China Satellite Navigation Conference (CSNC 2024) Proceedings: Volume II (Lecture Notes in Electrical Engineering, 1093) 981996931X, 9789819969319

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Lecture Notes in Electrical Engineering 1093

Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC 2024) Proceedings Volume II

Lecture Notes in Electrical Engineering

1093

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of 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, University of Karlsruhe (TH) IAIM, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dipartimento di Ingegneria dell’Informazione, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain 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, Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Intrinsic Innovation, Mountain View, CA, USA Yong Li, College of Electrical and Information Engineering, 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 Subhas Mukhopadhyay, School of Engineering, Macquarie University, NSW, Australia Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Department of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Federica Pascucci, Department di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA Kay Chen Tan, Department of Computing, Hong Kong Polytechnic University, Kowloon Tong, Hong Kong

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Changfeng Yang · Jun Xie Editors

China Satellite Navigation Conference (CSNC 2024) Proceedings Volume II

Editors Changfeng Yang China Satellite Navigation Engineering Centre Beijing, China

Jun Xie China Academy of Space Technology Beijing, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-6931-9 ISBN 978-981-99-6932-6 (eBook) https://doi.org/10.1007/978-981-99-6932-6 © Aerospace Information Research Institute 2024 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 Paper in this product is recyclable.

Editorial Board

Topic: S01: GNSS Applications Chairman Dangwei Wang, Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Vice-Chairman Shaojun Feng, Qianxun Spatial Intelligence Inc., Shanghai, China Changhui Xu, Chinese Academy of Surveying and Mapping, Beijing, China Caicong Wu, China Agricultural University, Beijing, China Jianping Xing, Shandong University, Jinan, China Jianhua Wei, BeiDou Application and Research Institute Co., Ltd. of Norinco Group, Beijing, China

Topic: S02: GNSS and Their Augmentations Chairman Rui Li, Beihang University, Beijing, China Vice-Chairman Long Yang, Beijing Future Navigation Technology Co., Ltd., Beijing, China Wenxiang Liu, National University of Defense Technology, Hunan, China Xingxing Li, Wuhan University, Hubei, China Yansong Meng, Xi’an Branch of China Academy of Space Technology, Shaanxi, China

Topic: S03: Satellite Orbit Determination and Precise Positioning Chairman Xiaogong Hu, Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Vice-Chairman Jianwen Li, Information Engineering University, Henan, China Jianghui Geng, Wuhan University, Hubei, China Bofeng Li, Tongji University, Shanghai, China Xiaolin Meng, The University of Nottingham, Nottingham, UK

vi

Editorial Board

Topic: S04: 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 Lijun Du, Xi’an Branch of China Academy of Space Technology, Shaanxi, China Ya Liu, National Time Service Center, Chinese Academy of Sciences, Shaanxi, China

Topic: S05: System Intelligent Operation and Autonomous Navigation Chairman Xingqun Zhan, Shanghai Jiao Tong University, Shanghai, China Vice-Chairman Haihong Wang, Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China Wenbin Gong, Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Yuxin Zhao, Harbin Engineering University, Heilongjiang, China Caibo Hu, Beijing Satellite Navigation Center, Beijing, China

Topic: S06: GNSS Signal Technologies Chairman Xiaochun Lu, National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Vice-Chairman Hongwei Zhou, China Academy of Space Technology, Beijing, China Dun Wang, Space Star Technology Co., LTD. Beijing, China Yang Li, The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China Zheng Yao, Tsinghua University, Beijing, China Xiaomei Tang, National University of Defense Technology, Hunan, China

Editorial Board

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Topic: S07: GNSS User Terminals Chairman Hong Li, Tsinghua University, Beijing, China Vice-Chairman Wenjun Zhao, Beijing Satellite Navigation Center, Beijing, China Zishen Li, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Liduan Wang, ComNav Technology Ltd., Shanghai, China Chengjun Guo, University of Electronic Science and Technology of China, Sichuan, China

Topic: S08: PNT Architectures and New Technologies Chairman Zhongliang Deng, Beijing University of Posts and Telecommunications, Beijing, China Vice-Chairman Baoguo Yu, The 54th Research Institute of China Electronics Technology Rong Zhang, Tsinghua University, Beijing, China Jiangning Xu, Naval University of Engineering, Hubei, China Jinsong Ping, The National Astronomical Observatories of the Chinese Academy of Sciences, Beijing, China Dongyan Wei, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Tianhe Xu, Shandong University, Jinan, China

viii

Editorial Board

Scientific Committee Senior Advisor Qingjun Bu, China National Administration of GNSS and Applications, Beijing, China Liheng Wang, China Aerospace Science and Technology Corporation, Beijing, China Yuzhu Wang, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China Guoxiang Ai, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Lehao Long, China Aerospace Science and Technology Corporation, Beijing, China Shuhua Ye, Shanghai Astronomical Observatories, Chinese Academy of Sciences, Shanghai, China Jingjun Guo, Tsinghua University, Beijing, China Daren Lv, The Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Yongcai Liu, China Aerospace Science and Industry Corporation, Beijing, China Jingnan Liu, Wuhan University, Hubei, China Jiadong Sun, China Aerospace Science and Technology Corporation, Beijing, China Zuhong Li, China Academy of Space Technology, Beijing, China Rongjun Shen, China Satellite Navigation System Committee, Beijing, China Chi Zhang, The former Electronic Information Foundation Department of General Equipment Department Xixiang Zhang, The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China Lvqian Zhang, China Aerospace Science and Technology Corporation, Beijing, China Junyong Chen, National Administration of Surveying, Mapping and Geo information, Beijing, China Benyao Fan, China Academy of Space Technology, Beijing, China Dongjin Luo, China People’s Liberation Army, Beijing, China Huilin Jiang, Changchun University of Science and Technology, Jilin, China Guohong Xia, China Aerospace Science and Industry Corporation, Beijing, China Peikang Huang, China Aerospace Science and Industry Corporation, Beijing, China Chong Cao, China Research Institute of Radio Wave Propagation (CETC 22), Beijing, China Faren Qi, China Academy of Space Technology, Beijing, China Rongsheng Su, China People’s Liberation Army, Beijing, China Shusen Tan, Beijing Satellite Navigation Center, Beijing, China Ziqing Wei, Xi’an Institute of Surveying and Mapping, Shaanxi, China

Editorial Board

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Chairman Changfeng Yang, China Satellite Navigation System Committee, Beijing, China

Vice-Chairman Yuanxi Yang, China National Administration of GNSS and Applications, Beijing, China Shiwei Fan, China Satellite Navigation Engineering Center, Beijing, China

Executive Chairman Jun Xie, China Academy of Space Technology, Beijing, China Lanbo Cai, China Satellite Navigation Office, Beijing, China

Committee Members Qun Ding, The 20th Research Institute of China Electronics Technology Group Corporation, Beijing, China Xiangrong Ding, Legislative Affairs Bureau of the Central Military, Beijing, China Xiancheng Ding, China Electronics Technology Group Corporation, Beijing, China Quan Yu, Peng Cheng Laboratory, Shenzhen, China Zhijian Yu, Taiyuan Satellite Launch Center of China’s Manned Space Project, Shanxi, China Jian Wang, Alibaba Group, Zhejiang, China Wei Wang, China Aerospace Science and Technology Corporation, Beijing, China Feixue Wang, National University of Defense Technology, Hunan, China Zhaoyao Wang, China Satellite Navigation Office, Beijing, China Shafei Wang, Academy of Military Sciences PLA China, Beijing, China Lihong Wang, Legislative Affairs Bureau of the Central Military, Beijing, China Chengqi Ran, China Satellite Navigation Office, Beijing, China Weimin Bao, China Aerospace Science and Technology Corporation, Beijing, China Yueguang Lv, Science and Technology Commission of the CPC Central Military Commission Zhaowen Zhuang, National University of Defense Technology, Hunan, China Chong Sun, Beijing Institute of Tracking and Communication Technology, Beijing, China Yadu Sun, Aerospace Engineering Research Institute of the PLA Strategic Support Force Xianyu Li, Research Institute of the PLA Rocket Force Minling Li, China Society for World Trade Organization Studies, Beijing, China Jun Yang, China Satellite Navigation Office, Beijing, China Hui Yang, China Academy of Space Technology, Beijing, China

x

Editorial Board

Longxu Xiao, Research Institute of the PLA Rocket Force Bin Wu, Beijing Institute of Tracking and Communication Technology, Beijing, China Yirong Wu, The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Weiqi Wu, Xichang Satellite Launch Center, Sichuan, China Haitao Wu, Aerospace, Chinese Academy of Sciences, Beijing, China Manqing Wu, China Electronics Technology Group Corporation, Beijing, China Jun Zhang, Beijing Institute of Technology, Beijing, China Zhijie Chen, National Core Laboratory of Airspace Technology Zhonggui Chen, The 5th Research Institute of China Aerospace Science and Technology Corporation, Beijing, China Jinping Chen, Beijing Satellite Navigation Center, Beijing, China Baojun Lin, Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Zhixin Zhou, Space Engineering University, Beijing, China Jianping Zhou, Chief Designer of China’s Manned Space Project Jianhua Zhou, Beijing Satellite Navigation Center, Beijing, China Jiancheng Fang, Beihang University, Beijing, China Wenjun Zhao, Beijing Satellite Navigation Center, Beijing, China Jiang Hu, BeiDou Application and Research Institute Co., Ltd. of Norinco Group, Beijing, China Jie Jiang, China Academy of Launch Vehicle Technology, Beijing, China Weiguang Gao, China Satellite Navigation Engineering Center, Beijing, China Shuren Guo, China Satellite Navigation Engineering Center, Beijing, China Huikang Huang, Ministry of Foreign Affairs of the People’s Republic of China, Beijing, China Xibin Cao, Harbin Institute of Technology, Heilongjiang, China Wenhai Jiao, China Satellite Navigation Engineering Center, Beijing, China Yi Zeng, China Electronics Corporation, Beijing, China Yi Cai, BeiDou ground-based augmentation system Chief Engineer Baoguo Yu, The 54th Research Institute of China Electronics Technology

Executive Members Jun Shen, Beijing Unistrong Science and Technology Co., Ltd. Beijing, China Dangwei Wang, Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Rui Li, Beihang University, Beijing, China Xiaogong Hu, Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Aimin Zhang, National Institute of Metrology, Beijing, China Xingqun Zhan, Shanghai Jiao Tong University, Shanghai, China Xiaochun Lu, National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Hong Li, Tsinghua University, Beijing, China

Editorial Board

xi

Zhongliang Deng, Beijing University of Posts and Telecommunications, Beijing, China Junlin Yang, Beihang University, Beijing, China

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 14th China Satellite Navigation Conference (CSNC 2024) is held during 2024, Jinan, China. Including technical seminars, academic exchanges, forums, exhibitions and lectures. The main topics are as followed:

Conference Topics S01 S02 S03 S04 S05 S06 S07 S08

GNSS Applications GNSS and Their Augmentations Satellite Orbit Determination and Precise Positioning Time Frequencies and Precision Timing System Intelligent Operation and Autonomous Navigation GNSS Signal Technologies GNSS User Terminals PNT Architectures and New Technologies.

The proceedings (Lecture Notes in Electrical Engineering) have 151 papers in eight topics of the conference, which were selected through a strict peer-review process from 345 papers presented at CSNC2024. In addition, another 170 papers were selected as the electronic proceedings of CSNC2024, 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 299 referees and 53 session chairmen who are listed as members of editorial board. The assistance of CNSC2024’s organizing committees and the Springer editorial office is highly appreciated. Beijing, China

Changfeng Yang Jun Xie

Contents

GNSS and Their Augmentations A Study on SBAS-RTK Integrated Positioning Technologies . . . . . . . . . . . . . . . . . Yuechen Wang and Jun Shen

3

Research on the TESLA Authentication Algorithm for BDSBAS . . . . . . . . . . . . . Ying Chen, Jun Lu, Chengeng Su, Xiao Chen, and Xiang Tian

13

Single Satellite Positioning Method and Error Characteristic Analysis of LEO Navigation Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guodong Yao, Zhigang Huang, Hongwei Zhou, and Xinxing Zhang

28

A High Dynamic Positioning Algorithm for Ka Band LEO Satellites in Beam Polling Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mingxia Li, Yun Zhao, Qiuli Chen, and Ping Li

40

Spoofing Monitoring Method Research of GNSS Based on LEO Doppler Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zishan Zhao, Zhigang Huang, Yongchao Wang, and Kai Yin

55

Credibility Monitoring Research of BDS Based on LEO/INS . . . . . . . . . . . . . . . . Kai Yin, Rui Li, Zishan Zhao, and Qiuli Chen ARAIM Integrity and Continuity Considering Fault Detection and Exclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rui Sun, Chengdong Xu, Guoxian Huang, Jing Zhao, and Zhiwei Lu A Coupled RTK/INS Positioning Method Based on Robust Estimation . . . . . . . . Huizhen Yu, Xianliang Teng, Shuguo Pan, Min Zhang, Jian Shen, and Wang Gao

68

81

94

Optimal Allocation Method of Integrity Risk Indicator for Multiple Risk Sources in PPP-RTK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Fengze Du, Liang Li, Ruiji Li, and Qiwei Ye Reliability and Backup Strategy Analysis of Low-Earth Orbit Navigation Constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Hao Zhang, Ping Li, Jin Jun Zheng, Gong Zhang, and Fu Jian Ma

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Contents

An Asynchronous Observation Positioning Algorithm Based on Factor Graph Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Chuang Zhou, Jiaolong Wei, and Zuping Tang Evaluation and Analysis of Uplink Signal Interference in GEO Satellite System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Xuyu Wang, Dongfang Jiang, Bingjie Liu, Li Wang, Haoyuan Yu, Hai Sha, Heng Wei, and Yingying Zhao Impact of Temporally Correlated Error on ARAIM ISM During Ionospheric Storm Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Jin Chang, Zhongjun Qu, Xiaotang Lian, and Zhongzhi Wang Scintillation Identification Based on Spectral Features . . . . . . . . . . . . . . . . . . . . . . 168 Dun Liu, Li Chen, Shan Guo, and Qinglin Zhu Centimeter-Level Real-Time Orbit Determination and Accuracy Analysis of LEO Satellite with POD4LEO Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Quan Zhou, Lang Bian, YanSong Meng, Dan Liu, YiZhe Jia, Lin Han, Peng Zhang, XiaLu Zhang, and MinShu Zhang Impact Analysis of BeiDou Satellite Integrity Events in 2022 . . . . . . . . . . . . . . . . 190 Yansen Wang, Rui Li, Yongchao Wang, and Tiantian Yang Analysis of Navigation Augmentation Performance Based on LEO Satellite Communication Constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Xing Li, Kun Jiang, Ping Li, Xiaomei Tang, and Xia Guo Research on BDSBAS Service Coverage Area Assessment Methodology . . . . . . 215 Tianyi Li, Rui Li, Jing Li, and Tiantian Yang A New Coupled Method for Pseudolite System-Augmented GNSS Real-Time Kinematic PPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Caoming Fan, Zheng Yao, Yanchen Dong, and Jianping Xing BDS-3 Signal in Space Ranging Errors Performance and On-Orbit Status Monitoring and Evaluation Based on Historical Data from 2020 ~ 2022 . . . . . . . 239 Lei Chen, Weiguang Gao, Hongliang Cai, Xuanzuo Liu, Haoyu Kan, Liqian Fan, and Zhigang Hu Epoch Completeness Rate Analysis of BDS-3 PPP-B2b Augmentation Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Xinying Dong, Junbo Shi, Chenhao Ouyang, Xinyue Li, and Wenjie Peng

Contents

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GNSS Global PPP System Technology: Bottleneck and Development Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Yansong Meng, Jun Xie, Xing Li, Tao Yan, Ye Tian, Yun Zhou, Quan Zhou, Lang Bian, and Weiwei Wang GNSS Signal Technologies Polarization-Spatial Joint Anti-jamming Algorithm for GNSS Receiver in High Dynamic Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Siyuan Jiang, Runnan Wang, Shuai Liu, and Ming Jin MCSK Signal for LEO Satellite Constellation Based Navigation Augmentation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Tao Yan, Ying Wang, Tian Li, Ye Tian, Bo Qu, and Lang Bian The Interference Analysis and Evaluation of DME to BeiDou-3/B2a . . . . . . . . . . 305 Jian-ming Zhang, Fei Xu, and Shi-chong Li Spreading Code Authentication Technique Based on CSK Modulation . . . . . . . . 322 Siyuan Chen, Xiaohui Ba, Baigen Cai, Wei Jiang, Jian Wang, and Xu Li Anti-Multipath Localization Method Based on MEDLL and WLS . . . . . . . . . . . . 334 Yuan Feng, Jingyuan Xa, Jiaolong Wei, and Zuping Tang A Design of Navigation Enhancement Signal Based on Communication Satellite Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Ping Li, Hongwei Zhou, Xiaozhun Cui, Zuping Tang, and Duo Zhang HsPWM Satellite Navigation Signal Generation and Analysis . . . . . . . . . . . . . . . . 357 Ying Wang and Tao Yan A Fast Configuration Optimization Algorithm for GNSS-based InBSAR System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Ruihong Lv, Feifeng Liu, Zhanze Wang, Xiaojing Wu, and Jiahao Gao GNSS Carrier Tracking via a Variational Bayesian Adaptive Kalman Filter for High Dynamic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Song Li, Chunjiang Ma, Pengcheng Ma, Honglei Lin, Xiaomei Tang, and Feixue Wang BOC Signal Spoofing Detection Based on Multi-correlator Signal Quality Monitoring Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Mingxuan Liang, Zhengkun Chen, Zhijian Zhou, Xuelin Yuan, and Xiangwei Zhu

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Contents

A GNSS Spoofing Detection Method Based on CNN-DOA . . . . . . . . . . . . . . . . . . 402 Chuhan Huang, Zhengkun Chen, Xinzhi Peng, Jianjun Lu, Xuelin Yuan, and Xiangwei Zhu Analysis of Anti-Repeater-Spoofing Performance of GNSS Nulling Anti-Jamming Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Binbin Ren, Shaojie Ni, Feiqiang Chen, Zukun Lu, and Yifan Sun Design and Performance Assessment of a Time-Varying Channel Simulator for High-Mobility Satellite Navigation Scenarios . . . . . . . . . . . . . . . . . . 428 Shun Zhou, Shiyun Yu, Wei Shi, and Yongyang Hu Research on Receiving and Processing Technology of Short-Time Burst Spread Spectrum Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Yaohui Chen, Qijia Dong, Dun Wang, Shenyang Li, Zhenxing Xu, Shangna Zhang, Guoji Zou, and Yali Liu Identifying GNSS NLOS Using Visual Label and Ensemble Tree Under Complex City Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Zhenbang Xu, Xin Li, Xinjuan Han, Yuxuan Zhou, and Linyang Li Research on the Index System of BDS-3 Signal Quality Evaluating Methods Based on High-Gain Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 Chengyan He, Rui Liu, Ji Guo, and Ling Wang GNSS User Terminals Study on the Influence of Antenna Arrays Anti-Jamming Algorithms on GNSS Receiver Single Point Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Yaoding Wang, Si Chen, Yuzhuo Hou, and Chengeng Su Research of Precise Point Positioning Model Based on Smartphone . . . . . . . . . . . 495 Yuxiang Ge, Zengke Li, Zan Liu, Yifan Wang, and Yangyang Wang A Fast Positioning Method of Navigation Receiver Assisted by Doppler Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Yinyin Tang, Junyong Lu, Junhong Feng, and Kai Li The Group Delay Calibration of the Standard Antenna and the Group Delay Measurement of the Beidou Airborne Antenna . . . . . . . . . . . . . . . . . . . . . . . 516 Haoyu Lin, Pan Huang, and Wenze Yuan An Improved Algorithm of Unambiguous Acquisition Based on BOC Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Junyu Du, Zhongliang Deng, Zhenke Ding, and Chengfeng Wu

Contents

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A Three-Layer Parallel Implementation of the DPE Receiver Based on GPU . . . 535 Qiongqiong Jia and Weipeng Li GNSS Anti-sapoofing Method Based on Signal Transmission Time Density Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 Xinran Zhang, Zhiquan Liu, Maolin Chen, Chuan Wang, and Taotao Liang Research on Spoofing Detection Based on C/N0 Measurements for GNSS Array Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 Jinyuan Liu, Yuchen Xie, Feiqiang Chen, Shaojie Ni, and Guangfu Sun A Fast C/N0 Estimation Method Based on the Ratio of Acquisition Correlation Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 Yimin Ma, Hong Li, Ziheng Zhou, Zhenyang Wu, Wenhao Li, and Mingquan Lu Development and Evaluation of GPS L2C Software Receiver Baseband Signal Processing Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 Zhenyang Wu, Hong Li, Ziheng Zhou, Yimin Ma, Lingtao Wang, and Mingquan Lu Algorithm Optimization and Terminal Validation of BDSBAS Ionospheric Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590 Ang Liu, Ningbo Wang, Zishen Li, Liang Wang, Zhiyu Wang, and Hong Yuan Research on Intelligent Navigation Algorithm of Long and Short Term Memory Network Based on Firework Algorithm Optimization in Satellite Blocking Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 Yu Rui, Rong Wang, Jingxin Zhao, Zhi Xiong, and Jianye Liu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

GNSS and Their Augmentations

A Study on SBAS-RTK Integrated Positioning Technologies Yuechen Wang1(B)

and Jun Shen2

1 Correlation Semiconductor Co., Ltd., Zhengzhou 451162, China [email protected], [email protected] 2 UniStrong Science & Technology Co., Ltd., Beijing 101111, China

Abstract. With the emergence of new GNSS applications such as autonomous driving and UAV, it is necessary to consider integrity requirements of real-time kinematic (RTK), to ensure the security and reliability of positioning, on the basis of high-precision services. The performance of RTK depends on the data quality of the reference station, the distance between the user and the reference station, etc. GNSS service anomalies, environmental occlusions and interferences, reference station faults and other factors may lead to RTK fault and cannot meet the requirements of high-performance applications. In order to improve the RTK performance, this paper presents initial research on the processing of SBAS-RTK integrated positioning. First, RTK fault factors are analyzed and their effects are evaluated by simulation to summarize the main risk events. Next, SBAS and RTK differential data are integrated for data detection, weighted positioning and data check to eliminate the impact of various risk events and improve the reliability of RTK. Finally, based on the simulation tests, the performance of the algorithm is verified and evaluated. The results show that the SBAS-RTK integrated positioning can identify the faults of more than 3 m in the RTK differential data and effectively ensure the reliability of positioning. Keywords: SBAS-RTK · Integrated positioning · Data detection · Fault identification

1 Introduction As an important method of GNSS high-precision positioning, real-time kinematic (RTK) plays a significant role with the advantages of high accuracy and short convergence time in various applications, such as surveying and mapping [1, 2]. With the emergence of new applications, such as automatic driving and UAV, RTK needs to provide even higher performance in reliability on the basis of high-precision to meet the requirements of security. As a type of local area differential system of GNSS, RTK provides users around the RTK reference station with corrections in the observation space representation (OSR) by broadcasting the coordinates and observations of the station. User can apply the doubledifference (DD) model to eliminate satellite’s orbit and clock errors, atmospheric delay © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 3–12, 2024. https://doi.org/10.1007/978-981-99-6932-6_1

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Y. Wang and J. Shen

errors, receiver clock errors, etc., and achieve high-precision baseline solution, obtain accurate real-time position information [3]. It can be seen that the performance of RTK may be affected by several factors, as the GNSS constellation anomalies, atmospheric delay disturbances, environmental occlusions and interferences, and the faults of the reference station may all lead to RTK faults. In order to improve the reliability of RTK services, this paper uses the corrected data and integrity data of the Satellite Based Augmentation System (SBAS) [4] to carry out a study on SBAS-RTK integrated positioning. The main risk events are identified by analysing RTK service failure factors. Based on the integrated processing of SBAS and RTK differential data, the detection of RTK differential data is carried out, and the detection results is used to achieve weighted filtering positioning and data check. Through the fault simulation test, the SBAS-RTK integrated positioning can identify the RTK differential data anomalies greater than 3 m, and guarantee the real-time positioning accuracy and reliability effectively.

2 RTK Service Risk Analysis 2.1 RTK Fault Factor Table 1 summarizes the main fault factors and their impacts in the space segment (SS), propagation segment (PS), ground segment (GS) and user segment (US) in RTK service. 1. The faults in the SS and the PS will affect the reference station and users at the same time. Except the satellite clock fault, other anomalies cannot be eliminated through DD processing. What’s more, clock fault may affect the approximate position of single point positioning (SPP) in the RTK positioning. 2. The faults of GS are mainly related to the performance of RTK reference station. The data quality and time delay will affect the performance of RTK directly. 3. The faults of US, such as signal occlusion, interference, multipath, cannot be eliminated by RTK corrections. The design of user receiver is required to reduce the impact of local risk events in RTK positioning. It can be seen that the integrity risk factors in RTK mainly come from the SS, the PS and the GS. The measurement errors of the RTK reference station and the user are inconsistent and cannot be eliminated by DD processing, which may reduce the RTK accuracy and even lead to integrity risk. 2.2 Performance Impact Analysis The RTK data with a 2-km baseline is collected in Beijing to analyse the impact of risk events on RTK performance. To simplify the analysis scenario, several fault modes are simulated by adding ranging errors of different magnitudes to the measurements of RTK reference station. GPS L1C/A and L2, BDS B1I and B3I are used, with single-satellite fault (SSF) and dual-satellite fault (DSF) in each GNSS constellation respectively. The magnitudes of fault are selected as 1, 3 and 5 m, and real-time faults vary within the peak range randomly. The test duration is 2 h and the sampling interval is 1 s. DD and

A Study on SBAS-RTK Integrated Positioning Technologies

5

Table 1. Fault factors and impact in RTK Segment

Fault factors

Fault influence

SS

Satellite orbit unplanned maneuver

The range error increases, the RTK accuracy decreases: the longer the baseline, the greater the influence

Satellite clock anomalies

The ranging error increases, which can be eliminated by DD model, but affects the approximate position of SPP

Satellite signal distortion

The ranging error increases, even loss lock of signals, the RTK accuracy decreases

Ionosphere scintillation

The carrier-noise ratio is reduced, even loss lock of signals, the RTK accuracy decreases

Ionosphere storm

The ranging error increases, the error changes dramatically in time and space, the RTK accuracy decreases

Base station anomaly

RTK correction accuracy decreases

Data loss or interruption

The differential age increases, the RTK accuracy decreases

Occlusion

The carrier-noise ratio is reduced, even loss lock of signals, the RTK accuracy decreases

PS

GS

US

Interference Multipath

The ranging error increases and the RTK accuracy decreases

non-combination model are used in RTK positioning, ionosphere and troposphere errors are eliminated and Lambda is used to fix ambiguity [5]. The SSF and DSF positioning results are shown in Figs. 1 and 2, the statistics of performance are shown in Table 2. 1. In the SSF mode, with the increase of fault, the accuracy and fixed ratio of RTK decline gradually. It is difficult to achieve fast and accurate convergence. The horizontal and vertical errors are biased. When the anomaly exceeds 3 m, the bias increases significantly and the fixed rates drop below 50%. 2. In the DSF mode, the performance is further deteriorated while the ambiguity cannot be fixed any more. The maximum of errors is at meter level. The position converges to abnormal values with large biases. 3. Comparing the RMS and 99.9% accuracy in different fault mode, with the increase of the magnitude and number of faults, the deterioration of 99.9% accuracy is more significant. RTK fault has greater impact on high-precision and high-reliability applications.

6

Y. Wang and J. Shen Table 2. Performance of RTK positioning in various fault modes

Fault mode

Magnitude (m)

Horizontal accuracy/m

Vertical accuracy/m

RMS

99.9%

RMS

99.9%

Fixed rate (%)

Fault free

–

0.023

0.025

0.046

0.055

100

SSF

1

0.102

0.414

0.120

0.978

73.7

3

0.306

0.591

0.304

3.365

46.2

5

0.643

0.796

0.674

5.940

42.9

1

0.118

0.590

0.169

1.884

0

3

0.433

1.822

0.520

5.723

0

5

4.040

5.833

2.151

12.735

0

DSF

Fig. 1. RTK positioning errors in the SSF mode

3 SBAS-RTK Integrated Positioning In order to improve the reliability of the RTK positioning, SBAS-RTK integrated positioning was investigated. An SBAS receives GNSS signals through ground monitoring stations and provides corrections and integrity parameters of satellite orbit, clock and ionosphere delay in real time, which can improve the integrity of the SS and PS in GNSS service. SBAS and RTK data are integrated to achieve RTK corrections detection, and to determine satellite status and weighted parameters. Then, the weighted positioning is performed and the residuals are used for data check to improve the accuracy and reliability. Figure 3 shows the processing flow of SBAS-RTK integrated positioning, and the core steps are introduced below.

A Study on SBAS-RTK Integrated Positioning Technologies

7

Fig. 2. RTK positioning errors in the DSF mode

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9('93KYYGMK

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;TG\GORGHRK

,GOR

6GYY 9GZKRROZK9ZGZ[Y *KZKXSOTGZOUT

Fig. 3. Data processing flow of SBAS-RTK integrated positioning

3.1 SBAS Positioning In order to eliminate the impact of GNSS faults on the calculation of user’s approximate location, single frequency SBAS or dual-frequency multi-constellation (DFMC) SBAS is used to position and replace the SPP in RTK. The SBAS integrity parameters are used as weight to achieve least square positioning and obtain the position and protection levels

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Y. Wang and J. Shen

[6, 7]. Considering that the approximate position mainly plays the role of selecting or calculating the differential data of reference station, the alarm limits can be selected as the requirements of non-precision approach phase in ICAO. When the horizontal protection level exceeds 220 m, the approximate position is abnormal and RTK positioning cannot be performed. 3.2 Data Detection To achieve the data detection, SBAS corrections and integrity data, RTK reference station coordinates and observation data are used, which can identify the orbit and clock faults, ionosphere anomalies, reference station anomalies and other risks, to ensure the RTK reliability. 1. Satellite status initialization. The dual-frequency range error (DFRE) of the DFMC SBAS and the grid ionosphere vertical error (GIVE) of the single frequency SBAS are used to initialize the satellite status in RTK. a. DFMC SBAS can provide integrity monitoring of multi-constellation satellites: when DFREI ≤ 11, the satellite is ‘available’; when 11 < DFREI < 15, the satellite is ‘low-weighted’; when DFREI = 15, the satellite is ‘unavailable’. b. Single frequency SBAS can provide ionosphere monitoring. Using the corresponding standard deviation of GIVEI, the standard deviation of ionosphere delay error at the ionosphere puncture point σUIVE is calculated by distance weighting [6]: when σUIVE < 15, the satellite is ‘available’; when 5 ≤ σUIVE ≤ 45, the satellite is ‘low-weighted’; and when σUIVE > 45, the satellite is ‘unavailable’. 2. Code pseudo-range detection  of the reference station. The RTK reference station  coordinates Xref Yref Zref and observations are used to calculate the code pseudorange residuals of each satellite, as shown in Eq. (1). The P and PR are the ionospherefree code pseudo-range and residuals respectively, R is the distance between satellite   j and station, Xsbas Ysbas Zsbas and Tsbas are the SBAS corrected orbit and clock of the satellite, Tropj is the tropospheric delay at the reference station calculated by the SBAS model. PR = P − R − c · Tsbas − Trop,  R = (Xref − Xsbas )2 + (Yref − Ysbas )2 + (Zref − Zsbas )2

(1)

Taking the satellite with the highest elevation with ‘available’ status as the refj erence satellite to calculate the single-difference PRi and the detection threshold j j THpr,i , as shown in Eq. (2). The σi is the standard deviation of SBAS corrected code pseudo-range residuals, which is calculated by DFREI; the Kdtc is the factor and its typical value is 3.29. When the single-difference exceeds the threshold, set the satellite status to ‘low-weighed’.  j

j

refsat

PRi = PRi − PRi

j

, THpr,i = Kdtc ·

j

2

refsat 2

σDFREI + σDFREI

(2)

A Study on SBAS-RTK Integrated Positioning Technologies

9

3. Carrier phase detection of the reference station. Similar to code pseudo-range detection, the SBAS corrected carrier phase residuals are also calculated, and the receiver clock offset and integer ambiguity are eliminated based on the time smoothing [8]. Set the status to ‘unavailable’ for satellite that can’t complete ambiguity resolution. For satellites with fixed ambiguity, the carrier phase residual is corrected and compared j with the detection threshold THph,i . If the threshold is exceeded, the satellite status is set to ‘unavailable’, as shown in Eq. (3), which is also calculated by DFREI with the consideration that the carrier phase accuracy is higher than the code pseudo-range, so the standard deviation is reduced by 100, Kph is also set to 3.29 as a factor. j

j

THph,i = Kph · σDFREI /100

(3)

3.3 Weighted RTK Positioning The DD measurements are calculated between the reference station and the user. According to the detection satellite status, the weight is determined to calculate the observation noise matrix of Kalman filtering in Eq. (4), where the R is the noise matrix, its diagonal element ri,i,meas is the variance of code and carrier, and the mark meas is pr for code and is ph for carrier. The off-diagonal element ri,j,meas is the covariance of measurements. 2 , the The variance is calculated based on the statistical accuracy of observations σmeas elevation of satellite E and satellite status Wi . For the ‘available’ satellite, the Wi is 1, and the reference satellite must be ‘available’; for the ‘low-weighted’ satellite, the Wi is amplified and the typical factor is 10.0. In addition, the ‘unavailable’ satellites will be excluded. ⎡ ⎤ r1,1,pr r1,2,pr ··· 0 ⎢ r2,1,pr r2,2,pr · · · ⎥ 0 ⎢ ⎥ R=⎢ . ⎥ . . .. .. r ⎣ .. ⎦ (n−1),n,ph 0 0 rn,n−1,ph rn,n,ph ⎧ 2 Wi · σmeas ⎪ 2 ⎪ 2 , E < 30◦ ⎨ σi,meas + σrefsat,meas , i = j 2E sin 2 ri,j,meas=pr or ph = , σi,meas = 2 2 ⎪ σrefsat,meas , i = j ⎪ ⎩ Wi · σmeas , E ≥ 30◦ sinE (4)

3.4 Data Check The posterior DD residuals are calculated by positioning results and compared with the data check threshold, which is generated by the standard deviation of measurements, to determine whether there is fault. If all residuals meet the requirements in Eq. (5), the check is passed so that the positioning results can be output and the satellite status can be saved as an input of the next epoch. In Eq. (5), the ∇PRrefsat,i and ∇PH refsat,i are the DD residuals of code and carrier, the Kchk is the factor of data check with a typical value of 4.0.

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Y. Wang and J. Shen

If any DD cannot meet the requirements in Eq. (5), an additional check is carried out. When the number of abnormal DD is greater than half of the total number of DD, the mean value meanmeas and median value medianmeas of all DD residuals are compared to determine whether the reference satellite is faulty, as shown in Eq. (6). Max{} is the maximum function; THchk is the threshold with a typical value of 0.15. When Eq. (6) is satisfied, the reference satellite is abnormal and is set as ‘unavailable’. Otherwise, other satellites with ‘low-weighted’ status and with the largest absolute value of DD will be set as ‘unavailable’. When the data check fails, the weighted positioning and the data check shall be performed again according to the new satellite status, until the data check passes or the number of iteration reaches the threshold, which can be set as 3 typically. ⎧  refsat i ⎪ 2 2 ⎨ ∇PRrefsat,i = (PRiuser − PRrefsat user ) − (PRref − PRref ) ≤ Kchk · σi,pr + σrefsat,pr  refsat refsat ⎪ i i 2 + σ2 ⎩ ∇PHrefsat,i = (PHuser − PHuser ) − (PHref − PHref ) ≤ Kchk · σi,ph refsat,ph (5) |medianmeas − meanmeas | < THchk , meas = pr or ph Max{medianmeas , meanmeas }

(6)

4 Test and Verification Based on the data processing above, an SBAS receiver is used to receive single frequency and DFMC SBAS service signals from BDSBAS [9]. Based on the simulated fault modes in Sect. 2.2, the same data is processed again to evaluate the performance of SBAS-RTK integrated position. The results in SSF and DSF modes are shown in Fig. 4 and Fig. 5 respectively, the statistical performance is shown in Table 3. 1. In the fault free mode, the performance of SBAS-RTK is almost the same as RTK. There are false alarms in a few epochs, which has little effect on the positioning performance with enough available satellites. 2. In the SSF mode, the performance of the integrated position is good enough to effectively identify anomalies above 3 m and almost reaches the level of fault free mode. The fixed rate is slightly lower under the abnormal of 1 m, and there are centimetre-level jumps caused by float solutions. 3. In the DFS mode, the integrated position can identify the anomalies above 3 m, the accuracy is consistent with the fault free and the fixed rate is reduced to 95%. For faults below 1 m, the missed alert rate in the detection is higher and the SBAS-RTK results may be affected by abnormal satellites. The fixed rate is reduced seriously and there are jumps and drifts in the positioning error. 4. The RMS and the accuracy of 99.9% are almost the same in different fault modes. SBAS-RTK improves the reliability of positioning effectively. 5. As the faults are simulated, while the real-time BDSBAS cannot monitoring any fault, the integrated positioning using SBAS parameters in fault-free condition, which leads to a higher missed alert rate. In addition, SBAS has some limitations in the accuracy

A Study on SBAS-RTK Integrated Positioning Technologies

11

of corrections and the fault magnitude of integrity monitoring, its sensitivity is lower to ‘small’ faults which may affect the performance of RTK. With the decrease of fault magnitude, the missed alert rate of SBAS-RTK will increase.

Fig. 4. SBAS-RTK integrated positioning errors in the SSF mode

Fig. 5. SBAS-RTK integrated positioning errors in the DSF mode

5 Summary In this paper, the data processing of SBAS-RTK integrated positioning is studied by the differential data from SBAS and RTK. The fault events in RTK are summarized and the risk factors affecting the reliability are determined.

12

Y. Wang and J. Shen Table 3. Performance of SBAS-RTK positioning in various fault modes

Fault mode

Magnitude (m)

Horizontal accuracy/m

Vertical accuracy/m

RMS

99.9%

RMS

99.9%

Fixed rate (%)

Fault free

–

0.023

0.030

0.050

0.057

100

SSF

1

0.024

0.035

0.051

0.061

98.6

3

0.023

0.030

0.050

0.056

99.8

5

0.023

0.030

0.050

0.056

99.8

1

0.034

0.045

0.063

0.074

63.5

3

0.024

0.043

0.051

0.064

95.1

5

0.024

0.040

0.051

0.061

95.1

DSF

By adding fault simulation to the measured data, the RTK performance in different fault modes is analyzed. With the increase of magnitude and number of faults, the accuracy and fixed rate of RTK decreases significantly, with incorrect fixed ambiguity or convergence position. Based on the SBAS data, the SBAS-RTK integrated position processing is carried out. The data test shows that, through SBAS single point positioning, data detection, weighted RTK positioning and data check, the integrated positioning can identify faults above 3 m, and the positioning accuracy and fixed rate are consistent with the fault free mode, which can improve the reliability of RTK service effectively.

References 1. He H, Li J, Yang Y et al (2014) Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning. GPS Solut 18(3):393–403 2. Liu W, Wu M, Zhang X et al (2021) Single-epoch RTK performance assessment of tightly combined BDS-2 and newly complete BDS-3. Satell Navig 2:6 3. Yuan Y, Mi X, Zhang B (2020) Initial assessment of single- and dual-frequency BDS-3 RTK positioning. Satell Navig 1:31 4. Li R, Zheng S, Wang E et al (2020) Advances in BeiDou navigation satellite system (BDS) and satellite navigation augmentation technologies. Satell Navig 1:12 5. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70(1–2):65–82 6. (2018) International standards and recommended practices, Chicago convention on international civil aviation annex 10 for aeronautical communication, Vol 1: Radio navigation equipment, 7th edn. International Civil Aviation Organization 7. European Organization for Civil Aviation Equipment (2022) EUROCAE ED-259A, Minimum operational performance standards for dual-frequency multi-constellation satellite-based augmentation system airborne equipment, 2022.7 8. Wang Y, Shen J (2020) Real-time integrity monitoring for a wide area precise positioning system. Satell Navig 1:24 9. Wang Y, Lin T, Shen J (2021) Design and performance evaluation of BDSBAS aviation test receiver. In: China satellite navigation conference (CSNC) 2021 proceedings

Research on the TESLA Authentication Algorithm for BDSBAS Ying Chen1 , Jun Lu1 , Chengeng Su1 , Xiao Chen2(B) , and Xiang Tian2 1 Beijing Institute of Tracking and Communication Technology, Beijing 100094, China 2 Airspace Information Innovation Institute, Chinese Academy of Sciences (CAS),

Beijing 100094, China [email protected]

Abstract. In view of the public signal format of the Satellite-Based Augmentation System (SBAS), there is a risk of spoofing attack security threats. The navigation message authentication technology can improve the anti-spoofing ability of SBAS on the system side. At present, Europe and the United States have carried out research on SBAS message authentication technology and actively promoted the standardization of SBAS message authentication. In this paper, aiming at the construction and development of the Beidou Satellite Based Augmentation System (BDSBAS), the design of the TESLA authentication protocol based on the Chinese commercial cryptography standard is carried out. Simulation verification. The simulation results can provide theoretical support for the standardization of BDSBAS message authentication. Keywords: Beidou satellite-based augmentation system · Message authentication · TESLA · MAC

1 Introduction With the wide application of satellite navigation technology, the requirement for satellite navigation performance is also increasing. To further improve the integrity of the satellite navigation system and meet the navigation needs of civil aviation from the route flight stage to the vertical guidance precision approach stage, the Satellite-Based Augmentation System (SBAS) came into being as the times require [1]. SBAS is a system that uses Geosynchronous Earth Orbit (GEO) satellites to broadcast differential and integrityenhanced signals, but the format of SBAS broadcast signals is open, and there is a threat of spoofing attacks. In response to the security problem of SBAS spoofing attacks, Europe and the United States have proposed SBAS message authentication technology [2, 3]. SBAS message authentication technology refers to adding a special authentication message to the SBAS navigation message so that the receiver can confirm whether the SBAS signal comes from the real GEO satellite and whether the message has been tampered with [4]. On the basis of not affecting the normal SBAS service of existing users, SBAS message authentication improves the user’s anti-spoofing ability by adding information integrity verification and © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 13–27, 2024. https://doi.org/10.1007/978-981-99-6932-6_2

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Y. Chen et al.

signal source identity authentication [5]. The European Union proposed the European Geostationary Navigation Overlay Service (EGNOS) message authentication scheme in 2016 [6] and then developed the EGNOS Authentication Security Test-bed (EAST), initially designed the message authentication protocol, the format of the authentication message, and the authentication performance indicators, and continued to carry out the evaluation of message authentication. In 2019, Europe and the United States established a joint working group to refine and simulate the SBAS authentication scheme and to standardize the SBAS message authentication [7]. In May 2021, the United States, Europe and Japan established the SBAS message authentication standardization group, and China joined the group in 2022 to promote SBAS message authentication. One of the current focuses of discussion is the evaluation of BigMAC and LittleMAC schemes [8]. Compared with foreign research on SBAS message authentication technology, relevant domestic units have carried out research on Beidou Satellite-Based Augmentation System (BDSBAS) message authentication technology, which is mainly based on the elliptical digital signature and Timed Efficient Streaming Loss-tolerant Authentication Protocol (TESLA) BigMAC scheme [9, 10], lack of simulation verification of the LittleMAC scheme. In this paper, for the BDSBAS system, the design of the TESLA authentication protocol based on the Chinese commercial cryptography standard is carried out, and the simulation verification of the key performance of the BigMAC and LittleMAC schemes is carried out. This paper first briefly expounds the principle of SBAS message authentication, then proposes the design of BigMAC and LittleMAC schemes based on Chinese commercial cryptographic algorithms, and finally simulates and analyzes the key indicators of the two schemes.

2 Principles of SBAS Message Authentication 2.1 Authentication Principle The principle of SBAS navigation message authentication is as follows Fig. 1 as shown, the SBAS satellite terminal also broadcasts the authentication message s and the key k in addition to the original message m of sending the SBAS. The SBAS message has not been tampered with. The specific process is as follows: System side: s = VGk (m) User side: V k (m, s) = true? VGK () indicates that the authentication message is generated using key k; Vk () indicates that the message authentication process is performed using key k.

Research on the TESLA Authentication Algorithm for BDSBAS

SBAS Message m

15

Key K

Authentication message generation

Message authentication

Authentication message s Delayed Key K

processing

SBAS Message m

Fig. 1. The principle of SBAS message authentication

2.2 SBAS Authentication Structure The SBAS system is composed of three parts: one is the space segment GEO satellites; the second is the ground segment, which includes monitoring stations, data processing centers and uploading stations; and the third is the user terminal, which includes GNSS/SBAS receivers. Compared with the existing SBAS system structure, an authentication service center will be added in the ground segment to support SBAS message authentication. The system framework after adding the SBAS message authentication is as follows: Fig. 2 shown. The authentication service center generates authentication messages such as Message Authentication Code (MAC) or digital signatures, and the data processing center packages the authentication messages and differential integrity data products to generate SBAS messages, which are posted to the GEO satellite for broadcasting. The user terminal receives the SBAS signal broadcast by the GEO satellite and demodulates it to obtain the authentication message. Based on the authentication message, it authenticates whether the SBAS signal is broadcast from the real GEO and whether the SBAS message is forged. Since it is difficult for SBAS spoofers to forge digital signatures or MAC, navigation message authentication will improve the navigation signal anti spoofing capability.

SBAS satellite

Airline users

Injecting stations Spoofing attack devices

Data Authentication Service Ground monitoring Processing Centre Centre stations

Fig. 2. SBAS system structure (adding the authentication)

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Y. Chen et al.

3 BDSBAS Message Authentication Design 3.1 Chinese Commercial Cryptography Standard Algorithm From the perspective of independent and controllable cryptographic algorithms, BDSBAS message authentication prefers Chinese commercial cryptography standard algorithms [11, 12], including the SM2 digital signature algorithm, SM3 hash algorithm and SM3-based hash-based message authentication code (HMAC) algorithm. (1) SM2 digital signature algorithm The SM2 algorithm is an elliptic curve digital signature algorithm with a security level of 128 bits, a private key length of 256 bits, a public key length of 512 bits, and a signature length of 512 bits. (2) SM3 hash algorithm The SM3 algorithm is a Hash function, the security level is 128 bits, and the length of the output hash value is 256 bits. (3) SM3-based HMAC algorithm The HMAC algorithm is a method of constructing a message authentication code using a hash function, wherein the hash function adopts the SM3 algorithm. 3.2 Design of the TESLA Authentication Protocol Based on the Chinese Commercial Cryptography Algorithm TESLA is a broadcast authentication protocol [13] that provides message authentication and message integrity protection by delayed key broadcasting. 3.2.1 SBAS System Side The SBAS system side implements the TESLA protocol (see details Fig. 3), including one-way key generation, MAC generation, delayed key broadcasting, and digital signatures of root key. Key generaon k0

Sign

k1

F

M1

...

kL-1

F ML-1

HMAC

Sign(k0)

MAC1||M1||k0

F

kL ML

MACL-1

MAC1

Sign(k0)

HMAC

...

MACL-1||ML-1||kL-2

Key send

Fig. 3. TESLA protocol principle [14]

(1) One-way key generation

HMAC

MACL

MACL||ML||kL-1

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One-way key generation generates a key chain of length L according to the Hash function. First, select a random number as KeyL , and then use the Hash function of the SM3 algorithm F() Generate the keychain. KeyL−1 = F(KeyL )

(1)

Key0 = F(Key1 )

(2)

In this way, we construct a set of one-way key chains, and the specific generation sequence is KeyL , KeyL−1 , …, Key1 , Key0 . (2) Message authentication code generation The MAC confirms the integrity and performs authentication. In this paper, the HMAC() function based on the SM3 algorithm is used to generate the MAC. MACL = HMAC(KeyL , ML )

(3)

The keychain used to generate the MAC is in the reverse order of generating the keychain, that is, Key0 is used first, and KeyL is used last. (3) Key delay broadcast The system broadcasts the SBAS message, MAC and key to the user. From the aspect of authentication security, the TESLA protocol adopts the key delay broadcast strategy, that is, the key delays the MAC by one epoch at the same time. For example, at time i, the system broadcasts MAC i , M i and Keyi−1 . (4) Digital signature of root key To prevent attackers from forging the entire key chain, the system signs the root key Key0 and sends the digital signature to the user. 3.3 SBAS User The SBAS receiver needs to verify the system public key, root key digital signature, root key and HMAC step by step to complete the SBAS message authentication. The first step is system public key verification, to verify the authenticity of the public key advertised by the SBAS system. Verify_ECDSASM 2 () indicates the SM2 digital signature verification algorithm, K pub represents the system public key, K CA_pub represents the CA public key, and DS CA represents the CA digital signature. The second step is to verify the correctness of the SBAS broadcast digital signature, using the system public key, digital signature and root key to verify. If the verification is passed, it means that the current root key has not been tampered with, where Key0 means the root key, Salt means the salt value, and DS represents the SBAS broadcast digital signature. The third step is to use the root key to verify the authenticity of the currently received key, use the current key to perform multiple hash functions to obtain the calculated value of the root key, and determine whether it is consistent with the verified root key Key0 , where trunc() represents the truncation bit operation, HashSM 3 () represents the SM3-based

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hash function, Keyi represents the i key, and Key0 represents the root key computed by the receiver. The fourth step is to authenticate the current SBAS message according to the current message, the MAC and the delayed key, where M i represents the current SBAS message and Keyi represents the current key.   (4) Verify_ECDSASM 2 Kpub , KCA_pub , DSCA   Verify_ECDSASM 2 Key0 , Salt, Kpub , DS

(5)

Key0 = trunc(HashSM 3 (Keyi ||salt))

(6)

MACi  = trunc(HMACSM 3 (Mi , Keyi ))

(7)

3.4 Message Design The SBAS authentication message includes the TESLA keychain, MAC and Over the Air Rekeying (OTAR) parameters. Since the length of the SBAS message frame is only 250 bits, the length that can be used to place the authentication message frame is 212 bits for SBAS L1 and 216 bits for SBAS L5. The key length of the SM3 algorithm is 256 bits, and the MAC length is also 256 bits. It is difficult to put the key and the MAC into the same frame message, so the TESLA key and the MAC need to be truncated. According to the truncation strategy of MAC length, message design is divided into two schemes: BigMAC and LittleMAC. 3.5 BigMAC The BigMAC message design includes 115 bit key, 30 bit MAC and 71 bit OTAR parameters. Please refer to the BigMAC message format for details Fig. 4. 250 bits 115 bits TESLA Key 30 bits MAC

6 bits MT identifier

71 bits OTAR 24 bits CRC

4 bits preamber

Fig. 4. BigMAC authentication message structure

The broadcast cycle of the integrity message is 6 s. Based on the authentication requirements of the integrity message, it is necessary to perform message authentication every 6 s. Five frames are used for SBAS differential and integrity message transmission, and 1 frame is used for SBAS authentication message transmission. Figure 5 is the BigMAC message broadcast sequence, where M i represents the existing SBAS differential and integrity message, MAC is the MAC value, Key is the delay key, and OTAR is the over-the-air key update message. Since the TESLA protocol adopts the key delay broadcast, the key corresponding to the MAC is broadcast with a delay of 6 s.

Research on the TESLA Authentication Algorithm for BDSBAS 1s Mi

1s …...

MA C

Mi+4

Key

19

1s OT AR

Mi+6

…...

Mi+10

MA C

Key

OT AR

Fig. 5. BigMAC message broadcast sequence

3.6 LittleMAC Compared with BigMAC, which can only authenticate the first 5 frames of the authentication message in a unified manner and cannot authenticate one of the 5 frames, the LittleMAC method can realize the separate authentication of the first 5 frames of messages and put the 5 MAC values into one frame at the same time. The MAC of the BigMAC scheme is 30 bits, and the MAC of the LittleMAC scheme is 16 bits. The structure of the LittleMAC message is as follows Fig. 6. 250 bits 128-bit TESLA Key 5 16-bit MACs

24 bit CRC

6-bits MT identifier

8bit Reserved

4-bits preamble

Fig. 6. LittleMAC authentication message structure

Figure 7 is the LittleMAC message broadcast sequence, where M i represents the existing SBAS differential and integrity messages, MAC i corresponds to the MAC value of Mi, and Keyi is the MAC i corresponding to the delay key—MAC i+4 and is broadcast with a delay of 6 s. 1S Mi

1S Mi+4

1S

1S

…...

Mi+10

MACi+6 MACi+7 MACi+8 MACi+9 MACi+10 Key

1S Mi+6

1S

…...

MACi

MACi+1 MACi+2 MACi+3 MACi+4

Key

Fig. 7. LittleMAC message broadcast sequence

4 Simulation Experiment 4.1 Key Performance Indicators The key performance indicators of SBAS message authentication include security, the Time Between Authentication (TBA), Authentication Latency (AL) and Authentication Error Rate (AER).

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(1) Security SBAS authentication security is determined by TESLA key security and MAC security. • Key security Key security refers to the probability of guessing the key by means of computer brute force cracking, which is represented by Ps , and its attack success probability is shown in the following formula [15]:   HL Rh T (8) Ps = 1 + L N HL =

L−1  m=0

1 1 1 1 ≈ lnL + γ + − + 2 L−m 2L 12L 120L4

(9)

where Rh is the computing power of the attacker, in hashes/second; L is the length of the TESLA keychain; HL is the number of L harmonics; N is the possible number of key guesses, for a key length of n bits, N = 2n ; γ represents Euler’s constant; and T represents the time that can be used to attack the keychain, in seconds. • MAC Security MAC security refers to the probability of guessing the MAC by random guessing. For an MAC length of n bits, the probability P of being able to guess at random can be expressed as: P=

1 2n

(10)

The probability Px that can be guessed correctly according to multiple guesses can be expressed as   1 x Px = 1 − 1 − n (11) 2 x represents the number of guesses. The BigMAC scheme guesses 1 time every 6 s; the LittleMAC scheme guesses 5 times every 6 s. According to the duration of 1 h, under BigMAC conditions, x = 600; under LittleMAC conditions, x = 3000. (2) Time Between Authentication TBA represents the time interval between two SBAS message authentications. Its expression is as follows: TBA = M + A

(12)

M represents the number of text frames between two authentications, and A represents the number of authentication frames between two authentications.

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(3) Authentication Latency AL indicates the time delay required by the receiver from receiving a frame of data to be authenticated to outputting the authentication result. Since TESLA adopts the key delay broadcasting mechanism, MAL needs to receive at least two frames of authentication messages. The authentication delay is divided into the maximum authentication delay and the minimum authentication delay, and its expression is as follows: ALMAX = M + A + D − 1

(13)

ALMIN = A + D

(14)

AL MAX represents the maximum authentication delay, AL MIN represents the minimum authentication delay, M represents the number of message frames between two authentications, A represents the number of authentication frames between two authentications, and D represents the number of TESLA delay key frames. (4) Authentication Error Rate AER represents the probability of authentication failure, which means the ratio of the number of authentication failures to the total number of authentications, and its expression is as follows: ˆ



AER = 1 − (1 − PER)M + A

(15)



where PER represents the Packet Error Ratio, M indicates the number of SBAS message frames to be authenticated, and A indicates the number of authentication message frames. 

4.2 Simulation Analysis 4.2.1 Security (1) Key security For the simulation of brute force attack, two key lengths of LittleMAC and BigMAC are simulated. According to the Bitman Antminer S19 Pro platform, the computing speed can reach 110 TH/s [16]. According to Eqs. 8 and 9, assume that R h is 25,000 × (1.1 × 1014) hash/s, and T is selected as 6 s. The LittleMAC key length is 115 bits, and the BigMAC key length is 128 bits. The vertical axis represents the key length, the horizontal axis represents the keychain update cycle (unit: 2 weeks), and the color represents the probability of cracking. Therefore, it can be seen that the key chain of either LittleMAC or BigMAC has quite high security (Fig. 8). (2) MAC Security For the MAC attack, LittleMAC and BigMAC, are simulated. For details, see Fig. 9. The horizontal axis is the number of attacks. Under the LittleMAC scheme, each frame of authentication message broadcasts 5 sets of MACs, which is equivalent to 5 MACs every 6 s, and can be attacked 3000 times in 1 h. On the BigMAC scheme, each frame of

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Fig. 8. Security analysis diagram of key length and key chain length

authentication message broadcasts 1 set of MACs, which is equivalent to 1 MAC every 6 s, and can be attacked 600 times in 1 h. The vertical axis is the MAC length, wherein the length of LittleMAC is 16 bits, and the length of BigMAC is 30 bits. Different colors in the figure represent the probability of being broken. The picture shows the probability of attacking for 1 h. The probability of LittleMAC being broken once is 0.04, and the probability of BigMAC being broken once is 5.6E-7. Therefore, in terms of MAC security, BigMAC is much more secure than LittleMAC.

Fig. 9. MAC security analysis chart

4.2.2 TBA and AL (1) Theoretical value Calculate TBA according to Formula 12. Both BigMAC and LittleMAC add 1 frame of authentication message every 5 frames of SBAS message, so the TBA is 6 s. Calculate AL according to Eqs. 13 and 14. The maximum authentication delay AL MAX of BigMAC and LittleMAC is 11 s, and the minimum authentication delay AL MIN is 7 s. Down Table 1 For the theoretical values of TBA and AL, the theoretical values of BigMAC and LittleMAC are the same.

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Table 1. TBA and AL theoretical value TBA (s)

AL MAX (s)

AL MIN (s)

BigMAC

6

11

7

LittleMAC

6

11

7

(2) TBA at different packet error rates In the actual environment, there will be a certain bit error rate in the reception of SBAS messages, resulting in the demodulation packet error rate. When there are different packet error rates, the two indicators TBA and AL will change at user side end. The simulation test draws the TBA obtained by the receiver by setting different packet error rates PER as follows Fig. 10. The simulation test adopts 10,000 simulations, in which the represents different PER values, and the ordinate represents the receiver time. From the simulation test results, when the packet error rate is not greater than 10E-3, the average time of TBA is slightly higher than the theoretical value. According to Eq. 12, the TBA simulation values of BigMAC and LittleMAC are the same.

Fig. 10. TBA emulation value when there is an error packet

Table 2 shows in detail Fig. 10 the time results of 5 packet error rates. When the packet error rate increases from 10e-5 to 10e-1, the average time of TBA increases from 6 to 40.35 s, and the maximum time increases from 6 to 276 s. When the packet error rate is greater than 10e-2, the TBA will increase sharply. (3) AL at different packet error rates By setting different packet error rates PER, the AL obtained by the receiver is as follows Fig. 11. The simulation test adopts 10,000 simulations, in which the abscissa represents different PER values, and the ordinate represents the receiver time. The blue line in the figure represents the BigMAC scheme, the yellow line represents the LittleMAC scheme, the solid line represents the average time of ALMAX , and the dotted line represents the average time of AL MAX . From the simulation test results, when the packet error rate is not greater than 10E-2, the packet error rate has little effect on the AL of BigMAC and LittleMAC; when the packet error rate is greater than 10E-2, BigMAC is greatly affected.

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Y. Chen et al. Table 2. TBA simulation values for different packet error rates

Packet error rate PER

TBA average time (s)

TBA max time (s)

TBA minimum time (s)

10e-1

40.35

276

6

10e-2

7.59

30

6

10e-3

6.06

12

6

10e-4

6

6

6

10e-5

6

6

6

Fig. 11. AL simulation values at different packet error rates

Table 3 shows in detail Fig. 11 the AL time results for the 5 packet error rates of 16.24 s. It can be seen that the packet error rate has a greater impact on BigMAC. When the packet error rate is greater than 10e-2, the TBA will increase sharply. The AL MAX time of the LittleMAC scheme does not change much, while the AL MAX time of the BigMAC scheme increases to 26.24 s. Table 3. AL simulation values of different packet error rates Packet error rate PER LittleMAC

BigMAC

AL MIN time (s) AL MAX time (s) AL MIN time (s) AL MAX time (s) 10e-1

8.92

12.92

22.24

26.24

10e-2

7.12

11.12

7.72

11.72

10e-3

7.04

11.04

7.24

11.24

10e-4

7

11

7.02

11.02

10e-5

7

11

7

11

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4.2.3 AER AER represents the probability of authentication failure when the receiver receives an error code. The simulation test draws the AER obtained by the receiver by setting different packet error rates PER as follows Fig. 12. The abscissa represents different PER values, the ordinate represents AER, the blue line represents the AER of the BigMAC scheme, and the yellow line represents the AER of the LittleMAC scheme. From the simulation test results, AER and PER increase exponentially. When the packet error rate is greater than 10E-3, the PERs of the BigMAC and LittleMAC schemes both increase sharply, and the PER of the LittleMAC scheme increases relatively slowly.

Fig. 12. AER at different packet error rates

Table 4 shows in detail Fig. 12 the AER results of the 5 packet error rates. When the packet error rate increases from 10e-5 to 10e-1, the AER of the LittleMAC scheme increases from 0.00002 to 0.1516, and the AER of the BigMAC scheme increases from 0.00006 to 0.4689. It can be seen that the packet error rate has a greater impact on BigMAC. When the packet error rate is greater than 10e-1, the AER of the LittleMAC scheme is slightly larger than the PER, while the AER of the BigMAC scheme increases to 0.4689, and the authentication service is nearly 50% unavailable. Table 4. AER simulation values for different packet error rates Packet error rate PER

LittleMAC

BigMAC

10e-1

0.1516

0.4689

10e-2

0.0161

0.0511

10e-3

0.0018

0.0064

10e-4

0.00017

0.00059

10e-5

0.00002

0.00006

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5 Conclusion SBAS navigation message authentication is one of the important development directions of SBAS in the future. In this paper, the design of BigMAC and LittleMAC message authentication schemes under the TESLA protocol based on the Chinese commercial cryptography standard is carried out, and simulation experiments are carried out for key performance indicators such as the Time Between Authentication, Authentication Latency and Authentication Error Rate. The conclusions are as follows: (1) From the aspect of key security, the keys of BigMAC and LittleMAC have strong security; however, from the aspect of MAC security, the MAC security of the BigMAC scheme is much higher than that of the LittleMAC scheme. According to the probability of being broken once in an hour, the probability of LittleMAC being broken once is 0.04, and the probability of BigMAC being broken once is 5.6E-7. (2) In the authentication interval, BigMAC and LittleMAC have the same authentication interval. In terms of authentication delay, when there is a certain packet error rate, it will affect the authentication delay index; when the packet error rate is large (0.1), the impact on LittleMAC is smaller. (3) In terms of authentication error rate, BigMAC is more sensitive to packet error rate than LittleMAC. When the packet error rate is greater than 0.1, the authentication service of the BigMAC scheme is nearly 50% unavailable.

