience.

References 1. https://www.tianyancha.com/?jsid=SEM-BAIDU-PZ-SY-20201109-BIAOTI. Accessed 20 Dec 2020 2. See Beijing Intellectual Property Court (2019) No. 9193, Jing73 Xingchu, Taidou Microelectronics Technology Co., Ltd. and other first-instance administrative judgments of SIPO 3. Jing, X.: The Name of Beidou Need Legislation Protection. http://epaper.cbt.com.cn/ep_m/ cbtm/html/2018/06/14/03/03_48.htm

Research on Business Model Innovation of Beidou Satellite Navigation System Qingyi Gao1(B) , Jiachen Fan2 , Jinping Yu3 , and Wuxiang Zhu4 1 Beihang University, Beijing 100191, China 2 Tongji University, Shanghai 200092, China 3 China Industrial Control Systems Cyber Emergence Response Team, Beijing 100040, China 4 Tsinghua University, Beijing 100084, China

Abstract. With the completion of the global constellation deployment of beidou3, Beidou satellite navigation system has entered the stage of industrial application. In this paper, the business model structure of GPS, GLONASS, Galileo and Beidou system is analyzed from the perspective of resource capacity complementarity and transaction value. Through comparative analysis, this paper studies the interaction, main practices, characteristics and effectiveness of Beidou business model, and discusses the optimization direction of Beidou system business model in the future. It assist Beidou Systems and related companies to optimize their business models and strengthen their competitive advantages in the global GNSS market. Keywords: Beidou · Satellite navigation · Business model · Competitive advantage

1 Introduction The deployment of the Beidou system’s global networking system was completed, means the development of Beidou shifted from system construction to industrial application; Now, Beidou industrial application became one of the eight key directions for improving the core competitiveness of China’s manufacturing industry. Beidou application is an important area of business model innovation, and business model innovation is an accelerator for the development of the Beidou system. Relevant scholars have successively studied the industrial application foundation and application methods of the Beidou system in the fields of ship dynamic monitoring, geological disaster monitoring, smart grid construction, and vehicle navigation (Huang et al. 2020; Zhu et al. 2020). However, there has not yet been a systematic study of the business model of Beidou industry application. Therefore, it is of great significance to study the business model architecture and innovative methods of the Beidou system industry application. The definition and building blocks of business models are not unified yet. Amit and Zott define a business model as “transaction content, structure and mechanism designed to create value.” (Amit and Zott 2001); Wei Wei and Zhu Wuxiang defined business model as “transaction structure between focus enterprises and stakeholders”, and proposed a four-module description framework for business models—the resource capacity © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 588–597, 2021. https://doi.org/10.1007/978-981-16-3146-7_55

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of the transaction subject, the transaction method and carrier, source and distribution of transaction income, transaction conflict and transaction risk management (Wei et al. 2012; Tan et al. 2019). Based on Wei Zhu’s business model theory, this paper studies and analyzes the innovative characteristics of the Beidou satellite navigation system business model, and puts forward some suggestions.

2 Status of Business Models of Foreign Satellite Navigation Industry The global satellite navigation (GNSS) industry application is a hotspot of competition among major aerospace countries. The 2019 Global Satellite Navigation Market Report released by the European Global Navigation Satellite System Agency (GSA) shows that the total global GNSS market in 2019 is about 150.7 billion euros. It is estimated that the total GNSS market value will reach 324.4 billion euros in 2029. Studying the business model and transaction structure of GPS, GLONASS, and Galileo can provide a reference for evaluating and optimizing the business model of Beidou system. First, we analysis of business model of GPS and GLONASS system. The development model of GPS system and GLONASS system are highly similar, this section only introduces the industrial application model of GPS system as a representative (see Fig. 1).

Fig. 1. GPS & GLONASS business model

Industrial manufacturers produce and sell related products based on GNSS technology. The GNSS system will receive revenue in the form of service authorization fees. In this process, the government will provide policy support. Companies in other industries use GNSS equipment to improve value creation capabilities. We takes precision agriculture as an example (see Fig. 2). GPS industry manufacturers obtain sales revenue by providing GPS products and pay authorization fees. Irrigation equipment manufacturers use GPS technology to upgrade their irrigation equipment and provide precise irrigation solutions to farms. Agricultural machinery manufacturers produce advanced agricultural machinery and obtain sales revenue. Agricultural machinery cooperatives purchase large-scale agricultural machinery equipment from agricultural machinery manufacturers to provide facilities and services

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Fig. 2. GPS system precision agriculture business model

to members and charge corresponding fees. Together with the remote sensing satellite system, the GPS system provides “positioning + remote sensing” services to agricultural information integration system manufacturers. Second, we analyse Galileo system’s business model. The Galileo system is a civil GNSS system built by the European Union. Based on its own resource capacity and the characteristics of the EU’s aerospace industry, the Galileo system has explored a set of industrial application models with EU characteristics (see Fig. 3).

Fig. 3. Galileo system’s business model

The Galileo system was initially built, deployed and operated by the franchise group (GOC), and the GOC enjoyed the franchise rights of the project. GOC has become the main manufacturer of basic products and terminal products in the EU GNSS industry, which limits the development speed and innovation capabilities of Galileo system supporting industries. At the same time, the eight companies have been unable to reach an agreement on the distribution of benefits, resulting in increased project delays. Last, based on the above analysis, this article summarizes the characteristics of the GNSS system business model. Business activity structure. The business activity structure of the GNSS system generally consists of the production and sales of GNSS equipment and other industry-enabling business activities; The transaction subject. There are differences in the structure of transaction entities in different business activities of the GNSS system. In the remaining two business activities, the transaction body structure tends to be diversified; The transaction method. The GNSS system uses authorization to conduct transactions with GNSS industry manufacturers and other industry entities. Devices produced by GNSS industry manufacturers need to be authorized by the GNSS system to

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use related functions and services. Enterprises and consumers in other industries can obtain authorization for GNSS-related functions as long as they purchase GNSS basic products or terminal products; The transaction income. GNSS revenue comes from service authorization revenue. A part of the licensing fee included in a single product is transferred to other industrial enterprises and consumers through the sale and purchase relationship; The transaction risk. The GNSS system manages national defense risks through confidentiality of technical information. The government promotes legislation and introduces management measures, and strengthens market supervision to manage opportunistic risks.

3 Business Model Innovation of Beidou System The Beidou system has obvious advantages in the application and development of GNSS industry. As shown in Fig. 4, in 2019, the Asia-Pacific region held 3.4 billion GNSS terminal equipment, with a total output value of 46 billion euros, accounting for 53.2% of the global GNSS terminal equipment holdings and 30.5% of the global GNSS industry output value. It shows that the Asia-Pacific region is the most important market for the GNSS industry.

(a)

(b)

Fig. 4. GNSS market development. Data source: GSA

The Beidou system has stronger advantages in resource capabilities. The advantages of the Beidou system in terms of resources and capabilities are mainly reflected in the following four points: 1. More product diversity and better transaction value; 2. Higher system autonomy and more sufficient follow-up capital supply; 3. More abundant operating resources and endogenous Stronger development momentum; 4. More prominent operating capabilities and better operating efficiency (see Table 1). According to the “2020 China Satellite Navigation and Location Service Industry Development White Paper”, the total output value of Chinese GNSS industry in 2019 has reached 345 billion yuan; the sales of domestic Beidou chips and modules exceeded 100 million; the sales of terminal products reached 460 million units; the sets of terminal products with Beidou compatible chips are more than 700 million; the number of industry enterprises reached 14,000; and there are more than 500,000 employees. The business model of Beidou’s industrial application is also continuously diversified. Through the innovation of business models, the Beidou system has been deeply integrated into the

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GNSS system

Beidou system

GPS system

GLONASS system

Galileo system

Product

Five services

Three services

Three services

Three services

Factors of production

Sufficient funds

Sufficient funds

Funds tight

Funds need to be negotiated

Operating resources

Military & Civilian Military & Great market Civilian Great market

Military & Civilian Limited market

Civilian Limited market

Management capacity

Multi-ownership companies

Private enterprise Private enterprise

Private enterprise

transformation of industries. The “Beidou + Innovation” development model continues to rise. 3.1 National Will, National System, Government-Led, Special-Driven The construction and development of the Beidou system is a centralized manifestation of the will of the country. It is made by government-led enterprises and is completed based on major scientific and technological projects. The strong guidance of the national strategy and the advantages of the new national system are important guarantees for the development, construction and improvement of the Beidou system, and also provide a huge boost for the innovation of the Beidou industry and its business model. The strategic position of Beidou Project has effectively improved the efficiency of resource and capacity mobilization. Beidou system industry application activities can obtain more, more timely, and more targeted economic, technical, and social resources needed by itself, providing a substantial resource and capability foundation for business model innovation; Demand bottoming effect. Beidou industrial application activities can maximize the effective demand of the government and related institutions, and provide a demand basis for industrial application development and business model innovation; Technological special projects accelerate technological upgrading. The technology R&D efficiency of special science and technology projects is much higher than that of commercial technology R&D. It can more efficiently promote the technology upgrade of the Beidou system and strengthen the resource capacity foundation of the Beidou industry application business model. 3.2 First-Class Standards, Outstanding Characteristics, Resource Sharing, and Win-Win Cooperation The Beidou system industry application model has the basic characteristics of the international GNSS business model and can provide support for subsequent application model innovation (see Fig. 5).

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Fig. 5. Business model of Beidou system

The Beidou industry manufacturer group, pays service authorization fees to the Beidou system to obtain technology licenses, produce products including GNSS, and obtain sales revenue. The government actively guides the formation of a satellite navigation industry manufacturer structure with state-owned enterprises and mixed-ownership enterprises as the mainstay and private enterprises as equals, and get income through taxation. Other industrial enterprises use the functional services provided by the Beidou system to improve their product efficiency or business activity efficiency. For example, Beidou system helps shared bicycle companies to solve the problems of “difficult to find a car” and “random parking” through functional services (see Fig. 6).

Fig. 6. Beidou + shared bicycle transaction structure

3.3 Enterprise Main Body, Market Operation, Diversified Investment, Efficiency First In the application process of the Beidou satellite industry, a corporate model with stateowned enterprises and mixed-ownership enterprises as the mainstay and private enterprises participating has been formed. At the same time, these enterprises have also begun to jointly build a Beidou high-precision service business ecosystem. Among them, the business ecosystem in Qianxun SI is the most typical (see Fig. 7). Qianxun SI produces and sells Beidou hardware and software products. At the same time, Qianxun SI provides GNSS positioning algorithms and other technologies to leading companies in these other industries such as Qualcomm Technology and DJI Innovation to help the latter optimize product and service design, and obtain sales revenue and project revenue sharing. And Qianxun SI establish an industrial innovation system through multiple means.

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Fig. 7. Qianxun SI transaction structure

3.4 Demand-Driven, Industry-Led, Beidou + Industry, Interactive Development There are obvious industrialization differences in the application of Beidou industry. Based on the characteristics of the industry and transaction needs, each industry body structure will cross-border integration of Beidou technology with advanced technologies such as Internet technology and Internet of Things technology. The business model of Beidou industry application in the fishery field is shown in Fig. 8.

Fig. 8. The transaction structure of fishery integration solution

Fishermen obtain the ability to transmit information through the Beidou system without geographical restrictions at a low cost, which will effectively reduce operational safety risks. The fishery administration system can accurately manage the fishing boats operations. The “Sea Fresh” publish aquatic product supply information on the platform in real time during operation, to connect with seafood buyers and conduct real-time online transactions.

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3.5 Regional Revitalization, Top-Down Linkage, Policy Incentives, Focus on Application Beidou industry application activities also showed obvious regional characteristics. Local governments formulate more targeted industrial policies based on the characteristics of the region to maximize the social and economic benefits of Beidou industrial applications. At present, more than 40 Beidou industrial parks have been built in China, and the top six areas of Beidou industry application (Beijing-Tianjin-Hebei, Pearl River Delta, Yangtze River Delta, Central China, Hubei, Henan, Hunan, Sichuan, Shaanxi, Chongqing, and Hainan) have been established. The industry’s contribution rate is over 80%, which has strongly promoted the use of Beidou software and hardware equipment and the innovation of related business activities in the relevant regions. 3.6 Independent Innovation, Daring to Be the First, Patent Protection, Leading and Surpassing The Beidou satellite navigation technology innovation has achieved remarkable results. The first is that technological innovations such as short messages and inter-satellite links have realized “dare to be the first and others have nothing to do”, leading the application of related industries. Second, intellectual property (IP) protection has promoted the industrialization of Beidou satellite navigation innovations and provided important legal guarantees. As of the end of 2019, the total number of Beidou satellite navigation patent applications has exceeded 70,000, ranking first in the world. The third is to have a certain amount of core patents in key technical fields such as navigation system, radio frequency unit, signal processing, and complete the international patent layout to gradually establish comparative advantages. The patent documents reflect that the hot spots and scope of China’s satellite navigation technology application are further expanding, penetrating into various technical fields of the industry.

4 Enlightenment and Reflection Based on the above analysis, the innovation of the Beidou industry application business model has the main characteristics of “3456”, where “3” refers to three aspects, namely all-round, full system, and all elements, and “4” refers to four modules, namely transaction subject, transaction Methods, transaction revenue and expenditure, transaction risk management, “56” refers to 56 key elements (see Table 2).

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Table 2. The overall framework of Beidou industry application business model innovation Round elements system

Transaction subject

Means of transaction

Transaction revenue and expenditure

Transaction risk control

1. Enterprise

(1) Leading enterprises, small enterprises (2) Multi-ownership enterprise

(14) Product sales (15) Equity investment, etc.

(29) New business creating (30) Ability empowerment

2. Industry

(3) Industry associations (4) Agriculture, manufacturing, and service industries

(16) Industry ecosystem (17) Product sales (18) Industrial solutions

(31) Economies of scale (32) Inter-industry integration and creativity

3. Area

(5) All provinces, municipalities and autonomous regions (6) Subjects across provinces, cities and regions

(19) Form a cross-regional ecological community (20) Integrated system within the region (21) Diversified integration among regions

(33) Economies of scale (34) Inter-regional integration and creation

4. National

(7) Relevant state departments (8) Cross-industry ecosystem (9) Cross-regional ecosystem

(22) Integrated ecosystem (23) System construction (24) Investment and financing

(35) Economies of scale (36) Domestic integration and creation

(10) Departments (11) BD subject (12) International organizations (13) Governmental organizations

(25) Transnational ecosystem (26) Transnational infrastructure (27) Investment (28) Service trade

(38) Economies of scale (39) International integration and creation

(40) Market risk (41) Security risks (42) Quality risk (43) Technical risk (44) Operational risk (45) Contract risk (46) Information risk (47) Human risk (48) Manage risk (49) Financial risk (50) Policy risk (51) Legal risk (52) Institutional risk (53) Mechanism risk (54) Environmental risk (55) Political risk (56) Diplomatic risks After completing the risk identification, take preventive and control measures for the risk category

5. International

(37) Tax effect

5 Enlightenment and Suggestions In order to further improve the quality, level and efficiency of the business model innovation of Beidou Application, the following suggestions are hereby made: First, from the strategic perspective of the development of the Beidou industry, enhance the understanding of the importance of business model innovation. Second, tap the advantages of resource capabilities, and optimize the business model of the Beidou system based on the accuracy advantages of the Beidou system, as well as the unique position report and short message functions. Third, strengthen policy guidance. Establish a “national policy + industry policy + regional policy” multi-level policy structure system to promote business model innovation in an all-round, system-wide, and all-factor way. Fourth, strengthen the construction of the Beidou industrial ecosystem, accelerate the upgrading and iteration of standards and the transformation and application of international standards, increase the cultivation and deployment of international patents and high-value patents. Fifth, explore new paths such as diversification of investment entities, mixed ownership reform, etc.; Strengthen the top-level planning and organization management of business model innovation, establish and improve the chief economist (accountant) system, stimulate the vitality of enterprise entities, improve the application efficiency. Sixth, take the innovation of the Beidou industry application business model as the fulcrum to promote the construction of dual cycles. When organizing the implementation of the “14th Five-Year” Beidou application industry development plan and

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mid- and long-term development goals, business model innovation should be deployed simultaneously.

References Amit, R., Zott, C.: Value creation in E-business. J. Strat. Manag. (2001). https://doi.org/10.1002/ smj.187 Zhu, H., Li, J., Xu, A., et al.: High-precision BDS augmented positioning method for disaster emergency environment on smart device. J. Whugis. (2020). https://doi.org/10.13203/j.whugis 20200123 Huang, Z., Pan, M., Chen, C., et al.: Data collection and transmission technology for emergency environment monitoring based on integration of LoRa and BDS. Whugis (2020). https://doi. org/10.13203/j.whugis20190207 Tan, Z., Wei, W., Zhu, W.: The structure and value creation process of business ecosystem—A case of the Xiaomi eco-chain. Manag. Rev. (2019). https://doi.org/10.14120/j.cnki.cn11-5057/ f.2019.07.005

Insights and U.S. GPS International Cooperation Under Legal Regulation Linlin Niu(B) Beihang University, Beijing 100191, China

Abstract. The U.S. National Space Policy, enacted on December 9, 2020, states that the United States shall lead, encourage, and expand international cooperation in mutually beneficial space activities to ensure compatibility and interoperability. Based on this principle, the U.S. has been actively engaged in international cooperative activities with foreign governments and international organizations related to GPS. Now, it has developed a comprehensive legal system for international cooperation: all international cooperation actions of GPS comply with the laws and regulations of the United States, international treaties or agreements signed by the United States and other applicable international laws, and are strategically consistent with the national and homeland security requirements, foreign policy and national interests of the United States. Thanks to the maturity of its legal system, the United States has basically achieved its high-level goal of promoting GPS technology innovation and maintaining U.S. leadership and technological leadership in the field of satellite navigation, as well as the basic goal of meeting the growing national security, homeland security, economic security, civil needs science and commercial needs. In this paper, we will study the U.S. Code, SPD-7, National Space Policy, the U.S. Radio Navigation Plan, then analyze the legal system of the U.S. GPS international cooperation in terms of subject, legal content, and legal mode to provide legal advice for the international cooperation activities of China’s BDS. Keywords: GPS · International cooperation · Legal system · Space policy

1 Introduction GPS is a kind of satellite navigation system developed by the United States DoD, which can provide global users with all-round, all-weather, all-time, high-precision positioning, navigation, timing (PNT) information and services. The multi-purpose services it provides are an indispensable part of American national security, economic growth, traffic safety and homeland security, and are also an important part of the global economic infrastructure. The continuous development of GPS-based services not only brings opportunities, risks and threats to the national security, homeland security and economic security of the United States, but also brings risks and threats. One of the United States’ responses is to actively encourage GPS related international cooperation activities and to provide legal guarantees for international cooperation through a number of different © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 598–606, 2021. https://doi.org/10.1007/978-981-16-3146-7_56

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laws and regulations. A complete set of strategic objectives has been formed: the highlevel goal is to promote GPS technological innovation and maintain the United States’ leadership and technological leadership in GNSS; the basic goal is to meet the growing national security, homeland security and economic security needs. The development goal of China’s BDS is to provide safe and reliable PNT services to global users according to law. The study of the legal system of American GPS international cooperation has reference significance for China’s BDS to enhance the consensus of international cooperation and enhance the effectiveness of BDS’s participation in the international community.

2 Main Body and Responsibility of the International Cooperation of US GPS 2.1 The United States Federal Government The main bodies responsible for coordinating and managing international cooperation in satellite navigation in the United States federal government include Congress, the President, the State Department and the Office of the United States Trade Representative. Under 51 U.S.C. §50112, Congress encouraged the President to enter into international agreements with foreign governments and international organizations to promote cooperation with foreign governments and international organizations in the field of satellite navigation, thereby promoting GPS and their enhancement systems outside the United States and making them internationally recognized standards, promoting GPS application and promotion worldwide [1]. The State Department, represented by the Secretary of State, is responsible for specific foreign affairs related to satellite navigation. Under the SPD-7, the Secretary of State is primarily responsible for promoting the use of GPS and its enhancement of services and standards to foreign Governments and other international organizations and for encouraging the development of GPS -based foreign civilian satellite services and systems. In accordance with the National Space Policy, the Office of the United States Trade Representative has the primary responsibility for international trade agreements to which the United States is a party, signs international trade agreements with other countries after consultation with other relevant departments and agencies, and actively leads the negotiation and implementation of relevant trade rules governing space goods and services. 2.2 GPS-Related Functional Institutions The GPS coverage rate is 98%, which is applied to many functional areas of the United States. The United States defines the responsibilities of various functional agencies GPS international cooperation by laws and regulations. This article briefly introduces the United States DoD, DoT, NASA, DoC and their responsibilities directly related to GPS international cooperation. The United States DoD is responsible for leading cooperative negotiations with foreign defense organizations on access to GPS military information or services and for providing United States allied forces with GPS national security services, user equipment, information and technology. Under 16 U.S.C. §1607, the Secretary of Defense and

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the Secretary of State should participate jointly in the United States’ dealings with allies so that GPS military user equipment can receive PNT signals from allies and negotiate other possible agreements in due course on enhancing PNT capabilities. As the lead department, DoT handles international cooperation matters related to U.S. GPS civilian to support key U.S. transportation, homeland security and other important civilian and commercial applications. According to the SPD-7, the Secretary of transportation, in coordination with the Secretary of State, should promote international participation in the use of space-based PNT services in the United States for the development of civilian transport applications. NASA is an administrative scientific research agency dedicated to developing and implementing space programs. In accordance with the National Space Policy, the Secretary of NASA, in cooperation with other relevant agencies, federal laboratories and business partners, and in cooperation with international partners under applicable law, should continue to operate the International Space Station, while developing separate commercial platforms to maintain the continued presence and utilization of the United States in low Earth orbit and to make a transition away from the International Space Station. The DoC is responsible for the management of international trade in satellite navigation, import and export controls and international protection of the electromagnetic spectrum from damage and interference. According to the SPD-7, the Secretary of Commerce, in coordination with the Secretary of State, the Secretary of Defence, the Secretary of Transport and the Secretary of NASA, seeks to protect the radio spectrum used by GPS systems and their enhancement systems through appropriate national and international spectrum surveillance and management practices. With regard to foreign trade, the Secretary of Commerce carries out economic research related to GPS applications, formulates guidelines on export licensing related to GPS, and promotes fair trade in GPS related goods and services in global markets. 2.3 US National Space-Based PNT Executive Committee Under the SPD-7, the National Space-based PNT Executive Committee of the United States is an inter-agency organization with the establishment of the National Spacebased PNT Advisory Committee, the Implementation Steering Group and the Coordination Office, comprising the Secretary of Finance, Justice, the Interior, Agriculture, Commerce, Energy, Homeland Security, the Office of the Director of National Intelligence, the Joint Chiefs of Staff and NASA or its designated representatives. The PNT Executive Committee coordinated efforts to advise its member agencies and presidents on technical maintenance, GPS modernization, service security and policy issues related to space-based PNT services in the United States through the establishment of a sound organizational structure and long-term operational mechanisms.

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3 Statutory Content of International GPS Cooperation in the United States 3.1 System Operation Cooperation The satellite navigation system itself has the characteristics of large investment, high risk, high scientific and technological requirements and slow income, which determines that the development of satellite navigation needs cooperation between countries [2]. As far as the coordination of frequency tracks is concerned, the United States, in accordance with the rules established by the International Telecommunication Union, carries out the coordination of frequency tracks of the GPS system through friendly consultation with foreign countries (as shown in Table 1), actively participates in the development of the rules of the International Telecommunication Union and related activities, and cooperates with relevant countries to expand satellite navigation frequency resources. Table 1. United States and foreign agreements on frequency track coordination Partner

Time (year) A cooperation agreement

Cooperation content

The European Union 2004

Agreement for the Promotion, Provision and Use of GPS and Galileo Satellite Navigation System Applications

Emphasize national security compatibility and spectrum use, and strengthen bilateral interoperability and frequency coordination

Russia

2004

Joint Statement by U.S. GPS and Russian GLONASS

The parties collaborate to maximize the maintenance of their own spectrum for satellite navigation and timing signals

China

2007

Joint Statement on Civil Signal Compatibility and Interoperability between GPS and BDS

Provides that GPS and BDS have radio frequency compatibility under the framework of the International Telecommunication Union (ITU), according to the bilateral harmonization of frequency compatibility completed in 2010

For systems compatibility and interoperability, the United States Government has been encouraging greater compatibility and interoperability between domestic and foreign space-based PNT systems in global civil, commercial and scientific applications. The well-designed receiver can obtain more satellite signals by using other PNT systems, which brings benefits such as GPS elasticity enhancement, redundancy enhancement and

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system performance improvement. Now, the United States has signed cooperation agreements with the European Union, Russia, Japan, India, Australia and so on (as shown in Table 2) to enhance the compatibility and interoperability between GPS and various systems. Table 2. U.S. GPS official website document on enhancing compatibility and interoperability with foreign countries Partner

Time (year)

A cooperation agreement

China

2014–2017

2

The European Union

2004–2016

11

Russia

2004–2006

2

Japan

1998–2017

15

India

2007–2008

2

Australia

2007–2010

2

Britain

2013

1

3.2 Industry Application Cooperation The surveying and mapping community was one of the first industries to use GPS, and under 10 U.S.C. article 454, the Secretary of Defense authorized the NGA to exchange or provide map, cartographic and geodetic data supplies and services to foreign Governments and international organizations. With regard to road traffic, under chapter II of the United States Radio Navigation Plan of 2019, the DoT is responsible for the preparation and promulgation of the United States civil PNT plan, leading the development of civilian applications of space-based PNT services and encouraging the development of GPS-based PNT services and systems abroad to provide navigation for certain systems used by the civil sector and the military, and the Department of Transportation has now established GPS -based traffic navigation systems with the FAA in many other parts of the world to provide air navigation as required by international treaties. In the U.S. maritime industry, under chapter 6 of the american radio navigation plan 2019, the USCG led the development of a prototype maritime digital broadcasting system as an enhanced means of transmitting coastal emergency marine safety information to ships worldwide to meet the requirements of the global maritime distress and safety system by developing cooperative research and development agreements. 3.3 International Economic and Trade Cooperation The United States encourages foreign Governments and international organizations to purchase and use United States commercial space services and capabilities through international cooperation and to take active measures to promote the export of commercial

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space products and services in the United States, including space products and services developed by small and medium-sized enterprises, consistent with United States technology transfer and non-proliferation objectives. The overall guidelines would be to continue to support the export of space-based PNT capabilities currently available on or to be provided on the global market for civilian or other non-United States lists of military supplies, the United States PNT capabilities appearing on the United States lists of military supplies or the United States commercial control lists, and the need to issue export licences on a case-by-case basis under the International Arms Trade Regulations or the Export Control Regulations and other applicable laws, treaties and regulations. Export of sensitive or advanced PNT information, systems, technologies and components will be subject to case-by-case approval in accordance with existing laws and regulations and relevant national security and foreign policy objectives and considerations. 3.4 Security Cooperation Safeguarding national security and strengthening national defense construction is one of the fundamental purposes of developing GNSS and carrying out international cooperation. GPS provide two levels of services—standard positioning services (SPS) and precision positioning services (PPS), which are only available to the United States Armed Forces, United States federal agencies and some allied and government forces for reasons of national security. The United States DoD encourages allied military forces to use GPS services for national security, including GPS national security services, user equipment, information and technology. The use of these military forces facilitates interoperability between the United States and allied military forces and maintains excellent space-based PNT military capabilities, thus maintaining the United States’ dominant position in negotiating cooperation with foreign defense departments on access to GPS military services and access to information.

4 The Legal Model of the International Cooperation of US GPS 4.1 International Cooperation Under the Framework of International Conventions International conventions generally refer to multilateral treaties on rules in a particular field adopted under the auspices of international organizations or at international conferences. The United States, as a member State in the area of satellite navigation, is closely associated with the IMO, ICAO and the ITU on GPS matters of international cooperation, and the United States GPS therefore need to comply with national conventions developed by international organizations when undertaking international cooperation activities. Taking the cooperation between the United States and the IMO as an example, in 1996 the IMO approved operational GPS satellite systems as an integral part of the world radio navigation system, and the United States accordingly provided in the Radio Navigation Plan that the provision of PNT services and systems was in accordance with the standards and guidelines of the IMO and that military vessels could use civil PNT systems in peacetime in accordance with the policy of the DoD, provided that they were in accordance with the norms established by the IMO for the provision of equivalent performance and safety.

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4.2 International Cooperation Under Bilateral Treaties The U.S. policy laws on satellite navigation specify the areas of cooperation, content and forms of cooperation with foreign governments and international organizations, which greatly enhance the degree of strategic mutual trust between the United States and foreign countries, and carry out different levels of bilateral cooperation with different countries according to the degree and importance of strategic mutual trust [3]. First of all, for countries such as the North Atlantic Treaty Organization, the European Union, Japan and India, the United States cooperates from system to application, The US Space Policy stipulates that GPS national security services, user equipment, information and technology can be used by allied military forces. Second, for potential competitors, such as Russia and China, the United States, on the one hand, through signing a joint statement with the other party to establish a communication mechanism to jointly explore the technical aspects of satellite navigation, on the other hand, according to the provisions of article 113 of title 10 of the United States Code, the defense report submitted annually by the Secretary of Defense should include a comprehensive and net assessment of the defense capabilities and plans of potential United States competitors. Finally, for other countries that do not have satellite navigation systems, the United States has focused on expanding and occupying its market for satellite navigation applications, putting forward compatible and interoperable, user-oriented service commitments, advocating open markets, interference detection and mitigation, and maintaining the dominant position of GPS and its applications in the market on various international occasions and platforms. 4.3 Other Forms of International Cooperation The United States has expressed its wish to lead international cooperation in space activities in a number of laws, regulations and policy documents, such as the National Space Policy, SPD-7. Departments and agencies under the coordination of the Secretary of State, should demonstrate the leading role of the United States in space-related forums and activities. Under policy guidance, the United States actively participates in international rule-making in the field of satellite navigation, hosts the ION and is active in numerous satellite navigation front conference platforms, such as the ICG, the COPUOS and the United Nations Global Navigation System Applications Seminar. Through these platforms, U.S. continuously increases its voice and operational opportunities in the international competitive environment, creating new markets for United States commercial space capabilities and services.

5 The Enlightenment of the American GPS International Cooperation Legal System to China 5.1 Promote Top-Level Legislation to Ensure All-Round Development of International Cooperation in Satellite Navigation The development goal of BDS is to serve the whole world and benefit mankind. It must be equipped with a complete set of international cooperation laws and regulations to

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ensure the comprehensive cooperation between BDS and other national satellite navigation systems. BDS and GPS have a huge gap in the protection of the rule of law. So far, China has not a law in the field of satellite navigation that can lead the overall situation, which makes the development of international cooperation in BDS lack the necessary legal basis. Therefore, it is an inevitable way to guarantee and promote international cooperation to perfect the top-level legal formulation and promote the construction of satellite navigation legal system. China should make every effort to promote the introduction of the regulations on satellite navigation as soon as possible, and begin to study, draft and promote Chinese PNT Law and the BDS Special Law on International Cooperation, clarify the responsibilities of the relevant institutions of BDS International Cooperation, consolidate the main responsibility of international cooperation, point out the direction of international cooperation, and provide soft power support with the rule of law as the center for BDS international cooperation. 5.2 Improve the Satellite Navigation Management System and Establish a Coordination Mechanism for the Smooth Progress of International Cooperation The management system with clear division of labor and effective operation can provide strong organizational guarantee for BDS international cooperation. Strengthening the exchange and cooperation between the competent institutions and the competent institutions and enterprises and academic sessions is conducive to the modernization of the management system and management ability in the field of international cooperation in satellite navigation in China. In perfecting the system of satellite navigation management, China should also make the system regular and legal, give clear rights and responsibilities to the competent agencies, and at the same time, establish and strengthen inter-agency and institutional partnerships with enterprises and academia through cooperation, collaboration, information sharing, innovative procurement and the establishment of common goals. Through the establishment of high-level and authoritative national centralized and unified management of satellite navigation, the clarification of the responsibilities of various departments related to international cooperation, the formulation of implementation and response strategies to encourage the sharing of technology and the exchange of expertise among institutions and organizations, and the joint efforts of various parties to strengthen our ability to achieve the strategic objectives of satellite navigation. 5.3 Construct a Chinese Satellite Navigation Discourse System of “ValuePractice-Communication” in Order to Build Consensus for International Cooperation China’s satellite navigation started late. Under the current international discourse pattern of GPS, the construction of the “value-practice-communication” trinity of China’s satellite navigation discourse system is conducive to eliminating the misunderstanding or doubt of the international community about the BDS. Condense the consensus of international cooperation. BDS has unique value. It can provide seven kinds of services, such as PNT service, international search and rescue service, global short message communication service, regional short message communication service, star base enhancement

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service, foundation enhancement service, precision single point positioning service and so on. The value that the satellite navigation system can bring to the world is the decisive factor in the formation of the international discourse pattern in the field of satellite navigation, but the enhancement of the system value does not automatically bring about the promotion of the right to speak. It is necessary to transform the system value into the right to speak through the way of constructing the discourse system [4]. The relevant departments of our country should step up the propaganda of the BDS and its application, actively participate in international conferences, international rule-making, international standard-setting, foreign trade and other activities, tell the BDS story well in the practice of international cooperation, spread the BDS voice, and explain the BDS value concept. Legal language is recognized by the international community. Only by carrying out international cooperation on the rule of law in satellite navigation can we provide legal support for enhancing China’s institutional voice in the global open and compatible satellite navigation order.

6 Conclusion The law is the best commitment, only if the clear management responsibilities, continuous support construction, safe operation and maintenance, reliable service commitment, strong industrial security into the law, global users can believe that BDS has the ability to provide first-class services [5]. The development of international cooperation in the BDS requires enhancing the trust of international users through the commitment to the rule of law, forming a coherent discourse system with the international community through the language of the rule of law and safeguarding the core interests of the country through the rule of law. China must actively build the framework of the rule of law of BDS international cooperation, with the “BDS under the rule of law” for “China’s BDS, world’s BDS, the first-class BDS” on the international stage escort.

References 1. Aldrich, D.: United States code, 1992 (CD-ROM). Gov. Inf. Q. 12(2), 230–232 (1995) 2. Zhao, B.: Research on the legal regulation of BDS. Harbin Institute of Technology (2015) 3. Li, P.: Progress of the U.S. GPS system and its international cooperation. Int. Space (04), 38–45 (2015) 4. Feng, X., Hu, R.: The construction of the discourse system of “One Belt, One Road” in the context of the community of human destiny. J. Xiamen Univ. (Philos. Soc. Sci. Ed.) (01), 12–21 (2021) 5. Yang, J.: Building China’s BDS Under the Rule of Law. Rule of Law Daily (2020)

Study on the Legal Model of International Cooperation in the Field of Satellite Navigation Xiaomeng Fan(B) Beihang University, Beijing, China

Abstract. The current rules and order of international cooperation among States in the field of satellites depend mainly on three legal models: multilateral cooperation under international conventions, bilateral cooperation under intergovernmental agreements and guidelines for global regional conferences. These three legal models show different characteristics in terms of legal effect, normative content and timeliness and flexibility of normative matters. Combined with these characteristics, the path selection of countries in the process of international cooperation in the field of satellite navigation shows a certain trend. These will provide development ideas for China to develop international competition and cooperation in the field of satellite navigation. Keywords: Satellite navigation · International cooperation · Legal model

1 Introduction 2020 is a milestone in the development of world satellite navigation. The successful networking of Beidou system indicates that the world satellite navigation has formally formed a multi- constellation pattern composed GNSS four global navigation satellite systems (GNSS) and two regional navigation systems. Under this pattern, competition is bound to be a long-term trend in the field of satellite navigation due to national strategic considerations, but the development of satellite navigation technology and the global scope of services also determine that countries must achieve good cooperation in the field. In the past long-term practice, the international cooperation of countries in the field of satellite navigation has formed its mature legal model, which provides effective guidance for countries to carry out international cooperation.

2 Mode 1: Multilateral Cooperation Under International Conventions is the Basic Form of International Cooperation in the Field of Satellite Navigation 2.1 Legal Framework of the International Telecommunication Union ITU is the statutory body for the coordination of inter-State satellite navigation for the development of orbital frequency resources. It relies mainly on the distribution and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 607–614, 2021. https://doi.org/10.1007/978-981-16-3146-7_57

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management of global radio frequency spectrum and satellite orbit resources within the legal framework of the ITU Basic Act, the International Telecommunication Union Organization Act (ITU) and its Supplementary Act, the International Telecommunication Union Convention (ITU Convention) and the International Telecommunication Rules and the International Radio Rules.1 The organic law and the ITU Convention are the basic regulations governing ITU members. In terms of content, the organic law provides detailed provisions on the qualifications, procedures, rights and obligations of States to become members of ITU, in order to ensure that their members are able to regulate matters related to the field of domestic satellite navigation in accordance with their guidelines. In terms of ensuring legal effectiveness, the organic law ensures that ITU has the legal power in the territory of each of its members to exercise its functions and to fulfil its purposes, thus ensuring the mandatory nature of the organic law for its members.2 As part of the governance framework of ITU, the most closely related to GNSS is the Radiocommunication Sector Conference, whose main task is to develop standards for the radio communication system and to make equitable, rational, economical and efficient use of radio spectrum resources. The outcome of the Conference was presented in the Interim Final Document, which included all changes to the radio rules to accommodate the rapid development of existing systems in the world and the spectrum requirements of advanced radio technologies under development. Since the rule was based on consensus among members, it would also be the main basis for national authorities to formulate domestic rules. 2.2 IMO Convention The Convention of the International Maritime Organization (IMO) is a constitutional document of IMO.3 In the field of satellite navigation, it has developed relevant performance standards and parameters for navigation aids and navigation systems in the field of satellite navigation, provided for the handling of related legal issues, and extended these provisions to Governments and intergovernmental organizations, which play a role in the international maritime community in minimizing the performance objectives, standardization and cost of user equipment.4 In terms of effectiveness, the Maritime Convention provides that any State may become a member of the International Maritime Organization, subject to the provisions of the Maritime Convention, and that no State or place of trust that violates the resolutions of the General Assembly of the United Nations may become or continue to be a member of the Organization. Furthermore, the International Maritime Organization has the authority to confirm whether a navigation system is part of a global navigation system. This provision and function makes IMO provisions mandatory for States. For example, the Russian Federation Radio Navigation Plan 2019 sets out IMO requirements in the area of navigation as considerations for the documents. 1 Constitution of the International Telecommunication Union (December 22,1992), Article 1. 2 Constitution of the International Telecommunication Union (December 22,1992), Article 6. 3 Russian Radio Navigation Plan (2019), Chapter 2. 4 Convention on the International Maritime Organization (March 17 1958), Article 10.

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2.3 Convention on International Civil Aviation Convention on International Civil Aviation (hereinafter referred to as the Civil Aviation Convention) is an international convention established by the International Civil Aviation Organization (ICAO) on issues related to international civil aviation.in the field of satellite navigation, it is responsible for setting standards for internationally used civil aviation PNT systems, such as GNSS performance parameters and key performance parameters such as system signal accuracy, completeness, continuity, availability and robustness.5 As stipulated in the Convention, in order to facilitate air navigation, ICAO is required to develop and modify international standards and recommended measures and procedures, as required, on projects such as communications systems, navigational aids and aviation maps and charts in the field of satellite navigation.6 In terms of effectiveness, the Convention provides that any State which fails to comply fully with any of the international standards and procedures provided for in the Convention or whose regulations and measures are not fully adapted to the changes in international standards and procedures shall, in adopting regulations and measures different from those provided for in international standards, inform ICAO of the difference between the two, indicating the action to be taken, and that ICAO shall inform other States of the situation.7 The United States Radio Navigation Plan 2019, for example, provides that appropriate standards for PNT systems are coordinated by ICAO and issued for international aviation use to ensure worldwide interoperability; military aircraft may use civil PNT systems in peacetime that are consistent with the policy of the Department of Defense, provided that they comply with the norms established by ICAO to provide equal performance and security. In addition to the above three major international organizations, IATA, the Radio Commission for International Maritime Transport and the Committee on the Peaceful Uses of Outer Space are also important bodies for international cooperation in the field of satellite navigation, and their conventions and documents are important components of international rules in the field of satellite navigation.

3 Mode 2: Bilateral Cooperation Under Intergovernmental Agreements is an Important Form of International Cooperation in the Field of Satellite Navigation 3.1 Cooperation Between the United States and Europe, Russia and China1 America’s GPS is the world’s first global navigation satellite system, with the subsequent Glonas system, Galileo system and our Beidou system have varying degrees of international cooperation. The most extensive and close cooperation with GPS is the Galileo system, which began with the United States-EU GPS/Galileo Cooperation Agreement signed by the United States and the European Union in 2004, which established four working groups 5 European Radio Navigation Plan (2018), Chapter 6. 6 Convention on International Civil Aviation (December 7,1944), Article 37. 7 Convention on International Civil Aviation (December 7,1944), Article 38.

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responsible for radio frequency compatibility and interoperability, trade and civil use, the design and development of next-generation systems, and GPS and Galileo cooperation on security issues. On the basis of this working group, the United States and the European Union have continued to cooperate by signing agreements such as the Agreement on the Promotion, Provision and Use of GPS and Galileo-related Applications and the Joint Statement on Cooperation between GPS and Galileo to achieve full cooperation in the field of satellite navigation. Compared with the European Union, the scope of cooperation between the United States and Russia is narrower. Since the start of cooperation, work has focused on compatibility and interoperability between GPS and GLONASS systems. To better achieve the goal, the two sides set up two working groups and signed agreements such as the Joint Statement on the United States G PS and Russian GLONASS to regulate cooperation matters. In contrast, the United States and our country have less cooperation, in addition to a few technical coordination, until 2014, the two sides on civil cooperation between the system to carry out bilateral consultations, gradually opened the curtain of cooperation. 3.2 EU-Russia-China Cooperation2 The framework for cooperation between the two sides in the field of satellite navigation established the Agreement on Cooperation between the European Community and its member States and China on Civil Navigation Systems (Galileo), signed in Beijing on 30 October 2003. In October 2004, the two sides further cooperated and signed the Galileo Technical Cooperation Agreement, which established China’s management status in the Galileo system, established China’s right to participate in related projects in the development and verification phase of Galileo Navigation, and established a legal and operational framework for China’s participation in the Galileo Plan, marking the entry into a substantive stage of cooperation in the Sino-European Galileo Plan, but the cooperation relationship gradually became loose after 2005. Compared with China, the cooperative relationship between Russia and the European Union is relatively stable. In September 2005, Russia and Europe signed the EuroRussian Cooperation Agreement on Galileo and Glonas, which covers the compatibility and interoperability of the two systems and matters related to Russian assistance in the development of Galileo in Europe. On the basis of the agreement, Russia and Europe have maintained close cooperation in the field of satellite navigation in recent years, covering compatibility and interoperability, satellite search and rescue, satellite navigation technology, navigation satellite launch and many other aspects. These cooperation plans and results will be published in the European-Russian report on public space cooperation. 3.3 Cooperation Between Russia and China3 At present, the international cooperation between Russia and China in the field of satellite navigation is the most comprehensive and stable. In 2014, the two sides signed the Memorandum of Understanding on Cooperation between the China Satellite Navigation System Committee and the Russian Federal Space Agency in the Field of Global Satellite Navigation, clearly established the “China-Russia Strategic Cooperation Project

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Committee on Satellite Navigation”, and put forward four key areas of follow-up cooperation: enhancement of systems, compatibility and interoperability, monitoring and evaluation, and application promotion, marking the formal inclusion of Sino-Russian satellite navigation cooperation as a strategic project for Sino-Russian cooperation in the framework of the regular meeting mechanism between the Chinese and Russian prime ministers. Since then, based on the above framework, China and Russia have signed a series of agreements and joint statements on system compatibility and interoperability, time interoperability and system technology application cooperation, which provide the basis for the two sides to continue to carry out in-depth cooperation in the field of satellite navigation.

4 Mode 3: Global Regional Conference Guidelines as an Effective Complement to International Cooperation in the Field of Satellite Navigation4 4.1 Global International Conferences and Forums In the field of satellite navigation, there are mainly two authoritative global international conferences and forums. One is the United Nations International Committee on Global Navigation Satellite Systems, or ICG, which promotes collaboration among major satellite operators. Since 2005, ICG has held 14 conferences, providing a platform for operators to discuss and exchange information on user needs, applications and overall trends in technology development. Second, the United Nations Global Navigation Satellite System Application Seminar is one of a series of regional seminars and international conferences held by the United Nations Outer Space Division to promote the application of GNSS. In addition to hearing the reports on the progress of GNSS made by the United States, Russia, Europe and China, the conference will also organize discussions on relevant topics and discuss the frontier issues of satellite navigation. 4.2 Regional International Conferences and Forums In addition to international conferences and forums on satellite navigation under the United Nations framework, the various navigation conferences and societies organized by the Governments of the United States, Russia, Europe, Germany and China and the satellite navigation community also provide platforms for academic and technical exchanges on satellite navigation worldwide. One of the earliest is the American Navigation Society, dedicated to the development of positioning, navigation and timing technology, is one of the most concerned global satellite navigation academic non-profit professional organizations. Since the end of the 20th century, the European Navigation Conference, Munich Navigation Summit and Moscow International Navigation Forum have emerged. After 10 years of development, the conference has been ICG as one of the three international academic conferences on satellite navigation, which has played a great role in promoting academic innovation, technological innovation, theoretical innovation and application innovation in the field of satellite navigation.