References 1. Li R, Zheng SY, Wang ES et al (2020) Advances in BeiDou navigation satellite system (BDS) and satellite navigation augmentation technologies. Satell Navig 1:12. https://doi.org/ 10.1186/s43020-020-00010-2 2. Chiara AD, Broi GD, Pozzobon O et al (2016) Authentication concepts for satellite-based augmentation systems. In: Proceedings of the 29th international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2016), pp 3208–3221 3. Enge P, Walter T (2014) Digital message authentication for SBAS (and APNT). In: Proceedings of the 27th international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2014), pp 1328–1336 4. Chen Y, Gao W, Chen X et al (2021) Advances of SBAS authentication technologies. Satell Navig 2(1):1–7. https://doi.org/10.1186/s43020-021-00043-1 5. Chen X, Luo R, Liu T, Yuan H, Wu H (2023) Satellite navigation signal authentication in GNSS: a survey on technology evolution, status, and perspective for BDS. Remote Sens 15:1462 6. Chiara AD, Broi GD, Pozzobon O et al (2017) SBAS authentication proposals and performance assessment. In: Proceedings of the 30th international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2017), pp 2106–2116 7. Fernández-Hernández I, Walter T, Neish AM et al (2021) SBAS message authentication: a review of protocols, figures of merit and standardization plans. In: Proceedings of the 2021 international technical meeting of the Institute of Navigation, pp 111–124 8. Neish A, Walter T, Powell JD (2019) SBAS data authentication: a concept of operations. In: Proceedings of the 32nd international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), pp 1812–1823

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9. Mu SL, Chen Y, Liu T et al (2021) Design of message authentication and OTAR broadcast strategy for BDSBAS. J Beijing Univ Aeronaut Astronaut 47(07):1453–1461 (in Chinese). https://doi.org/10.13700/j.bh.1001-5965.2020.0222 10. Chen X, Tian X, Luo R et al. Research on BDSBAS message authentication technology based on TESLA protocol. J Beijing Univ Aeronaut Astronaut 1–11. https://doi.org/10.13700/j.bh. 1001-5965.2021.0669 11. China National Standardization Management Committee (2017) GB/T 32918.2—2016. SM2 elliptic curve signature algorithm, Part 2: Digital signature algorithm. China Standard Press, Beijing 12. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China (2017) Information security techniques—SM3 cryptographic hash algorithm GB/T 32905—2016. Standards Press of China, Beijing (in Chinese) 13. Perrig A, Canetti R, Tygar JD et al (2000) Efficient authentication and signing of multicast streams over lossy channels. In: Proceeding 2000 IEEE symposium on security and privacy. S&P 2000. IEEE, pp 56–73 14. Caparra G (2017) Authentication and integrity protection at data and physical layer for critical infrastructures 15. Neish A, Walter T, Enge P (2018) Parameter selection for the TESLA keychain. In: Proceedings of the 31st international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2018), pp 2155–2171 16. Bitmain Online Store (2021) https://shop.bitmain.com/product/detail?pid=000202012221 65500548JAa69Gvu067A

Single Satellite Positioning Method and Error Characteristic Analysis of LEO Navigation Satellites Guodong Yao1(B) , Zhigang Huang1 , Hongwei Zhou2 , and Xinxing Zhang2 1 Beihang University, Beijing, China

[email protected] 2 China Academy of Space Technology, Beijing, China

Abstract. Aiming at the problem of few visible satellites and short visible time for LEO cooperative navigation constellation leading to the difficulty of positioning, this paper studies multi-epoch positioning method based on the idea of replacing time to space. Taking advantage of the characteristics of the LEO satellite, such as high angular velocity and high signal landing power, through limited time of navigation signal observation, the pseudo-range and Doppler frequency positioning algorithm based on least squares method is adopted to achieve reliable positioning of static or quasistatic users. On this basis, the paper analyzes the Cramer-Rao lower bound of the positioning error, and through simulation analysis based on the error ellipsoid theory, it is found that the single LEO satellite multi-epoch positioning error distribution shows strong directivity, and the size and distribution of the positioning error is related to the relative position of user and satellite track. Therefore, the paper suggests that the positioning error of single LEO satellite is not suitable to be divided into horizontal and vertical errors according to the error analysis method of GNSS because of the anisotropy of each direction, but should be described separately by the three directions of east, north and vertical. The paper can provide technical support for the system design and positioning application of future LEO navigation satellites. Keywords: LEO satellite · Pseudo-range and doppler · CRLB · Error ellipsoid

1 Introduction In 2020, BeiDou Navigation Satellite System (BDS) was been constructed and put into operation. Since BDS provided services, it has been widely used in various fields, such as serving the country’s important infrastructure, and it has produced significant economic and social benefits. However, Global Navigation System (GNSS) is unreliable in urban environments and deep jungle, and is susceptible to jamming and spoofing. In contrast, Low Earth Orbit (LEO) satellites have the following advantages [1]. Firstly, the orbital altitude of a LEO satellite is about one-twentieth that of a navigation satellite, so that the user can receive signal with higher SNR from LEO satellites. Secondly, due to the design pattern integrating communication and navigation, LEO satellites have excellent capabilities of anti-jamming and anti-spoofing. In addition, LEO satellites have faster relative speed, which makes Doppler frequency is more attractive to navigation. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 28–39, 2024. https://doi.org/10.1007/978-981-99-6932-6_3

Single Satellite Positioning Method and Error Characteristic

29

Generally, there are three modes of LEO satellites positioning [2]. First, signal of opportunity (SoO), such as the angle of arrival (AOA), received signal strength (RSS) and Doppler frequency shift of the signal from LEO communication satellites can be used for positioning. Due to the large number of LEO communication satellites, resources of SoO are very rich, but we cannot obtain the precise position and velocity of a LEO satellite. We can only roughly estimate the position of the satellite through two-line elements (TLE) orbital parameters, which causes that the position of satellite we calculate often have an error of several kilometers leading to a large positioning deviation. References [3–5] analyze the structure and characteristic of communication signal from Iridium and ORBCOMM satellites, and use the extracted Doppler frequency information for positioning, achieving the positioning accuracy of about 100 m. Reference [6] proposes to combine LEO satellites opportunistic Doppler frequency and inertial navigation system to achieve the positioning of high dynamic users. In order to solve the problem of inaccurate orbit determination of LEO satellites, references [1, 7] propose a model called Synchronous Tracking and Navigation (STAN), which can simultaneously achieve the function of positioning for users and orbit determining for LEO satellites, and the positioning accuracy can be up to 100 m. Second, LEO satellites assist GNSS for positioning. Reference [8] shows that Luojia1 LEO satellite developed by Wuhan University equipped with navigation enhancement load which enhances the navigation signal, improves the measurement accuracy of pseudo-range and Doppler frequency from navigation satellites, and thus improves the positioning accuracy. Reference [9] proposes to use Tianxiang-1 satellite to assist GNSS in precise point positioning (PPP), which reduces the convergence time of PPP to several minutes. In addition, the Hong Yan [10] LEO satellites of China Aerospace Science and Technology and the Hong Yun [11] LEO satellites of China Aerospace Science and Industry under construction will carry navigation enhancement loads, too. Third, cooperative signal from LEO satellites can be used for positioning, which means designing special navigation signal for LEO satellites. Its disadvantage is that the size of a LEO satellite is generally small, and it is difficult to carry navigation signal transmitting modules, high-precision atomic clocks and other navigation loads in such a small size. In addition, it is not easy to determine the orbit of a LEO satellite, because the closer the satellite is to the earth, the more serious the irregularity of the orbit due to the non-uniformity of the earth’s shape is. So, reference [12] proposes that 6 more parameters can be added to the original 16 ephemeris parameters to determine the position of LEO satellites. At present, more LEO satellites are mainly used for communication, while there are not many LEO satellites carrying special navigation loads. Therefore, aiming at the problem that the number of visible satellites of LEO navigation satellites is small, this paper realizes the algorithm of LEO single satellite multi-epoch positioning by using pseudo-range and Doppler frequency observation, and analyzes the Cramer Rao Lower Bound (CRLB) of positioning error. Although, the references [13, 14] discusses the algorithm of single satellite positioning, and also gives the simulation results in different scenarios, they do not analyze the positioning results from the perspective of positioning error distribution. In this paper, from the perspective of error distribution, the positioning

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error ellipsoid is proposed to analyze the LEO single satellite positioning results, and the directivity of positioning error distribution is discussed.

2 Single Satellite Pseudo-Range and Doppler Positioning Principle and Error Modeling 2.1 Measurement Model In the Earth-Centered Earth-Fixed (ECEF) coordinate system, the position and velocity of a satellite at the time i are ri and vi , the position of the static user is r, then the pseudo-range observation between the satellite and the user is expressed as Xρi = r − ri  + δt + ερi

(1)

where, δt is the clock error of receiver, ερi is the measurement error of pseudo-range, 2 . The Doppler obeying Gaussian distribution whose mean is zero and variance is σρi observation is expressed as Xdi = −vi ·

f0 r − ri · + δf + εdi r − ri  c

(2)

where, f0 is the carrier frequency of the signal; c is the speed of light in vacuum; δf is the frequency offset of the receiver; εdi is the measurement error of Doppler frequency obeying Gaussian distribution whose mean is zero and variance is σdi2 . Supposing that Xρi and Xρj is independent; Xdi and Xdj is independent; ερi and ερj is independent; εdi and εdj is independent when i is not equal to j; ερi and εdj is independent. The combination of pseudo-range and Doppler frequency observations can be expressed as T  X = X Tρ , X Td

(3)

T  X ρ = Xρ1 , Xρ2 , · · · , XρN

(4)

X d = [Xd 1 , Xd 2 , · · · , XdN ]T

(5)

where,

The state to be solved is expressed as:  T θ = rT , δt , δf

(6)

Single Satellite Positioning Method and Error Characteristic

31

2.2 LSM Positioning Algorithm Utilizing Pseudo-Range and Doppler The least squares method (LSM) for LEO single satellite positioning based on Newton iteration method is sensitive to the initial value of the position, and improper setting of the initial value will lead the iteration to non-convergence. Therefore, it is necessary to have prior information about the position of user, or determine the initial value of the position through grid searching method. Supposing the initial estimated value of state is T  θ = rT , δ t , δ f

(7)

 T r = x, y, z

(8)

















Thus, the estimated pseudo-range and Doppler frequency are   ρi θ = r − ri  + δ t 





(9)

  r − ri f0 di θ = −vi · · + δf (10) r − ri  c     Near the estimated value, the Taylor expansion of ρi θ and di θ can be written in matrix form to 











X = Hθ

(11)

where, X is the residual matrix,  T X = X ρ1 , X ρ2 , · · · , X ρN , X f 1 , X f 2 , · · · , X fN

(12)

  X ρi = Xρi − ρi θ

(13)

  X fi = Xdi − di θ

(14)







and H is coefficient matrix when θ = θ . ⎡

⎤ mT1 1 0 ⎢ mT 1 0 ⎥ ⎢ 2 ⎥ ⎢ ⎥ .. ⎢ ⎥ . ⎢ ⎥ ⎢ T ⎥ ⎢ mN 1 0 ⎥ H=⎢ T ⎥ ⎢ n1 0 1 ⎥ ⎢ T ⎥ ⎢ n 01 ⎥ ⎢ 2 ⎥ ⎢ ⎥ .. ⎣ ⎦ . T nN 0 1

(15)

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rˆ − ri ∂ρi (θ )   r = rˆ =  rˆ − ri  ∂r   rˆ − ri f rˆ − ri vi ∂d i (θ )  ×  ×  0 ni = r = rˆ =  rˆ − ri  rˆ − ri  rˆ − ri  c ∂r mi =

(16)

(17)

θ is the unknown quantity to be solved of the Eq. (11), and its LSM solution is: −1  H T C −1 X θ = H T C −1 H

(18)

where, C is the covariance matrix of the observations.   2 2 2 2 C = diag σρ1 , σρ2 , · · · , σρN , σd21 , σd22 , · · · , σdN

(19)

Then we can iterate θ 0 . θˆ = θˆ + θ

(20)

θ 2 <

(21)

Repeat the above processes until

where, ∈ is convergence threshold. The traditional GNSS pseudo-range positioning describes the quality of the geometric observation configuration of the satellite by the user through the Dilution of Precision (DOP) [15], which can be multiplied by the ranging accuracy to obtain the positioning accuracy. However, when there are multiple types of observations, DOP is no longer applicable and we choose to use CRLB to describe the positioning accuracy. 2.3 CRLB of Positioning Error In the case of Gaussian observation, it is assumed that the observations obey Gaussian distribution represented by the following expression: X ∼ N (μ(θ), C(θ))

(22) 

μ(θ) and C(θ) may both be related to θ . The Fisher information of θ matrix is given by the following formula:  [I(θ)]ij =

∂μ(θ ) ∂θi

T

C −1 (θ )



   ∂μ(θ ) 1 ∂C(θ ) −1 ∂C(θ) + tr C −1 (θ ) C (θ ) ∂θj 2 ∂θi ∂θj

(23)

where, ⎡ ⎢ ∂μ(θ ) ⎢ =⎢ ⎢ ∂θi ⎣

∂[μ(θ)]1 ∂θi ∂[μ(θ)]2 ∂θi

.. .

∂[μ(θ)]N ∂θi

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

(24)

Single Satellite Positioning Method and Error Characteristic

⎡ ⎢ ∂C(θ ) ⎢ =⎢ ⎢ ∂θi ⎣

∂[C(θ)]11 ∂[C(θ)]12 ∂θi ∂θi ∂[C(θ)]21 ∂[C(θ)]22 ∂θi ∂θi

.. .

.. .

∂[C(θ)]N 1 ∂[C(θ)]N 2 ∂θi ∂θi

··· ··· .. . ···

∂[C(θ )]1N ∂θi ∂[C(θ)]2N ∂θi

.. .

∂[C(θ)]NN ∂θi

33

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

(25)

When the observations include pseudo-range and Doppler frequency, μ(θ ) = [ρ1 (θ ), ρ2 (θ ), · · · , ρN (θ ), d1 (θ ), d2 (θ ), · · · , dN (θ )]T

(26)

H is the coefficient matrix when θ is unbiased [16, 17], and the Fisher information matrix of θ can be calculated by Eq. (27). 

I(θ) = H T C −1 H

(27)

According to the CRLB theorem, the estimated value of θi obeys     var θˆi ≥ I −1 (θ )

(28)

ii

Through Fisher information matrix, we can get the estimation error of user position r when the estimation is optimal unbiased estimation, but we cannot accurately know the directivity of the positioning error, so we need to use the theory of error ellipsoid. 2.4 Error Ellipsoid of Positioning Error

  According to Sect. 2.3, the estimated value of the state obeys var θ i  −1 [ H T C −1 H ]ii . Supposing that 

 −1 G = H T C −1 H

≥

(29)

is a real, symmetric and positive-defined matrix, which can be decomposed to G = UU T where, U is a matrix composed of the eigenvectors of matrix G, ⎡ ⎤ u11 u12 u13 u14 u15 ⎢u u u u u ⎥ ⎢ 21 22 23 24 25 ⎥ ⎢ ⎥ U = ⎢ u31 u32 u33 u34 u35 ⎥ ⎢ ⎥ ⎣ u41 u42 u43 u44 u45 ⎦ u51 u52 u53 u54 u55

(30)

(31)

and  is a diagonal matrix composed of the eigenvalues of matrix G. Λ = diag(λ1 , λ2 , λ3 , λ4 , λ5 )

(32)

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The eigenvalues are sorted in descending order (λ1 ≥ λ2 ≥ λ3 ≥ λ4 ≥ λ5 ). From U and , we can get ⎡ ⎤ u11 u12 u13 U g = ⎣ u21 u22 u23 ⎦ (33) u31 u32 u33 and g = diag(λ1 , λ2 , λ3 )

(34)

where, U g can be decomposed to: ⎡

⎤⎡ ⎤ q11 q12 q13 R11 R12 R13 U g = QR = ⎣ q21 q22 q23 ⎦⎣ 0 R22 R23 ⎦ q31 q32 q33 0 0 R33 Then the directions of the three axes of the error ellipsoid are [18] ⎧ T  ⎪ ⎨ q1 = q11 , q21 , q31  T q2 = q12 , q22 , q32 ⎪   ⎩ T q3 = q13 , q23 , q33 which can be converted to in the astrological coordinate system ⎧ T  ⎪ ⎨ p1 = p11 , p21 , p31  T p = p ,p ,p ⎪ 2  12 22 32 T ⎩ p3 = p13 , p23 , p33

3

33

13

(36)

(37)

The lengths of the three semi axes of the error ellipsoid are ⎧ √ L1 = λ1 × R ⎪ ⎪ 11 ⎨ √ L2 = λ2 × R22 × 1 − R212   ⎪ ⎪ ⎩ L = √λ × R × 1 − R2 × 1 − R2 3

(35)

(38)

22

The theoretical values of the positioning error in the astrological coordinate system are

⎧  ⎪ ⎪ σeast = (p11 L1 )2 + (p12 L2 )2 + (p13 L3 )2 ⎪ ⎨  σ = (p L )2 + (p22 L2 )2 + (p23 L3 )2 north ⎪  21 1 ⎪ ⎪ ⎩σ = (p L )2 + (p L )2 + (p L )2 vetical

31 1

32 2

(39)

33 3

The axes of error ellipsoid reflect the directionality of the positioning error distribution, while the lengths of axes represent the root mean squares error (RMSE) of positioning error in corresponding axes, which reflect the difference of the location error in different directions.

Single Satellite Positioning Method and Error Characteristic

35

3 Simulation and Verification 3.1 Simulation Conditions At present, LEO satellites are mainly used for communication, and navigation functions are considered only on this basis. In order to achieve full coverage of communication signals, the design of LEO Constellations generally give priority to polar orbit constellations. In order to analyze the precision of LEO single satellite pseudo-range and doppler frequency positioning, this paper designs a near polar LEO constellation with 60 satellites by reference to the Iridium. A series of simulations are carried out in the way of Monte Carlo simulation, and the simulation parameters are shown in Table 1. Table 1. Simulation parameters Parameters

Values

Units

Constellation

60/6/3

–

Orbit altitude

1175

Km

Orbit inclination

86.5

Degree

Signal frequency

1520

MHz

Lowest visible elevation of satellite

10

Degree

Beam angle of satellite signal

55

Degree

Ranging error

4.5

Meter

Doppler frequency error

1

Hz

Sampling interval

1

Second

Monto Carlo simulation times

1000

–

3.2 Simulation Results Three typical user positions are selected, and the sky maps of satellite transit are as follows Fig. 1. In scene 1 and 2, the users are located in the middle and low latitudes, and satellites pass through the east side and the zenith position of the user respectively. In scene 3, the user is located in the high latitude, and the satellite passes through the zenith of user obliquely. Monte Carlo simulations obtain the distribution of pseudo-range and Doppler frequency positioning error in ENU coordinate system under three scenes, and projects the error on the horizontal plane and the north-vertical plane. The error distribution maps are as follows Figs. 2, 3, 4. From the positioning error distribution map, it can be seen that the error distribution of LEO single satellite positioning shows strong directionality. This is because polar satellites are used in the simulation, and the movement speed of LEO satellites is very

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Fig. 1. Sky maps of LEO satellites

Fig. 2. Positioning error distribution of user 1

Fig. 3. Positioning error distribution of user 2

fast leading that transit time is about 10 min. The movement tracks of LEO satellites seen from the sky map are approximately straight lines, meaning that the distribution of satellite observations from users are highly directional, which makes the distribution of positioning errors show strong directivity. The relative position between the user and the motion track of satellite determines the size and distribution of the positioning error. In the middle and low latitude, the trajectories of satellites are almost from the direction of due south to due north, so that the north error of positioning is less than the east error, especially when the satellite crosses from the zenith of the user (scene 2) and the east error is far greater than the north error. In the high latitude, the motion trajectories of satellites cross the zenith

Single Satellite Positioning Method and Error Characteristic

37

Fig. 4. Positioning error distribution of user 3

position of users obliquely, which results that the magnitude of the north error and the east error is equivalent. Table 2 shows the statistics of positioning error, CRLB and theoretical value of axes of error ellipsoid under three scenes. Table 2. Statistics and theoretical values of positioning error Scene

RMS of positioning error(m)

1

133.84

2

3

CRLB(m)

Axes of error ellipsoid (ENU)

Length of axes(m)

24.72

(0.64, 0.71, 0.29) (−0.75, 0.51, 0.42) (0.15, −0.49, 0.86)

124.71 1.46 0.36

176.82

172.38

(0.99, −0.01, 0.02) (0.02, 0.01, −0.99) (0.01, 0.99, 0.01)

172.38 0.65 0.22

303.15

297.93

(0.52, −0.85, 0.11) (−0.06, 0.09, 0.99) (0.85, 0.52, 0.01)

297.93 0.63 0.21

From the perspective of the error ellipsoid, the ratio of the length of major axis to the length of minor axis in LEO single satellite positioning error ellipsoid is particularly large. The theoretical calculation values of axes of the error ellipsoid given in Table 2 verify this conclusion. Therefore, when analyzing the size of single satellite positioning error in all directions, we should mainly consider the relative position relationship between the users and the movement tracks of satellites. Generally speaking, the error along the direction of the track is small, and the error along the direction perpendicular to that track is large. Due to the directionality of error distribution of single satellite multi-epoch positioning, the positioning error is usually decomposed into three directions of north, east and vertical to describe from the aspects of universal expression and easy judgment.

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It is worth noting that in the positioning error distribution in Figs. 2, 3, 4, the center of the error discrete points is not the coordinate origin. In the process of multi-epoch accumulation of observations, due to the existence of frequency offset, the error of receiver clock is not constant, which introduces deviations to the pseudo-range observations, so that the distribution of the positioning error deviates from the coordinate origin.

4 Conclusion In this paper, the method and error characteristics of LEO single satellite multi-epoch pseudo-range and Doppler positioning are theoretically deduced and simulated. First, the LSM algorithm of pseudo-range and Doppler positioning is derived, and then the CRLB of positioning error is derived. On this basis, the axes and the lengths of axes of the positioning error ellipsoid are analyzed. Three typical scenes are selected for simulation analysis. The results show that the distribution of LEO single satellite multiepoch positioning error shows strong directionality, and the size and direction distribution of the positioning error are related to the relative position between the user and the motion track of satellite. In addition, the existence of receiver frequency offset makes the distribution of the positioning error deviate from the coordinate origin. The work of this paper provides technical support for LEO satellite positioning system when there are not sufficient visible satellites. Acknowledgements. The authors would like to thank the support of the National Key R&D Program of China (2022YFB3904302).

References 1. Kassas Z, Morales J, Khalife J (2019) New-age satellite-based navigation–STAN: simultaneous tracking and navigation with LEO satellite signals. Inside GNSS Mag 14(4):56–65 2. Prol FS, Ferre RM, Saleem Z, et al. (2022) Position, navigation, and timing (PNT) through Low Earth Orbit (LEO) satellites: a survey on current status, challenges, and opportunities. IEEE Access 3. Qin HL, Tan ZZ, Cong L et al (2019) Positioning technology based on IRIDIUM signals of opportunity. J Beijing Univ Aeronaut Astronaut 45(9):1691–1699 (in Chinese) 4. Qin HL, Zhao C, Du YS, Sun GY, Zhou GT (2020) Research on the Application of iridium/INS integrated positioning technology in ship. Navig Position & Timing 7(02):35–41 5. Qin HL, Li ZQ, Zhao C, Fusion positioning based on iridium/ORBCOMM signals of opportunity. J Beijing Univ Aeronaut Astronaut. https://doi.org/10.13700/j.bh.1001-5965.2021. 0041 6. Jardak N, Jault Q (2022) The potential of LEO satellite-based opportunistic navigation for high dynamic applications. Sensors 22(7):2541 7. Morales JJ, Khalife J, Cruz US, et al (2019) Orbit modeling for simultaneous tracking and navigation using LEO satellite signals. In: Proceedings of the 32nd international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2019). 2019:2090– 2099 8. Lei WANG, Ruizhi CHEN, Deren LI, Baoguo YU, Cailun WU (2018) Quality assessment of the LEO navigation augmentation signals from Luojia-1A satellite. Geomat Inf Sci Wuhan Univ 43(12):2191–2196

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9. Cailun WU, Yuquan SHU, Gang WANG et al (2020) Design and performance evaluation of Tianxiang-1 navigation enhancement signal. Radio Eng 50(9):748–753 10. Meng Y, Bian L, Wang Y et al (2018) Global navigation augmentation system based on Hongyan satellite constellation. Space Int 10:20–27 11. CNAGA (China National Administration of GNSS and Applications) (2017) CASIC plans to launch 156 small satellites for the Hongyun program 12. Meng L, Chen J, Wang J et al (2021) Broadcast ephemerides for LEO augmentation satellites based on nonsingular elements. GPS Solut 25(4):1–11 13. Li X-B, Yang J, Feng X-Z (2009–2011) Study and simulation of passive localization from frequency measurements by single satellite. Computer Eng Appl 45:63–66 14. Song YZ, Hu XG, Huang Y, Wang QY (2013) Simulation and performance analysis of single satellite doppler positioning system. J Spacecr TT&C Technol 32(01):84–88 15. Xie G (2009) Principles of GPS and receiver design. Publishing House of Electronics Industry 16. Jiang M, Qin H, Zhao C et al (2022) LEO Doppler-aided GNSS position estimation. GPS Solut 26(1):1–18 17. Kay S M. Fundamentals of statistical signal processing: estimation theory[M]. Prentice-Hall, Inc., 1993 18. Wang M, Ma GY, Ma LH et al (2012) A study on geometric feature of error ellipsoid in satellite positioning systems. J Astronaut 33(11):1593–1600

A High Dynamic Positioning Algorithm for Ka Band LEO Satellites in Beam Polling Mode Mingxia Li1(B) , Yun Zhao1 , Qiuli Chen2 , and Ping Li2 1 Beihang University, Beijing, China

[email protected] 2 China Academy of Space Technology, Beijing, China

Abstract. Aiming at the problem of low precision positioning solutions for high dynamic users caused by Ka band LEO communication and navigation integrated satellites in point beam polling mode, a LEO satellite/inertial integrated navigation and positioning algorithm based on accumulated error estimation and correction is proposed. A extended Kalman filtering estimator is used to achieve the state error estimation at the output of inertial navigation. By the error correction, the rapid growth of nonlinear error is suppressed when low precision inertial sensors is used for integrated navigation, and the positioning accuracy for high dynamic users is improved. The simulation results show that in the condition of low precision inertial navigation the proposed algorithm can significantly improve the dynamic positioning performance. The three dimensional positioning and velocity measurement accuracy of high dynamic users can reach below 10 m (1σ) and 0.1 m/s (1σ) respectively. Keywords: Ka Band · LEO Satellites · Integrated Navigation · Accumulated Error Estimation and Correction · Kalman Filtering

1 Introduction Since the Iridium satellite system was built in 1998, the LEO constellation has entered a rapid development stage. At present, the use of LEO satellites for precise orbit determination, navigation satellites enhancement and other applications are developing rapidly. Compared with medium and high earth orbit satellites, LEO satellites can provide higher level signals. Therefore, in some environments with severe shielding and signal interference, LEO satellites have significant advantages [1]. With the development of the emerging constellation, the functions of LEO satellite constellations have also been greatly expanded, such as communication, navigation, remote sensing, and monitoring. Many LEO satellites will integrate navigation functions and can independently broadcast navigation signals to serve positioning. The LEO communication and navigation satellites have the advantages of high landing power, easily identification, and strong anti-interference and anti-deception in the complex electromagnetic environment, which brings new opportunities for positioning and navigation [2]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 40–54, 2024. https://doi.org/10.1007/978-981-99-6932-6_4

A High Dynamic Positioning Algorithm for Ka Band

41

The low frequency spectrum resources are increasingly crowded, and Q, V, Ka band with higher available spectrum bandwidth become important resources for satellite communication and navigation [3]. Ka band satellite communication has the advantages of wide frequency band range and strong anti-interference performance, providing a new means for high-speed satellite communication, high-definition television, satellite news collection and other services [4]. In addition, unlike the wide beam antenna used by the Global Navigation Satellite (GPS), the Ka band signal frequency is high. In order to reduce the loss, multi beam and phased array technology are used to meet the requirements of point-to-point beam communication and on-board exchange [5]. Based on this, it is of great significance to study the satellite navigation system combined with the LEO constellation and Ka band to promote the development of LEO navigation. Due to the fact that Ka-band satellites broadcast signals in the form of point beams and the low orbit height of the satellite, it is not possible to meet the needs of high dynamic users for long-term and high-precision positioning. This paper adopts the tight coupling combination mode, and conducts accumulated error estimation and correction on the output of the Strap-down Inertial Navigation System (SINS), and then through simulation, it is verified that the algorithm can improve the positioning accuracy of high dynamic users provided with navigation services by LEO Ka band satellites.

2 Pseudo range And Doppler Positioning Equation Pseudo range is the distance between the receiver and satellites. However, because the receiver clock is not synchronized with the satellite clock, the measured distance is not a geometric distance in the mathematical sense, but includes the clock difference between transmission and reception, which is called pseudo range. The mathematical expression of pseudo distance is:  2  2  2  (1) x(n) − x + y(n) − y + z (n) − z + δtu + ερ ρc = where, ρc is pseudo range observation measurement, X = [x, y, z] is user position, X (n) = [x(n) , y(n) , z (n) ] is satellite position at observation time, and ερ is random measurement error, which is gaussian white noise with mean value of 0 m and standard deviation of 4.5 m. δtu is clock error, and the model is: δtu = β0 + β1 (t − t0 ) + β2 (t − t0 )2

(2)

where, the binomial coefficient β0 , β1 , β2 is 15 m, 1.5 m/s and 0.15 m/s2 respectively. Parameter t0 is taken as 0 s. Doppler positioning refers to positioning calculation based on Doppler principle. Due to the relative speed between the user and the satellite, there is a deviation between the signal frequency received by the user transmitted by the satellite. This deviation is called Doppler frequency shift. According to the principle of Doppler effect, the relationship between the signal frequency received by the user and transmission is as follows:     [VUT − Vs ] · [XUT − Xs ] f xUT , yUT , zUT , vx UT , vy UT , vz UT , tu = 1 − cXUT − Xs 

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f0 + f + εf

(3)

where, f is the frequency received by the user receiver, XUT = [xUT , yUT , zUT ] is the user position, Xs = [xs , ys , zs ] is the satellite position at the observation time, VUT = [vxUT , vyUT , vzUT ] is the user speed, Vs = [vxs , vys , vzs ] is the satellite speed, f0 is the original signal transmission frequency, taken as 20 GHz, c is the speed of light, f is the frequency offset, εf is the random measurement error, which is Gaussian white noise with mean value of 0 Hz and standard deviation of 1 Hz.

3 Low Orbit Ka Band Signal Positioning Mode 3.1 Polling Mode According to the relationship between radio wave length and frequency, the higher the frequency of electromagnetic wave is, the shorter the wavelength is, the more the period of propagation at the same distance is, and the greater the loss is. The approximate frequency range of Ka band electromagnetic wave is 30/20 GHz, and the propagation attenuation of communication signal is large. However, the spot beam can concentrate the RF energy into a narrow beam with a very small coverage area, thus reducing the loss, and obtain higher radiation power [6]. The typical spot beam beam angle is 1.7°2°, covering only a small area. The beam section is circular, and the signal cannot be detected outside this area, as shown in Fig. 1 [7].

Fig. 1. Schematic diagram of point beam coverage

In this paper, the point beam is scanned in different small circles according to certain rules in the satellite coverage area, which is called polling mode. Therefore, Ka band signals are intermittent point-to-point scanning signals when they are used for navigation. Only when the beam scans to users in the small circle can signals be obtained and measurements be observed. 3.2 Problems in Low Earth Orbit Ka Band Satellite Positioning Because the Ka band signal uses polling mode to broadcast signals, and observation measurement is sparse during positioning, the accuracy of the filter state equation extrapolation model has a great impact on the positioning results, especially for high dynamic users, the positioning accuracy is low, so the integrated navigation positioning algorithm can be used to improve the positioning accuracy [8–10].

A High Dynamic Positioning Algorithm for Ka Band

43

During integrated navigation with SINS, due to the low orbit height of the low earth orbit satellite, if open-loop correction is adopted, the rounding error of Taylor expansion of the observation equation has a great impact on the linearization of the equation, and the linear filtering equation has a growing model error, which rapidly increases the integrated navigation positioning error in a short time. Closed-loop correction can be used to solve this problem. However, filter noise and bug will directly affect the work of the closed-loop system, reducing the reliability, and it is difficult to achieve in engineering. Therefore, this paper proposes a low earth orbit satellite/inertial integrated navigation and positioning algorithm based on accumulated error estimation and correction.

4 Integrated Navigation Positioning Algorithm 4.1 Tightly Coupled Mode In the tightly coupled mode, the satellite navigation system and SINS system are no longer completely independent, and can better realize mutual assistance. When there are not enough satellites to provide navigation solutions for the satellite navigation receiver, the solution can still be performed based on SINS and the pseudo range and pseudo range rate observations of a small number of satellites. The tight coupling structure is shown in Fig. 2 [11].

Fig. 2. Tight coupling structure

4.2 Principle of Accumulated Error Estimation and Correction Open loop correction is the subtraction of the optimal estimate of the error state quantity obtained after filtering and the error state quantity output from inertial navigation.Closedloop correction is to feedback the error estimate of the filtered output to adjust the internal state parameters of the subsystem. The accumulated error estimation and correction is different from the feedback correction in form. Instead of using the filter error estimation to adjust the internal parameters of the subsystem, the error estimation is accumulated at the output end of each subsystem for offset correction to achieve the same effect as closed-loop correction. The accumulated error estimation and correction system is shown in Fig. 3 [12]. Because the accumulated error estimates and subsystem parameter errors increase synchronously, the subtracted filter inputs are always kept small, ensuring the accuracy of

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Fig. 3. Structure of accumulated error estimation and correction

the linear filter equation; Moreover, since the correction is to offset the subsystem output by accumulated error, which is simple to implement in engineering, and filter noise and bug will not affect the subsystem operation, so the accumulated error estimation and correction method has the advantages of both open-loop and closed-loop correction, and is an effective method for the combined system in engineering [12].

5 The Design of Kalman Filter Kalman filtering is developed from Wiener filtering. It was first used for variable estimation of stochastic processes, and then it is quickly applied to various optimal filtering and optimal control problems [13, 14]. Kalman filter equation is: ⎧   ⎪ Xk|k−1 = k|k−1 Xk−1|k−1 + uk|k−1 ⎪ ⎪ ⎪ T T ⎪ ⎪ ⎨ Pk|k−1 = k|k−1 Pk−1|k−1 k|k−1 +  k|k−1 Qk−1|k−1  k|k−1    (4) Xk|k = Xk|k−1 + Kk (Zk − Hk Xk|k−1 ) ⎪ ⎪   −1 ⎪ ⎪ Kk = Pk|k−1 HkT Hk Pk|k−1 HkT + Rk ⎪ ⎪ ⎩ Pk|k = (I − Kk Hk )Pk|k−1 5.1 State Variables The coordinate system is selected as the East-North-Up coordinate system (ENU), and the state variables are selected as 12 dimensions, as shown in the following formula:  T X = δλ δL δh δVe δVn δVu φe φn φu tu ˙tu ¨tu (5) where, δλ, δL, δh are the position error state variables, δVe , δVn , δVu are the speed error state variables, φe , φn , φu are the platform angle error state variables, and tu , ˙tu , ¨tu are the clock difference state variable, frequency offset state variable, and frequency drift state variable respectively. 5.2 State Transition Matrix The coefficient matrix of the continuous system state equation can be obtained from the SINS error propagation equation, and then the discrete system state equation transfer matrix can be obtained through discretization. Its form is too complex, so it will not be repeated here. The specific calculation method can be referred to [15].

A High Dynamic Positioning Algorithm for Ka Band

45

5.3 Accumulated Variables Generally, only some state variables of the system (such as position, speed, time and frequency) are subject to accumulated error estimation and correction [16]. In this paper, the accumulated variables are the longitude and latitude error state variables. Before the next filtering, the longitude and latitude error state variables are set to zero. 5.4 Observation Calculation Calculating observation matrix with pseudo range observation as an example, and the specific calculation steps are as follows: (1) For the k-th filtering, the system output position of SINS after the last filtering offset correction is: ⎧ k−1  ⎪ ⎪ λi ⎨ λˆ k−1 = λk−1 − i=1 (6) k−1  ⎪ ⎪ ⎩ Lˆ k−1 = Lk−1 − Li i=1

The system output speed of SINS after the last filter offset correction is: ⎧ k−1  ⎪  ⎪ vei ⎨ Ve,k−1 = Ve,k−1 − i=1

(7)

k−1  ⎪ ⎪ ⎩  Vn,k−1 = Vn,k−1 − vni i=1

Then the predicted position of user for the k-th time is: ⎧ k−1  ⎪ ⎪ λi − ⎨ λu,k = λk − ⎪ ⎪ ⎩

i=1

Lu,k = Lk −

k−1  i=1

t (RN +h) cos Lu,k−1

Li −

t RM +h

∗

∗

k−1 

k−1  i=1

vei (8)

vni

i=1

  (2) After the coordinate transformation of  λu,k , Lu,k , hu,k to the Earth-Centered, Earth Fixed (ECEF) system, xu,k , yu,k , zu,k is obtained, and the distance ρSINS,k between the user position output by SINS and the satellite can be obtained in the k-th filtering.Then the observation equation of the system is: ρ = ρSINS,k − ρk (9) f = fSINS,k − fk where, ρk and fk are pseudo range observation and Doppler shift observation of satellite navigation system respectively.

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5.5 Measurement Matrix The measurement matrix of the Kalman filter is obtained by first order linearization at the state prediction value, that is, the measurement matrix can be obtained through the partial derivative of the observation equation to the state variable. Since the observation is calculated in the ECEF coordinate, and the state variables are the position error and velocity error in the ENU coordinate, it is necessary to convert the measurement matrix from the ECEF coordinate to the ENU coordinate. The transformation relationship between (xu , yu , zu )T and (δλ, δL, δh)T is: ⎞ ⎛ ⎞ δλ xu ⎝ yu ⎠ = N ∗ ⎝ δL ⎠ zu δh ⎛

(10)

where, xu , yu , zu are the position error state variables in ECEF coordinate, ⎛

⎞ −(RN + h) cos L sin λ −(RN + h) sin L cos λ cos L cos λ N = ⎝ (RN + h) cos L cos λ −(RN + h) sin L sin λ cos L sin λ ⎠ 0 (RN (1 − e2 ) + h) cos L sin L

(11)

The transformation relationship between (vx , vy , vz )T and (ve , vn , vu )T is: ⎛

⎞ ⎛ ⎞ vx δve ⎝ vy ⎠ = S ∗ ⎝ δvn ⎠ vz δvu

(12)

where, vx , vy , vz are the speed error state variables in ECEF coordinate, ⎡

⎤ − sin λ − sin L cos λ cos L cos λ S = ⎣ cos λ − sin L sin λ cos L sin λ ⎦ 0 cos L sin L Then the measurement matrix is    ⎧ ∂ρ ∂ρ ∂ρ ⎪ ⎨ H1 = ∂x ∂y ∂z · N , 0, 0, 0, 0, 0, 0, −1, 0, 0      f0 ∂f ∂f ∂f ∂f ∂f ∂f ⎪ ⎩ H2 = ∂x ∂y ∂z · N , ∂ x˙ ∂ y˙ ∂ z˙ · S, 0, 0, 0, 0, − c , 0

(13)

(14)

5.6 Q Matrix and R Matrix The Q matrix is often determined by the parameters such as gyro and accelerometer bias. The noise matrix of integrated navigation system is: W = ( [0]1∗9 ωrx ωry ωrz ωax ωay ωaz )T

(15)

A High Dynamic Positioning Algorithm for Ka Band

47

where, ωri and ωai are the gyro drift rate and accelerometer deviation of SINS respectively. For the discrete state equation, its driving noise variance matrix Qk is converted from the driving noise variance matrix Q of the continuous state equation, and the calculation formula is: ⎧ ∞  i 2 3 T ⎪ ⎪ Qk = Mi Ti! = 1! M 1 + T2! M2 + T3! M3 + · · · ⎪ ⎪ ⎨ i=1   ¯ = E WW T M1 = Q (16) ⎪ T +F Q ⎪ ¯ ¯ ⎪ = QF M k ⎪ k ⎩ 2 ¯ + 2Fk QF ¯ T ¯ 2T + F 2 Q M3 = QF k

k

k

where, T is the extrapolation interval of Kalman filter, and Fk is the coefficient matrix of the state equation of continuous system. The user clock difference can be approximately described by a Singer model with a time constant of 0, and the driving noise variance matrix is. ⎡ 5 4 3⎤ T T T

⎢ 204 83 62 ⎥ Qt = ⎣ T8 T3 T2 ⎦ T3 T2 6 2 T

(17)

Assuming that the observation noises of each observation are uncorrelated, the covariance matrix R of the observation noises can be set as:   σρ2 R= (18) σf2 The diagonal elements in the matrix are the variances of pseudo range and Doppler frequency shift measurement errors from top to bottom. 5.7 Setting of Initial Value of State Variables and Initial P Matrix The initial estimate of each state variable can be taken as the error value of SINS initial alignment, and then P0 should be the square of the error value of SINS initial alignment.

6 Simulation and Result Analysis 6.1 Simulation Parameter Setting Earth Model The earth model parameters are selected according to the basic geodetic parameters of WGS-84 coordinate system. Constellation Model Two constellations in the low earth orbit are adopted and the specific parameters are shown in Table 1.

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Constellation paramters

Constellation 1

Constellation 2

Number of satellites

144

432

Number of tracks

12

24

Number satellites of per track

12

18

Orbit height/km

1175

1150

Orbit inclination/degree

86.5

60

User Model The user makes a circular motion of the plane at a height of 10000 m in Beijing area (40°N, 116°E), and the equation of motion is ⎧ ⎪ ⎨ eUT (t) = ρ sin(α(t)) nUT (t) = ρ cos(α(t)) (19) ⎪ ⎩ uUT (t) = 10000 where, ρ is the radius of motion, which is taken to be 1000 m, and α(t) = sign ∗ ω ∗ t is the azimuthal angle. sign represents the direction of the circular motion, + 1 represents a left turn, and −1 represents a right turn. ω is the angular velocity of the circular motion, which is taken to be 0.25 rad/s. t represents the time of motion. SINS Parameter Setting The SINS system is mainly composed of gyres and accelerometers. In this paper, extrapolation is made from the SINS initial alignment error into the error propagation equation to obtain the SINS positioning results of user position and velocity at each moment. The precision and initial alignment errors of the SINS are listed in Tables 2, 3 respectively. Table 2. Accuracy of gyroscope and accelerometer SINS devices

Standard deviation (zero mean Gaussian noise)

Micromechanical gyri NV-GYT125

10°/h

Accelerometer

9.8 × 10−6 m/s2

6.2 Simulation Result Available Satellites The simulation time is chosen to be 600 s, and the number of available satellites per calendar period is counted. The results are shown in Fig. 4 and Table 4.

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Table 3. SINS initial alignment error SINS error measure

1σ

Longitude error

0.1 arc minutes

Latitude error

0.1 arc minutes

Height error

10 m

Eastern velocity error

0.1 m/s

North velocity error

0.1 m/s

UP velocity error

0.1 m/s

Fig. 4. Trend of available satellites over time

Table 4. Statistics of the number of available satellites Item

Not-Polling

Polling

Max

23

8

Min

19

0

Mean

21

3

As can be seen by Table 4, when LEO satellites in beam polling mode, the number of available satellites is substantially reduced and the real-time positioning requirement that the number of available satellites is 4 cannot be reached most of the time, which cannot meet the continuous locating requirement of high dynamic users. Positioning Results When the open-loop correction is employed, the SINS and the integrated navigation positioning results are shown in Figs. 5, 6 respectively. It can be seen from Figs. 5 and 6 that the positioning error of integrated navigation starts to increase at about 400 s. At this time, the positioning error of SINS is about 2701 m in the longitude direction and about 8145 m in the latitude direction. Due to the low accuracy of the gyroscope adopted by SINS and the rapid accumulation of the

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Fig. 5. SINS positioning results

Fig. 6. Integrated navigation positioning results

positioning error, the rounding error of the integrated navigation observation equation in the first order linearization also increases, and the model error of the linear filtering equation appears, leading to the rapid increase of the integrated navigation positioning error. After the accumulated error estimation and correction is adopted, the positioning results of SINS and integrated navigation are shown in Figs. 7, 8 respectively.

Fig. 7. SINS positioning results

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Fig. 8. Integrated navigation positioning results

It can be seen from Figs. 7, 8 that the integrated navigation positioning error does not increase in the whole simulation process. The maximum of SINS positioning error is 6009 m in the longitude direction and 21380 m in the latitude direction. Even if SINS error increases, the positioning results of integrated navigation still remains within 20 m. So the accumulated error estimation and correction eliminates the influence of the cumulative error on the filter input, so that the system can work stably and accurately. Speed Simulation Results When the open-loop correction is employed, the SINS and the integrated navigation speed simulation results are shown in Figs. 9, 10 respectively.

Fig. 9. Speed simulation results of SINS

Fig. 10. Speed simulation results of integrated navigation

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After the accumulated error estimation and correction is adopted, the speed simulation results of SINS and integrated navigation are shown in Figs. 11, 12 respectively.

Fig. 11. Speed simulation results of SINS

Fig. 12. Speed simulation results of integrated navigation

It can be seen from Figs. 10, 12 that the speed error of integrated navigation does not increase when accumulated error estimation and correction is adopted. Although the speed error state variables are not accumulated, the SINS output is corrected by the accumulated value of position error after each filtering, so that the position error of SINS remains small before the next filtering, and the SINS velocity error grows slowly. Therefore, when the observation equation is linearized for the first order, the rounding error remains small, and the velocity measurement accuracy is still accurate. Table 5 below shows data statistics of integrated navigation simulation results with accumulated error estimation and correction and open loop correction.

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Table 5. Data statistics of integrated navigation simulation results with accumulated error estimation and correction and open loop correction Correction method

1σ

East

North

Up

Accumulated error estimation and correction

Positioning accuracy/m

5.600

3.170

6.760

Speed accuracy/m/s

0.018

0.019

0.065

Open loop correction

Positioning accuracy/m

5.308

3.780

6.820

Speed accuracy/m/s

0.013

0.012

0.083

7 Conclusion In this paper, under the condition that the low earth orbit Ka band satellite polling mode cannot achieve high-precision positioning for high dynamic users, a low earth orbit satellite/inertial integrated navigation and positioning algorithm based on accumulated error estimation and correction is proposed. By accumulating the error estimates and correcting the SINS output, the problem that the integrated navigation positioning accuracy decreases with the increase of time when using open-loop correction is solved, and the positioning accuracy for dynamic users is effectively improved. The simulation results show that: (1) Under the Ka band satellites polling mode, the positioning and velocity measurement accuracy of high dynamic users of the integrated navigation system can reach below 10 m (1 σ) and 0.1 m/s (1 σ) respectively. (2) Closed-loop correction can be realized by using accumulated error estimation and correction, so that integrated navigation system consisting of the low earth orbit satellites and low precision inertial navigation can work stably for a long time. Acknowledgements. The authors would like to thank the support of the National Key R&D Program of China (2022YFB3904302).

References 1. Li H, Wei Y, Du X (2021) Development status of LEO constellations and LEO satellite navigation algorithms. Tactical Missile Technol 03:57–66 2. Su Y, Liu Y, Zhou Y, Yuan J, Cao H, Shi J (2019) Broadband LEO satellite communications: architectures and key technologies. IEEE Wirel Commun 26(2):55–61 3. Jiancheng L (2021) Analyzing the advantages of low earth orbit broadband satellite communication from the on orbit test of the first galaxy spaceflight satellite. Digit Commun World 02:22–24 4. Wei D, Xiao T (2012) Research on the status quo and development trend of Ka broadband communication satellite antenna technology. J Microw Sci 28(S2):54–56. https://doi.org/10. 14183/j.cnki.1005-6122.2012.s2.093 5. Wang Meng L (2021) Research on characteristics and application of Ka frequency band. Digit Commun World 11:58–61

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6. Qi W, Yifan W (2010) Development and application status of Ka band communication satellite. Satell Netw 08:20–27 7. Zhang X, Qian W (2009) Spot beam design and optimization of satellite borne multi beam antenna for LEO satellite system. Telecommun Technol 49(07):31–35 8. Fumei W, Yuanxi Y (2010) On board GPS/INS/Odometer integrated navigation algorithm with additional speed prior information. J Astronaut Astronaut 31(10):2314–2320 9. Wang X-L, Li Y-F (2012) An innovative scheme for SINS/GPS ultra-tight integration system with low-grade IMU. Aerosp Sci Technol 23(1) 10. Man X, Sun F, Liu S, et al, Analysis of positioning performance on combined BDS/GPS/GLONASS 11. Han Z, Research on integrated positioning technology of satellite navigation and inertial navigation. Hebei 12. University of Science and Technology (2020). https://doi.org/10.27107/d.cnki.ghbku.2020. 000533 13. Shikai Z, Qiongqiong Z, Ziming D (2001) Closed loop correction of integrated navigation system using error estimation accumulation. J Electron 09:1221–1224 14. Carosio A, Cina A, Piras M (2005) The robust statistics method applied to the kalman filter: theory and application. In: ION GNSS 18th international technical meeting of the satellite division. The Institute of Navigation, Long Beach, pp 525–535 15. Grewal MS (2001) Kalman filtering theory and practice using matlab. Wiley, New Jersey 16. Liu C (2020) Research on GNSS/INS integrated navigation and positioning data processing algorithm. University of Chinese Academy of Sciences (National Time Service Center of Chinese Academy of Sciences) 17. Li C, Honglei Q (2008) Software design and simulation of JTIDS/BA/INS/GPS integrated navigation processor. J Astronaut Astronaut 04:1233–1238

Spoofing Monitoring Method Research of GNSS Based on LEO Doppler Measurement Zishan Zhao1(B) , Zhigang Huang1 , Yongchao Wang2 , and Kai Yin1 1 Beihang University, Beijing, China

[email protected] 2 Aviation Data Communication Corporation, Beijing, China

Abstract. Communication and navigation integration will be a staple of integrated PNT system. LEO satellites, served as an important part of the system, provide support for constructing the future PNT system and improving its service performance. Spoofing is a potential factor to affect reliability of GNSS services, LEO satellites can provide reliable information as independent navigation sources and show good anti-spoofing performance with dual-direction communication links and authentication function, which improve the anti-spoofing performance of the whole system. A LEO-aided GNSS spoofing monitoring algorithm is proposed, constructing a subset-separating detection model based on Chi-square distribution in velocity domain with LEO doppler measurements and GNSS pseudorange rates to detect and recognize spoofed navigation satellites by divided space into subsets. The simulation results show that the novel algorithm can detect and recognize fault navigation satellites effectively, and positioning accuracy after exclusion of spoofed satellites can be ensured. LEO can improve anti-spoofing performance of GNSS observably. Keywords: Low-earth-orbit satellites · Doppler · Global navigation satellite system · Spoofing monitoring

1 Introduction Global Navigation Satellite System can provide positioning and timing services, but the vulnerability of its signal makes it easy to be spoofed. With continuous update of spoofing and interference, anti-spoofing has received more and more attention in the world. The GSWG4 document released by the International Civil Aviation Organization (ICAO) states that the second-generation satellites of Galileo will increase advanced jamming and spoofing protection mechanisms to safeguard signal [1] on the system side. For spoofing and interference, common technologies mainly include signal power monitoring [2], password authentication [3, 4], antenna array processing [5] and use of auxiliary navigation information [6] and other detection methods. The rise of low-earth-orbit satellites provides new ideas for the development of antispoofing technology. As the key direction of communication and guidance integration © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 55–67, 2024. https://doi.org/10.1007/978-981-99-6932-6_5

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in the comprehensive Positioning, Navigation and Timing (PNT) system [7], how to use LEO satellites to assist and enhance GNSS, and even provide navigation and positioning services independently, has become one of the research hotspots at home and abroad [8]. LEO satellites with the function of dual-direction communication authentication show good anti-spoofing performance, and can provide reliable redundant observation information for satellite navigation systems. Literature [9] proposes a spoofing monitoring algorithm based on pseudorange, but the current observations of LEO satellites have not been confirmed, and they are not expected to be able to provide navigation and positioning services based on pseudorange. First, LEO satellites will not carry atomic clocks. Second, they will not broadcast downlink signals that support pseudorange measurements through a calibrated connection between transmission time tags and transmitter clock time [10]; Meanwhile, if LEO satellites maintain strict time synchronization with navigation satellites, it will increase the complexity of system construction. But the use of doppler observation measurement can effectively avoid this problem. Therefore, the present study seeks to perform navigation using doppler shift as the only navigation observable. Based on the above analysis, this paper proposes a spoofing monitoring algorithm based on LEO doppler, and constructs a subset-separating detection model based on Chisquare distribution, combining pseudorange rates of GNSS with doppler measurements of LEO satellites. The model uses an improved Receiver Autonomous Integrity Monitoring (RAIM) technology to detect and recognize the direction of spoofed satellites by dividing space into subsets and rotating subsets to supplement the existing technologies in the information level.

2 Spoofing Monitoring Algorithm Based on Doppler 2.1 Spoofing Interference Scenario The forwarded spoofing signal is generated based on real signals at the current stage, which is very similar to the real one and is difficult to detect by the receiver. When the interference source spoofs the real satellite signals by forwarded spoofing, the array antenna can effectively detect the spoofing with the angle greater than 5° between the incident direction of spoofing signal and the real one [11]. In this paper we discuss a model for detecting spoofing at the information level. The spoofing scenario is a fan-shaped area swept out by the left and right offset of 15° with the connection between the spoofing source and the target receiver as the center. In order to ensure that each subset has visible stars in each epoch, we spoof and monitor visible satellites in the range of 90° each time in our simulation.

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2.2 Default Detection Algorithm The basic equation of GNSS satellites positioning by pseudorange is as follows:   2  2  2 ρc = x(s) − x + y(s) − y + z (s) − z + δtu

(1)

The basic equation of LEO satellites positioning by doppler is as follows: vx (x − x(s) ) + vy (y − y(s) ) + vz (z − z (s) ) fd (x, y, z, δfu ) =  f0 + δfu + εf c (x − x(s) )2 + (y − y(s) )2 + (z − z (s) )2

(2)

where X (s) = [x(s) , y(s) , z (s) ] is the position of satellites at observation time, V (s) = (s) (s) (s) [vx , vy , vz ] is velocity of satellites, X = [x, y, z] is position of receiver, δtu is clock bias, f0 is transmission signal frequency, δfu is clock frequency bias of receiver, εf is frequency error. The doppler observation equation after linearization is:      x0 − x(s) P0 − X (s) V T vx f0 − fd (x, y, z, δfu ) = (x − x0 ) c r r3      y0 − y(s) P0 − X (s) V T vy − + (3) (y − y0 ) r r3      z0 − z (s) P0 − X (s) V T vz + − (z − z0 ) + (δf − δf0 ) + h.o.t r r3 First the initial position of the receiver is obtained by the joint positioning of LEO doppler measurements and GNSS pseudorange, and then a subset-separating detection model based on Chi-square distribution is constructed. To maintain consistency of dimension, observations of GNSS satellites should be converted into pseudorange rates, using average pseudorange rates instead of doppler in a short interval. Pseudorange rate equals the ratio of the difference between pseudorange and time interval. ρ˙ =

ρt − ρt−t t

(4)

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Constructing a new G matrix GNSS pseudorange rates and LEO doppler measurements: ⎡ ⎤ gx,1 gy,2 gz,3 10000 ⎢ .. .. .. .. .. .. .. .. ⎥ ⎢ . . . . . . . .⎥ ⎢ ⎥ ⎢ gy,s gz,s 1 0 0 0 0⎥ gx,s ⎢ ⎥ ⎢ ⎥ gy,s+1 gz,s+1 0 1 0 0 0⎥ gx,s+1 ⎢ ⎢ .. .. .. .. .. .. .. .. ⎥ ⎢ ⎥ ⎢ . . . . . . . .⎥ ⎢ ⎥ ⎢ gy,s+m gz,s+m 0 1 0 0 0⎥ gx,s+m ⎢ ⎥ ⎢ gx,s+m+1 gy,s+m+1 gz,s+m+1 0 0 1 0 0 ⎥ ⎢ ⎥ ⎢ .. .. .. .. .. .. .. .. ⎥ (5) G=⎢ ⎥ . . . . . . . . ⎢ ⎥ ⎢ g ⎥ gy,s+m+p gz,s+m+p 0 0 1 0 0 ⎥ x,s+m+p ⎢ ⎢ g ⎥ ⎢ x,s+m+p+1 gy,s+m+p+1 gz,s+m+p+1 0 0 0 1 0 ⎥ ⎢ .. .. .. .. .. .. .. .. ⎥ ⎢ ⎥ . . . . . . . .⎥ ⎢ ⎢ ⎥ ⎢ gx,s+m+p+q gy,s+m+p+q gz,s+m+p+q 0 0 0 1 0 ⎥ ⎢ ⎥ ⎢ gx,s+m+p+q+1 gy,s+m+p+q+1 gz,s+m+p+q+1 0 0 0 0 1 ⎥ ⎢ ⎥ .. .. .. .. .. .. .. .. ⎥ ⎢ ⎣ . . . . . . . .⎦ gx,s+m+p+q+l gy,s+m+p+q+l gz,s+m+p+q+l 0 0 0 0 1 where s is the number of visible satellites of BDS, m is the number of visible satellites of GPS, p is the number of visible satellites of Galileo, q is the number of visible satellites of GLONASS, l is the number of visible satellites of LEO satellites, gxi , gyi and gzi (i = 1, 2 . . . m) are: ⎧      x0 −x(si) P0 −X (si) ViT ⎪ vxi ⎪ gxi = ri − ⎪ ⎪ ri3 ⎪ ⎪      ⎨ y0 −y(si) P0 −X (si) ViT vyi gyi = ri − (6) ri3 ⎪ ⎪      ⎪ ⎪ z0 −z (si) P0 −X (si) ViT ⎪ ⎪ ⎩ gzi = vrzii − r3 i

Assuming that the total number of all visible satellites is n, according to the weighted least squares residual principle, the linearized joint observation equation is: y = Gx + ε

(7)

where y is an n × 1 vector represented differences between measurement pseudorange rate and predicted pseudorange rate; G is an n × 8 geometric matrix in which n is the number of visible satellites; x is an 8 × 1 vector represented the incremental deviation of the nominal state generated by the linearization process; ε is the n × 1 measurement error vector. According to the weighted least squares principle, the weighted least squares solution of the current user state is obtained: −1  G T Wy (8) xˆ = G T WG

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Construct pseudorange rate and doppler residual vector: yˆ = G xˆ

(9)

b = y − yˆ

(10)

Construct weighted sum of squares of pseudorange rate residuals: εWSSE = bT Wb

(11)

When all satellites are normal, mean value of doppler residual vector is 0. When there exist spoofing satellites, mean value of doppler residual vector is not 0 and standardized test statistics εWSSE /σ 2 follows a decentralized chi-square distribution with n-4 freedom degree. If there is no spoofing, E(ε) = 0, εWSSE /σ 2 ∼ χ 2 (n − 4). If there exists spoofing, E(ε) = 0, εWSSE /σ 2 ∼ χ 2 (n − 4, λ). The decentralized parameter λ = E(εWSSE )/σ 2 . The detection threshold TD is determined by the false alarm probability PFA , the formula is as follows:  TD fx2 (x)dx = 1 − PFA (12) 0

(n−4)

If εWSSE /σ 2 < TD , no fault is detected; If εWSSE /σ 2 > TD , fault is detected and an alarm would be given (Fig. 1).

Fig. 1. Chi-square test diagram

The detection algorithm steps of spoofing based on GNSS pseudorange rates and LEO doppler measurements are as follows: i. Get GNSS pseudorange and LEO doppler measurements; ii. Check whether the current is the first epoch: if it is, the running ends and shows current RAIM detection is unavailable; otherwise go to iii; iii. Delete GNSS satellites that cannot both be seen at current epoch and the previous one;

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iv. Judge whether the current number of visible satellites is more than 5. If it is, go to v; otherwise, the current RAIM detection is unavailable; v. Based on the least square method, the initial position of the user is estimated by the joint positioning of pseudorange and doppler measurements; vi. (pseudorange of the current epoch minus pseudorange of the previous epoch) divided by the epoch interval, obtain the average pseudorange change rate of the GNSS navigation satellites in the former and latter epoch; vii. Use observations of GNSS pseudorange and LEO doppler obtained by vi to conduct joint doppler positioning and obtain doppler residuals. If the satellite cannot both be observed at last and current epoch, the satellite will not participate in the detection; viii. Construct test statistics based on doppler residuals and calculate detection thresholds based on false alarm rate; ix. Compare the values of test statistics and detection thresholds, if the test statistics are smaller than the detection thresholds, it indicates that no fault occurs in the current epoch and the operation is terminated; otherwise, an alarm is generated to the user, indicating that a fault occurs in the current calendar and the running is terminated (Fig. 2).

2.3 Recognition Algorithm of Spoofing LEO satellites have good performance of anti-spoofing and can provide redundant observations as reliable navigation sources. When spoofing exists, there is no guarantee that the signal of only one satellite is being spoofed, so the traditional RAIM recognition algorithm is no longer applicable. In this section we propose a subset-separating detection model based on Chi-square distribution in velocity domain, which draws on the idea of RAIM diversity to detect and recognize the direction of the spoofed satellites. Once a spoofing is recognized in a certain direction, all visible satellites in that direction are deleted. In this paper, the visible satellites are divided into four subsets according to the azimuth: northeast, northwest, southwest and southeast, and the LEO satellites are combined with GNSS satellites in every direction to perform a consistency test until the direction in which the spoofed satellite is recognized (Fig. 3). The specific steps of forwarding spoofing identification algorithm are as follows: i. Execute RAIM on all pseudorange observations, T stands for test statistics, TD stands for detection threshold. If T < TD , all visible satellites are normal and the flow is over, otherwise, go to ii; ii. Divide visible GNSS satellites into four subsets according to the azimuth and count n = 1; iii. Combine LEO satellites with visible GNSS satellites in any three subsets to execute RAIM. If T < TD , satellites in these three subsets are not spoofed, and the subset rested is the one with spoofed satellites, then the algorithm flow is over; otherwise, go to iv; iv. Judge n value, if n = 4, go to v; or make n = n + 1 and jump to iii; v. Rotate each subset 45° counterclockwise if there exists spoofed GNSS satellite right on the subset dividing line;

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Fig. 2. Flow chart of spoofing detection algorithm.

vi. Repeat step iii until the subset with spoofed satellites is recognized; otherwise, go to vii; vii. Judge value n, if n < 8, let n = n + 1, then jump to vi; otherwise, the algorithm flow is over and recognition failure, an alarm would be shown to the user that there is spoofing in the current pseudorange observation.

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Fig. 3. Flow chart of spoofing recognition algorithm

3 Simulation and Result Analysis 3.1 Simulation Parameter and Index Setting To explore the effect of doppler-based LEO satellites on the anti-spoofing performance of GNSS, this paper selects the actual BDS-3, GPS, Galileo, GLONASS constellations, and two types of LEO constellations for spoofing monitoring research, and the user location is in Tianjin. We select a near-polar orbit LEO constellation composed of 72 satellites, and a mixed LEO constellation including 72 satellites with 55° and the rest with 86.5° orbit inclinations respectively. The constellation configuration is as follows (Table 1):

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Table 1. The constellation configuration Constellation

Orbit height/km

Number of satellites

Orbital inclination/degree

BDS-3

21528(MEO)

27

55

31

55

35786(IGSO) GPS

20200

Galileo

23222

22

56

GLONASS

19100

24

64.8

Scene 1

1175

72

86.5

Scene 2

1175

144

55/86.5

LEO

According to the Minimum Operating Performance Standards (MOPS), the false alarm rate in this paper is set to 3.33 × 10−7 . The evaluation indexes are detection rate and recognition rate, the detection rate is defined as (the number of epochs detected spoofing)/(total epochs), and the recognition rate is defined as (the number of epochs recognized spoofing)/(the total number of epochs detected spoofing). 3.2 Simulation Result The simulation duration is 86400 s, 1 s as an epoch; the number of visible satellites in different LEO constellations in a day is shown in Fig. 4:

Fig. 4. The left picture shows the number of visible satellites in Tianjin with 72 LEO in one day. The right one shows the number of visible satellites in Tianjin with 144 LEO in the same day

GNSS visible satellites are divided into four subset evenly. In each epoch, GNSS visible satellites in one random subset are selected to add fault sizes ranging from 0 to 100 m at 5 m intervals in pseudorange domain, and such fault is manifested as pseudorange deviation. Considering that the pseudorange deviation is added to all satellites in the selected subset and number of satellites is changing all the time, we use total pseudorange deviation as abscissa of the pictures, while each satellite equally apportioned the 2-norm of total pseudorange deviation. Assuming that the spoofed satellites are located in the

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second quadrant, the position and number of satellites before and after deleting them in an epoch are shown as follows (Fig. 5):

Fig. 5. The picture on the left shows satellites position before deleting spoofed satellites. The picture on the right shows satellites position after deleting spoofed satellites.

The spoofing detection rate and recognition rate in different fault size are shown as follows (Fig. 6):

Fig. 6. The left picture shows spoofing detection rate. The right one shows spoofing recognition rate.

When the equivalent step pseudorange deviation caused by forwarding spoofing is less than 10 m, the spoofing cannot be detected in all three scenarios, and the detection rate of GNSS is always lower than that with LEO. When the pseudorange deviation is between 15 m ~ 30 m, the detection rate of 72 LEO satellites is a little higher than that of 144 LEO ones. When the pseudorange deviation is between 35 m ~ 55 m, the detection rate is highest with 144 LEO satellites assisted, followed by 72 LEO satellites. When LEO satellites are not introduced, the detection rate of GNSS reaches more than 90% when the pseudorange deviation is 45 m, and the detection rate reaches more than 90% when the pseudorange deviation is 35 m after adding LEO constellations. Under the 90% spoofing detection rate index, the anti-spoofing performance of GNSS assisted by LEO

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constellations is improved by 22%. It can be seen that LEO constellations can improve the spoofing detection performance of GNSS after the spoofing reaches a certain size. The spoofing recognition rate of GNSS reaches more than 90% at 70 m pseudorange deviation. In the scenario of 72 LEO satellites, the spoofing recognition rate reaches more than 90% when the pseudorange deviation is 40 m, and with 144 LEO satellites, the recognition rate reaches more than 90% when the pseudorange deviation was 35 m. Under the 90% spoofing recognition rate index, the spoofing recognition performance of GNSS is improved by more than 40% assisted by LEO constellations. 3.3 Analysis of Simulation Results After the pseudorange deviation can be detected, the spoofing detection performance of GNSS with LEO constellations is better than that without LEO, thus, LEO can significantly improve the anti-spoofing performance of GNSS. Assuming that the interference source is in the southeast direction of the target receiver, adding a deviation of 100 m to the pseudorange measurement in the southeast direction, the simulation results of 144 LEO-aided GNSS are shown in Figs. 7, 8.

Fig. 7. The picture on the left shows positioning error (before recognition). The picture on the right shows positioning error (after recognition).

Fig. 8. The picture on the left shows DOP (without spoofing). The picture on the right shows DOP (after deleting spoofed satellites).

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In Fig. 7, the positioning error of 95% before spoofing recognition is 25.03 m, the positioning error after recognition is 2.25 m, and the positioning accuracy is 1.65 m without spoofing. In Fig. 8, it can be seen that there is only a small increase in DOP after deleting spoofed satellites in one quadrant compared to the situation with no fault. Therefore, the algorithm can ensure the accuracy of positioning services after deleting the spoofed satellites and DOP is less affected, so that the algorithm is effective.

4 Conclusion Based on GNSS pseudorange rate and LEO doppler shift, a subset-separating detection model based on Chi-square distribution in velocity domain is proposed, and the antispoofing performance of the system with or without LEO constellation assisted GNSS is analyzed. Experimental results show that the spoofing monitoring algorithm can detect and recognise the direction of the spoofed satellites, and can ensure that the accuracy of the positioning service can be equivalent to that of GNSS without spoofing after removing the spoofed satellites. The anti-spoofing performance of the LEO satellites can be significantly improved after the spoofing reaches a certain size. Acknowledgments. The authors would like to thank the support of the National Key R&D Program of China (2022YFB3904302).

References 1. Li L, Liu X, Xiao W, et al (2020) Analysis on the influence of BeiDou satellite Pseudorange bias on positioning. In: 2020 IEEE 3rd international conference on information communication and signal processing (ICICSP). IEEE, pp 399–404 2. International Civil Aviation Organization. GNSS Manual Redlines_master v1.5 [EB/OL]. https://portal.icao.int/nsp/MeetingDocuments/GSWG4_wp7_DOC,2022-11-07 3. Humphreys TE (2013) Detection strategy for cryptographic GNSS anti-spoofing. IEEE Trans Aerosp Electron Syst 49(2):1073–1090 4. Wu Z, Zhang Y, Liu R (2020) BD-II NMA&SSI: an scheme of anti-spoofing and open BeiDou II D2 navigation message authentication. IEEE Access 8:23759–23775 5. Broumandan A, Jafarnia-Jahromi A, Daneshmand S, Lachapelle G (2016) Overview of Spatial Processing Approaches for GNSS structural interference detection and mitigation. Proc IEEE 104(6):1246–1257 6. Kujur B, Khanafseh S, Pervan B (2020) A solution separation monitor using INS for detecting GNSS spoofing. In: Proceedings of the 33rd international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2020). pp 3210–3226 7. Yu B-G, Bao Y-C, Yang M-H, Li J-J, Cui S (2022) Conceptual framework and research progress on communication and navigation integration. Navig Position Timing 9(02):1–14 8. Nie X, Zheng J, Fan B (2022) Study on development of technology path for LEO satellite navigation system. Spacecr Eng 31(1):116–124 9. Yin K, Li R, Wang C, Teng J (2022) Credibility research of BeiDou navigation satellites based on LEO constellation enhancement. In: Yang C, Xie J (eds) China satellite navigation conference (CSNC 2022) proceedings. CSNC 2022. Lecture notes in electrical engineering, vol 909. Springer, Singapore

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10. Psiaki ML (2021) Navigation using carrier Doppler shift from a LEO constellation: TRANSIT on steroids. Navigation 68:621–641 11. Chen J (2001) Research of GPS integrity augmentation. PLA Information Engineering University

Credibility Monitoring Research of BDS Based on LEO/INS Kai Yin1(B) , Rui Li1 , Zishan Zhao1 , and Qiuli Chen2 1 Beihang University, Beijing, China

[email protected] 2 China Academy of Space Technology, Beijing, China

Abstract. The reliability of satellites navigation system has always been the focus of international community, the risks of integrity and hostile interference are important factors affecting the reliability of airborne satellites navigation system. LEO satellites with advantages of running in low orbits, having rapid change of satellite geometry and strong anti-interference capability of satellite signal, can significantly enhance the credibility of BDS. But when most or even all satellites are spoofed, LEO satellites and BDS navigation system can hardly detect and recognize faults. Hence, we add inertial navigation system as an independent navigation source to the whole system and propose a credibility algorithm based on inertial navigation system, combining INS with all visible satellites to detect and recognize fault satellites in more directions, constructing chi-square test statistics based on the Kalman Filter innovation sequence on the basis of satisfying the need of integrity. The simulation results show that LEO/INS-aided system can detect and recognize fault satellites in more than one directions. Under the indexes of 90% integrity default detection rate and recognition rate, compared with single BDS system, the two indexes of the INS-aided system improve about 20% and 40% respectively. For hostile faults, the LEO satellites can significantly improve the anti-spoofing performance of integrated navigation system, the detection rate increases about 25% and the recognition rate increases more than 30%. Keywords: Low-earth-orbit satellite · Inertial navigation system · BeiDou navigation satellite system · Credibility monitoring

1 Introduction BeiDou-3 Navigation Satellite System (BDS-3) can provide positioning, navigation and timing services for China and even the world [1]. However, BDS-3 has problems such as weak landing signal and vulnerable to external spoofing and interference. In recent years, many experts and scholars at home and abroad have proposed a series of anti-spoofing technologies at the signal level, such as navigation signal authentication [2, 3], antenna array technology [4, 5], signal quality monitoring [6] and so on. We showed in prior work that a solution to improving credibility performance of navigation system with LEO based on Least Square range residual method in the information level [7], which demonstrated that LEO satellites can improve integrity and anti-spoofing performance © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 68–80, 2024. https://doi.org/10.1007/978-981-99-6932-6_6

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in single direction significantly. But with multi-directions spoofing, there would be limitations for LEO to detect and recognize fault navigation satellites. The above method did not consider the situation when the number of fault satellites is more than the correct ones, so that the correct information may be considered wrong to be excluded because of the poor amount of LEO which can hardly positioning independently. The advantages of Inertial Navigation System include that independence to external information, not being interfered by radio signals, and good robustness. It is highly complementary with satellite navigation system [8], and can provide more redundant information as an independent navigation source. However, its accuracy mainly depends on the inertial measuring device, and the position error will accumulate over time, so it is not suitable for long time independent navigation. Some scholars have studied Receiver Autonomous Integrity Monitoring (RAIM) method based on Kalman filter [9], and utilized redundant information provided by inertial navigation monitor spoofing of navigation satellites [10, 11]. Kalman sequential filtering uses historical information to derive the current optimal estimate value, which increases the judgment of historical information. While the traditional snapshot method RAIM can only use current information, which has limitations on fault detection and recognition. In this paper we propose a LEO/INS-aided chi-square distribution subset-separated detection algorithm based on Kalman filter innovation sequence to improve the credibility of the system in the scenario of large-scale navigation satellites spoofing monitoring, in which INS acts as an independent positioning source to provide independent and reliable positioning solutions in a short period of time, and LEO acts as a reliable navigation source to provide reliable redundant information.

2 Credibility Monitoring Algorithm 2.1 Kalman Filter Algorithm A discrete linear system is described by a process equation and a measurement equation: .

(1)

where Xk and Xk−1 are state variables in k and k − 1 epoch respectively; k|k−1 is the state transition matrix of the process model, k−1 is the input coefficient matrix, Wk−1 is process noise vector, Zk is the measurement vector, Hk is the observation matrix, and Vk is the measurement noise vector. Wk−1 and Vk are uncorrelated white Gaussian noise sequences. According to the estimated value of previous moment Xˆ k−1 and the measurement of k moment Zk , the optimal estimate of k moment Xˆ k can be obtained. Kalman filter process is as follows: State step prediction formula: Xˆ k/k−1 = k/k−1 Xˆ k−1

(2)

State step mean-square error formula: Pk/k−1 = k/k−1 Pk−1 Tk/k−1 + Qk−1

(3)

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Kalman gain formula: Kk = Pk/k−1 HkT [Hk Pk/k−1 HkT + Rk ]−1

(4)

State estimation formula: Xˆ k = Xˆ k/k−1 + Kk [Zk − Hk Xˆ k/k−1 ]

(5)

State estimation mean-square error formula: Pk = [I − Kk Hk ]Pk/k−1

(6)

2.2 Integrated Navigation System Design The state variables of the integrated navigation filter selects 12 dimensions, including three-dimensional user position error, three-dimensional speed error, three-dimensional platform angle error, clock bias, frequency offset and frequency drift: T  X = δλ δL δh δVe δVn δVu φe φn φu tu ˙tu ¨tu

(7)

LEO/BDS/SINS is tightly-coupled, using pseudorange difference ρ as the observation. ρi = ρˆi − ρi , ρˆi is the estimated pseudorange calculated by the user position output by INS at k time and the satellite position provided by the ephemeris, ρi is the observation pseudorange of visible star i. The Taylor expansion at the INS output value ru,k with only one-order term existing: xi,k − xu,k y − yu,k  ˆx +  i,k  ˆy ρi,k = ρˆi,k − ρi,k =  ri,k − ru,k  u,k ri,k − ru,k  u,k zi,k − zu,k  ˆz − ˆtu,k + (8) ri,k − ru,k  u,k    where ri,k − ru,k  = (xi,k − xu,k )2 + (yi,k − yu,k )2 + (zi,k − zu,k )2 is the real distance between user and satellites. Measurement formula at k epoch: ⎛ ⎞ 0 · · · 0 −1 0 ⎜ ⎟ H = ⎝A • N ... . . . ... ... ... ⎠ (9) 0 . . . 0 −1 0 where matrix A is cosine array in the unit vector direction of all visible satellites. ⎞ ⎛ ax1,k ay1,k az1,k ⎜ .. .. ⎟ (10) A = ⎝ ... . . ⎠ axi,k ayi,k azi,k y − yu,k xi,k − xu,k z − zu,k  , a  i,k  , a =  i,k  axi,k =  ri,k − ru,k  yi,k ri,k − ru,k  zi,k ri,k − ru,k 

(11)

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Noise of the system: W = ( 0 0 0 0 0 0 0 0 0 ωrx ωry ωrz ωax ωay ωaz )T

(12)

where ωri is the gyro drift rate of SINS; ωai is the accelerometer deviation. The error of the inertial navigation system mainly considers the position error (in Longitude-LatitudeAltitude coordinate system), speed error (in ENU coordinate system), and platform error (platform angle error in ENU coordinate system) caused by gyro drift and accelerometer zero bias. 2.3 Fault Detection Algorithm In the SINS/BDS tightly-coupled system, the filter detect the fault of BDS through the consistency verification between the observed pseudorange and the estimated pseudorange of each visible star, in which the estimated pseudorange is calculated by user position output from INS and the satellite position from ephemeris, even if the number of visible stars is less than 5, fault detection and recognition can be carried out. In the credibility monitoring of INS assisted BDS, Zˆ k = Hk Xˆ k/k−1 is the one-step state estimation measurement prediction value, which is the measurement prediction value obtained from multiplying the error state estimated value derived from the state update of the INS error propagation equation by the measurement array Hk , the prediction value of the pseudorange difference. The coupled SINS/BDS filter residual: rk = Zk − Hk Xˆ k/k−1

(13)

When no fault occurs, rk is a white noise sequence with zero mean and its variance is: Ak = Hk Pk/k−1 HkT + Rk

(14)

When one or more BDS satellites are faulty, it will be reflected in the change of measurement vector Zk , and the measurement prediction value Zˆ k is no longer an unbiased estimate of Zk , and rk is no longer zero-mean white noise, so it can be used to detect faulty stars and achieve fault detection. Constructing test statistic as: λk = rkT A−1 k rk

(15)

When there is no fault, λk follows the chi-square distribution of m freedom degree λk ∼ χ 2 (m), m is dimension of Zk , which means the number of BDS visible satellites participating in the BDS/SINS filter measurement update. The criteria to detect fault is: λk < TD indicates that no fault is detected; λk > TD indicates that a fault is detected and an alarm is generated. The detection threshold TD can be calculated by the false alarm probability PFA (Fig. 1).

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Fig. 1. Diagram of Chi-square test

Since the spoofing probability is unknown, we choose to design the parameters of Kalman filter according to the integrity requirements. According to the navigation performance requirements set by the International Civil Aviation Organization, the integrity risk of the non-precision approach stage is required to be 10–7 /h, the prior failure probability of a single satellite is 10–5 , and the alarm leakage rate is 10–3 . According to the Minimum Operating Performance Standards (MOPS) file, the false alarm rate PFA is set to be 3.33 × 10−7 . 2.4 Fault Recognition Algorithm The LEO constellation can improve the geometry of visible satellites, while INS provides an independent and reliable positioning source that enables the monitoring of faulty satellites in multi-directions. When there is no spoofing, RAIM eliminates spoofed and fault satellites through the idea of diversity. RAIM recognition algorithm is no longer applicable when multi-direction spoofing interferences exist. In this paper, drawing on the RAIM algorithm diversity idea, the recognition of faulty satellites is turned into the recognition of faulty satellites’ directions by dividing all visible satellites into four directions based on azimuth: northeast, northwest, southwest and southeast, with INS as an independent positioning source and LEO satellites as trusted navigation sources. Consistency verification between INS and visible BDS satellites in several directions is conducted until the directions of the faulty satellites are identified. The fault recognition algorithm is as follows: i. Test statistic T is conducted, if T < T D , it indicates that all visible satellites are normal and end the operation, otherwise fault exists, go to ii; ii. Judge if there exist LEO satellites, if none, go to iv; otherwise iii; iii. Combine INS with LEO satellites, construct observation and test statistic T, if T < T D , it indicates that LEO satellites are normal; otherwise LEO satellites have integrity faults and need to delete fault satellites; then v; iv. According to the azimuth, divide BDS visible satellites into four directions; v. Combine LEO satellites with BDS visible satellites in every direction and construct four subsets; make n = 1;

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vi. Combine INS with all the visible satellites (including BDS and LEO) in subset n (n = 1, 2, 3, 4) and construct observation and test statistics again for Chi-square detection based on residual; If T < T D , it shows that BDS satellites in this subset are normal, and sign them as normal satellites; otherwise, they are signed suspect; vii. Make n = n + 1, judge n value, if n Ti ∩ {qi,1  < Ti,1 ∩ qi,2  < Ti,2 ∩ . . . ∩ qi,j  < Ti,j ∩ . . . ∩ qi,h  < Ti,h , Sj  ⊂ Si }         |qi | > Ti ∩ {qi,1  > Ti,1 ∪ qi,2  > Ti,2 ∪ . . . ∪ qi,j  > Ti,j ∪ . . . ∪ qi,h  > Ti,h , Sj  ⊂ Si }

|q1 | > T1 ∪ |q2 | > T2 ∪ . . . ∪ |qh | > Th

Formulation

Table 1. FDE events describing.

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Furthermore, to make the continuity risk equation more rigorous, we will introduce two critical multipliers β and γ as in the prior research [14]. The multiplier β is introduced to account for the average number of aircraft simultaneously losing continuity due to using common navigation services. The multiplier γ is introduced to quantify the continuity loss due to multiple exposures to the same faults. Thus, Eq. (4) is further rewritten as: PFD ≤ β · γ ·

h 

PHi

(5)

i=1

where β = 3 and γ = 1.1 are assumed in this paper [14]. It is worth mentioning that, PHi used for integrity in Eq. (1) and for continuity in Eq. (2) are different. Because the integrity requirement is given in an approachspecific sense versus the continuity requirement in an average sense. Thus, a conversion is required for fault prior probabilities to fit different requirements, referring to [10, 13]. 2.2 The Need Analysis of Fault Exclusion for Dual-Constellation GPS/BDS The LPV-200 navigation performance requirements include the continuity requirement, the integrity requirement I req , the vertical alert limit, and the alert time (AT), as shown in Table 2 [3]. Among them, the overall continuity requirement is allocated to limit each term loss of continuity of Eq. (3), and the details are summarized in Table 3 [16]. Table 2. The LPV-200 navigation performance requirements. Requirement index

Value

Requirement index

Value

Continuity requirement

8 × 10–6

Vertical alert limit

35 m

Integrity requirement

2 × 10–7

Alert time

6s

Table 3. The continuity requirement allocations. PFA, req

PFD, req

Pother, req

2 × 10–6

5 × 10–6

1 × 10–6

To identify whether or not fault exclusion algorithms are needed for dualconstellation GPS/BDS, the relationship between the upper bound of PFD and the number of satellites is investigated for given prior probabilities of satellite fault Psat = 10–5 and constellation fault Pconst = 10–4 . And the mapping relation is illustrated in Fig. 1 according to Eq. (5). As revealed in Fig. 1, the upper bound of PFD is a monotonically ascending function of the number of satellites. Therefore, it implies that the overall continuity requirement

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may not be satisfied and fault exclusion algorithms will be required when the solid blue line is above the dashed black line. The number of satellites corresponding to the critical circumstance is equal to 17, called the critical satellite number. Unfortunately, it is quite likely that the number of visible satellites exceeds 17 for dual-constellation GPS/BDS, which happens 96.34% of the time of the day, as shown in Fig. 2. The simulation conditions are tabulated in Table 4. Thus, it is apparently essential to implement fault exclusion algorithms at the airborne receiver to enhance continuous navigation services.

Fig. 1. The mapping relation between the upper bound of PFD and the number of satellites.

Fig. 2. The number of visible satellites with time.

2.3 Integrity and Continuity Risk Considering FDE In the case of considering FDE, the complete description of integrity risk needs to accommodate all possible situations, where hazardous misleading information exists in

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the full-set position estimation solution and sub-set position estimation solutions after excluding satellite(s) under fault mode j. PHMI =

h 

P{|ε0 | > , ND|Hi }PHi +

i=0

h h      P εj  > , D, Ej |Hi PHi

(6)

i=0 j=1

The first right-hand side term in Eq. (6) is the same as the integrity risk in Eq. (1) for FD, and the second term corresponds to the integrity risk of performing fault exclusions. In parallel, the continuity risk is given to describe mission interruption occurrences when a fault is detected but can not be excluded. PLOC = P{D, NE |H0 }PH0 +

h 

P{D, NE |Hi }PHi + Pother

(7)

i=1

Comparing to Eq. (2), the continuity risk in Eq. (7) is lowered by performing fault exclusions. However, the expense of this reduction is expressed as the second right-hand side term in Eq. (6), which increases the integrity risk.

3 Integrity and Continuity Risk Bounds for FDE In this section, we focus on deriving the upper bounds on the integrity and continuity risk based on MHSS. Meanwhile, we introduce the PL as an alternative to evaluate the integrity risk and allocate the continuity requirement between FDE tests for each fault hypothesis using the critical parameter. 3.1 Integrity Risk Evaluation Integrity risk evaluation directly using Eq. (6) is challenging, because it is complicated and computationally intensive to formulate the joint distribution of estimation errors. Moreover, there is a correlation between the estimation errors and the FDE test statistics in the joint probabilities [15]. In response, an upper bound for PHMI is derived in Appendix A in [15] to prevent the excessively computational load and overcome correlations. The resulting integrity risk bound is given by: PHMI ≤ P{|ε0 | > |H0 }PH0 +

h 

P{|εi | + Ti > |Hi }PHi

i=1

+

h     P εj  > |H0 PH0 j=1

+

h h   j=1 i=1 Si ⊂Sj

h h         P εj  > |Hi PHi + P εj,i  + Tj,i > |Hi PHi j=1 i=1 Si ⊂Sj

(8)

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where the first two right-hand side terms are the upper bound of PHMI for FD. The distribution of each term right-hand side term in Eq. (8) under the specific fault hypothesis is known, and can be expressed as:  PHMI ≤ 2Q

     h h     − Ti  2Q 2Q PH0 + PHi + PH0 σ0 σi σj i=1

+

h 

h 

j=1 i=1 Si ⊂Sj

j=1

   h h    − Tj,i  PHi + PHi 2Q 2Q σj σj,i 

(9)

j=1 i=1 Si ⊂Sj

where Q(∗) = 1 − (∗), and (∗) is the standard normal cumulative distribution function (CDF); σ0 and σi represent the standard deviations of the full-set positioning estimation error and sub-set positioning estimation errors respectively; T i and T j,i designate detection and exclusion thresholds respectively, which will be described in the next subsection. As one can see from Eq. (9) that the upper bound of PHMI is related to only the second and fifth right-hand side terms for given  and simulation conditions. In other words, it is related to only the detection and exclusion thresholds. Interestingly, the second and fifth terms are monotonically ascending functions of T i and T j,i , respectively. To meet the integrity requirement, a commonly adopted approach is to compute a position error bound called the protection level such that the actual position would fall within the bound with sufficient probability. The protection level can be calculated by displacing l with PL in Eq. (9) and then bound the probability of HMI with I req, q . PHMI ≤ Ireq,q − PNM

(10)

where I req, q is the integrity requirement allocated to the direction of interest ‘q’; PNM is the prior probability of very rarely occurring faults that do not require monitoring. 3.2 Continuity Risk Allocation For FD, the continuity requirement is generally allocated to limit the probability of false alarms, such that the overall continuity requirement may not be guaranteed. In response, we provide an allocation scheme ensuring to satisfy the overall continuity requirement based on the parameter in [15]. Primarily, an upper bound on the probability of LOC derived in Appendix B in [15] is given by: PLOC − Pother ≤

h 

P{|qi | > Ti |H0 }PH0

i=1

+

h h   j=1 i=1 Si ⊂Sj

   P qj,i  > Tj,i |Hi PHi ≤ Creq − Pother

(11)

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The second part of this inequality indicates that the probability of LOC due to FDE under each fault hypothesis composes a large fraction of the continuity requirement, except for the Pother . Hence, the C req − Pother can be allocated equally to each fault hypothesis: P{|qi | > Ti |H0 }PH0 +

h 

    P qj,i  > Tj,i |Hi PHi ≤ Creq,i , Creq,i = Creq − Pother /h

i=1 Si ⊂Sj

(12) Actually, the C req, i can be further allocated to detection and exclusion tests through a parameter λ: P{|qi | > Ti |H0 }PH0 ≤ Creq,i,d = λ · Creq,i , h 

   P qj,i  > Tj,i |Hi PHi ≤ Creq,i,e = (1 − λ) · Creq,i

(13)

i=1 Si ⊂Sj

Then, the detection and exclusion thresholds can be determined according to Eq. (13):  

 Creq,i,e −1 Creq,i,d 2 −1 σ i , Tj,i = Q σ2 Ti = Q (14) 2PH0 2(h − 1)PHi j,i where Q−1 (∗) is the inverse tail probability distribution of the two-tailed standard normal distribution; σ 2 i and σ 2 j,i are the standard deviations of the solution separation. According to Eq. (14), we can find that the detection threshold T i is a monotonically descending function of λ, while the exclusion threshold T j,i is a monotonically ascending function of λ. Meanwhile, reviewing the relationship between the upper bound of PHMI and T i and T j,i discussed in Sect. 3.1, we can further conclude that there must exist a λ that minimizes the upper bound of integrity risk, or equivalently the minimum PL. The critical parameter λ will be determined in the subsequent section.

4 Performance Evaluation In this section, we design two experiments based on real GPS and BDS ephemeris data. The goal of the first experiment is to determine the range of the parameter λ The second experiment is conducted to demonstrate the effect of the determined λ on ARAIM availability. 4.1 Simulation Conditions Setting In this paper, simulation parameters needed to carry out two experiments are described in Table 4, where real satellite navigation files and observation data are collected from 00:00:00 to 23:59:59 on February 13, 2022 at a 1 Hz sampling rate, thereby obtaining altogether 86,400 epochs.

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Parameter

Value

Parameter

Value

Constellation GPS + BDS Psat

1 × 10–5

Mask angle

7°

Pconst

1 × 10–4

VAL

35 m

Sampling site

39.9598°N, 116.3152°E, Altitude 58 m

Vertical I req

1 × 10–7

Sampling period

00:00:00 to 23:59:59 on February 13, 2022

PNM

9 × 10–8

Sampling frequency 1 Hz

Meanwhile, in this paper, the residual tropospheric error, receiver noise, multipath error and user range accuracy from navigation files are taken into consideration as the pseudo-range errors. These errors are modelled to obey the elevation-related Gaussian distributions, as listed in Table 5 [9]. Table 5. Prior error models for pseudo-range. Error Residual tropospheric error

Standard deviation of error (m)

1/2 0.12 × 1.001/ 0.002001 + sin2 θ

Receiver noise

0.15 + 0.43e−θ/6.9

Multipath error

0.13 + 0.53 × e−θ/10

User range accuracy for integrity

2.4

User range error for continuity

1.6

*θ represents the elevation angle.

4.2 Parameter Determination The current experiment determines the range of the parameter λ by a numerical method. To make the parameter more accurate, we calculate the integrity risk for given different λ, which increases from 0 to 1 with a step of 0.01. Then, the λ corresponding to the minimum integrity risk is found. The above processes are repeated at each epoch, and the final statistical results are presented in Fig. 3. The left and right vertical axes in Fig. 3 can be regarded as the probability density and cumulative probability density, respectively. As illustrated in Fig. 3, the minimum integrity risk obtained at different epoch maybe correspond to different λ, however, these λ do not surpass 0.46. In addition, it is clear from Fig. 3 that a majority of optimal λ is within the scope of 0.3 with the percentage of 93.65%. Therefore, we can deem that the integrity risk or equivalently the PL is approximatively minimum corresponding to the range of 0–0.3 for 24 h. To further clarify the influence of λ within 0.3 on the integrity risk, we investigate the relationship

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between the integrity risk and the parameter λ, where λ are valued to 0.05, 0.15, and 0.25, respectively. The mapping relation is plotted in Fig. 4.

Fig. 3. The number of minimum integrity risk with λ.

Fig. 4. The mapping relation between the integrity risk and λ.

As can be seen from Fig. 4, differences in the integrity risk are negligible when λ are equal to 0.05 and 0.15 respectively. However, the integrity risk increases obviously when λ equals to 0.25. Thus, the final determined λ can be assigned to 0.05 or 0.15. 4.3 Availability Analysis Availability refers to the proportion of time when integrity and continuity requirements are simultaneously satisfied, i.e., while meeting the continuity requirement, the percentage of time that PL does not exceed AL. In the present experiment, PLs in the vertical direction computed using λ = 0.15 and λ = 0.50 are compared with VAL for 24 h to demonstrate the significant improvement of the determined parameter in availability. Meanwhile, the VPLs calculated using

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ARAIM for detection only are displayed to validate the reduction of ARAIM considering exclusion in availability. The resulting VPL curves are depicted in Fig. 5 and the availability of different methods is summarized in Table 6. As shown in Fig. 5 and Table 6, differences in availability are obtained for FD versus FDE when using dual-constellation GPS/BDS ARAIM to achieve the LPV-200 performance requirements. Despite the most availability of 96.26%, ARAIM for FD remains vulnerable to the continuity requirement so that causes unacceptable service outage periods. On the contrary, ARAIM for FDE when λ is equal to 0.50 offers only 83.48% overall availability in spite of meeting the continuity requirement. In contrast, ARAIM for FDE when λ is equal to 0.15 is a better compromise, which provides more availability of 88.70% and continuous navigation services.

Fig. 5. The VPL comparisons for different methods.

Table 6. The availability of different methods. Method

Availability (%)

Average VPL (m)

Improvement in availability (%)

Satisfy the C req

ARAIM for FD

96.26

22.45

12.78

Uncertain

ARAIM for FDE λ = 0.15

88.70

25.46

5.22

Yes

ARAIM for FDE λ = 0.50

83.48

27.17

0

Yes

5 Conclusion In the multi-constellation global navigation satellite system, the increased likelihood of faults due to the large number of satellites can be a real issue demanding prompt solutions, which will cause more mission interruptions. In response, this article analyses the need

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of fault exclusions for dual-constellation GPS/BDS based on the LPV-200 navigation performance requirements, meanwhile, determines the satellite number corresponding to the critical case. Then a critical parameter is introduced in the advanced receiver autonomous integrity monitoring (ARAIM) algorithm considering both fault detection and exclusion to enhance the overall navigation service performance. A continuity budget allocation scheme is developed based on the proposed parameter. This scheme not only satisfies the continuity requirement but also minimizes the integrity performance sacrifices. Simulation results suggest that: (1) comparing the ARAIM for fault detection only, the ARAIM algorithm based on the determined parameter can ensure to meet the continuity requirement; (2) comparing the ARAIM in [15], the ARAIM algorithm based on the determined parameter achieves a 5.22% improvement in availability.

References 1. Bijjahalli S, Sabatini R, Gardi A (2020) Advances in intelligent and autonomous navigation systems for small UAS. Prog Aerosp Sci 115:100617 2. Song D, Shi C, Wang ZP et al (2020) Correlation-weighted least squares residual algorithm for RAIM. Chin J Aeronaut 33(5):1505–1516 3. ICAO, Annex 10, Aeronautical telecommunications, vol 1 (radio navigation aids). https:// www.pilot18.com/icao-annex-10-telecommunication/. Last accessed 26 April 2022 4. Joerger M, Langel S, Pervan B (2016) Integrity risk minimisation in RAIM Part 2: Optimal estimator design. J Navig 69(4):709–728 5. Liu BY, Gao Y, Gao YT et al (2022) HPL calculation improvement for Chi-squared residualbased ARAIM. GPS Solut 26(2):1–13 6. Blanch J, Walter T (2020) Fast protection levels for fault detection with an application to advanced RAIM. IEEE Trans Aerosp Electron Syst 57(1):55–65 7. El-Mowafy A, Yang C (2016) Limited sensitivity analysis of ARAIM availability for LPV-200 over Australia using real data. Adv Space Res 57(2):659–670 8. Milner C, Pervan B (2020) Bounding fault probabilities for advanced RAIM. IEEE Trans Aerosp Electron Syst 56(4):2947–2958 9. Blanch J, Walker T, Enge P et al (2015) Baseline advanced RAIM user algorithm and possible improvements. IEEE Trans Aerosp Electron Syst 51(1):713–732 10. Joerger M, Zhai YW, Martini I et al (2020) ARAIM continuity and availability assertions, assumptions, and evaluation methods. In: Proceedings of the 2020 international technical meeting of the Institute of Navigation, pp 404–420 11. Zhai YW, Zhan XQ, Joerger M et al (2019) Impact quantification of satellite outages on air navigation continuity. IET Radar Sonar Navig 13(3):376–383 12. Blanch J, Walker T, Enge P (2010) RAIM with optimal integrity and continuity allocations under multiple failure. IEEE Trans Aerosp Electron Syst 46(3):1235–1247 13. Li L, Wang H, Jia C et al (2017) Integrity and continuity allocation for the RAIM with multiple constellations. GPS Solut 21(4):1503–1513 14. Zhai YW, Joerger M, Pervan B (2015) Continuity and availability in dual-frequency multiconstellation ARAIM. In: Proceedings of the 28th international technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2015), pp 664–674 15. Joerger M, Pervan B (2016) Fault detection and exclusion using solution separation and chi-squared ARAIM. IEEE Trans Aerosp Electron Syst 52(2):726–742 16. Zhai YW, Joerger M, Pervan B (2018) Fault exclusion in multi-constellation global navigation satellite systems. J Navig 71(6):1281–1298

A Coupled RTK/INS Positioning Method Based on Robust Estimation Huizhen Yu1 , Xianliang Teng2 , Shuguo Pan1,2(B) , Min Zhang2 , Jian Shen2 , and Wang Gao1 1 School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China

[email protected]

2 State Key Laboratory of Smart Grid Protection and Control, Nari Group Corporation,

Nanjing 211106, Jiangsu, China [email protected]

Abstract. In the urban environment, the positioning results of RTK/INS integrated navigation are often influenced by grosses, which degrades the positioning accuracy and damages the stability of the navigation system. To solve this dilemma, a loose coupled RTK/INS positioning method based on robust estimation is proposed. Firstly, during RTK positioning, for eliminating corrupted measurements caused by Non-Line-of-Sight (NLOS) signals and multipath, this paper researches the RTK positioning algorithm based on bifactor robust estimation. In this method, the ambiguity is fixed and solved back into the Double-Difference (DD) equation in least square model. The posterior residual vector is used for the bifactor robust processing to eliminate the influence of some abnormal observations. Then, the RTK positioning results are loosely integrated with Inertial Navigation System (INS), and the robust processing based on Huber equivalent weight function is implemented in the process of the Kalman filter update. Finally, the proposed algorithm is validated by vehicle data in a typical urban environment. The experimental results show that compared with the traditional least squares-based RTK, the accuracy of the bifactor RTK method is improved by 2.48 cm in the horizontal direction. Meanwhile, in contrast with the RTK/INS method based on the single robust processing, the accuracy of the proposed robust bifactor error method in the horizontal direction is increased by 3.85 cm. The navigation accuracy and reliability are significantly enhanced. In dynamic environment, this research has certain theoretical reference and practical value for vehicular and autonomous driving applications. Keywords: RTK/INS · Kalman filter · Bifactor processing · Loose coupled · Huber equivalent weight function

1 Introduction Global Navigation Satellite System (GNSS) can provide Position Navigation and Timing(PNT) services globally. Using GNSS carrier phase observations, the Real-Time Kinematic (RTK) can realize centimetre-level positioning accuracy. Inertial Navigation © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 94–104, 2024. https://doi.org/10.1007/978-981-99-6932-6_8

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System (INS) with high updating frequency has strong autonomy and cannot be disturbed by the external environment. The above two systems can complement each other effectively, which is a hot research in the field of navigation. In the urban environment, GNSS signals are easy to be interfered by Non-Line-ofSight (NLOS) and multipath signals, which causes gross errors in the observed values and further the deviation of the least square estimation [1, 2]. The appearance of gross error could seriously affect the accuracy of position and velocity for RTK solution, and it can also further influence the reliability of integrated navigation solutions. It has always been the focus of scholars to deal with the gross error of the observed value and the result. Robust estimation is an effective method [3]. Reference [4] has introduced a series of IGG robust estimation methods. Yang et al. proposed a bifactor robust estimation method, which constructs a bifactor equivalent weight by the function of variance expansion function and weight factor contraction function. It not only keeps the symmetry of the equivalent weight matrix as well as the covariance matrix, but also the correlation of the original noise covariance matrix. Aimed at correlated observations, the mentioned robust estimation method above is classical at present. Reference [6] presented an improved algorithm for bifactor robust estimation of relevant observations. When the gross is less, this method can still increase the calculation efficiency except for maintaining the accuracy of parameter estimation. Based on the IGG-III function, Ref. [7] researched an equivalent weight function with adaptive thresholds, which has stronger resistance and better reliability than the equivalent weight method with artificial settings of critical ones. For GNSS/INS integrated navigation, Kalman filter has been maturely applied and developed due to its significant real-time property. However, the interface of observation often leads to the divergence of filter and the failure of the fusion system. To solve the above problems, Ref. [8] introduced the extended robust Kalman filter (EKF) based on innovation chi-square test, which can still work when there is no observation redundancy. By constructing an adaptive factor based on predictive residual, Ref. [9] proposed a RTK/INS tight integrated algorithm based on robust Kalman filter, and validated that the navigation accuracy and reliability of the algorithm were significantly improved. The above algorithms are only used in the process of GNSS observation or integrated navigation. However, in the loose GNSS/INS integration, the position and velocity are usually used as rather than the original observed values. Therefore, the gross error interference cannot be suppressed specifically. In addition, aimed at the robust Kalman filter, sufficient normal observation is a necessary prerequisite for the effective implementation of robust estimation. For this, to solve the problem of observation deviation caused by NLOS signal and multipath effect in the process of RTK positioning, this paper firstly studies the bifactor robust RTK positioning. Then, based on the correlated least model after the fixed ambiguity solution, this method uses the posterior residuals to perform the bifactor operation, to eliminate the influence of some abnormal observations. Then, the RTK localization results were integrated with INS loosely, and the Huber equivalent weight function was applied to the update process of Kalman filtering. Thus the accuracy and reliability of integrated navigation and positioning results are further enhanced. Finally, the effectiveness and superiority of the proposed method are verified by the positioning results and comparative experimental analysis in real test.

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The structure of the paper is as follows: in the second part, the introduces the basic theory of robust RTK was introduced; The third part introduces the robust Kalman filtering algorithm; The fourth part is the experimental results and analysis of the measured data. The fifth part gives the conclusion of the article.

2 The Basic Theory of Robust RTK 2.1 Mathematical Model of RTK RTK positioning is a high precision positioning technology in the satellite navigation system. It mainly uses the carrier phase for relative differential positioning and can also carry out real-time dynamic positioning. The original pseudorange and carrier non-difference non-combination observation equations of receiver m for satellite i are:  i i i + c(δtrm − δtsi ) − Vionim − Vtropm + ερmi ρm = Pm (1) i i i i λϕm = Pm + c(δtrm − δtsi ) + Vionm − Vtropm − λNmi + ερmi where ρ is pseudorange observation value, ϕ is the carrier phase observation value (less than one circle), P is the geometric distance between the receiver and the satellite, δtr and δts represent the receiver and satellite clock difference, Vion and Vtrop represent ionospheric and tropospheric corrections, N is the ambiguity of the whole circle, ε is observation noise, λ represents the carrier wavelength, c is the speed of light. The single difference between the station and the reference station n can eliminate the satellite clock difference and reduce the ionospheric and tropospheric errors. ⎧ i,j i,j ⎨ ∇ρm,n = ∇Pm,n + ερ i,j m,n (2) i,j i,j i,j ⎩ λ∇ϕm,n = ∇Pm,n + λ∇Nm,n + ερ i,j m,n

where ∇ represents the double difference operator. Equation (3) was linearized to obtain the ambiguity solution, and then the ambiguity can be fixed by the LAMBDA algorithm [12]. Finally, the fixed ambiguities are substituted back to obtain the positioning results of RTK, and then the high precision position and velocity solution results are calculated. However, because of the dynamic environment and the external interference, the observation of RTK is easy to produce the gross error, which can affect the accuracy of positioning results. The effective control of gross error is a necessary step to ensure the reliability of GNSS positioning results. After fixed ambiguity is solved and substituted, the DD equation is: lk = Ak xk + εk

(4)

where lk stands for double difference observation, Ak represents the coefficient matrix, εk is the noise vector, the noise covariance matrix is represented by matrix Clk , xk is the parameter vector.

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Under the least squares estimation, the state and error covariance matrices are: −1  ATk Clk lk xk = ATk Clk Ak

(5)

−1  Qxˆ k = ATk Clk Ak

(6)



The residual νk and its covariance Qvk are: −1 −1   ATk Clk lk − ATk Clk Ak ATk Clk Ak xˆ k vk = lk − Ak xk = ATk Clk Ak

−1  T T = εk I − Ak Clk Ak Ak Clk 

 −1 T if S = I − ATk Clk Ak Ak Clk , then:     Qvk = E vkT vk = E S T εkT εk S T   = S T E εkT εk S = S T Qεk S

(7)

(8)

Bifactor robust estimation is to construct an equivalent weight matrix for outlier processing. The variance-covariance matrix Dxˆ and the weight matrix Clk = (D/σ02 )−1 are symmetrically positive definite off-diagonal matrices. σ02 is the variance factor. Thus, the posterior variance-covariance matrix Dxˆ of parameter estimation can be approximately expressed as: −1  σˆ 02 Dxˆ = ATk Clk Ak

(9)

The estimation of the different factors in the equation σˆ 02 is: vT Clk v r

σˆ 02 =

(10)

where r is the number of redundant observation. Its bifactor equivalent weight matrix is: ⎡

p11 γ11 p12 γ12

   ⎢ ⎢ p21 γ21 p22 γ22 P = pij = pij γij = ⎢ . .. ⎣ .. . pn1 γn1 pn2 γn2

⎤ · · · p1n γ1n · · · p2n γ2n ⎥ ⎥ .. ⎥ .. . . ⎦

(11)

· · · pnn γnn

where, pij and P ij are weight elements in row i, column j of weight matrix P and equivalent weight P, respectively; γij =

√

γii γjj

(12)

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where γii and γjj are adaptive weight reduction factors, and Huber function and Hampel function can be used to obtain the corresponding weight. In this paper, the IGG-III equivalent weight function is used: ⎧ 1, ⎪ ⎪   |vi /σi | ≤ k0 ⎨ k0 k1 − |vi /σi | 2 γij = (13) , k0 < |vi /σi | ≤ k1 ⎪ k1 − k0 ⎪ |vi /σi | > k1 ⎩ |vi /σi | 0, where vi /σi is the standardized residual of the ith observation value; k0 and k1 are the corresponding critical  values,  which need to be determined according to the application scenario, and k0 ∈ 2.0 3.0 , k1 ∈ 4.5 8.5 . The state and residual after the bifactor robust estimation is: −1  AT Pl (14) xˆ = AT PA v = Aˆx − l

(15)

3 Robust Kalman Filtering Algorithm 3.1 Mathematical Model of RTK/INS Coupled Navigation Integrated navigation refers to the combination of two or more kinds of navigation systems with different characteristics. This can achieve the complementation. Finally, the system with high precision, strong stability, continuous positioning and high robustness is achieved. In RTK/INS integrated navigation, 15-dimensional state parameters are often used to construct state model, which are expressed as follows:   (16) Xk = δφ, δν, δp, ∇a , ∇g where δφ, δν and δp are attitude, velocity, and position of eastern, northern, and upward (NEU) directions. ∇a , ∇g denote the accelerometer and gyro bias vectors. The state equation and linearized observation equation in discrete form are shown as follows, respectively.  Xk = k/k−1 Xk−1 + Wk−1 (17) Zk = Hk Xk + Vk where Xk is state vector at epoch k. k/k−1 represents state transition matrix from epoch k − 1 to k. Zk is measurement vector. Hk denotes linearized relationship between state Xk and measurement Zk . Wk and Vk are process noise vector and measurement noise vector, and Qk and Rk are associated covariance matrixes, respectively.

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Extended Kalman Filter (EKF) in discrete form consists of two core steps of prediction and update: ⎧ Xˆ k/k−1 = k/k−1 Xˆ k−1 ⎪ ⎪ ⎪ ⎪ T ⎪ ⎪ ⎪ Pk/k−1 = k/k−1 Pk−1 k/k−1 + Qk−1 ⎪ ⎪  −1 ⎨ Kk = Pk/k−1 HkT Hk Pk/k−1 HkT + Rk (18) ⎪ ⎪ ⎪ ⎪ Pk = (I − Kk Hk )Pk/k−1 ⎪ ⎪ ⎪   ⎪ ⎪ ⎩ Xˆ = Xˆ ˆ k/k−1 k k/k−1 + Kk Zk − Hk X where Kk is Kalman gain matrix, which is computed by predicted error covariance matrix Pk/k−1 , measurement matrix Hk and covariance matrix Rk of noise Vk ; Xˆ k/k−1 is predictive state vector; Xˆ k−1 and Xˆ k are the state estimation results of epoch k − 1 and epoch k respectively. Pk−1 and Pk are the state estimation covariance matrix of epoch k − 1 and epoch k respectively; I is the identity matrix. 3.2 Robust Kalman Filter Based on Innovation In the Kalman filtering, the innovation δrk is defined as the difference between the predicted value of the state and the current measured value. Its expression is as follows: δrk = Zk − Hk Xˆ k,k−1

(19)

Theoretically, the innovation is a white noise sequence, which follows a normal distribution with a mean of zero.  (20) δrk ∼ N 0, Hk Pk,k−1 HkT + Rk Let Jk = Hk Pk,k−1 HkT + Rk , take the test statistic as Tk , so: δγk(ii) Tkii =  Jk(ii) where the subscript ii represents the diagonal element in the matrix. The adaptive factor α is as follows:    1,   T k,i  ≤ TD αii = TD /Tk,i  , Tk,i  > TD

(21)

(22)

where TD denotes the boundary conditions where outliers occur. Compared with traditional EKF, the original filtering gain of robust Kalman filter is updated as follows:  −1 1 T T K k = Pk/k−1 Hk Hk Pk/k−1 Hk + Rk (23) α where K denotes robust Kalman filter gain. A flowchart of the proposed RTK/INS positioning method based on robust estimation in this paper is as follows, the general steps include:

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1. According to the presudorange and carrier received, based on the DD equation, the fixed ambiguity solution is obtained; 2. The fixed ambiguities are substituted back into the observation Eq. (4), and Eqs. (5)– (15) are used for bifactor robust estimation; 3. The position and velocity of the RTK is provided, respectively; 4. The above RTK solution is fused with data of inertial system by Kalman filtering; 5. In the updating process of Kalman filter, the adaptive robust factor is constructed by the innovation, and the new filtering gain is calculated; 6. Finally, reliable integrated navigation results are given (Fig. 1).

Fig. 1. A flowchart of the proposed RTK/INS positioning method based on robust estimation

4 Analysis of Experimental Results 4.1 Experimental Environment To verify the effectiveness of the proposed algorithm, this paper implemented a group of vehicle integrated navigation experiments and real test was collected around Jiulong Lake Campus of the Southeast University. The data started at about 14:00 pm on April 29, 2022. The original satellite signals were collected by UM482. The bias of the gyro and accelerometer bias are√2.3◦ /h and 1 mg,√and the random walk coefficient of gyro and accelerometer are 0.13◦ / h and 0.05 mg/ Hz, respectively. The sampling frequency is 100 Hz. The GPS, BDS and Galileo are used, and the cut-off angle of the satellite is 15°. In the bifactor robust IGG-III weight function, the value of k0 is 2.0, and the value of k1 is 5.0. In the robust Kalman filter the threshold value of TD is 2.5. The overall experimental trajectory is shown in Fig. 2. Figure 3 shows the change of the visible satellites in the process of dynamic test. Among them, the number of satellites varies dramatically from 200 to 400 s, because GNSS signals are blocked by urban trees and other obstacles. This leads to some gross errors in the original GNSS observations. In the LAMBDA algorithm, when the Ratio value is 2.5, the fixed rate is 88%. For evaluating the algorithm correctly, this paper uses the calculation results of Inertial Explorer 8.7 as the standard.

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Fig. 2. The trajectory of the real test in the dynamic environment

Fig. 3. The evolution of visible satellite number

4.2 Analysis of Experimental Results To illustrate the superiority of the bifactor robust RTK positioning algorithm, this paper firstly uses the traditional least square RTK algorithm and the bifactor robust RTK algorithm to process the original satellite observation data, respectively. Scheme 1 is the result of traditional least square RTK fixed solution; Scheme 2 is the result of the bifactor robust RTK algorithm; Scheme 3 is the result integration of traditional least square RTK and INS by EKF; Scheme 4 is the integration result of bifactor robust RTK and INS by EKF. In the figure, they are respectively represented by M1, M2, M1–1, and M2–1. The position errors of eastern (E) and northern (N) directions are shown in Fig. 4, and the Root Mean Square (RMS) errors are depicted in Table 1. Figure 4 shows the comparison of positioning errors between classical RTK and bifactor robust RTK algorithm. The RTK positioning errors were kept within 5 cm during most of the running time. In particular, from 325 to 335 s, the error is the largest and its amplitude is about 1 m, compared with other epochs. In the 200 to 300 s and 380 to the 450 s, there has a decimeter error, the range within 20 cm. However, the method researched in this paper can obviously eliminate this terrible situation. Since the bifactor robust estimation can identify the gross error and de-weight or even zero weight processing. Within 325–335 s, the positioning accuracy is improved significantly. Similarly, the bias is almost completely eliminated within 200–300 s and 380 to 450 s. Further, it can be seen from Table 1 that the RMS of positioning errors in the eastern and northern directions are decreased from 0.092 m and 0.0458 m to 0.0629 m and 0.0361 m, respectively. The statistical results further show the superiority of bifactor robust RTK.

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Fig. 4. The position error of M1 and M2 Table 1. The comparison on RMS between M1 and M2 Direction

M2–1

M2–2

Accuracy improvement

E/m

0.092

0.0692

0.0228

N/m

0.0458

0.0361

0.0097

Fig. 5. The position error of M1–1 and M2–1

Figure 5 shows part of the positioning results from the EKF-based classical RTK and bifactor robust RTK integrated with INS, respectively. The figure shows that bifactor robust RTK can effectively reduce the influence of gross errors from GNSS on integrated navigation results. 4.3 Comparison of Classical Kalman and Robust Kalman Filter In this part, to elaborate the effectiveness of the proposed algorithm, the traditional Kalman filter and robust Kalman filter were used for GNSS/INS integrated navigation

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data. The RTK results after bifactor robust processing were fused with INS based on EKF and robust EKF, respectively. Compared with the results obtained by scheme 4, the scheme 5 is referred to the integration between bifactor robust RTK and INS based on the robust EKF and represented by M2–2. Figure 5 shows the comparison results of the above methods (M2–1 and M2–2). As seen from the figure, most of the positioning errors from the traditional loose integration based on EKF are limited within 0.5 m. On the contrary, the error of the robust EKF has been reduced to a certain extend. The proposed method has obvious advantages, especially between the 250 and 450 s. Because the variance inflation factor based on the standard innovation can further effectively control the influence of gross errors, and improve the integration positioning performance. In the eastern and northern directions, the Table 2 shows the RMS comparison between the positioning results of scheme 4 and scheme 5. Compared with scheme 4, the presented method has the improvement with the amplitudes of 2.48 cm and 2.94 cm, respectively. Table 2. The comparison on RMS between M2–1 and M2–1 Direction

M2–1

M2–2

Accuracy improvement

E/m

0.1677

0.1429

0.0248

N/m

0.1946

0.1652

0.0294

Combining the experiment 1 and experiment 2, the double robust strategies effectively suppress the effect of gross error on integrated navigation results, and the superiority of the proposed algorithm is verified (Fig. 6).

Fig. 6. The position error of M2–1 and M2–2

5 Conclusion In challenging environment, gross errors will disturb positioning reliability in integrated navigation. Therefor, this paper firstly studies the bifactor robust RTK algorithm. Then, based on Kalman filter, it is integrated with the position information of the INS, and the

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reliability of integrated navigation results is further improved by constructing adaptive innovation-based robust factor. The effectiveness and superiority of the algorithm are verified by the real test. The experimental results showed that, compared with the classical RTK algorithm, the RMS of the bifactor RTK algorithm was improved by 2.28 cm and 0.97 cm in the eastern and the northern direction, respectively. In contrast with the coupled navigation result from single robust EKF, the RMS of the double robust result is improved by 2.48 cm and 2.94 cm in the eastern and northern direction, respectively. The proposed method can reduce the gross error in RTK solution and improve the positioning accuracy of the integrated system. Acknowledgments. This work was supported by the Science and Technology Project of State Grid Corporation of China under Grant No. 5700-202140340A-0-0-00.

References 1. Amiri-Simkooei A (2003) Formulation of L1 norm minimization in Gauss-Markov models. J Surv Eng 129(1):37–43; 2(5):99–110 (2016) 2. Peng J, Li S, Shi Y et al. The mean squares error matrix of inequality constrained M estimate and the conditions for improving solutions. Acta Geodaetica et 3. Song L, Yang Y (1999) Discuss of gross error correction and elimination. Bull Surv Mapp 6:5–6 4. Yang Y (1993) Robust estimation and application. Bayi Press, Beijing 5. Yang Y, Ren X, Xu Y (2013) Main progress of adaptively robust filter with applications in navigation. J Navig Position 1(01):9–15.https://doi.org/10.16547/j.cnki.10-1096,2013. 01.006 6. Chen J, Shen Y (2020) An improved robust estimation algorithm for correlated observations. J Geodesy Geodyn 40(05):507–511. https://doi.org/10.14075/j.jgg.2020.05.013 7. Jiang C, Zhang S, Zhang Q (2017) Equivalent weight function and robust estimation method with adaptive criterion. J China Univ Min Technol 46(04):911–916. https://doi.org/10.13247/ j.cnki.jcumt.000714 8. Miao Y, Zhou W, Tian L, Cui Z (2016) Extended robust Kalman filter based on innovation chi-square test algorithm and its application. Geomat Inf Sci Wuhan Univ 41(02):269–273. https://doi.org/10.13203/j.whugis20130666 9. Chu C, Huang L, Du Z, Ye S (2019) Application of robust estimation in RTK/INS tightlycoupled algorithms. GNSS World China 44(05):18–25. https://doi.org/10.13442/j.gnss.10089268.2019.05.003 10. Skaloud J, Meurer M, Crespillo OG, Medina D (2018) Tightly coupled GNSS/INS integration based on robust M-estimators. In: 2018 IEEE/ION position, location and navigation symposium (PLANS) 11. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy (Print) 70(1–2):65–82

Optimal Allocation Method of Integrity Risk Indicator for Multiple Risk Sources in PPP-RTK Fengze Du, Liang Li, Ruiji Li(B) , and Qiwei Ye College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China [email protected]

Abstract. The application of PPP-RTK technology in life safety-related fields has strict requirements for accuracy and integrity, requiring the construction of a complete monitoring and control system for multiple risk sources. Aiming at the lack of authoritative indicator system for multiple risk sources of PPP-RTK integrity services, as well as the traditional average allocation and proportional allocation based on empirical data, which fails to fully consider the needs of various risk source integrity risk indicators, resulting in the difficulty of ensuring the availability of overall monitoring of risk sources, this paper proposes an optimal allocation method for multiple risk source integrity risk indicators for PPP-RTK integrity services. Based on the theory of multiple hypothetical solution separation, this method obtains multiple risk source integrity risk indicators by assigning and adjusting the risk indicators of the integrity of various risk sources to make the virtual protection level of the positioning domain equal. Simulation experiments show that compared with the traditional method, this method realizes the construction of multiple risk source index systems that match the requirements of risk source integrity indicators. At the same time, this paper tests the availability of risk source integrated monitoring by 1 times, 1.5 times and 2 standard deviations, and the results show that the availability of the proposed method is increased by 1.38%, 9.75% and 12.72%, respectively. Keywords: Integrity monitoring · Optimal allocation of indicators · MHSS · Availability

1 Introduction Integrity risk is an important parameter that characterizes the navigation performance required by the navigation and positioning system, and it needs to be monitored comprehensively and strictly [1]. For any positioning system, integrity risk monitoring needs to set up corresponding monitors for all potential risk sources in each link of the system to monitor and eliminate faults [2]. As an emerging positioning system, PPP-RTK (Real Time Kinematic-Precise Point Positioning) also needs a suitable integrity risk index system. However, its authoritative index system is still lacking. The following will analyze the problems existing in the existing system and the traditional method from the three © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 105–114, 2024. https://doi.org/10.1007/978-981-99-6932-6_9

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aspects of the distribution structure, distribution method and distribution framework of the integrity risk index, and analyze the reasons why it is not suitable for the PPP-RTK system. In terms of structure, taking GBAS (Ground Based Augment System) as an example, the aviation system minimum performance standard issued by RTCA (Radio Technical Commission for Aeronautics) proposes an integrity risk index allocation method for GBAS, and includes an integrity risk fault tree example [3]. The fault tree only includes system-side risk sources [4], and there is a division of labor between PPP-RTK systemside monitoring and user-side monitoring. Obviously, the existing index system cannot meet the requirement that PPP-RTK is applicable to both the system end and the user end. In terms of approach, the allocation method proposed by RTCA is widely used. In this method, for each risk source contained in the two categories, the proportional distribution is carried out based on the criterion of equal missed detection rate, that is, the index is adjusted to make the missed detection rate of each monitor equal. In addition, in the absence of sufficient failure samples leading to the lack of prior probability, the criterion of equal distribution is adopted [3]. The problem with these two traditional methods is that missed detection rate cannot fully reflect the monitoring performance of the monitor. Integrity risk indicators are misaligned with the actual needs of monitors, which makes it difficult to guarantee the availability of risk source monitoring. In terms of framework, the existing index system relies on long-term data collection, the prior failure probability can be regarded as a fixed value, so the allocation result is determined and does not change with time. For PPP-RTK, since there is no credible prior failure probability experience value, the system needs to collect data and make statistics to obtain the prior failure probability and other parameters required by the allocation algorithm, and the indicators are required to be updated with the parameter update. Static Allocation frameworks cannot meet this need. Aiming at the above three types of problems, this paper constructs a virtual protection level as a unified dimension of monitoring measurement under the PPP-RTK system. On this basis, it proposes an integrity risk indicator allocation criterion with a consistent protection level. Source overall monitoring availability, and then establish a PPP-RTK integrity risk indicator system that can be updated periodically.

2 The Principle of Integrity Risk Index Optimal Allocation Method The integrity monitoring system includes risk source monitors set for each type of risk source, and each type of monitor calculates a test metric (Test Metric) to indicate the existence of a specific type of fault or problem [5]. Among them, the monitoring metric generally refers to the quantitative value that characterizes the monitoring performance of the monitor and the monitoring algorithm and measurement domain of each monitor vary. The integrity risk indicator system serves the integrity risk monitoring system, and is required to ensure the normal operation of the monitoring system, so as to ensure the overall monitoring availability of risk sources. According to the above requirements for the index system, the optimal allocation method of the index is proposed, which needs to solve the problems in the three aspects mentioned in the introduction in sequence.

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First, as mentioned in the introduction, the index system of PPP-RTK requires both the system end and the user end, which requires the selection of monitoring metrics with unified expressions and unified domains to support the construction of allocation algorithms. On the system side, because the protection level is not used, Shively et al. proposed a method for constructing the performance boundary of the measurement domain of the monitor. This method converts the protection level of the positioning domain into a geometry-independent MERR (Maximum Allowable Undetected Pseudorange Error) [6, 7]. Zaugg et al. regarded MERR as a unified monitoring measure for system-side monitors, and adjusted the integrity risk according to the variance to make some MERRs equal to achieve the purpose of indicator allocation [5]. On the user side, since there is a protection level, the protection level is directly used as a monitoring metric [8]. It can be seen that the MERR at the system side and the protection at the user side can be converted by the formula [5], that is, the monitoring metrics at the system side and the user side can be regarded as the mapping of protection levels on different domains. Thanks to the processing of residuals in the PPP-RTK system, the residual distribution of various risk sources in the form of a Gaussian distribution can be directly obtained by enveloping the residuals [9, 10]. Therefore, this method constructs a virtual protection level as System-side and user-side unified monitoring metrics. Secondly, the different allocation criteria on the system side and the user end lead to different allocation methods. To build a unified allocation method, the allocation criteria should be determined first. Since the monitoring system should ensure the availability first, this method regards the maximum availability as the allocation criterion, which is equivalent to the minimum virtual protection level according to the definition of availability. This process of minimizing the protection level by adjusting the integrity risk is common in various improvements to the RAIM algorithm [11, 12]. Among them, the integrity optimal allocation algorithm based on multiple hypothesis solution separation proposed by Blanch et al. end-to-end applications [13]. However, this method only adjusts the integrity risk based on the failure mode, and is not suitable for index allocation and protection level calculation of multiple risk sources. The failure mode only distinguishes the satellite where the failure occurred, and does not distinguish which risk source caused the failure, resulting in integrity risk. Can only be distributed among satellites. This method realizes the allocation of integrity risk indicators among risk sources by redefining the failure mode of the solution separation algorithm. The detailed definition is shown in Sect. 3.