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5 Advantages and Disadvantages of the Existing Legal Model of International Cooperation in the Field of Satellite Navigation and the Choice of National Development Paths 5.1 Comparison of the Three Legal Models of International Cooperation in the Field of Satellite Navigation 5.1.1 The Dimension of Legal Effect In terms of legal effect, international conventions under the framework of international organizations are the ideal mode of international cooperation. First, international organizations hold the resources necessary for States to develop satellite navigation, which constitutes a power relationship that requires each State to obtain the corresponding resources and interests by complying with international conventions. Secondly, international organizations represent a world order and accepted standards, and members must adopt a series of norms set out by them in order to obtain the opportunity to integrate into the world order and thus to seek opportunities for development. Finally, international organizations based on the consensus of many countries in the global scope were born and developed, and their basic governance concepts and organizational objectives could at least be supported by their members. Then the international conventions and laws constructed on this basis will naturally become the code of conduct for the development of countries in the field of satellite navigation. In contrast to international conventions, intergovernmental agreements and guidelines for international conferences decline in legal effect in turn. The binding force of an intergovernmental agreement is limited to the parties to the agreement, which changes at any time as political, diplomatic and technical factors change, making its legal effect greatly compromised. The guide to international and regional meetings, as an outcome document of the General Assembly, is only instructive to individual countries and has little legal effect. 5.1.2 Takes the Legal Norm Content Dimension In terms of the content of legal norms, intergovernmental agreement is a good legal model of international cooperation, which can realize the all-round cooperation between countries in the field of satellite navigation at the same time in depth and breadth. Taking the memorandum of understanding signed by China and Russia on cooperation between the China Satellite Navigation System Committee and the Russian Federation Space Agency in the field of global satellite navigation as an example, it not only clarifies the key areas of follow-up cooperation between the two sides, but also forms a regular meeting mechanism between the two countries in the field of satellite navigation, which provides a solid legal and organizational guarantee for extensive cooperation between the two countries. Compared with intergovernmental agreements, international conventions and guidance documents of international conferences provide for general matters of international development and application in the field of satellite navigation, and the depth and breadth of normative content are far less than.

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5.1.3 Take the Timeliness of Normative Items as the Dimension In terms of flexibility and timeliness of normative matters, international/regional conference guidelines have great advantages. As mentioned earlier, at present, major satellite navigation powers, such as the United States, Europe, China and Russia, have hosted a number of international conferences in an annual format, which include not only national experts in the field of satellite navigation, but also national civil institutions in the field of satellite navigation. On the other hand, international conventions and intergovernmental agreements, their complex legislative procedures and the low decision-making efficiency caused by national negotiations make them show a kind of legislative lag, which is difficult to solve the emerging problems in the field of satellite navigation. 5.2 Options for National Development Paths Under the Existing Legal Model of International Cooperation in the Field of Satellite Navigation 5.2.1 Active Participation in International Organizations and Ownership of International Rule-Making Initiative and Voice According to the regulation of international conventions, countries must develop GNSS systems in accordance with the provisions of international conventions and technical standards and performance norms approved by international organizations. Therefore, the right to formulate standards and rules has become an important competition goal for countries. Guided by this objective, the Companies Act of the State Space Group of the Russian Federation provides for the participation of federal administrative bodies at the national and international levels in the development and coordination of control guidelines for the safe implementation of space activities.The United States National Space Policy 2020 also provides for working with like-minded international partners to establish standards of safe and responsible conduct, expand international cooperation and strengthen United States leadership in space. 5.2.2 Take the Initiative to Seek Bilateral Cooperation and Strengthen All-Round Exchanges and Cooperation Among Major Satellite Navigation Countries With the development of GNSS, the coexistence of multiple constellations has become a trend, and with the vulnerability of GNSS caused by the increasing dependence of various industries on GNSS, countries have to focus on inter-State cooperation. In order to achieve technical breakthroughs, and then solve the problem of GNSS vulnerability. In recent years, the United States and the European Union, Japan and other countries have signed a number of memorandums of understanding and cooperation agreements to achieve technology sharing in the field of satellite navigation. 5.2.3 Building Prosperity Navigation Conference and Strengthening the International Influence and Authority of Satellite Navigation Conference At present, several countries and regions in the world with GNSS have established their own annual satellite navigation meetings and societies to show the world the latest

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progress in the development of their satellite navigation systems and their industries, and to discuss countermeasures against common development bottlenecks. In recent years, the satellite navigation conferences organized by various countries have become more and more committed to involving different stakeholders in order to brainstorm and work together to provide advanced guidance for the development of satellite navigation, enhance the authority and influence of their meetings, and then promote their satellite navigation systems.

6 Conclusion The path selection of international cooperation in satellite navigation abroad provides a reference for China. First, with the help of the platform of international organizations, we should actively integrate into international standards, develop advanced navigation technology, and establish the right to speak in international organizations and the leading power to formulate international rules and standards. Second, strive to seek cooperation with large satellite navigation countries. In recent years, the cooperation between China and Russia in the field of satellite navigation has become more mature, stable, tough and fruitful, but the cooperation with the United States and the European Union is very few. Therefore, we should seek as much cooperation with the United States and Europe as possible to achieve technology sharing and mutual benefit. Third, strengthen the construction of China Satellite Navigation Annual Conference, regard it as the promotion platform for the application of Beidou system industry and the development site of Beidou market, gather industry strength and international vision, Build it into a very international influential satellite navigation academic exchange authority platform, better serve the Beidou cause. In addition, as far as our country is concerned, legal construction is also the top priority. In this respect, the gap between our country and foreign countries is very far away. It is urgent to improve our satellite navigation legal system as soon as possible, and to ensure international cooperation in various fields, such as management system, system operation, industry application, international economy, trade and security.

References 1. U. S. efforts related to GPS cooperation with other countries and international organizations [EB/OL]. https://www.gps.gov/policy/cooperation/,2021-01-04/2021-01-31 2. Zhao, S.: An inventory of international cooperation among large satellite navigation countrie. Int. Space 10(03), 24–29 (2014) 3. Cooperation between Russian and Russian Powers in Satellite Navigation [EB/OL ]]1. http:// www.beidou.gov.cn/zt/gjhz/201909/t20190923_19012.html,2019-09-19/2021-01-31 4. Xiaochun, L.: Beidou International Cooperation [EB/OL]] on the Multilateral Stage. http:// www.beidou.gov.cn/yw/xwzx/201801/t20180115_13970.html. 2018-01-15/2021-01-31

Study on the Security Protection System of Foreign Satellite Navigation System Infrastructure Wenqing Zhang(B) and Chen Yu Beihang University, Beijing, China

Abstract. In 2020, the Beidou-3 global satellite navigation system announced the official opening, officially providing services to the world, and the Beidou system has also entered a new era of scale, industrialization, internationalization and popularization. New era gave birth to the new requirements, how to provide safer, more stable, more reliable, higher-quality fixed navigation users worldwide location service has become a new target. In order to provide better navigation and positioning services, we must not only pay attention to technological innovation, but also maintain the safety of the satellite navigation system. Security issues have long been the focus of attention of all countries, and are also the main points of centralized regulation of laws and regulations. Infrastructure security is the most basic and most important point in system security. This article starts with the security protection system of satellite navigation systems and infrastructure, focusing on combing and analyzing the security protection systems of the three global satellite navigation systems in the United States, Russia, and the European Union. From the aspect, we will elaborate on the specific measures taken by foreign satellite navigation systems to protect their infrastructure. Keywords: Satellite navigation · Infrastructure · Global navigation satellite system · Safety · Policies and regulations

1 Introduction With Compass III global satellite navigation system of the completion of the opening, the Beidou system into the global service new era, but also from built using both into to use mainly the new stage. The face of the new stage, the new situation brought about the new opportunities, new requirements, new challenges, the protection of satellite navigation systems can be a long-term safe and stable in operation is essential. Satellite navigation system due to the application of the basic and extensive, The satellite navigation system is not only critical infrastructure facilities is critical infrastructure of the foundation. Earlier this year, the United States Trump government has released a new PNT Policy – “America’s first 7 number space policy directive: space-based positioning, navigation and timing policies” once again reaffirmed the infrastructure of importance. At the same time he stressed the system’s security has not only innings limited to physical attacks, further including cyber attacks and electromagnetic interference. Focus on learning learn © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 615–622, 2021. https://doi.org/10.1007/978-981-16-3146-7_58

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from other global satellite navigation system in protecting the infrastructure aspects of institutional policy experience.Satellite navigation system infrastructure means supporting the underlying physical devices satellite navigation system operated by the sign part of the space, ground control segment and the user terminals of three parts, but in systems involving infrastructure security protection only covers the space constellation infrastructure and ground Control infrastructure, including: satellites, spacecraft, master control stations, reference stations, injection stations, etc. Because the user terminal is only used for data reception and has a wide range of applications, no corresponding protection measures have been set for the user terminal in the legal systems of various countries.

2 Satellite Navigation System Infrastructure Safety Management System An all- management system refers to the form of the system by, for mention for stable and reliable satellite navigation and positioning satellite navigation services infrastructure facilities protect the integrity of integrity and service performance of its physical facilities. For the protection of national security the most basic infrastructure of satellite navigation systems approach is the object of legal protection as infrastructure, the needle on the satellite navigation infrastructure to build this particular object management system compatible. By the object of certification, and other means of clear ownership rights in the Department of satellite navigation systems infrastructure planning and design stage of the system to secure considerable strict management. 2.1 The Legal Scope of the Satellite Navigation System Infrastructure The basis of the security protection of satellite navigation infrastructure is to delimit the scope of the protection objects and clarify the attributes of the legal protection objects. The European satellite navigation system mainly provides Galileo satellite navigation system and European synchronous satellite navigation enhanced service system (EGNOS) two system services. The EU will Ou Zhou satellite navigation system infrastructure group into day basis facilities and ground infrastructure, space-based infrastructure master to a satellite group consists of all operational satellites and the required ground spare satellites, the ground infrastructure priorities include Control centers and other ground centers, networks and sites [1]. The United States did not directly define the scope of satellite navigation system infrastructure in the form of satellite navigation legislation. Instead, it adopted a method of adapting to supporting policies and regulations to harmonize the national economic security, national public health or safety of the system and assets. Constraint and management. “USA Patriot Act” conferred with key infrastructures sense: physical and virtual systems and assets vital to the United States. It can be seen from this that the physical infrastructure and the operation control system involved in the US satellite navigation system are all the targets of key infrastructure protection, and are managed according to the requirements of Presidential Order No. 7 [2]. Russia is simply a representation to belong to the facility’s satellite navigation system, power to establish on this basis, for protection.

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2.2 Ownership of Satellite Navigation System Infrastructure system After clarifying the boundaries of the object of protection, the way the United States, Russia and the European Union protect the infrastructure of satellite navigation systems is to establish corresponding rights for the object to be protected through laws, giving the owner the right to protect the infrastructure of the satellite navigation system. Obligations and other civil obligations that the subject must not violate, as well as the ownership of national jurisdiction over satellite navigation infrastructure. Russia and the EU law in the satellite navigation primarily by determining the actual infrastructure funded the construction of infrastructure party system ownership of facilities. Russia has clarified the ownership of navigation equipment and facilities through laws in the field of satellite navigation. Russia stipulates that all navigation equipment and facilities belong to the Russian Federation, the main body of the Russian Federation, municipal agencies, natural persons or legal persons [3]. established the legal status for all navigation equipment facilities. And with particular emphasis on the part of a satellite navigation system, as well as benefit the ground with the spacecraft and space systems of the Russian federal budget funds to build the infrastructure facilities owned by the State of the Russian Federation, the state-owned aviation aircraft as absolute owned production protection. Russian state-owned Asset management model is based on federal property relations as the core, integrated views of various sectors management to exercise ownership management. State-owned asset management related laws and regulations formulated by the State, local governments responsible for carrying out the line. Similarly, the Union made it clear that since the European Union is responsible in principle for providing all funds for the Galileo and EGNOS programs, it has obtained the ownership of all tangible and intangible assets constructed and developed in the two programs. 2.3 Satellite Navigation System Infrastructure Certification and Declaration In the process of system development and construction, pre-protection of satellite navigation infrastructure has already begun. Through the certification and declaration system of the control infrastructure, the security of the satellite navigation infrastructure is controlled from two aspects. First, finalize the necessary certification requirements and application procedures. In Russia, for all to Section science and socio-economic legislation of the Russian Federation for the purpose of spacecraft and space infrastructure are required according to Luo E Federation legal requirements subject to inspection. In addition to outside of this, including supporting the development of aerospace equipment and related equipment used should also be required by the related necessity certification and reporting. Second, the statutory legal responsibility to strengthen the implementation of the declaration and certification work. In the Russian Aerospace Activities Law, certification agencies, space equipment development units and related persons responsible for violation of the necessary certification declaration procedures or requirements shall bear the responsibilities stipulated by the laws of the Russian Federation.

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3 Specifications for the safety activities of the satellite Navigation System Infrastructure Safe activity specification refers to the criteria and plan requirements for activities in the entire life cycle from the development, construction, operation and maintenance of satellite navigation system infrastructure to decommissioning. Including the control of the subject qualifications of development, construction, and operation and maintenance, the safety considerations and planning and deployment of the overall system infrastructure in the design and development stage, and the system specifications established by the management of the operation and maintenance activities to ensure system security. The US, Russia and Europe three navigation satellite system provider, market access, safety -wide planning, construction safety, security, operation and maintenance four aspects for the stable operation of satellite navigation activities to make the norm. 3.1 Market Access System for Satellite Navigation System Infrastructure Due to the obvious national defense characteristics of the satellite navigation system, the huge investment in the system, and the wide range of coverage, all countries are invested and managed by the state as the main body, and a strict market access mechanism has been designed in the satellite navigation field to control the satellite navigation system. Especially the orderly and safe construction of infrastructure. The most prominent market access system is Russia. Russian Federation will manage floor space and management of infrastructure facilities and space segment facilities to carry satellite navigation system classified management, you are required to obtain a license to carry a different live within the permitted range of motion. Russian Federation Government “On licensing of space activities” decree will fire arrows and space technology, product development, production, testing and repair work are clearly classified as a license is required by the national authority and to obtain the appropriate licenses before implementation of space activities Space activities of space activities. At the same time, if construction, operation and maintenance units carry out the development, production, installation, testing, commissioning, operation, maintenance, improvement and modernization services of ground space infrastructure technology and equipment, they need to obtain another corresponding space license. 3.2 Satellite Navigation System Infrastructure Safety Planning System Security infrastructure planning satellite navigation system by strengthening capacity building system, improve the overall planning of the system, clear system development and construction side need to take into account security issues before infrastructure construction projects begin to ensure that the satellite navigation system running along smoothly. For the security planning of the system infrastructure, countries have provided guidance mainly from the following three perspectives: One is the assignment of responsibilities. The US National Space-based Positioning, Navigation and Timing Executive Committee, the Coordination Office and the SpaceBased PNT Advisory Committee are responsible for formulating the organization’s work

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plan and planning. And called for “National Space PNT Five-Year Plan” is updated every year to accommodate the comprehensive “National Space PNT strategy,” the war strategy involving national security, homeland security, infrastructure protection, economic efficiency and user equipment such as negative, in order to optimize the United States And international use of the US space-based PNT system, including GPS and GPS augmentation system. The United States Code requires the Secretary of Defense and the Secretary of Transportation to jointly formulate the “Federal Radio Navigation Plan” to sort out and study all radio navigation systems of the United States government, make overall plans and put forward corresponding legislative proposals or action plans [1]. The second is to set goals. American policymakers distinctive style, and more to promote and enhance the capacity of the system from the establishment of a target for the authorities angle safe full of. Such as the National Space-Based Positioning, Navigation time coordination office and is responsible for assessing the US space-based PNT infrastructure modernization program, including the development, deployment and operation of new and improved national security and civil services, to keep these areas exceed or at least equal the same in Foreign space-based PNT services. The third is to assign tasks. Europe mostly emphasizes the full consideration of the safety of system infrastructure in the various stages of system design, construction, and operation in the form of planning plans, and puts forward corresponding requirements. In the design stage, the EU requires that the Galileo plan should fully consider the security requirements of the system infrastructure. During the construction phase, the European Commission considered the importance of the system’s ground infrastructure to the Galileo and EGNOS plans and its impact on system safety. The European Commission is responsible for determining the location of the infrastructure. The location selection process should take into account the geographical and technical constraints related to the optimal geographical distribution of the ground infrastructure, as well as the existence of existing installations and equipment suitable for the relevant task [2].

4 Supervision of the Safety Activities of the Satellite Navigation System Infrastructure Foreign countries’ monitoring mechanisms for satellite navigation system infrastructure activities are mainly implemented from two aspects: the operation evaluation mechanism and the accident handling mechanism. The key to the safety supervision of the satellite navigation system infrastructure is to do a good job in supervision, inspection and evaluation. Including regular review, supervision and inspection, the quality assessment of infrastructure and the assessment of operating status are improved through policies and regulations. A regular review of satellite navigation infrastructure, supervision and inspection. The EU protects the facilities of the Galileo satellite navigation system no less than the protection of critical infrastructure in Europe. The European Union requires that the protection procedures or equivalent standards for critical infrastructure in Europe be determined. And complete the corresponding protection program or an equivalent standard within a year after the facility was recognized standards, while ensuring such protection measures and standards for regular review [3].

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On the other hand is the supervision and inspection of the infrastructure, including the monitoring of project implementation Governor examination of normative technical document management supervision and inspection. The European Union supervises and inspects the quality of the contract implementation of the system builder. The European Commission defines the key decision-making stages and achieves the purpose of monitoring and evaluating the implementation of the plan by comparing plan requirements and actual results [4]. The government of the Russian Federation has given group companies the power to supervise laws and regulations in the specified areas of activity. The main scope of supervision includes the preparation of normative technical and organizational management documents by the group company [5]. Unified control and supervision of the safety of infrastructure projects from the perspective of standards and specifications. The second is the quality assessment of satellite navigation infrastructure. Russian insurance company based in the powers and functions of the security barrier of space activities have, asking them in conjunction with relevant federal agencies to develop security measures, including space infrastructure during the project to protect the safety of the work list. The third is a satellite-based navigation operational condition assessment infrastructure. Assignment to the United States Department of Defense will run primarily responsible for the assessment, mainly for infrastructure that is core space segment payload charge of running the energy efficiency evaluation. The Secretary of Defense needs to cooperate with other departments and agencies to evaluate the utility and feasibility of carrying auxiliary payloads on GPS satellites, monitor the operating status of satellite navigation in real time, and troubleshoot the causes of problems.

5 Inspirations and suggestions Due the infrastructure safety protection system is an important part of the satellite navigation safety protection system. United States, Russia, the European Union satellite navigation basic common facilities security protection system that one is in close contact with the national critical infrastructure protection; the second is the construction has a programmatic, systematic; Beidou system should fully draw on international experience in a timely manner by the relevant system Set up and implement to improve the protection capability of system infrastructure. 5.1 Sound Policies and Regulations System, According to Law Protection System Infrastructure Recommended by law in the form of norms Beidou satellite navigation system infrastructure, accelerate promote satellite navigation field of special regulations in the introduction. The United States fully completed GPS in 1994, and introduced the “U.S. Global Positioning System Policy” in 1996. At present, the United States has formed a relatively complete PNT legal system, and adjusted and updated it in due course to actively adapt to new trends and solve new problems. Russia put into use the GLONASS system in 1996, and issued a presidential decree on the “GLONASS Satellite Navigation System” in early 1999, and formulated 4 laws related to satellite navigation. Since

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the beginning of the development and construction of the Galileo system, the European Union has enacted laws regulating satellite navigation activities. In contrast China, in a special satellite navigation of the Basic Law is to promote the process is relatively slow, the lack of command of the documents, and other related laws in the protection of the Beidou system security and development is also inadequate. Need from the law’s point of view, for the Beidou system, basic facilities of limits, risk prevention level, specific initiatives to be divided. Accelerate promote satellite navigation field of special legislation, the provisions expressly infrastructure of the construction, maintenance and supervision and management units corresponding responsibilities, implement protective measures. For the Beidou system stability to provide global services to provide solid of institutional basis. 5.2 Establishment of Satellite Navigation Infrastructure, the Whole Chain Security Protection System Satellite navigation basic facilities is the system running the foundation of the foundation. The United States’ awareness of the risk prevention of satellite navigation services has continued to deepen along with the expansion and development of technology and services. It has become an irreversible development trend to realize that negative impacts will spread to a wider range and more core government functions, and there is an urgent need to increase risks. The efficiency of the plan and disposal, as well as the appropriate alternatives provided to key departments. Continuous issued a number of policy investigation hazards, reduce risk, combing the formation of Wei satellite navigation safety risk prevention system. Improve the risk management and control mechanism. Including the alternative plan when the service is abnormal, the crisis management and tracking mechanism, the daily exercise mechanism, and the risk management mechanism for the import and export of satellite navigation services. Especially in infrastructure and manufacturing links particularly closely, with reference to the United States for system security, especially spare parts and equipment facilities of the origin of the investigation and the replacement way be risk anticipation and disposal.

6 Conclusion Beidou system as the world’s four major satellite navigation system is one of the positive towards global service of a new phase, in order to provide a more reliable, more stable, more high-quality of satellite navigation positioning service, should give full attention to infrastructure in system development in the important role, should also be put into more and more outstanding of research resources for protection mode and the system continuously iterative update. Other three satellite navigation systems in this regard has more advanced the system experience, worth the Beidou system study and learn. Attention to policies and regulations construction is not only the better of norms and safeguards system development, it is the Big Dipper to the world to provide the best of commitment.