3 Integrity Risk Index Optimization Allocation Steps 3.1 Failure Mode Settings FM (Failure mode) is the prerequisite for the use of multiple hypothesis resolution separation algorithms. The optimal allocation method only uses the fault mode for satellite faults as the allocation unit [12–14], which is used to describe all current satellites affected by satellite faults. The observed state of, it is assumed that the risk source causes a fault in a certain satellite. This paper redefines the failure mode for the multi-type risk sources of PPP-RTK integrity monitoring, and clarifies two types of assumptions: first, the failure mode is

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only affected by one type of risk source at the same time, and there is no concurrent situation of multiple risk sources; secondly, the same time The risk source only affects a single satellite. Take the failure mode FMij as an example: if FM12 exists, then this failure mode represents the assumption that the first type of risk source causes the failure and affects the second satellite. 3.2 Construction of Protection Level The main idea of the monitor metric calculation method for optimal allocation is to calculate the virtual protection level for each failure mode based on the method of multiple hypothesis solution separation. According to the failure mode setting, the formula of PL (protection level) of multiple risk sources is as follows: XPLij = KHMI,ij σij + Bij + Kcont,ij σss,ij + Bss,ij

(1)

In the formula, the X contained in the virtual protection level XPL indicates that the direction of the protection level is arbitrary, and the specific explanation of the scalar multiplier K, standard deviation σ and model deviation B is as follows: (1) Scalar multiplier K: obtained from the integrity and continuity risks through the inverse cumulative distribution function Q−1 ,   IRij KHMI,ij = Q−1 1 − 2Pprior,i (2)   CRij Kcont,ij = Q−1 1 − 2 K HMI,ij and K cont,ij respectively represent the distribution function quantiles of integrity risk IRij and continuity risk CRij . That is, after the residual distribution model is normalized to the standard Gaussian distribution, the mapping of the integrity of the probability domain and the continuity risk in the positioning domain. Which domain this risk is mapped to depends on the domain where the standard deviation multiplied by the scalar multiplier is located, and is determined by the construction form of the transformation matrix h. (2) Standard deviation σ; σ is synthesized by covariance matrix C (i) through transformation matrix h( j) , σij2 = h(j) C (i) h(j)T 2 σss,ij = (h(j) − h(0) )C (i) (h(j) − h(j) )T

(3)

In the formula, the conversion matrix h( j) is (GjT W −1 Gj )−1 GjT W , which is only related to the geometry of the satellite and not affected by the type of risk source; C (i) is composed of the standard deviation of each risk source and is only affected by the type of risk source. Since each risk source is independent of each other, the covariance matrix is a diagonal matrix, as shown in formula (4), ⎤ ⎡ 2 σi,1 0 0 ⎥ ⎢ C (i) = ⎣ 0 . . . 0 ⎦ (4) 0

2 0 σi,n

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(3) Model deviation B: B is synthesized from the maximum nominal deviation b, N  

 (j)  hn bin

Bij =

n=1 N 

  (j)  hn − h(0) n bin

Bss,ij =

(5)

n=1

In the formula, the index n is the satellite index, and N is the number of visible satellites. Since the conversion matrix h is only affected by the satellite failure, the actual meaning of the Bij formula is: the qth row (1 × N) of the conversion matrix h( j) corresponding to the satellite failure j, and the column vector bi (N × 1) of the maximum nominal deviation from the risk source i. Wherein, the row index q is determined by the PL direction, and if it is VPL, q is equal to 3. 3.3 Allocation Model Construction Construct the allocation model according to the allocation criteria, set the maximum value of the virtual protection level of each failure mode as the objective function, and add constraints, the model is as follows, Minimize max(KHMI,ij σij + Bij + Kcont,ij σss,ij + Bss,ij ) ij

IRreq =

N mod

IRij

ij

subject to CRreq =

N mod

(6)

CRij

ij

In formula (6), IRij and CRij are integrity and continuity risks of failure mode ij, and IRreq and CRreq are integrity and continuity budgets, respectively. The problem that the algorithm needs to solve is to allocate the indicators to the corresponding failure modes under the constraints of the integrity and continuity total budget, so as to minimize the objective function. Obviously, the distribution problem of minimizing the objective function is an optimal problem, and the Lagrange multiplier method can be used to solve the distribution result.

4 Simulation Experiment This section uses the GPS 770th week ephemeris file as the simulation data to verify and analyze the proposed method. First, analyze the influencing factors of the allocation algorithm: From the expression of the virtual protection level, the allocation ratio of the integrity risk index is affected by the standard deviation, prior failure probability and maximum deviation. In this paper, the above three parameters are called ISM (Integrity Support Message). In Sect. 4.1, the control variable method is used to compare the influence of ISM parameters on the index ratio, and the sensitivity of the index ratio to ISM

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parameters is divided by calculating the RD (Relative Difference). At the same time, a global simulation of integrity risk index allocation is carried out to verify whether the allocation algorithm can achieve the purpose of ensuring the availability of overall monitoring, and adjust the performance of the ISM parameter detection allocation algorithm under harsh conditions and improve performance compared with traditional methods. 4.1 Sensitivity Analysis of ISM Parameters In the sensitivity analysis experiment, Jinan (36°N, 117°E) was used as the simulation site, two risk sources RS1 and RS2 with the same ISM parameters were set, and the values of the parameters shown in Table 1 were used as the reference values of the ISM parameters. The integrity risk ratio when equal is used as the ratio reference value. By adding a single ISM parameter value in the form of a percentage, and recalculating the comparison between the risk ratio and the reference value, the impact of the ISM parameter value on the allocation algorithm is evaluated. Note that for all Integrity Risk Ratio plots in this section, “X%” should be interpreted as the ISM parameter deviates by X% from the reference baseline. Table 1. ISM parameter setting Parameter

Set value

Domain

Risk source

Pprior

1 × 10–4 /approach

Probability

RS1 RS2

σ

5 cm

Measurement

b

3 cm

Measurement

RS1 RS2 RS1 RS2

Based on the parameter settings in Table 1, the ISM parameters of RS2 are increased by 5%, 10%, and 15% respectively, and the integrity risk of GPS every 5 min within 24 h on the first day of the 770th week is calculated by the integrity risk index allocation algorithm, The integrity risk ratio of IR2/IR1 is given.

Fig. 1. Integrity risk ratio variation when Pprior , bias and σ deviates

As shown in Fig. 1, the influence of the standard deviation is much greater than that of the other two under the deviation of the same order of magnitude, which is determined

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by the structure of the analytical expression of the protection level: the deviation of the standard deviation of the measurement domain is mapped to the positioning domain through the transformation matrix h, and the scalar The amplification of multiplier K affects the protection level; the offset of deviation is not amplified by scalar multiplier; the offset of prior failure probability is neither mapped by transformation matrix nor amplified by scalar multiplier. Therefore, the influence of the standard deviation is significant and cannot be ignored, the influence of the deviation is small, and the influence of the prior probability is almost negligible compared with the influence of the standard deviation. In addition, the change of the integrity risk ratio caused by the deviation of the prior failure probability is a linear change, while the other two changes are nonlinear. This is because the prior failure probability only directly affects the missed detection rate. Adjusting the integrity risk in the same proportion can keep the missed detection rate unchanged, so that the virtual protection level is equal; while the standard deviation and deviation directly affect the size of the virtual protection level, it is necessary to adjust the scalar multiplied by the integrity risk K, between the two is converted by the inverse cumulative distribution function of the standard Gaussian distribution, obviously this conversion relationship is nonlinear. In order to further divide the sensitivity of the integrity risk ratio to the ISM parameters, the relative deviation is calculated according to the comment expression (*) [15], and the sensitivity division is shown in Table 2. Table 2. Integrity risk ratio sensitivity ISM

Significant (RD* > 100%) Fairly small (RD* > 10%) Negligible (RD* < = 10%) ×

Pprior σ b

× ×

4.2 Global Simulation of Optimal Distribution of Integrity Risk Indicators In this section, the integrity risk index algorithm is simulated by taking satellite ephemeris anomalies, troposphere anomalies, ionosphere anomalies, and user terminal failures as risk sources. The grid point interval is set to 5°, the simulation duration is set to 24 h, and the allocation algorithm is executed for each grid point every 5 min. The allocation results of the global simulation index optimization allocation method and the traditional average allocation method are shown in Table 3, and the protection level and integrity indicators included are all the mean values of the results of all grid points and full sampling time. It can be seen that the optimal allocation algorithm can achieve the purpose of allocating integrity risk indicators according to the virtual protection level consistency criterion, and the protection level is reduced by an average of 11.25% compared with the traditional method (take the vertical as an example).

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Risk source

Traditional Optimal allocation allocation VPL (m) VPL (m)

Traditional allocation indicator

Optimal allocation indicator

Ephemeris fault

0.572

0.536

5 × 10–08

1.50 × 10–08

Ionospheric anomaly

0.598

0.536

5 × 10–08

7.99 × 10–08

Troposphere anomaly

0.604

0.536

5 × 10–08

7.49 × 10–08

User end failure

0.602

0.536

5 × 10–08

3.01 × 10–08

0.536

2 × 10–07

2 × 10–07

Total

0.604

Secondly, in order to improve the overall usability of the test monitoring system, set the alarm limit to 1.1 m [16], and draw a global usability simulation map (Fig. 2).

Fig. 2. Global availability simulation of average allocation (up) and optimal allocation (down)

Obviously, compared with the traditional allocation method, using the optimal allocation method can obtain higher availability, and the global average availability is 96.61% and 97.99%, respectively. In order to further detect the availability improvement brought about by the optimized allocation method under harsh conditions, an availability stress test is carried out, which calculates the global average availability under harsh conditions by directly amplifying the standard deviation. As shown in Table 4, enlarging the standard deviation does not affect the performance of the optimized allocation.

5 Summary This paper proposes an optimal allocation method of PPP-RTK multiple risk source integrity risk indicators to solve the problems of lack of authoritative index system for multiple risk sources of PPP-RTK integrity service and difficulty in guaranteeing availability of risk source overall monitoring. The proposed method adopts the method

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Table 4. Global average availability Amplification coefficient

Traditional allocation (%)

Optimal allocation (%)

Increased availability (%)

1.00

96.61

97.99

1.38

1.25

90.61

95.24

4.63

1.50

78.96

88.71

9.75

1.75

68.16

77.97

9.81

2.00

55.16

67.88

12.72

of constructing a virtual protection level, which realizes the simultaneous distribution of the integrity risk indicators of the PPP-RTK multi-risk source system end-user, and meets the requirement of synchronous update of the integrity risk indicators and ISM parameters. The proposed method demonstrates its superior performance in guaranteeing the availability of coordinated monitoring through global availability simulation and availability stress test. Thus, it is proved that the index system constructed by the proposed optimal allocation method is reliable. The optimization allocation method proposed in this paper is highly dependent on the Gaussian residual distribution generated by the PPP-RTK system in order to make the constructed monitoring metric analytical formula applicable to all monitors, and is not applicable to other systems. The follow-up theoretical improvement of the proposed method can start with improving the monitoring measurement construction method, and extending the allocation method to other systems such as GBAS and SBAS. Acknowledgements. This research was jointly funded by the National Key Research and Development Program (No. 2021YFB3901300), the National Natural Science Foundation of China (Nos. 61773132, 61633008, 61803115, 62003109), the 145 High-tech Ship Innovation Project sponsored by the Chinese Ministry of Industry and Information Technology, the Heilongjiang Province Research Science Fund for Excellent Young Scholars (No. YQ2020F009), and the Fundamental Research Funds for Central Universities (Nos. 3072019CF0401, 3072020CFT0403).

References 1. Li L (2012) Research on positioning and integrity monitoring technology of ground-based augmentation system. Harbin Engineering University 2. Niu F (2008) Theory and technique on GNSS integrity augment. The PLA Information Engineering University 3. RTCA/DO-245-A (2004) Minimum aviation system performance standards for local area augmentation system. RTCA, Washington 4. Chen JX (2018) Research on GBAS equipment operation permit system. Civil Aviation University of China 5. Zaugg T (2001) A new evaluation of maximum allowable errors and missed detection probabilities for LAAS ranging source monitors. In: Proceedings of the 57th annual meeting of the Institute of Navigation, Albuquerque, pp 187–194

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6. Shively CA (1999) Derivation of acceptable error limits for satellite signal faults in LAAS. In: Proceedings of the 12th international technical meeting of the Satellite Division of the Institute of Navigation, Nashville, pp 761–770 7. Shively CA (2001) Preliminary analysis of requirements for CAT IIIB LAAS. In: Proceedings of the 57th annual meeting of the Institute of Navigation, Albuquerque, pp 705–714 8. Li L, Zhao L, Yang F et al (2015) A novel ARAIM approach in probability domain for combined GPS and Galileo. In: Proceedings of the 28th international technical meeting of the Satellite Division of the Institute of Navigation, Tampa, pp 649–657 9. DeCleene B (2000) Defining pseudorange integrity—overbounding. In: Meeting of the Satellite Division of the Institute of Navigation, Salt Lake City, pp 1916–1924 10. Rife J, Pullen S, Enge P et al (2006) Paired overbounding for nonideal LAAS and WAAS error distributions. IEEE Trans Aerosp Electron Syst 42(4):1386–1395 11. Hwang PY, Brown RG (2006) RAIM-FDE revisited: a new breakthrough in availability performance with NIO RAIM (novel integrity-optimized RAIM). Navigation 53(1):41–51 12. Li L, Wang H, Jia C et al (2017) Integrity and continuity allocation for the RAIM with multiple constellations. GPS Solut 21(4):1503–1513 13. Blanch J, Walter T, Enge P (2010) RAIM with optimal integrity and continuity allocations under multiple failures. IEEE Trans Aerosp Electron Syst 46(3):1235–1247 14. Joerger M, Chan FC, Pervan B (2014) Solution separation versus residual-based RAIM: solution separation versus residual-based RAIM. Navigation 61(4):273–291 15. Lee Y, She J, Odeh A et al (2019) Horizontal advanced RAIM performance sensitivity to mischaracterizations in integrity support message values. In: 32nd International technical meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, Florida, pp 775–794 16. Du Y, Wang J, Rizos C et al (2021) Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell Navig 2(1):3

Reliability and Backup Strategy Analysis of Low-Earth Orbit Navigation Constellation Hao Zhang(B) , Ping Li, Jin Jun Zheng, Gong Zhang, and Fu Jian Ma Institute of Telecommunication and Navigation Satellites, China Academy of Space Technology, Beijing, China [email protected]

Abstract. In order to realize the requirement of stable operation of Leo Navigation system, redundant backup of constellation system should be designed in constellation networking stage and constellation operation stage respectively. A certain number of satellites to be launched should be backed up on the ground ahead of time to ensure system reliability is maintained above a certain level. In this paper, by comparing several kinds of reliability calculation methods of constellation system and the strategy of constellation network supplement, the optimal scheme of accuracy and calculation resource consumption is selected synthetically. The author complete design the number of satellite backup and launch plan in the operation phase based on requirements of different levels of single satellite reliability and system reliability. In this paper, author apply Monte Carlo method multiple sampling to the life distribution of a single satellite and compare it with the real-time operating hours of satellites in orbit to obtain the current system reliability, which can be used to obtain the constellation system reliability at any time and get different network backup strategy. The analysis results show that this method can provide a quantitative basis for the design and optimization of the backup strategy of navigation constellation. Keywords: Leo navigation constellation · Network success rate · Constellation reliability · Constellation backup

1 Introduction In order to provide continuous and stable navigation services on a global or regional basis, constellation of satellites should work together to provide services with zero delay service. A satellite constellation consists of a multitude of orbital planes, each of which is composed of a number of satellites [1]. By means of carefully designed satellite orbits, the satellites maintain a relatively stable geometry in space through coordinated control. In real life, high-performance satellites and components can be mass-produced on assembly lines as companies like OneWeb, SpaceX, Boeing, and others build huge broadband constellations in low-earth orbit with tens of thousands of satellites [2], a low-orbit navigation constellation can be constructed at the cost of just one GPS satellite.

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 115–125, 2024. https://doi.org/10.1007/978-981-99-6932-6_10

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2 Constellation Configuration and Reliability Requirements 2.1 Constellation Configuration Design In this paper, a constellation configuration was designed with the goal of achieving the minimum five overlaps within 60° north and south latitude to support the analysis of constellation reliability and backup strategy. The research results of this paper can also be applied to the analysis of other constellation configurations. The basic configuration of the constellation is Walker-delta 150/10/8, with an orbital inclination of 50.4° and an orbital altitude of 1230 km. See Fig. 1 for its three-dimensional configuration.

Fig. 1. Constellation configuration

2.2 Constellation Launch Program The initial constellation is designed with 150 satellites in orbit, and there are 10 orbital planes and 15 satellites in each orbital plane when the networking work is completed. The initial launch plan is shown in Table 1. 2.3 Constellation System Reliability Requirements Due to the different task characteristics of the networking stage and the system operation stage, the assessment is divided into two parts. In the networking phase, one rocket launch failure is allowed, and at least 9 rocket launches are required for fixed-point success. At least 115 satellites must be successfully placed into orbit. 2.4 Single Satellite Reliability Design and Principle of Network Supplement The reliability of a single satellite is designed according to the two types of life at the end of 0.6 with 5-year-satellite and the end of 0.6 with 8-year-satellite. During the ground satellite supplement, the satellite in orbit is supplemented by 15 satellites with 1 arrow each time to the constellation. From an economic point of view, the last network replenishment of the system should be less than or equal to 15, that is, the minimum number of launches to meet the reliability requirements of the system.

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Table 1. Constellation launch plan Time (month)

Launch group and number of one-group-satellite

Note

T0

The first group:15 satellites

2 months orbit drift, 1 month test

T0 + 1

The second group:15 satellites

T0 + 2

The third group:15 satellites

T0 + 3

The fourth group:15 satellites

T0 + 4

The fifth group:15 satellites

T0 + 5

The sixth group:15 satellites

T0 + 6

The seventh group:15 satellites

T0 + 7

The eighth group:15 satellites

T0 + 8

The ninth group:15 satellites

T0 + 9

The tenth group:15 satellites

3 Satellite Reliability Model and Constellation Reliability Calculation Method 3.1 Satellite Reliability Model [3] GPS summarized the failure mode of single satellite, which can be divided into two categories [4]: Dissipation failure refers to the failure caused by the accumulation of certain dissipation to a certain extent; Random failure means that the final failure is not a cumulative effect which is not clearly predicted. A Weibull distribution model is established for random failures. The reliability model based on random fault and loss fault fully draws on the experience of GNSS constellation and is more in line with the actual situation of navigation satellites. Its model is expressed as, R(t) = e

−(t/α)β

α · t

  1 (t − μ) dt exp − √ 2σ 2 2π σ

(1)

α is the scale parameter, μ is the mean value and σ is the standard deviation. Ochieng assumed that the satellite fault mode density function followed the exponential ratio to obtain the corresponding lifetime, and obtained the satellite reliability exponential model: R(t) = e−λt

(2)

where λ is the failure rate and its value is 1/MTBF. The description method of the satellite reliability model cannot represent the early failure in the bathtub curve and the aging trend after the end of the life cycle. As the traditional single satellite reliability model of communication satellite adopts exponential model, the single satellite reliability model in this paper adopts exponential distribution model.In the future we can further refine the model as needed.

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3.2 Reliability Calculation Method of Constellation System 3.2.1 State Probability Method The method is simple and intuitive [5]. Pk (t) =

k=N 

Pk,N (t)

(3)

N    1 − Rj,n (t)

(4)

CNk

Pk,n (t) =

k  i=1

Ri,n (t) ·

j=k+1

Pk (t) is the constellation state probability of k satellites failure in constellation at t-time; CkN is all combinations of N satellites with k satellite failures; Pk,n (t) is the nth constellation state probability with k satellites fault; Ri,n (t) is the reliability of K working satellites under the nth choose; [1 − Rj,n (t)] is the failure probability of (N-K) failed satellites under the nth combination. From the time when the test satellite is in orbit to the time when the network is formed, there are ten batches of different single-satellite reliability. The network is made up of more than ten different satellite reliability, more than hundred satellites and also the system reliability computational complexity is huge. The system reliability of 30 satellites with different reliability can hardly be calculated on the author’s computer, which can not be used to calculate the reliability of all satellite systems in this scale of satellite constellation. A suitable method should be found. 3.2.2 Monte Carlo [6] Monte Carlo stochastic simulation is an experimental method on probability, according to a certain probability distribution method to generate random number to simulate the possible random phenomenon. Compared with the traditional method, it has the following advantages: (1) the simple state (1 or 0) of the satellite obtained by sampling can avoid the hardware cost caused by the large number of floating-point operation, and (2) the computer is good at random sampling many times. Through the local test, the method can be applied to the reliability calculation of large-scale constellation system, and the input parameters of the system can be changed and the arbitrary expansion of the constellation system can be carried out through the design program, and the new ground backup strategy and the reliability calculation of the constellation system can be generated rapidly and iteratively. The calculation flow of constellation reliability using Monte Carlo is as follows. The number of operational satellites in orbit is obtained by comparing the reliability of the satellites in orbit with the life expectancy of the satellites with exponential distribution. The number of operational satellites in orbit is more than 115, which is a successful test (Fig. 2).

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Fig. 2. Constellation reliability calculation use Monte Carlo

4 Constellation Network Supplement and Reliability Analysis in Operation Phase The factors that affect the long-term stable operation of constellation include [7] the constellation supplement time and system reliability constraints, ground network replenish batch, network supplement time, single-satellite reliability and so on. The ground network patching operation should be completed at the right time according to the reliability requirements of 2.4-segment constellation system, the constellation operation time, the initial launch batch of the same launch batch under the constraint of 2.2-segment constellation configuration. 4.1 Analysis of Constellation Backup Criterion The efficiency should be improved step by step with the increase of the coverage weights Users only use LEO signal to solve the location problem need to ensure the minimum coverage of more than 4-fold. With the increase of the number of covers, the efficiency is improved step by step. In order to simplify the analysis reasonably, the coverage of constellations is used as the criterion of constellations. Considering the random distribution of the failed satellites in the constellation, the number of constellations tolerant failure satellites is analyzed based on the probability of meeting the minimum 4-fold coverage ≥98% in the 60° latitude of the south and the north. According to the analysis method of Fig. 3, the number of failed satellites N is 25, 30 and 35 respectively, and 300 times of simulation is carried out under the number of each kind of failed satellites. According to the statistics of 300 simulation results, when 35 satellites fail same time at random, the ratio of meeting the minimum 4-fold coverage is 98.95%, and the constellation available criterion of meeting ≥98% is satisfied. Therefore, the random failure of 35 constellations or the number of health satellites ≥115 can be used as criteria for constellations. 4.2 Strategy of Network Supplement and Reliability Analysis The system reliability at a given time can be obtained by completing a Monte Carlo calculation according to Fig. 4, and the system reliability at different time can be obtained

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Fig. 3. System coverage impact analyses process with different broken satellites

by repeated application of Monte Carlo calculation according to different time. Comparing with the expected value, we can judge whether the ground complement operation should carried out or not. If the system reliability at that exact time don’t meet the system require, we should supplement a batch of 15 satellites from ground network. When system reliability at that exact time meet the system require but system runtime don’t reaches 108 months, all satellites in orbit working hours plus one month. When the system reliability is over 0.7 and reaches 108 months, the simulation is completed, and the “Constellation System network supplement strategy” and “Constellation System reliability” in different months are obtained.

Fig. 4. Constellation reliability and orbit satellites replenish use Monte Carlo

The life of a single satellite follows an exponential distribution with a life span of 5 and 8 years for satellites. Design program input network satellite launch plan (in month), single-batch network satellite number, system reliability requirement, least number of healthy satellites and so on. The strategy of constellation net satellite replenish and the system reliability at different time can be obtained by program calculation. 4.3 5-Year Lifetime Satellite According to the above Fig. 4, using the Monte Carlo method to carry out the simulation, the specific parameters are set as follows,

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Sate_fit: Single satellite failure rate data, currently selected 5-year life satellite. Launch_month: Network status 150 satellite launch plan; Start_Month: The system reliability is calculated from the set month, and the successful networking is calculated from the 12th month of the launch of the experimental satellite; One group simulate times: In this case, it is set as 100 tests, which should be larger than the current minimum working satellite in orbit, and should be about 115 satellites at the time of network supplement; Groups simulate times: Calculation of multiple tests, this example is set to 100 tests of the month system reliability. After many simulation experiments, the basis of choosing the two simulation times is the optimum computer time without affecting the data. Trust_value: Set the confidence level to 0.6 for current month system reliability selected from multiple tests. System_reliability: Set the system reliability, when the monthly system reliability does not meet the requirements, should be launched ahead of schedule in the month to complete the new satellite network work, this example is 0.7. Broken_sate_number: The number of satellites allowed to fail is 35 at the successful time of network construction, and the corresponding number of launches will be increased after network supplement. The simulation results are shown in Fig. 5 (Table 2).

Fig. 5. Constellation satellites supplement strategy with 5-year-satellite Table 2. Satellites replenish time and constellation reliability System reliability require

Satellites one batch

Replenish satellites System (month) reliability at replenish time

0.7

15

21, 34, 47, 62, 76, 90

System reliability at end-life of constellation

0.68, 0.73, 0.71, 0.95 0.69, 0.7, 0.73

It can be seen that for the 5-year life of the satellite constellation during the operation of the need for the orbit replenish 6 times from ground. In this case, the simulation step

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size is set to 1 month, and there is a slight fluctuation at 0.7 in the system before network repair. If the simulation step size is changed to 1 week or 1 day, more accurate network replenish strategy will be obtained, and also it requires a large amount of computing resources and longer computing cycles. At the same time, the reliability of the system at the end of its life is 0.95, which is much higher than 0.7, so it should be considered to reduce the number of satellites in one batch to meet the system requirements and reduce the operation cost. 4.4 8-Year Lifetime Satellite The simulation parameters are the same as those of the 5-year-old satellite, but the failure rate of the single satellite is changed to the 8-year-old satellite (Fig. 6; Table 3). Table 3. Satellites replenish time and constellation reliability System reliability require

Satellites one batch

Replenish satellites System (month) reliability at replenish time

System reliability at end-life of constellation

0.7

15

38, 60, 82

0.9

0.69, 0.7, 0.69

Fig. 6. Constellation satellites supplement strategy with 8-year-satellite

It can be seen that for the 8-year life of the satellite constellation during the operation of the need for ground network replenish 3 times. Similarly, end-of-life 0.9 should be considered in the final launch by reducing the number of satellite launches in the same batch to reduce costs. 4.5 Backup Mode Optimization According to the analysis of the previous section, the number of the network supplement satellites should be optimized. After the optimization of the network strategy as follows,

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5-year and 8-year satellite constellation system should ensure that no increase in the number of launches, to ensure the reliability of the system to reduce the last launch of the number of satellites. It can be seen from the simulation that the number of satellites launched in the same batch of 5-year life satellites is reduced from 15 to 11, and the number of satellites launched in the same batch of 8-man life satellites is reduced from 15 to 9 (Figs. 7 and 8; Tables 4 and 5). Table 4. Satellites replenish time and constellation reliability System reliability require

Satellites one batch

Replenish satellites System (month) reliability at replenish time

0.7

11

20, 34, 47, 62, 76, 86

System reliability at end-life of constellation

0.69, 0.68, 0.72, 0.73 0.7, 0.7, 0.72

Table 5. Satellites replenish time and constellation reliability System reliability require

Satellites one batch

Replenish satellites System (month) reliability at replenish time

System reliability at end-life of constellation

0.7

9

38, 60, 82

0.68

0.7, 0.69, 0.69

Fig. 7. Optimized strategy with 5-year satellite

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Fig. 8. Optimized strategy with 8-year satellite

Through the optimized design of the network supplement strategy, one batch of the 5year satellite constellation’s network supplement is reduced from 15 to 11 (the reliability of the system can not be guaranteed by reducing the number to 10), and the reliability of the system at the end of its life is 0.73; One batch of the 8-year satellite constellation’s network supplement is reduced from 15 to 9 and the system has an end-of-life reliability of 0.68. On the requirement of the number of rocket launches unchanged, the number of satellites launches in the same batch reduced until exactly meet the reliability of the constellation system, at the same time system operation cost reduced to the greatest extent.

5 Summary In this paper, the reliability analysis of a navigation constellation is carried out in the networking stage and the running stage. Based on this, the strategy design of the ground network is carried out. And the Monte Carlo method program is designed to realize the optimal design of constellation network supplement, and it can support the change of system input parameters and arbitrary expansion of constellation system, and can quickly generate new network supplement strategies. In the future, further analysis should be carried out from the following aspects: 1. The reliability of constellation system under more complex single-satellite model; 2. The reliability of constellation system considering the comprehensive performance of hybrid constellation system; 3. Consider mission degradation and business-oriented constellation system availability 4. Constellation Reliability and evaluation for other more complex scenarios.

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References 1. Zhang X, Ma F (2019) Review of GNSS enhancement for low-orbit navigation. J Geodesy Geo Inf Sci 48(9):1073–1087 2. Wang X, Hu M, Zhao Y, Xu J (2020) Constellation backup strategy research progress. China Space Sci Technol 40(3):43–55 3. Li H, Zheng H, Wang W (2013) Research on spare satellites strategy of navigation constellation based on system availability. In: Proceedings of China satellite navigation (CSNC), Wuhan, pp 293–304 4. Ochieng WY, Sheridan KF, Sauer K (2002) An assessment of the RAIM performance of a combined Galileo/GPS navigation system using the marginally detectable errors (MDE) algorithm. GPS Solut 5(3):42–51 5. Zhang H, Meng D, Zong Y (2018) A modeling and analysis strategy of constellation availability using on-orbit and ground added launch backup and its application in the reliability design for a remote sensing satellite. Adv Mech Eng 10(4):1–6 6. Zheng H, Ren L (2009) Availability analysis of satellite constellation. In: 2009 8th international conference on reliability, maintainability and safety. IEEE, pp 245–248 7. Tang L (2018) Study on improving the success rate of Long March launch in our country. Aerosp Ind Manag Res Discuss 12:7–9

An Asynchronous Observation Positioning Algorithm Based on Factor Graph Optimization Chuang Zhou, Jiaolong Wei(B) , and Zuping Tang Huazhong University of Science and Technology, Wuhan 430000, China [email protected]

Abstract. Broadcasting integrated signal of communication and navigation in low earth orbiting (LEO) broadband constellation to achieve the navigation augmentation is an existing trend. Considering the needs of communication services, the integrated signal generally has burst characteristics, and the receiver only receives the signal from the satellite in some specific time slots, and the observation has obvious asynchronous arrival characteristics. Such asynchronous arrival observations are quite different from the synchronous observations obtained by receiving the continuous navigation signals broadcast by the existing GNSS satellites, which will lead to many problems if using the traditional positioning method. Combining the characteristics of asynchronous observations, this paper proposes an asynchronous observation positioning algorithm based on factor graph optimization (FGO), which can use asynchronous observation in multiple epochs for joint estimation to reduce positioning error. Simulation shows that the positioning algorithm based on FGO can effectively improve the positioning accuracy compared with the traditional method. Keywords: Positioning algorithm · LEO navigation augmentation · Integrated signal of communication and navigation · Asynchronous observation · Factor graph optimization

1 Introduction Global Navigation Satellite System (GNSS) can provide users with all-weather, allday, high-precision positioning, navigation and timing services. LEO satellites have the advantages of rapid geometric change and higher signal landing power, so it has unique advantages to use LEO satellite platforms as GNSS navigation signal augmentation sources. At present, the development of LEO navigation augmentation has become a consensus, and many countries have proposed a signal enhancement system based on LEO satellites. In 2002, the United States proposed an augmented navigation system combining GPS and Iridium satellite system [1] to improve the performance of GPS receivers in complex environments. Kepler, the European third-generation satellite navigation system, uses LEO satellites as part of a constellation [2], aiming to achieve centimeter-level orbital accuracy, global real-time precision single-point positioning. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 126–136, 2024. https://doi.org/10.1007/978-981-99-6932-6_11

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With the rapid construction of low orbit Internet broadband constellation such as Starkink, research on LEO navigation enhancement based on LEO broadband communication constellation has become a new development trend. Most of the existing researches on the independent navigation performance of LEO navigation augmentation system start from the geometric distribution and ranging error [3, 4], and all assume the same multi-sphere convergence positioning principle as the existing GNSS. However, there are differences between the use of LEO broadband satellites for navigation enhancement and the construction of independent LEO navigation augmentation systems which broadcast continuous signals. At present, there is a trend to realize the integration of communication and navigation functions based on integrated signal broadcasting. Considering the needs of communication services, the integrated signal has the characteristics of burst, and the receiver only receives the signal from the satellite in some specific time slots. The observation obtained has obvious asynchronous arrival characteristics, which is called asynchronous observation. For traditional synchronous observations, since the observations belong to the same epoch, the state of the receiver in the epoch can be uniquely determined using the trilateration principle. Asynchronous observations belong to different epochs, while the receiver state may change over epochs, so the application of the trilateration principle has great limitations. For example, if using Weighted Least Square (WLS) method for synchronous observations, the equation will be underdetermined and cannot be solved. And the researches on asynchronous observations generally focus on the heterogeneous asynchronous observations caused by different output frequencies of multi-sensors in integrated navigation. There are generally two solutions: One is to use improved filters to fuse the positioning results of different sensors. For example, in reference [5], a federated Kalman filter algorithm based on multi-scale model is proposed for INS/satellite/altimeter/attitude instrument, which effectively suppresses the influence of inaccurate estimation. Reference [6] developed an adaptive Kalman Filter algorithm based on variational Bayesian approximation for INS/Doppler velocity meter/inclinometer/depth meter, and this algorithm can greatly improve the positioning accuracy compared with the traditional extended Kalman filter (EKF) algorithm. However, if the algorithm is directly applied to the asynchronous observation of satellite navigation, the above distributed filtering method will degenerate to sequential filtering. Another traditional method is the time registration method, which processes the observation sequence of each sensor through interpolation or extrapolation, so that each sensor can provide virtual observation data at the same time [7]. For example, reference [8] uses the time registration method based on Taylor expansion combined with Modified Gain Extended Kalman Filter (MGEKF) to solve the problem of multi-radar cooperative detection of targets, and its detection accuracy is higher than that of traditional least squares time registration. However, the virtual observations will introduce large noise which cannot be accurately quantified. Different from above integrated navigation, the main problem here is the state cannot be estimated accurately by few observations. In order to make full use of multiple observations, this paper introduces the method of Factor Graph Optimization (FGO). The theory of FGO was proposed by Kschischang in

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2001 [9], aiming to transform the global function with many variables into the product of multiple local potential functions to reduce the processing difficulty. FGO is widely used in Simultaneous Localization and Mapping (SLAM) and also been studied in the field of GNSS/INS (Inertial Navigation System) integrated navigation. For example, reference [10] proposed an FGO method with fixed generation rate of variable nodes and closed solution of Inertial Measurement Unit (IMU) to connect variable nodes and observation nodes. Reference [11], aiming at the combination of GNSS differential positioning and INS, analyzes the size of the sliding window. Reference [12] compares the effect of FGO method and EKF method in tightly coupled positioning and loosely coupled positioning, and analyzes the source of advantages of FGO method compared with EKF method in detail. Compared with the filtering method, the FGO method can use observations in multiple epochs for state estimation to improve accuracy, and subsequent observations can be used to further correct the state estimation of the previous epoch, which leads to higher applicability. In this paper, the model of asynchronous observation system will be proposed, and then the basic principle and algorithm flow of factor graph optimization method will be described. Finally, simulation will be used to test the proposed algorithm and corresponding conclusions will be given.

2 Model of Asynchronous Observation System Asynchronous observation system can be described by a discrete time system, which involves two parts: dynamic model and observation model. xi = f(xi−1 ) + wi

(1)

xi = f(xi−1 ) + wi

(2)

State Eq. (1) describes a dynamic model of the system. The vector xi represents the state of the receiver at ti , the function f represents the state transition function, and the vector wi represents the noise of the state transition process. Positioning is to estimate the state vector xi . For a receiver with general dynamic conditions, we need to consider position xi /yi /zi , speed vxi /vyi /vzi , clock difference δti and clock drift δfi of receiver: xi = [xi vxi yi vyi zi vzi δti δfi ]T

(3)

State transition function f can be expressed as a linear function as shown in Eq. (4), where Ai,i−1 is the state transition matrix shown in Eq. (5): f(xi−1 ) = Ai,i−1 xi−1 ⎤ 0 0 0 Ax|i,i−1  ⎢ 0 0 0 ⎥ Ay|i,i−1 1 Ti,i−1 ⎥ ⎢ , Ax\y\z|i,i−1 = , =⎣ 0 ⎦ 0 1 0 0 Az|i,i−1 0 0 0 At|i,i−1

(4)

⎡

Ai,i−1

Ti,i−1 = ti − ti−1

(5)

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State transition noise vector wi is generally assumed as Gaussian noise with zero st mean: wi ∼ N (0,  st i ).  i is the noise covariance matric shown in (6): st st st st  st i = diag( i,x ,  i,y ,  i,z ,  i,t ) ⎡ ⎡ ⎤ 3 2 Ti,i−1 Ti,i−1 S S vd 2 ⎦ ⎣ vd 23 ⎣ St Ti,i−1 +2 Sf  st , d = x/y/z,  st i,t = i,d = Ti,i−1 T Svd 2 Svd Ti,i−1 Sf i,i−1 2

2 Ti,i−1 2

Sf

2 Ti,i−1 2

⎤ ⎦

Sf Ti,i−1 (6)

The Svd , d = x/y/z represent acceleration power density in three directions, St and Sf represent noise power density of clock error and clock drift. Those noise power density could be prior information. Methods in this paper use ideal prior noise power density to build the noise covariance matric. Another way is to use adaptive noise estimator, which is adaptable in both EKF and FGO methods. Measurement Eq. (2) describes the observation model of the system. The vector zi represents the observation at ti , the function h represents the measurement function, and the vector vi represents the measurement noise. The main difference between the asynchronous and the synchronous observation system is the limit on the ti : in the asynchronous observation system, the observation vector exists only when the ti takes in some discrete time slots, while there is no limit in synchronous situation. The above differences are derived from the arrival time characteristics of asynchronous/synchronous observations, as shown in Fig. 1. In the synchronous observation system, the navigation signals of multiple satellites can be received at any time, such as T1 , T2 and Tu due to the continuous broadcasting, and the dimension of the observation vector relies on the number of visible stars. In the asynchronous situation, because the satellite signal is short burst, the signal from satellites can only be received at a few moments such as T1 and T2 . If the receiver uses pseudo-range observation and Doppler observation, then in the asynchronous observation system, zi = [ ρi bi ]T , with ρi and bi represent the pseudo-range and the pseudo-range rate calculated by Doppler observation. And the measurement function can be expressed as: T

h(xi ) = hρ (xi ) hb (xi ) ⎤ ⎡ (x(s) − xi )2 + (y(s) − yi )2 + (z (s) − zi )2 + δti ⎦ (s) (s) (s) (s) = ⎣ (vx(s) −vxi )(x(s) √−xi )+(vy −vyi )(y −yi )+(vz −vzi )(z −zi ) + δfi

(7)

(x(s) −xi )2 +(y(s) −yi )2 +(z (s) −zi )2

In Eq. (7), x(s) /y(s) /z (s) is the position of the corresponding satellite at the time of signal transmission, and vx(s) /vy(s) /vz (s) the is speed, which can be calculated through the signal transmission time and ephemeris data. ρ ob b Measurement noise vector vi follows vi ∼ N (0,  ob i ),  i = diag(i , i ), for ρ the noise of pseudo-range and pseudo-range rate are independent, with i , ib being the noise variance respectively.

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Fig. 1. Arrival feature of asynchronous/synchronous observation

Fig. 2. Factor graph of multi-variable optimization

3 Basic Principle and Algorithm Flow the FGO Method 3.1 Fundamental Principle Factor graph is a form of probability graph, which contains interconnected variable nodes and factor nodes. The variable nodes represent the variables to be estimated, and the factor node represents the probability of the variables under certain conditions. When solving state estimation problem, FGO method uses the observation in multiple epochs for joint estimation, and the joint estimation is regarded as a multi-variable maximum a posteriori probability (MAP) problem. T ]T to represent observations, X= [xT ,xT ,...,xT ]T to represent Use Z= [z1T ,z2T ,...,zN 0 1 N the state sequence, where the state x0 is the prior state with the existing

prior distribution information. According to Bayes formula p(X|Z) = p(X)p(Z|X) p(Z), since the denominator p(Z) is not a function of the state sequence, Then the MAP problem can be expressed as: X∗ = arg max p(X|Z) = arg max p(X)p(Z|X) X

X

(8)

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The FGO method can convert p(X)p(Z|X) into the product of multiple local probability density functions (PDF) according to the node connection: p(X)p(Z|X) = p(x0 )

N  

p(xi |xi−1 )p(zi |xi )

(9)

i=1

The derivation of Eq. (9) assumes that the system follows a first-order Markov process, and system noise at different times are independent. The above decomposition process can be more clearly shown by the Fig. 2. The local PDFs in Eq. (9) is generally ob obtained by modeling the system noise. With wi ∼ N (0,  st i ), vi ∼ N (0,  i ), the conditional PDF of the state can be obtained according to the dynamic system model shown in Eq. (1):   2  1 −1 1 4 2 p(xi |xi−1 ) = (2π )  st exp(− eitr (X) st ) i i 2

(10)

eitr (X)=xi − f(xi−1 ) is state transition residual function, abbreviated as eitr (X). According to the measurement model shown in Eq. (2), the conditional PDF of pseudo-range and pseudo-range rate can be written as:

p(ρi |xi ) =

 2  ob,ρ  exp(− 21 ei (X) ρ )  ρ1 (2π ) i  2

i

1 2

, p(bi |xi ) =

 2   exp(− 21 eiob,b (X) b )  1 (2π ) ib  2

i

1 2

(11)

ob,ρ

ei (X)=ρi − hρ (xi ) and eiob,b (X)=bi − hb (xi ) are pseudo-range/pseudo-range rate ob,ρ and eiob,b . The prior information of the state x0 residual function, abbreviated as ei is generally given in the form of estimated value and mean square error matrix, E.g.: x0 ∼ N (ˆx0 ,  p ). The edge PDF of the state can be obtained as: p(X)p(Z|X) = p(x0 )

N 

 p(xi |xi−1 )p(zi |xi )

(12)

i=1

ep (X) = x0 − xˆ 0 is prior residual function, abbreviated as ep . And  · 2R represents the square of Mahalanobis distance: x2R =xT R−1 x. By substituting the above local PDFs into Eq. (3-3) and taking logarithm, the MAP problem can be transformed into the least squares (LS) problem: N   2    2  2   ob,ρ 2  X∗ = arg min(ep  p + (ei  ρ + eiob,b  b + eitr  st )) X

i=1

i

i

(13)

i

Equation (13) is the final expression of multi-state estimation in asynchronous observation system based on FGO method.

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3.2 Algorithm Flow There are many mature methods to solve LS problem. In this paper, Gauss-Newton method is adopted [13]. Since the length of state sequence cannot increase without limit, a time sliding window is generally set to constrain the number of observations used, as shown in Fig. 3.

Fig. 3. Time sliding window T ]T , and the correSliding window 1 limits the observation as Z = [z1T ,z2T ,...,zN sponding state sequence X = [x0T ,x1T ,...,xNT ]T . For Sliding window 2, the required prior distribution information is given by the estimation of X = [x0T ,x1T ,...,xNT ]T , which involves the probability marginalization step of extracting the information of a single state from the state sequence. Combined with the above requirements, the algorithm can be divided into two steps: (a) Iteration solution: according to the objective function shown in Eq. (3-9), denote those residual functions as en , n = 1, 2, ..., (3N + 1), and the corresponding covariance matrices as  n , n = 1, 2, ..., (3N + 1). The initial solution of the iteration X0 can be derived from the given prior state through the state transition equation. In the process of the Kth iteration, calculate the residual functions and their Jacobian matrix at Xk−1 :

Jn =

3N +1 3N +1   ∂en |Xk−1 , n = 1, 2, ..., (3N + 1),  = JnT  −1 J , ξ = − JnT  −1 n n n en ∂X n=1

i=n

(14)  is the information matrix of the Xk−1 and ξ is the information vector. The iterative increment X can be calculated as  · X = ξ. The mean square error matrix of the state sequence can be approximated by using the inverse of the information matrix [13]. (b) Probability marginalization: the next sliding window requires the estimated value of a single state and the mean square error matrix as prior information. Extracting estimated value of a single state is easy, but it is complicated to extract the mean square error matrix. The common method is to use the Schur complement. Obtain the information matrix of a single state and then calculate the its inverse matrix as the mean square error matrix. For example, calculate the mean square error matrix  N of the last state xN : −1  N  (bb − ba −1 aa ab ) , −1   aa ab cov(Xm arg , Xm arg ) cov(Xm arg , xN )   −1 = = . X ba bb cov(Xm arg , xN )T N

(15)

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4 Simulation 4.1 Simulation Parameters Since there is no existing LEO augmentation system using burst signal, observations can only be generated by simulation. A LEO Walker constellation in an altitude of 1150 km with 12 orbital planes and 216 satellites is assumed. The signal transmission time of kth satellite could be expressed as: Ts(k) = n +

k , n ∈ Z, k = 1, 2, ..., 216 216

(16)

The signal reception time is related to the specific visible star situation. Due to the uncertain position of the receiver, the visible situation have great randomness, and the time of reception also has great randomness.

Fig. 4. Example of signal reception time on receiver

In Fig. 4, the points with different colors represent the reception time of different satellite signals. The reception time sequence is periodic in the whole, but random inside the cycle. Since propagation delay changes with different distance, the reception interval of same satellite may fluctuate around 1 s. The receiver is set to have time-varying velocity and acceleration, with the average of 30 m/s and 3 m/s2 . The observation shadowing angle is set to a 20°. The simulation duration is set to 2000 s. The observation noises are set to a constant: pseudo-range noise has a zero mean and a standard deviation of 2 m, pseudo-range rate noise has a zero mean and a standard deviation of 0.2 m/s. The receiver clock error is equivalent to 5 m pseudo-range error. 4.2 Simulation Result In order to verify the feasibility and effectiveness of the FGO method, the extended Kalman filter method combined with time registration, abbreviated as TREKF, and the sequential extended Kalam filter, abbreviated as SEKF, are used as a control. To explore how the size of sliding window effect in the FGO method, sliding windows of 1 s, 5 s and 10 s are selected, abbreviated as FGO_1/5/10. Noting that the FGO method output a joint estimation of real-time (zero lag) and lagged states. For example, FGO_1 output a joint estimation of states during [t0 − 1, t0 ] at time t0 , then then real-time state refers to the state closest to t0 , and the maximal lagged state refers to the state closest to t0 − 1. SEKF and TREKF both output a single real-time state estimation. Figures 5 and 6 shows a comparison of FGO maximal lagged estimation and traditional methods. Those five methods in legends have 3D positioning error of

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Fig. 5. Comparison of 3D error

Fig. 6. Errors in ENU coordinate system

4.85 m\4.00 m\3.57 m\2.49 m\2.22 m. It can be seen that the FGO method have a better accuracy over the traditional methods with the lagged estimation, and the TREKF has a poor result compared with SEKF. Figure 7 shows a comparison of real-time estimation by FGO and SEFK in a short time period. According to further processing over the FGO result, the positioning errors of lagged state in the middle are show in the Table 1.

Fig. 7. Comparison of 3D error of real-time estimation

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Table 1. 3D-RMSE comparison in different lag time. Method

Lag 10 s

Lag 5 s

Lag 1 s

Real-time

TREKF

–

–

–

4.85 m

SEKF

–

–

–

4.00 m

FGO_1

–

–

3.57 m

4.02 m

FGO_5

–

2.49 m

3.47 m

3.95 m

FGO_10

2.22 m

2.70 m

3.65 m

4.01 m

Figure 7 shows the detail of positioning error. The data point of FGO methods always fall on the data point of SEKF, like the sampling with different frequency. It means the FGO methods, regardless of sliding window sizes, have an almost identical estimation result in real-time state with the SEKF. The table shows positioning RMSE with different lag time in different methods. For FGO method with 1/5/10 sliding window, the error mainly depends on the lag time, instead of the sliding window size. Using the SEKF real-time estimation as a base level, the FGO method with 1/5/10 sliding window has a 11%, 35% and 44% accuracy improvement respectively.

5 Conclusion Aiming at the positioning problem of asynchronous observation, this paper proposes a positioning algorithm based on FGO. This method can make full use of observation in multiple epochs for joint state estimation to improve the positioning accuracy. The simulation test shows the flaw of time registration method and the relationship between the lag time and positioning errors: For real-time estimation, the FGO method has the almost identical result with the SEKF method, regardless of sliding window sizes. For lagged estimation, the positioning error has a negative correlation with the lag time; the size of sliding window only influences the acceptable lag time range and the output frequency. Those relationship can be explained by the system model: the FGO and SEFK uses the same asynchronous observation model. When using the same observation for realtime state estimation, they are equivalent. For lagged state estimation, the FGO method could use subsequent observation for further correction, similar with the smoothing of state estimation. The further study could start with the model improvement, such as using higher order of system model to fit the joint state estimation in FGO method.

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References 1. (2011) The global positioning system for military users: current modernization plans and alternatives. Congress of the United States Congressional Budget Office 2. Kepler GC (2018) Satellite navigation without clocks and ground infrastructure. In: Proceedings of the 31st international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2018). 2018:849–856 3. Reid TGR, Neish AM, Walter T et al (2018) Broadband LEO constellations for navigation. Navig J Inst Navig 65(2):205–220 4. Soualle F (2018) Perspectives of PNT services supported by mega-constellations. In: International technical symposium on navigation and timing 2018 5. (2021) Heterogeneous and asynchronous multi-sensor integrated navigation algorithm based on federated filtering. Aerosp Control39(05):27–31+38 6. Davari N, Gholami A (2019) Variational Bayesian adaptive Kalman filter for asynchronous multirate multi-sensor integrated navigation system. Ocean Eng 174:108–116 7. Peng Y, Xu Y, Jin H (2005) Analysis of time registration algorithm in multi-sensor data fusion system. Radar Confront (02):16–19+34 8. Wang X, Chen K, Wang M et al (2019) Time registration algorithm based on multi-missiles cooperative target detection. In: 2019 IEEE international conference on unmanned systems and artificial intelligence (ICUSAI). IEEE, pp 75–79 9. Kschischang FR, Frey BJ, Loeliger HA (2001) Factor graphs and the sum-product algorithm. IEEE Trans Inf Theory 47(2):498–519 10. Bai S, Lai J, Lyu P et al (2022) A novel plug-and-play factor graph method for asynchronous absolute/relative measurements fusion in multi-sensor positioning. IEEE Trans Ind Electron 11. Zhao S, Chen Y, Farrell JA (2016) High-precision vehicle navigation in urban environments using an MEM’s IMU and single-frequency GPS receiver. IEEE Trans Intell Transp Syst 17(10):2854–2867 12. Wen W, Pfeifer T, Bai X et al (2020) Comparison of extended Kalman filter and factor graph optimization for GNSS/INS integrated navigation system. Navig J Inst Navig 68(2) 13. Madsen K, Nielsen HB, Tingleff O (2004) Methods for non-linear least squares problems 14. Ly A, Marsman M, Verhagen J et al (2017) A tutorial on Fisher information. J Math Psychol 80:40–55

Evaluation and Analysis of Uplink Signal Interference in GEO Satellite System Xuyu Wang(B) , Dongfang Jiang, Bingjie Liu, Li Wang, Haoyuan Yu, Hai Sha, Heng Wei, and Yingying Zhao 32021 Troops of the PLA, Beijing 100094, China [email protected]

Abstract. Aiming at the problem of uplink signal interference in the satelliteearth link of GEO satellite system, this paper analyzes the satellite communication link interference model and interference evaluation methods, and the link interference model is constructed by considering various factors comprehensively. Then, the interference evaluation method based on the spectral separation coefficient is used to quantitatively evaluate the attenuation of carrier-to-noise ratio of the useful signals received by the receiving station from multiple dimensions. The results show that the interference effect increases with the increase of uplink interference signal power, and presents an exponential increase after reaching a certain value; Under the same interference signal power, the increase of the number of interference stations will lead to the decrease of the attenuation rate of carrier-to-noise ratio of useful signals and gradually moderate. The closer the interference station is deployed to the area near the transmitting station, the more obvious the interference effect will be. However, due to the power characteristics of the satellite transparent transponder, its position change in the nearby region has little influence on the interference effect. Keywords: GEO satellite system · Uplink interference · Interference evaluation · Carrier-to-noise ratio attenuation

1 Introduction Electronic countermeasure against satellite-earth link of satellite navigation system will be an important mode of navigation warfare in the future. The interruption or performance degradation of measurement and data links between ground stations of satellite navigation system will directly affect the generation of high-precision data of satellite ephemeris and clock correction and the timely transmission of up-loading information, posing a serious threat to the ground operation and control system of satellite navigation system. The satellite-earth link of satellite navigation system is mainly composed of uplink, downlink and satellite system. Compared with downlink interference, uplink interference can forward interference signals and useful signals to downlink together, thus reducing the carrier-to-noise ratio and affecting system performance [1]. Meanwhile, with the © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 137–153, 2024. https://doi.org/10.1007/978-981-99-6932-6_12

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gradual increase of interference power, the output power amplifier of satellite transponder will be pushed to saturation state. That is, the phenomenon of “power grabbing” causes useful signals to fail to be forwarded. Therefore, uplink interference is a very effective interference method with advantages such as wider interference range and difficulty in tracing [2]. At present, there are some literatures on uplink signal interference. Based on the interference distribution between satellite systems, Dong Suhui [3] proposed an evaluation method based on the extreme value of the interference function, focusing on the analysis of the influence of the distribution of disturbed and interfered GSO satellites on the interference-to-noise ratio of the co-direction uplink. Xu Jing [4] considers the influence of the number of interference stations, interference power, interference frequency, communication data transmission rate, modulation mode and other factors on the interference effect, and evaluates the performance of satellite communication uplink through the carrier-to-noise ratio and bit error rate. Liu Guanyi [5] studied the power conditions of the transponder under different working conditions, obtained the gain of the transponder under different uplink interference power ranges, and established the link calculation model under interference conditions on this basis. The analytical methods used in the above literatures have certain reference significance for theoretical calculation. On this basis, this paper will focus on the further study of the satellite-earth link interference model and interference assessment analysis method, so as to provide a strong theoretical support for the interference countermeasures strategy between ground stations in navigation warfare. This paper focuses on the signal interference problem in the satellite-earth link of the satellite navigation system, and studies the broadband interference and evaluation methods of the GEO satellite uplink. Firstly, the link interference model is established, including the uplink, satellite receiving gain, satellite transponder and downlink model. Then, it introduces the interference evaluation calculation method based on spectral separation coefficient under the condition of single signal interference and multi-signal interference. Finally, based on the above model and method, the reduction of carrierto-noise ratio of ground station received signal is quantitatively evaluated and analyzed from multiple dimensions such as interference power, number of interference stations and location of interference stations.

2 Analysis of Uplink Interference in GEO Satellite System GEO satellite system is composed of ground launching station, GEO satellite and receiving station. Its main functions include two aspects: first, it is used for time synchronization between stations; The second is used for data transmission between stations. Under the unified scheduling of the control system, the inter-station time synchronization and data transmission subsystem completes the data communication task between the transmitting station and the receiving station through GEO satellite. Therefore, the use of high-power interference stations to implement strong interference on the uplink will bring great harm to the GEO satellite system uplink communication, which will cause the whole satellite navigation system can not carry out normal positioning, timing and other work. The uplink interference diagram of GEO satellite system is shown in Fig. 1.

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GEO satellite

useful signal

interference signal

disturbed signal

interference station transmitter station

receiving station

Fig. 1. Diagram of uplink interference in GEO satellite system

2.1 Uplink Calculation Model Useful signals transmitted from the ground transmitting station are transmitted to GEO satellite through the uplink, and the power of useful signals received by the satellite receiving antenna is: CU =

Pu Gu GR EIRPu · GR = Lu Lu

(1)

And: Lu = Lul + Lua + Lus where, CU is the useful signal power received by the satellite antenna, Gu is the transmission gain value of the antenna of the transmitting station, Pu is the transmission power of the transmitting station, GR is the gain value of the satellite receiving antenna, Lu is the total transmission loss of the uplink of useful signals, and EIRPu is the effective omnidirectional radiated power of the transmitting station. Lul is the free space loss, Lua is the space propagation atmospheric loss, Lus is the loss of other uncertain factors. The calculation equation of free space loss is:  Lul =

4π Rf c

2 (2)

where, R is the transmission distance of the signal, f is the carrier frequency of the signal and the speed of light c = 3 × 108 m/s. Similarly, the interference signal transmitted by the interference station is transmitted to the GEO satellite through the uplink, and the power of the interference signal received by the satellite receiving antenna is: CI =

Pi Gi GR EIRPi · GR = Li Li

(3)

where, CI is the interference signal power received by the satellite antenna, Pi is the transmitting power of the interference station, Gi is the transmitting gain of the antenna of the interference station, EIRPi is the effective omnidirectional radiated power of the interference station, and Li is the total transmission loss of the uplink of the interference signal.

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Therefore, the carrier-to-noise ratio of useful signal and interference signal of the uplink are respectively: CU Pu Gu GR EIRPu GR 1 = = · · Nu KTu Lu Lu Tu K

(4)

Pi Gi GR EIRPi · GR 1 CI = = · · Nu KTu Li Li Tu K

(5)

where, Nu is the uplink noise power spectrum density of the satellite receiver, K is the Boltzmann constant, K ≈ −228.6 dBW/K, Tu is the noise temperature of the satellite receiving antenna. Because the receiving gain of satellite antenna is different in all directions, for useful signal and interference signal, the incidence Angle between them and the satellite is different, the satellite receiving gain is also different. According to the provisions of the Reference Recommendation ITU-R S.672-4 [6] of antenna orientation diagram on GEO, the relationship between signal incident Angle and signal antenna receiving gain is as follows: ⎧ GR (ϕ) = Gm − 3(ϕ/ϕ0 )2 (dB), ϕ0 ≤ ϕ ≤ 2.58ϕ0 ⎪ ⎪ ⎪ ⎨ GR (ϕ) = Gm − 20 (dB), 2.58ϕ0 < ϕ ≤ 6.32ϕ0 (6) ⎪ GR (ϕ) = Gm − 25 log(ϕ/ϕ0 ) (dB), 6.32ϕ0 < ϕ ≤ ϕ1 ⎪ ⎪ ⎩ GR (ϕ) = 0 dB, ϕ1 < ϕ ⎧ ⎨ ϕ = 32λ 0 D And: ⎩ ϕ1 = 6.32 · ϕ0 · 100.04(Gm −20) where, Gm is the maximum gain (dB) in the main lobe, ϕ0 is half of the 3 dB beam width (less than 3 dB) on the relevant plane (°), ϕ1 is the value of ϕ when the third equation GR (ϕ) of Eq. (6) is equal to 0 dB, D is the antenna diameter, λ is the wavelength. 2.2 Performance Analysis of Transparent Transponder Under Interference Conditions The satellite transparent transponder receives the weak signal from the ground, converts the signal frequency into the downlink signal, and then uses the power amplifier to amplify the signal power to realize the relay and forwarding of the signal. The power amplification of the satellite transparent transponder mainly uses TWTA (traveling wave tube amplifier), whose power characteristics are shown in Fig. 2. It should be noted that the performance analysis of the transparent transponder in this paper is based on the premise that there is no AGC or limiting protection on the satellite. As shown in Fig. 2, when the interference signal power transmitted by the interference station is small, that is, the total input power of TWTA is less than the power of the linear operating point, the TWTA works in the linear region, and then the satellite repeater gain is constant. When the total power is greater than the power of the linear operating point, the TWTA enters a nonlinear state, the power amplifier is nonlinear, the power

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Saturation operating point

POUT BOo BOi Linear operating point

PIN

Power input

Fig. 2. Power characteristics of traveling-wave tube amplifiers

gain decreases gradually, and the gain attenuation speed increases gradually with the increase of the interference power. At this time, the interference signal will occupy the power resources of useful signals. That is, the phenomenon of “power grabbing”. When the total input power is greater than the input power at the saturation operating point, the TWTA works in the saturated state, the output power is a constant value, and the power gain decreases rapidly with a constant attenuation rate. The input power and output power of the linear operating point are: Ae SFD GR BOi EIRPss = BOo

Pinline =

(7)

Poutline

(8)

The input power and output power of the saturated operating point are respectively: Ae SFD GR

(9)

Poutsat = EIRPss

(10)

Pinsat =

where, SFD is the saturation flux density of the transponder, BOi is the input rollback of the transponder, BOo is the output rollback of the transponder, EIRPSS is the constant λ2 output power value, and the effective area of the antenna Ae = GR 4π . For TWTA linear operating stage, the satellite transparent transponder power gain in this stage can be obtained according to the input power and output power of the linear operating point: G=

Poutline Pinline

(11)

For TWTA nonlinear operating stage, Saleh model can be used to describe its nonlinear characteristics [7], and the forwarder gain expression is as follows: α G= (12) √ (1 + βPin ) Pin

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where, Pin is the sum of the useful signal power and interference signal power of the transponder input. Therefore, parameters α and β can be obtained by substituting the linear operating point and the saturated operating point into the above equation. For TWTA saturation operating stage, the transponder output power is constant, and the useful signal will be affected by the compression effect and the intermodulation noise caused by the interference signal. The power characteristic of this stage is: Poutsat = EIRPss = Pin G + Pi

(13)

G×CU And: Pi = γ ×10 2[BOo ]/10 Where, Pi is the intermodulated noise power at the saturation stage, and γ is usually 5.38 [8]. According to the above, the transponder gain of this stage can be obtained:

G=

EIRPss CU 5.38×102[BOo ]/10

+ CU + CI

(14)

As can be seen from the above equation, when the power of useful signals remains unchanged, the repeater gain G will decrease with the gradual increase of the power of interference signals CI , that is, the compression degree of useful signals will gradually increase. In summary, when the power of the input useful signal of the transponder is known, the relationship between the satellite transparent transponder gain G and the input interference signal power of the transponder CI is as follows [5]: ⎧ 4π · EIRPSS BOi λ2 SFD ⎪ ⎪ , C + C ≤ ⎪G = U I ⎪ ⎪ λ2 BOo SFD 4π BOi ⎪ ⎪ ⎪ ⎨ α λ2 SFD λ2 SFD G= , ≤ CU + CI ≤ √ (15) 4π (1 + β(CU + CI )) CU + CI 4π BOi ⎪ ⎪ ⎪ ⎪ ⎪ EIRPSS λ2 SFD ⎪ ⎪ ⎪ G = , ≤ CU + CI ⎩ CU 4π 2[BOo ]/10 + CU + CI 5.38·10

2.3 Downlink Calculation Model Interference signals and useful signals are amplified by the power of the transparent transponder of the satellite and then sent to the ground receiving station through the transmitting antenna. The power of useful signals and interference signals received by the receiving station are respectively: CU =

CU GGsat Gr EIRPu · Gr = Lu Lu

(16)

CI =

EIRPi · Gr CI GGsat Gr =  Li Li

(17)

where, CU is the useful signal power received by the receiving station, CI is the interference signal power received by the receiving station, Gsat is the gain of the satellite

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transmitting antenna, Gr is the gain of the receiving station receiving antenna, Lu is the total transmission loss of the downlink of useful signals, Li is the total transmission loss of the downlink of interference signals, and EIRPu is the effective omnidirectional radiation power of the satellite useful signals. EIRPi is the effective omnidirectional radiated power of satellite interference signal. At the same time, it can be obtained that the carrier-to-noise ratio of useful signal and interference signal of downlink are respectively: CU CU GGr EIRPu Gr 1 = = · · Nd KTd Lu Lu Td K

(18)

CI EIRPi Gr 1 CI GGr = = · · Nd KTd Li Li Td K

(19)

where, Nd is the noise power spectrum density of the receiving station, and Td is the noise temperature of the receiving station receiving antenna. Finally, by combining the uplink calculation model and downlink calculation model, the total link carrier-to-noise ratio of useful signal and interference signal can be obtained as follows:   −1  −1  CU CU −1 C = + (20) N0 Nu Nd  −1  −1  CT CI CI  −1 = + (21) N0 Nu Nd

3 Signal Interference Calculation Method Based on Spectral Separation Coefficient 3.1 Single-Signal Interference Calculation Method Spectrum separation coefficient (SSC) is used to calculate the noise amount caused by a single external signal entering the receiver at the same time with the desired signal, so it can be used as a measure to measure the interaction and interference between different signals in the same band, and is defined as [9]: +β

r/ 2

κX ,I =

SX ,βr (f )SI ,βr (f )df

(22)

−βr / 2

where, SX ,βr (f ) and SI ,βr (f ) respectively represent the expected signal sX (t) and the interference signal sI (t) normalized power spectral density on the bandwidth βr . According to the above equation, the spectral separation coefficient κX ,I represents the power spectral density overlap degree between the desired signal and a certain interference signal. The higher the overlap degree, the larger the spectral separation coefficient κX ,I , and the higher the interference degree between the two signals [10].