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References 1. 10 USC 2281: Global Positioning System. https://uscode.house.gov/view.xhtml?req=granul eid:USC-prelim-title10-section2281&num=0&edition=prelim. Accessed 2021 2. REGULATION (EU) No 512/2014 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 16 April 2014:amending Regulation (EU) No 912/2010 setting up the European GNSS Agency. https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A3201 4R0512&qid=1616935790372. Accessed 2020 3. On the further implementation of the European satellite navigation programmes (EGNOS and Galileo). https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A3 2010L0040&qid=1616924985704. Accessed 2020 4. Council Regulation (EC) No 876/2002 of 21 May 2002 setting up the Galileo Joint Undertaking THE COUNCIL OF THE EUROPEAN UNION. https://eur-lex.europa.eu/legal-content/EN/ TXT/?uri=CELEX%3A32002R0876&qid=1616931960626. Accessed 2020 5. REGULATION (EU) No 1285/2013 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 11 December 2013. https://eur-lex.europa.eu/legal-content/EN/TXT/?uri= CELEX%3A32013R1285&qid=1616925495046. Accessed 2020 6. Russian Law of navigation activities. Russian Federation.http://docs.cntd.ru/document/902 142618. Accessed 2020 7. RUSSIAN FEDERATION On Space Activities. Russian Federation. http://docs.cntd.ru/doc ument/9033683. Accessed 2020 8. On the approval of the Administrative Regulations of the State Corporation for Space Activities Roscosmos state service for the issuance of permits for the construction and commissioning of space infrastructure facilities under the control of the State Corporation for Space Activities.ROSCOSMOS STATE SPACE CORPORATION. http://docs.cntd.ru/document/542 614517. Accessed 2020 9. On the approval of the Administrative Regulations of the Federal Space Agency for the provision of public services for the licensing of space activities. FEDERAL SPACE AGENCY. http://docs.cntd.ru/document/499011012. Accessed 2020

The Standardization Status and Standard Sets Construction of Beidou Satellite Navigation System Kai Wang, Weijia Wang(B) , Ying Liu, Ji Guo, Xiangyi Zhang, and Dongliang Liu No.89 xiaotun road, Fengtai, Beijing, China

Abstract. In this Paper, we summarize the current status of relevant standard setting and revision of Beidou satellite navigation system, and systematically state the demonstration and construction progress of the Beidou satellite navigation system standard system. Besides, we show that the standards at all levels play an important role in the construction and operation of the Beidou satellite navigation system. In addition, with the demonstration progress of the national comprehensive PNT system, we tend to state the development priorities and main tasks of the standardization work in the future, and try to put forward the research and demonstration ideas for the national comprehensive PNT standard system. Keywords: Satellite navigation · Standard · PNT

1 Introduction Beidou satellite navigation system (hereinafter referred to as “Beidou system”) is one of system engineering with the largest scale, the most complicated technology, the most powerful systematicness and the most onerous construction task in China’s space history till now. This engineering is widely based on the development and construction work carried out by domestic dominant scientific units and technical workers in various fields. Beidou system has completed global network project construction as of June 2020, with service areas covering the whole world, providing seven services for various users, accumulating rich experience in the aspects of engineering construction, operation, maintenance, application and promotion, and achieving many innovative results such as new techniques, mechanisms and products. Therefore, systematic sorting of series standards formed is of great significance for related subsequent work of the engineering. Since the beginning of development and construction, Beidou system has been carrying out demonstration of standardization. With the development of Beidou system construction, the standardization work has certain advantages in seizing technical frontier, leading scientific and technological innovation, guiding engineering practice, normalizing application and promotion, exploring international market and seeking economic benefits, plays a greater role in driving the technical development, application and promotion of Beidou system and enhancing international competitiveness, and is of great importance for the improvement of competitiveness and sustainable development of the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 623–634, 2021. https://doi.org/10.1007/978-981-16-3146-7_59

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Beidou satellite navigation industry. Organized by National Technical Committee for Standardization of Beidou Satellite Navigation (hereinafter referred to as “Committee for Standardization of Beidou”), great achievements in the demonstration planning of standardization work for Beidou system, the development and construction of standard system and the development and revision of standards at different levels have been accomplished during the National 13th Five-year Plan. This paper aims to put forward the major work of subsequent domestic standardization in the field of Beidou system and national comprehensive positioning, navigation and timing (PNT) standard system construction demonstration through scientific demonstration of basic framework, branch structure and standard details of Beidou system standard system and systematic sorting of domestic standard development and revision status of Beidou system in combination with the new requirements for the demonstration of national comprehensive PNT system, so as to guide the development and revision of related standards for Beidou system in the future, and lay a foundation for the demonstration of national comprehensive PNT standard system.

2 Progress of Standard System Development and Construction Beidou Satellite Navigation Standard System (version 1.0) was officially issued by China Satellite Navigation Administration Office in 2015. This standard system comprehensively plans the standards of Beidou system in terms of foundation, engineering, operation and maintenance as well as application, with clear classification and distinct gradation, highlighting the features of Beidou system, providing basis for the smooth development and revision of engineering standards for Beidou, and effectively guiding the development and revision of standards at different levels in related fields of Beidou system. Since 2018, with the rapid advance of engineering construction and application promotion of BDS-3, in order to guarantee the engineering construction of BDS-3, ensure steady operation, promote technical development, serve various applications and realize resource sharing and maximum benefit, the standard system should be further optimized and upgraded based on Beidou Satellite Navigation Standard System (version 1.0), so as to consolidate existing technological results, sum up engineering construction experience and drive the extensive use of Beidou system in all industries at home and aboard, thus the demonstration and construction of Beidou Satellite Navigation Standard System (version 2.0) have started gradually. At present, the draft for comments on Beidou Satellite Navigation Standard System (version 2.0) has been prepared. Now we’re asking related parties for their opinions. Comparatively, version 2.0 inherits the primary framework of version 1.0, mainly including four branches: foundation standards, engineering construction standards, operation and maintenance standards and application standards. The branch of foundation standards plans the terms, space-time datum and project management standards with wide applicability in satellite navigation technology and application; the branch of engineering construction standards separately divides relevant systems with Beidou features according to the characteristics and demands of Beidou system engineering development and construction to offer strong support for the engineering construction of Beidou

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system; the branch of operation and maintenance standards details the operation and maintenance work based on full-lifecycle operation, service delivery and maintenance management for each part of Beidou system to comprehensively guarantee the continuity of Beidou system service. In close connection with the actual needs of national Beidou satellite navigation application and promotion and industrialization development, the branch of application standards plans the general service and interface, foundation application products, engineering standards and industrial application standards in Beidou application by taking key links in the field of satellite navigation application into overall consideration. The framework diagram of standard system (version 2.0) is as shown in Fig. 1.

Fig. 1. Framework of standard system (version 2.0)

The compilation process of standard system (version 2.0) follows the principles of “demand orientation, simplification and feasibility, internationalization”. Facing the development of Beidou satellite navigation industry, the actual application demands were fully demonstrated, the requirements of standards in new application fields were taken into account, and Beidou related standards newly released in recent years were supplemented; on the basis of ensuring the practicability, integrity and operability of system, system planning realizes preciseness and simplicity, avoiding missing standards and repeated content to restrain industrial development; system planning is compatible with other global satellite navigation systems based on Beidou system, and the planned standards should coordinate with internationally existing standards, and the projects with demands for international standardization in the field of Beidou have been planned as a whole. Six branches of engineering standards such as ground test verification system standards, satellite based augmentation system standards, Beidou short message standards, international application standards, low orbit augmentation standards and timefrequency application standards were added based on two engineering standards-original foundation enhancement system standard and global continuous monitoring and evaluation system standard according to the needs of Beidou system application and promotion, comprehensively considering the attributes of BDS-3 aiming at international application and promotion after its building, and reflecting the characteristic service of Beidou system and the extensiveness of its application.

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3 Status of Standard Setting 3.1 National Standards Developed Under the Jurisdiction of the Committee for Standardization of Beidou The Committee for Standardization of Beidou officially issued 28 national standards such as Terminology for Beidou Satellite Navigation at the end of 2020, achieving new breakthroughs in national standard setting in the field of Beidou. Such standards will greatly fill the gap of national standards in the field of Beidou, provide support for Beidou’s innovative development, offer standard basis for Beidou related terminal development and detection certification, and provide standard guarantee for extensive application and promotion of Beidou in territory, navigation, geology, forestry, ocean and other industries on a national scale (Table 1). Table 1. Statistical table for national standards developed under the jurisdiction of the Committee for Standardization of Beidou No.

Standard name

Standard number

1

Specification for data interface of national BeiDou augmentation system data processing center

GB/T 37018-2018

2

Specification for national BeiDou augmentation system dissemination interface Part 1: mobile communication network

GB/T 37019.1-2018

3

Specification for national BeiDou augmentation system dissemination interface Part 2: China Mobile Multi-media Broadcasting

GB/T 37019.2-2018

4

Specification for national BeiDou augmentation system dissemination interface Part 3: Digital audio broadcasting in FM band

GB/T 37019.3-2018

5

Terminology for BeiDou Navigation Satellite System (BDS)

GB/T 39267-2020

6

General specification for GNSS navigation receivers onboard LEO satellite

GB/T 39268-2020

7

Quality requirements for international GNSS monitoring and assessment system (iGMAS) Part 1: observation data

GB/T 39396.1-2020

8

Quality requirements for international GNSS monitoring and assessment system (iGMAS) Part 2: products

GB/T 39396.2-2020

9

File format of international GNSS Monitoring and Assessment System Part1: observation data

GB/T 39397.1-2020

10

File format of international GNSS Monitoring and Assessment system Part2: product

GB/T 39397.2-2020

11

The monitoring and assessment parameters of international GNSS monitoring and assessment system (iGMAS)

GB/T 39398-2020 (continued)

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Table 1. (continued) No.

Standard name

Standard number

12

General specification for BeiDou navigation satellite system geodetic receiver

GB/T 39399-2020

13

BeiDou grid location code

GB/T 39409-2020

14

General specification for GNSS geodetic receivers onboard LEO satellite

GB/T 39410-2020

15

Technical requirements of BeiDou satellite common-view time transfer

GB/T 39411-2020

16

Performance requirements and test methods for BeiDou navigation satellite system signal simulator

GB/T 39413-2020

17

Interface specification for signal in space of Beidou navigation satellite system Part 1: open service signal B1C

GB/T 39414.1-2020

18

Interface specification for signal in space of Beidou satellite navigation system Part 2: open service signal B2a

GB/T 39414.2-2020

19

Interface specification for signal in space of Beidou satellite navigation system Part 3: open service signal B1I

GB/T 39414.3-2020

20

Interface specification for signal in space of Beidou satellite navigation system Part 4: open service signal B3I

GB/T 39414.4-2020

21

Specifications for precision service products of BeiDou navigation satellite system

GB/T 39467-2020

22

Performance requirements and test methods for BeiDou navigation satellite system signal record and playback devices

GB/T 39472-2020

23

Open service performance standard for BeiDou navigation satellite system

GB/T 39473-2020

24

GNSS receiver independent exchange format

GB/T 27606-2020

25

Interface Specification of application development middleware for navigation electronic map

GB/T 39584-2020

26

Technical specification for communication network system of BeiDou ground-based augmentation system

GB/T 39723-2020

27

Technical specifications and testing methods for cesium atomic clock

GB/T 39724-2020

28

Technical requirement for data processing center of BeiDou ground-based augmentation system

GB/T 39783-2021

29

Technical specification for reference station construction and acceptance of BeiDou ground-based augmentation system Part1: Construction specification

GB/T 39772.1-2021

30

Technical specification for reference station construction and acceptance of BeiDou ground-based augmentation system Part2: Acceptance specification

GB/T 39772.2-2021

31

Coordinate System of BeiDou Navigation Satellite System

GB/T 39787-2021

32

Technical requirement for reference station joining BeiDou ground-based augmentation system

GB/T 39721-2021

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So far, 32 national standards have been issued accumulatively, covering general basics, engineering construction, application and promotion and so on, of which General Basic Standard Terminology for Beidou Satellite Navigation provides general-purpose language in the professional field of navigation, and can serve as a reference for relevant standard compilation. Series national standards such as Interface Specification for Signal in Space of Beidou Satellite Navigation System and Service Performance Specification for Beidou Navigation Satellite System define the constraints of open service signals between Beidou system space constellation and user terminal in detail. The issuance in the form of national standard can serve as important basis for the design, development and application of Beidou satellite navigation products on a national scale, is an important bridge between Beidou system and users, and has great significance for driving the nationwide application of Beidou system. Five series national standards including Global Continuous Monitoring and Evaluation System (iGMAS) are centered around the format and quality requirements for data and product files of iGMAS and the requirements for monitoring and evaluation parameters, can drive the development level and reliability of high-precision measurement receiver, further propel the application of iGMAS data and products in various industries, and promote China’s discourse power in the fields of international satellite navigation monitoring and evaluation. 3.2 National Standards for Beidou Developed Under the Leadership of the Industry Some standards related to satellite navigation have been developed under the jurisdiction of relevant departments and organizations (such as the Ministry of Industry and Information Technology and the Technical Committee for Standardization of National Geographic Information) in addition of the Committee for Standardization of Beidou, mainly involving the application of Beidou system in the industries of traffic, sailing, surveying and mapping and electricity. These standards, such as Satellite Positioning Personal Position Information Service System, Satellite Positioning Ship Information Service System, Satellite Positioning Vehicle Information Service System and Electric System Beidou Satellite Timing Application Interface developed by the Ministry of Industry and Information Technology and standards in terms of navigation electric map and positioning base station developed by the Technical Committee for Standardization of National Geographic Information, will be included in standard system (version 2.0) in the form of inclusion, and their application and implementation will greatly drive the widespread and in-depth application of Beidou system in relevant industries (Table 2). 3.3 Engineering Standards for Beidou Since 2014, under the guidance of China Administration Office for Satellite Navigation System, the jurisdiction organization of the Committee for Standardization of Beidou has carried out the development and revision of engineering standards for Beidou. Such engineering standards aim to solve the urgent needs of Beidou related enterprises for standards, and are important supplement of national standards, industrial standards and group standards, and some engineering standards suitable for transformation can be upgraded to industrial standards or national standards after being issued. Up to now, three groups

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Table 2. Statistical table for national standards developed under the jurisdiction of relevant departments and organizations No. Standard name

Standard number

1

Terminlogy for navigation

GB/T 9390-2017

2

Satellite positioning personal position information service system GB/T 29841.1-2013 (PPISS) - Part 1: Function description

3

Satellite positioning personal position information service system GB/T 29841.2-2013 (PPISS) - Part 2: Information protocol for terminal and service center

4

Satellite positioning personal position information service system GB/T 29841.3-2013 (PPISS) - Part 3: Information security specification

5

Satellite positioning personal position information service system GB/T 29841.4-2013 (PPISS) - Part 4: General specification of terminal

6

Temporal systems for satellite navigation and positioning

GB/T 29842-2013

7

Satellite positioning ship information service system (SISS) —Part 1: Function description

GB/T 30287.1-2013

8

Satellite positioning ship information service system (SISS) —Part 2: Information protocol for shipborne station and service center

GB/T 30287.2-2013

9

Satellite positioning ship information service system (SISS) —Part 3: Information security specification

GB/T 30287.3-2013

10

Satellite positioning ship information service system (SISS) —Part 4: General specification for ship-born terminal

GB/T 30287.4-2013

11

Coordinate system for navigation satellite system

GB/T 30288-2013

12

Satellite positioning vehicle information service system (VISS) —Part 1: Function description

GB/T 30290.1-2013

13

Satellite positioning vehicle information service system (VISS) —Part 2: Information protocol for vehicle terminal and service center

GB/T 30290.2-2013

14

Satellite positioning vehicle information service system (VISS) —Part 3: Information security specification

GB/T 30290.3-2013

15

Satellite positioning vehicle information service system (VISS) —Part 4: General specification for vehicle terminal

GB/T 30290.4-2013

16

Physical storage format for navigation electronic map in vehicle system

GB/T 30291-2013

17

Physical storage format for navigation electronic map in personal position

GB/T 30292-2013

18

General specification for in-vehicle satellite navigation equipment GB/T 19392-2013

19

Specification for the ground-based GNSS water vapor remote sensing observation

GB/T 33700-2017 (continued)

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No. Standard name

Standard number

20

Global navigation satellite system for vehicles engaged in road transport—Technical specifications for the platform

GB/T 35658-2017

21

Internet-based transmission of GNSS augmentation information—Part 1: Broadcast architecture

GB/T 34966.1-2017

22

Internet-based transmission of GNSS augmentation information—Part 2: Interface requirements

GB/T 34966.2-2017

23

Internet-based transmission of GNSS augmentation information—Part 3: Data transmission format

GB/T 34966.3-2017

24

Specifications for basic product of the reference stations using global navigation satellite system

GB/T 35767-2017

25

Specification for service and management system of the reference GB/T 35768-2017 stations using global navigation satellite system

26

Specification for service of the reference stations using global navigation satellite system

GB/T 35769-2017

27

Application interface of BDS timing for power system—Part 1: Technical specification

GB/T 37911.1-2019

28

Application interface of BDS timing for power system—Part 2:Testing specification

GB/T 37911.2-2019

29

Technical requirements for BDS timing terminal

GB/T 37937-2019

30

Test methods for BDS timing terminal

GB/T 37943-2019

31

Data transmission interface protocol of global navigation satellite system reference station

GB/T 39607-2020

32

Terms for global navigation satellite system reference station

GB/T 39611-2020

33

Quality assessment specifications for reference stations using global navigation satellite system

GB/T 39614-2020

34

Specifications for testing of reference stations using global navigation satellite system

GB/T 39615-2020

35

Specification for network real-time kinematic (RTK) surveys based on the reference stations using global navigation satellite system

GB/T 39616-2020

36

Specifications for operation and maintenance of the reference stations using global navigation satellite system

GB/T 39618-2020

of engineering standards for Beidou (32 in total) have been issued in 2015, 2017 and 2019 respectively, covering many major fields such as data formats, chips, antennas, modules, terminals, simulators, navigation maps, navigation software and ground based augmentation system construction, effectively normalizing the data formats, index systems and test methods of products based on Beidou, and gradually changing the situation that domestic satellite navigation criterion is dominated by American GPS.

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58 engineering standards for Beidou are now under development, and will be issued in 2021 successively as planned (Table 3). Table 3. Statistical table for engineering standards developed under the jurisdiction of the Committee for Standardization of Beidou No. Standard name

Standard number

1

Terminology for BeiDou Navigation Satellite System (BDS)

BD 110001-2015

2

BeiDou/Global Navigation Satellite System (GNSS) receiver independent exchange format

BD 410001-2015

3

BeiDou/Global Navigation Satellite System (GNSS) receiver differential data format

BD 410002-2015

4

BeiDou/Global Navigation Satellite System (GNSS) receiver differential data format (II)

BD 410003-2015

5

Navigation and positioning data output format for BeiDou/Global Navigation Satellite System(GNSS) receiver

BD 410004-2015

6

General specification for RFIC of BeiDou/Global Navigation Satellite Systems (GNSS) receiver

BD 420001-2015

7

Performance requirements and test methods for BeiDou/Global Navigation Satellite Systems (GNSS) geodetic OEM board

BD 420002-2015

8

Performance requirements and test methods for BeiDou/Global Navigation Satellite Systems (GNSS) geodetic antenna

BD 420003-2015

9

Performance requirements and test methods for BeiDou/Global Navigation Satellite Systems (GNSS) navigation antenna

BD 420004-2015

10

Performance requirements and test methods for BeiDou/Global Navigation Satellite Systems (GNSS) navigation unit

BD 420005-2015

11

Performance requirements and test methods for BeiDou/Global Navigation Satellite Systems (GNSS) timing unit

BD 420006-2015

12

Performance requirements and test methods for BDS RDSS unit

BD 420007-2015

13

全球卫星导航系统 (GNSS) 导航电子地图应用开发中间件接口 规范

BD 420008-2015

14

General specification for BeiDou/Global Navigation Satellite Systems (GNSS) geodetic receivers

BD 420009-2015

15

General specification for BeiDou/Global Navigation Satellite Systems (GNSS) navigation devices

BD 420010-2015

16

General specification for BeiDou/Global Navigation Satellite Systems (GNSS) positioning devices

BD 420011-2015

17

Performance requirements and test methods of BeiDou/Global Navigation Satellite System(GNSS) signal simulator

BD 420012-2015 (continued)

632

K. Wang et al. Table 3. (continued)

No. Standard name

Standard number

18

Construction specification for reference station of BDS ground-based augmentation system

BD 440013-2017

19

Data storing and exporting requirements for reference station of BDS ground-based augmentation system

BD 440017-2017

20

Data interface specification of BDS ground-based augmentation system national data integrated processing system

BD 440015-2017

21

Interface specification for data dissemination based on mobile BD 440018-2017 communication network of BDS ground-based augmentation system

22

Qualification evaluation requirements for joining reference station network of BDS ground-based augmentation system

23

Interface specification for China mobile multi-media broadcasting BD 440019-2017 data broadcast Interface of BDS ground-based augmentation system

24

Regulation for operation and maintenance of BDS ground-based augmentation system reference station

25

Drafting guidelines for project standard

BD 130002-2017

26

Rules for formats and publication of project standard

BD 130003-2017

27

Requirements and test method for BDS/GNSS baseline processing and network adjustment software

BD 420020-2019

28

Requirements and test method for BDS/GNSS network RTK server software

BD 420021-2019

29

Observation data quality assessment methods for BeiDou/Global Navigation Satellite Systems geodetic receiver

BD 420022-2019

30

General specification for Global Navigation Satellite System RTK receiver

BD 420023-2019

31

Specification for Global Navigation Satellite System high precision geographic information collection handheld terminal

BD 420024-2019

32

Definitions and descriptions for BDS/GNSS satellite parameters for high precision application

BD 420025-2019

BD 440016-2017

BD 440014-2017

4 Suggestions and Thinking 4.1 Strengthen the Propaganda of System, and Guide the Development and Revision of Standards As one of top documents for the standardization of Beidou, Beidou satellite navigation standard system guides the development and revision of standards at all levels to some extent. Seen from the quantity and grade of standards issued or approved, the national standards approved are limited, and only 32 engineering standards for Beidou were issued, which cannot meet the requirements of engineering construction, steady

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operation, application, promotion, industrialization and the internationalized application of Beidou for standards, and standard setting is disconnected from technological innovation, industrial development and social demands. The standard system (version 2.0) gives full consideration to the influence of technical development and stable operation on standardization work, and scientifically and reasonably adjusts the details of standards, so it will meet the requirements of China’s Beidou navigation field for the development and revision of standards in the next three to five years. In order to achieve the unified planning, organization, deployment and harmonization of setting for standards regarding Beidou, standard system is recommended to be effectively publicized and popularized at the right time, so as to give full play to the planning and guidance of standard system, the demonstration for project approval of relevant standards is recommended to be carried out according to the planning of standard system in principle, and dynamic update and maintenance of standard system shall be done well according to technical development and related requirements at the same time. 4.2 Strengthen the Publicizing and Implementation of Standards, and Promote Implementation and Application With the development and issuance of national standards and engineering standards in the field of Beidou, China has got out of the situation that there are no standards in the field of Beidou, but major deficiencies still exist in the aspects of publicizing and implementation, transformation and application of relevant standards, resulting in unsatisfactory application of standards issued and weakness in achievement transformation effects of standards. With the in-depth proceeding of setting of standards at different levels in the field of Beidou, the number of standards will increase year by year, so how to fully implement and broadly apply the standards and promote industrialization will become one of priorities currently and in the near future. Therefore, the enhancement of publicizing and implementation of standards at different levels in the field of Beidou and periodic publicizing and implementation, application implementation and effect analysis of engineering standards will further exert the application effects of standards, accelerate the implementation and application of standards, improve the efficiency of application, reduce repetitive construction in the field of Beidou, and facilitate the application and promotion of Beidou system in all walks of life. 4.3 Strengthen the Demand Demonstration of Comprehensive PNT Standard System, and Drive Relevant Integrated Standard Research In 2035, China will establish a more ubiquitous, integrated and intelligent national PNT system. It can be predicted that the construction of comprehensive PNT system will be more complicated and arduous than Beidou system, involving numerous innovative outcomes, such as new technology, new mechanism and new products, numerous PNT means with big technical difficulty and high degree of innovation (including Beidou system) will be blended and built, and interfaces, protocols, regulations and requirements of different technical mechanisms in many fields will be opened up.