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Based on the spectral separation coefficient, the equivalent carrier-to-noise ratio of signal acquisition, carrier tracking and data bit demodulation under signal interference is [11]: 

And: λ =

+βr / 2 −βr / 2

C N0

 = eff

  CI κX ,I −1 C 1+ N0 N0 λ

(23)

SX ,∞ (f )df

where, C represents the expected signal power, CI represents the interference signal power, and N0 represents the spectral density of noise power. If the receiving bandwidth βr is wide enough so that the power of the signal SX (f ) basically enters the receiving bandwidth, λ ≈ 1. Therefore, the attenuation of the carrier-to-noise ratio of the interference effect is:     CI κX ,I −1 C C 1+ = (24) N0 eff N0 N0 λ The attenuation of the carrier-to-noise ratio in dB is obtained by simplifying Eq. (24):     CI κX ,I C = 10 lg 1 + (25) N0 N0 λ According to Eq. (25), the smaller the spectral separation coefficient κX ,I is, the smaller the attenuation of the carrier-to-noise ratio is, and the smaller the signal interference influence degree is. 3.2 Multi-signal Interference Calculation Method Based on single-signal interference calculation method, the equivalent carrier-to-noise ratio of signal acquisition, carrier tracking and data bit demodulation caused by multisignal interference can be obtained similarly: 

C N0

 eff

⎛ C⎝ = 1+ N0

 i

CIi κX ,Ii N0 λ

⎞−1 ⎠

(26)

where, CIi represents the power of the i interference signal sIi (t), and κX ,Ii represents the spectral separation coefficient between the interference signal sIi (t) and the expected signal sX (t). The attenuation of the corresponding carrier-to-noise ratio is (in dB):  ⎛ ⎞ CIi κX ,Ii   C i ⎠ = 10 lg⎝1 + (27) N0 N0 λ

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4 Analysis of the Influence of Uplink Interference on the Carrier-to-Noise Ratio This section aims to study the influence of uplink interference on the carrier-to-noise ratio of the useful signal received by the receiving station from the perspective of quantitative analysis. The main factors include the power of the interference signal transmitted by the interference station, the number of interference stations and the geographical location of the interference station. 4.1 Influence of Interference Signal Power When analyzing the carrier-to-noise ratio attenuation of useful signals received by the receiving station under the condition that the interference station transmits interference signals of different powers, the position of the interference station and the disturbed GEO satellite is fixed, so the distance between the interference station and the disturbed GEO satellite remains unchanged regardless of how the interference power changes, that is, the transmission distance of the interference signal and the transmission loss of the interference uplink Li are both fixed. At the same time, the incident Angle of interference signal is unchanged, and the signal receiving gain is also constant. The uplink interference scenario constructed during the analysis is shown in Fig. 1. The atmospheric loss of space propagation is about 0.8 dB, and the loss of other uncertain factors is about 0.8 dB. Other related parameters of the link are shown in Tables 1, 2, 3 and 4. Table 1. Transmitting station related parameters Parameter

Value

Uplink transmitting frequency f

6000 MHz

Power amplifier output power Pu

15 dBw

Antenna transmitting gain Gu

10 dB

Table 2. Interference station related parameters Parameter

Value

Uplink transmitting frequency f

6000 MHz

Antenna transmitting gain Gi

20 dB

The locations of GEO satellites (0°N, 37°E), transmitting stations (23°N, 29°E), receiving stations (23°N, 37°E) and interference stations (23°N, 34°E) were kept fixed, and the interference power set of interference stations was established, denoted as Pi = {Pi1 , Pi2 , . . . , Pin }, 10 ≤ Pi ≤ 30 (dBw), with a power interval of 1 dBw. In this paper,

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Parameter

Value

Maximum antenna receive gain Gm

28 dB

Antenna transmitting gain Gsat

20 dB

Antenna noise temperature Tu

290 K

Saturated radiated power EIRPSS

49 dBw

Input rollback BOi

6 dB

Output rollback BOo

3 dB

Saturation flux density SFD

−90 dB/m2

Diameter of satellite receiving antenna D

3m

Table 4. Receiving station related parameters Parameter

Value

Receiving antenna quality factor G/T

32 dB/K

Downlink transmitting frequency f

4000 MHz

it is assumed that the receiving station has infinite bandwidth βr , that is λ ≈ 1, the spectral separation coefficient between the useful signal and the interference signal is − 71.86 calculated according to Eq. (22) [12]. Figure 3 shows the carrier-to-noise ratio attenuation curve of useful signals of GEO satellite downlink received by the receiving station under the circumstance that the interference station transmits interference signals of different powers. The coordinate axes represent the carrier-to-noise ratio attenuation and interference signal power respectively, which graphically reflects the influence of interference signals of different powers on the value and rate of change. As can be seen from Fig. 3, with the continuous increase of uplink interference signal power of the interference station, the reduction range of the carrier-to-noise of useful signals is also increasing, that is, the interference effect on signals is more significant. When the uplink interference signal power is less than 20 dBw, the reduction range of carrier-to-noise ratio is less than 1 dB and the range change is small, while when the signal power is greater than 20 dBw, the reduction range of the carrier-to-noise ratio will change significantly, showing an exponential increase. Under different interference power, the specific results of the carrier-to-noise ratio attenuation of useful signal caused by uplink interference signal are shown in Table 5. Figure 4 shows the transparent transponder power gain curve of GEO satellite with different uplink interference signal power. The coordinate axes represent transponder gain and interference signal power respectively, which reflects the influence of different power interference signals on amplifier power characteristics.

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Fig. 3. Attenuation curve of useful signal carrier-to-noise ratio under different interference power

Table 5. Calculation results of attenuation of useful signal carrier-to-noise ratio under different interference power Interference power/dBw

The carrier-to-noise ratio attenuation/dB

10

0.10

15

0.31

20

0.90

25

2.38

30

5.20

Fig. 4. Power gain curves of satellite transparent transponder under different interference power

As can be seen from Fig. 4, when the uplink signal interference power is less than 26 dBw, the transponder is in the linear operating region, and the transponder gain is constant 179 dB. When the uplink interference power is between 26 dBw and 27 dBw, the transponder gain gradually decreases, and when the interference power is 27 dBw,

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the transponder gain is 178.7 dB. When the interference power is greater than 27 dBw, the transponder gain decreases rapidly with a constant attenuation. 4.2 Influence of the Number of Interference Stations The locations of the disturbed GEO satellite (0°N, 37°E), the transmitting station (23°N, 29°E) and the receiving station (23°N, 37°E) are kept fixed. Similarly, the relevant parameters are calculated by using links in Tables 1, 2, 3 and 4 of Sect. 4.1, and the number of interference stations is set up, denoted as N = {N1 , N2 , . . . , Nn }, 1 ≤ N ≤ 5 Meanwhile, it is assumed that the distance between each interference station is ignored. Therefore, the position of each interference station is (23°N, 34°E). Because the relative positions between the transmitting station, interference station and the disturbed GEO satellite remain unchanged, the transmission distance and the transmission loss of the interference signal, and the reception gain of the interference signal are all constant values. Based on the conclusions in Sect. 4.1, the interference signal power variation range of the interference station is kept unchanged, that is Pi = {Pi1 , Pi2 , . . . , Pin }, 10 ≤ Pi ≤ 30 (dBw), and the power interval is 1 dBw. Further interference analysis is carried out for different numbers of interference stations. For the whole interference link, the influence of multiple interference signals superposition on the power performance of the satellite transparent transponder and on the reduction of the carrier-to-noise ratio of useful signals should be considered. Figure 5 shows the carrier-to-noise ratio attenuation curve of useful signals of GEO satellite downlink received by the receiving station under different numbers of interference stations. The coordinate axes represent the carrier-to-noise ratio attenuation and interference signal power respectively.

Fig. 5. Attenuation curve of useful signal carrier-to-noise ratio under different number of interference stations

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As can be seen from Fig. 5, with the increase of interference power of interference stations, the attenuation of useful signal the carrier-to-noise ratio also increases gradually and tends to be linear. Meanwhile, the interference power required for linearization is different with different number of interference stations. The linearization of 5 interference stations requires 23 dBw interference power while that of 1 interference station requires 28 dBw interference power. By comparing the number of interference stations, it can be seen that when the interference power is small, the interference degree of different interference stations to useful signals has a small difference. However, with the gradual increase of the interference power, the interference degree difference also gradually increases, and tends to be stable after reaching a certain interference power. Figure 6 shows the carrier-to-noise ratio attenuation curve of useful signals when the interference power is 25 dBw with different number of interference stations. The axes represent the carrier-to-noise ratio attenuation and number of interference stations respectively.

Fig. 6. Attenuation curve of useful signal carrier-to-noise ratio under different number of interference stations deployed when the interference power is 25 dBw

Table 6. Calculation results of attenuation of useful signal carrier-to-noise ratio under different number of interference stations when the interference power is 25 dBw Number of interference stations

The carrier-to-noise ratio attenuation/dB

1

2.38

2

3.91

3

5.04

4

5.93

5

6.67

As can be seen from Fig. 6, with the increase of the number of interference stations deployed, the range of the carrier-to-noise ratio decline gradually increases. When the

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number of interference stations is small, the trend of the carrier-to-noise ratio decline is faster; however, when the number of interference stations increases to a certain number, the rate of the carrier-to-noise ratio decline gradually tends to moderate with the increase of the number of interference stations (Table 6). 4.3 The Effect of Interference Station Deployment Location In the analysis process of this section, the influence of the deployment location of interference station on the carrier-to-noise ratio of useful signals is mainly analyzed. The interference station is selected near the location of the transmitting station (23°N, 29°E). The analysis method is similar to that of the above two sections, but the difference is that the distance between the interference station and the disturbed GEO satellite is different due to the different deployment locations of the interference station, that is, the transmission distance of the interference signal and the transmission loss of the interference uplink are different. Meanwhile, the incident Angle of the interference and the signal receiving gain is different. The locations of the disturbed GEO satellite (0°N, 37°E), the transmitting station (23°N, 29°E) and the receiving station (23°N, 37°E) were kept fixed, and the relevant parameters in Tables 1, 2, 3 and 4 in Sect. 4.1. The deployment location set of the interference station was established, denoted as Q = {Q1 , Q2 , . . . , Qn }, Qi = [Lqi , Bqi , Hqi ]T , i = 1, 2, . . . , n, Lqi , Bqi , Hqi and respectively the longitude, latitude and height of the interference station. In this paper, it is assumed that the height of all interference stations is 0 m, the latitude and longitude interval is 1°, and the transmitting power of each interference station is the same as 25 dBw. Figure 7 shows the attenuation distribution of carrier-to-noise ratio of useful signals under different deployment locations of interference stations. The coordinate axes represent longitude and latitude of jamming stations respectively.

Fig. 7. Attenuation distribution diagram of useful signal carrier-to-noise ratio under different positions of interference stations

As shown in Fig. 7, the distribution diagram of the carrier-to-noise ratio attenuation shows a trend of gradually decreasing outward with the vicinity of the transmitting station

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as the center. After reaching a certain boundary, the decrease of the carrier-to-noise ratio will approach 0. When the interference station is placed near the transmitting station, namely the yellow area in the center of the figure, the interference on the uplink signal is larger due to the small incidence Angle of the interference signal in this area and the larger reception gain of the satellite antenna. The maximum attenuation of the carrier-to-noise ratio occurs in the position with the latitude difference of 3° and longitude difference of 1.5° from the transmitting station, namely, the position of the jamming station is (20°N 30.5°E). At this time, the decrease of the carrier-to-noise ratio is affected by the incident Angle and signal transmission distance, and the maximum attenuation is 6.51 dB. At the same time, the interference signal power transmitted by the interference stations deployed in the central region makes the satellite transparent transponder reach saturation stage, resulting in the constant output power of the transponder. Therefore, the distribution of the interference stations in different locations in this region has little influence on the interference of useful signals. For the interference countermeasures strategy between ground stations, in order to make the useful signals received by the enemy station lose frames to achieve the result of information decoding failure, it is necessary to determine the reduction of the carrierto-noise ratio, so as to obtain the interference signal power required by the interference station. Therefore, based on the above calculation results, the transmitting power of interference signals deployed at different geographical locations can be analyzed in reverse under the condition of constant reduction in the carrier-to-noise ratio of useful signals. Figure 8 shows the power distribution of transmitted interference signals required by interference stations in different geographical locations with the reduction of the carrier-to-noise ratio is 2 dB. The coordinate axes represent the deployment longitude and latitude of interference stations respectively.

Fig. 8. Power distribution diagram of transmitted interference signal required by interference stations under different positions when the attenuation of carrier-to-noise ratio is 2 dB

It can be seen from Fig. 8 that the closer the area is to the transmitting station, the smaller the power of the interference signal needed to be transmitted when the reduction of the carrier-to-noise ratio is constant. Similarly, due to the power characteristics of the

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transparent transponder of the satellite, the distribution of the interference station in the central area has little influence on the power of the required interference signal, and the minimum transmitted power of the interference station in the distribution is 17.3 dBw. The maximum value is 37.5 dBw. Based on the above analysis, the interference power and the deployment position of interference stations can be selected according to the interference degree required by the interference strategy.

5 Conclusion In this paper, the uplink signal interference in the satellite-earth link of GEO satellite navigation system is studied, and the link interference model is constructed by considering various factors comprehensively, and the interference evaluation method based on spectral separation coefficient is used to simulate and analyze the reduction of the carrier-to-noise ratio of useful signal receiving from multiple dimensions. The simulation results show that: (1) With the continuous increase of uplink interference signal power, the decrease of the carrier-to-noise ratio of useful signal is also increasing. When the interference signal power is small, the decrease of the carrier-to-noise ratio has a small change, while when the signal power is greater than a certain value, the decrease of the carrier-to-noise ratio will have a significant change, showing an exponential increase. (2) When the interference power is small, the difference of interference degree caused by different number of interference stations is small. With the increase of interference power, the difference of interference degree also increases and gradually tends to be stable. Under the condition of the same power, when the number of interference stations increases to a certain amount, the increase of the number will lead to the decrease of the carrier-to-noise ratio attenuation rate and gradually moderate. (3) Due to the influence of the incident Angle and transmission distance of the interfered signals, the closer the interference station is deployed to the area near the transmitting station, the stronger the interference on the useful signals will be and the more obvious the effect will be. However, due to the power characteristics of the satellite transparent transponder, the position deployment of the interference station in the central area has little influence on the signal interference effect.

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6. ITU-R (1997) Satellite antenna radiation pattern for use as a design objective in the fixedsatellite service employing geostationary satellites: ITU-R S. 672-4. ITU, Geneva 7. Gang Y, Jing S (2008) Simulation analysis of the influence of nonlinear power amplifier on digital communication. Electron Eng 34(09):7–10 8. Eftekharietal R, Lee J, Perillan L (2013) Communications design considerations in interference limited satellite networks. In: Communications satellite systems conference, 2013, pp 504–511 9. Betz JW (1999) The offset carrier modulation for GPS modernization. In: Proceedings of ION NTM 99. San Diego, CA, pp 639–648 10. Jianjun Z, Xiaochun L, Hong Y (2010) Evaluation and analysis of intrasystem interference performance of the satellite navigation signal. In: The first China satellite navigation annual conference, 2010, pp 491–502 11. Gang X (2015) Principles of GNSS: GPS, GLONASS, and Galileo. Publishing House of Electronic Industry, Beijing, p 6 12. Xinyan Z, Xiaodong Z, Shusen T (2009) Simulation and analysis of interference between compass and GPS in L1 band. J Geomat Sci Technol 26(03):216–219

Impact of Temporally Correlated Error on ARAIM ISM During Ionospheric Storm Period Jin Chang(B) , Zhongjun Qu, Xiaotang Lian, and Zhongzhi Wang AVIC Xi’an Flight Automatic Control Research Institute, Xian, China [email protected]

Abstract. Ionospheric delay error is one of the main errors of satellite navigation system. The unstable physical characteristics of ionosphere can severely affect the performance of satellite navigation. Therefore, civil aviation standards require that the impact of ionospheric anomalies (especially ionospheric storms) should be considered in integrity monitoring. To meet the safety requirement of satellite navigation service in civil aviation, it is urgent to analyze the performance of dual-frequency multi-constellation integrity monitoring under stormy condition. In this paper, the empirical model and temporally correlated stochastic error model are used to analyze the ionospheric errors in carrier smoothed code. The Gaussian overbound method is then applied to conservatively represent the error distribution of the temporally corelated stochastic error model. The worst-case overbounding result is used to revise Integrity Support Message (ISM) and evaluate the performance of Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm under stormy condition. The experimental results show that the occurrence of ionospheric storm is able to increase the nominal bias and error variance in ISM and degrade the performance of ARAIM. This study provides an effective method to refine the ISM in ARAIM during ionospheric storm period. Keywords: Integrity monitoring · Ionospheric delay error · Ionospheric storm · Higher order ionospheric error · Temporally corelated stochastic error model

1 Introduction The ionosphere refers to the atmosphere from 50 km to 1000 km above the sea level. When satellite navigation signals pass through the ionosphere, their speed and propagation direction are changed due to the influences of electrons and ions, resulting in temporally correlated ionospheric delay error in pseudorange and carrier phase measurements [1–3]. In general, ionospheric delay leads to measurement errors of several meters [4]. However, when solar radiation is intensified, the occurrence of ionospheric anomaly leads to measurement errors up to tens of meters [4]. Since the mid and low latitude regions are susceptible to ionospheric anomalies [5], to ensure the flight safety of civil aircraft, Radio Technical Commission for Aeronautics (RTCA) have clearly pointed out that the integrity monitoring of airborne satellite navigation equipment needs to consider the impact of ionospheric anomalies (especially ionospheric storms) [6]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 154–167, 2024. https://doi.org/10.1007/978-981-99-6932-6_13

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Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is designed for Dual-Frequency Multi-constellation (DFMC) Global Navigation Satellite System (GNSS). With the dual-frequency correction, up to 95% ionospheric errors are eliminated [1]. Since the remaining ionospheric delay error (higher-order terms of ionospheric error) have little influence on the positioning results (roughly 2–4 cm) [7], ARAIM does not consider the impact of ionospheric error on integrity monitoring results under normal condition. When ionospheric storm occurs, the increase of Total Electron Content (TEC) leads to the increments of high-order ionospheric error, which degrades the performance of dual-frequency correction. To ensure the conservativeness and accuracy of airborne integrity monitoring results, it is necessary to quantify the impact of ionospheric storms on ARAIM and its Integrity Support Message (ISM). To evaluate the impact of ionospheric storms on ARAIM ISM, the ionospheric delay error is represented by the sum of empirical model and temporally correlated stochastic error model. By performing two step Gaussian overbound method on each sampling epoch, a conservative representation of the temporally correlated stochastic error is obtained. After quantifying the effects of dual-frequency correction and smoothing filter on the high-order ionospheric error, the ISM during ionospheric storm period is acquired. Using the revised ISM, the global performance of airborne ARAIM under stormy condition is evaluated.

2 Ionospheric Delay Error Under Stormy Conditions For ionospheric delay error, the first-order term is main part, the second-order term is 2 orders of magnitude smaller than the first-order term, and the third-order term is 3 orders of magnitude smaller than the first-order term [8]. Therefore, we only discuss the first-order and second-order terms of ionospheric error in this paper. In pseudorange measurement, the first-order term IP,1 and the second-order term IP,2 can be expressed as [9]:  40.3 Ne dL IP,1 = (1) f2  7527.87c Ne |B0 |cosθB dL (2) IP,2 = f3 where Ne is the electron density; L represents the signal propagation path; c is the speed of light in a vacuum; B0 represents the geomagnetic induction vector at the ionosphere pierce point; θB represents the angle between B0 and the line-of-sight direction at ionosphere pierce point; f is the signal frequency of GNSS. In carrier phase measurement, the first-order term I,1 and the second-order term I,2 can be expressed as [9]:  40.3 Ne dL I,1 = − (3) f2  7527.87c Ne |B0 |cosθB dL (4) I,2 = − 2f 3

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In Eqs. (1) and (2), the maximum value of |B0 | and cosθB can be determined along the signal propagation path, which is able to conservatively represent the first-order and the second-order ionospheric term. The maximum values of |B0 | and cosθB are represented by |Bmax | and cosθB,min respectively. If we denote Ne dL as S, IP,1 and IP,2 can be rewritten as: 40.3 (5) IP,1 = 2 S = K1 S f 7527.87c|Bmax |cosθB,min S = K2 S (6) IP,2 = f3 IP,1 and IP,2 can be simplified to Eqs. (7) and (8):  40.3 Ne dL I,1 = − = −K1 S f2  7527.87c Ne |B0 |cosθB dL 1 = − K2 S I,2 = − 3 2f 2

(7) (8)

Since ionospheric delay error has a great impact on GNSS positioning results, the single frequency receiver in civil aviation utilizes empirical model to reduce the ionospheric error in GNSS measurement. However, when ionospheric storm occurs, the ionospheric delay error cannot be eliminated only by empirical model [10]. By analyzing the large amount of data collected under stormy conditions, the remaining error can be represented by second-order Gauss Markov process [10], whose transfer function is:  4σs2 ξ ω03 (9) G(s) = 2 s + 2ξ ω0 s + ω02 where σs2 is the variance of the Gaussian white noise process; ξ is the damping ratio; ω0 is the natural frequency. During ionospheric storm period, it is difficult to obtain the data of global ionospheric delay error at different frequencies. Therefore, we use the empirical model and the temporally correlated stochastic error model in (9) to represent the ionospheric delay error pseudorange measurement at a fixed frequency under stormy conditions. The pseudorange ionospheric delay error IP (t) and the carrier phase ionospheric delay error I (t) at epoch t can be expressed as: IP (t) = IP,k (t) + P (t) = K1 S + K2 S

(10)

1 (11) I (t) = −K1 S − K2 S 2 where IP,k (t) represented the value calculated by ionospheric empirical model. P (t) is the random error that represents the uncorrected ionospheric delay error. According to (10), the TEC can be expressed as IP,k (t) + P (t) (12) K1 + K2 Then the ionospheric delay error in pseudorange and carrier phase measurements can be represented by using (12). S=

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3 The Conservative Representation of Gauss Markov Process Gaussian overbound method is widely used in GNSS integrity monitoring because it can conservatively represent any form of sampling distribution [11]. However, the statistical characteristics of stochastic process vary with time. Therefore, Gaussian overbound method needs to be applied at each sampling epoch to obtain the conservative representation of Gauss Markov process. Gaussian Markov process is a Gaussian process with Markovian characteristics. For a Gaussian process X (t), for ∀n, the random vector X = [X (t1 ), X (t2 ), · · · , X (tn )]T (X is formed by ∀t1 , t2 , · · · , tn ) follows the n-dimensional Gaussian distribution. Therefore, the distribution of the Gaussian Markov process at any sampling epoch follows 1-dimensional Gaussian distribution. Hence, it is reasonable to conservatively represent the Gauss-Markov process with the Gaussian distribution. To better understand the Gaussian overbound at different epochs, take Fig. 1 as an example, assuming that a Gaussian Markov process is sampled ten times (the sampling interval is T ), which corresponds to the ten curves in Fig. 1, the distributions of 200 T and 400 T are denoted as X (t1 ) and X (t2 ) respectively. Gaussian overbound at 200 T refers to overbound the sampling distribution at 200 T .

Fig. 1. Discrete Gaussian Markov process

If there is a discrete Gaussian Markov process XGM (tn ), for ∀n, XGM (tn ) follows Gaussian distribution. Using Gaussian overbound method, XGM (tn ) can be conservatively expressed as X GM (tn ). X GM (tn ) also follows Gaussian distribution (the mean value is μtn , the variance is σt2n ). The conservative representation of XGM (tn ) is to find max{μtn } and max{σt2n } (n = 1, 2, . . . ). 



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4 Measurement Error Caused by Ionospheric Storm In DFMC integrity monitoring milestone report released by ARAIM technical subgroup [12], carrier smoothed code is applied to DFMC positioning in civil aviation. There are two steps to generate the carrier smoothed code in civil aviation: 1. Calculate the ionosphere-free combination measurement; 2. Mitigate the noise in combination measurement by using first-order low-pass filter. The purpose of section is to analysis the measurement error in carrier smoothed code caused by ionospheric storm. 4.1 Ionosphere Error in Ionosphere-Free Combination Measurement Under Stormy Conditions Since dual frequency correction can completely eliminate the first-order ionospheric error, this section focuses on the second-order error in ionosphere-free combination measurement. The pseudorange ionosphere-free combination measurement ρ can be expressed as: ρ=

f12

ρ − 2 1

f12 − f2

f22 f12 − f22

ρ2

(13)

where ρ1 and ρ2 are pseudorange measurements at frequency f1 and f2 . Based on (2), the second-order ionospheric error in ρ can be conservatively expressed as: f22 7527.87c|Bmax |cosθB,min 7527.87c|Bmax |cosθB,min S − S f12 − f22 f13 f12 − f22 f23 1 =− 7527.87c|Bmax |cosθB,min S (14) f1 f2 (f1 + f2 )

I2, ρ =

f12

Based on (12) and (14) is rewritten as: I2, ρ = K3 S = K3

IP,k (t) + 2, ρ (t) K1 + K2

(15)

where 2, ρ (t) is the ionospheric error caused by random error P (t). The carrier phase ionosphere-free combination measurement φ can be expressed as: φ=

f12 f12

φ1 − f22

−

f22 f12

− f22

φ2

(16)

where φ1 and φ2 are carrier phase measurements at frequency f1 and f2 . Based on (8) and (15), the second-order ionospheric error in φ can be conservatively expressed as: I2, φ = −K3

IP,k (t) + 2, φ (t) 2(K1 + K2 )

where 2, φ (t) is the ionospheric error caused by random error P (t).

(17)

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4.2 Ionospheric Error in Carrier Smoothed Code During Storm Period Although the ionosphere-free combination measurement is able to eliminate most of the ionospheric delay error, the combination also amplifies the noise of the measurement [13]. Carrier smoothed code is applied to decrease the noise in the combination measurement. The structure of the smoothing filter is shown in Fig. 2. In Fig. 2, ρ is the pseudorange ionosphere-free combination measurement; φ is the carrier phase ionosphere-free combination measurement; ρφ is the difference between ρ and φ; F(s) is a fixed-gain first-order low-pass filter; When ρφ passing through the first-order low-pass filter, the result is denoted as ρφ ; ρ˜ is the carrier smoothed code. 

Fig. 2. The diagram of carrier smoothed code

According to Fig. 2, the error in ρφ caused by the second-order term of ionospheric error can be expressed as: I2, ρ − I2, φ =

3K3 IP,k (t) + 2, ρ (t) + 2, φ (t) 2(K1 + K2 )

(18)

Since the ionospheric delay calculated by empirical model usually represents the ionospheric error under normal condition, IP,k (t) cannot change drastically in a short period of time. Therefore, IP,k (t) can be considered as a constant which is denoted as IP,k0 . By using the Laplace transform, the filter input caused by IP,k (t) can be expressed as:   3K3 IP,k0 3K3 (19) IP,k (t) = L 2(K1 + K2 ) 2(K1 + K2 ) s After passing through the smoothing filter, the additional error I introduced by smoothing filter can be expressed as:   3K3 IP,k0 I = L−1 (20) (F(s) − 1) 2(K1 + K2 ) s Based on (20), the steady state of I can be expressed as:     IP,k0 τs 3K3 I s = lim s · =0 s→0 2(K1 + K2 ) τ s + 1 s

(21)

According to (21), for IP,k0 , the smoothing filter does not introduce additional error. The following analysis focuses on the random error in (18). Based on Sect. 3, the random error can be conservatively represented by a normal distribution. Assuming that the conservative representation of P (t) follows normal distribution, the mean value and

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standard deviation are denoted as μmax and σmax . Based on (14), the mean and variance of 2, ρ (t) can be expressed as:

μmax E 2, ρ (t) = K3 K1 + K2

(22)

2 2 1 7527.87c|Bmax |cosθB,min σmax D 2, ρ (t) = f1 f12 − f22 (K1 + K2 )2  2 2 7527.87c|Bmax |cosθB,min σmax 1 + f2 f12 − f22 (K1 + K2 )2

 2  2  2 f2 σmax f1 − K K = + − (f1 − f2 ) 3 (f1 − f2 ) 3 (K1 + K2 )2





(23)

According to (7) and (8), the mean and variance of 2, φ (t) can be expressed as:

E 2, φ (t) = −K3

μmax 2(K1 + K2 )

 2  2  2

f2 K 3 σmax f1 K 3 − + − D 2, φ (t) = 2(f1 − f2 ) 2(f1 − f2 ) (K1 + K2 )2

(24)

(25)

The discrete time-domain expression of the first-order low-pass filter F(s) can be written as: 

ρφ (tk ) =

1 N −1 ρφ (tk ) + ρφ (tk−1 ) N N 

(26)

where tk is the k-th sampling epoch. N = τ/Ts , Ts is the sampling interval, τ is the time constant of the filter. Let 2, ρφ (t) = 2, ρ (t)+2, φ (t), when 2, ρφ (t) passing through the filter, the result is denoted as  2, ρφ (t). Based on (26),  2, ρφ (tk ) is expressed as: 





 2, ρφ (tk ) =

1 N −1 2, ρφ (tk ) +  2, ρφ (tk−1 ) N N 

(27)

˜ the mean value of Considering the impact of IP,k (t), according to (27), in ρ, measurement error caused by ionosphere can be expressed as: ˜ k )) = K3 E(ρ(t

μmax 3K3 Ik0 + K1 + K2 2(K1 + K2 )

(28)

The variance of measurement error caused by ionosphere can be expressed as: 2 σρ(t ˜ k) =





1  D 2, ρ (tk ) + D 2, φ (tk ) + D 2, φ (tk ) 2N − 1

(29)

According to (28) and (29), the distribution of ionospheric error in carrier smoothed code is obtained.

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5 Simulation In this section, ionospheric error in carrier smoothed code during the storm period is conservatively quantified, and its impact on ISM is analyzed. Global ARAIM performance is then evaluated with the revised ISM. 5.1 Measurement Error Caused by the Second-Order Ionospheric Term To find the maximum of (2(K1 + K2 ))−1 3K3 IP,k (t), we need to find the maximum of (2(K1 + K2 ))−1 3K3 in advance. By using the 12th generation of International Geomagnetic Reference Field (IGRF-12) model, the variation range of |Bmax | can be determined (from 20000nT to 60000nT). As to cosθB,min , it varies from −1 to 1. According to the variation range of |Bmax | and cosθB,min . The variation range of (2(K1 + K2 ))−1 3K3 is shown in Fig. 3. The maximum of (2(K1 + K2 ))−1 3K3 equals to 0.0024.

3 Fig. 3. The range of variation of 2(K3K+K 1 2)

To obtain the global variation of IP,k (t), we first obtain the ionospheric delay error under normal conditions. Take ionospheric error at GPS L1 on October 16, 2022 as an example, as shown in Fig. 4, global ionospheric delay error varies from 0 m to 18 m. In this section, the Klobuchar model is selected as the empirical model. Based on [14, 15] and [16], Klobuchar model can approximately eliminate up to 70% of the ionosphere delay error. Therefore, the IP,k (t) ranges from 0 m to 13 m. 2 ˜ k )) and σρ(t To obtain E(ρ(t ˜ k ) , the conservative representation of P (t) should be determined at first. Based on [17], P (t) is a second order Gauss Markov process, which can be expressed as: ¨P (t) = −2ξ ω0 P (t) − ω02 ˙P (t) + w(t)

(30)

where w(t) is Gaussian white noise process, of which the variance is σ 2 . After the discretization (detailed derivation of discretization can be found in Appendix 7), the discretization form of (30) is rewritten as a AR(2) model: ∗ P,k = a1 P,k−1 + b1 P,k−2 + Twk−1

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Fig. 4. The global TEC on October 16th, 2022 and the corresponding ionospheric Delay for GPS L1 signal (the figure is from http://swaciweb.dlr.de)

  ∗ = (2 − 2ξ ω0 T )P,k−1 − ω02 T 2 + 1 − 2ξ ω0 T P,k−2 + Twk−1

(31)

∗ where T is the sampling interval. wk−1 is the discrete Gaussian white noise process. The 2

∗ variance of wk−1 is T 3 σ . Based on [10], σ 2 can be expressed as:

σ 2 = 4ξ ω03 σ2P (t)

(32)

In (32), σ2P (t) is denoted as [10]: σP (t)

 1  Re cos(E) − 2 = 1− τv = kv τv Re + 350

(33)

where Re is the earth’s radius in Km. E is the elevation angle of satellite. τv is represented as: ⎧ ⎨ 9 m, 0◦ ≤ |latitude| < 20◦ τv = 4.5 m, 20◦ ≤ |latitude| < 55◦ (34) ⎩ 6 m, 55◦ ≤ |latitude| < 90◦ When E equals to 0◦ , the maximum of kv can be obtained. Therefore, σP (t) can be represented by 4.4τv conservatively. Based on the discretization form of (30), the ionospheric temporally correlated stochastic errors at different latitudes are shown in Fig. 5. Since ionospheric storm can affect navigation service for several hours [18], to obtain the worst-case distribution of P (t), we assume that the duration time of ionospheric storm is 5 h and the sampling interval is set to 1s. Based on the overbound method described in Sect. 3, after discretizing P (t) at the low latitude 5000 times, the conservative representation of P (t) can be obtained. The overbounding results are shown in Fig. 6. Because the variance σ 2 in low latitude area is greater than it in middle latitude and high latitude areas, the overbounding result of P (t) in low latitude area can also conservatively represent the stochastic error model in middle and high latitude areas.

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Fig. 5. Discrete second-order Markov process driven by different Gaussian noise

5.2 Global simulation of ARAIM GPS L1/L5 and Galileo E1/E5a measurements are used in the simulation. The number of satellites in GPS and Galileo constellation is both 27. The navigation performance requirement in this simulation is based on Localizer Performance with Vertical Guidance200 (LPV-200) service. According to 5.1, the ionospheric delay error during the storm period follows the normal distribution with the mean value of 23.41 cm and the standard deviation of 31.34 cm. ARAIM usually uses bnorm in ISM to indicate the nominal bias of measurement error, which is set to 0.75 m in our simulation (based on [12]). Due to the occurrence of ionospheric storm, the additional bias caused by ionospheric delay error should be considered in ISM, the corrected nominal bias bnorm can be expressed as: bnorm = bnorm + 23.41cm

(35)

Moreover, ARAIM uses the square of User Range Accuracy (URA) σURA in ISM to calculate the variance of measurement error σs2 [19], which is set to 1m in our simulation (based on [12]). Due to the occurrence of ionospheric storm, the additional error variance caused by ionospheric delay error should be considered, the corrected variance σ˜ s2 of carrier smoothed code measurement can be expressed as: 2 2 2 σ˜ s2 = σURA + σtropo + σuser + (31.34cm)2

(36)

With the corrected nominal bias bnorm and error variance σ˜ s2 , the global simulation of ARAIM is shown in Fig. 7. The change of Vertical Protection Level (VPL) and Horizontal Protection Level (HPL) after using bnorm and σ˜ s2 is shown in Table 1. According to Table 1 and Fig. 7, during the ionospheric storm period, the optimistic integrity monitoring result can be obtained by unrevised ISM. The optimistic integrity monitoring result cannot reflect the real navigation performance and may mislead the pilot.

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(a) The overbounding results of

( ) in the low latitude area (

⁡

= 53.02 )

= 124.70

(b) The overbounding result when

(c) The overbounding result when

= 124.70 ˈ

⁡

= 53.02

Fig. 6. Overbounding results for ionospheric delay error in low latitude area

6 Conclusions Since the results of Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is susceptible to the ionospheric storm, this paper proposes an Integrity Support Message (ISM) correction strategy for ARAIM during ionospheric storm period. By analyzing the influence of ionosphere-free combination and smoothing filter on the temporally correlated ionospheric error during storm period, we obtain the correction value of

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a) Vertical protection level

b) Horizontal protection level

c) Global availability with revised ISM

d) Global availability with unrevised ISM

Fig. 7. Global simulation results of ARAIM using bnorm and σ˜ s2 Table 1. Protection Level difference between ARAIM using normal ISM and ARAIM using corrected ISM Mean (m)

Maximum (m)

ARAI HPL

10.5769

26.5432

ARAIM HPL with bnorm and σ˜ s2 ARAIM VPL

11.2676

28.1041

15.7196

40.1377

ARAIM VPL with bnorm and σ˜ s2

16.8189

42.6590

nominal bias and error variance in ISM. The simulation results show that, in GPS/Galileo dual frequency positioning scenario, the nominal bias and error variance in ISM are increased by 31% and 7% respectively, compared with the normal situation. The increase of ISM results in the change of global protection level up to 2.5 m. Regarding availability, revised ISM reduces the global coverage from 99.7% to 99.16%. The conclusion reflects that the impact of ionospheric storm on ARAIM cannot be ignored. During ionospheric storm period, the ISM in ARAIM shall be updated in time, otherwise, the optimistic

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integrity monitoring result calculated by unrevised ISM may mislead the pilot and affect the flight safety of civil aviation during approach phase.

7 Appendix For a second Gaussian Markov process, it can be represented as: x¨ 1 (t) = −2ξ ω0 x1 (t) − ω02 x˙ 1 (t) + w(t) Equation (37) can be rewritten as:  x˙ 1 (t) = x2 (t) x˙ 2 (t) = −2ξ ω0 x1 (t) − ω02 x2 (t) + w(t) After using the matrix representation, (38) is rewritten as:       x˙ 1 (t) x1 (t) 0 = (t) + x˙ 2 (t) x2 (t) w(t)      x1 (t) 0 0 1 + = w(t) −ω02 −2ξ ω0 x2 (t)

(37)

(38)

(39)

∗ Assuming that the discrete forms of x1 (t), x2 (t) and w(t) are x1,k , x2,k and wk−1 respectively, by using first order approximation, (39) is rewritten as:       0 x1,k−1 x1,k = (I + T (t)) + ∗ wk−1 x2,k x2,k − 1      0 1 T x1,k−1 + (40) = ∗ wk−1 −ω02 T 1 − 2ξ ω0 T x2,k−1

Based on (40), x2,k−1 and x2,k can be obtained:  x −x x2,k−1 = ( 1,k T 1,k−1 ) x −x x = ( 1,k+1 1,k ) 2,k

(41)

T

According to (40) and (41) is rewritten as:   ∗ x1,k = (2 − 2ξ ω0 T )x1,k−1 − ω02 T 2 + 1 − 2ξ ω0 T x1,k−2 + Twk−1 .

(42)

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Scintillation Identification Based on Spectral Features Dun Liu(B) , Li Chen, Shan Guo, and Qinglin Zhu The 22nd Research Institute, CETC, Qingdao, Shandong, China [email protected]

Abstract. Performance of machine learning (ML) methods to identify scintillation events is analyzed for a variety of scenarios. It shows that spectrum embodies various features on scintillation variation. Different methods can be developed with ML to find out potential scintillation impacts, and satisfied results generally could be arrived with accuracy of 95%. It also point out that the descending trend existed over Fresnel frequency is essential to distinguish a potential scintillation. So selecting a proper frequency band to make spectral features more distinguishable plays an important role in ML realization. It further shows that precise GNSS routine observations with the sampling rate of 1 Hz can be served to recognize scintillation event if a sound spectrum range has been chosen. When a set of parameters on spectrum characteristics could be derived and used for ML training, better performance can even be expected. Keywords: Ionospheric scintillation · Machine learning (ML) · Intensity spectrum · Classification

1 Introduction Ionospheric scintillation is one of the main factors in space environment that affects GNSS performance. It is caused by diffraction and refraction of small scale ionospheric irregularities. These irregularities change in complex process (rising, extending and decaying), and also spread and drift under control of geomagnetic field and wind field [1–3]. At the same time, GNSS satellites move regularly causing continuous variation of observing geometry. Scintillation effects on receiver depend on all these factors, and making the impacts a random and abrupt process at user side. System integrity is one of the important requirments for GNSS augmentation system. It requires that when the system cannot provide expected service, it should have the capability to provide timely warning message to users. The suddenness of ionospheric scintillation effect requires fast recognition of scintillation at system side or user side. In theoretical study, a scintillation phenomenon is generally identified by postprocessing method, in which a full scintillation process is determined when the effects of scintillation surpass a certain threshold during a certain continuous period. The procedure is generally made over a length of data lasting ten minutes to tens of minutes to ascertain the event [4]. Lengthy requirement of this process makes it impossible for real-time applications in real augmentation system. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 168–178, 2024. https://doi.org/10.1007/978-981-99-6932-6_14

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A series of work has been done about scintillation identification, most of which based on machine learning (ML) models trained by spectrum analysis result of scintillation signals. Results generally are achieved with an accuracy of more than 90% [5–7]. However more efforts are still needed to get insight into the identification process, such as which parameter shows a more essential feature, which feature, or a combination of features, can be selected to improve the accuracy, and how to optimize the recognition method with the selected feature? The answers to these questions will be helpful for a better detection method. In this paper a variety of scenarios is analyzed for scintillation identification under different time, region, system and spectrum features. The optimal spectrum feature is found from comparison. The results also show the feasibility of scintillation recognition with routine GNSS observation. The paper is organized as follow. In the second part different parameters depicting spectrum features are analyzed. Accuracy of scintillation identification using spectrum features is compared for different scenario in the third part. Then different spectrum feature and its effectiveness in scintillation identification is further discussed in part four, and conclusion is given as ending.

2 Scintillation Spectrum Features The phase screen theory of scintillation shows that intensity spectrum is closely related with spatial spectrum of ionospheric irregularity which causes the scintillation. As the result, features related with scintillation can be analyzed from intensity spectrum of GNSS signal. (1) Coefficients of signal intensity spectrum Theoretical analysis shows that intensity spectrum of satellite signals under scintillation effects will reach maximum at Fresnel frequency, and then follow a power law trend at higher frequency [8, 9]. This feature is shown in the intensity spectrum of measured GNSS signal, especially in the coefficients variation of spectrum. For the kth component in spectrum, Fk = F(ky), k = 0, 1, ..., N − 1,  2   Pn = F n  /N 

(1)

in which, 

Fn =

N −1 

Fk exp{ikn/N }

(2)

k=0 

F n is Discrete Fourier Transform of the raw signal. Here, Pn is spatial spectrum when y is spatial separation, and Pn is temporal spectrum when y is time interval. Conversion between spatial spectrum and temporal spectrum is realized by Fresnel frequency fF = veff /ρF [9].

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(2) Parameters of power spectrum The phase screen theory shows that scintillation intensity spectrum follows the power law form. At high frequency part it is approximated as [8] (f ) ≈

Tscin f 2ν

(3)

In which Tscin is phase spectrum strength and can be evaluated at 1 Hz, and phase spectrum index is p = 2v. (3) Amplitude scintillation index S 4 . Theoretical analysis shows that, the following relationship exists between amplitude scintillation index S4 and integral of (q), spectrum in spatial domain where q is the spatial wave number [9]. S42

1 = 2π

∞ (q) dq − 1

(4)

−∞

So amplitude scintillation index S 4 can also be treated as a description to spectrum features to a certain extend. Figure 1 shows an typical intensity spectrum with scintillation effect. Raw scintillation observation is made on L1 from GPS PRN18 satellite. The data, with a time length of 1 min and sampling rate of 20 Hz, is collected at Sanya Hainan (18°N, 109°E) on 24th Sep. 2013 (the same time interval and sampling rate for the following data). The data segment displayed is for UT 22:10. The blue curve shows intensity spectrum of GPS signal, while the red line is the fitting result of spectrum at the high frequency part (ranging from 0.3 Hz to 2 Hz in our analysis) for Tscin , p evaluation [8]. Estimation results of Tscin ,p and S 4 are also given here.

Fig. 1. Intensity spectrum for scintillation impacted signals (HNHK UT 22:10, GPS PRN 18 L1 signal)

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3 Scintillation Detection with Different Spectrum Features For ionospheric scintillation observation with different system at different time and site, identification accuracy achieved from ML methods is analyzed for different spectrum features. Results of SVM (Support Vector Machine) and NN (neutral network) method are discussed in detail here. SVMs are a type of supervised learning algorithm that can be used for classification or regression tasks. The main idea behind SVMs is to find a hyperplane that maximally separates the different classes in the training data. In this paper, a common two-class classification SVM model is used. While the NN approach is implemented using a multilayer forward-feed neural network. 3.1 Scintillation Data Process and Labeling The GPS scintillation observation at Guangzhou (GDGZ) and Haikou (HNHK) in 2003 and 2004 (the 23rd solar cycle), and GPS scintillation observation at Haikou in 2013 and BDS scintillation observation at Haikou in 2014 (the 24th solar cycle) are selected for analysis. Raw GNSS observations are first processed to derive parameters on scintillation events. Criteria commonly adopted in scintillation study is then used to label scintillation events. (1) Pre-process of scintillation data Raw data is processed firstly to screen out wrong data. Then epochs of good data are determined. Parameters about observation at each epoch are calculated with ephemeris, including azimuth and elevation angles. (2) Parameters calculation for scintillation Pre-processed data are divided into different segments with the length of 1 min. Short interrupt in each data segment is fixed when detected. If there is too much loss of data in a segment, this segment of data will be discarded. After that, data are filtered and scintillation index are calculated. Intensity spectrum is analyzed and feature parameters of spectrum are estimated for each segment data, including the spectrum strength and index [8]. (3) Identification and labeling of scintillation events Ionospheric scintillation processes are detected and identified according to the criteria commonly adopted in scintillation study [4]. With this definition, a scintillation process would last at least 15 min. Scintillation event is defined on a data segment basis (1 min length). A scintillation event is labeled as 1 only when the epoch of data segment is in a period of scintillation process and the S 4 value of the data segment is larger than 0.1. All the other data segments are then label as 0. The check was made automatically and then confirmed manually. Those events with wrong recognition or uncertainty will be removed. The resulting data set is shown in Table 1.

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2004

2013

2014

GDGZ

GPS L1 Sample rate 20 Hz 40 h

GPS L1 Sample rate 20 Hz 42 h

–

–

HNHK

GPS L1 Sample rate 20 Hz 34 h

GPS L1 Sample rate 20 Hz 40 h

GPS L 1/L2 Sample rate 20 Hz 80 h

BDS B1/B3 Sample rate 20 Hz 72 h

3.2 Training and Test of ML Models SVM and NN methods are used for scintillation identification and test. (1) Cross test with observations in different period/region/system All samples in a data set are used for model training, and then tested against with the data from other data sets. The data in the year of 2003 and 2004 are combined together for each site as they are from the same solar cycle (GDGZ 0304, and HNHK 0304 in Tables 2 and 3). The combined data set will make a balance with the data set in 2013 and 2014. (2) Effectiveness of various features on scintillation identification Different scintillation features are selected to train and test the identification model: (1) Scenario1: Coefficients of frequency components below 2 Hz are selected as input for ML methods. This is also the common practice in other works as higher frequencies shown as noise [5–7]. (2) Scenario 2: Coefficients for frequency components as high as 0.5 Hz are selected as input for ML methods. (3) Scenario 3: scintillation index S 4 , spectrum strength and spectrum index are selected as input for ML methods. 3.3 Identification Accuracy Scintillation identification is actually a two-class classification problem and the result can be depicted with confusion matrix and then the accuracy be calculated. As for the problem, the output of classifier can be divided into four kinds according to its real and identified classification results, namely true positive, false positive, true negative and false negative. If we define TP, FP, TN and FN as the number of samples in each type, then TP + FP + TN + FN = number of total samples. Accuracy of the classification can be expressed as [10]: Accuracy =

TP + TN . TP + FN + FP + TN

(5)

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3.4 Result of Scintillation Identifications Scintillation identification result for different scenario is shown in Tables 2 and 3. Table 2 shows results of SVM method with each line for different scenario, while Table 3 shows results of SVM and NN methods for scenario 3 only. As can be seen that: (1) Scintillation can be identified with satisfied results using ML method. Spectrum features are essential for scintillation event. The features do not vary much with time, place and observing system, and can be used for ML methods training. An accuracy of 95% generally could be archived, a result similar with other works [5, 6]. (2) Identification performance depends on different spectrum features. Selection of spectrum feature may affect the identification results. Specially, identification result of scenario 2 is better than that of scenario 1 (Table 1). This is an interesting result with great significance for scintillation detection. Generally, GNSS observation is collected with a sampling rate of 1 Hz. Consequently the effective cut-off frequency is 0.5 Hz when spectrum analysis is made (considering Nyquist rule). Result of scenario 2 shows the potential that a scintillation event might be recognized even with GNSS observation commonly available. Scenario 3 has a better result, which means the identification accuracy could be improved further when the spectrum features are processed appropriately. (3) Different ML methods show no apparent difference in identification. Scintillation identification is a typical two-class classification problem. Although identification model can be developed with different ML methods, similar accuracy is achieved for the same scenario, as the results in Table 2 shows. This indicates that when higher accuracy is further wanted, one has to resort to other boosting ways instead of a simple ML method attempt.

4 Deeper Analysis Different ML methods can be used to identify scintillation events with the similar results. This indicates that a hyper-plane might always be set up with various ML methods to separate scintillation events. As the result, the selection of scintillation features is to play an important role in discrimination. There are obvious features to distinguish the spectrum of scintillation signals. The spectrum has a maximum value near Fresnel frequency and then decreases downward following a power law trend with increasing frequency until reaches a noise floor. The noisy floor existing at higher frequency depends on sampling rate and receiver observing noise. The three scenarios in Sect. 3.2 stand for different description of these spectrum features. Accuracy for a scenario is actually a kind of reflection on the effectiveness of selected spectrum feature. As an example, scintillation observation on L1 signal of GPS PRN18 is analyzed in detail here. The observation was collected at Sanya Hainan on 24th Sep. 2013, and

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D. Liu et al. Table 2. Accuracy of SVM method for scintillation classification GDGZ 0304

HNHK 0304

HNHK 2013GPS

HNHK 2014BDS

GDGZ 0304

–

0.950 0.949 0.977

0.951 0.942 0.960

0.972 0.977 0.983

HNHK 0304

0.948 0.956 0.981

–

0.913 0.940 0.975

0.954 0.961 0.983

HNHK 2013GPS

0.968 0.971 0.985

0.953 0.960 0.987

–

0.969 0.974 0.981

HNHK 2014BDS

0.971 0.974 0.983

0.947 0.952 0.986

0.934 0.943 0.981

–

Table 3. Accuracy of SVM and neural network methods for scintillation classification GDGZ 0304

HNHK 0304

HNHK 2013GPS

HAIKOU 2014BDS

GDGZ 0304

–

0.977 0.979

0.960 0.979

0.983 0.978

HNHK 0304

0.981 0.980

–

0.975 0.975

0.983 0.978

HNHK 2013GPS

0.985 0.983

0.987 0.987

–

0.981 0.983

HNHK 2014BDS

0.983 0.980

0.986 0.987

0.981 0.981

–

measurement between UT 22:00–24:00 was processed with the procedures in Sect. 3.1. Analysis shows it is a scintillation process decaying gradually from strong event to disappearance. Identification error occurs frequently in this special case. Figure 2 shows scintillation index S 4 of this event and corresponding labels. Flag 1 is for scintillation events and flag 0 for no scintillation. To display conveniently, flag 1 is shown as 0.1 here. For this process, observation at UT 22:09 are identified as scintillation by SVM method, while observation at UT 22:40 are identified as no scintillation. These two cases have similar scintillation index (0.29 and 0.28 respectively). But the signal spectra differ much from each other as shown in Figs. 3 and 4. For observation at UT 22:09, the spectrum shows an obvious power law variation between the Fresnel frequency and cut-off frequency (at about 2 Hz). This trend can also be seen in Fig. 1. While for observation at UT 22:40, the intensity spectrum decreases

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Fig. 2. Scintillation index and event flags (HNHK UT 22:00–24:00, GPS PRN18 L1 signal)

abruptly from the maximum to a small value before 0.3 Hz, and then keeps nearly horizontal trend between 0.3 Hz and 2 Hz. As a comparison, observation at UT 22:58 shows a similar trend. Figure 5 shows that spectrum of this segment of signal decreases to a small value before 0.3 Hz and keeps nearly horizontal trend between 0.3 Hz and 2 Hz. The scintillation index is about 0.1 for the epoch of UT 22:58, which means the scintillation event decay almost to disappearance. As can be seen that spectrum at UT 22:40 behaves much similar as that at UT 22:58. Consequently, observation at UT 22:40 were identified as no scintillation when spectrum feature are taken as classification criteria for ML.

Fig. 3. Intensity spectrum for scintillation impacted signals (HNHK UT 22:09, GPS PRN 18 L1 signal)

Commonly available GNSS observation is made with sampling rate of 1 Hz. The cut-off frequency of its intensity spectrum is 0.5 Hz theoretically. As can be seen from Figs. 1, 3, 4 and 5, for strong scintillation, intensity spectrums decrease and show power law trend between Fresnel frequency and a frequency as higher as 2 Hz. While for weak scintillation, its intensity spectrum decreases more abruptly between Fresnel frequency and 0.2 Hz (or 0.3 Hz), and then behaves like noise at higher frequency. When 0.5 Hz is selected as cutting frequency and all coefficients for frequency components below it are

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Fig. 4. Intensity spectrum for scintillation impacted signals (HNHK UT 22:40, GPS PRN 18 L1 signal)

Fig. 5. Intensity spectrum for scintillation impacted signals (HNHK UT 23:58, GPS PRN 18 L1 signal)

used for ML methods training, intensity spectrum decrease “similarly” between Fresnel frequency and cutting frequency for not only strong but also weak scintillation. This will make it easier to establish a hyper-plane for scintillation identification. For those part between 0.5 Hz and higher cut-off frequency (determined by real sampling rate), spectrum looks more like noise for weak scintillation case. Including this part as training signal in ML method may decrease the identification capability, since in this part of spectrum, the feature of weak scintillation differs apparently from that of strong scintillation. This finding has great significance. It shows the potential that commonly available GNSS observation might be used for scintillation monitoring, such as those in CORS (Continuously Operating Reference Stations). It should be pointed out also that the identification will be hard when a geomagnetic storm occurred. As can be seen from Figs. 4 and 5, spectrum of weak scintillation signal decrease obviously between Fresnel frequency and 0.3 Hz but does not show the expected power law trend. This kind of variation in spectrum shows it is affected by large scale

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irregularities. This large scale irregularity may accompany a scintillation event, but also could be related to a geomagnetic storm event. If intensity spectrum is taken as a measurement, the variation of spectrum at each frequency component can then be treated as noise. When these noisy measurement are introduced into ML method for training or testing, errors would be introduced in identification process. The scintillation index, spectrum strength and spectrum slope are actually some kind of fitting results of intensity spectrum. This fitting process is like a filter to decrease observation noise in the spectrum. When these filtered results are used as training input for ML model, the accuracy will be improved.

5 Conclusion In this paper, the performance of scintillation identification method using various signal spectrum features are studied. The results show that: Spectrum is essential feature to describe scintillation variation and can be used to develop identifying method of scintillation with different ML methods. The identification accuracy can reach a level about 95%. Selection of spectrum features plays an important role in ML model realization. Commonly available 1 Hz observation can also be used to establish scintillation identification method based on spectrum feature. But one has to proceed with caution to distinguish scintillation event to a potential storm event. When refined parameters derived from signal intensity spectrum can be used for ML methods, the identification accuracy can be improved further. The required inputs can also be significantly reduced to make a concise model realization. For a even better accuracy, one has to resort to other boosting methods instead of a simple selection of ML methods. Acknowledgements. This research was supported by the National Key R&D Program of China (No. 2020YFB0505603), and “Ionospheric modeling through study of radio wave propagation and solar activity project phase II” (Contract No. APSCO/SP&PM/PROJECT/IONO II/IMP_C_001).

References 1. Kintner PM, Ledvina BM, De Paula ER (2007) GPS and ionospheric scintillations. Space Weather 23. https://doi.org/10.1029/2006SW000260 2. Kintner PM, Ledvina BM, de Paula ER, Kantor IJ (2004) Size, shape, orientation, speed, and duration of GPS equatorial anomaly scintillations. Radio Sci 39:RS2012. https://doi.org/10. 1029/2003RS002878 3. Basu S et al (1996) Scintillations, plasma drifts, and neutral winds in the equatorial ionosphere after sunset. J Geophys Res 101(12):26795–26809 4. McNeil WJ, Long AR, Kendra MJ (1997) Detection and characterization of equatorial scintillation for real-time operational support. Scientific Report #12, Phillips Laboratory, April 18, 1997

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5. Jiao Y, Hall JJ, Morton YT (2017) Automatic equatorial GPS amplitude scintillation detection using a machine learning algorithm. IEEE Trans Aerosp Electron Syst 53:405–418 6. Jiao Y, Hall JJ, Morton YT (2017) Performance evaluation of an automatic GPS ionospheric phase scintillation detector using a machine-learning algorithm. J Inst Navig 64:391–402 7. Makhlouf B (2019) GNSS ionospheric scintillations classification by machine learning. Polytechnic University of Turin, March 2019 8. Rino C (1979) A power law phase screen model for ionospheric scintillation: 1 weak scatter. Radio Sci 14:1135–1145 9. Carrano C, Rino C (2016) A theory of scintillation for two-component power law irregularity spectra: overview and numerical results. Radio Sci 51:789–813. https://doi.org/10.1002/201 5RS005903 10. Zhou Z (2016) Machine learning. Tsinghua University Press

Centimeter-Level Real-Time Orbit Determination and Accuracy Analysis of LEO Satellite with POD4LEO Software Quan Zhou(B) , Lang Bian, YanSong Meng, Dan Liu, YiZhe Jia, Lin Han, Peng Zhang, XiaLu Zhang, and MinShu Zhang China Academy of Space Technology, Xi’an, China [email protected]

Abstract. High precision and low delay satellite orbits are the key requirements for many Earth observation missions today. This paper briefly introduces the development of precision orbit determination of low orbit satellites, and the opportunities brought by GNSS satellite-based enhancement service for real-time centimeter-level orbit determination of low orbit satellites, then analyzes the orbit accuracy and clock error accuracy of current satellite-based enhancement real-time products, and then introduces the mathematical model of precision orbit determination of low orbit satellites with simplified dynamics real-time filtering solution in detail. At last, the Sentinel-3A satellite GPS observation data for 10 days were used to simulate the in-orbit mode by POD4LEO software. The results show that, compared with the scientific orbit provided by the European Copernicus Center, the RMS of the computed orbit in the radial, tangential, normal and threedimensional directions are 2.5 cm, 2.5 cm, 2.0 cm and 4.1 cm respectively, and the SISRE caused by the orbital error is about 3.0 cm. The effectiveness and feasibility of the real-time orbit determination method proposed in this paper and the developed software are verified, which has practical significance in the future low orbit navigation enhanced satellite or other low orbit satellite engineering applications. Keywords: LEO satellite · Reduced dynamic · SBAS · Real-time orbit determination

1 Introduction Low orbit satellite (LEO) technology has played an important role in Earth observation in the past few decades. As a high-precision earth observation platform, low-orbit satellites are widely used in many engineering and scientific fields such as ocean allocator, earth gravity field inversion, atmospheric monitoring and remote sensing [1–4]. With the rapid increase of global communication and other needs, the era of thousands of low-orbit satellite giant constellation is coming [5, 6].The precision orbit of low-orbit satellite is the space reference, and its accuracy directly affects and determines the application prospect and effect of satellite. At the same time, in terms of timeliness, some low-orbit satellites (such as weather satellites, military reconnaissance satellites, etc.) © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 179–189, 2024. https://doi.org/10.1007/978-981-99-6932-6_15

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also put forward higher requirements for real-time performance than in the past, such as rapid response to earthquake and tsunami, real-time monitoring of military targets, etc. Especially in the rapid development of low-orbit navigation enhancement system in recent years, in order to achieve users’ cm-level high-precision positioning, Low orbit navigation augmentation satellites need to have centimeter level real-time orbit determination accuracy [7, 8]. The orbit can be accurately determined after the fact or in real time by using the pseudo range and carrier phase observation data of the satellite-borne receiver of the low orbit satellite [1, 3]. In the aspect of post processing, the post precision ephemeris and precision clock difference products released by IGS can achieve up to 1–2 cm orbit determination accuracy [9, 10]. For real-time applications, GNSS broadcast ephemeris are usually used as space reference information of navigation satellites, and then kinesiology or simplified dynamics method is adopted for real-time data processing in orbit. Due to the limitation of GNSS broadcast ephemeris accuracy, the real-time orbit determination accuracy of LEO satellite is about 0.4–1.0 m [11–13]. In order to further improve the real-time positioning accuracy of GNSS navigation systems, major satellite navigation systems (such as China Beidou-3 PPP-B2b, Eu GALILEO HAS, Japan QZSS MADOCA, international scientific research organizations (such as IGS, CNES, Wuhan University, etc.), commercial companies (Fugro, Trimble, Chiumun, China Shipping Beidou, etc.) have developed their own GNSS satellite-based enhancement services, broadcasting GNSS to users in real time through Internet links or communication satellite links Precision correction of satellite orbit and clock error to improve users’ real-time positioning accuracy [14, 15]. GNSS space-based enhancement system orbit timing and other high-precision real-time products are disseminated, making real-time centimeter-level orbit determination of satellite-borne GNSS for low orbit satellites possible [16, 17]. In this paper, the key issues related to the autonomous real-time precision orbit determination of low-orbit satellites are studied. The real-time cm-level orbit determination capability of low-orbit satellites is realized by using the method of simplifying the real-time dynamic filtering solution based on GNSS observation values. Firstly, the recovery method and accuracy of GNSS space-based enhanced real-time precision orbit and clock difference products are analyzed and evaluated. Then, the real-time orbit determination principle of satellite-borne GNSS for low orbit satellites is introduced, and the observation model, dynamic model and parameter estimation method are given. Finally, using the satellite-borne GPS observation data collected by Sentinel-3A satellite for a total of 10 days from August 1, 2018 to August 10, 2018, The self-developed software POD4LEO (Precise Orbit Determination For Low Earth Orbit Satellite) was used to simulate the in-orbit mode for real-time precise orbit determination. By Copernicus and Europe center provides external scientific orbit (https://scihub.copernicus.eu/gnss/#/ home) comparative methods, analyzing the orbit determination results were evaluated, verify the correctness and feasibility of the developed software algorithm.