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Based on serving the construction of comprehensive PNT system, the demonstration research of comprehensive PNT standard system should be planned in advance to guide the development and revision of standards in relevant fields of comprehensive PNT system and serve the critical stages including the conceptual design, planning demonstration, engineering construction, operation and maintenance, stable operation, intelligent operation and maintenance, and application and promotion of comprehensive PNT system. The in-depth demonstration research (including technical system, data accommodation, system interface, service performance, test evaluation and reliability index system) of various PNT means will further determine key technical indexes and test methods, form a batch of draft standards in urgent need of engineering construction, lay a solid technical foundation for subsequent standard setting, ensure useful standards developed, realize the flexible integration and comprehensive utilization of various PNT means, and lay the foundation for the realization of comprehensive PNT system construction goal.

References 1. Xu, D.: BeiDou standardization work review and outlook, satellite application, Issue 7 (2020) 2. Xu, D.: BeiDou standardization work route summary, satellite application, Issue 2 (2018) 3. Xia, F.: Research of standard system construction method—taking the example of BeiDou satellite navigation system, China’s standardization, Issue 10 (2017) 4. Mai, L., et al.: Standardization of BeiDou GBAS standard system, China’s standardization, Issue 11 (2016)

Intellectual Property Risk and Prevention of BeiDou’s “Going-Out” Strategy Lin Su(B) , Jixuan Xiao, and Yuexuan Wang National Defense Intellectual Property Administration, Xicheng District, Beijing 100032, China

Abstract. With the acceleration of BeiDou’s industrialization process, the application of BeiDou’s relevant technology has penetrated into all industries. It is an inevitable trend for BeiDou to enter into and compete in the global market. However, due to the discrepancy in competitors’ intellectual property strategies, legal systems and enforcement mechanisms among different countries as well as high international concern over the intellectual property issues in China, the intellectual property situation confronting BeiDou’s “going-out” strategy has become ever more complex and severe. Based on the analysis of the types and causes of intellectual property risks faced by BeiDou’s “going-out” strategy, this paper puts forward measures to prevent and counter risks from the levels of the government, the industry and BeiDou enterprises, so as to promote BeiDou’s “going-out” strategy in a better way and eventually enhance the cooperation and development of global satellite navigation. Keywords: Intellectual property · BeiDou’s “going-out” strategy · Risk and prevention system

1 Introduction The BeiDou Navigation Satellite System, short for “BeiDou System”, is a global navigation satellite system independently constructed and operated by China. Since the completed construction of the BeiDou-3 basic system, BeiDou has been providing service for global users, and utilized in more than 30 countries or regions along the Belt and Road. BeiDou basic products domestically made have been exported to more than 120 countries or regions. At present, BeiDou has entered a new era of global service, prepared to contribute to building a community of shared future for mankind and to building a community of space-time service. This is a convincing example that China has transformed itself from a big country of intellectual property (IP) importation to one of IP creation. While BeiDou provides high-quality and open services for global users, it is an inevitable trend for BeiDou to enter into and compete in the global market [1]. However, in face of such challenges as the discrepancies in the competitors’ IP strategies, the capacity for scientific and technological innovation, the level of IP protection, and the complicated international IP system, we must pay special attention to the IP risks in BeiDou’s “going out”, have a clear understanding of the situation and tasks of IP protection and enhance the capability of risk prevention and resistance, so as to safeguard BeiDou’s “going out” strategy. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 635–642, 2021. https://doi.org/10.1007/978-981-16-3146-7_60

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2 IP Risks Confronting BeiDou’s “Going out” Strategy IP is a key step to technology protection. In advancing industrialization and internationalization, enterprises must attach importance to the protection of IP as well as identify and prevent IP risks. 2.1 IP Risks Out of Ambiguity in Ownership 2.1.1 The Risk of Losing Ownership Firstly, while excessive attention has been given to improving the quality of technology and service, little has been paid to taking advantage of the IP legal system to secure IP rights, consequently running the risk of rush registration by others or the risk of completely abandoning the chance of obtaining IP. One good example, as we all know, is artemisinin, the widely recognized novel medication developed by China. However, China is unable to patent it, largely because the relevant extraction technique has been publicized in research papers. Thus, the novelty requirement for patentability cannot be met. Secondly, for IP generated through commissioned development and cooperative development, there might be a lack of clear stipulation in the contracts as to the ownership of rights based on such IP. Consequently, BeiDou enterprises may lose the identity as right holders and the control over said IP, endangering BeiDou’s “going out” strategy. Thirdly, from the perspective of enterprises, BeiDou enterprises have, in general, failed to attach enough importance to IP risk management, including management of personnel and of IP information. On the one hand, BeiDou enterprises face a general lack of maintenance and management of their IP resources already obtained. In case of a change in the key registration information overseas, if BeiDou enterprises fail to apply to the relevant administrative departments for changes about the relevant IP information, this may have adverse effect on the IP license and transference afterwards. On the other hand, BeiDou enterprises are unable to respond to and handle IP risks properly [2]. What’s more, it is urgent that BeiDou enterprises improve management over their personnel. Unfamiliarity with legal knowledge, incapability of collecting evidence, erroneous litigation strategy and decision making of BeiDou enterprises will all lead to risks [3]. Fourthly, in the overall IP arrangement overseas, BeiDou enterprises must not only acquaint themselves with the legal procedure to acquire IP in other countries, but also get themselves ready for the possible obstruction from their competitors by means of IP application procedures or even malicious litigation. It has to be remembered that when applications are made to patent China’s high-speed railway technologies, competitors have tried various means to interfere, trying to obstruct their patent administrative departments from issuing patents to Chinese enterprises. 2.1.2 The Risk of Litigation for IP Infringement At present, the BeiDou system is still faced with the risk of “being strangled” in its core technology, which depends on other countries, particularly in the fields of chip development, integration and application service, as well as high-precision indoor navigation technology [1]. If, in the process of technology import, there have been improper review

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and insufficient risk evaluation, then BeiDou system is likely to be challenged by IP infringement litigation in going out. 2.2 IP Risks in the Internationalization of BeiDou Due to the differences in domestic and foreign legal environments and markets, when Chinese enterprises go overseas, they are often “not acclimated to the foreign environment”. In implementing BeiDou’s “going out” strategy, special attention should be paid to the following risks in IP protection. 2.2.1 Legal Environment Risks BeiDou enterprises can’t get around the legal and policy entry thresholds of other countries when they open up the global market. In addition, the legal environments and policy conditions vary greatly from country to country, which may lead to the deviation in the application of laws. Therefore, BeiDou enterprises should pay attention to legal environment risks [4]. First, the choice-of-law risk. When cooperating with foreign parties, Chinese enterprises often overlook international conventions and relevant provisions of laws in other countries, disdain the use of laws to protect their own rights and interests, and ignore their own rights and offer them to the other party for free when negotiating and signing contracts. Second, the application-of-law risk. There is a great distinction in law enforcement and judicial models among different countries, so it is difficult to predict how relevant departments will interpret and apply the legal provisions related to the bringing in of BeiDou industry. This brings uncertainty for BeiDou enterprises to go global [5]. Finally, the infringement litigation risk. In the process of conducting foreign trade, Chinese enterprises are often involved in litigation for infringement. In addition, foreign competitors may also bring IP litigations for no other reason but to damage the reputation of Chinese enterprises or exclude them from entering their markets [6]. 2.2.2 The Risk of IP Counterfeit and Embezzlement by Other Countries Some countries have low IP protection awareness. For example, some countries in the Middle East have not joined international organizations or signed international treaties in the field of patent application. Then they may bypass the supervision of international organizations and the constraints of international law. This thus enlarges the risk of BeiDou enterprises’ “going out” strategy [7].

3 IP Risks in BeiDou’s “Going Out” Strategy: Causal Analysis 3.1 Weak IP Protection Awareness and Lack of Overseas IP Risk Prevention and Control Mechanism With regard to IP creation, enterprises are more concerned with parameters like the number of IP or product sales than with the key to creation, i.e., complete cooperation contracts and proper IP layout.

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With regard to IP operation and management, in-house lawyers may be uncertain about the types, quantity and ownership in terms of relevant IP or the laws, policies and judicial practice regarding IP management in target foreign countries. Also, enterprises are likely to have an insufficient IP strategic planning for “going out” strategy [8]. Meanwhile, BeiDou enterprises lack a suitable and systematic IP risk prevention and control mechanism in foreign countries. Such a mechanism should cover research and development, brand building, trade, investment [6] and other aspects based on the realities of both the enterprises and domestic environment. With regard to IP protection, enterprises may be unfamiliar with foreign legal systems, short of practical experience in handling foreign disputes and incapable of bearing high court costs, when facing IP infringement or malicious prosecution. 3.2 Strategic Guidance Needed for BeiDou Enterprises to Implement the “Going Out” Strategy BeiDou enterprises are not self-sufficient in implementing the “Going out” strategy. Instead, they need the support of the government and cooperation of the industry. As China develops navigation satellite technology later than developed countries and lacks an overall IP strategy for navigation satellite systems, it is for the present incapable of providing guarantee for enterprises in terms of patent analysis and industrial alliance [9]. Each president of the United States would issue one edition of national space policy, and keep updating “GPS Policy” and “U.S. Space-Based Positioning, Navigation, and Timing Policy”. Similarly, in Russia, there have been presidential decrees and directives related to GLONASS and “Federal Law on Navigation Activities” has been released. But China has not yet established a legal system for BeiDou. Meanwhile, BeiDou System as a multidomain technology requires coordination among multiple government departments. Yet there is no dedicated administrative department regulating BeiDou enterprises in China. Nor is there an industry management mechanism to facilitate BeiDou’s “Going Out” strategy. In addition, BeiDou industrial association and industrial alliance have not yet taken shape. To promote the industrialization of BeiDou, relevant technologies need to be well applied in daily derivative products, such as software, books, and cultural and creative products. It also requires BeiDou industrial association and industrial alliance to provide dynamic information about relevant rights [1]. 3.3 Great Differences in Laws, Systems and Cultures Between Countries The targeted foreign countries for export of BeiDou industry mainly include emerging economies and developing countries [10]. However, these targeted countries have witnessed significant differences in economy, history, culture, law, and other respects, and the same is true with their enforcement of laws and legal provisions. Backed by the “Belt and Road Initiative”, BeiDou enterprises will enter more countries. Some of these countries are more easily to become the ideal terrain for counterfeits and embezzlement, due to their backward economies, technologies, weak innovative ability and awareness of IP rights protection, and incomplete IP systems [7].

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4 Measures and Suggestions for BeiDou IP “Going Out” 4.1 On Government Level 4.1.1 Increasing Support for BeiDou Enterprises and Deploying IP Strategies First, the government should focus on the construction of transportation infrastructure such as railways and highways, smart terminals, energy and power, equipment manufacturing and other industries. Moreover, it should accelerate the implementation of key and massive projects related to the construction and application of BeiDou system, vigorously support key enterprises and institutions to explore innovative cooperation models, and enhance its service in the Belt and Road countries [1] and regions, contributing to building a community of shared future for mankind and to building a community of space-time service. Second, the government should improve the strategic deployment of IP rights related to BeiDou system, enhance coordination and cooperation in order to establish a grand protection pattern. The government should establish a guiding and coordinating body according to the industrial layout, update and improve the national IP information platform in time [11], promote extraterritorial application of China’s IP laws and regulations, improve cross-border judicial collaboration, open up the channel for the creation, application, protection and management of BeiDou IP, perfect the integrated management system, strengthen systematic protective capability, implement the supporting policies for overseas development of enterprises, and improve the level of opening up to the outside world. 4.1.2 Advancing the Standardization of BeiDou Patent Technologies and the Internationalization of BeiDou Technology Standard From the perspective of national strategy, it is imperative for China to step up overall planning to bolster international cooperation and competition in the field of IP, and improve its patent technology in line with the standards of international patent technology. Besides, the Chinese government needs to refine the management mechanism in patent technology standardization and negotiate and resolve the contradictions between industrial standards and national standards. Meanwhile, it is urgent to incorporate BeiDou patent technologies into international navigation technology standards, break the trade barrier caused by the combination of technology patents and standards, and remove legal barriers for BeiDou “going out”. 4.2 On the Level of Industry 4.2.1 Attaching Importance to Overseas IP Layout to Realize Unified Management In the process of BeiDou’s “going out”, enterprises of related industries are suggested to work together and implement appropriate strategies based on the professional analysis of industrial associations [12]. Meanwhile, industries, universities and research institutes will form a patent alliance by conducting cooperation research and development, so as to avoid the disadvantage resulting from the enterprise’ sole research. In addition, in the process of industry-university-research institutes cooperation, attention should also be

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paid to unified management. Enterprises should sign complete agreements with research institutes to clarify IP ownership and the rights and obligations among all parties, and prevent research institutes from repeatedly licensing IP to third parties. 4.2.2 Establishing Overseas IP Protection Agencies and Risk Warning Systems Industrial associations can establish overseas IP protection agencies and risk warning systems. The importance of overseas IP protection agencies lies in the overall improvement of enterprises’ abilities to deal with overseas IP infringement disputes and to protect their own IP. The main services provided by these agencies include but not limited to the issuance of overseas IP protection guidelines, the establishment of BeiDou graded promotion catalogue for the Belt and Road and regions, the provision of litigation assistance fees, and the establishment of a special overseas IP protection fund. Relying on artificial intelligence or computer technology to collect and screen IP information, the risk warning systems can regularly issue overseas IP risk warnings, design warning indicators and establish early-warning models, and compile regional or national IP guidelines alone or jointly with government departments. The systems may give timely feedback to the enterprises, so as to help the enterprises to formulate prevention and control measures and response plans. 4.3 On the Level of Enterprises 4.3.1 Improving the Ability of IP Information Retrieval and Analysis Prior to “going out”, BeiDou enterprises should conduct comprehensive search and analysis of the related IP information. First of all, it is necessary to collect, analyse and master the general overseas IP information in the industry, have a good command of knowledge of the competitors’ IP license and transfer and other IP deals, and familiarize themselves with the main fields, legal basis, and characteristics of overseas IP protection. Secondly, BeiDou enterprises should be familiar with overseas IP systems. BeiDou enterprises should be fully aware of the local laws and regulations as well as the international treaties signed by both countries. With reference to relevant regulations defined by Chinese laws, the enterprises should identify the applicable laws and regulations in the course of trade at the initial stage, so as to deal with the potential legal discrepancy, avoid traps in the application of law, formulate efficient international risk warning and emergency mechanism, and establish foreign IP risk prevention mechanism. 4.3.2 Avoiding Spillover Risk of Patent Technology and Establishing BeiDou Famous Trademark System While introducing BeiDou products to the Belt and Road countries, China should pay more attention to preventing its patent technology from being copied or counterfeited. To cope with this issue, BeiDou enterprises can divide their products into multiple sub-products or multiple functional modules. These will then be delivered to different research and development networks and be utilized to apply for patents by different enterprises or individuals. At last, these various patents can be combined and integrated into a whole product. In this way, it will be hard for market competitors to command

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the core patents of a product by virtue of one sole patent [13], and thus the spillover of patent technology can be effectively avoided to a certain degree. In addition to active efforts in applying for patents, BeiDou enterprises should also attach great importance to the role of trademarks for BeiDou products. While improving their technological strength and product quality, the enterprises can, by means of their capital and product advantage, make their advertisements more creative and recognizable and put more advertisements in the target markets. Also, any promotion efforts should comply with the indigenous culture, cater to consumers’ cultural preference and at the same time respect local religions and customs. By doing this, the enterprises can set up a positive image and enhance the recognition of BeiDou trademarks, thus laying a solid foundation for the BeiDou “going out” strategy. 4.3.3 Improving BeiDou Enterprises’ Countermeasures Against Overseas Lawsuits BeiDou enterprises should set up their own IP archives to classify and sort out IP information and preserve their own IP research and development evidence, so as to make full use of the archives to safeguard their own IP interests when being sued or responding to the lawsuits outside the territory [14]. Enterprises should also make reasonable analysis of infringement risk and take appropriate actions in line with the local market conditions. They can reach a long-term service contract with law firms specialized in solving international IP disputes, and make full use of various approaches with the assistance from professionals to increase the probability of winning the case. At last, in the course of “going out”, BeiDou enterprises should weigh the pros and cons of different dispute resolution methods and employ international treaties and trade rules to protect their legitimate rights and interests.

5 Conclusion In this paper, the legal risks of BeiDou’s “going out” are predicted and the contributing factors are analysed from the perspective of IP. On this basis, the corresponding risk prevention measures are put forward from the aspect of the government, the industry and the enterprises. It is necessary to plan ahead to improve the risk prevention and control of BeiDou’s “going out”. By making a reasonable plan for patent strategy and seizing market and technical resources, relevant enterprises can take the initiative in international competition, assisting BeiDou enterprises in grasping the IP risk coping strategies to avoid risks in a reasonable way, enhance IP protection and application, and promote BeiDou “going out” smoothly. Finally, BeiDou will become another shining Chinese brand and advance the cooperation and development of global navigation satellite systems.

References 1. Zhang, L., Zhang, X., et al.: Facilitating BeiDou’s “going out.” Satell. Appl. 12, 47–51 (2018)

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2. Zhou, L., Lei, Y.: Recognition and Prevention of IP Risks in Enterprises. China Invent. Pat. 02, 54–61 (2020) 3. Daoyuan, Y., Zhang, L.: Intelectual Risks and Prevention in Going out of China’s High-Speed Rail. Hebei Law Sci. 09, 59–72 (2017) 4. Li, Y., Wang, L.: Recognition of and solutions to the legal risks in the implementation of the belt and road initiative. J. Chinese Acad. Governance 02, 77–81+127 (2017) 5. Ning, Z.: Challenges and countermeasures in the going out of state-owned enterprises under the belt and road initiative. Interrade 10, 44–47 (2017) 6. Lu, H., Wang, F.: Research on the IP risks in enterprises going out. J. Nanjing Univ. Sci. Technol. (Soc. Sci. Ed.) 27(02), 40–46 (2014) 7. Tao, Z., Ting, W.: Categories of overseas IP risks and procedure of warning under the belt and road initiative. Cont. Bridge Vision 11, 64–65 (2020) 8. Dong, X.: IP risks and prevention in enterprises going out. Mod. Econ. Res. 05, 44–48 (2017) 9. Lulu, Z., Suning, L., et al.: Status quo of patents in BeiDou satellite navigation industry and implications. China Invent. Pat. 09, 44–48 (2015) 10. Baoyi, X.: On the value of the belt and road initiative and legal risks. China Arab States Sci. Technol. Forum 11, 18–20 (2020) 11. Zhao, J., Lv, L.: On the IP protection of BeiDou navigation satellite system from the perspective of patent. J. Navig. Position. 02,101–105+110 (2020) 12. Shunde, L.: Patent risks in enterprises going out. Intellect. Prop. 01, 66–69 (2013) 13. Lianfeng, W., Dongfang, N.: Overseas IP risks and countermeasures for Chinese enterprises under the belt and road initiative. Intellect. Prop. 11, 94–97 (2016) 14. Heng, T., Zhu, Y., et al.: IP risk control for enterprises. Enterp. Manag. 10, 74–76 (2007)

The Consideration of BDS International Standardization in Civil Aviation Industry Xin Jiang, Zhan Zhang(B) , Zhe Fan, Tieshuai Li, and Boyuan Gong COMAC Beijing Aircraft Technology Research Institute, Beijing, China [email protected]

Abstract. The BeiDou satellite navigation system (BDS) is the core of China’s future civil aviation CNS/ATM system. In order to accelerate the application and innovative development of BDS in the international civil aviation, it is necessary to establish an international standard system for the BDS civil aviation industry. A framework recommendation of the BDS civil aviation international industrial standards is proposed according to the existing and planned international civil aviation standards of GNSS. At this stage, it is urgent to push forward the BDS core system industrial standard, including the core system airborne equipment industrial standard, focusing on the development procedures and technical content of RTCA DO-368 GLONASS/GPS airborne equipment industrial standard, which will provide a reference to develop a minimum operational performance standards (MOPS) for airborne equipment compatible with BDS. This paper will also give some consideration on the promotion of industrial standards for dual-frequency multi-constellation (DFMC) airborne equipment. Keywords: BDS international standardization · Airborne equipment · Industrial standards · Dual-frequency multi-constellation · Minimum operational performance standards

1 Introduction With the rapid growth of civil aviation industry, transoceanic and remote area flight activities become more frequent, the flight density in the terminal area are increasing, which needs higher requirement on the efficient operation of the air transportation system. In order to improve the efficiency and safety of civil aircrafts, Chinese civil aviation will gradually transition from land-based navigation to satellite-based navigation, according to Global Air Navigation Plan (GANP) and Aviation System Block Update (ASBU). Global Navigation Satellite System is a significant foundation of advanced air navigation system, core technology of performance based navigation (PBN), automatic dependent surveillance-broadcast (ADS-B) operation, and an important means to improve the safety level and service quality of air navigation. According to The Roadmap for the Implementation of BeiDou Satellite Navigation System in China Civil Aviation, the overall goal is to build BDS-based GNSS application, the primary tasks are to promote new air navigation system implementation and operation with satellite-based positioning, navigation and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 643–650, 2021. https://doi.org/10.1007/978-981-16-3146-7_61

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timing as the core, to facilitate the communication and coordination between domestic industries and international aviation industry standardization organizations, to draft and review Radio Technical Commission for Aeronautics (RTCA), European Organization for Civil Aviation Equipment (EUROCAE) related industry standards, and to promote the development of technical standards for airborne receivers and ground equipment compatible with BeiDou satellite navigation system. The international industrial standards for civil aviation are the technical basis for the development of avionics products and provide technical standards for airworthiness certification by national authorities. Since GPS, which relies on RTCA, published its first civil aviation industrial standards RTCA DO-208 on 1991, it has built a complete civil aviation industrial standards system, which significantly promote the global application of GPS in civil aviation. GLONASS started the civil aviation international standardization process on 2012, completed first Minimum Operational Performance standard (MOPS) compatible with GLONASS and GPS on 2017. Galileo, which relies on EUROCAE, established WG-62 working group, published first Dual-Frequency Multiple-Constellation (DFMC) civil aviation international industrial standard compatible with Galileo and GPS for airborne equipment. At present, the domestic standard system for BeiDou civil aviation applications is being built, including civil aviation industry standards, international civil aviation standards, etc., and significant progress has been made, but there is still a certain gap compared with advanced developed contries. With the official opening of BeiDou-3 global satellite navigation system on July 31, 2020, it is imperative to implement international standardization working process of BeiDou civil aviation industry in order to promote the application of BDS in civil aviation.

2 GNSS Civil Aviation International Standards System The prerequisite for GNSS to apply in civil aviation is that its space signals meet the space signal performance standards stipulated by ICAO, and also meet the international standards of civil aviation industry, mainly including RTCA, EUROCAE, ARINC and other industry standards, which define the minimum operational performance standards for airborne equipment and operation systems, minimum aviation system performance standards, space signal interfaces, etc. 2.1 RTCA GNSS Industrial Standards Radio Technical Commission for Aeronautics (RTCA) SC-159 is responsible for developing GNSS equipment standards using ABAS, GBAS and SBAS, associated environmental interference reports, and Interface Control Documents (ICD), with multiple Special Commission (SC) jointly developing comprehensive, industry-reviewed and Bureau-approved GNSS and related standards. 2.1.1 SC-159, GNSS Navigation Equipment Since its foundation on 1985, SC-159 has developed a series of MOPS and Minimum Aviation System Performance Standard (MASPS) for GPS and avionics equipment using

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augmentation systems, mainly using GPS L1 signal C/A code, these standards have been widely cited in Technical Standards Orders (TSO) and Advisory Circulars (AC) by FAA and other national authorities as the fundamental documents for equipment certification. As early as 1991, RTCA published first GPS MOPS DO-208 for GPS navigation use on En-Route and Non-Precision Approach, then FAA issued first GPS airborne equipment Technical Standards Orders TSO-C129, whose minimum performance refers to DO-208, the airborne equipment was classified, the function, performance and test procedures were demonstrated and modified based on DO-208. After that, The United States completed the implementation of Local Area Augmentation System (LAAS) and Wide Area Augmentation System (WAAS), and released MOPS for WAAS and LAAS on 1996 and 1998, respectively, and became an important basis to support the related TSO’s, citing DO-229F in TSO-C145, DO -253D in TSO-C161, TSO-C196 cited DO316, etc. Nowadays, SC-159 has issued 17 GNSS equipment standards, forming a more complete international standard system of GNSS equipment for civil aviation industry (Table 1). Table 1. International standards issued by SC-159 Number

Title

Release time

DO-373

MOPS for GNSS Airborne Active Antenna Equipment for the L1/E1 and L5/E5a Frequency Bands

June, 2018

DO-368

MOPS for GPS/GLONASS (FDMA + Antenna) L1-only Airborne Equipment

July, 2017

DO-327

Assessment of the LightSquared Ancillary Terrestrial Component Radio Interference Impact on GNSS L1 Band Airborne Receivers Operations

June, 2011

DO-316

MOPS for GPS/ABAS Airborne Equipment

April, 2009

DO-310

MOPS for GPS GRAS Airborne Equipment

March, 2008

DO-301

MOPS for GNSS Airborne Active Antenna Equipment for the L1 Frequency Band

December, 2006

DO-292

Assessment of Radio Frequency Interference Relevant to the GNSS L5/E5A Frequency Band

July, 2004

DO-261

NAVSTAR GPS L5 Signal Specification

December, 2000

DO-253D

MOPS for GPS LAAS Airborne Equipment

July, 2017

DO-247

The Role of the GNSS in Supporting Airport Surface Operations

January, 1999

DO-246E

GNSS-Based Precision Approach LAAS Signal-In-Space ICD

July, 2017

DO-245A

MASPS for LAAS

December, 2004

DO-235B

Assessment of Radio Frequency Interference Relevant to the GNSS L1 Frequency Band

March, 2008

DO-229F

MOPS for GPS/SBAS Airborne Equipment

June, 2020

DO-228

MOPS for GNSS Airborne Antenna Equipment

October, 1995

DO-217

MASPS DGNSS Instrument Approach System: (SCAT-1)

August, 1993

DO-208

MOPS for Airborne Supplemental Navigation Equipment Using GPS

January, 1991

2.1.2 Other GNSS Special Committees SC-227 was established on 2011, providing navigation performance standards for avionics design researchers, manufacturers, installation departments, ATC, service providers

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and users. It issued DO-283A MOPS for Required Navigation Performance for Area Navigation and DO-236B MASPS: Required Navigation Performance for Area Navigation, which harmonize with ICAO PBN Manual to support PBN operation using GNSS and support improving airspace capacity and operation efficiency. SC-186 was established on 1995, providing operational requirements and minimum performance standards for Automatic Dependent Surveillance-Broadcast (ADSB) airborne and ground application. The positioning source of ADS-B is based on GNSS, including requirements on GNSS minimum performance, ADS-B positioning and integrity. More than 70 ADS-B operation capability has been proved to be capable to improve safety, capacity and efficiency, the commission has issued more than 20 ADS-B documents, including MASPS and MOPS for ADS-B and aviation surveillance application, and ADS-B safety, performance and interchangeability documents. Besides, there are also SC-180, SC-205, SC-135 and SC-216 that issued hardware & software design certificate guidance for commercial avionics equipment, environment conditions and test procedures, installment certificate guidance, which are important part for GNSS navigation equipment design and test certification. 2.2 EUROCAE GNSS Industrial Standards European Organization for Civil Aviation Equipment (EUROCAE) is a non-profit organization founded by the aviation stakeholders from Europe and other regions, it has issued and published many standards and guidance documents in civil aviation that are widely cited by European Technical Standards Orders (ETSO). The standards developed by EUROCAE are based on EU’s own characteristics and complement or extend the RTCA standards. EUROCAE WG-62 has cooperated with RTCA SC-159 to focus on developing international industrial standards for GNSS receiver using Galileo, the primary goal is to support Galileo, EGNOS and other SBAS application in civil aviation. EUROCAE has scrapped ED-72, ED-131, mainly focus on developing industrial standards for new DFMC GNSS receiver. It has developed DO-373 with RTCA on 2018, published first DFMC airborne equipment MOPS ED-259 MOPS for Galileo/GPS/SBAS airborne equipment that specified the minimum performance for Galileo/GPS/SBAS airborne equipment on L1/E1 and L5/E5a frequency band. This standard is currently updating to ED-259A, and plan to release on 2022 after approval by RTCA PMC and EUROCAE TAC. WG-C was established by EUROCAE WG-62 and RTCA SC-159 for jointly developing ARAIM MOPS. EUROCAE has established itself as a DFMC standards development leadership in DFMC standard development. WG-28, WG-51, WG-85, and WG-105 have also published or are developing GNSSrelated industry standards, including ED-75, ED-95, ED-97, ED-109, ED-114, etc. 2.3 ARINC GNSS Industrial Standards Aeronautical Radio Inc (ARINC) was established on 1929, is now part of Rockwell Collins. Standards related to GNSS electronics are primarily developed by the ARINC Avionics Engineering Committee (AEEC), which specifies the composition, assembly,

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and function of the electronics. ARINC has developed a series of GNSS avionics performance specifications and standard specifications, including ARINC 743 “Airborne GPS Receiver”, ARINC 743A-5 “GNSS Sensor”, ARINC 743B “GNSS Landing System Sensor Unit”, ARINC 755 “Multi-Mode Receiver (MMR)”, ARINC 756–3 “GNSS Navigation Landing Unit (GNLU)”, ARINC 760–1 “GNSS Navigation Unit (GNLU)”, ARINC 743B “GNSS Landing System Sensor Unit”. 1 “GNSS Navigation Unit (GNU)”, etc. 2.4 BDS Civil Aviation Industrial International Standards It is of great significance to strengthen the development of BeiDou civil aviation industrial international standards for both satellite navigation systems and civil aviation. According to The Roadmap for the Implementation of BeiDou Satellite Navigation System in China Civil Aviation, the BeiDou avionics and ground equipment standard system will be initially established in the middle of the implementation plan (2022–2025). On the basis of sorting out GNSS international industrial standards, it is beneficial to clarify the framework of BDS standards system for sustainable and smooth promotion of BDS standardization. However, BDS standards system cannot directly copy GNSS-related standards, on the one hand, RTCA standards are mainly market-oriented, they are developed by market decisions, and the decisions are decentralized and unsystematic; on the other hand, if BDS wants to join RTCA and EUROCAE standard system, A MOPS compatible with BDS and other GNSS is needed to develop. Based on published and planned GNSS civil aviation standards, combined with BDS civil aviation application, a BDS standardization framework was proposed as shown in the figure below, where SFSC indicates single frequency single constellation, SFMC indicates single frequency multiple constellation, SFSC indicates single frequency single constellation, and SFMC indicates single frequency multiple constellation (Fig. 1).

Fig. 1. Proposed framework of BeiDou international industrial standards

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3 Core Constellation Industrial Standards The core constellation industrial standard is the core standard of the BDS civil aviation international industrial standard, and is one of the important evaluation documents required to be possessed in the constellation scoring board. The ICDs for B1C, B2a and B1I signals have been released and are constantly updated, the open service performance specification of BDS has been updated to version 2.0, but the core constellation industrial standard is still missing. In order to promote BDS global standardization work, it’s urgently needed to develop BDS core constellation industrial standard. The core constellation industrial standards include core constellation airborne equipment industry standards, core constellation airborne antenna industrial standards, and core constellation signal interference assessment. Among them, DO-208/DO-316 and DO-368 are industrial standards for core constellation airborne equipment of GPS and GLONASS respectively. Since BDS needs to join the international industrial standards organization in the form of compatibility with BDS and other GNSS, DO-368 is worth learning from. DO-368 is the first dual constellation industry standard developed by SC-159, which originated from an executive order issued by the Russian Ministry of Transport in 2012 to “require the use of GLONASS or GLONASS/GPS navigation equipment on civil aircraft”. At the 91st Working Group meeting of RTCA SC-159, Russian industry officially submitted the first MOPS draft and development plan to SC-159, which took 39 months to finalize the MOPS for GLONASS/GPS airborne equipment in 2017, promoting the application of GLONASS system in civil aviation. The minimum operational performance of the equipment regulated by DO-368 involves three operational requirements, including general requirements, En-route and Terminal approach requirements, lateral navigation (LNAV) approach requirements. For general requirements, the airworthiness, general performance, fire resistance, equipment interface, test effects, GPS signal processing requirements, satellite integrity status, step detector, GPS unhealthy identification, GPS healthy identification, satellite selection, initial acquisition time, GPS satellite acquisition time, satellite reaquisition time, sensitivity and dynamic range, equipment burn-out protection, integrity in the presence of interference, alarms/outputs, protection level, navigation alert, and other requirements are specified. For En-route and Terminal approach requirements, accuracy and integrity requirements, development assurance, hardware compliance, software compliance, FDEprovided integrity monitoring, time to alert, missed alert rate, false alert rate, exclusion failure rate, availability, equipment reliability, satellite tracking capability, dynamic tracking, position output, position output data update rate, position output data latency, position solution, smoothing, Smooth pseudo-range accuracy, velocity accuracy and other requirements are specified. For LNAV approach requirements, accuracy and integrity requirements, development assurance, hardware compliance, software compliance, FDE-provided integrity monitoring, time to alert, missed alert rate, false alert rate, exclusion failure rate, availability, equipment reliability, satellite tracking capability, dynamic tracking, position output, position output data update rate, position output data latency, position solution,

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smoothing, Smooth pseudo-range accuracy, velocity accuracy and other requirements are specified. Environmental testing refers to equipment performance testing under specific environmental input conditions, including power input testing, icing testing, RF and sensor signal susceptibility testing, lightning Ind. Trans. Susc. testing, lightning direct effect testing, crash safety shocks, etc.; testing performance includes accuracy, loss of navigation indication, loss of integrity indication, initial acquisition testing, susceptibility and dynamic range, system operation, etc. Equipment test procedures include step detector test, initial acquisition test, satellite reacquisition time test, interference rejection test, accuracy test, integrity test, etc. The equipment installation performance is based on the requirements in AC 20130A “Airworthiness Approval for Navigation or Flight Management Systems with Integrated Multi-Navigation Sensors” and AC 20-138A “Airworthiness Approval for GNSS Equipment”. The operational characteristics can be referred to the GPS operational characteristics information.

4 DFMC Industrial Standards SFSC GNSS is vulnerable to RF interference and ionosphere, which has high security risk in application implementation. the existing four major satellite navigation systems including GPS, GLONASS, BeiDou and Galileo are planning to provide dual-frequency navigation services for civil aviation users. DFMC GNSS equipment, as the next generation GNSS equipment, will improve the availability of positioning, navigation and timing, improve operation continuity for airspace users; provide global vertical guidance, and reduce Controlled Flight Into Terrain (CFIT) to further reduce the risk of air navigation system, provide safer and more efficient navigation for civil aviation in the next 20 years. Both RTCA and EUROCAE are actively engaged in promoting the standardization of DFMC GNSS equipment, and the standard validation and prototype development are supported by numerous projects, For example, the European Global Navigation Satellite Systems Agency (GSA) has initiated the EDG2E project for DFMC receiver development to support the testing and verification of DFMC standards and future equipment certification. Other projects include MUGG, GLAD, DARP, GESTA, etc., which have greatly contributed to the development of DFMC industry standards. BDS seized the opportunity of DFMC industrial standards development to join GNSS civil aviation industrial international standards system, is a necessary path to actively promote the recognition and application of BDS in civil aviation-related industries, it will provide strong support for the compatibility of multi constellations, the sharing of resources, the integration of world satellite navigation application chain and the enhancement of international competitiveness, which is of vital importance for promoting the global application of BeiDou in civil aviation. The following thoughts have been made on the promotion of BDS-compatible DFMC industrial standards. • Adhere to the “standard priority” principle. The DFMC industry standard serves as a guidance document and minimum performance requirement for the design, manufacture, testing and application of DFMC equipment. The initial version supports

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the development of DFMC equipment; the final version supports the airworthiness certification of DFMC equipment. • Because the development of civil aviation industrial standard is in a state of following, the development of BDS-compatible DFMC industrial standards requires fully strategic cooperation with institutions such as theoretical research, product development, quality assurance, testing and verification, installation and application, equipment certification, policy research, and commercial use. Integrate product chain to enhance the influence of BeiDou in ICAO and international industrial standards organization, take DFMC industrial standards as an entry point to activate GNSS airborne equipment manufactures and research institute, carry out research on GNSS airborne equipment and avionics integration, break through key technologies, form technical cluster advantages and competitive products. • Actively carry out cooperation with Europe and the United States in DFMC GNSS standard development, equipment design and application fields, learn from advanced foreign technologies, and participate in standard development in international industrial standard organizations, so as to accelerate the international standardization process of BeiDou civil aviation industry.

5 Conclusion With the official opening of BeiDou-3 global satellite navigation system and the rapid development of China’s civil aviation industry, it has become more and more urgent to promote the application of BeiDou in civil aviation and provide safer and more efficient air navigation services. Based on the existing and planned international standards of GNSS civil aviation industry, and China Civil Aviation BeiDou Satellite Navigation System Implementation Roadmap issued by CAAC, this paper proposes the framework of BeiDou international industrial standards. focuses on the analysis of core constellation industrial standards with reference to DO-368, brings up thoughts on the development of BDS-compatible DFMC industrial standards for international standardization of BeiDou civil aviation industry, provides reference for the international standardization of BeiDou civil aviation industry.

References 1. ICAO, Doc 9750: The 2016–2030 ICAO Global Air Navigation Plan (GANP). Fifth edition (2016) 2. China Civil Aviation BeiDou Satellite Navigation System Implementation Roadmap, CAAC (2019) 3. FAA: Airworthiness Approval of Positioning And Navigation System, AC 20-138D (2016) 4. RTCA SC-159: Terms of Reference (2020) 5. EUROCAE WG-62: WG-62 Galileo Strategy Terms of Reference (2003) 6. RTCA SC-159 DO-368: Minimum Operational Performance Standards for GPS/GLONASS (FDMA + antenna) L1-only Airborne Equipment (2017)

Preliminary Study on BDS Participation in ISO Standardization Yuxia Zhou1(B) , Qian Tan2 , Haofang Quan1 , Dengbang Kang1 , and Kanglian Zhao2 1 China Astronautics Standards Institute, Beijing, China 2 Nanjing University, Nanjing, China

Abstract. On the requirement of devlopment and revision of standards for global navigation satellite systems (GNSS) in the International Standardization Organization (ISO), the GNSS-related standards, which either have been standardized or are being developed in ISO, are firstly investigated in detail in this paper. Secondly, for promotion of the global application of the BeiDou Navigation Satellite System (BDS), the major areas and the key directions in the ISO technical committees are comprehensively analyzed for the future standardization by our nation. Furthermore, the specific measures and the cultivation projects that can be carried out in ISO are also presented. Keywords: ISO · International standards · Satellite navigation

1 Introduction International standards refer to the standards developed by the International Organization for Standardization (ISO), the International Electrotechnical Commission (IEC) and the International Telecommunication Union (ITU), as well as the standards developed by other international organizations, which are confirmed and published by ISO. International standards are applied consistently all over the world and are the results of standardization activities in which many countries and organizations participate. As a major Chinese space infrastructure to provide global public services, the BeiDou Navigation Satellite System (BDS) has always been developed with the principle of “BDS is developed by China, dedicated to the world, and aiming to be top-class”, serving the world and benefiting the mankind [1]. BDS has completed the deployment of its core global constellation and can provide a variety of special services to the world. BDS relevant international standardization has already been started in the International Civil Aviation Organization (ICAO), the International Maritime Organization (IMO) and 3GPP. The standardization of BDS search and rescue service in COSPAR is also underway. Significant results have been achieved in various works. As to support applications and products of BDS to provide services to users all over the world, the development of relevant international standards for special services and applications must be initiated as soon as possible. Especially, works need to be started in the three major international standard development organizations (ISO, IEC, ITU). However, current research on standardization in global navigation satellite systems (GNSS) in ISO is still very © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 651–658, 2021. https://doi.org/10.1007/978-981-16-3146-7_62

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limited. Advanced research of BDS’s involvement in ISO should be carried out. The development and revision process of GNSS-related standards in ISO should be studied. The major areas and the key directions of future standardization on GNSS in ISO should be analyzed. And the new established GNSS-related standard projects in ISO should also be actively participated. These are especially important for the improvement of the status of BDS in ISO and its international influence. With the requirement in promotion of BDS applications and international trade of BDS specific terminal products, it is essential to study and propose the suggestions on the cultivation of ISO standards of BDS, including specific services and key industry applications. A list of potential BDS-related standards should also be presented for current and future activities in ISO. Thus, solid technical foundations could be laid for the further involvement of BDS in ISO.

2 Satellite-Navigation-Related International Standard Projects in ISO There is no technical committee (TC) in ISO which is directly related to satellite navigation. The standardization work related to satellite navigation penetrates into work items of different TCs according to its application area. In the field of satellite navigation standardization, it can be divided into two major areas: satellite navigation engineering standards and satellite navigation application standards. 2.1 The Status Quo of International Standardization About Navigation Satellite Engineering Navigation satellite engineering standards are within the scope of standardization in the aerospace field, which is related to aerospace engineering such as the design, development, testing, interface, space data and information transmission of navigation satellites. The SC14 (Space System and Operation Subcommittee) and SC13 (Space Data and Information Transfer system Subcommittee) under TC20 (Aerospace Standardization Technical Committee) in ISO is responsible for the standardization of aerospace products related to aerospace technology in design, development, testing, interface and data transmission [2]. At present, there are three standards are developed by SC14 that are closely related to satellite navigation, which are all standard projects proposed and developed by Japan in WG1, thanks to the advantage of Japan as the convener of WG1. Specifically: 1) The standards that have been developed and officially released: ISO 18197:2015 Space systems -- Space based services requirements for centimetre class positioning 2) Standards under development: – ISO 22591:201X Space systems–Space-based service for a positioning system with high accuracy and safety support applications in low visibility due to weather conditions – ISO/AWI 24246 Space systems -- Requirements for Global Navigation Satellite System (GNSS) positioning augmentation centers.