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2 GNSS Real-Time Products Real-time precision orbit determination of low-orbit satellites requires high-precision real-time GNSS satellite orbit and clock difference as the temporal and spatial reference. GNSS real-time orbit is generally obtained by forecasting ultra-fast orbit, while real-time satellite clock difference is estimated by using global real-time station observation data after fixed forecast orbit [18]. The accuracy of GNSS orbit and clock difference directly determines the orbit determination accuracy of low orbit satellite. At the same time, the real-time product of GNSS satellite-based enhancement system actually broadcasts the correction of orbit position and clock difference given in precision orbit or precision clock difference and broadcast ephemeris. Therefore, after receiving GNSS real-time product, the low-orbit satellite first needs to recover GNSS precision orbit and precision clock difference. 2.1 Recovery Method The basic process of GNSS satellite-based enhanced real-time precision product recovery is as follows: Firstly, the correction category was determined according to the message type of the real-time product correction, and the data age IOD parameter of the message was obtained. The IOD parameter was used to match the corresponding broadcast ephemeris according to the principle of time recency. The position, speed and clock error information of GNSS satellite were calculated according to the broadcast ephemeris, and then the GNSS enhanced information correction was added for real-time precision orbit and clock error recovery. The correct real-time precision orbit and real-time precision clock difference can be obtained only when the satellite-enhanced correction data are analyzed correctly and the broadcast ephemeris are matched correctly [19]. The enhanced real-time orbit correction based on GNSS satellites is the difference projection of GNSS satellite precise coordinates and satellite coordinates given by broadcast ephemeris in three directions in the satellite system, namely, radial correction, tangential correction (along) correction and normal correction (cross) correction. However, GNSS positioning calculation is generally carried out under the earth solid system, so the orbit correction number needs to be converted to the earth solid system before correction. The calculation method of the conversion relationship between the satellite and the earth solid system is directly presented here, specifically as shown in the following formula, where, represents GNSS satellite position and velocity information calculated by broadcast ephemeris.     Xsat ×Vsat eA ×eC (1) eA eC eR = |VVsat | |X | |e | ×V ×e sat sat sat A C The number of orbit corrections in the geosolid system is obtained by multiplying the unit vectors in the radial, tangential and normal directions with the number of real-time orbit corrections:   T dX = eR eA eC dR dA dC (2) Finally, real-time precision orbit of GNSS satellite can be obtained through the following formula: XRP = Xsat − dX

(3)

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For the recovery of real-time satellite clock difference, it is also necessary to match the broadcast ephemeris. The GNSS satellite clock difference is calculated from the broadcast ephemeris, and then the GNSS real-time precision clock difference can be recovered by adding the correction of real clock difference: S dtRP = dt S + δdt S .

(4)

2.2 Orbit Accuracy In order to evaluate the accuracy of the current real-time product, this section collects the real-time correction data stream with the mount point CLK90 provided by CNES from GPST 2022-06-06 01:30:00 to 2022-06-06 07:30:00 for a total of 6 h. As a reference, the reference track uses the IGS Final Track product. Figure 1 shows the root mean square error (RMS) of the real-time orbit and the final orbit of the GPS satellite in the radial and three-dimensional directions. It can be seen from the figure that the mean RMS of the radial orbit is 1.85 cm, and the mean RMS of the three-dimensional direction is 4.15 cm.

Fig. 1. GPS real-time orbit product accuracy

2.3 Clock Error Accuracy Real clock difference products were also collected from CNES CLK90, and the time period was consistent with Sect. 2.2, with a total of 6 h. The reference was IGS final clock difference products. Considering that the clock difference accuracy of satellite navigation system is only a relative concept, the reference deviation will be absorbed by the receiver clock difference in the positioning process and does not affect the positioning accuracy. Therefore, the stability of the clock difference is used to evaluate its accuracy [15].

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Due to the different selection of time datum for clock difference products of different institutions, in order to eliminate the influence of time datum, the method of quadratic difference with the reference clock difference is usually adopted to obtain the time series of quadratic difference between the clock difference of each satellite and the reference star, and the STD value is counted as the precision index of clock difference. Figure 2 shows the statistical results of accuracy of GPS satellite real clock difference and IGS final clock difference products. It can be seen from the figure that the mean std of GPS real clock difference is 0.10 ns.

Fig. 2. GPS real clock error product accuracy

3 Mathematical Model 3.1 Observation Model In satellite navigation data processing, in order to eliminate the ionospheric influence, the ionospheric elimination combination of dual-frequency pseudo-distance and carrier phase is generally used. Considering that the operating height of low-orbit satellites is not affected by the tropospheric effect, its observation equation can be simplified as the following formula: sat sat = Rsat ρleo leo + Cdtleo − Cdt

(5)

sat sat sat ϕleo = Rsat + λNleo leo + Cdtleo − Cdt

(6)

sat and ϕ sat are respectively the pseudo-distance and phase observation values of where, ρleo leo the ionospheric combination, Rsat leo is the geometric distance between GNSS satellite and low-orbit satellite, C the vacuum speed of light, dt sat and dtleo are respectively the clock

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difference of the GNSS satellite and low-orbit satellite receiver, λ are the wavelength of sat are the parameters of the whole circle the ionospheric combination observation, and Nleo ambiguity of the satellite-borne receiver of low-orbit satellite. The above expressions ignore the influence of multipath, observation noise, antenna phase winding and antenna phase change. 3.2 Dynamics Model When low-orbit satellites orbit the earth, in addition to the gravity of the earth’s center, they are also affected by various perturbation forces, which change at the time of space motion. In order to obtain more accurate orbit of the satellite, it is necessary to conduct accurate modeling of various perturbation forces. These perturbation forces are mainly divided into conservative forces and non-conservative forces. The conservative forces include earth’s non-spherical perturbation force, N-body gravity, Earth tides, relativistic effects, etc., which are only related to the satellite position and have nothing to do with the satellite speed and characteristics, while the non-conservative forces include solar radiation pressure, Earth’s return radiation pressure, atmospheric drag, satellite thrust, etc., which are not only related to the satellite position and speed. Also related to satellite characteristics [1–3]. At the same time, in order to absorb model errors and the influence of unmodeled perturbations, empirical force perturbations are usually considered [13, 17]. Therefore, the dynamic equation of the low-orbit satellite is shown as follows: a=−

GMr + ag + ang + aw r3

(7)

e where, a is the satellite acceleration, − GM is the acceleration caused by gravity in r3 the center of the earth, ag is the acceleration caused by conservative force, ang is the acceleration caused by non-conservative force, and aw is the empirical force acceleration.

3.3 Estimation Method Parameter estimation is performed by extended Kalman filter method, whose equation of state and observation equation are shown as follows:  Xk = ϕk,k−1 Xk−1 + wk (8) Lk = Hk Xk + vk where, XK is the state vector of the system at tK moment, ϕk,k−1 is the state transfer matrix of the system state vector from tk−1 moment to tk moment, wk is the system noise vector, Lk is the observation quantity of the system at tk moment, Hk is the coefficient matrix of the observation equation, vk is the observation noise.For the simplified dynamic real-time filtering solution of precise orbit determination proposed in this paper, the state vector to be estimated is shown in the following equation.   (9) Xk = x, y, z, vx , vy , vz , cdtleo , Cd , Cr , aR , aC , aA , N   where, x, y, z, vx , vy , vz is the position and speed of the low-orbit satellite, cdtleo is the receiver clock difference, Cd is the atmospheric drag coefficient, Cr is the solar pressure

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coefficient, [aR , aC , aA ] is the empirical force acceleration parameter of the low-orbit satellite in the radial, normal and tangential directions, and N is the ambiguity parameter of the observation satellite.

4 Test and Results In this paper, based on the self-developed real-time precision orbit determination software POD4LEO, the satellite GPS observation data of the European ocean monitoring satellite Sentinel-3A (from August 1, 2018 to August 10, 2018) for a total of 10 days were simulated real-time precision orbit determination. In order to verify the correctness of the software algorithm and the optimal orbit determination accuracy, IGS final products were adopted for the GPS precision track and precision clock difference in data processing, and the scientific track provided by the European Copernicus Center was adopted for the reference track. The evaluation method of orbit accuracy is to make the difference between the calculated orbit and the reference orbit, and calculate the root mean square error RMS in the radial, tangential, normal and three-dimensional directions. At the same time, in order to evaluate the influence of orbit accuracy of low orbit satellite on user positioning, this paper also presents the space signal ranging accuracy of low orbit satellite which only considers orbit accuracy (SISREorb ). 4.1 Processing Strategy Table 1 describes the observation model, dynamic model and estimated parameters used for real-time orbit determination of low-orbit satellites. 4.2 Results Figure 3 shows the time series diagram of the radial, tangential, normal and threedimensional errors of Sentinel-3A satellite’s real-time filtering orbit and scientific orbit on August 2, 2018. As can be seen from the figure, due to the ambiguity parameter estimation, the real-time filtering solution has a convergence process, and it takes about 10 min for each direction to converge to within 10 cm. After convergence, the radial, tangential, normal and three-dimensional accuracy of each period is better than 10 cm. The statistical results show that the 95% fractional value of the tangential direction of orbit determination accuracy is 4.9 cm, and the RMS is 2.5 cm. The 95% quantile value in the normal direction was 3.9 cm, and the RMS was 2.0 cm. The 95% quantile value in radial direction was 5.1 cm, and the RMS was 2.5 cm. The 95% quantile value in the three-dimensional direction was 7.4 cm, and the RMS was 4.1 cm. Figure 4 shows the RMS statistical graph of the comparison results between Sentinel3A real-time filtering orbit and scientific orbit for 10 consecutive days. According to the statistical results of orbit determination on each day, the mean of tangential RMS is 2.9 cm, the mean of normal RMS is 1.9 cm, the mean of radial RMS is 3.4 cm and the mean of three-dimensional RMS is 4.9 cm.

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GPS observation model GPS observed value

LC/PC

GPS orbit

IGS Final Orbit

GPS clock

IGS Final Clock

GPS PCO/PCV

igs14.atx

Elevation constraints

7°

Interval

1s

Arc length

24h

Weight

Elevation

Model of dynamics Gravitational field

EGM2008, 90 * 90

Three body gravity

Solar and lunar gravity

Earth tide

Simple earth tide model

Relativity

Post-Newtonian correction

Solar pressure

Estimated

Atmosphere drag

Estimated

Empirical acceleration

ACR

Estimation Estimator

Extended Kalman filter

Parameter

Position, speed, receiver clock difference, atmospheric drag coefficient, solar pressure

Stochastic model

White noise model or random walk process

4.3 SISRE (Orbit) In order to further evaluate the influence of orbit accuracy in different directions on user positioning, this section calculates the spatial signal ranging error caused by orbit error of Sentinel-3A satellite by using the calculated radial, tangential and normal orbit accuracy values. The specific calculation formula is as follows:  (5) SISREorb = α 2 × dR + β 2 × (dA2 + dC 2 ) For sentinel-3A satellite, its orbital altitude is 815 km, corresponding to α 2 = 0.540, β 2 = 0.595 [20]. According to the above formula, the ten-day time of Sentinel-3A satellite is calculated. It can be seen from the results that the mean space signal ranging error caused by the orbit error is 3.0 cm (Fig. 5).

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Fig. 3. Time series of Sentinel-3A satellite 20180802 day imitation real-time orbit determination accuracy

Fig. 4. Sentinel-3A satellite simulation real-time orbit determination accuracy statistics

5 Summary This paper focuses on analyzing the orbit accuracy and clock error accuracy of the current GNSS satellite-based enhanced real-time products, and describes in detail the observation model, dynamic model and estimation method of the real-time dynamic filtering algorithm for orbit determination of low-orbit satellites. Using the observation data of Sentinel-3A satellite for 10 days, POD4LEO, a self-developed real-time precision orbit determination software for low-orbit satellites, was used to simulate real-time processing in orbit, and the following results were obtained: (1) Due to the need to estimate the ambiguity parameters, the convergence time of orbit determination is about 10 min; (2) After convergence, the RMS of 2.5 cm in radial direction, 2.0 cm in normal direction, 2.5 cm in tangential direction and 4.1 cm in three-dimensional direction can

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Fig. 5. SISRE statistics of Sentinel-3A satellite orbit

be achieved; (3) The space signal ranging error caused by the orbit error of the low-orbit satellite is about 3.0 cm. In summary, the simplified dynamic real-time filtering solution precise orbit determination scheme based on GNSS space-based enhancement products proposed in this paper is effective and feasible. The real-time precise orbit determination software POD4LEO developed by this algorithm has stable operation, excellent accuracy and reliable results. It has practical significance for engineering application in low orbit navigation enhanced satellite or other low orbit satellite in the future.

References 1. Qile Z, Jingnan L, Maorong G (2005) Research on precise orbit determination theory and software of GPS navigation constellation and low orbit satellite. Geomat Inform Sci Wuhan Univ 30(4):1 2. Qiang Z (2019) Research on key technologies of precise orbit determination of low-orbit satellites and their formation using GPS and Beidou. Wuhan University, Wuhan 3. Kuangcuilin (2008) Research on the theory and method of precise determination of low-orbit satellite orbit using GPS non-differential data. Wuhan University, Wuhan 4. Zhou Q, Guo J et al. Precise orbit determination for Haiyang 2A satellite using un-differenced DORIS code and phase measurements. In: The fifth Chinese satellite navigation annual conference 5. Yansong M, Tao Y, Lang B et al (2022) Global navigation enhancement based on low-orbit internet constellation: opportunities and challenges. Navig Positioning Timing 001:009 6. Xiaohong Z, Fujian M (2019) Review on the development of low-orbit navigation enhanced GNSS. Acta Geodaetica et Cartographica Sinica 48(9):15 7. Xingxing L et al (2019) LEO constellation augmented multi-GNSS for rapid PPP convergence. J Geodesy 93(5):749–764 8. Bofeng L, Haibo G et al (2019) LEO enhanced global navigation satellite system (LeGNSS) for real-time precise positioning services. Adv Space Res 63(1):73–93

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9. Jing G, Qile Z, Min L et al (2013) Determination of CM-class precision orbit of Haiyang 2A satellite using satellite-borne GPS observation data. J Wuhan Univ: Inform Sci Ed 10. Li M, Mu R et al (2022) Precise orbit determination for the Haiyang-2D satellite using new onboard BDS-3 B1C/B2a signal measurements. GPS Solut 26(4):1–12 11. Li M, Zhao Q et al (2022) Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations. Adv Space Res. https://doi.org/10. 1016/j.asr.2022.09.050 12. Hauschild A, Montenbruck O (2021) Precise real-time navigation of LEO satellites using GNSS broadcast ephemerides. Navigation 68. https://doi.org/10.1002/navi.416.2022(007 ):051 13. Fuhong W, Sanli L, Xuewen G et al (2020) Study on real-time orbit determination model of spaceborne GPS/BDS sub-meter stage for Fengyun-3C satellite. Geomat Inform Sci Wuhan Univ 1:6 14. Li B, Ge H et al (2022) Comprehensive assessment of real-time precise products from IGS analysis centers. Satellite Navig (001):003 15. Liang C (2020) Research on key issues and service performance analysis of Beidou GNSS global enhancement system. Wuhan University, Wuhan 16. Allahvirdi-Zadeh A, Wang K (2021) POD of small LEO satellites based on precise real-time MADOCA and SBAS-aided PPP corrections. GPS Solut 25, Article number 31. https://doi. org/10.1007/s10291-020-01078-8 17. Zhang W, Wang F, Gong X et al (2021) A Cm-class satellite-borne GPS real-time orbit determination method considering IGS-RTS data receiving interruption. Geomat Inform Sci Wuhan Univ 46(11):8 18. Chen L, Zhao Q (2017) GNSS global real-time augmentation positioning: real-time precise satellite clock estimation, prototype system construction and performance analysis. Adv Space Res 61(10):1016 19. Tao J, Liu J, Zhao Q (2021) Initial assessment of the BDS-3 PPP-B2b RTS compared with the CNES RTS. GPS Solut 25. https://doi.org/10.1007/s10291-021-01168-1 20. Tyler R, Neish A, Walter T, Enge PK (2016) Leveraging commercial broadband LEO constellations for navigating, 2300-2314. https://doi.org/10.33012/2016.14729

Impact Analysis of BeiDou Satellite Integrity Events in 2022 Yansen Wang1 , Rui Li1(B) , Yongchao Wang2 , and Tiantian Yang3 1 Beihang University, Beijing, China

[email protected]

2 Civil Aviation Data Communication Co., Ltd., Beijing, China 3 Technical Center of Air Traffic Management Bureau of CAAC, Beijing, China

Abstract. With the completion of the technical revision of BeiDou System in international civil aviation standards, the accuracy, continuity, integrity of BeiDou System will become the focus of global civil aviation users. During the assessment of the BeiDou open service performance, it was found that in March 2022, the BDS- 3 MEO-3 (PRN21) satellite had a serious abnormal event. The event occurred in which PRN21 satellite had a frequency offset fault of the satellite clock and last-ed 20 h. The satellite clock error in the event produced a slope fault of 0.76 m/s, and the maximum satellite clock error reached 36616 m. According to the B1I signal message health identifier, the events are divided into 13 h of integrity events and 7 h of continuity events. In accordance with the performance evaluation methods stipulated in the international civil aviation standards, the accuracy, continuity and integrity of the BeiDou satellite space signal performance were evaluated in this quarter. The results show that the single satellite integrity risk of the system in the quarter caused by the event is 2.23 × (10(−4) ), and the continuity risk of PRN21 satellite is 0.398%, both of which are far higher than the ones in the same quarter in 2021. Receiver Autonomous Integrity Monitoring (RAIM) was performed to monitor the faults, and the algorithm achieved fault detection and recognition when the satellite clock error reached 16m which meet the integrity requirements of enroute, terminal, NPA. Based on the analysis of this incident, reasonable suggestions are put forward for the aviation application of the BeiDou System. Keywords: BeiDou system · Integrity system · Signal-in-space performance evaluation

1 Introduction The BDS-3 (BeiDou System-3) was put into operation on July 31, 2020. On 22 June 2021, at the sixth meeting of the ICAO Navigation Expert Group, the ICAO discussed and considered the introduction of BDS in SARPs (International Standard and Recommended Practices) of aeronautical telecommunication ANNEX 10 to the Convention on International Civil Aviation [1]. The requirements of service performance of BDS are described. Since then, the accuracy, continuity, integrity and other key performance of © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 190–199, 2024. https://doi.org/10.1007/978-981-99-6932-6_16

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the BDS have become the focus of global civil aviation users. With reference to performance requirements commitment to ICAO, assessment of BDS-3 is performed by using public data, broadcast ephemeris and precision ephemeris of IGS and the Test and Assessment Research Center of China Satellite Navigation Office (CSNO-TARC). Through data analyzing, an abnormal event of the Beidou-3 System MEO-3 (PRN21 satellite) was found on March 25, 26, 2022. The Instantaneous user range error (IURE), satellite clock error and ephemeris error are calculated. Receiver Autonomous Integrity Monitoring (RAIM) was used to deal with the fault. In addition, the impact of the events on the BDS spatial signal performance in the quarter was analyzed, and the results of first quarter in 2021 were compared. Finally, the paper puts forward some reasonable suggestions for the aviation application of BDS. Unless otherwise stated, the time reference in this paper is BDT.

2 Integrity Performance Assessment Methods and Description of Abnormal Event Phenomena 2.1 Integrity Performance Assessment Methods Integrity represents the credibility of information provided by the navigation system and the ability of timely alarms when faults occur, including the probability of integrity, alarm time, and alarm threshold. The following Table 1 shows the integrity requirements of SARPS for the BDS single satellite (take B1I for example) [5]. Table 1. BDS single satellite integrity requirements BDS single satellite Alarm threshold

Alarm time

Probability of integrity

URE > 4.42 × URA for B1I

300 s (60 min mean time to notify)

1 × 10–5

The 4.42 times the upper bound of User Range accuracy in URA index table is used to determine the integrity alarm threshold (Not to Exceed, NTE). The single satellite integrity state of B1I signal can be defined as:

FPsat_hour (SVh , thour ) =

⎧ ⎨

(SISure ≥ 4.42 × SISA, without an alert within 300 s) (HS = 0, SIF = 0, DIF = 0) ⎩ 0 other 1

The process of integrity assessment algorithm is as follows: 1. Satellite Broadcasting Position calculation: Using the B1I/B3I Broadcasting ephemeris, the satellite position (B3I antenna phase center, BDT) with the output frequency of 1 Hz is obtained.

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2. Calculation of satellite precision position and precision clock bias: Using precision ephemeris and precision clock bias product generated by the IGS (International GNSS Service), the precision position (satellite centroid, GPST) and precision clock bias (B1I/B3I combination frequency point phase center) with the output frequency of 1 Hz is obtained by the ninth-order Lagrangian interpolation method. 3. Unification of Position and clock bias reference: Since the position reference of BDS broadcast ephemeris is the antenna phase center of B3I, and the position reference of precision ephemeris provided by WHU is at the satellite centroid, the difference of ephemeris position reference will introduce errors of submeter to meter level. The satellite Phase Center Offset (PCO) parameter provided on the CSNO-TARC website ECEF is the three-dimensional position vector of the can be used for correction. XAPC ECEF is the phase center of the satellite antenna in the ECEF coordinate system, XCOM three-dimensional position vector of the satellite centroid in the ECEF coordinate system, and A is the rotation matrix from the satellite’s ECI coordinate system to the ECEF coordinate system. ECEF ECEF = XCOM + A · PCO XAPC

(2)

The clock biased is unified to B1I/B3I combination frequency point phase center using TGD parameters. After the procession above, there is still a systematic deviation Tc [4] between the broadcast clock bias and the precision clock bias. In general, the mean systematic deviation of satellite clock errors in the same epoch is zero independently. The deviation can be eliminated by the following algorithm [9]. Tc =

1 n 1 n δtis − δt i i=1 i=1 s n n

(3)

4. The worst user location (WUL) method is used to calculate the instantaneous user ranging error, and the NTE threshold and MTN (Mean Time to Notify) is combined to judge whether abnormal events occur and the number of abnormal events.

Fig. 1. The two cases of analytical method to solve the worst user location

In the Fig. 1, the point P represents satellite precise position, point B represents satellite broadcast position, Point G and point H are the edge points of the coverage area of the satellite signal on the earth surface (the elevation Angle of point G and point H is

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set at 5°). Point O represents center of the earth. The steps to calculate the projection of the ephemeris error in the direction of the worst user are as follows: ➀ Calculating ephemeris error projection PBG /PBH , the calculation method is shown in the following type:   −  2  2  2 − →  → PB = xb − xp , yb − yp , zb − zp , |PB| = xb − xp + yb − yp + zb − zp (4) − → − → PBG = |PB| cos(ω − β), PBH = |PB| cos(ω + β)

(5)

Among them, “β”, “ω” can be determined through the geometric relationships, take MEO satellites for example, the MEO satellite orbit height is about 27906.1 km for Beidou system, radius of the earth is about 6378.137 km,  OGP =  OHP = 95°, β can be calculated using sine theorem β = 19.4° and Omega uses the law of cosines. Then calculating satellite clock bias error, CE is the satellite clock error, and (s) δtcorrected (t) represents the satellite clock bias calculated from the broadcast ephemeris, (s) (t) is the clock bias given by the precise ephemeris. δtreal

(s) (s) (t) − δtreal (t) CE = c · δtcorrected ➁ Figuring out the worst user location: according to the value range of “ω”, the determination of the worst user position direction can be divided into two cases [8]: − → − → Case one: when β < ω < π-β, PG or PH is the worst direction, as shown in the left figure. The higher one in |PBG -CE| and |PBH -CE| is the maximum instantaneous user range error. − → Case two: when ω ≤ β or ω ≥ π-β, PB is in the coverage of satellite and have the most projection value in it’s owns direction as shown in the right figure. However, − → the satellite clock error influence needs to be taken into consideration to determine PB direction is whether the worst user location. The higher one in |PB-CE|, |PBG -CE| and |PBH -CE| is the maximum instantaneous user range error. 2.2 Integrity Performance Assessment Methods At about 15:38 on March 25, 2022, the PRN 21 satellite clock produced a 0.76 m/s ramp fault. According to the B1I message health flag, the events are divided into 13 h of integrity events and 7 h of continuous events (Data source: IGS IAC satellite precision clock bias products; IGS WUM precision ephemeris; B1I/B3I broadcast ephemeris from CSNO-TARC). From 05:00 on March 26, HS was set to 1and lasted for 7 h, navigation file ephemeris interrupted for 5 h and returned to normal at 12:00. The change of HS indicator of B1I signal of PRN21 satellite is shown in the Fig. 2:

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Fig. 2. C21 B1I signal HS flag changes in the event

The 2-day footprint of the satellite’s subsatellite point was drawn according to the almanac is shown in the Fig. 3. At around 13:00 on March 26, Beijing time, the satellite entered the Chinese airspace (data source: PRN21 satellite almanac on March 25 issued by CSNO-TARC).

Fig. 3. Track of C21 subsatellite point

The satellite’s ephemeris errors in the XYZ direction and RCA direction in the earth-centered coordinate system on May 25 and 26 is normal after calculation. At 15:37 on March 25, 2022 (BDST), the satellite clock generated a slope fault with a slope of 0.76 m/s (frequency offset of Hz) and a maximum clock error of 36616 m. At 5:00 on March 26, 2022, HS was set to 1, and the HS and satellite clock error returned to normal about 7 h later (Fig. 4). After calculation, the WUL IURE changes in two days are as follows (Fig. 5). On March 25, 2022, IURE reached 22.053 m and exceeded NTE (21.437) at 2022.3.25 15:38:08. Until 2022.3.26 05:00: 00 when the satellite HS was set to 1, IURE showed a rising trend, and a 13 h single satellite integrity event occurred according to BDS 1h MTN (mean time to notify). After HS was set to 1, the continuity event

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Fig. 4. C21 B1I signal satellite clock error

Fig. 5. C21 B1I signal satellite WUL IURE

of Unscheduled interruption occurred. At 2022.3.26 12:00:00, both HS flag and IURE returned to normal, and the continuity event lasted for 7 h.

3 The Impact of Abnormal Event The 13-h integrity event and the 7 h continuity event of PRN21 satellite caused the increasement of the single satellite integrity risk and continuity risk in the first quarter of 2022. Key service performance such as accuracy, continuity and integrity were compared and assessed in the first quarter of 2021 and 2022 to analyze the impact of the abnormal event. 3.1 Comparison of Accuracy Assessment Result and Impact Analysis of the Event in the First Quarter of 2022 and 2021 According to the ICAO SARPS, the 95% user ranging error for any BDS satellite is no higher than 4.6 m. Thus, IURE is obtained using the worst user location method and a sliding window with a 7-day period and a step unit of 1 day. 95% IURE in the sliding window was counted as URE of the day (Table 2). Affected by the integrity event on March 25th and 26th, the 13h SIS URE on two days seriously exceeded the limit and polluted the evaluation results of the sliding window on eight days. As a result, the accuracy of PRN21 satellite was seriously abnormal in the first quarter.

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IGSO

MEO

First semester in 2022

C38

3.038

3.497

C39

2.635

3.247

C40

2.867

3.195

C19

2.299

2.433

C20

2.552

2.415

C21

1.771

17745.379

C22

1.685

1.643

C23

1.707

2.007

C24

1.562

1.775

C25

2.245

2.232

C26

1.767

1.839

C27

2.465

2.363

C28

0.909

0.918

C29

1.001

1.153

C30

1.567

1.840

C32

1.577

2.045

C33

1.567

1.554

C34

1.838

1.536

C35

1.912

1.642

C36

1.697

1.633

C37

1.687

1.642

C41

2.236

2.288

C42

2.315

2.696

C43

1.732

1.869

C44

1.853

1.896

C45

2.098

1.639

C46

1.979

1.316

3.2 Comparison of Continuity Assessment Result and Impact Analysis of the Event in the First Quarter of 2022 and 2021 Continuity refers to the probability of unavailability due to unscheduled outages. The continuity performance stipulated in the BeiDou Navigation Satellite System Open Service Performance Standard (Version 3.0) are as follows [3] (Table 3).

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Table 3. BDS continuity requirements Signal type

SIS continuity standard

B1C, B2a, B2b, B1I, B3I

SIS continuity

≥0.998/h

This paper uses continuous sliding window method for assessment. 1h sliding window and 1min step unit was carried out to complete the quarterly evaluation [10].The continuity risks for the first quarter of 2021 and 2022 as follows Table 4. Table 4. The comparison of BDS continuity risk between the first quarter of 2021 and 2022

IGSO

MEO

First semester in 2021

First semester in 2022

C38

0

0.00279

C39

0

0.00417

C40

0.00278

0.00324

C20

0.00648

0

C21

0

0.00398

C22

0.00139

0

C23

0

0.00046

C26

0.00046

0

C30

0.00139

0

C32

0

0.00046

C36

0

0.00046

C44

0.00185

0

C46

0

0.00279

Other MEOs

0

0

Affected by the continuity event on March 26th, the continuity risk in the first quarter exceeded the limit of 2×10−3 /h. In addition, there is no public information of scheduled interruption for routine satellite orbit adjustment, the continuity risk of several satellites is relatively high. 3.3 Comparison of Continuity Assessment Result and Impact Analysis of the Event in the First Quarter of 2022 and 2021 No integrity event was found in the first quarter of 2021, and the single satellite integrity risk in this quarter was 0. Affected by the event, 13h integrity events occurred in the first quarter of 2022. The integrity risk of B1I signal single satellite in the first quarter

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of 2022 can be calculated as:



PSat =

SVi thour

(FPsathour (SVi , thour )

Nhours × NSV 13 = 2.23 × 10−4 = 27 × 24 × 90

The results exceed the limit of 1 × 10−5 single satellite integrity risk.

4 RAIM Fault Detection and Exclusion As a traditional monitoring method, receiver autonomous integrity monitoring has been widely used in en-route and terminal area as well as Non-precision Approach (NPA), which provides horizontal navigation and aims at detecting and recognizing single satellite faults in a single constellation. Using the 1 Hz observation data of IGS MEKA station on March 25th of 15min when the fault first occurred, the B1C/B2a BDS broadcast ephemeris, BDS B1C/B2a dual frequency combination RAIM FDE was used for fault detection and exclusion. The RAIM recognizing algorithm adopts the M-1 method [6]. Referring to DO-229F route and terminal stage RAIM integrity requirements, Input parameters was set. The horizontal alarm threshold is set to 556 m, missing alarm rate is 0.001/sample, false alarm rate is 3.33 × 10−7 /sample, and exclusion failure rate is 0.001/sample [3]. The results show that the initial detection and exclusion epoch of the C21 satellite by RAIM/FDE is 15:38:01 on March 25, 2022. At the same time, the C21 satellite IURE is 17m and the star clock error is 16m. The results of visible satellite numbers and positioning results are shown in the following Table 5. Table 5. The positioning result of RAIM detection and exclusion Satellite numbers in vision

95%HPE/m

MI/HMI numbers

NPA availability

7–8

3.08

0/0

100%

5 Conclusion On March 25th and 26th, 2022, the BDS-3 MEO-3 satellite experienced a 13 h integrity event caused by the satellite clock fault. It is found that a 0.76 m/s satellite clock ramp fault occurred for the B1I signal in the event, and the maximum satellite clock error reached 36616 m, resulting in IURE continuously exceeding NTE. The continuous event of unscheduled interruption occurred after the HS was set to 1, which lasted for 7 h. This incident seriously affected the accuracy, continuity and integrity assessment results of

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the BDS in this quarter. Compared with the assessment results of the same quarter in 2021, the space in signal continuity risk of C21 satellite increased to 0.398%, and the integrity risk of the BDS single satellite increased to 2.23 × 10−4 . Continuity risk and single satellite integrity risk is beyond SARPs commitments for BDS. RAIM is used to detect and recognize the faults, and it is verified that RAIM can realize the detection and exclusion of the faulty satellite. Based on the impact of this incident, the following suggestions are put forward for the future aviation application of BDS: 1. The BDS should enhance the stability of its satellite clock, and enable the SAIM function (Satellite Autonomous Integrity Monitoring) to effectively deal with such integrity events timely. 2. The user with receiver autonomous integrity monitoring (RAIM) facility can effectively deal with such single-satellite integrity events. 3. For satellite routine orbit adjustments, BDS shall, as promised to ICAO, publicize scheduled interruption information in advance to effectively reduce system continuity risks. Acknowledgement. Thank “the Technical Cooperation Project of Civil Aviation Application Verification and Evaluation of BDSBAS” for providing funding for this project.

References 1. International Civil Aviation Organization (2006) Aeronautical telecommunications. Annex, October 2006 2. China Satellite Navigation Office. BeiDou navigation satellite system open service performance standard (version 3.0) [EB/OL]. http://www.beidou.gov.cn/xt/gfxz/,2021-05-26 3. RTCA SC-159, Minimum operational performance standards for global positioning system/satellite-based augmentation system airborne equipment, DO-229F. Radio Technical Commission for Aeronautics, Washington, DC, 11 June 2020 4. China Satellite Navigation Office. BeiDou Navigation satellite system signal-in-space interface control document open service signal B1I (version 3.0) [EB/OL]. http://www.beidou. gov.cn/xt/gfxz/201902/P020190227592987952674.pdf 5. The Preliminary Performance Assessment Results of BeiDou System [EB/OL]. https://por tal.icao.int/nsp/MeetingDocuments/JSP9June2022/IPs/,2022-06-21 6. Chen J (2001) Research of GPS integrity augmentation. Institute of Surveying and Mapping, Information Engineering University 7. Tang Y (2015) Research on evaluation method of GNSS aviation application performance. Beihang University, Beijing, China 8. Sun S (2016) Signal-In-space performance research of GPS/BDS in China region. Beihang University, Beijing, China 9. Zhang R (2019) BDS signal-in-space user range error evaluation considering different antenna phase center offset models. Geomat Inform Sci Wuhan Univ 44(6):806–813. https://doi.org/ 10.13203/j.whugis20180388 10. Wang J (2021) Comparison and optimization of SIS continuity evaluation of navigation satellite. In: Proceedings of the 12th China satellite navigation annual conference—S03 navigation signal and signal processing, pp 108–113. https://doi.org/10.26914/c.cnkihy.2021.002 374.Author, F.: Article title. Journal 2(5):99–110 (2016)

Analysis of Navigation Augmentation Performance Based on LEO Satellite Communication Constellation Xing Li1(B) , Kun Jiang1 , Ping Li2 , Xiaomei Tang3 , and Xia Guo1 1 Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China

[email protected]

2 China Academy of Space Technology, Beijing 100094, China 3 National University of Defense Technology, Changsha 410073, China

Abstract. With the rapid development of LEO communication constellations, the performance enhancement of existing medium and high orbit constellations has been realized by making full use of the characteristics of LEO communication satellites, such as high transmission rate, low orbit height and large constellation scale, which has attracted extensive attention and become a research hotspot. Based on the systematic analysis of the available resources of the LEO communication constellation, this paper presents a system architecture of navigation augmentation based on the LEO communication constellation. It analyzes the available constellation and frequency resources. The performance of improving the reception sensitivity of BeiDou user terminals and providing emergency backup positioning based on the LEO communication constellation is quantitatively evaluated through theoretical calculation and simulation analysis. The research results can provide a reference for designing and constructing an integrated positioning, navigation, and timing service system. Keywords: Low Earth Orbit (LEO) communication constellation · Navigation Augmentation · Positioning · Navigation · and Timing (PNT) architecture

1 Introduction After more than two decades of development, the BeiDou Satellite Navigation System (BDS) has achieved leap-forward development from active to passive and from regional to global. The BDS-3 Global Navigation Satellite System was officially completed and implemented in 2020. The space segment of the system is composed of 30 satellites (24MEO + 3GEO + 3IGSO). With the support of the ground control system, it can provide global users with positioning and timing services of better than 10 m, the timing of better than 20 ns, and availability of better than 99%, with better performance in the Asia-Pacific region. However, constrained by international rules, the satellite navigation system’s landing signal power is easily interfered with and blocked, so the service capability is insufficient in a complex environment. First of all, due to the restrictions of ITU rules, the landing © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 200–214, 2024. https://doi.org/10.1007/978-981-99-6932-6_17

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level of the satellite navigation signal is only about −160dBW, which makes GNSS systems vulnerable to electronic interference, blocking, and spoofing. A jammer with a transmitting power of 20W could deny service to a block. Secondly, in urban, indoor, canyons, forests and other sheltered environments, the number of visible navigation satellites may not meet the positioning requirements. In extreme cases, this will lead to the unavailability of satellite navigation. Several signal or information augmentation techniques have been developed to compensate for these weaknesses. In signal augmentation it can be realized by ground-based broadcasting, but its coverage is limited and inconvenient to layout and maintain. It can also be realized through space-based broadcasting. However, in the past, it mainly relies on MEO and GEO satellites, which puts forward high requirements on satellite power consumption and antenna size, but the cost is relatively high. Regarding information augmentation, navigation message parameters and correction information can be broadcast through various communication channels such as ground mobile communication and satellite communication. However, there is no stable communication channel with global coverage to broadcast this augmented information. With the rapid development of the LEO communication satellite constellation, some new solutions to the above problems have been provided [1–8]. By utilizing the advantages of the LEO communication satellite constellation, such as high landing power, large transmission bandwidth and global wide area coverage, the positioning and timing of the MEO and GEO satellite constellation can be supplemented and augmented. Based on the analysis of the available satellites and frequency resources of the LEO communication constellation, this paper introduces the navigation augmentation system architecture based on the LEO communication constellation. It analyzes the supplementary augmentation service performance under resource constraints. The research results can provide a reference for developing the next generation of comprehensive PNT systems.

2 An Architecture of Navigation Augmentation System Based on LEO Communication Constellation 2.1 Overall System Architecture The navigation augmentation system based on the Leo communication constellation makes use of the available Leo communication satellite resources in space, adopts the technical system of integration into the communication system, and broadcasts BDS/GNSS augmentation messages and communication and navigation fusion signals by loading the corresponding navigation function loads on the communication satellites without excessive increase in satellite costs. The following Fig. 1 shows the system architecture for the complementary augmentation of BDS/GNSS positioning and timing. Space Segment The space segment consists of the BDS/GNSS and LEO communication constellation. The LEO communication constellation can rely on the planned construction of the Satellite Internet and other LEO constellations. Some of them are selected to carry the navigation function payload, configure high-precision space-borne GNSS receiver,

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receive the GNSS downlink navigation signal, and generate the time-frequency reference of the BDS/GNSS system. The obtained BDS/GNSS satellite observation data are used to generate and broadcast navigation augmentation signals based on the conduction fusion’s signal processing load. The communication channel broadcasts navigation messages, precision corrections, integrity, and other information. Finally, the navigation augmentation service based on the LEO communication constellation is realized. Ground Segment The ground segment comprises an operation and control centre, gateway station and monitoring station. The operation and control centre collects the observation data of the LEO conduction fusion signal and the BDS/GNSS signal from the ground monitoring station, as well as the observation data of the LEO satellite to the BDS/GNSS signal. And then performs the system time synchronization processing, the satellite clock error prediction, the satellite precision orbit processing and the broadcast ephemeris prediction and generates the corresponding BDS/GNSS augmented message. The navigation augmentation of BDS/GNSS is realized by broadcasting to users from the gateway station to the LEO satellite. User Segment The user segment is mainly the user terminal configured in various platforms and carriers to provide users with navigation augmentation services. There are three service types. The first type is to broadcast navigation augmentation information through the communication link to achieve rapid acquisition, sensitivity improvement and accuracy enhancement of the auxiliary receiver. The second and third types are based on LEO narrowband and wide-band communication signals to realize specific emergency backup positioning and timing capabilities. 2.2 Spatial-Temporal Reference In order to provide positioning and timing service to ground users, the orbit and time information of the LEO satellite must be determined first. However, on the one hand, due to the orbital characteristics of LEO satellites, the atmospheric drag, the non-spherical gravity of the earth and the general relativistic effects on satellites are significantly higher than those of medium and high-orbit satellites. Therefore, selecting more elaborate mechanical model parameters and processing strategies is necessary to achieve decimeter or even centimetre orbit determination accuracy [9]. On the other hand, it is considered that the coverage area of a single LEO satellite is only about 1/10 of that of a single GEO satellite [10]. So it takes a vast number of satellites to achieve multiple coverages. The design and manufacture of satellites must be more strictly controlled, and it is impossible to equip all the satellites with high-performance atomic clocks. Therefore, a more optimized way to maintain the satellite-bone time frequency is necessary to ensure better user performance.

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Fig. 1. Architecture design of the navigation augmentation system based on LEO communication constellation

Determination and Prediction of the Satellite Orbit Using satellite-borne BDS/GNSS receivers to determine the precision orbit of the LEO satellite is the most economical and feasible technical way at present. The satelliteborne GNSS receiver is used to measure the dual-frequency pseudo-distance and carrier phase equidistance information from the phase centre of the GNSS antenna to the phase centre of the GNSS satellite antenna. The GNSS satellite orbit is taken as the spatial reference information source, and the least squares algorithm or filtering algorithm is adopted to estimate and forecast the satellite orbit. The satellite-borne GNSS receiver is used to measure the dual-frequency pseudo-distance and carrier phase equidistance information from the phase centre of the GNSS antenna to the phase centre of the GNSS satellite antenna. Taking GNSS satellite orbit as the spatial reference information source, the least square algorithm or filtering algorithm estimates and forecasts the satellite orbit using dynamics or simplified dynamics methods. For post-precision users, the centimetre-level high-precision orbit of LEO satellites can be obtained by processing products based on post-GNSS high-precision orbit and clock difference. For navigation services of LEO satellites, orbit and clock difference information of GNSS satellites can be obtained through real-time ephemeris broadcast by GNSS satellites. Then the orbit information of LEO satellites can be determined. Previous studies have shown that using the dual-frequency pseudo-distance/carrier phase measurement values of BDS-3 or

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Galileo satellites [11]. The LEO satellite’s decimeter-level real-time orbit determination accuracy can be achieved with radial position error better than 0.15 m and tangential and normal position error better than 0.2 m (Figs. 2 and 3).

Fig. 2. RMS statistics of 3D errors in real-time orbit determination of LEO satellites under different system combinations [11]

Establishment and Maintenance of Satellite Time Reference Combing GNSS time-frequency has driven high crystal oscillators, and the miniaturized atomic clock is a feasible solution to balance performance and cost. Since BDS/GNSS satellites are equipped with high-precision and high-stability atomic clocks, time-frequency information can be transmitted to users through GNSS signals. The GNSS navigation signal is received by the GNSS receiver of the LEO satellite to obtain the deviation of the local time frequency of the LEO satellite from that of the GNSS satellite. Then the frequency deviation of the local time frequency is adjusted and corrected. Therefore, the local time-frequency stability of the LEO satellite can be ensured to be close to the time-frequency stability of the GNSS atomic clock, and the purpose of improving the time-frequency stability of the highly stable crystal oscillator is finally achieved. After using GNSS time-frequency control, the time-frequency stability of the highly stable crystal oscillator can reach 2E-12@10s, 5E-13@100s, and 2 – 3E13@1000s, which is comparable to the performance of a miniaturized atomic clock. The timing uncertainty of conversion to the time dimensions 100 s and 1000 s is about 50ps and 200ps, which can meet the service requirements. The stability index of the time-frequency source is shown in the following Table 1.

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Fig. 3. GPS P(Y), Galileo E1\E5a, BDS-3 B1C\B2a simulation measurements of LEO Satellite in radial, tangential, normal position errors [11]

Table 1. Stability index of time-frequency source

Second

Miniaturized atomic clocks

OCXO

2–3E-12

1–2E-12

Ten-second

8E-13

5E-12

Hundred-second

5E-13

2E-11

Thousand-second

2–3E-13

2E-10

2.3 Constellation and Frequency Different from specially designed LEO navigation constellations, the realization of navigation augmentation capability based on LEO communication constellations largely relies on the orbit and frequency of existing constellations and provides specific incremental capabilities through practical optimization design without affecting the communication mission as much as possible. For performance analysis later in this paper, orbit and frequency configurations of these two constellations are assumed, as shown in the following Table 2 and Figs. 4, 5.

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No.

Indicator

LEO Narrow-band communication constellation

LEO wide-band communication constellation

Constellation 1

Constellation 1

Constellation 2

72

72

288

1

Quantity of satellites

2

Quantity of orbital planes 6

6

12

3

Quantity of satellites in orbit

12

12

24

4

Orbital altitude

1000 km

1000 km

1050 km

5

Orbit inclination

86.5°

86.5°

55°

6

Phase factor

3

3

1

7

Frequency

L

Ka

Ka

Fig. 4. “72” LEO narrowband communication constellation

Coverage Performance of LEO Narrowband Communication Constellation The user observation cutoff Angle was set as 10°, and the number of visible satellites in different latitudes was analyzed. It is shown in Fig. 6 that in the middle and low latitudes areas, the visible number is small, and the minimum visible number is 1. The number of visible satellites in the high latitude region is large, and the maximum number of visible satellites is 10.

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Fig. 5. “72+288” LEO wide-band communication constellation

Fig. 6. Coverage of 72 LEOs, elevation mask: 10°

Coverage Performance of LEO Wide-Band Communication Constellation Considering the spatial propagation characteristics of the Ka-band signal, the observation cutoff Angle is set as 20°. The number of visible satellites in different latitudes around the world is analyzed. The minimum visible number is 1, and the maximum visible number is 15, as shown in Fig. 7. The global average DOP values at different latitudes are shown in Fig. 8.

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Fig. 7. Coverage of 72+288 LEOs, elevation mask: 20°

3 Analysis of Navigation Augmentation Performance Based on LEO Communication Constellation 3.1 Improving Reception Sensitivity of BDS/GNSS Terminal Based on Communication-Aided Channel The information-aided based on the LEO communication system can improve the acquisition and tracking sensitivity of the user terminals. With the help of the LEO communication service channel, the user terminal can obtain the satellite navigation message and get its own probability position and rough time deviation by using the LEO communication signal. The precision of usually available auxiliary information is shown in the following Table 3. The user terminal can perform coherent integration across message symbols based on this aid information by stripping the navigation message. On the other hand, based on the preliminary information such as navigation message, position, time and frequency, the dynamic and Doppler of the user terminal relative to the navigation satellite can be estimated. This way, the signal-to-noise ratio (SNR) increment is obtained to improve the capture and tracking sensitivity. As for B1C, B2A, B1I, and B3A signals of the BDS, the improvement of the aid sensitivity of LEO communication is related to the accuracy level of the aid information and the signal characteristics. In the B1C, B2A, B1I and B3A signals of the BDS, the improvement of the aid sensitivity of LEO communication is related to the accuracy level of the aid information and the signal characteristics. With the precise time (below millisecond) aid and the message aid, the capture sensitivity of 5.2 dB– 11.2 dB and the tracking sensitivity of 12.5 dB–15.5 dB can be improved. The specific analysis results are shown in Tables 4 and 5.

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Table 3. Communication-aided information accuracy level Aid level

Communication-aided information accuracy

Rough time aid

Time accuracy: ms < t < 10s Precise ephemeris Initial position accuracy: < 150 km

Precise time aid

Time accuracy: < ms Precise ephemeris Initial position accuracy: < 10 km

Precise time aid Message aid

Time Accuracy: < ms Navigation message aid Initial position accuracy: < 10 km

Precise time aid Message aid Frequency synchronism

Time accuracy: < ms Navigation message aid Synchronous aid of communication frequency

Table 4. Capture sensitivity improvement Aid level

Capture sensitivity improvement (dB) B1C

B2A

B1I

B3A

Rough time aid

4.6 dB

1.1 dB

3.9 dB

8.7 dB

Precise time aid Message aid

6.2 dB

5.2 dB

9.7 dB

11.2 dB

Table 5. Tracking sensitivity improvement Aid level

Tracking sensitivity improvement B1C

B2A

B1I

B3A

Rough time aid

11.2 dB

9.4 dB

1.8 dB

6.4 dB

Precise time aid Message aid

dB

15.5 dB

15.5 dB

5 dB

3.2 Positioning Performance Based on LEO Narrow-band Communication Signal Considering the coverage characteristics of LEO narrowband communication signals, it can only ensure more than 1 repeat coverage in most parts of the world. Therefore, positioning is mainly achieved by combining Doppler and pseudo-distance measurements.

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The observation equations are shown in Eqs. (1) and (2): ⎡ ⎤ vxi (x − xi ) + vyi (y − yi ) + vzi (z − zi ) ⎦ + ni i = 1, 2 . . . , K fi = f0 ⎣1 +  2 2 2 c (x − xi ) + (y − yi ) + (z − zi )

(1)

where fi represents the Doppler measurement value of the LEO satellite for the first observation, (x, y, z) represents the user’s three-dimensional coordinate position, (xi , yi , zi ) and (vxi , vyi , vzi ) respectively represent the satellite’s three-dimensional position and velocity at the i time of observation, c represents the velocity of light, and ni represents the observation noise.   2 x − xj + (y − yi )2 + (z − zi )2 + cτu + mj j = 1, 2, . . . , L ρj = (2) where ρj represents the pseudo-distance measurement value obtained by receiving the jth satellite (x, y, z) and (xj , yj , zj ) respectively represent the three-dimensional coordinate position of the user and the J-th satellite; c represents the velocity of light; τu represent the user clock difference; mj represent the observation noise. Taking static users in the mid-latitude region (30°N, 0°E on the grid) as an example, the simulation parameters shown in Table 6 are adopted, where the primary error of UERE is considered the pseudo-distance measurement error. The code chip with the signal pseudo-code rate of 500 kHz and the code ring tracking accuracy of 0.005 is used for calculation, and the corresponding ranging error is 3 m. As well as combing with atmospheric transmission delay, transceiver channel delay, antenna phase centre error and other factors, UERE is estimated at 5 m. The positioning solution was Monte Carlo simulated 100 times, and the statistical results are shown in Table 7. According to the results, when the initial position error is 1000 m, the positioning error is better than 43.3 m. When the initial position error is 10000 m, the positioning error is better than 50.8 m. A range of 15°longitude and 0–90°latitude around the trajectory of the sub-satellite point of a single satellite was taken for positioning solution. The statistical results can be equivalent to the global positioning performance. The positioning error results are shown in Fig. 8, and the statistical data are shown in Table 8. As can be seen from the results, the maximum positioning error is 253.3 m, the average is 20.0 m, and the proportion of error better than 50 m is 91.3%. 3.3 Positioning Performance Based on LEO Wide-band Communication Signal A narrow beam usually covers LEO wide-band communication. To provide navigation services based on LEO wideband communication signals, it is necessary to dispatch more than four satellite beams with a better geometric configuration at the same time or within the same period (generally at the second level) to point to the user area applying for navigation services. In this operating mode, the positioning error follows the formula σP = PDOP · σUERE . According to the constellation configuration defined in Sect. 2.3, the global average DOP values for different latitudes are shown in Fig. 9, and the global average PDOP value is 8.0. Considering the ranging signal rate of 10 MHz and the

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Table 6. Simulation parameter configuration of positioning solution experiment based on LEO communication constellation Type

Parameter configuration

Signal frequency/MHz

1625

Positioning time/s

480

Data sampling rate/Hz

1

User 3D velocity/(m/s)

0

User 3D acceleration/(m/s2)

0

User clock deviation/s

0

User clock drift/(s/s)

0.3

User frequency drift (s/s2)

0

Combination mode of the observation data

Pseudo-distance + Pseudo-distance rate

UERE/m

5

Measurement accuracy of pseudo-distance rate/(m/s) 0.2 User position (e.g. Mid-latitudes area)

(30°N, 0°E)

Initial deviation in the X direction/m

1000 or 10000

Initial deviation in the Y direction/m

1000 or 10000

Initial deviation in the Z direction/m

1000 or 10000

Table 7. The statistical result of the position solution (30°N, 0°E static users) Deviation of initial value/m

Positioning error/m E

N

U

3D

1000

26.7

1.3

34.1

43.3

10000

39.7

2.9

31.5

50.8

tracking accuracy of 0.005 code chip, the UERE is estimated to be about 1.2 m by comprehensively considering the atmospheric delay, phase centre, channel delay and orbit and clock error. According to the positioning error formula, the global average positioning error is about 9.6 m.

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Fig. 8. Global positioning error based on LEO narrowband communication signals

Table 8. Global positioning error statistics based on LEO narrowband communication signals Global positioning error statistics Typical value statistics

Interval statistics

Maximum

253.3 m

≥100m

2.6%

Mean

20.0 m

>50 m & 99.999%

>99.9%

>99%

>95%

>90%

Below 90%

Coverage percentage

0%

0%

91.27%

96.03%

98.41%

1.59%

3.4 BDSBAS Ionospheric Grids Coverage Area Assessment This section uses the above data for positioning and evaluates the GIVE integrity of all GPS satellites at all stations for each grid area, that is, the envelope of GIVE to ionospheric delay error. The ionospheric grid point (IGP) region in China and its surrounding areas (10°N–55°N, 75°E–135°E) is spaced by 5° latitude and longitude, including a total of 96 grid areas. The specific methods for assessing the area covered by the ionospheric grid are as follows: the receiver position and satellite position of the monitoring station are calculated through observation data and precision ephemeris, so as to calculate the latitude and longitude coordinates of the ionospheric puncture point, and the ionospheric grid point delay value and delay error (GIVE) are obtained by single-frequency SBAS messages, and the ionospheric puncture point delay value and user ionospheric delay error are obtained by interpolation. (UIVE); The true value of ionospheric puncture

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point delay was obtained by data preprocessing, and then the ionospheric puncture point delay value was used to obtain the delay error. The envelope of the puncture point UIVE for the delay error is calculated. The latitude and longitude of all puncture points are statistically summarized into the grid area to which they belong, and finally the GIVE envelope rate of each grid point is statistically obtained, which is used as an indicator for the evaluation of the coverage area of ionospheric grid. The results of the assessment of ionospheric grid coverage in China and its surrounding areas in October 2021 are shown in Fig. 7 and Tables 6, 7.

Fig. 7. Ionospheric grid coverage area evaluation results (2021.10)

Table 6. Statistics on the number of ionospheric grid coverage area (2021.10) Availability

>99.999%

99.9%–99.999%

99%–99.9%

95%–99%

90%–95%

Below 90%

Number of ionospheric grid coverage area

5

32

33

9

7

11

Table 7. Statistics on ionospheric grid coverage area (2021.10) Availability

>99.999%

>99.9%

>99%

>95%

>90%

Below 90%

Coverage percentage

5.15%

38.14%

72.16%

81.44%

88.66%

11.34%

From the analysis of the above results, it can be seen that the grid coverage of the area south of 30°N in China is poor, and most areas do not reach 99% envelope rate, that

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is, ionospheric anomalies occur. Almost all areas north of 30°N in China have reached 99% envelope rate. Therefore, it can be verified that the main reason why most of the BDSBAS single-frequency service areas in southern China are below 99% availability is ionospheric anomalies. Comparing the above results with the results in Fig. 2, it is clear that the availability of single-frequency enhancement services in southern China is poor due to ionospheric anomalies, which was not detected by grid point evaluation method. Similarly, the results of the assessment of ionospheric grid coverage in China and its surrounding areas in August 2021 are shown in Fig. 8 and Tables 8 and 9.

Fig. 8. Ionospheric grid coverage area evaluation results (2021.08) Table 8. Statistics on the number of ionospheric grid coverage area (2021.08) Availability

>99.999%

99.9%–99.999%

99%–99.9%

95%–99%

90%–95%

Below 90%

Number of ionospheric grid coverage area

6

8

53

26

3

1

Table 9. Statistics on ionospheric grid coverage area (2021.08) Availability

>99.999%

>99.9%

>99%

>95%

>90%

Below 90%

Coverage percentage

6.18%

14.43%

69.07%

95.87%

98.97%

1.03%

According to the comparative analysis of the statistical table of ionospheric grid coverage areas in August and October 2021, the area with service availability above

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90% and above 95% in August is significantly more than the area in October, indicating that the ionosphere is in an active period in October. From the comparative analysis of Figs. 8 and 7, it can be seen that the grid coverage of the area south of 30°N in China is higher than during the active period during the ionospheric calm period, which can explain the better service availability of monitoring stations in August compared with October. From the above analysis, it can be seen that during the ionospheric calm period, most BDSBAS single-frequency service areas in China can achieve 99% coverage of APV-I level availability. During the active period of the ionosphere, the BDSBAS singlefrequency service area in northern China can achieve 99% coverage of APV-I availability, while most of the BDSBAS single-frequency service area in southern China is below 99% availability due to ionospheric anomalies. Compared with the grid point evaluation method, the proposed method can clearly show that the availability of single-frequency enhanced services is poor due to ionospheric anomalies in southern China, so this method is more suitable for BDSBAS service coverage area assessment.

4 Conclusions This paper studies the SBAS service coverage area evaluation method, briefly describes the grid point evaluation method used for WAAS service coverage area evaluation in WAAS performance report, and uses the grid point evaluation method to evaluate and verify the BDSBAS service area. This paper then points out that BDSBAS and WAAS are currently in different stages, so the grid point evaluation method used by WAAS is debatable for the evaluation of BDSBAS service coverage area. Based on this, this paper proposes a service coverage area assessment method suitable for BDSBAS, which realizes the accurate evaluation of ionospheric grid coverage area and positioning service coverage area through national multi-station dense network monitoring. The evaluation results show that the BDSBAS single-frequency service area in northern China can achieve 99% coverage of APV-I level availability, while most BDSBAS single-frequency service areas in southern China are STC (fix) > TC > STC (float) > GNSS-only. The corresponding positioning error is shown in Fig. 7. it takes only about 10 s for GNSS ambiguity to converge under the DF-TC model, so DF-TC(10s) is still taken as the analysis objective here. But in STC model, whether ambiguity is fixed or not, the performance is not as good as TC model. Even STC (float) positioning error is larger than GNSS-only. The main reason is that in STC model, the positioning accuracy reflected by the position covariance of PLS is often artificially high, which makes it difficult to reasonably use PLS position information to constrain GNSS, which is another important disadvantage of STC model.

1E+09

GNSS-only TC STC(float) STC(fix) DF-TC

1E+07 1E+05 1E+03 1E+01 0

150

300 450 600 Time (s)

750

900

Fig. 6. Condition number for cofactor matrix of GNSS ambiguity under different couple models with PLS augmentation for 10 s

It can be seen from the previous analysis that the TC model is superior to the STC model. Therefore, the STC model is no longer considered here, and only the TC and DF-TC are analyzed and compared. Figure 8 shows the condition number of GNSS

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Fig. 7. Positioning errors under different couple models with PLS augmentation for 10 s

Condition number for cofactor matrix of GNSS ambiguity

ambiguity covariance under DF-TC and TC models under different augmentation time, which reflects the gain brought by the ambiguity fixed solution. Figure 7 shows that it takes only about 10s for GNSS ambiguity to converge under the DF-TC model, so DF-TC(10s) is still taken as the analysis objective here. It can be seen that DF-TC (10s) is always better than TC (15s), and the performance of DF-TC (10s) exceeds TC (20s) after 450 s. When the time reaches 900 s, DF-TC (10s) even exceeds TC (30s) and TC (40s). This also indicates that DF-TC has more and more obvious advantages in the later stage. The corresponding positioning error is shown in Fig. 9. The TC (10s) positioning error fluctuates large, indicating that the GNSS ambiguity does not converge. TC (15s) has basically converged, and there is a slight divergence when PLS disappears, but the positioning error remains within 0.2 m. There is no significant difference between TC (20s), TC (30s), TC (40s) and DF-TC (10s), which indicates that PLS ambiguity fixing can significantly shorten the augmentation time required for GNSS. 1E+09

TC(10s) TC(20s) TC(40s)

1E+07

TC(15s) TC(30s) DF-TC(10s)

1E+05 1E+03 1E+01 0

150

300 450 600 Time (s)

750

900

Fig. 8. Condition number for cofactor matrix of GNSS ambiguity under DF-TC and TC models with different PLS augmentation time

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Fig. 9. Positioning errors for DF-TC and TC models with different augmentation time

4 Conclusions In order to make full use of PLS augmentation information in a short augmentation time, this paper proposes a DF-TC model, which can use PLS fixed solution more safely and reliably. Experiments show that PLS ambiguity resolution can significantly reduce the augmentation time required for GNSS. For example, when the PLS ambiguity is not resolved, GNSS requires PLS augmentation for 20 s to maintain stable convergence. However, when the PLS ambiguity is correctly resolved, GNSS only needs 10 s augmentation to maintain stable convergence, which significantly shortens the required augmentation time. This means that the required coverage area of PLS can be smaller, more flexible and convenient to use. From the perspective of PLS-augmentation GNSS ambiguity condition number reduction, the TC model is superior to the STC model regardless of PLS ambiguity is fixed or not in the case of short-term augmentation. In addition, PLS is helpful for GNSS ambiguity resolution, and in turn, GNSS is also helpful for PLS ambiguity resolution. This makes the PLS ambiguity under the TC model easier to be resolved than that under the STC model, then the PLS with fixed ambiguity may bring greater contribution to GNSS. Acknowledgements. We are very grateful to CNES/Nav for providing real-time products. This work is supported by National Key Research and Development Program of China, Beidou Precise Spatiotemporal Information Fusion Application and Intelligent Service System, under Grant No. 2021YFB1407001, National Natural Science Foundation of China (NSFC), under Grant 42274018, and Shandong Hi-Speed Group Provincial Project, Beidou High Precision Transportation Application Technology Research, under Grant BNR2021RC01015.