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– A new project submitted by Japan in March 2019, ISO/AWI 24245 Space systems -- Global Navigation Satellite System (GNSS) device codes, failed in the project review process in 2019 and the application was resubmitted after the project was revised in April 2020, in which Chinese experts also participated. 2.2 The Status Quo of International Standardization About Satellite Navigation Application Satellite navigation mainly provides PNT services to users in the fields of transportation, surveying, mapping, etc. Through database and literature research, the technical committees and the standards related to satellite navigation application have been developed in ISO are as follows [3]: 1) TC8 Ships and marine technology: Its scope is shipbuilding and ship operation, including ocean-going vessels, inland navigation vessels, offshore structures, shipto-shore interfaces and Design, construction, structural components, outfitting parts, equipment, methods and technology used in all other offshore structures required by IMO. It excludes electrical and electronic equipment on board ships and marine structures, which are within the scope of IEC/TC 18 and IEC/TC 80. – Among the standards issued by the committee, there are two standards related to satellite navigation: (1) ISO 22090–3:2014 Ships and marine technology -Transmitting heading devices (THDS) -- Part 3: GNSS principles ships and marine technology; (2) ISO 19018:2020 Ships and marine technology --Terms, Abbreviations, Graphical symbols and conceptions on navigation. 2) TC204 Intelligent transport systems: Now there are 18 working groups affiliated to the Intelligent Transportation System Technical Committee established in 1992, whose main areas involved include: – The standards related to satellite navigation released by it are as follows: (1) ISO 17267:2009 Navigation systems -- Application programming interface (API); (2) ISO 17438–1:2016 Intelligent transport systems — Indoor navigation for personal and vehicles station –Part1: general information and use case definitions; (3) ISO/TR 22086–1:2019 Intelligent transport systems (ITS) — networkbased precise positioning infrastructure for land transportation—Part1: general information and use case definitions. 3) TC23 Tractors and machinery for agriculture and forestry: The Technical Committee was established in 1952. The secretariat is located in France. There are 11 sub-technical committees under which they are engaged in general testing, operator comfort and safety, tractors, plant protection equipment, harvesting and storage equipment, lawn and gardening power equipment. Research in the fields of forestry machinery, portable forestry machinery, operation control symbols and other displays, irrigation and drainage equipment and systems, and agricultural electronics, etc. The standards related to satellite navigation mainly include:

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– ISO 10975:2009 Tractors and machinery for agriculture -- Auto-guidance systems for operator-controlled tractors and self-propelled machines -- Safety requirements. – -ISO 12188–1:2010 Tractors and machinery for agriculture and forestry -- Test procedures for positioning and guidance systems in agriculture -- Part 1: Dynamic testing of satellite-based positioning devices. – ISO 12188–2:2012 Tractors and machinery for agriculture and forestry -- Test procedures for positioning and guidance systems in agriculture -- Part 2: Testing of satellite-based auto-guidance systems during straight and level travel. – ISO 11783 Tractors and machinery for agriculture and forestry -- Serial control and communications data network. 4) TC172 Optics and photonics: The technical committee has 7 sub-committees and 28 working groups, mainly involving optical basics, optical materials and components, telescopes, microscopes and endoscopes, geodetic instruments, ophthalmic optics and instruments, and laser fields. It released one standard for satellite navigation: ISO 17123–8:2015 Optics and optical instruments -- Field procedures for testing geodetic and surveying instruments -- Part 8: GNSS field measurement systems in real-time kinematic.

3 Preliminary Consideration on the Development of BDS-Related ISO International Standards 3.1 Consideration for Developing BDS-Related ISO Standards The development of international standards should be globally recognized, that is, the standards developed can support the improvement of international trade, should meet the needs of the international community and the global market, and should not become trade barriers. In order to prevent the use of international standards as barriers to global trade, a very key point in establishing a globally recognized set of principles for international standards is the principle of consistency, that is, the decision made is a consensus among stakeholders and then it is possible to form an international standard. The purpose of all international standards is to form standards that are internationally recognized and acceptable to ensure economic goals, such as trade and commerce, and to protect the environment, health and safety. At this stage, the various technical committees affiliated to ISO are set up for the products, processes and services involved in a certain application field. The standardization of products, processes and services within a certain business area is carried out by the standard committee. It does not set up a standard committee around a specific professional and technical field, so there is no technical committee (TC) directly related to satellite navigation in ISO, and the standardization related to satellite navigation will penetrate into the work of technical committees of ISO according to its application field. Therefore, the international standardization work in the ISO organization is different from that in the International Civil Aviation Organization or the International Maritime Organization. The selection and cultivation of international standard projects and how to connect with the relevant standard committees are the first step to carry out the work.

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The development of the BDS international standardization can be carried out from many aspects: 1) In the existing ISO international standards, there are GPS application standards and GNSS application standards, which need to supplement or add the application of BDS. 2) For this goal, the work that needs to be carried out is to sort out the existing ISO standards, analyze the details of each standard at length and the technical content of each standard, and find out what needs to be done from the perspective of supplementing BDS elements. At the same time, according to the specific release time and review time of each standard, we will give suggestions on how to revise the relevant standards. 3) We can analyze the current situation of the application and promotion of BDS products in China and focus on the development of international standard projects that have already carried out or will carry out international cooperation in the near future. From the perspective of market promotion and application, suggestions can be given to cultivate and formulate international standard projects. 3.2 Cultivation Analysis of Relevant Standard Projects at the Top Level of BDS From the perspective of cultivating new international standards, the standardization projects can be specificly divided into two categories: 1) International standards related to the construction and operation of aerospace systems: The international standard project in this field is a new type of standard project related to the design, interface, experiment of satellite and satellite constellation, formed during the construction of the BDS. 2) Standards closely related to satellites developed at the system level to provide support for application services: For example, the top level application standards of interface control specification, service performance specification and spatial signal detection issued by GNSS suppliers at present. Since the standardization projects in this direction are tightly coupled with satellites, they can be classified into the standardization business category of the aerospace field according to the business field. From the perspective of supporting BDS application, standardization work should be carried out around the latter. China published “Beidou satellite navigation system application service system” in December 2019, which introduces that BDS provides seven kinds of services and has two functions: navigation and positioning, communication and data transmission. It provides three services: navigation timing, full text short message communication, and international search and rescue services all over the world. In the area of Chinese border, it provides four services: satellite-based enhancement, ground-based enhancement, Precision Point Positioning, and regional short message communication. At present, Beidou’s international standardization work has carried out the formulation of relevant international standards in the fields of international civil aviation, international maritime affairs, mobile communications and international search and

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rescue. According to the analysis of multiple factors, if the ISO develop the standards of top-level application services, the standardization of the Precision Point Positioning (PPP) service can be developed in the ISO. There is already a international standard for high-precision navigation and positioning applications of satellite-based augmentation systems, that is, ISO 18197:2015 Space systems -- Space based services requirements for centimetre class positioning. This standard is about a positioning system that broadcasts the centimeter-level accuracy of enhanced data through satellites. The characteristics of the system are as follows. 1) Centimeter-level positioning accuracy: In order to meet the development needs of positioning services such as precision agriculture, map surveying, requirements for centimeter-level positioning accuracy are put forward. 2) Wide area positioning: It is of significance to broadcast enhanced data to users at any time, anywhere, and in a wide area covering 1,000 km through satellites. Even if there are no data networks in a certain area, it is no need for additional ground network infrastructure. In addition, since the positioning signal and enhanced data broadcast by satellite can be received at the same time, only one set of circuits is required for the antenna and receiver of the satellite network. 3) Real-time: The user terminal needs real-time fuzzy solution calculation, and using enhanced data broadcast by satellites can achieve centimeter-level positioning accuracy. On the other hand, the user terminal will be able to achieve real-time defuzzification by receiving the enhanced data broadcast via system. Based on the analysis of the state of the satellite navigation standardization work developed by the ISO/TC20 Technical Committee, in order to support the Beidou highprecision positioning service, what we can carry out is to propose a revision of the ISO 18197:2015 put forward by the WG1 affiliated to ISO/TC20/SC14, supplement the technical content of Beidou to ensure that Beidou’s PPP service can meet the actual needs of global users. 3.3 Consideration for ISO Standards Related to BDS Application Based on the actual terminal applications and promotion of BDS products, the ISO international standardization of satellite navigation applications should be distributed to the corresponding standard committees to carry out work. The object of standardization is basically the relevant standards of satellite navigation product terminals, which can be general navigation chip, module or sensor standards, or terminal equipment standards applied in the industry. The above-mentioned standardization work can be carried out from two aspects. 1) Revise standards in organizations that have published standards of GNSS, and add the relevant standard of BDS. The standardization work needs to analyze the technical state of the published standards related to GNSS, give revision proposal for the standards that are about to be reviewed or the standard projects that have already undergone revision work, and participate in the revision of specific standards. At

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present, TCs that have GNSS-related standards mainly include 4 standard committees: 1) TC8 Ships and marine technology; 2) TC 204 Intelligent transport systems; 3) TC23 Tractors and machinery for agriculture and forestry; 4) TC172 Optics and photonics. 2) Develop relevant standards for GNSS applications that are compatible with BDS. The standardization work in this direction should focus on the products, terminals or modules that our country has or will be promoted and applied in overseas markets or will be applied on a large scale to sort out the projects that can formulate international standards, carry out the formulation of international standards, and directly connect with the relevant TC and domestic technology centralized units to start the relevant work. 3) Now the BDS industry has begun to go out of the country and enter the ASEAN market first, and it has expanded the market in the “the Belt and Road” region. Products of BDS have been exported to over 100 countries, providing users with diversified choices and better application experience. Land right confirmation, precision agriculture, digital construction, vehicle and ship supervision, and smart port solutions based on BDS have been successfully applied in ASEAN, South Asia, Eastern Europe, West Asia, Africa, etc. We can carry out the cultivation of international standard projects in the above direction, combine with the standard committees in the ISO organization to carry out applications, and rely on domestic counterparts to jointly carry out the promotion of international standard projects.

4 Conclusions With the rapid development of international trade, the role of standards has become increasingly prominent, and international standards have become the entry permit for the global market. At the same time, the competition is intensifying among countries. The country that has an advantage in standards will have a place in the international market. In this situation, the United States, Russia, the European Union, and Japan actively strive for the initiative in international standardization activities, give full play to their own technological advantages, and strive to reflect their own requirements in international standards and reflect their own interests. Since Beidou’s international standardization work in the ISO organization has just started, it is necessary to start related work by selecting one or two standardization projects, exploring in specific work, and summing up all the experience, which can lay the foundation for continuing to carry out related work in the future. The international standardization work itself is a long-term and complex task that requires a large number of tests to support it. In China, the work of developing relevant standards under the leadership of ISO and IEC organizations is still in its infancy. However, the ISO standards related to satellite navigation, especially Beidou satellite navigation, have not yet been launched. To achieve the zero breakthrough in the organization’s standard formulation, it needs close cooperation with all the institutes and researchers. On behalf of China, the Science and Technology Innovation Department of the National Standards Committee participates in various activities organized by ISO and IEC, fully understands the work of relevant units and experts in my country in the ISO

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and IEC organizations, puts all the standard projects submitted by our country on record, undertakes standardization work of the whole country in the three major international organizations, and will provide great help and guidance for BDS to develop relevant international standards. Therefore, international standardization work needs to be coordinated and promoted by everyone. It is mainly to develop relevant international standards for the promotion of BDS applications. Now it has achieved certain results in the fields of aviation, navigation and mobile communications. In the future, BDS application products will go abroad to support our country’s One Belt One Road strategy and serve the countries along the One Belt One Road in more fields. Acknowledgment. This article is written on the basis of the achievements of the Beidou special standardization research project in 2019. The authors would like to express the gratitude to China Satellite Navigation Office and China Satellite Navigation Engineering Center for their support to this subject. Thanks for the strong support from Beidou Satellite Navigation Standardization Technical Committee (SAC/TC 544).

References 1. Report on the development of Beidou Satellite Navigation System, China Satellite Navigation Office, 2019.12. 2. https://www.iso.org/committee/46614.html 3. https://www.iso.org/committee/47002.html 4. https://www.iso.org/standards.html 5. Service architecture of the Beidou Satellite Navigation System, China Satellite Navigation Office, 2019.12 6. ISO 18197:2015 Space systems – Space based services requirements for centimetre class positioning 7. 2020 Whitepaper on the Development of the Chinese Satellite Navigation and Position Service Industry, GNSS & LBS Association of China, 2020.10

Research on Protocol Architecture and Standard System of Next Generation Navigation Integrated Space and Onboard Network Xiongwen He1,2(B) , Mingwei Xu1 , Dong Yan2 , Zheng Qi2 , Hongcheng Yan2 , Lijun Yang2 , and Weisong Jia2 1 Department of Computer Science and Technology, Tsinghua University, Beijing, China 2 Beijing Institute of Spacecraft System Engineering, China Academy of Space Technology,

Beijing, China

Abstract. This paper focuses on the requirements of integrated space and onboard high-speed networking, standardization of satellite ground interface, reliable transmission, dynamic routing and dynamic access of the next generation navigation satellite constellation, conducts a comprehensive investigation on the protocols of Consultative Committee for Space Data Systems (CCSDS), ECSS, Internet Engineering Task Force (IETF) and other international standards organizations, establishes integrated space and onboard network protocol architecture for next generation navigation satellites. The standards involved in the protocol architecture are systematically constructed, and suggestions on standard formulation and application are given, so as to provide technical support for the establishment of next generation navigation network protocol architecture. Keywords: Navigation · Integrated space and onboard network · Protocol architecture · Standard system

1 Introduction The transmission rate, network size and services carried by the next generation navigation network will be greatly improved, it may need to support dynamic access and dynamic routing of multiple satellites, need more powerful information service mechanism and file transfer mechanism, and realize integrated space and onboard networking, all of which need corresponding standards. Through the research on the communication protocol architecture and standard of the next generation navigation network, we can realize the standard in advance, so as to design the interface and standard protocol of the navigation inter satellite link, the satellite ground link and the onboard link on this basis, in order to provide reference for the construction of the next generation navigation network. At the same time, it can lay a foundation for the future realization of the interconnection of navigation, remote sensing, communication and other satellites. Based on the requirements of the next generation navigation satellite and the existing technology foundation, this paper combines the existing protocol system of CCSDS, the protocol system of European Cooperation for Space Standardization (ECSS) and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 659–673, 2021. https://doi.org/10.1007/978-981-16-3146-7_63

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the protocol system of IETF, and proposes the integrated space and onboard network protocol architecture and standard system for the next generation navigation satellite system.

2 Related Research 2.1 Foreign Research After a long period of development and application, terrestrial network and space-based network protocols have finally formed three representative standard protocol systems, namely CCSDS protocol, ECSS protocol, and IETF protocol. CCSDS was established in 1982 which has 11 member organizations and 33 observer organizations. It is mainly responsible for the development of technical standards for space data systems. More than 300 recommendations developed by it have been applied in more than 1,000 spacecraft worldwide. CCSDS has designed and developed a series of protocols suitable for space missions, including space link services, space internetworking services, and spacecraft standard interface services. The space communication protocol architecture [1] established by it is divided into application layer, transport layer, network layer, data link layer, and physical layer. The focus of its recent development and research in space communication protocols is Delay-Tolerant Networking (DTN), which focuses on solving the problems caused by long delays and interrupted links in the space environment. The onboard communication protocol architecture [2] established by CCSDS is divided into four layers: application layer, application support layer, transfer layer and subnetwork layer. The focus of recent development and research is the SOIS Electronics Data Sheet (SEDS) [3], through which SEDS can realize the digital description of various interfaces and communication protocols, so as to automatically generate related codes, interfaces, and test cases through tools and so on, in order to improve development efficiency. ECSS was established in 1993 and is mainly responsible for the formulation of European space engineering standards, including E10 system engineering, E20 electronic and optical engineering, E30 mechanical engineering, E40 software engineering, E50 communication engineering, E60 control engineering, E70 ground system and operation engineering, etc. Among them, the E50 and E70 series of standards have adopted a large number of CCSDS standards, and developed more detailed standards on this basis. For example, telemetry and telecommand packet utilization standards (PUS) [4] from the E70 series is based on the CCSDS space packet protocol (SPP) [5] standard and further specify the packet’s secondary header structure and data field structure to facilitate standardization of the application layer interface between ground and spacecraft. In the E50 series, 1553B bus protocol [6], spacewire bus protocol [7] and many other spacecraft internal interface protocols are developed, which can be used as a supplement to CCSDS. IETF was established at the end of 1985. It is the world’s most authoritative technical standardization organization for the Internet. It is mainly responsible for the development and formulation of Internet-related technical specifications. The core protocol of the Internet is the TCP/IP protocol cluster, which consists of four layers: application layer, transport layer, network layer, and network interface layer. Due to the rapid development of the Internet, the IPv4 addresses as the core of the Internet have all been allocated,

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and the IETF has designed the next generation Internet Protocol IPv6 [8]. In June 2012, the Internet Society held the World IPv6 Launch Anniversary, the global IPv6 network was officially launched, and many well-known websites such as Google and Facebook began to permanently support IPv6 access. Currently, IETF is further developing related standard protocols around IPv6. 2.2 Domestic Research Since the 1980s, China has begun to conduct a series of studies on CCSDS recommendations. Under the promotion of the Beijing Institute of Spacecraft System Engineering (ISSE), the China Academy of Space Technology (CAST) was the first organization to become a CCSDS observer organization in China. ISSE has carried out continuous follow-up research on the CCSDS communication protocol standard, and led the design of satellite-to-ground interface protocols, inter-satellite network protocol and on-board network protocols for CAST spacecrafts in various fields such as navigation, deep space, remote sensing, and manned. ISSE has a wealth of engineering development experience in network protocol design. In the pre-research, ISSE integrated the telecommand space data link protocol, the COP-1 protocol, the Advanced Orbiting System (AOS) space data link protocol, and the Spacecraft Onboard Interface Services (SOIS), space packet protocol, Asynchronous Message Service (AMS), and multiple spacecraft protocols such as PUS formulated by ECSS, establishing a unified space subnet and onboard subnet hierarchical information service mechanism and protocol architecture [9], and implements the standard protocol through onboard avionics system hardware and software. The protocol in the above-mentioned architecture has been applied in orbit by spacecraft in many fields. Other domestic organizations and universities have also carried out a lot of work on networking protocols. The Chinese Academy of Sciences (CAS), Beijing Institute of Tracking and Telecommunication Technology (BITTT), etc. all apply the CCSDS standard protocols in spacecraft and ground systems. Tsinghua University took the lead in building the second-generation China Education and Research Computer Network (CERNET2) based on IPv6, and carried out many researches on the application of IPv6 in space, and designed TCP +, OSPF +, ND + and other improved protocols for space. Nanjing University has carried out a lot of research work on the DTN protocol and established a network simulation system. On November 26, 2017, the General Office of the Central Committee of the Communist Party of China and the General Office of the State Council issued the "Promoting Internet Protocol Version 6 (IPv6)", which began to accelerate the application of IPv6 protocol in China. 2.3 Summary A comparative analysis of relevant domestic and foreign research is as follows: (1) The CCSDS protocol adopts a layered architecture and has been widely used in spacecraft at home and abroad. At present, CCSDS has considered compatibility with the terrestrial Internet and supports the transmission of the IP protocol on

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the CCSDS data link, which will play a positive role in promoting the subsequent construction of the space-ground integrated network. (2) The terrestrial Internet protocol launched by the IETF adopts a layered architecture and is currently in the stage of transitioning from IPv4 to IPv6. If space and ground integration is achieved, the deployment of IPv6 in spacecraft needs to be considered. (3) The ECSS protocol is further refined on the basis of the CCSDS-compatible protocol, which can be used as a supplement to the CCSDS protocol and will help to further enhance the degree of standardization. In summary, the CCSDS layered protocol architecture can be considered as the mainstay, and IP and ECSS related protocols in the terrestrial Internet protocol architecture can be added to build the next-generation navigation space and onboard integrated protocol architecture.

3 Next-Generation Navigation System Space and Onboard Integrated Network Protocol Architecture 3.1 Requirement Analysis The next-generation navigation system network communication protocol standards involve multiple levels such as the physical layer, data link layer, network layer, transport layer, and application layer. There are different standards for different levels to choose from, but which standard to choose requires comprehensive consideration of the navigation system specific needs. For example, inter-satellite/satellite-ground link characteristics, satellite dynamic access procedures, network routing strategies, transmission strategies, information security mechanisms, application layer service characteristics, etc., (1) Requirement analysis of physical layer standards In order to meet the transmission requirements of various types of space applications, the next-generation navigation system will be equipped with abundant physical links, including: a) Inter-satellite/satellite-to-ground link is expected to be used for high-speed backbone data transmission. b) Intra-satellite links, including high-speed and low-speed, are used to transmit high-speed payload data, low-speed control data, etc., with emphasis on the unified transmission of platform and payload, and minimize the number of interfaces and unified interface standards to facilitate integration and test. (2) Data link layer standard demand analysis The next-generation navigation system has multiple types of heterogeneous links including inter-satellite, satellite-ground, and intra-satellite. Each link should be supported by data link layer protocols and standards. In order to adapt to the future navigation system networking, richer and more complex communication and data

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transmission requirements, a more efficient, reliable and unified link layer protocol is required. a) The space link part, including inter-satellite link, satellite-ground link etc., try to use a unified data link layer protocol, which can effectively support data integrated transmission, reduce the cost of protocol conversion, and improve data transmission efficiency. b) In the intra-satellite link part, a unified data link protocol standard is established for various interfaces. (3) Analysis of network layer standard requirements The network layer protocol of the next generation navigation system has the following requirements: a) Adapt to the trend of satellite networking and establish a global address system, which can easily realize the integrated interconnection between satellites, satellites and grounds, and intra-satellites. b) It is compatible with the Internet network layer protocol used on the ground, and facilitates further integration with the ground network in the future. c) Compatible with the CCSDS protocol system used in spacecraft. d) It can support flexible routing strategies, and support the selection of static routing strategies or dynamic routing strategies as needed. e) Need to consider network security and establish corresponding mechanisms. (4) Analysis of requirements for transport layer standards With the opening of navigation constellations and the continuous enrichment of user applications, the transport layer will become more important. The transport layer protocol has the following requirements: a) Compatible with the Internet transport layer protocol used on the ground: Like the network layer protocol, the transport layer protocol should also consider compatibility with the ground network transport layer, so as to better achieve interconnection with ground device. b) Be able to distinguish the application layer protocol used to transmit data: The transport layer protocol should be able to distinguish the different types of space applications carried by the data part, so as to better support richer and more complex space applications and achieve more efficient and targeted application transfer support. c) Taking into account the influence of factors such as long space delay, in order to ensure the transmission efficiency, the reliability of the transmission can be considered in combination with other layer protocols. (5) Analysis of application layer standard requirements The next-generation navigation system should be able to provide more services to support richer applications, which should include but not limited to the following:

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a) Navigation-related application information, including information transmission such as autonomous navigation, and global position report. b) Ground support application information. c) Extended application information. 3.2 The General Architecture Design of Protocol According to the results of the previous requirement analysis, the principles of the general architecture design of the next-generation navigation network protocol are: 1) Layered design to support future protocol extension and upgrade; 2) Realize the integrated design of satellite-ground, inter-satellite, intra-satellite, and ground protocols through a unified network layer; 3) Support dynamic routing and on-demand access; 4) Support reliable transmission; 5) Support multiple applications. According to the previous analysis, referring to the CCSDS protocol architecture, and integrating the IETF and ECSS protocols, the next generation navigation system space and onboard integrated protocol architecture designed in this paper is shown in the following figure. The protocol architecture includes satellite-to-ground, inter-satellite, and intra-satellite protocols, considering the compatibility with existing satellites and subsequent extension protocols (Fig. 1).

Application Specific Protocol

Application Layer PUS

AMS

BP CFDP

Transport Layer

LTP

Network Layer

SPP

Data Link Sublayer

Subnetwork Layer

Data SynchroniLink zation and Layer Coding Sublayer Physical Layer

IPv6

Message Transfer Service

Device Virtualization Service

TCP

IPSec

UDP

IP over CCSDS

Subnetwork Service

USLP Protocol

Dynamic Access Protocol

TM synchronization and coding

Optical Communication Synchronization and Coding

Data link Layer

RF modulation

Laser communication physical layer

Physical Layer

Inter-satellite communication

Device Access Service

Encapsulation Service

Packet Service

Convergence Layer

Device Data Pooling Service

Dynamic routing protocol

Memory Access Service

Synchronization Service

Convergence Protocol 1553B Protocol

Time Access Service

...

Intra-satellite Link

Intra-satellite communication

Fig. 1. Space and onboard integrated protocol architecture

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The architecture is divided into four layers, from top to bottom are the application layer, transport layer, network layer, and subnetwork layer. The main features of the architecture are: 1) Application layer: Realize telecommand and telemetry standardization through PUS, support multi-satellite information sharing through Asynchronous Message Service (AMS) [10], and realize the coexistence of multiple transmission protocols through Bundle Protocol (BP) [11], Through the CCSDS File Delivery Protocol (CFDP) [12] to support the standardized transmission of files, through the message transfer service [13] to achieve information sharing within the satellite, through the device access service [14], device virtualization service [15] And the device data pooling service [16] to achieve a unified access interface to the device, through the time access service to achieve a unified access interface to time. It also supports application-specific protocols. 2) Transport layer: through Licklider Transmission Protocol (LTP) [17]/User Datagram Protocol (UDP) [18] to achieve multiple transmission quality support. 3) Network layer: Realize the integrated design of satellite-ground, inter-satellite, intrasatellite, and ground protocols through IPv6. Encapsulation service [19], IP over CCSDS protocol [20] are used to transmit the IPv6 protocol through the CCSDS space link. In addition, it is compatible with simple space packet protocol, and provides dynamic routing protocols for dynamic routing among various types of nodes. 4) Subnetwork layer: Space communication is realized through the Unified Space Link Protocol (USLP) [21]. The inter-satellite link layer is unified, providing dynamic access protocols to support dynamic access of various nodes, and the physical layer supports two systems: optics and microwave; intra-satellite communication is through packet service [22], memory access service [23], and synchronization service [24] and 1553B bus communication protocol etc. realize the unification of bus interface and protocol. 3.2.1 Application Layer The application layer is the highest layer in the system structure, which directly provides services for various applications of users, and can directly design specific application protocols according to the needs of users. It is recommended to follow the relevant protocols developed by CCSDS and ECSS, or use user-specific protocols to complete related tasks. The following services can be used for navigation applications: 1) The telemetry and telecommand information can be encapsulated by PUS, in accordance with the service of the PUS standard. 2) The data transmitted to other spacecraft can be transmitted according to the application layer format of other spacecraft, and the format is distinguished by the subject of AMS or UDP port number. 3) Information sharing between multiple satellites and between computers within the satellite is realized through AMS and message transmission services.

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4) The device access inside the satellite is realized through device access service, device virtualization service, and device data pooling service. 5) Time access inside the satellite is realized through time access service. 3.2.2 Transport Layer The transport layer provides two services, reliable transmission and unreliable transmission, as well as security services. 1) The unreliable transmission service adopts the UDP protocol. 2) Reliable transmission services adopt TCP, LTP, etc. 3) Security services use IPSec. According to the different protocols in the network layer, the protocols of this layer can be distinguished by the protocol identification in the IP protocol in the network layer, the protocol identification in the encapsulation service, and the application process identification in the space packet protocol. For navigation applications, important information such as command can be realized through reliable transmission services, and other information can be realized through unreliable transmission services. 3.2.3 Network Layer The main function of the network layer is to realize the transparent transmission of data in the space network and onboard network and to provide network management functions, including routing, congestion control, and dynamic access. 1) he network layer is compatible with the terrestrial IPv6 protocol and CCSDS encapsulation service, space packet protocol, IP over CCSDS (IPoC) protocol, and development of dynamic routing protocols suitable for space. The protocols of this layer are distinguished by the packet version number in each protocol header and the protocol identifier in the encapsulation service. 2) The protocol data unit (PDU) of the network layer protocol is transmitted on the space link through the space data link protocol. Among them, the PDU of the space packet protocol can be directly transmitted through the link protocol. IPv6 PDUs should be encapsulated through IPoC and encapsulation service before they can be transmitted over the space data link. In the next-generation satellite navigation system, the space and intra-satellite network layer protocols can be unified through IPv6. That is, the space communication network layer uses IPv6, and IPv6 is also used in the intra-satellite high-speed network communication. At the same time, in order to be compatible with some inherited devices, the space packet protocol can still be used in the inherited 1553B bus.

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3.2.4 Subnetwork Layer The subnetwork layer is located below the network layer and provides a series of services for the upper layer to call, including space communication and intra-satellite communication. 1) Space communication. Space communication provides the transmission of various data such as IP packets, space packets, and encapsulated packets at the network layer and above, including two parts: data link layer and physical layer. The data link layer includes two sublayers: data link protocol sublayer, synchronization and channel coding sublayer. The data link protocol sublayer adopts unified space data link protocol to integrate satellite-to-earth/inter-satellite protocol Unite. The synchronization and channel coding sublayer adopts telemetry synchronization and channel coding standards, optical communication channel coding and synchronization standards. The physical layer follows the radio frequency and modulation, optical communication physical layer standards. 2) Intra-satellite communication. Hierarchical division includes subnetwork layer services, convergence layer, data link layer, and physical layer. The subnetwork layer service uses the spacecraft onboard interface service (SOIS) packet service, memory access service, and synchronization service. The role of the convergence layer is that if the services of a particular data link cannot fully satisfy the services of the subnetwork layer, the convergence layer corresponding to the data link will provide additional protocols to increase functions to meet the needs of the subnetwork layer services. If the service of a particular data link can directly meet the service requirements of the subnetwork layer, the convergence layer can directly connect to the data link layer. Data link layer and physical layer include 1553B bus, TTE bus and other related interfaces and protocols.

4 Next-Generation Navigation Space and Onboard Integrated Network Protocol Standard System According to the overall framework of the protocol described above, in order to facilitate subsequent system construction, a relevant protocol standard system needs to be established. The planned next-generation navigation space and onboard integrated network protocol standard system are shown in the following table (Table 1). At present, some protocols in the protocol architecture have international standards such as CCSDS, ECSS, IETF, etc., and relying on the Space Data and Information Transmission Subcommittee (SDITS) of the National Aerospace Technology and Application Standardization Technical Committee (NATAST), the transformation from international standards to national standards has begun. In addition, some of the protocols in the framework have not yet had international/domestic standards, so it is suggested that they should be re formulated by SDITS.

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Table 1. Standard system of next-generation navigation space and intra-satellite integrated network protocol NO

Layer

Related standard

Way of developing standard

1

System architecture

Next-generation navigation space and intra-satellite integrated network protocol architecture

Research and develop national standard

2

Application layer

Application Specific Data Format

Research and develop national standard

3

Telecommand and telemetry packet utilization standard

Adopt PUS standard and develop national standard

4

Device data pooling service

Adopt CCSDS SOIS Device data pooling service and develop national standard

5

Device virtualization service

Adopt CCSDS SOIS Device virtualization service and develop national standard

6

Device access service

Adopt CCSDS SOIS Device access service and develop national standard

7

Time access service

Adopt CCSDS SOIS Time access service and develop national standard

8

Asynchronous message service

Adopt CCSDS Asynchronous message service and develop national standard (continued)

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Table 1. (continued) NO

Related standard

Way of developing standard

9

Message transfer service

Adopt CCSDS SOIS Message transfer service standard and develop national standard

10

File delivery protocol

Adopt CCSDS CFDP standard and develop national standard

11

Bundle protocol

Adopt CCSDS BP standard and develop national standard

Licklider transmission protocol

Adopting CCSDS LTP, and develop national standard

13

UDP protocol

Adopt IETF UDP standard and develop national standard

14

TCP protocol

Adopt IETF TCP standard and develop national standard

15

IPSec protocol

Adopt IETF IPSec standard and develop national standard

Space packet protocol

Adopt CCSDS SPP standard and develop national standard

IPv6 protocol

Adopt IETF IPv6 standard and develop national standard

12

16

17

Layer

Transport layer

Network layer

(continued)

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NO

Related standard

Way of developing standard

18

Encapsulation service

Adopt CCSDS Encapsulation service standard and develop national standard

19

IP over CCSDS protocol

Adopt IP over CCSDS protocol and develop national standard

20

Dynamic routing protocol

Research and develop national standard

21

Layer

Subnetwork layer-space communication

Data link layer-data link Unified space data Adopt CCSDS protocol sublayer link protocol USLP and develop national standard

22

23

Data link layer-synchronization and channel coding sublayer

24

25

Physical layer

Dynamic access protocol

Research and develop national standard

Telemetry synchronization and channel coding

Adopt CCSDS telemetry synchronization and channel coding standard, national standard already existed

Optical communication coding and synchronization

Adopt CCSDS optical communication coding and synchronization standard, and develop national standard

Radio frequency and modulation

Adopt CCSDS radio frequency and modulation standards and develop national standard (continued)

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Table 1. (continued) NO

Layer

Related standard

26

Way of developing standard Optical communication physical layer

Adopting the standard CCSDS optical communication physical layer and develop national standard

Packet service

Adopt CCSDS SOIS packet service and develop national standard

28

Memory access service

Adopt CCSDS SOIS memory access service and develop national standard

29

synchronization service

Adopt CCSDS SOIS synchronization service and develop national standard

27

Subnetwork layer-onboard communication

Subnetwork service

30

Convergence layer

Convergence layer Research and develop national standard

31

Data link layer and Physical layer

U.S. military standard 1553B bus link protocol

Adopted the US military standard 1553B standard and develop national standard

Onboard discrete interface

Research and develop national standard

32

5 Conclusions According to the requirements of next generation navigation network construction, the protocol architecture of next generation navigation space and onboard integrated network designed in this paper integrates a variety of standardized services and protocols through hierarchical design, which can lay a technical foundation for the subsequent realization of

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inter-satellite, satellite-ground and intra-satellite integrated networking. These standards are not only applicable to the next generation navigation network, but also applicable to remote sensing, telecommunication, deep space and other fields. The adoption of unified standards will help to realize the interconnection between heterogeneous satellites in different fields and improve the comprehensive application efficiency. Some standards in the proposed protocol architecture need to be further studied, such as dynamic routing protocol, dynamic access protocol, etc. Acknowledgments. This study is funded by a Young Top Talent Fund of Aerospace Science and Technology Corporation awarded to the first author in 2018. This work is also supported by the ‘The National Key Research and Development Program’ of China (No. 2018YFB1800301).

References 1. CCSDS. 130.0-G-3 Overview of Space Communications Protocols. Washington: CCSDS (2014) 2. CCSDS. 850.0-G-2 Spacecraft Onboard Interface Services. Washington: CCSDS (2013) 3. CCSDS. 876.0-B-1 Spacecraft Onboard Interface Services—Specification for Dictionary of Terms for Electronic Data Sheets for Onboard Components. Washington: CCSDS (2019) 4. ECSS. ECSS-E-70–41A Space Engineering: Ground Systems and Operations-Telemetry and Telecommand Packet Utilization. Noordwijk: ECSS (2003) 5. CCSDS. 133.0-B-1 Space Packet Protocol. Washington: CCSDS (2003) 6. ECSS.ECSS-E-ST-50–13C Interface and Communication Protocol for MIL-STD-1553B Data Bus on Board Spacecraft. Noordwijk: ECSS (2008) 7. ECSS.ECSS-E-ST-50–12C SpaceWire - Links, Nodes, Routers and Networks. Noordwijk: ECSS (2008) 8. IETF.RFC8200 Internet Protocol, Version 6(IPv6) Specification. Reston: IETF (2017) 9. He, X.: Service and protocol architecture design of spacecraft avionics system. Spacecr. Eng. 26(1), 71–78 (2017) 10. CCSDS. 735.1-B-1 Asynchronous Message Service. Washington: CCSDS (2011) 11. CCSDS. 734.2-B-1 CCSDS Bundle Protocol Specification. Washington: CCSDS (2015) 12. CCSDS. 727.0-B-4 CCSDS File Delivery Protocol (CFDP). Washington: CCSDS (2007) 13. CCSDS. 875.0-M-1-S Spacecraft Onboard Interface Services--Message Transfer Service. Washington: CCSDS (2012) 14. CCSDS. 871.0-M-1-S Spacecraft Onboard Interface Services--Device Access Service. Washington: CCSDS (2013) 15. CCSDS. 871.2-M-1-S Spacecraft Onboard Interface Services--Device Virtualization Service. Washington: CCSDS (2014) 16. CCSDS. 871.1-M-1-S Spacecraft Onboard Interface Services--Device Data Pooling Service. Washington: CCSDS (2012) 17. CCSDS. 734.1-B-1 Licklider Transmission Protocol (LTP) for CCSDS. Washington: CCSDS (2015) 18. Postel, J.: RFC 768 User datagram protocol. Reston: ISOC (1980) 19. CCSDS. 133.1-B-2 Encapsulation Service. Washington: CCSDS (2009) 20. CCSDS. 702.1-B-1 IP over CCSDS Space Links. Washington: CCSDS (2012) 21. CCSDS. 732.1-B-1 Unified Space Data Link Protocol. Washington: CCSDS (2018) 22. CCSDS. 851.0-M-1 Spacecraft Onboard Interface Services--Subnetwork Packet Service. Washington: CCSDS (2009)

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23. CCSDS. 852.0-M-1 Spacecraft Onboard Interface Services--Subnetwork Memory Access Service. Washington: CCSDS (2009) 24. CCSDS. 853.0-M-1 Spacecraft Onboard Interface Services--Subnetwork Synchronisation Service. Washington: CCSDS (2009)

Author Index

B Bai, Qintao, 378 Bai, Yan, 158 Bao, Jinchen, 413 Bian, Lang, 193 C Cao, Kejin, 527 Chang, Jin, 105 Chen, Feiqiang, 356 Chen, Huaang, 518 Chen, Jiang, 172, 180 Chen, Junhao, 413 Chen, Lei, 273 Chen, Shuai, 466 Chen, Sifei, 17, 44 Chen, Xin, 203, 324 Chen, Yanjun, 134 Chen, Ying, 573 Chen, Yu, 466 Chen, Yuwei, 466 Cheng, Yuanming, 298 Cui, Jingzhong, 172, 180 Cui, Xiaowei, 483 D Deng, Xiwen, 435, 445 Deng, Zhongliang, 435, 445 Dong, Jichao, 558 Dong, Pengling, 172, 180 Dong, Richang, 3 Dong, Zhiqiang, 378 Dou, Xinyu, 378

F Fan, Jiachen, 588 Fan, Xiaomeng, 607 Fan, Zhe, 643 Fang, Kun, 558 Fang, Yuankun, 95 Feng, Sen, 95 Fu, Dong, 423 G Gang, Ou, 473 Gao, Qingyi, 588 Gao, Shuaihe, 95, 158 Gao, Yuan, 518 Gao, Yuping, 158 Ge, Xia, 224 Gong, Boyuan, 643 Gong, Hang, 37, 53, 423 Gu, Mingxing, 239, 252 Gu, Shiming, 265 Guo, Ji, 623 Guo, Yanming, 158 H Han, Zibin, 158 Hao, Yunqing, 378 He, Di, 203 He, Xiaoxing, 298 He, Xiongwen, 659 He, Yifeng, 118 Hu, Daping, 273 Hu, Wei, 265 Hu, Yuan, 239, 252 Huang, Kai, 128, 134

© Aerospace Information Research Institute 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 774, pp. 675–678, 2021. https://doi.org/10.1007/978-981-16-3146-7

676 Huang, Liangyu, 172, 180 Huang, Weiquan, 26 Huang, Xinming, 37, 284, 456 Huang, Yangbo, 314, 496 Huangfu, Songtao, 105 Hyyppä, Juha, 466 J Jia, Qiongqiong, 334 Jia, Weisong, 105, 659 Jia, Xiaolin, 505 Jiang, Changhui, 466 Jiang, Shiwen, 445 Jiang, Xin, 643 K Kang, Dengbang, 651 Ke, Zhang, 456 L Li, Bao, 527 Li, Guojun, 74 Li, Hui, 26 Li, Jingyuan, 273, 456 Li, Junyao, 62 Li, Liang, 26 Li, Menghao, 26 Li, Nan, 26 Li, Pingli, 378 Li, Song, 366 Li, Tian, 193 Li, Tieshuai, 643 Li, Xiao, 558 Li, Xin, 558 Li, Xinrui, 378 Li, Yining, 17 Li, Yuanhao, 44 Lian, Jiqing, 180 Lin, Honglei, 549 Lin, Yongxin, 74 Liu, Chang, 17, 44 Liu, Cheng, 573 Liu, Dongliang, 623 Liu, Gang, 483 Liu, Jingrong, 435 Liu, Shuo, 128, 134 Liu, Wei, 239, 252 Liu, Wenxiang, 473 Liu, Xuan, 118 Liu, Xuhui, 496 Liu, Yaxuan, 128, 134

Author Index Liu, Ying, 142, 623 Liu, Yuan, 573 Liu, Zengjun, 273, 456, 549 Liu, Zhe, 344 Liu, Zhidong, 172, 180 Lou, Chengqian, 573 Lou, Shengqiang, 314, 496 Lu, Jun, 3 Lu, Mingquan, 397, 483 Lu, Tieding, 298 Lu, Xiaochun, 158 Lu, Yushan, 128, 134 Lu, Zukun, 356 Luo, Kai, 435 Luo, Zhengwang, 527 M Ma, Chunjiang, 344, 366, 549 Ma, Junjie, 397 Ma, Ming, 53, 423 Ma, Pei, 172, 180 Ma, Pengcheng, 344, 366 Ma, Yinguang, 172, 180 Mei, Ganghua, 62 Meng, Yansong, 193 Meng, Yinan, 3 Ming, Gang, 62 Mou, Minghui, 239, 252 N Ni, Shaojie, 356, 496 Niu, Linlin, 598 O Ou, Gang, 344, 423, 456 P Pan, Zhibing, 158 Peng, Jing, 37, 423 Q Qi, Zheng, 659 Qiu, Ming, 540 Quan, Haofang, 651 R Ren, Binbin, 356 Ren, Zhiling, 37 S Shao, Yilun, 203 Shen, Feng, 387 Shen, Jianhua, 3, 573 Shen, Jiemin, 224 Shi, Rong, 413

Author Index Si, Yibo, 518 Su, Lin, 635 Sun, Guangfu, 273, 284, 366 Sun, GuangFu, 53 Sun, Guangfu, 549 Sun, Leyuan, 95 Sun, Pengyue, 314, 496 Sun, Rui, 540

T Tan, Qian, 651 Tang, Chengpan, 3 Tang, Guoshun, 445 Tang, Shihao, 435 Tang, Xiaomei, 284, 314, 344, 366, 549 Tao, Rui, 298 Tian, Xiancai, 265 Tian, Ye, 193

W Wang, Bohao, 466 Wang, Dongjun, 180 Wang, Fang, 62 Wang, Haibin, 473 Wang, Haichun, 265 Wang, Ji, 180 Wang, Jiale, 17 Wang, Jianxiang, 180 Wang, Jiawei, 74 Wang, Jie, 473 Wang, Kai, 623 Wang, Liang, 128, 134 Wang, Lixia, 378 Wang, Lu, 180 Wang, Maolei, 86, 142 Wang, Pengfei, 62 Wang, Renlong, 26 Wang, Shengzheng, 239, 252 Wang, Shichao, 86, 142 Wang, Shiwei, 172, 180 Wang, Wei, 53, 573 Wang, Weijia, 623 Wang, Weili, 128 Wang, Xin, 298 Wang, Yanhui, 17, 44 Wang, Yiming, 334 Wang, Ying, 193 Wang, Yuexuan, 635 Wang, Yuxuan, 582 Wang, Zhipeng, 558

677 Wei, Kefan, 483 Wu, Jian, 356 Wu, Juan, 505 Wu, Renbiao, 334 Wu, Yiwei, 86 X Xiao, Feng, 95 Xiao, Jixuan, 635 Xiao, Shenghong, 86 Xie, Jun, 180 Xie, Weihua, 324 Xu, Lina, 215 Xu, Mingwei, 659 Xu, Shaohang, 17, 44 Xue, Dalei, 118 Xue, Yiming, 378 Y Yan, Dong, 659 Yan, Hongcheng, 659 Yan, Tao, 193 Yang, Bin, 86, 142 Yang, Fuxing, 445 Yang, He, 128, 134 Yang, Hui, 105 Yang, Jun, 95, 172, 180 Yang, Lijun, 659 Yang, Wei, 172, 180 Yang, Yufei, 86 Yao, Zheng, 224, 397 Yu, Chen, 615 Yu, Jinping, 588 Yu, MeiTing, 53 Yu, Wenxian, 203, 324 Yuan, Haibo, 142 Yuan, Lifang, 105 Z Zang, Ting, 505 Zhai, Junwu, 105 Zhang, Dezhi, 265 Zhang, Di, 74 Zhang, Gong, 3 Zhang, Jiancheng, 215 Zhang, Junwei, 265 Zhang, Ke, 273 Zhang, Lin, 142 Zhang, Longping, 265 Zhang, Mengting, 215 Zhang, Pan, 118 Zhang, Shuangcheng, 378 Zhang, Tao, 324 Zhang, Weinan, 224 Zhang, Wenqing, 615

678 Zhang, Xiangyi, 623 Zhang, Zhan, 643 Zhao, Feng, 62 Zhao, Kanglian, 651 Zhao, Xin, 284 Zhao, Yulong, 172, 180 Zhao, Yuqing, 387 Zhen, Weimin, 324

Author Index Zheng, Ning, 172, 180 Zhong, Chuhan, 378 Zhong, Xingwang, 118 Zhou, Dong, 387 Zhou, Yuxia, 651 Zhu, Wuxiang, 588 Zhu, Yinbing, 527 Zukun, Lu, 473