References Fan C, Yao Z, Wang S, Xing J (2022) Pseudolite system-augmented GNSS real-time kinematic PPP. J Geodesy 96(10):77. https://doi.org/10.1007/s00190-022-01663-4 Fan C, Yao Z, Yun S, Xing J (2021) Ground-based PPP-RTK for pseudolite systems. J Geodesy 95(12):133. https://doi.org/10.1007/s00190-021-01589-3

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BDS-3 Signal in Space Ranging Errors Performance and On-Orbit Status Monitoring and Evaluation Based on Historical Data from 2020 ~ 2022 Lei Chen1 , Weiguang Gao1 , Hongliang Cai1 , Xuanzuo Liu2 , Haoyu Kan2 , Liqian Fan3 , and Zhigang Hu2(B) 1 Beijing Institute of Tracking & Telecommunication Technology, Beijing 100094, People’s

Republic of China 2 GNSS Research Center, Wuhan University, Wuhan 430079, People’s Republic of China

[email protected] 3 University of Information Engineering University, Zhengzhou 450052, People’s Republic of

China

Abstract. Signal in Space (SIS) performance, particularly SIS Range Error (SISRE), is the core index for evaluating the navigation, positioning, and timing accuracy and integrity monitoring of the Global Navigation Satellite System (GNSS). In this research, the SISRE performance and on-orbit status of BDS-3 satellites are monitored and evaluated comprehensively based on the historical data composed of the broadcast ephemeris and observation data from IGS and iGMAS tracking stations from July 31, 2020, to May 31, 2022. The performance evaluation results show that the average accuracy of BDS-3 SISRE is 0.25 m, which is much better than the system design index. Based on the independent monitoring results, from the annual average of satellite on-orbit adjustment from 2020 to 2022, the overall operation of the system is good and tends to be stable. It is worth noting that the MEO satellite had two unplanned outages of satellite clocks whose health information was not updated or lagged in updating. Therefore, it is suggested that the system extensively use monitoring methods such as the inter-satellite link (ISL) and Satellite Autonomous Integrity Monitoring (SAIM) in the future to strengthen the worldwide monitoring of BDS-3 satellite on-orbit operation status. Keywords: BDS · SISRE · Performance monitoring and evaluation · Integrity

1 Introduction The BeiDou Navigation Satellite System (BDS) was officially completed on July 31, 2020, and provides up to seven services [1, 2]. Among them, Positioning, velocity, and timing (PVT) is the most basic and most used service in the Global Navigation Satellite System (GNSS). © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 239–252, 2024. https://doi.org/10.1007/978-981-99-6932-6_20

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For Radio Navigation Satellite Service (RNSS) users, the navigation ephemeris provides coordinates and time references [3] and is a core component of SIS [4]. And the SISRE reflects the combined effect of the geometric error between the actual position of the satellite and the predicted position expressed in its ephemeris, and the error of the satellite clock, and ultimately affects the positioning accuracy of real-time users. Therefore, SISRE performance is the core index to evaluate the PVT accuracy and integrity monitoring of the GNSS system [5, 6]. In recent years, with the completion of BDS, many scholars have carried out performance evaluation research. Hu et al. carried out the BDS-2 service performance research earlier and derived the SISRE calculation methods of BDS Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites [6–8]. Based on the 1-year data accumulated by Multi-GNSS Experiment (MGEX), Montenbruck et al. analyzed and compared the SISRE accuracy of BDS-2, GPS, and GLONASS [9], and concluded that the accuracy of BDS-2 SISRE is about 1.5 m, which is better than GLONASS (1.9 m), but slightly worse than GPS (0.7 m). Compared with BDS-2, BDS-3 is designed with new navigation signals and equipped with higher-precision hydrogen clocks, and new rubidium clocks and supports inter-satellite links for the first time [10], and its orbit and clock accuracy have been greatly improved [11], and its SISRE accuracy has also been significantly improved from the evaluation results [12–14]. Based on the evaluation of the SISRE performance, scholars have carried out relevant research focusing on the characteristics of the BDS SIS. Chen et al. analyzed the correlation between the error of orbit and clock and found that the correlation between the error of along, cross, radial, and clock of the three types of satellite orbits of BDS is not obvious, and in terms of the correlation between orbital radial error and clock error, GEO satellite has the most obvious correlation, MEO satellite has the smallest one, and IGSO satellite correlation is the second [15]. For the Time Group delay (TGD) in the broadcast ephemeris, Zhang et al. found that there was a systematic biase between the same frequency TGD of BDS-2 and BDS-3, and there was also a systematic deviation between broadcast products and precise products, and in the long-term evaluation, using the Differential Code Bias (DCB) as a reference, it was found that the accuracy of BDS-3 TGD continued to improve with the stable operation of the system [15–17]. For the abnormal detection of BDS SIS, Fan et al. carried out the analysis of the status of BDS-2 satellites on-orbit operation based on the broadcast ephemeris parameters [18], while Wang et al. conducted a preliminary evaluation of the standard performance and anomalies of BDS-2 and BDS-3 SIS, and found that compared with BDS-2 satellites, the probability of abnormalities of BDS-3 satellites decreased, which will meet the design specification and further improve in future [19]. Therefore, with the continuous increase of the on-orbit operation time of the BDS-3, it is of great significance to monitor and evaluate the SISRE performance and on-orbit status of the BDS-3 for analyzing and finding the characteristics and historical SIS outages: On the one hand, the monitoring and evaluation can verify whether the performance of the SISRE meets the expected requirements of the satellite system design; On the other hand, the historical SIS outages of the system can be counted and identified, and scientific satellite monitoring method can be used to quickly identify the source of the SIS outages, which can not only minimize the system risk and user loss, but also provide a basis for

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improving or enhancing the system performance for the subsequent development of the BDS-3. In accordance with the historical data during 2020 ~ 2022, this research first briefly introduces the accuracy evaluation method of BDS-3 SISRE and the satellite on-orbit adjustment and identification method, and focuses on the overall evaluation of the SISRE performance of BDS-3, statistically analyzes the outages and causes of the SIS of each satellite, especially the unplanned outage adjustments of BDS-3, which provides important support for the intelligent operation and maintenance of satellites of BDS-3 in the future.

2 Methodology 2.1 Signal in Space Range Error Performance Evaluation The performance of the SISRE is determined by the error of the satellite’s orbit and clock broadcast by the broadcast ephemeris. In order to calculate the satellite orbit and clock difference error, the broadcast ephemerides are usually compared with the precision ephemerides and clock, and the SISRE of the satellite is calculated [7]. For the orbital error assessment, the orbital coordinates calculated from the broadcast ephemeris and the precision ephemeris are differenced, and the errors are converted to radial (R), cross (C), and along (A) directions, and corrected by the phase center offset (PCO) of the antenna [12, 15]. To evaluate the clock error, the clock delay calculated from the broadcast ephemeris and precision ephemeris is differenced to obtain the first difference, and the secondary difference is obtained by subtracting the reference star primary difference reference. Additionally, the PCO and TGD parameter corrections are considered for the rigorous clock difference assessment [12, 15]. According to previous research on the correlation between orbit and clock and the calculation methods of SISRE of BeiDou’s heterogeneous constellations, for different constellations of BDS-3, the SISRE in this paper is calculated according to the following formula: ⎧  ⎨ SISREBDS(MEO) = (0.98R)2 + T 2 + 1 (A2 + C 2 ) 54  (1) ⎩ SISRE = (0.99R − T )2 + 1 (A2 + C 2 ) BDS(GEO,IGSO)

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When considering only the influence of satellite orbital error on the SISRE, the formula is converted as follows: ⎧  ⎨ SISREBDS_orb(MEO) = (0.98R)2 + 1 (A2 + C 2 ) 54  (2) ⎩ SISRE = (0.99R)2 + 1 (A2 + C 2 ) BDS_orb(GEO,IGSO)

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After obtaining the SISRE, it can be used to evaluate the performance and detect the outage of the SIS. For different signals of the BDS-3, the system designs different integrity parameters to predict the SISRE performance [20].

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2.2 Observation-Based Outage Detection of Satellite Signal in Space Due to the influence of certain lag in the precision orbit and clock products, the SISRE evaluation method provided in Sect. 2.1 is mainly used for post-event analysis, and cannot be used for real-time outage detection of satellite SIS. Because of the real-time feature of the observation data, User Equivalent Range Error (UERE) is available for real-time outage detection of satellite SIS, which is the combined effect of SISRE, ionosphere delay, troposphere delay, multipath effect, and observation noise, and is calculated as follows. After obtaining the pseudo-range observation value of the tracking stations with known precise coordinates at a certain moment, after correcting the errors including the ionosphere delay, troposphere delay, TGD, earth rotation, and relativity, the pseudorange observation value and calculation value between the satellite and the tracking station are calculated. Then, to obtain the residuals of the observation value, i.e., the observation value minus the calculation value (Observation Minus Calculation, OMC). Similarly, after obtaining the OMC of all satellites in the same epoch, the receiver clock error is deducted based on the center of gravity principle to obtain the UERE of each satellite. The formula is as follows:     (3) UERE = P − ρ + c · δtr − δt s − TGD + Iono + Trop + o In the formula, P is the pseudo-range observation value, ρ is the geometric distance between the satellite and the ground calculated by the broadcast ephemeris and the station position, c is the light speed, Iono is the ionospheric delay, Trop is the tropospheric delay, o is errors that are not modeled, including multipath, observation noise, etc., δt r is the receiver clock error, δt s is the satellite clock error, and TGD is the time group delay. When the SIS outages appear, it will directly cause the UERE of the user to be abnormal as well. When the UERE of the visible observation station of a certain satellite exceeds the threshold, it can be inferred that the satellite has SIS outages, and the time of the satellite SIS outages and the system response can be determined according to the overrun time of UERE. 2.3 Analysis Method of BeiDou Satellite On-Orbit Operation Status While obtaining the time of each satellite SIS outage, a specific analysis based on the satellite status reflected by the broadcast ephemeris orbit and clock error parameters is conducted, for mining the information of on-orbit status, including planned operations, unplanned outages, and others, of the satellite SIS outage time. Due to system design indicator constraints, the system needs to adjust the frequency and phase of the atomic clock carried by the satellite, leading to a direct UERE overrun caused a mismatch between the real observed values and the advance forecast satellite clock model, which is not difficult to detect in real-time outage monitoring and can be analyzed according to the changes of the health information and clock correction parameters. Meanwhile, because of the special orbital position requirements, the GEO and IGSO satellites gradually deviate from the design orbits under the influence of various perturbation forces after a long period of operation. Therefore, such satellites require

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periodic perform on-orbit maneuvering adjustments, and the SIS outages induced by such operations are also detected by real-time outage monitoring. Research has shown that the semi-major axis and eccentricity of the orbit change significantly after a satellite performs on-orbit maneuvering adjustments [21]. Hence, the orbital maneuver can be accurately judged by comparing the health information and ephemeris parameters before and after the maneuver. The above frequency and phase adjustments of satellite clocks and orbital maneuvers are part of the planned operations, which require advance notification to users as required and mandatory broadcast of unhealthy information for satellites during the operations. Although the planned operation will affect the availability index of single satellite, it will not affect the system integrity and continuity indicators.

3 Performance Evaluation and On-Orbit Operational Status Analysis of BDS-3 Satellites To study the SIS performance of BDS-3 and its on-orbit operation status, the historical data from July 31, 2020, to May 31, 2022, are collected, including observations and precise orbit/clock products from IGS (ftp://igs.gnsswhu.cn), the navigation ephemeris and the GNSS satellite health information file with a sample rate of 30 s to recording the health status of BDS-3 satellites from the International GNSS Monitoring & Assessment System(iGMAS). 3.1 BDS-3 Broadcast Orbit and Clock Error Evaluation The SISRE performance depends on the accuracy of the model generated by the ground operation and control center such as broadcast orbit and clock, which is a crucial index in the performance index system. In this section, the long-term orbit and clock accuracy of broadcast ephemeris are statistically analyzed according to the formulae in Chap. 2 by comparing with the precision orbit/clock products, and the results are shown in Fig. 1. For satellite orbit accuracy, the root mean square (RMS) error is calculated, where Along, Cross, and Radial denote the tangential, normal and radial accuracy of the broadcast ephemeris orbit respectively. As is shown in Fig. 1, the MEO satellite has the best orbital accuracy, with along, cross, and radial accuracies of 0.32 m, 0.29 m, and 0.08 m, followed by the IGSO (0.51 m, 0.45 m, and 0.1 6 m). The GEO, due to the relatively weak observation geometry, has the poorest orbital error, with along, cross, and radial accuracies of 3.55 m, 1.14 m, and 0.26 m. Overall speaking, the orbital accuracies of different satellites of the same type are consistent. The radial accuracy of all the satellites is significantly better than the along and cross directions, which benefits from that GNSS observations are mainly related to the geometric distance measurement of the satellite, which effectively constrains the radial direction in precise orbit determination, thus improving the radial accuracy of the orbit. For BDS-3 broadcast clock accuracy, the broadcast clock was compared with the precise clock products, and the standard deviation (STD) is used for the statistics. The STDs of MEO, IGSO, and GEO are 0.22, 0.30, and 0.26 m respectively, and the accuracy

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Fig. 1. Orbit and clock error distribution of BDS-3 satellites

of MEO is slightly better than that of IGSO and GEO. The Fig. 2 also shows that although some of the satellites are equipped with hydrogen clocks which are meant to have better performance than rubidium clocks, there is no significant difference between the two types of clocks in terms of the STD. Further analysis of the statistical results shows that the accuracy of the clock difference tends to be more stable for each of the BDS-3 satellites as the operating time increases (not shown in this paper due to limited space). 3.2 BDS-3 Signal in Space Range Error Evaluation On the basis of the broadcast orbit, clock difference error assessment, the SISRE, and SISRE orbit only (SISREorb) were statistically analyzed for the period 31 July 2020 to 31 May 2022, with RMS for all of the above indicators, and the results are shown in Fig. 2. Without considering the influence of satellite clock difference, the overall SISREorb of the MEO/IGSO/GEO satellites are relatively consistent and stable, about 0.10 m/0.18 m/0.47 m, respectively. After considering the influence of the clock, the consistency of the SISRE of each satellite decreases, and the overall SISRE is 0.25 m. IGSO is better than MEO and GEO in terms of the average of the three types of satellite SISRE accuracy (Fig. 3). We notice that the User Range Accuracy Index (URAI) is provided in the ephemerides broadcast by B1I and B3I, and the integrity alarm threshold is designed to be 4.17 times

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Fig. 2. The accuracy of the BDS-3 satellites SISRE

Fig. 3. Cumulative distribution of SISRE for each satellite of BDS-3

the URA value for system integrity evaluation [22, 23]. Through the statistics of URAI in the historical broadcast ephemeris, it is found that this value is fixed and advertised as 2 (4 m after conversion). Figure 4 provides the cumulative distribution function results of the spatial signal accuracy of each satellite, and the design value (4.17URA, i.e., 16.68 m) encapsulates 99.999% of the SISRE of each BDS-3 satellite. 3.3 Analysis of the On-Orbit Operational Status of the BDS-3 Satellites In this section, the SISRE exceeding the threshold specified by the system or at least three sites with UERE exceeding 8 m at the same time are the prerequisites for the SIS outage discrimination. Combined with the UEREs from the ground tracking stations, we integrate the health status information files of GNSS satellites from the iGMAS stations, the health information in the broadcast ephemeris to count the occurrence time of each satellite’s SIS

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outage and conduct a specific analysis of the satellite’s on-orbit operation status based on the independent monitoring methods. Statistics and analysis of the causes of satellite unhealthy times show that most of the periods when SIS outages occur are marked as unhealthy, mainly due to satellite clock frequency and phase adjustments by the planned operations. As the system marks satellites as unhealthy in advance, it does not affect the specific use of users, but some unplanned outage events deserve priority attention. In Table 1, the results of the analysis were classified by on-orbit adjustment type and satellite type, and the results are shown. Overall, the SIS outages of BDS-3 satellites are mainly the result of the adjustments of satellite clocks, orbits, and the combined effects of the two, including the phase and frequency adjustment of clock, and orbital maneuvering adjustments. Table 1. BDS-3 satellite on-orbit operational adjustment classification Type

GEO

IGSO

MEO

SUM

Clock frequency adjustment

3

1

43

47

Clock phase adjustment

7

1

10

18

Orbital maneuvering

Approximately every 28 days

Approximately every 28 days

1

–

Analysis Table 1 shows that most of the outages in the SIS of MEO are caused by planned adjustments related to satellite clocks. During the evaluation period, there were a total of 53 SIS outages related to satellite clocks, 43 times and 10 times of frequency and phase adjustment, respectively, and fewer times of atomic clock adjustments for IGSO and GEO satellites, which is also related to the fewer number of these two types of satellites. Meanwhile, in terms of the average annual adjustment times, IGSO satellites also have fewer planned adjustment times than MEO and GEO satellites. To explain the above phenomenon, the frequent adjustment of the atomic clock of the MEO satellite is initially analyzed to be related to the type of atomic clock on board. At present, MEO satellites have satellites carrying rubidium atomic clocks and hydrogen atomic clocks, and the frequency accuracy of hydrogen atomic clocks is better than that of rubidium atomic clocks, the frequency drift rate of atomic clocks is smaller, and the short-term stability is better than that of rubidium atomic clocks. Thus, the number of satellite clock adjustments decreased due to the hydrogen atomic clock carried by the IGSO satellite and GEO satellite. However, the IGSO and GEO satellites have more SIS outages related to satellite orbits, causing by planned orbital maneuver adjustment and able to be discerned by the health information and ephemeris parameters. Taking C38 and C59 satellites as an example, the semi-major axis and eccentricity of the orbit time series of the above two satellites, as shown in Fig. 4. When the satellite performs orbital maneuvers, the above parameters have high consistency and show a variety of significant jumps.

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Fig. 4. Time series of partial orbital parameters of IGSO/GEO satellites

As with the C38, there is a consistent change in the orbital parameters of the IGSO satellites when orbital maneuvers are performed. After combining the orbital maneuver time of the satellite, the planned orbital maneuvering times of the C38, C39, and C40 satellites are all 4 during the analysis period. Specifically, the average time of each satellite from the unhealthy information in ephemeris to the recovery of health is about 7h43min, 9h4min, and 8h38min, respectively, the average satellite unavailable time lasts about 8h30min. And the interval of orbital maneuver adjustment of C38, C39 and C40 satellites is 147.5, 145.9 and 160.8 days. Similarly, GEO planned orbital maneuvers were more frequent, with 22 orbit adjustments (approximately every 29.5 days) for C59 and 27 times for C60 (approximately every 25.1 days) during the analysis period. As far as the evaluation results are concerned, when the GEO satellite makes orbital maneuver adjustments, the average satellite unavailable time lasts about 5 h and 45 min. However, MEO satellites performed

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fewer orbital maneuver adjustments. Only C28 satellites performed one orbital maneuver from October 30 to 31, 2021, and the semi-axis and eccentricity of the orbit before and after adjustment underwent obvious jumps. Table 2. BDS-3 satellite on-orbit operational adjustment classification Time

GEO

IGSO

MEO

Sum

2020/07/31–12/31 (154 days)

11

3

9

23

2021/01/01–12/31 (365 days)

27

6

33

66

2022/01/01–05/31 (151 days)

11

3

14

28

Further, the annual planned adjustment of the operation of the BDS-3 satellites on orbit is counted according to the year. As shown in Table 2, in terms of the statistical values of each year, the annual average is flat overall, the number of planned adjustments of IGSO satellites are the least, and the MEO and GEO satellites are basically the same, which shows that the overall operation of the system tends to be stable. According to the previous analysis it is known that the GEO and IGSO satellites are mainly subject to periodic orbital maneuver adjustments, while MEO satellite on-orbit adjustments are mainly related to satellite clock operations. It is worth noting that the BDS official document states that planned operations on-orbit are required to provide advance notice to inform users when a satellite SIS is not expected to perform as it is specified [24]. Although the orbital maneuvers and satellite clock frequency and phase adjustments identified during analysis period were promptly annotated with unhealthy information before the actual operation, very little information about planned operations is available in advance from published sources (www.cnso-tarc.cn/support/announcement), and still requires continuous improvement. From the office document [24], it is clear that if planned operations are not notified to the user in advance, even if the unhealthy information is applied in advance, it can only be considered unplanned outages, which will affect the continuity, availability, and the integrity of BDS. 3.4 BDS-3 Satellite Signal in Space Unplanned Outages on Orbit When a satellite fails, it will have varying degrees of impact on user safety. Through analysis and evaluation, we find that the MEO satellite had two SIS unplanned outages of UERE overrun, but the satellite health information was not updated or lagged to update, which as follows: (1) the C21 satellite left China and perform satellite clock phase adjustment from March 25 to 26, 2022, resulting in UERE overrun, and the broadcast satellite health status lagged update;

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(2) On April 30, 2021, the C21 satellite made a satellite clock frequency adjustment, causing the user’s UERE to exceed the limit, but the broadcast satellite health status was not updated. The following is a specific analysis of the lagging health information update event of the C21 satellite: According to the analysis of UERE overruns, it was determined that the unplanned outage event occurred from 15 h 38 min on March 25, 2022, to 11hour39min on March 26, 2022, in BDS Time (BDT), but the satellite health information and satellite unhealthy information of the iGMAS tracking stations were found at 04 hour39min on the March 26, much later than the time when UERE anomalies. When the satellite was anomalous, the system did not respond the first time, and the unhealthy marker was injected about 13 h later.

Fig. 5. CLGY station UERE time series during the satellite unplanned outage (BDT)

Combined with the ground track of satellite, when the satellite unplanned outage appeared, it had just left China and could not be monitored by domestic observation stations. And the satellite was injected with unhealthy information when the satellite flew to the Mediterranean region. However, this entire unplanned outage period was observed by the CLGY station of iGMAS. Figure 5 shows the UERE time series of the CLGY station from March 25, 2022, to March 26, 2022, as shown, the station had a severe UERE overrun from 15 h 38 min on March 25 to 04 h 39 min on the March 26, and the UERE returned to normal after completing the clock phase adjustment and broadcasting the ephemeris at 11hour00min on the March 26 in BDT. To analyze the specific cause of the above unplanned outage, the satellite clock bias(a0) term time series of C21 during this unplanned outage period, is shown in Fig. 6. Green dots indicate that the satellite is healthy and available, while red squares indicate that the satellite is unhealthy and unavailable. It is further noted that the corresponding a0 is missing because of no ephemeris for 7–10 h broadcast. Figure 6 indicates that the system adjusted the phase of the satellite after detecting the satellite unplanned outage. When the operation finished, the a0 changed by about 906890.37ns. However, due to

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Fig. 6. Broadcast clock a0 time series during the satellite unplanned outage (BDT)

the limitations of ground monitoring stations outside the country, the satellite cannot be monitored in real-time, resulting in the occurrence of this unplanned outage event, which may have a huge impact on user safety. For the C21 satellite frequency adjustment without updating the health information on April 30, 2021, the reason is similar, because the satellite is above South America, it is impossible to monitor the satellite unplanned outage in time and update the ephemeris status. And the clock difference between the ephemeris before and after adjustment is about 62.52 ns, causing the UERE results of overseas observation stations to exceed the limit. Therefore, through the analysis of the above two C21 satellites SIS unplanned outage events caused by the clock, the combination of three types of data: global observation station UERE overrun, precise products difference analysis and iGMAS tracking station satellite health status information is reasonable and reliable for analyzing the unplanned outages of BDS-3, in view of the current problem of overseas satellite ground station limitation. Furthermore, the system should comprehensively use monitoring means such as the ISL and SAIM to strengthen the monitoring of satellite on-orbit operation outside the country to ensure the normal operation of the system in the future.

4 Conclusions Based on the independent monitoring results, SIS performance and on-orbit operational status of the BDS-3 satellites are evaluated in depth by analyzing the multi-source historical data of IGS and iGMAS from 2020 to 2022, covering the period of it’s opening to the present. Firstly, BDS-3 broadcast orbit, clock, and SISRE are evaluated. MEO satellites have the best orbital accuracy, with along, cross, and radial accuracies of 0.32 m, 0.29 m, and 0.08 m, followed by IGSO (0.51 m, 0.45 m, 0.16 m). GEO satellites have the largest orbit

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error due to relatively weak observation geometry conditions. The clock bias accuracy of the MEO/IGSO/GEO satellites is consistent as a whole, and the STD values of the MEO, IGSO, and GEO satellite clock biases are 0.22 m, 0.30 m, and 0.26 m, respectively. By comparing individuals within the MEO/IGSO/GEO satellite types, it can be seen that the difference of orbital accuracies of the same type of satellite is small. The radial accuracy of all satellites is significantly better than the along and cross directions, and the contribution of the radial accuracy to the SISRE is also the greatest. For the SISRE performance of different satellites, after considering the comprehensive influence of the orbital clock error, the overall SISRE of the BDS-3 satellite is 0.25 m, and the basic integrity parameters of the system design can cover 99.999% of the SISRE. Secondly, the UERE monitoring method combined with observation data, satellite health information and the precise products difference method can be used to systematically analyze satellite SIS outages. The results show that the SIS outages of current satellites in orbit is mainly caused by satellite clock frequency and phase adjustment and orbital maneuvering. Among them, MEO satellites mainly adjust satellite atomic clocks, while IGSO and GEO satellites perform planned maneuvering. The orbital maneuvering periods of IGSO/GEO are 28 days and 160 days, respectively. Thirdly, two unplanned outage events are found on individual satellites. After careful analysis in this paper, it is believed that the C21 satellite has one satellite clock unplanned outage event in 2021 and another in 2022, during which the health information of the satellite in the ephemeris is not updated or the update is delayed. The reason may be that the satellite is in a position outside the country that cannot be monitored in real time. To conclude, this article systematically analyzes the performance of BDS-3 SISRE, the main types of SIS outages caused by planned operations (satellite clock frequency and phase adjustment, orbital maneuvering).The above analysis results provide support for rapid identification and prediction of system faults, performance improvement of system integrity, and subsequent intelligent operation and maintenance.

References 1. CSNO (2021) BeiDou satellite navigation system rule of law report. Office C S N, Beijing 2. Yang Y, Liu L, Li J et al (2021) Featured services and performance of BDS-3. Sci Bull 66(20):2135–2143 3. Jiao W (2003) Researches on the realization of satellite navigation coordinate reference system. Graduate School of Chinese Academy of Sciences, Shanghai 4. USDOD (2020) Global positioning system standard positioning service performance standard, 5th edn 5. Heng L, Gao GX, Walter T, et al (2010) GPS signal-in-space anomalies in the last decade: data mining of 400,000,000 GPS navigation messages. In: Proceedings of the 23rd international technical meeting of the satellite division of the institute of navigation (ION GNSS 2010), Portland 6. Chen G, Hu Z, Wang G, et al (2015) Assessment of BDS signal-in-space accuracy and standard positioning performance during 2013 and 2014. In: Sun J, Liu J, Fan S, et al (2015) China satellite navigation conference (CSNC) 2015 proceedings: volume I. Springer, Berlin, Heidelberg, pp 437–53 7. Hu Z (2013) BeiDou navigation satellite system performance assessment theory and experimental verification. Wuhan University, Wuhan

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8. Hu Z, Chen G, Zhang Q, et al (2013) An initial evaluation about BDS navigation message accuracy. In: Sun J, Jiao W, Wu H, et al (eds) China satellite navigation conference (CSNC) 2013 proceedings. Springer, Berlin, Heidelberg, pp 479–91 9. Montenbruck O, Steigenberger P, Hauschild A (2015) Broadcast versus precise ephemerides: a multi-GNSS perspective. GPS Solut 19(2):321–333 10. Yang Y, Lu M, Han C (2016) Some notes on interoperability of GNSS. Acta Geodaetica et Cartographica Sinica 45(3):253–259 11. Li X, Zhu Y, Zheng K et al (2020) Precise orbit and clock products of Galileo, BDS and QZSS from MGEX since 2018: comparison and PPP validation. Remote Sens 12(9):1415 12. Lv Y, Geng T, Zhao Q et al (2020) Initial assessment of BDS-3 preliminary system signalin-space range error. GPS Solut 24(1):1–13 13. Yang Y, Mao Y, Sun B (2020) Basic performance and future developments of BeiDou global navigation satellite system. Satell Navig 1(1):1–8 14. Liu W, Hao J, Lv Z et al (2020) Evaluation and comparative analysis of BDS-3 signal-in-space range error. Acta Geodaetica et Cartographica Sinica 49(09):1213–1221 15. Chen G, Zhou R, Hu Z et al (2021) Statistical characterization of the signal-in-space errors of the BDS: a comparison between BDS-2 and BDS-3. GPS Solut 25(3):112 16. Zhang Y, Kubo N, Chen J et al (2020) Apparent clock and TGD biases between BDS-2 and BDS-3. GPS Solut 24(1):1–15 17. Song X, Geng C, Fang C, et al (2022) Performance analysis of BDS-3 satellite broadcast clock error. China Satellite Navigation Conference (CSNC), Beijing, China 18. Fan L, Zhang Q, Huang G et al (2017) On-orbit operation state analysis of beidou satellite based on the broadcast ephemeris. J Geod Geodyn 37(01):58–61 19. Wang S, Zhai Y, Zhan X (2021) Characterizing BDS signal-in-space performance from integrity perspective. Navigation 68(1):157–183 20. Xin J, Guo J, Tian Y et al (2021) Difference of the integrity parameters in the BDS-2 and the BDS-3. Sci Surv Mapp 46(05):14–19 21. Fan L (2018) Research on signal-in-space error anomaly detection and performance assessment of BDS satellites. Chang’an University, Xian’an 22. CSNO (2019) BeiDou navigation satellite system signal in space interface control document open service signal B1I (version 3.0). Office C S N. Beijing 23. Liu C, Cao Y, Zhang G et al (2021) Design and performance analysis of BDS-3 integrity concept. Remote Sens 13(15):2860 24. CSNO (2021) BeiDou navigation satellite system open service performance standard (version 3.0). Office C S N. Beijing

Epoch Completeness Rate Analysis of BDS-3 PPP-B2b Augmentation Messages Xinying Dong, Junbo Shi(B) , Chenhao Ouyang, Xinyue Li, and Wenjie Peng School of Geodesy and Geomatics, Wuhan University, Wuhan, China [email protected]

Abstract. As an important feature of BeiDou Navigation Satellite System (BDS), BeiDou augmentation services includes ground-based augmentation service, satellite-based augmentation service and Precise Point Positioning (PPP) service, which are crucial to the promotion of high-precision “BeiDou +” applications. BDS PPP service broadcasts augmentation messages via three BDS Geostationary Earth Orbit (GEO) satellites (C59, C60, C61). Previous studies have evaluated the performance of BDS PPP service, mainly analyzing the accuracy of the recovered PPP-B2b precise products and assessing the static and simulatekinematic positioning accuracy, but lack the epoch completeness rate analysis of raw augmentation messages. In this paper, we developed our own BDS-3 PPP-B2b augmentation message real-time acquisition and decoding software, which can automatically store, decode, and display augmentation messages in real time. Based on this software and a set of GNSS receiver and antenna, PPPB2b augmentation messages from August 28th to September 3rd, 2022, were analyzed. The results show that: (1) in terms of the satellite system, the average epoch completeness rates of both BDS-3 and GPS are higher than 98.55%, and BDS-3 is slightly better than GPS; (2) in terms of message types, the minimum epoch completeness rates are: 99.98% for type 1 satellite mask, 99.85% for type 4 clock correction, 98.91% for type 3 DCB correction, and 96.66% for type 2 orbit correction; (3) in terms of two GEO satellites, the average epoch completeness rates broadcasted from C59 (100.00%/99.51%/99.51%/99.95% for BDS-3, 100.00%/98.55%/99.90% for GPS) and C60 (99.98%/99.51%/99.50%/99.94% for BDS-3, 99.98%/98.55%/99.88% for GPS) are almost the same. Keywords: BDS-3 · Precise point positioning service · PPP-B2b · Augmentation messages · Epoch completeness rate

1 Instruction On December 27, 2019, the press conference for the first anniversary of BeiDou Satellite Navigation System 3 (BDS-3) providing global services was held. The China Satellite Navigation System Management Office released the B2b signal for Radio Navigation Satellite System (RNSS) service, as well as the PPP-B2b signal for Precise Point Positioning (PPP) service [1, 2]. On July 31, 2020, the BDS-3 was officially announced to the world. The BDS-3 global constellation consists of 24 Medium Earth Orbit (MEO) © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 253–262, 2024. https://doi.org/10.1007/978-981-99-6932-6_21

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satellites, 3 Inclined Geosynchronous Orbit (IGSO) satellites, and 3 Geostationary Orbit (GEO) satellites [3]. As one of the seven unique services provided by BDS-3, the BDS PPP service broadcasts state space augmentation messages through the PPP-B2b signal of three GEO satellites (C59, C60, C61), providing open and free high-precision positioning services [4]. The PPP-B2b signal is a high-precision augmentation signal released by BDS for the first time. Scholars have conducted relevant researches concerning the structure of the PPP-B2b signal and the augmentation messages. Based on the Interface Control Document (ICD), He et al. [5] introduced the structure, types, and decoding results of PPPB2b augmentation messages. Ren et al. [6] compared the PPP-B2b precise orbit/clock products with broadcast ephemeris and found that the PPP-B2b augmentation messages greatly improve the orbit and clock accuracy of broadcast ephemeris. Xu et al. [7] further studied the accuracy comparison between PPP-B2b and CNES real-time orbit/clock products. As for PPP-B2b positioning performance evaluation, Tao et al. [8] used observation data from six iGMAS stations located in China during August 2020 to verify that realtime PPP based on PPP-B2b augmentation messages could achieve centimeter-level static positioning accuracy after convergence. Huang et al. [9], Xiao et al. [10], and Liu et al. [11] have also verified that BDS PPP service can provide centimeter-level static and decimeter-level kinematic positioning accuracy in and around China. However, existing studies only focus on the accuracy analysis of the PPP-B2b precise orbit/clock/Differential Code Bias (DCB) products obtained after matching and recovery, as well as the evaluation of static and simulate-kinematic positioning performance, while lacking an epoch completeness rate analysis of the original PPP-B2b augmentation messages. Therefore, this paper implements a real-time acquisition and decoding software to analyze the epoch completeness rate of BDS-3 PPP-B2b augmentation messages. Based on the decoded messages, the epoch completeness rate of the augmentation messages for various satellite systems, the epoch completeness rate of various augmentation message types, and the epoch completeness rate of various GEO satellites are explored.

2 PPP-B2b Augmentation Message According to the PPP-B2b signal ICD (version 1.0) released in July 2020, the BDS PPPB2b augmentation signal is broadcast through three GEO satellites, and the transmission time length of each message frame is 1 s. The basic frame structure is shown in Fig. 1 [12]. When decoding the data stream, the starting position of the augmentation messages’ basic frame is identified by the preamble, and the PRN of the GEO satellite broadcasting the message, the type identifier of the augmentation message (1: satellite mask, 2: satellite orbit correction and user range accuracy index, 3: differential code bias, 4: satellite clock correction, 63: null message, etc.), the time corresponding to the corrections, etc. are decoded in sequence. Finally, the content of the message data field is decoded according to the specific message type.

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Fig. 1. Basic frame structure of BDS-3 PPP-B2b augmentation message [12]

Based on the above decoding process, this paper implements a BDS-3 PPP-B2b augmentation message real-time acquisition and decoding software with interface shown in Fig. 2. The software can automatically store the raw bits received from the serial port connected to the GNSS receiving chip, then decode and display augmentation messages including satellite masks, orbit corrections, DCB, and clock corrections in the real-time mode.

Fig. 2. BDS-3 PPP-B2b augmentation message real-time acquisition and decoding software

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3 Result and Analysis The PPP-B2b augmentation message collection experiment was conducted on the campus of Wuhan University, using a set of SinoGNSS K803 receiving chip and Huaxin GPS 1000 navigation antenna. The SinoGNSS K803 was used to receive both GNSS observation and PPP-B2b augmentation messages. The antenna was placed on the building roof of the School of Geodesy and Geomatics, and connected to the K803 board through a cable. The board was placed in-house and connected to the desktop via a serial port connecting cable. The software in Fig. 2 was operating on the desktop to continuously collect PPP-B2b augmentation messages. This paper analyzed the epoch completeness rate of PPP-B2b augmentation messages from August 28 to September 3, 2022 (day of year 240–246). Figures 3, 4 show the four types of augmentation messages (1: satellite mask, 2: orbit correction, 3: DCB correction, 4: clock correction) broadcasted by C59 and C60 during the experiment period for BDS-3 (C19-C46) and GPS (G01-G32) satellites, respectively. As of September 2022, PPP-B2b signal does not provide DCB correction for GPS satellites, so it is not included in Fig. 4. Since the generation of PPP-B2b augmentation messages mainly relies on the ground monitoring station network within China, the message coverage was limited and full arc tracking observations cannot be achieved for MEO satellites. In comparison, the effective observation timespan of IGSO satellites is longer than that of MEO satellites, so the continuity of IGSO satellites (red in Fig. 3) is significantly better than that of MEO satellites (yellow in Fig. 3). Decoding results of the PPP-B2b augmentation messages are analyzed, and the epoch completeness rate of each satellite is statistically calculated on the satellite arc basis. If next 10 epochs are empty for a certain epoch, a single arc ends at this epoch; then the epoch completeness rate of the satellite can be obtained by dividing the number of valid epochs in all arcs by the total epochs of all arcs observed.

Fig. 3. Augmentation messages for BDS-3 satellites (DOY 240 ~ 246, 2022)

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Fig. 4. Augmentation message for GPS satellites (DOY 240 ~ 246, 2022)

3.1 Satellite Mask The first decoded message type is the satellite mask, providing a flag to indicate which satellite correction is broadcasted. Figures 3(a), 4(a) respectively show the satellite mask for BDS-3 (C19 ~ C46) and GPS (G01 ~ G32) satellites during the experimental period. Table 1 provides the epoch completeness rates of each satellite in the received satellite mask messages from C59 and C60. During the experimental period, C59 and C60 respectively broadcasted 12,600 and 12,597 satellite mask messages including valid broadcast identifiers for 24 BDS-3 MEO satellites (C19 ~ C30, C32 ~ C37, C41 ~ C46), 3 BDS-3 IGSO satellites (C38 ~ C40), and 32 GPS MEO satellites (G01 ~ G32). Table 1. Epoch completeness rate of satellite mask indicator for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022) GEO satellite PRN

C59

C60

BDS-3 MEO

12,600

12,597

BDS-3 IGSO

12,600

12,597

GPS MEO

12,600

12,597

Theoretical total number of epochs

12,600

12,600

Epoch completeness rate

100.00%

99.98%

Actual valid number of epochs

3.2 Orbit Correction The second decoded message type is the orbit correction, which provides information on satellite orbit radius/tangential/normal correction and user range accuracy index. Each message broadcasts corrections for six satellites. Figures 3(b), 4(b) respectively show the orbit correction for BDS-3 (C19 ~ C46) and GPS (G01 ~ G32) satellites during the experimental period. Figure 5 and Table 2 present the epoch completeness rates of each satellite in the received orbit correction messages from C59 and C60. For BDS-3 MEO satellites, except

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for C21 which did not receive any augmentation message during the experimental period, the average number of valid epochs was 4,080.13 and 4,079.70 with corresponding epoch completeness rates of 99.47% and 99.47% for C59 and C60, respectively. For BDS-3 IGSO satellites, the average number of valid epochs was 9,633.33 and 9,632.67, with corresponding epoch completeness rates of 99.80% and 99.80% for C59 and C60, respectively. For GPS MEO satellites, except for G17 and G28 which did not receive any augmentation message during the experimental period, the average number of valid epochs for other satellites was 3,872.27 and 3,872.07, with corresponding epoch completeness rates of 98.55% and 98.55% for C59 and C60, respectively. Table 2. Epoch completeness rate of orbit corrections for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022) GEO satellite PRN Average epoch completeness rate

C59 (%)

C60 (%)

BDS-3 MEO

99.47

99.47

BDS-3 IGSO

99.80

99.80

GPS MEO

98.55

98.55

Fig. 5. Epoch completeness rate of orbit corrections for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022)

3.3 DCB Correction The third decoded message type includes inter-signal bias correction information between different signal branches of each satellite. The number of satellites and tracking modes broadcasted in each message is not fixed. Figure 3(c) shows the DCB of BDS-3 satellites (C19 ~ C46) during the experiment. Figure 6 and Table 3 provide the epoch completeness rate of each satellite in the received DCB correction messages from C59 and C60. For BDS-3 MEO satellites, except for C21, which did not receive any augmentation message during the experiment, the average number of valid epochs for other satellites was 4,080.26 and 4,079.39 with corresponding epoch completeness rates of 99.47% and 99.46% for C59 and C60, respectively. For BDS-3 IGSO satellites, the average number of valid epochs was 9,634.00 and

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9,633.33 with corresponding epoch completeness rates of 99.81% and 99.81% for C59 and C60, respectively (Table 3). Table 3. Epoch completeness rate of DCB corrections for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022) GEO satellite PRN Average epoch completeness rate

C59

C60

BDS-3 MEO

99.47%

99.46%

BDS-3 IGSO

99.81%

99.81%

GPS MEO

–

–

Fig. 6. Epoch completeness rate of DCB corrections for BDS-3 satellites (DOY 240 ~ 246, 2022)

3.4 Clock Correction The fourth decoded message type contains the clock correction for each satellite, and each message broadcasts the corrections for 23 satellites. Figures 3(d), 4(c) respectively show the clock correction for BDS-3 satellites (C19-C46) and GPS satellites (G01-G32) during the experiment. Figure 7 and Table 4 show the epoch completeness rates of clock correction received from C59 and C60 for each satellite. For BDS-3 MEO satellites, except for C21, which did not receive any augmentation messages throughout the experiment, the average number of effective epochs for other satellites were 32,406.30 and 32,399.87, and the corresponding epoch completeness rates were 99.95% and 99.93% for C59 and C60, respectively. For BDS-3 IGSO satellites, the average number of effective epochs were 76,618.33 and 76,604.33, and the corresponding epoch completeness rates were 99.98% and 99.96% for C59 and C60, respectively. For GPS MEO satellites, except for G17 and G28, which did not receive any augmentation messages throughout the experiment, the average number of effective epochs for other satellites were 30,718.40 and 30,714.03, and the corresponding epoch completeness rates were 99.90% and 99.88% for C59 and C60, respectively. Table 5 and Fig. 8 summarize the epoch completeness rates for four augmentation message types received from C59 and C60. It can be observed that:

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Table 4. Epoch completeness rate of clock corrections for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022) GEO satellite PRN Average epoch completeness rate

C59 (%)

C60 (%)

BDS-3 MEO

99.95

99.93

BDS-3 IGSO

99.98

99.96

GPS MEO

99.90

99.88

Fig. 7. Epoch completeness rate of clock corrections for BDS-3 and GPS satellites (DOY 240 ~ 246, 2022)

(1) The average epoch completeness rate of PPP-B2b augmentation messages is higher than 98.55%, and BDS-3 slightly performs better than GPS. The epoch completeness rate for all BDS-3 satellites (C19 ~ C20, C22 ~ C30, C32 ~ C46) is above 98.91%, and the epoch completeness rate for all GPS satellites (G01 ~ G16, G18 ~ G27, G29 ~ G32) is above 96.66%. (2) Among the four message types, the minimum epoch completeness rates for C59 and C60 is highest for satellite mask (99.98%), followed by clock correction (99.85%), DCB correction (98.91%), and orbit correction (96.66%). (3) The epoch completeness rates for C59 and C60 is almost the same. For C59, the average epoch completeness rates of four augmentation message types are 100.00%/99.51%/99.51%/99.95% for BDS-3 and 100.00%/98.55%/99.90% for GPS. For C60, the average epoch completeness rates are 99.98%/99.51%/99.50%/99.94% for BDS-3 and 99.98%/98.55%/99.88% for GPS.

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Table 5. Summary of epoch completeness rates for four augmentation message types GEO C59

Satellite system

1

2

3

4

Average

100.00%

99.51%

99.51%

99.95%

Minimum

100.00%

98.91%

98.91%

99.85%

Average

100.00%

98.55%

–

99.90%

Minimum

100.00%

96.66%

–

99.50%

BDS-3

Average

99.98%

99.51%

99.50%

99.94%

Minimum

99.98%

98.91%

98.91%

99.85%

GPS

Average

99.98%

98.55%

–

99.88%

Minimum

99.98%

96.66%

–

99.50%

BDS-3 GPS

C60

MsgType

Fig. 8. Epoch completeness rate comparison of four message types

4 Conclusion This paper developed a BDS-3 PPP-B2b augmentation message real-time acquisition and decoding software, and decoded seven days of PPP-B2b augmentation messages. The decoded four message types were analyzed for epoch completeness rate. The conclusions are as follows: (1) the average epoch completeness rate of PPP-B2b augmentation messages is higher than 98.55%, and BDS-3 is slightly better than GPS. (2) the minimum epoch completeness rate for the four message types is highest for satellite mask (99.98%), followed by clock correction (99.85%), DCB correction (98.91%), and orbit correction (96.66%). (3) the average epoch completeness rates of messages broadcasted by C59 (100.00%/99.51%/99.51%/99.95% for BDS-3, 100.00%/98.55%/99.90% for GPS) and C60 (99.98%/99.51%/99.50%/99.94% for BDS-3, 99.98%/98.55%/99.88% for GPS) are almost the same.

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Our BDS-3 PPP-B2b augmentation message real-time acquisition and decoding software has been operating since August 2022, and so far collected for more than eight months, which can be used for further studies. Acknowledgements. The study is funded by National Natural Science Foundation of China (No.42274050 and No.42204044), Fund of National Dam Safety Research Center (No.CX2020B04), and Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University (No.20–02-04).

References 1. China Satellite Navigation Office (2019) BeiDou navigation satellite system signal in space interface control document precise point positioning service signal PPP-B2b (beta version) [EB/OL]. http://www.beidou.gov.cn 2. China Satellite Navigation Office (2019) BeiDou navigation satellite system signal in space interface control document open service signal B2b (beta version) [EB/OL]. http://www.bei dou.gov.cn 3. Yang Y, Gao W, Guo S et al (2019) Introduction to BeiDou-3 navigation satellite system. Navigation 66(1):7–18 4. Yang Y, Ding Q, Gao W et al (2022) Principle and performance of BDSBAS and PPP-B2b of BDS-3. Satell Navig 3(1):5 5. He X, Liu C, Chen Y, et al (2020) Analysis of B2b signal of BDS III satellite. Appl Electron Tech 46(03):14+13 (in Chinese). https://doi.org/10.16157/j.issn.0258-7998.209006 6. Ren Z, Gong H, Peng J et al (2021) Performance assessment of real-time precise point positioning using BDS PPP-B2b service signal. Adv Space Res 68(8):3242–3254 7. Xu Y, Yang Y, Li J (2021) Performance evaluation of BDS-3 PPP-B2b precise point positioning service. GPS Solut 25(4):142 8. Tao J, Liu J, Hu Z et al (2021) Initial assessment of the BDS-3 PPP-B2b RTS compared with the CNES RTS. GPS Solut 25(4):131 9. Huang L, Meng X (2021) Accuracy analysis of precise point positioning using BDS 3 PPP-B2b signals. J Geod Geodyn 41(5):4 (in Chinese). https://doi.org/10.14075/j.jgg.2021.05.014 10. Xiao H, Wang J, Guo H, et al (2022) Real-time precise point positioning precision analysis based on PPP-B2b service. Bull Surv Mapp (04):117–121 (in Chinese). https://doi.org/10. 13474/j.cnki.11-2246.2022.0121 11. Liu Y, Yang C, Zhang M (2022) Comprehensive analyses of PPP-B2b performance in China and surrounding areas. Remote Sens 14(3):643 12. China Satellite Navigation Office (2020) BeiDou navigation satellite system signal in space interface control document precise point positioning service signal PPP-B2b (version 1.0) [EB/OL]. http://www.beidou.gov.cn

GNSS Global PPP System Technology: Bottleneck and Development Direction Yansong Meng1(B) , Jun Xie2 , Xing Li3 , Tao Yan1 , Ye Tian1 , Yun Zhou1 , Quan Zhou1 , Lang Bian1 , and Weiwei Wang1 1 China Academy of Space Technology (Xi’an), Xi’an, China

[email protected]

2 China Academy of Space Technology, Beijing, China 3 Beijing Institute of Tracking and Telecommunication Technology, Beijing, China

Abstract. The basic navigation and positioning service and precise single-point positioning service of contemporary global navigation satellite systems (GNSS) and its augmented systems mainly serve people and machines that are supervised or operated by people. Its system architecture and signal framework have undergone nearly 40 years of application and performance continuous improvement, and have encountered the bottleneck of the contradiction between accuracy and real-time performance that cannot be reconciled. It is urgent to research at the level of system architecture and signal framework to seek breakthroughs, and solve the contradiction between dm/cm-level positioning accuracy and second-level realtime performance from the system design source so that GNSS can step into the next generation, serve the machine independently, and provide real-time and accurate space-time information support for the intelligent era and society of “No Man, intelligence and IoT”. The paper first summarizes that the contemporary GNSS system adopts “sub-meter-level broadcast ephemeris + m/cm-level code pseudorange measurement signal” to realize instantaneous meter-level positioning, and further adopts “cm-level precision ephemeris enhancement + cm/mm-level carrier pseudorange measurement signal”. After 10 to 40 min of initialization and convergence, cm-level positioning is realized. Secondly, the current status of the space-time reference establishment, maintenance and synchronization system architecture, the current status of civil space signal framework, and the current status of civilian message structure are analyzed one by one, and the bottleneck of the contradiction between accuracy and real-time is summarized and analyzed. Then, it is proposed to use a new generation of code-based precision point positioning system (NextGen-Code-PPP) to realize instantaneous dm-level positioning, which is “cm-level broadcast ephemeris + cm-level code pseudorange measurement signal”, and further use “cm/mm-level carrier pseudorange measurement” to realize instantaneous cm-level positioning system-level solutions. Finally, the space-time reference system architecture and signal frame sources, such as the space “net” ground “net” space-time reference, unambiguous instantaneous cmscale space meta signals, high-power fast message signals of UHF/VHF and other new frequency bands are analyzed, and a feasible conclusion is given.

Yansong Meng and Jun Xie: These authos are co-first authors © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 263–279, 2024. https://doi.org/10.1007/978-981-99-6932-6_22

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Y. Meng et al. Keywords: Dm/cm-level positioning · Second-level real-time · Cm-level broadcast ephemeris · Cm-level code pseudorange measurement signals · Space “net” ground “net” · Space-time reference · Unambiguous instantaneous cm-level space meta-signal · Fast message structure

1 Introduction Since the full operation of the global positioning system (GPS) in 1995, after 27 years of development, in the open sky application scenario, the instantaneous positioning accuracy of radio determination satellite service (RNSS) basic navigation has been improved from tens of meters to the meter-level, and it has been widely used in various industries. Currently, there are four global satellite navigation systems (GNSS) in the world: GPS of the United States, GLONASS of Russia, Beidou of China, and Galileo of Europe, and two regional satellite navigation systems of Japan QZSS and India NavIC. The systems follow the principle of compatibility and interoperability, collectively referred to as GNSS. These systems all provide RNSS standard single-point positioning services based on pseudocode code measurement. By improving the accuracy of broadcasting ephemeris space signals to the dm/sub-meter-level and broadcasting dual-/multi-frequency signals, the standard positioning accuracy is improved to the meter level. Limited by the pseudocode rate and landing power of first civilian signals (GPS L1C/A, GLONASS G1, Beidou B1C, Galileo E1C, etc.), the accuracy of pseudo-code ranging has become a bottleneck factor for the improvement of basic navigation and positioning accuracy. Among these systems, China Beidou, European Galileo, and Japan’s QZSS also provide precise point positioning (PPP) services based on carrier phase. By broadcasting precise ephemeris, the space signal accuracy is improved to the dm/cm level, but it takes 10 ~ 40 min to initialize the convergence time. At the same time, the current satellite-based PPP/PPPAR and PPP-RTK services broadcast information at a rate of 500bps ~ 2kpbs, and the landing power is equivalent to basic navigation signals such as L1C/A, so the robustness of precision ephemeris reception is a big challenge. High-precision positioning is the basic requirement for autonomous driving. To keep the vehicle in the lane at all times, the positioning accuracy of highway application scenarios requires 20cm (95%), and local street application scenarios require a positioning accuracy of 10cm (95%) [1, 2], to ensure a good user experience, it is required that dm/cm-level positioning be realized instantaneously, that is, to achieve second-level real-time performance. At present, the precise point positioning system based on carrier phase observations takes a long time to converge, and the low-earth-orbit (LEO) satellite signal enhancement technology system is expected to achieve a convergence time of minutes. Further use of PPP-RTK, RTK and other information enhancement technology systems in regional and local areas can further shorten the convergence time and even reaches the second level. But it is difficult to achieve dm/cm-level positioning with second-level convergence globally [1]. While the standard single-point positioning system based on pseudocode can achieve instantaneous positioning, the positioning accuracy currently cannot reach the dm/cm level. Carrier-based fast dm/cm-level positioning is a current research hotspot, and research on instantaneous dm/cm-level positioning based on pseudocode has not

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yet started. The service capabilities defined by the current generation of GNSS are most widely used for people and machines that are supervised or operated by people. Its system architecture and signal system have undergone 40 years of application and continuous development and improvement, and have encountered a contradiction between accuracy and real-time performance that is difficult to reconcile. It is urgent to research the system architecture and signal framework to seek a breakthrough and completely solve the contradiction between dm/cm-level positioning accuracy and second-level real-time performance from the design source so that GNSS can step into the next generation, fully serve the machine independently, and provide real-time and accurate space-time information support for the intelligent society in the unmanned and intelligent era. In this paper, we first analyze the current technical status and bottlenecks of the contemporary GNSS global precision point positioning service from the system design source and put forward the relevant bottlenecks. Then, we analyze the next-generation GNSS to solve these bottlenecks from the design source. Finally, a preliminary and feasible conclusion is given.

2 Current Technology Status and Bottlenecks of GNSS Global PPP Positioning Systems The positioning accuracy of dual-frequency standard single-point positioning service based on code pseudorange is mainly composed of SISRE and UEE, as shown in Table 1, where SISRE is mainly determined by the precision of satellite orbit and satellite clock in the broadcast ephemeris, and further by the performance and implementation level of maintaining and synchronizing system architecture based on space-time reference. And UEE is mainly determined by satellite signal and receiver parameters, and satellite signal design plays a fundamental and decisive role. Table 1. Core indicator realization of the main GNSS open sky standard single-point positioning service [3, 4] Dual frequency

SISRE(m,RMS)

UEE(m,RMS)

UERE(m,RMS)

GPS

L1/L2P(Y)

0.6

0.7

0.9

BDS-3

B1C/B2a

0.4

0.5

0.6

Galileo

E1/E5a

0.2

0.5

0.5

As shown in Fig. 1, the current GNSS system is based on meter-level, sub-meterlevel, dm-level (typically sub-meter-level) broadcast ephemeris, and meter-level/dmlevel unambiguous dual-frequency code pseudorange measurement signals, to achieve the instantaneous positioning accuracy of the global open sky application scene. Mainly rely on the space-time reference maintenance and refinement system architecture of the space “satellite” ground “net” to achieve typical sub-meter broadcast ephemeris accuracy. And rely on the traditional “single” signal (single carrier single modulation

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Service Type

Service Realization Technology System

Service performance

Broadcast ephemeris - sub-meter precision Basic navigation, positioning service Contemporary GNSS

Precise positioning is basic Navigation positioning is fundamental

Precise point positioning service

Space signal - m/dm level dualfrequency code pseudorange without ambiguity

Instantaneous meter level positioning

Space signal - cm/mm-Level dual-frequency Carrier pseudorange with ambiguity

Space “satellite” ground “net” space-time reference maintenance and refinement

Traditional “single” signal

Code-SPP

Precision ephemeris - cm-level precision

System architecture and signal framework

10-40 min convergence, dm/cm level positioning

Ground-based measurement + Signal enhancement Traditional “single” signal

Carrier-SPP

Fig. 1. Current status of contemporary GNSS positioning service technology

signal, no more than 2 signal components) to achieve m/dm-level unambiguous dualfrequency code pseudo-range measurement. The precise point positioning service is based on the basic navigation and positioning service, through the enhancement method, adding broadcast precise ephemeris information to the broadcast ephemeris, and finally, the cm-level SISRE accuracy is achieved, and the cm/mm level carrier pseudorange measurement with ambiguity is used to make up for the accuracy lack of UEE. However, since the code pseudorange accuracy initially designed by GNSS is at the m/dm level, it cannot support instantaneous carrier ambiguity resolution. Only by changing time to precision, after 10 ~ 40 min of initial convergence processing to achieve ambiguity resolution and the final cm-level positioning. The bottlenecks caused by the design source of the contemporary GNSS global precision point positioning system are: 1. Due to the limitation of the space-time reference maintenance and refinement system architecture of the space “satellite” ground “net”, the broadcast ephemeris accuracy is sub-meter and dm-level, which cannot support cm-level broadcast ephemeris (typical 50bps information rate). 2. Limited by the signal landing power (~−130dBm) of the initial design of contemporary GNSS and the pseudo-code rate (~1MHz) of the first civilian signal of dualfrequency combination, the pseudo-range accuracy of the code is at the m/dm-level, and the instantaneous carrier phase ambiguity resolution can not be supported. 3. The broadcast rate of basic navigation messages is ~50bps, and the ephemeris collection time is tens of seconds, which cannot support the realization of second-level first positioning time. 2.1 Current Status of GNSS Space-Time Reference Establishment, Maintenance and Synchronization System Architecture The establishment, maintenance and synchronization of contemporary GNSS space-time references all adopt the space “satellite” ground “net” architecture, as shown in Fig. 2. The ground segment establishes and maintains the space-time coordinate system, mainly through satellite-ground one-way measurement to determine the orbit, clock error and the parameters of the signal bias model, which are transmitted to each satellite in the space

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segment at a certain frequency (ranging from 1 time/15 min to 1 time/day). The satellites adopt a medium-high orbit design, a low light pressure design, a stable attitude control design, an atomic clock and other measures, and have certain orbit-keeping and timekeeping capabilities, such as SISRE 0.5m(RMS)@1 h. And satellites transmit space-time reference information to users by broadcasting navigation signals and messages. The space “satellite” ground “net” architecture regards each satellite in the space segment as an independent individual. The satellite and ground adopt a one-way measurement system, and the orbit and clock error are coupled together. The measurement topology is limited by the ground station layout, and the measurement accuracy is affected by the environment segment, so the accuracy of SISRE has basically reached the ceiling. Beidou-3 took the lead in adopting high-precision measurement inter-satellite links. As an extension of the satellite-ground link, the inter-satellite link has taken the first step to breaking the ceiling.

Space "satellite"

Satellite by satellite upload (once every 1 minute to 1 day) Satellite by satellite upload (once every 1 minute to 1 day)

Environment segment

Ground "net"

Control staon

Monitoring Staon

Upload staon

Fig. 2. Contemporary GNSS space “satellite” ground “net” space-time reference system architecture

2.2 Current Status of GNSS Civil Space Signal System The space signal system and minimum landing power of the four major contemporary satellite navigation systems are shown in Table 2, including GPS L1C/L1C/A/L2/L5 signals [5–7], BDS B1I/B1C/B2a/B2b/ B2/B3I signals [8–12], E1B-C/E6B-C/E5a/E5b signals of Galileo [13], and L1OF/L2OF signals of GLONASS [14], where the B2 signal

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of BDS can adopt constant envelope modulation technology, which is ACE-BOC(15,10) [15]. And the E5 signal of Galileo can adopt constant envelope modulation technology, which is AltBOC(15,10). In a typical scenario, the noise spectral density N 0 = −204 dBW/Hz, the typical code tracking accuracy under the open sky can be obtained, as shown in Table 2, it can be seen that the civilian signal L1C/A/L2C/B1I/L1OF/L2OF accuracy is at the meter-level, and the accuracy of civil signal L1C/L5/B1C/B3I/B2a/B2b is at decimeter-level. Since the above-mentioned signal is characterized by single-frequency and single-modulation, it can be called a traditional “single” signal when the signal component is less than 2. B2/E5 signal is essentially a dual-frequency, four-component, constant-envelope composite signal, and it is a new type of ultra-wideband pseudo code measurement signal, code tracking accuracy can reach centimeter level. The L1 frequency first civil signal is used in dual-frequency standard single-point positioning, and its landing power and pseudo-code rate are derived from the original design of GPS, which restrict the further improvement of pseudo-range precision of dual-frequency code. 2.3 Current Status of GNSS Civil Message Structure There are three main types of contemporary GNSS civilian message structure, the first type is the basic navigation message, the second type is the SBAS message, and the third type is the PPP message. Basic navigation messages include broadcast messages broadcast by GPS (L1C/A LNAV, GPS L1C CNAV2, GPS L2C/L5C CNAV) [5–7], BDS (B1I/B3I D1, BDS B1C B-CNAV1, BDS B2a B-CNAV2) [8–11], Galileo (E5a F/NAV, E5a F/NAV) [13] and GLONASS (L1OF/ L2OF) [14], and it can be seen that the information rate is between 25 and 125bps; SBAS Messages are broadcast on GEO satellites with an information rate of 250bps [17, 18]; PPP messages are mainly provided by QZSS L6 signals [19], BDS PPP-B2b [20] and Galileo E6-B [21], with an information rate of 500–2000 bps. The impact of the message frame structure on the first positioning time is mainly reflected in the acquisition time of important positioning information such as CED + GST (ephemeris, satellite clock parameters and system time). Through analysis and comparison, the data rate is normalized to 50bps to compare CED + GST. It can be seen that the data collection time is tens of seconds, and it is impossible to achieve the second-level first positioning time only by relying on GNSS to obtain the message (Fig. 3).

3 Future Development Direction of Next-Generation GNSS Global PPP System Technology As shown in Fig. 4, according to the current status and bottlenecks of GNSS global PPP system technology, the next generation of GNSS urgently needs to research system architecture and signal framework to seek breakthroughs and solve the contradiction between dm/cm-level positioning accuracy and second-level real-time performance from the system design source. The main technical development directions are as follows:

GLONASS

Galileo

BDS

0.511

10.23

1246 + n × BPSK 0.4375

AltBOC(15,10)

10.23

10.23

L2OF

1191.795

E5

QPSK(10)

QPSK(10)

0.511

1207.14

E5b

5.115

1.023

10.23

10.23

10.23

10.23

1602 + n × BPSK 0.5625

1176.45

E5a

QPSK(5)

CBOC(6,1,1/11)

QPSK(10)

BPSK(10)

1.023

2.406

L1OF

1278.75

E6B + C

ACE-BOC(15,10)

1191.795

1575.42

1207.14

B2b

B2

1176.45

B2a

E1B + C

QPSK(10)

1268.52

B3I

QMBOC(6,1/1/11)

1575.42

B1C

BPSK(2)

1561.098

10.23

1176.45

L5

B1I

QPSK(10)

1.023 1.023

BPSK(1)

1.023

TDDM + BPSK(1)

TMBOC(6,1,1/11)

Code rate (Mcps)

1227.6

1575.42

Modulation mode

L2C

L1C

GPS

Center frequency (MHz)

L1C/A

Signal

System

7.3125

7.3125

51.15

20.46

20.46

40.92

24.552

51.15

20.46

20.46

20.46

32.736

24

30.69

30.69

Bandwidth (MHz)

41 48 47 50.5

−163 −156 −157 −153.5

48.75 51.75

−155.25 −152.25

−161

43

43

48.75

−155.25

−161

48.75

−155.25

46.75

45

−159

−157.25

50 41

−154 −163

5.8648

5.8648

0.0184

0.1148

0.1148

0.3225

0.1800

0.0185

0.1413

0.1254

0.2965

0.2054

2.0384

0.0991

2.2114

2.2114

45.5

−158.5 45.5

0.1650

47

−157 −158.5

Code tracking accuracy(2σ) (m)

Minimum Carrier-to-noise receiving power ratio (dB-Hz) (dBW)

Table 2. Four major GNSS civilian signal systems and receiving power

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Y. Meng et al. Normalized time to get CED+GST(50bps) 80 79s 70 I/NAV 60

T 95%

50

CED +GST

40 35.5s 30

NAV

29.6s 20

F/NAV

10

CED +GST

31.9s CNAV

31.9s CNAV

18.02s

0

CNAV2

Galileo E1-B Galileo E5-a GPS L1C

CED +GST GPS L1C/A

CED +GST GPS L2C

CED +GST GPS L5

Fig. 3 CED + GST acquisition time in GNSS main signal message (50bps information rate)

1. Develop the space “net” ground “net” space-time reference system technology, adopt inter-satellite laser measurement network, realize real-time ten-picosecondlevel time-physics synchronization accuracy in the constellation, and realize cmlevel orbit accuracy, and then achieve cm-level dual-frequency SISRE accuracy of broadcast ephemeris. 2. Develop unambiguous instantaneous cm-level space meta-signal technology, so that the UEE accuracy based on dual-frequency code pseudo-range measurement signals can reach cm-level, and realize instantaneous dm/cm-level standard singlepoint positioning based on dual-frequency code pseudo-range, and further realize the instantaneous resolution of carrier phase ambiguity. 3. Develop new frequency bands such as the UHF/VHF frequency band with high landing power and fast message signal technology to achieve fast ephemeris broadcasting within seconds, support the instantaneous resolution of carrier ambiguity, support the first positioning time at the second level, and improve the message demodulation robustness by multi-frame coherent accumulation.

3.1 Instantaneous Dm-Level Standard Point Positioning Based on Code Pseudorange Using the standard point positioning system based on pseudo-code to achieve open sky instantaneous dm-level positioning, it is necessary to improve the accuracy of SISRE and UEE to the cm-level, as shown in Table 3. Under the framework of a 50bps basic navigation message, the SISRE improvement is to improve the precision of the satellite orbit and clock to the cm-level, while the UEE improvement is to improve the measurement accuracy of pseudo-code in both frequency bands to the cm-level. At present, the basic navigation message, PPP message and satellite orbit accuracy are shown in Table 4. This shows that the orbit accuracy of the BDS-3 basic navigation

GNSS Global PPP System Technology: Bottleneck System

Service Implementation Technology System

Service Type

Service performance

Broadcast ephemeris - sub-meter precision Basic navigation, positioning service

Space signal - m/dm level dualfrequency code pseudorange without ambiguity

Precise positioning is basic Navigation positioning is fundamental

Contemporary GNSS

System architecture and signal framework Space “satellite” ground “net” space-time reference maintenance and refinement

Traditional “single” signal

Code-SPP Precision ephemeris - cm-level precision

Precise point positioning service

Instantaneous meter level positioning

271

Space signal - cm/mm-Level dual-frequency Carrier pseudorange with ambiguity

10-40 min convergence, dm/cm level positioning

Ground-based measurement + Signal enhancement

Carrier-SPP

Broadcast ephemeris - cm-level precision

Basic navigation, positioning service

Independent

Space signal - m/dm level dualfrequency code pseudorange without ambiguity

Next generation GNSS

Instantaneous meter level positioning

Code-SPP Broadcast ephemeris - cm-level precision

Next Generation precise point positioning service

Instantaneous dmlevel positioning

Space signal - cm level dualfrequency code pseudorange without ambiguity Space signal - cm/mm level dual-frequency code pseudorange with ambiguity

Traditional “single” signal

Space “net” ground “net” space-time reference maintenance and refinement

New “element” signal Instantaneous cmlevel positioning

UHF and other new frequency high-power fast message signal

NextGen-Code-PPP

Fig. 4. Current status of GNSS positioning service technology and the development direction of the next generation

Table 3. Index allocation of instantaneous dm-level standard single-point positioning based on code pseudorange Project

SISRE (cm, 95%)

UEE (cm, 95%)

UERE (cm, 95%)

Horizontal positioning accuracy * (cm, 95%)

Vertical positioning accuracy * (cm, 95%)

Index

6

8

10

13

23

* In calculation, HDOP is set to 1.3, and VDOP is set to 2.3[3]

message has reached the sub-decimeter level, and there is room for further excavation and upgrading. In the future, the second-generation Galileo and GPS IIIF will also add high-precision inter-satellite links, it can be predicted that the precision of GNSS basic navigation messages in the future will reach the cm-level. At present, the accuracy of basic navigation message, PPP message and satellite clock error is shown in Table 5, which shows that the accuracy of basic navigation message clock error is at the dm level, which is the main bottleneck for further improvement of accuracy, in the future, it is necessary to adopt the system innovation design to improve

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Y. Meng et al. Table 4. Satellite orbit accuracy of the main GNSS and its augmentation systems

GNSS system and message type

Basic navigation message [3, 22, 23]

PPP message [24–33]

GPS

Orbit precision: 21cm(RMS) Broadcasting frequency: 2 h

/

BDS-3

Orbit precision: 8cm(RMS) Broadcasting frequency: 1 h

Orbit precision: 5.5cm(RMS) Broadcasting frequency: 48s PPP-B2b

Galileo

Orbit precision: 12cm(RMS) Broadcasting frequency: 10 min

Orbit precision: 3.4cm(RMS) Broadcasting frequency: 50s Galileo HAS

QZSS

/

Orbit precision: 3.8cm(RMS) MADOCA L6E PPP

Fugro G4

/

Orbit precision: 3-4cm (3DRMS)

the clock error accuracy to cm-level while the structure of the basic navigation message is basically unchanged. 3.2 Next-Generation GNSS Space “Net” Ground “Net” Space-Time Reference System Architecture User positioning mainly requires time synchronization precision between satellites in constellations. The higher the time synchronization precision, the higher the positioning precision. For example, if the real-time synchronization accuracy between constellation satellites reaches 30ps, the cm-level positioning requirements can be met. Using laser inter-satellite links can realize that the time synchronization accuracy of the whole network in space segment is better than 30ps. On this basis, using laser inter-satellite links to achieve mm-scale interstellar distance measurement, the orbit precision can be improved to within 1 cm-level, to meet the accuracy requirements of cm-level SISRE. The concept of the Kepler system is proposed by German Aerospace Center (DLR), which adopts new optical time-frequency, optical inter-satellite link and LEO satellite monitoring technology to reduce dependence on the ground and achieve a 1 cm level SISRE accuracy [34]. In the space “net” ground “net” system architecture, the space segment is connected by optical two-way inter-satellite links to form a space “net” in real-time, which establishes the space-based space-time reference GNSS(SPACE) as a whole, thereby avoiding the influence of the environment segment. And the system can realize that orbit and clock

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Table 5. Clock error accuracy of the main GNSS and its augmentation systems GNSS system and message type Basic navigation message [3, 22, 23]

PPP message [24–33]

GPS

Clock error precision: 50cm(RMS) Broadcasting frequency: 2 h

/

BDS-3

Clock error precision: 42cm(RMS) Broadcasting frequency: 1 h

Clock error precision: 0.11ns(std) Broadcasting frequency: 6s PPP-B2b

Galileo

Clock error precision: Clock error precision: 18cm(RMS) 0.15ns(std) Broadcasting frequency: 10 min Broadcasting frequency: 10s Galileo HAS

QZSS

/

Clock error precision: 0.08ns(std) MADOCA L6E PPP

Fugro G4

/

Clock error precision: 0.1ns(std)

decoupling, the mm-scale high-precision observation, and the improvement of the measurement topology geometry, and greatly enhance the space-time reference relative synchronization capability of the space segment. And a new atomic clock technology, a new satellite platform, and orbit measurement and control technology are used to achieve the establishment and maintenance of high-precision space-based space-time reference, and to conduct a “Quasi reference level” space-ground comparison with the ground segment GNSS(Earth), the comparison frequency dropped to more than 7 days, greatly reduce the demand for high-precision real-time satellite-ground measurement, and reduce the impact of the environmental segment to improve accuracy through data accumulation. LEO satellite is used to realize space-based monitoring above the environment segment, and decouple the influence of the environment segment on the high-precision estimate of signal deviation and PCV signal characteristics in time-frequency and space-domain [34] (Fig. 5). The satellite-ground measurement is responsible for the near real-time measurement of satellite orbit and clock error under the space “net” ground “net” structure and is transferred to be responsible for the comparison and synchronization of the space-ground time reference, the traceability to the international standard time, and for the synchronization between the space-based space-time reference and the BDS coordinate system under the space “net” ground “net” framework.

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Y. Meng et al. Space "net" maintain GNSST(SPACE), and realize the real-me and ps-level me synchronizaon between satellites in the constellaon

Tradional downlink navigaon

Quasi reference level comparison between space and ground, and synchronizaon of GNSST(SPACE) and GNSST(EARTH)

UHF/VHF and other new frequency downlink navigaon

LEO enhancement layer: space-based monitoring above the environment segment, UHF/VHF and other new frequency band high-power signal enhancement

Environment segment

Ground "net" maintain GNSST(EARTH)

Control staon

Monitoring and comparison staon

Upload staon

Fig. 5. The next generation GNSS space “net” ground “net” space-time reference system architecture

The time-frequency transfer of the space laser has completed the ground verification and the on-orbit experiment [35]. Using a coherent communication system, the twoway data rate is 1Gbps. The experimental system is shown in Fig. 6, and the verification system includes optical terminal A, optical terminal simulator B, optical simulation channels, satellite time-frequency simulator, test computer, etc. The satellite time-frequency simulator provides 1PPS/10.23MHz signals for ranging, and the test computer compares the bidirectional pseudorange to solve the clock error.

1pps/10.23MHz

Time-frequency system

Analog opcal path

1pps/10.23MHz

Opcal terminal simulator B

Optical terminal A Ranging results A

Test Computer

Ranging results B

Fig. 6. Space laser two-way time-frequency transfer ground verification system

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The ground verification results are shown in Fig. 7, which simulate the attenuation of 40000 km inter-satellite distance. The measurement accuracy of inter-satellite clock error is better than 2ps (1σ).

Fig. 7. Space laser time-frequency transfer ground verification results

3.3 Next-Generation GNSS Unambiguous Instantaneous Cm-Level Space Meta-Signal It can be seen from the previous analysis that the code-tracking accuracy of traditional single signals is at the m/dm level. And the B2 signal measurement accuracy can reach the cm level, where the B2 signal jointly tracks B2a and B2b. This is a dual-frequency signal processing method, which is called GNSS meta-signals processing in the paper [36]. That is, the two GNSS signals located at adjacent frequencies are processed uniformly as an ultra-wideband signal to achieve code-based high-precision positioning without ambiguity, and the joint processing method of E5A + E6-BC and E5B + E6-BC dualfrequency meta signal is studied. Paper [37, 38] analyzed the B1I + B1C coherent joint processing of BDS and pointed out that this method has the potential to realize code-based high-precision measurement without ambiguity. For BDS-3, this paper considers four dual-frequency meta-signal combination schemes: B2, B2a + B3I, B2b + B3I, and B1I + B1C. The power spectrum and correlation functions of the last three dual-frequency signals are shown in Fig. 8, and the code-tracking performance of the dual-frequency meta-signal under typical conditions is shown in Table 6.

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(a) B2b+B3I

(b) B2a+B3I

(c) B1C+B1I Fig. 8. Power spectrum and correlation functions of the dual-frequency signals

It can be seen that the combined accuracy of four kinds of dual-frequency meta signals can reach centimeter accuracy by analysis. At the same time, it can be seen from Fig. 8 that there are multiple side peaks in the correlation function, and there are real and imaginary parts, especially the joint signal of B1C + B1I, which has complex reception and challenges in reception robustness. 3.4 High Power Fast Message Signal in New Frequency Bands Such as UHF/VHF With the development of LEO constellations, navigation enhancement based on LEO constellations has become a research hotspot. The low-frequency bands represented by UHF/VHF have shown great advantages. Under the premise of equal emission of

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Table 6. The code measurement accuracy of dual-frequency signal Signal

Center frequency (MHz)

B2

1191.795

B2a + B3I

1222.485

Bandwidth (MHz)

Received power (dBW)

Receiving carrier noise ratio (dB-Hz)

Code tracking accuracy (2σ ) (m)

51.15

−153.5

50.5

0.0185

112.53

−155.2

48.8

0.0077

B2b + B3I

1237.83

81.84

−156.03

47.97

0.0127

B1I + B1C

1568259

32.736

−157.5

46.5

0.0585

EIRP, higher signal landing power can be achieved. The LEO navigation program of the Navigation Innovation and Support Program (NAVISP) studies the design scheme of VHF frequency band navigation signals [39]. Taking the UHF frequency band (460470MHz) of 5G low frequency as an example [40], for an LEO satellite at an orbital altitude of 1000 km, only a signal emission EIRP of 17dBW (50W) and an elevation angle of more than 10° is required to achieve a landing power of −139 dBW. Compared with BDS B1C, the landing power of signals from the LEO satellite is increased by 20 dB. The landing power is increased by 20 dB, and the carrier-to-noise ratio can reach 65 dB-Hz. Even if the code rate is only 1.023 Mcps and the bandwidth is 4.092 MHz, the code tracking accuracy (1σ) of 12.88 cm can be achieved, which is in the same order as the carrier wavelength (64.52 cm) of the UHF frequency band (460–470MHz). Combined with B2 and other ultra-wideband meta signals, it can support achieving carrier phase integer ambiguity resolution in theory, and the precision of instantaneous pseudo range can reach mm level based on carrier phase integer ambiguity resolution. If the UHF frequency band landing power is increased by 20 dB, and the structure of the broadcast message remains unchanged, the message broadcast rate can be increased by 100 times, and the message collection time will be reduced by 100 times. The message collection time will be realized within seconds, greatly speeding up the time for the first positioning. At the same time, the reliability of message collection can be greatly improved by using the characteristics of repeated broadcasting of messages to conduct multi-frame coherent accumulation.

4 Conclusion The standard single-point positioning based on pseudo-code can achieve real-time positioning. However, the current generation of GNSS is limited by the pseudo-code measurement accuracy of the first civil signal, making the ceiling of pseudo-code standard single-point positioning accuracy at the sub-meter level. And the cm-level user positioning must carry out higher precision carrier phase measurement, and it needs 10 ~ 40 min to initialize the convergence time to achieve carrier phase ambiguity resolution. The precision and real-time are limited by the positioning principle and the design source, so it is impossible to achieve the global standard instantaneous cm-level positioning by

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GNSS alone. This paper tries to analyze the system design source and concludes that the cm-level broadcast ephemeris accuracy is achieved by using the space “net” ground “net” space-time reference system architecture, while the basic navigation message transmission bandwidth is not increased and the basic navigation message structure is basically unchanged. The “B1C + B1I” joint signals and B2 signals are used as the unambiguous instantaneous cm-level space meta signals to realize the dual-frequency cm-level code pseudo-range measurement accuracy, and then achieve the instantaneous dm-level positioning accuracy of “cm-level broadcast ephemeris + cm-level code pseudo-range measurement signal”. The “cm/mm carrier pseudorange measurement” is further used to achieve instantaneous cm-level positioning. At the same time, it is proposed that LEO satellites use new frequency bands such as UHF/VHF to achieve a 20 dB higher landing power, support pseudo-code instantaneous carrier phase ambiguity resolution, realize cm/mm-level instantaneous code and carrier combined pseudo-range measurement, and realize 100 times fast message broadcasting, supports second-level fast first positioning and multi-frame coherent accumulation of highly reliable message reception. Finally, instantaneous cm/dm-level position based on a new generation of a code-based precise point positioning system for open sky application scenarios can be achieved.

References 1. Reid TGR, Houts SE, Cammarata R, Mills G, Agarwal S, Vora A, Pandey G (2019) Localization requirements for autonomous vehicles. SAE Int J Connect Autom Veh 2(3), 173–190 2. Kafka P (2012) The automotive standard ISO 26262, the innovative driver for enhanced safety assessment & technology for motor cars. Proc Eng 45:2–10 3. Montenbruck O, Steigenberger P, Hauschild A (2020) Comparing the ‘Big 4’—a user’s view on GNSS performance. In: 2020 IEEE/ION Position, location and navigation symposium (PLANS), pp 407–418. https://doi.org/10.1109/PLANS46316.2020 4. Global positining system standard positioning service perfermance standard, 5th edn, April 2020 5. Navstar GPS Space Segment/Navigation User Segment Interfaces (IS-GPS-200) (2018) 6. Navstar GPS Space Segment/Navigation User Segment L5 Interfaces (IS-GPS-705E) (2018) 7. Navstar GPS Space Segment/Navigation User Segment L1C Interfaces (IS-GPS-800E) (2018) 8. China Satellite Navigation Office (2019) BeiDou navigation satellite system signal in space interface control document open service signal B1I (version 3.0) 9. China Satellite Navigation Office (2018) BeiDou navigation satellite system signal in space interface control document open service signal B3I (version 1.0) 10. China Satellite Navigation Office (2017) BeiDou navigation satellite system signal in space interface control document open service signal B1C (version 1.0) 11. China Satellite Navigation Office. BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B2a (Version 1.0). 2017 12. China Satellite Navigation Office (2019) BeiDou navigation satellite system signal in space interface control document open service signal B2b (beta version) 13. European GNSS (Galileo) open service signal-in-space interface control document, issue 2.0, 2021 14. GLONASS interface control document navigational radiosignal in bands L1, L2 (Edition 5.1), 2018 15. Lu M (2018) Overview of the BDS III signals. 13th stanford PNT symposium

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16. Kaplan ED, Hegarty CJ (2017) Understanding GPS: principles and applications, 3rd edn. Artech House 17. EGNOS open service service definition document (2013). European Commission 18. SBAS L5 DFMC interface control document (SBAS L5 DFMC ICD) (2016). IWG 19. Quasi-Zenith satellite system interface specification centimeter-level augmentation service (IS-QZSS-L6-001) (2018). Cabinet Office 20. China Satellite Navigation Office (2019) BeiDou navigation satellite system signal in space interface control document precise point positioning service signal PPP-B2b (beta version) 21. European global navigation satellite systems agency (2020) Galileo high accuracy service (HAS) 22. Hauschild A, Montenbruck O (2021) Precise real-time navigation of LEO satellites using GNSS broadcast ephemerides. Navig: J Inst Navig 68(1) 23. Xi Z, Liu C, Zhang F, Wu Q, Hu X (2022) Accuracy evaluation and comparative analysis of four major GNSS broadcast ephemeris. GeomatS Inf Sci Wuhan Univ 47(2):208–218 24. Tao J, Liu J, Zhigang H, Zhao Q, Chen G, Boxiao J (2021) Initial assessment of the BDS-3 PPP-B2b RTS compared with the CNES TRS. GPS Solut 25:131 25. Liu Y, Yang C, Zhang M (2022) Comprehensive analyses of PPP-B2b performance in China and surrounding ares. Remote Sens 14(3):643 26. Yangyin X, Yang Y, Li J (2021) Performance evaluation of BDS-3 PPP-B2b precise point positioning service. GPS Solut 25:142 27. Geng T, Zhao Q (2022) Real-time ocean precise point positioning with BDS-3 service signal PPP-B2b. Measurement 203(2):111911 28. Fang R, Lv H, Hu Z, Wang G, Zheng J, Zhou R, Xiao K, Li M, Liu J (2022) GPS/BDS precise point positioning with B2b products for high-rate seismogeodesy: application to the 2021 Mw 7.4 Maduo earthquake. GeoPhysical J Int 231(3):2079–2090 29. Ren Z, Sun G (2021) Performance assessment of realtime precise point positioning using BDS PPP-B2b service signal. Adv Space Res 68(8):3242–3254 30. Fernandez-Hernandez I, Chamorro-Moreno A, Cancela-Diaz S et al (2022) Galileo high accuracy service: initial definition and performance. GPS Solut 26:65 31. Martini L, Susi M, Paonni M, et al (2022) Satellite anomaly detection with PPP corrections: a case study with galileo’s high accuracy service. IONITM2022, California, pp 1246–1262 32. Allahvirdi-Zadeh A, Wang K, el-Mowafy A (2021) POD of small LEO satellites based on precise realtime MADOCA and SBAS-aided PPP corrections. GPS Solut 25:31 33. Hauschild A, Tegedor J, Montenbruck O, Visser H, Markgraf M (2016) Precise onboard orbit determination for LEO satellites with real-time orbit and clock corrections. ION GNSS+ 2016, Oregon, pp 3715–3723 34. Günther C (2018) Kepler- satellite navigation without clocks and ground infrastructure. In: 31st international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2018), Florida, pp 849–856 35. Meng Y, Zhang Z, Wang G (2018) Free-space Two-Way Optical Time-frequency Transfer (FTWOTT) based on GEO/IGSO and MEO satellites. In: Proceedings of the 2018 precise time and time interval meeting, ION PTTI 2018, Reston, Virginia 36. García-Molina JA (2021) Unambiguous meta-signal processing a path to code-based highaccuracy PNT. InsideGNSS 37. Gao Y, Yao Z, Lu M (2020) Exploring the ultra-high -precision ranging potential of BDS B1 signal. ION GNSS+ 2020, 3626–3646 38. Qi Y, Yao Z, Gao Y, Mingquan L (2022) Robust unambiguous ranging technique for BDS-3 B1 wideband composite signals. GPS Solut 26:115 39. Palfreyman A (2019) Complementary PNT infrastructure in LEO. NAVISP Industry Day 40. Meng Y, Yan T, Bian L et al (2022) LEO Broadband satellite constellations based global navigation augmentation: opportunity and challenge. Navig Position & Timing 9(1):12–24

GNSS Signal Technologies

Polarization-Spatial Joint Anti-jamming Algorithm for GNSS Receiver in High Dynamic Environment Siyuan Jiang1(B)

, Runnan Wang2 , Shuai Liu1(B) , and Ming Jin2

1 School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin,

China [email protected], [email protected] 2 School of Information Science and Engineering, Harbin Institute of Technology, Weihai, China

Abstract. In order to address the problem that the anti-jamming performance of GNSS receiver array is seriously degraded in high dynamic environment, a polarization-spatial joint null broadening beamforming algorithm based on matrix reconstruction is proposed in this paper. Firstly, the received signal model of polarization sensitive array (PSA) is established. Then, the Capon spectrum is reset by setting the virtual interference in the interference and polarization angles’ neighborhood. Secondly, the interference-plus-noise covariance matrix (IPNCM) is reconstructed by the Capon spectrum, which realizes the polarization-spatial joint null broadening. Finally, the conjugate gradient (CG) method is utilized to get the polarization adaptive weight vector, which avoids the high computational complexity caused by matrix inversion. The simulation results show that this algorithm can effectively broaden the null, which has good suppression effect on high dynamic interference, and have less computational complexity compared with similar algorithms. Keywords: Adaptive beamforming · Polarization sensitive array · Null broadening · Matrix reconstruction · Conjugate gradient

1 Introduction As an effective anti-jamming technology, adaptive beamforming is widely used in Global Navigation Satellite System (GNSS) [1]. With the continuous development of space technology, the first GPS satellite was launched by the United States in the late 1970s, and the completion of the BDS marked the growing maturity of the GNSS. In the wave of military modernization, many weapons and equipment, such as fighter jets and missiles, are equipped with GNSS. Due to high-speed warplanes and missiles is in a highly dynamic environment, GNSS receivers will also move at high speed [2]. High speed movement or vibration of the GNSS receiver platform can cause a deviation between the beamforming pattern’s null and the actual position of the interference [3]. The literature [4] concluded that the deviation is generally within 1°, and this deviation will cause the interference to move outside the pattern null, which makes the algorithm unable to effectively suppress the interference. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 283–294, 2024. https://doi.org/10.1007/978-981-99-6932-6_23

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In traditional beamforming algorithms, the null broadening technology is often used to solve the mismatch of interference steering vector. The null broadening technology was first proposed by Mailloux and Zatman [5, 6]. After summarizing the methods of Mailloux and Zatman, Guerci proposed the concept of covariance matrix taper (CMT), and broaden nulls by Hadamard product of sample covariance matrix (SCM) and Tapered matrix [7]. It can generate a wide null in the interference direction without prior information of the interference. However, it broadens the null, meanwhile the null becomes shallow. Thus, it is insufficient to suppress the interference. Li Wenxing proposed a projection-based null broadening method [8], which constructs the interference subspace projection matrix using the prior information. Then, it broadened the null by projecting the snapshot data. Because the projection transformation can improve the orthogonality of signal space and noise space, it deepened the null. Nevertheless, this method involves the eigenvalue decomposition, which causes the high computational complexity. In addition, the degree of deepening null is limited. Wang Haiyang proposed a matrix reconstruction based null broadening method for space-time adaptive beamforming, which achieves wide nulls in spatial and frequency domains [9]. Compared with the traditional spatial beamformer, the polarization-spatial beamformer has better anti-jamming ability, because the polarization information can be fully utilized. Wang extended the MVDR algorithm from spatial to polarization-spatial joint domians [10]. This algorithm is sensitive to signal steering vector’s mismatch. Liu analyzed the filtering performance of eigenspace-based (ESB) algorithm on PSA [11]. Although ESB beamforming is not sensitive to interference steering vector’s mismatch, the performance of this algorithm drops sharply at low signal-to-noise ratio (SNR) [12, 13]. Xie Ming proposed the polarization-spatial joint covariance matrix taper (PSACMT), which realized a wide null in polarization-spatial domain [14]. However, it has the high computational complexity caused by high dimensional polarization covariance matrix inversion. In order to perform well in high dynamic environment, this paper proposes a polarization null broadening method based on matrix reconstruction. The method first resets the Capon spectrum by adding virtual sources in presumed interference’s neighborhood; On this basis, the polarization-spatial double integration is performed on the reset Capon spectrum to complete the interference-plus-noise covariance matrix reconstruction. Then, the conjugate gradient method is used to solve the weight vector, which avoids the high-dimension matrix inversion. It improves the real-time performance of the algorithm; Finally, the effectiveness of the method is verified by simulation.

2 Signal Model In this paper, N polarization sensitive arrays are used to form a uniform linear array (ULA), as shown in Fig. 1. Considering one desired signal and M interferences, the array received signal model can be expressed as: x(t) = As(t) + n(t)

(1)

where the array received data is x(t), the array manifold matrix is A, the incident signal vector is s(t), and the additive white Gaussian noise vector is n(t).

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Fig. 1. Uniform linear array composed of mutually orthogonal dipoles

Considering the polarization characteristics of electromagnetic wave, the PSA manifold matrix can be expressed as: A = [a(θ1 , ϕ1 , γ1 , η1 ), . . . , a(θM , ϕM , γM , ηM )]

(2)

s(t) = [s1 (t), · · · , sM (t)]T

(3)

n(t) = [n1 (t), · · · , n2N (t)]T

(4)

where θ, ϕ, γ , η represent the pitch angle, azimuth angle, polarization angle and polarization phase difference, respectively. The signal receiving model can be further expressed as: x(t) = a(θ0 , ϕ0 , γ0 , η0 )s0 (t) +

M 

a(θm , ϕm , γm , ηm )sm (t) + n(t)

(5)

m=1

The array signal steering vector a(θ, ϕ, γ , η) can be expressed as: a(θ, ϕ, γ , η) = ap (θ, ϕ, γ , η) ⊗ as (θ )

(6)

where ap (θ, ϕ, γ , η) is polarization steering vector and as (θ ) is spatial steering vector, respectively. The key of polarization sensitive array signal model is the establishment of polarization steering vector [15, 16]. According to (6), the polarization steering vector ap (θ, ϕ, γ , η) can be expressed as:  ap (θ, ϕ, γ , η) =

− sin ϕ cos θ cos ϕ cos ϕ cos θ sin ϕ



cos γ sin γ ejη

 (7)

Because ULA is adopted in this paper, the array azimuth angle is fixed at 90°, assuming the signal polarization phase difference is η0 , the polarization steering vector can be simplified as:      − cos γ −1 0 cos γ = (8) ap (θ, γ ) = cos θ sin γ ejη0 0 cos θ sin γ ejη0

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The steering vector as (θ ) is expressed as:   as (θ ) = 1, ejφ1 , · · · , ejφN −1

(9)

Here, φn = − 2πλnd sin θ , (0 ≤ n ≤ N − 1) is the phase difference, and λ is the signal wavelength. According to (6)–(9), the steering vector can be expressed as: a(θ, γ ) = ap (θ, γ ) ⊗ as (θ )

(10)

where  ⊗ is Kronecker product and a(θ, γ ) is 2N × 1-dimensional column vector. Under the maximum signal-to-interference-noise ratio criterion, the optimal polarized Capon beamforming (PCB) weight vector can be transformed into an optimization problem [17]: min wH Rin w w

(11)

H

s.t. w a0 = 1

According to the Lagrange multiplier method, the optimal weight vector wopt is: wopt =

R−1 in a0

−1 aH 0 Rin a0

=μR−1 in a0

(12)

where a0 is the desired signal steering vector, Rin is the interference-plus-noise covariance matrix, μ is a scalar which only affects the output signal power.

3 Algorithm Description 3.1 Polarization Covariance Matrix Reconstruction of Array The reconstruction method based on interference-plus-noise covariance matrix proposed in this paper can effectively solve the problem of the algorithm performance degradation caused by the mismatch of the interference steering vector in the high dynamic environment. The interference-plus-noise covariance matrix reconstruction method is given by integrating Capon spectrum in the angular region of the interference range [18]. The reconstructed interference-plus-noise covariance matrix Rin of the traditional scalar array can be written as:  Rin = P(θ )a(θ )aH (θ )d θ (13) 



θ

where P(θ ) =

1



is Capon spectrum, R =

1 K

K

aH (θ)

−1

k=1 x(k)x

H (k)

is sampling R a(θ) covariance matrix, θ is angle region containing desired signal, θ is angle region without desired signal, and a(θ ) is signal steering vector. 

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Considering the signal polarization information, the interference-plus-noise covariance matrix Rin of the polarization sensitive array is: ¨ Rin = P(θ, γ )a(θ, γ )aH (θ, γ )d θ d γ (14) 



ψ

Here, P(θ, γ ) =

1 

aH (θ,γ )R

−1

a(θ,γ )

is polarization-spatial Capon spectrum, ψ is the angle

area containing the polarization angle of the desired signal and the pitch angle, ψ is the complement of ψ, a(θ, γ ) is the steering vector with pitch angle θ and polarization angle γ . We can divide ψ into multiple regions containing interference [19]. Equation (14) can be expressed as: ¨ (15) Rin = Ri + Rn = P(θ, γ )a(θ, γ )aH (θ, γ )d θ d γ + σ 2n I 2N 







ψ 1 ∪ψ 2 ∪···∪ψ M

where ψ m (m = 1, · · · , M ) is the m-th interference angle and polarization two 2N 2 dimensional integration area, σˆ n = i=M +1 λi /(2N − M ) and λi are the eigenvalues 

of R. 3.2 Null Widening Method In this paper, the method of adding virtual interference sources near the actual interference is used to reset the polarization-spatial Capon spectrum to achieve null broadening. Assuming that the spatial and polarization angle intervals are θ and γ , respectively. The spatial and polarization broadening angle ranges are Bθ and Cγ , respectively. The m-th interference in the spatial and polarization region can be represented by the two-dimensional matrix ψ m 



ψm =

⎡

θm −

⎢

⎢ θ − B ⎢ m 2 ⎢ ⎢ ⎢ ⎢ ⎣

θm +













. . .

  θm + B2 θ, γm − C2 − 1 γ





⎤

B θ, γ − C γ θm − B2 θ, γm − C2 − 1 γ ··· θm − B2 θ, γm + C2 γ 2  m 2 



 



 ⎥ C B C − 1 θ, γm − 2 γ θm − 2 − 1 θ, γm − 2 − 1 γ · · · θm − B2 − 1 θ, γm + C2 γ ⎥ ⎥ ⎥

. . .

B θ, γ − C γ m 2 2

..

⎥ ⎥ ⎥ ⎦

. . .

.

···

 θm + B2 θ, γm + C2 γ

(16) 



Combining (17), the discrete Capon spectrum P (ψ m ) is: 



P (ψ m ) =

⎡ P θm −

⎢

⎢P θ − B ⎢ m 2 ⎢ ⎢ ⎢ ⎢ ⎣

P θm +















⎤

. . .

 B P θm + 2 θ, γm + C2 γ

⎥ ⎥ ⎥ ⎦

B θ, γ − C γ P θm − B2 θ, γm − C2 − 1 γ ··· P θm − B2 θ, γm + C2 γ 2  m 2 



 



 ⎥ − 1 θ, γm − C2 γ P θm − B2 − 1 θ, γm − C2 − 1 γ · · · P θm − B2 − 1 θ, γm + C2 γ ⎥ ⎥ ⎥

. . .

B θ, γ − C γ m 2 2



. . .

  B P θm + 2 θ, γm − C2 − 1 γ

..

.

···

(17)

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The Capon spectrum of the m-th interference shown in (17) within the twodimensional discrete summation range is shown in Fig. 2, and the gray scale in the figure represents the size of the Capon spectrum.

Fig. 2. The two-dimensional angle range of the m-th interference

Fig. 3. The two-dimensional angle range after adding virtual interferences

Set virtual interferences in the two-dimensional discrete summation area of the true interference, and set the power of the virtual interference source to the maximum value P(θm , γm ) of Capon spectrum in the discrete summation area. The power setting method of the virtual interference source can enhance the interference suppression. The Capon spectrum after reset is shown in Fig. 3. After reset, Capon spectrum can be expressed as: ⎤ ⎡ ⎤ 1 1 ··· 1 P(θm , γm ) P(θm , γm ) · · · P(θm , γm ) ⎢1 1 ··· 1⎥ ⎢ P(θm , γm ) P(θm , γm ) · · · P(θm , γm ) ⎥ ⎥ ⎢ ⎥  m ) = ⎢ = P(θ , γ P(ψ ) ⎥ ⎢. . . .⎥ ⎢ m m .. .. . .. .. ⎦ ⎣ .. .. . . .. ⎦ ⎣ . . . ⎡

P(θm , γm ) P(θm , γm ) · · · P(θm , γm ) ⎡ ⎤ 1 1 ··· 1 ⎢1 1 ··· 1⎥ ⎢ ⎥ = Pmaxm ⎢ . . . . ⎥ ⎣ .. .. . . .. ⎦ 1 1 ··· 1

1 1 ··· 1

(18)

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From the above discussion, the covariance matrix of the m-th interference reconstruction can be expressed as:       B C Pmaxm a θm − Rm = − b θ, γm − − c γ aH 2 2 b=0 c=0       B C θm − − b θ, γm − − c γ θ γ 2 2 C B  



(19)



Finally, M-th reconstructed interference-plus-noise covariance matrix Rin is: 

Rin =

M 



Rm + σ 2n I 2N 

m=1 M  B  C 

      B C − b θ, γm − − c γ = Pmaxm a θm − 2 2 m=1 b=0 c=0 2N       λi B C aH θm − − b θ, γm − − c γ θ γ + i=M +1 I 2N . 2 2 2N − M

(20)

Substituting (20) into (12), the polarization beamforming weight vector after nulling broadening can be obtained. 3.3 Solving Weight Vector Based on Conjugate Gradient Method Compared with the traditional scalar array, the polarization sensitive array is generally composed of mutually orthogonal electric dipoles, the order of the covariance matrix of the scalar array is N (R ∈ C N ×N ), while the order of the covariance matrix of the polarization sensitive array is 2N (R ∈ C 2N ×2N ). To reduce the computational complexity of high-dimensional polarization matrices, we use the conjugate gradient method to solve the weight vector, which avoids the inverse of the matrix. The specific process of the conjugate gradient method to solve the weight vector is as follows: Substituting (20) into (12) to get: 

wINCM =

−1

Rin a0



−1 aH 0 Rin a0 

−1

=μ Rin a0

(21)

where μ is scalar, which does not affect algorithm performance, it can be set as σˆ n2 . Multiply Eq. (21) by Rin to get: 



Rin wINCM = σ 2n a0 

(22)

Using conjugate gradient method for (22) to obtain the initial value of the residual vector r as: 

r0 = σ 20 a0 − Rin w0 

(23)

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where w0 is the all one vector of order 2N × 1. The initial value of the search vector is set to: p1 = r0

(24)

The expression for the iteration step α is: αi =

ri−1 2 

pH i Rin pi

(25)

The weight vector based on conjugate gradient method is: Wi = Wi−1 + αi pi

(26)

When the norm of the residual vector is less than the preset value ε, the iteration is ended to obtain the optimal weight vector wINCM −CG = Wi .

4 Simulation Simulation conditions: a uniform linear array composed of 16 dipoles is adopted, the array element spacing is d = λ/2, and the number of sampling snapshots is K = 100. Since GNSS navigation signals are generally circular polarized electromagnetic waves, the fixed polarization phase difference is η = 90◦ , the desired signal parameters are  ◦ ◦ (θ0 , γ0 ) = 0 , 45 ,SNR = −20 dB, and the interference parameters are (θ1 , γ1 ) = (40◦ , 45◦ ) and INR = 30 dB.The threshold value ε for the end of the conjugate gradient method iteration is 0.1, and the polarization angle broadening angle γ and space elevation angle broadening angle θ are both 2◦ . Under the above simulation conditions, the proposed algorithm is compared with the polarization domain SPMVDR algorithm [10], the characteristic subspace EsMVDR algorithm [11], the PSA-CMT algorithm based on the polarization-spatial joint cone [14] and the optimal algorithm to verify the pattern, output signal-to-interference-noise ratio and other performance. Simulation Experiment 1: polarization-spatial joint pattern. According to the above simulation conditions, the pattern of null broadening in the polarization domain is as followed. From Fig. 4(a) and (b), it can be seen that the pattern can form two-dimensional null in polarization and the spatial domain. Figure 4(b) shows that the null depth is >90 dB. Simulation experiment 2: verification of anti-dynamic interference ability. Fixed SNR = 0 dB, carried out 200 Monte Carlo experiments, simulate and analyze the change trend of output SINR of each algorithm under the condition that the deviation angles θ and γ of the spatial pitch angle θ and polarization angle γ of the jamming signal are from −2◦ to 2◦ , and the simulation results are shown in Fig. 5. It can be seen from Fig. 5 that when the mismatch angle is ψ ≤ 2◦ , the SPMVDR and EsMVDR polarization-spatial joint beamforming algorithm is more sensitive to the

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angle mismatch of jamming signals due to the unwidened null, and its performance will be severely degraded in the case of small angle mismatch. The algorithm proposed in this paper has deeper null than the similar PSA-CMT algorithm, and the output SINR is closer to the ideal performance. The algorithm proposed in this paper can reduce the output signal to interference noise ratio by max(Mag(t))

(9)

MAG  max(Mag(t))

(10)

Even

At this time, the signal becomes a narrow pulse train, which will be more complex and flexible. In practice, the typical practice is to make MAG = MTc , where M is an integer, and M ≥ 1. At this time, the design parameter M can change the overall pulse width and affect the signal characteristics. There are two ways to realize the navigation baseband signal. The first way is to set the ideal infinite bandwidth digital generation conditions. Whether in the form of BPSK or BOC, it can be expressed as a finite multi-level signal. Therefore, the multi-level amplitude is mapped to a multi time value of q(t). The second is a relatively practical limited bandwidth, quasi continuous signal. At this time, the signal is filtered by the first band limiting filter. At this time, the sampling interval Tc needs to be changed for processing, and the required bit rate is higher to ensure the signal quality. In order to observe its spectrum and other characteristics without losing accuracy, 0 is replaced by −1. Since the signal can be seen as a series of pulses, only the real part of the signal can be represented as x(t) =

N −1  i=0

(−1)i 

t − αi qi

(11)

where, N is the number of chips in a cycle; qi = q(t)Tc is the duration of the ith chip; αi = (nTc + (n + q(t))Tc )/2 = nTc + q(t)Tc /2 is the central moment of each chip. So the signal of one cycle can be seen as a rectangular pulse train with a delay of time αi and a width of qi . Therefore, its Fourier transform can be written as X (f ) =

N −1 

(−1)i qi sin c(fqi )e−j2π f αi

(12)

i=0

Because the spread spectrum code is pseudorandom, the Fourier transform represents the envelope of the spectrum. Its power spectral density (PSD) is 1 |X (f )| T N −1 N −1 1  = (−1)i+k sin(π Ti f ) sin(π Tk f ) cos(2π(αi − αk )f ) T π 2f 2 P(f ) =

i=0 k=0

(13)

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Therefore, its autocorrelation function is  BW R(τ ) = P(f )ej2π f τ df 1 = Tπ2

−BW N −1 N −1  

(14) (−1)

i+k

sin(π Ti f ) sin(π Tk f ) cos(2π(αi − αk )f )

i=0 k=0

where, BW represents the unilateral integration bandwidth. In the process of implementation, the specific forms of q(t) are slightly different for different signals. BPSK signal For BPSK signals, baseband signals can be represented by removing orthogonal branches sBB_BPSK (t) =

+∞ 

(p(t,nTc , (n + q(t)Tc ))

(15)

n=−∞

where, Tc = 1/fc , fc is the spread spectrum code rate. q(t) = D(t) xor cn

(16)

where D(t) is the value of the modulated data in {0,1}, cn is the spread spectrum code sequence, and is the value in {0,1}; xor is an exclusive OR operation. It can be seen that the signal waveform will show a complete switching state; It is two-level and binary. QPSK signal In baseband signal expression qI (t) = DI (t) xor cIn , qQ (t) = DQ (t) xor cQn

(17)

wherein, DI (t) and DQ (t) are message data modulated on in-phase and quadrature branches. cIn and cQn are modulated spread spectrum code sequences on in-phase and orthogonal branches. CBOC or CBCS signal CBOC is a type of CBCS. For CBCS signals, the chip waveform is CBOC is a special case of CBCS. For CBCS signals, the chip waveform is √ pCBCS (t) = 1 − γ pBCS(k1 ,n) (t) ± γ pBCS(k2 ,n) (t) (18) Therefore, at wherein, pBCS(k1 ,n) (t) and ,n) (t)√take values within √{−1,1},√ √ there are √ pBCS(k2√ √ √ most four level states { 1 − γ + γ , 1 − γ − γ , − 1 − γ + γ , − 1 − γ − γ } of CBCS chip, which can be normalized to within [0,1], then √ 

√ γ 1−γ , , 0 (19) q(t) ∈ 1, √ √ √ √ 1−γ + γ 1−γ + γ

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1 For the E1C signal of Galileo, γ = 11   10 1 pBOC(1,1) (t) ± pBOC(6,1) (t) pCBOC (t) = 11 11

(20)

The four states of q(t) are  q(t) ∈ 1, √

√ 10 10 + 1

1



,√ ,0 10 + 1

(21)

AltBOC or PSK-like signal AltBOC signal baseband of Galileo system has only 8 different values, which can be regarded as an 8PSK modulation sBB_AltBOC (t) = ejkπ/4 , k = {0, 1, 2, 3, 4, 5, 6, 7}

(22)

For this signal

 kπ  kπ qI (t) = 0.5 + 0.5 ∗ Re ej 4 = 0.5 + 0.5 ∗ cos 4

 kπ  kπ qQ (t) = 0.5 + 0.5 ∗ Im ej 4 = 0.5 + 0.5 ∗ sin 4

(23)

The minimum generated clock frequency of AltBOC (15,10) is 15 * 8 * 1.023 = 120 * 1.023 MHz = 122.76 MHz, so = 122.76 MHz. To ensure the quality of generation, the sampling rate of this method needs to be larger than 122.76 MHz and an integer multiple of 122.76 MHz. For POCET signal and higher-order PSK signal, similar to AltBOC signal     (24) qI (t) = 0.5 + 0.5 ∗ Re ejϕ , qQ (t) = 0.5 + 0.5 ∗ Im ejϕ It is worth noting that after such mapping, the signal can no longer depict the overall correlation peak and spectrum in the shape of a single chip. 2.2 Carrier Signal Generation and Modulation The generation of carrier signal is represented as carrRF (t) = carrI (t) + jcarrQ (t)

(25)

carrI (t) = 0.5 + 0.5 ∗ Sign(cos(2π fRF t + ε) carrQ (t) = 0.5 + 0.5 ∗ Sign(sin(2π fRF t + ε)

(26)

where, ε is a small positive number, in order to prevent the symbolic function Sign() from having a value of 0.

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The modulation method is sI (t) = sBB_I (t) xor carrI (t) − sBB_Q (t) xor carrQ (t) sQ (t) = sBB_Q (t) xor carrI (t) + sBB_I (t) xor carrQ (t)

(27)

Since there are addition and subtraction operations, there are three levels 0, 2, and −2 after modulation. At this time, the sampling rate is doubled. Continue to use the amplitude time method to level the three-level and two-level. sRF_I (t) = B ·

+∞    p (t,nT , (n + qI (t)T ) n=−∞

sRF_Q (t) = B ·

+∞    p (t,nT , (n + qQ (t)T )

(28)

n=−∞

where qI (t) = p

1 (sI (t) + 2) 4

qQ rime(t) =

 1 sQ (t) + 2 4

(29)

It should be noted that the combination of baseband and carrier belongs to the process of modulation. During the modulation process, XOR operation is required to remove the DC caused by the original baseband signal offset. This signal transforms amplitude domain quantization into time domain quantization, and the quantization accuracy in time domain mainly depends on the sampling rate. The duration of each data is finally quantized as an integral multiple of the sampling period. q(t) ≈

1 kTs =k T Tfs

(30)

where fs is the sampling clock frequency and Ts is the corresponding sampling clock cycle. The main way to improve the distortion is to minimize the quantization error

 kTs e(t) = q(t) − (31) T It can be seen that when the chip time is determined, one of the means is to increase and decrease. For amplitude quantization, the highest bit DAC that supports IF and RF generation is about 16 bits. However, the current maximum speed of single bit output interface SERDES has exceeded 100 Gbps, and supports free light modulation and optical fiber transmission. With the breakthrough of related technologies, it can be even higher in the future. There is almost no limit in this area. In particular, the current navigation signal baseband does not exceed 8 levels, and related delay means can be used to continuously reduce the quantization impact.

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3 Generation Method of Navigation Signal In the signal generation of traditional navigation satellite payloads, as shown in Fig. 1, FPGA/ASIC is generally used to generate digital IF signals, then DAC is used to convert digital to analog IF signals, and up converter is used to convert them to the required Lband. Due to mirror image, local oscillator leakage, and out of band redundant signals, input filters need to be used to limit the band and then enter the power amplifier. After that, output filtering and antenna broadcasting will be carried out. The current navigation signal design aims at constant envelope under infinite bandwidth, but the payload components and the limited bandwidth processing in implementation have broadened the working point of the amplifier. Since the navigation signal needs constant power broadcasting, in order to make full use of the power efficiency, the power amplifier is generally set to work in the saturated area and nonlinear area, which makes it difficult to ensure the high linearity of the power amplifier at the saturated area. The binary signal can greatly simplify the load design. FPGA/ASIC directly outputs the single bit signal stream from the high-speed serial interface IO, passes through the pulse power amplifier, passes through the band-pass filter for frequency selection, and then sends it to the antenna for broadcasting, as shown in Fig. 2. The spaceborne pulse power amplifier with constant peak power is widely used in radar satellite and other applications. The peak power (ten thousand watts) is much higher than the continuous wave power amplifier (one hundred watts), so the loss of out of band power becomes an acceptable cost.

FPGA /ASIC

Input filter

DAC

CW PA

Up converter

Output filter

Amplitude phase network

Antenna array element

Fig. 1. Legacy on-board payload design

FPGA/ ASIC

DPA

BP filter

Amplitude phase network

Antenna array element

Fig. 2. Novel on-board payload design

The fixed starting point of the signal pulse is conducive to reducing the complexity of generation and reception. In the case of the need to improve the rate and anti-interference, the position of the starting point of the pulse can also be modulated twice to form a time hopping pattern. A generation process is shown in Fig. 3. When the baseband signal is filtered or the number of levels is large, the signal can only be modulated by using the NCO sampling method of the numerical control

HsPWM Satellite Navigation Signal Generation and Analysis

Baseband waveform

Bias

365

PWM

Insert 0

Fig. 3. 2-level PWM process

oscillator, which also brings the advantage of flexible time delay adjustment at the cost of signal quality degradation. Some simulation test results are shown in Figs. 4 and 5. The AltBOC signal is generated using this sampling rate 3 * 5 * 8 * 233 * 1.023 = 28,603.08 MHz.

Fig. 4. Binary conversion of real part (left) and imaginary part (right) of AltBOC baseband signal

Fig. 5. Comparison of original AltBOC and PWM power spectrum

In summary, this implementation method has better feasibility when the least common multiple of signal elements is small. From the analysis, the correlation loss after power normalization is within 0.5 dB. The tracking performance gradually approximates with the improvement of sampling rate and theory.

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4 Conclusion High quality navigation signal generation and flexible countermeasure capability have become important indicators of navigation signal and payload design. In addition, the development and construction of navigation satellite system are also faced with the uncertainty requirements of signal system test and various performance requirements upgrading. Increasing the digitization rate as much as possible is an important aspect to meet this demand. Using the 2 level PWM (named HsPWM) method to generate the navigation signal can eliminate the DAC, omit the frequency converter, and use the digital fixed amplifier to greatly improve the digitization rate. Because of digital generation and distortion determination, delay stability and signal quality can be better guaranteed. Through the digital control of pulse delay, the signal with better anti-interference performance can be designed. Furthermore, since the use of power amplifiers with poor linearity near the saturation point is avoided, the synthesis of multiple signal components cannot even be restricted by the strict constraints of constant envelope, and more flexible multiplexing methods are used in high-speed time domain, which is expected to break through the existing load constraints and achieve better signal broadcasting with better comprehensive performance.

References 1. Chapman D, Hinks J, Anderson J (2020) Way, way out in front navigation technology satellite-3: the vanguard for space-based PNT. InsideGNSS 2. Ngo KD, Koretzky EV (2018) Global positioning system phased array using all-digital beam forming and direct digital waveform systhesis methods. United States Patent. US9921313B2 3. Hall DM, Ngo KD (2020) On-orbit reprogrammable digital signal generator system for generation of hopping multi-band global positioning system signals. United States Patent. US10732294B1 4. Ying W, Tao Y, Xiao L, Yingsong L, Yin L, Wenshan L (2019) A parallel structure RF signal generating method. China Invention Patent. ZL201710644634.4 5. Liu H, Yang Z, Xu Q, Chen L, Zhang L (2020) A piecewise pre-ditortion optimization method based on spaceborne digital filter. Acta Geodaetica et Cartographica Sinica 49(9):1235–1242 6. Ying W, Tao Y, Yansong M, lang B, Guoyong W, Wenying L (2021) High-precision satellite navigation signal predistortion method. China Invention Patent. ZL201810987419.9

A Fast Configuration Optimization Algorithm for GNSS-based InBSAR System Ruihong Lv1,2 , Feifeng Liu1,2 , Zhanze Wang1,2(B) , Xiaojing Wu1,2 , and Jiahao Gao1,2 1 School of Information and Electronics, Beijing Institute of Technology, Beijing, China

[email protected] 2 Key Laboratory of Electronic and Information Technology in Satellite Navigation (Beijing

Institute of Technology), Ministry of Education, Beijing 100081, China

Abstract. The Global Navigation Satellite System-based Synthetic Aperture Radar Interferometry (GNSS-based InBSAR) uses in-orbit satellites as transmitters, and the receiver is stationary on the ground, which uses repeat-pass interference to realize deformation inversion. Compared with the traditional InSAR system, GNSS-based InBSAR has obvious advantages such as short revisit time, wide coverage and low system cost. This paper proposes a fast configuration optimization algorithm for GNSS-based InBSAR to solve the problem that the traditional configuration optimization algorithm consumes a lot of computing resources and does not have the ability to deploy quickly in disaster areas. This method simulates the trajectory of actual satellites in a repeat-pass period by polynomial fitting, and quickly optimizes the resolution and three-dimensional deformation accuracy at each time in a repeat-pass period, to obtain the best experimental configuration. This method can greatly reduce storage resources and simulation calculation time, and achieve rapid configuration optimization selection. The effectiveness of the algorithm is verified by the experimental data. Keywords: GNSS-based InSAR · 3D deformation retrieval · Resolution optimization · PDOP · Configuration optimization

1 Introduction The Global Navigation Satellite System-based Synthetic Aperture Radar Interferometry (GNSS-based InBSAR) uses in-orbit satellites as transmitters, and the receiver is stationary on the ground, which realize continuous deformation monitoring by obtaining the navigation satellites repeat-pass SAR images sequence [1, 2]. GNSS-based InBSAR has a series of advantages. First, for Beidou system, the period of IGSO satellites is only 1 day, which enables rapid deformation monitoring. Second, there are 10 IGSO satellites in orbit, which can guarantee multi-angle observation for one target and then achieve the three-dimensional deformation detection. Third, the cost of the GNSS-based system is low due to that it only requires a receiver to continuously complete 3-D deformation retrieval, i.e., there are no costs at the transmitter. Based on the above outstanding advantages, the GNSS based InBSAR system has received extensive attention, and has great potential in the field of 3D deformation monitoring. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 367–378, 2024. https://doi.org/10.1007/978-981-99-6932-6_30

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There are many researches of deformation retrieval experiments using GNSS-based InBSAR system. Researchers from Beijing Institute of Technology used transponder to artificially construct Persistent Scatterers (PSs) and collected 16 sets of repeat-pass data using 4 Beidou-2 IGSO satellites [3]. Using the proposed 3D deformation retrieval algorithm, they successfully achieved accuracy better than 5 mm 3D deformation retrieval. Wang et al. [4] proposed a multiangle images association algorithm for GNSS-based InSAR system to improve the image resolution. To realize 3D deformation retrieval, at least three satellites are needed to illuminate the scene from different angles at the same time. The larger the spatial distribution range, the higher the accuracy of 3D deformation retrieval. In the field of GNSS, Position Dilution of Precision (PDOP) is commonly used to represent the accuracy of satellite positioning. Sharp et al. [5] and Zhang et al. [6] analyzed the application of PDOP in GNSS positioning. However, the GNSS-based InBSAR system uses interferometric phase to achieve deformation inversion. The signal processing method and error form are different from those of GNSS positioning. Therefore, it is necessary to appropriately expand PDOP so that it can be applied to the evaluation of deformation retrieval accuracy. In addition, using GNSS satellites as transmitters also brings some problems. Due to the large number of satellites in orbit, the efficiency and accuracy of three-dimensional deformation retrieval of different satellites are different at different times. Therefore, Wang et al. [7] proposed an optimization model for repeat-pass data acquisition, using the real trajectory of the satellite for 3D deformation inversion experiment design, and obtained the optimal data acquisition strategy. However, this method needs to use the satellite trajectory as a priori input, which consumes a lot of computing time and storage resources and cannot meet the requirements of rapid equipment deployment and monitoring in landslide disaster areas. In this paper, a fast configuration optimization algorithm for GNSS-based InBSAR system is proposed. The remaining parts of the paper are arranged as follows. Section 2 introduces the experiment system and the configuration optimization model. Section 3 proposes the proposed configuration optimization algorithm. Section 4 shows the results of the algorithm and raw data, and Sect. 5 draws the conclusion.

2 GNSS-Based InBSAR Configuration Optimization Model The configuration of the GNSS-based InBSAR system is shown in Fig. 1. The system uses the northeast sky coordinate system, and the transmitter uses the Beidou IGSO satellite. The receiver is stationary and placed at the origin of the system. The receiver has two antennas, which respectively receive the echo signal and the direct wave signal. The parameters of the system are shown in Table 1. Three-dimensional deformation monitoring requires to combine the observation results of multiple satellites at different angles. The following aspects need to be considered in the selection of experimental time and satellites. First, unlike the traditional InSAR system, due to the low bandwidth of the navigation satellite signal, the resolution of SAR image is poor, and the phase of PS in the image will be affected by other weak targets, the lower the resolution, the greater the impact [8]. Secondly, the accuracy of the interferometric phase is also related to the elevation angle of the satellite. The larger

A Fast Configuration Optimization Algorithm for GNSS-based InBSAR System

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Fig. 1. Bistatic configuration of GNSS-based InBSAR.

Table 1. System parameters Parameters

Value

Carrier frequency

1268.52 MHz (B3I)

Transmitter signal

C/A code

Effective signal bandwidth

10.23 MHz

Orbit height

About 36000 km

Equivalent PRT

1 ms

Synthetic aperture time

600 s

the elevation angle, the higher the accuracy of the interferometric phase. Finally, the 3D deformation retrieval accuracy depends on the configuration of the system, which is the topological relationship between each satellite, the receiver, and the scene. Therefore, it is necessary to optimize the selection of each satellite. In this paper, PDOP is used to evaluate the deformation retrieval accuracy. It is related to the spatial geometric distribution of the satellites used. The larger the spatial distribution range, the smaller the PDOP value and the higher the accuracy. Therefore, considering the resolution, elevation angle and PDOP, a GNSS-based InBSAR configuration optimization model is proposed as follows: {t, SC} = arg min σ (t, SC)  ρ(t, SC) > ρthre s.t. , ς (t, SC) > ςthre

(1)

where t is the experimental time, SC is the satellite combination. ρ, ς and σ are the resolution, elevation angle and theoretical 3D deformation accuracy, respectively. ρthre , ςthre are the thresholds.

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3 Fast Configuration Optimization Algorithm Based on the model in Sect. 2, a fast configuration optimization algorithm for GNSSbased InBSAR is proposed. Firstly, the satellite trajectory is simulated, and then the resolution and elevation angle of each satellite at each time are calculated and screened, and the theoretical accuracy of the three-dimensional deformation at each available time is calculated according to the screening results, and finally the best experiment time and satellite combination are obtained. The algorithm flow is shown in Fig. 2.

Fig. 2. GNSS based InBSAR fast configuration optimization algorithm process.

3.1 Satellite Trajectory Fitting The Beidou IGSO satellite orbit altitude is about 35786 km, the orbit inclination angle is 55°, and its sub-satellite point trajectory is in the shape of “8”. In a period, the azimuth and elevation angles of the satellites at different times are different, so the satellite trajectory can be calculated according to the azimuth angle and the elevation angle. In addition, since the satellite is not in regular circular motion, and its radius will also change, so polynomial fitting can be used to calculate the satellite trajectory: ⎧ ⎨ R(t) = a0 + a1 t + a2 t 2 + a3 t 3 (2) θ (t) = b0 + b1 t + b2 t 2 + b3 t 3 , ⎩ 2 3 ς (t) = c0 + c1 t + c2 t + c3 t

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where a, b, c are coefficients of third-order polynomial fitting, R is the distance from satellite to receiver, θ is the azimuth degree and ς is the elevation angle. Using polynomial coefficients as input, the satellite trajectory can be expressed as follows: ⎡ ⎤ R(t) sin θ (t) cos ς (t) PS = ⎣ R(t) cos θ (t) cos ς (t) ⎦, (3) R(t) sin ς (t) where WT is satellite position coordinates. This method only needs polynomial coefficients as input to calculate satellite trajectory, which can greatly reduce the storage space and computing resources used by the algorithm. The input for satellite trajectory fitting is obtained by calculating ephemeris parameters. It is worth mentioning that the position of the satellite after each heavy orbit is not the same, so it is necessary to update the ephemeris to reduce baseline error. 3.2 Resolution and Elevation Angle Optimization According to the satellite trajectory, the resolution and elevation angle of the satellite at each moment can be calculated. When the receiver is stationary, the projection of the resolution of the system in the range and azimuth directions on the imaging plane can be expressed as [9]: ρr =

0.586c

2B cos(β/2)T r 0.886λ ρa = , 2Tint ωTA  TTA a

(4)

where ρr and ρa represent the resolution in the range direction and the azimuth direction, respectively. c is the speed of light, B is the effective bandwidth, β is the bistatic angle and  is its corresponding unit vector. ωTA is the equivalent angular velocity of the satellite motion and  TA is its corresponding unit vector. λ is the wavelength, Tint is the synthetic aperture time. r and a are the unit vectors in the range direction and azimuth direction respectively. According to the satellite trajectory, the resolution of the range and azimuth of the satellite at each moment can be calculated. Furthermore, the area of each resolution unit can be calculated approximately, the formula is as follows: S = ρa ρr sin φ,

(5)

where φ is the angle between r and 

a . For a satellite at position Ps = Psx , Psy , Psz , its elevation angle can be expressed as: Psz ς = arctan( ). 2 + P2 Psx sy

(6)

According to the satellite trajectory, the elevation angle of the satellite at each moment can be calculated. If the elevation angle is too low, it will increase the error of the signal

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passing through the atmosphere and increase the phase noise of the signal. In this paper, the elevation angle threshold is set as 15°, and the satellite whose elevation angle does not reach the threshold cannot be used. 3.3 Theoretical Deformation Retrieval Accuracy PDOP is commonly used in GNSS positioning to calculate the accuracy. This paper expands the definition of PDOP and combines it with the spatial coherence coefficient at different angles to calculate the theoretical accuracy of 3D deformation retrieval. Based on the idea of PDOP, the 3D deformation inversion error δLP can be expressed as [3]:

−1 HT n, δLP = HT H where n is the noise, H is satellite observation matrix. Therefore, the variance of estimation error can be calculated as: 

−1

−1 HT E nnT H HT H . D(δLP ) = HT H

(7)

(8)

The above formula shows that  theoretical accuracy can be improved by optimiz the ing the satellite position H. E nnT mainly affects the one-dimensional deformation monitoring accuracy, which is related to the interferometric phase error. In PS-InSAR processing, the coherence coefficient can be approximated as the spatial coherence coefficient [7]:   ¨     ˜ |2 exp −j 2π r P Q ; t n2 − r P Q ; t n1 dxdy, |W (9) γ ≈ γspa = λ   ˜ is the resolution unit of the PS point after normalization, r P Q ; t is the distance where W between satellite and target at time t, t n1 and t n2 indicate the same time within two repeat-orbit periods of the satellite. Therefore, the one-dimensional deformation retrieval accuracy σw can be expressed as:  λ λ 1 − γ2 σϕ = σw = 2π 2π 2γ 2 (10)  2 λ 1 − γspa ≈ , 2 2π 2γspa where σϕ is the standard deviation of the interferometric phase. Furthermore, the onedimensional monitoring accuracy of each satellite can be expressed as: 



2 2 2 . (11) E nnT = diag σw1 , σw2 · · · σwM

A Fast Configuration Optimization Algorithm for GNSS-based InBSAR System

Then, the 3D deformation accuracy can be rewritten as: 

−1

−1 2 2 2 H HT H D(δD) = HT H HT diag σw1 , σw2 · · · σwM ⎞ ⎛ D11 D12 D13 ⎟ ⎜ = ⎝ D21 D22 D23 ⎠. D31 D32 D33

373

(12)

According to the definition of PDOP, the accuracy of 3D deformation inversion can be expressed as:  σ = D11 + D22 + D33 (13) So far, through satellite trajectory simulation, combined with the results of resolution, elevation angle and theoretical 3D deformation retrieval accuracy, the experimental configuration with the highest accuracy can be optimized.

4 Experimental Results and Analysis 4.1 Experimental Scene Introduction The experiment was carried out in the in Fengjie County, Chongqing City. And the experimental scene is shown in Fig. 3. The scene is mainly composed of houses, farmland and vegetation.

Fig. 3. Experiment scene and configuration.

The receiver of the GNSS-based InBSAR system consists of two antennas, which are direct signal antenna and echo antenna.

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4.2 Configuration Optimization Results Satellite trajectory simulation The experiment was carried out on August 19, 2022. The selected satellites include 7 Beidou-2 IGSO satellites and 3 Beidou-3 IGSO satellites. The repeat-pass period of IGSO satellite is about 1 day. In this algorithm, one period is evenly divided into 96-time interval, and the interval between adjacent time points is 15 min, from which the optimal acquisition time is selected. Firstly, the satellite trajectory is calculated by the almanac data, and the azimuth and elevation angle of the satellite are obtained by polynomial fitting. Then the satellite trajectory is calculated using the azimuth and elevation angles, and the results are shown in the Fig. 4.

Fig. 4. Beidou-3 IGSO1 movement track.

Configuration optimization According to the experimental requirements, the resolution unit area should be less than 150 m2 and the elevation angle is required to be greater than 15°. Calculate the resolution and elevation angle of each satellite based on the satellite trajectory, and the results are shown in the Fig. 5. According to the threshold of resolution and elevation angle, the qualified experiment time and satellites are selected. And then use the selection results to calculate the accuracy of theoretical deformation retrieval. Figure 6 (a) shows the variation of spatial coherence coefficient, which is used as the error input for calculating the theoretical accuracy of three-dimensional deformation. 3D deformation retrieval requires at least 3 available satellites. For the time when the number of available satellites meets the requirements, the theoretical accuracy of the optimal 3D deformation is calculated. And the result is shown in the Fig. 6 (b). The experiment requires the theoretical accuracy to be within 6 mm. According to Fig. 6 (b), the selected time are 9:45 and 16:00, and the accuracy is 5.17 mm and 5.63 mm, respectively. The final experimental design results are shown in Table 2.

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375

Elevation Angle 120

90

1

1

110

2

3

80

2

3

100

4

70

4 90

60

5

80

6

7

70

8

Satellite number

Satellite number

5

50

6

7

40

8

60

30

9

9

50

20

10

10

10

20

30

40

50

60

70

80

90

10

20

Experimental time

30

40

50

60

70

80

90

Experimental time

(a)

(b)

Fig. 5. (a) Is the result of SAR image resolution and (b) is the elevation angle of each satellite. Spatial coherence coefficient 10 1 9 2 0.95

8

3 7 4 0.9

6 5

0.85

7

8

0.8

9

Theoretical accuracy (mm)

Satellite number

5 6

4

3

2

1

0.75

10

0 10

20

30

40

50

Experimental time

(a)

60

70

80

90

0

4

8

12

16

20

24

Experimental time

(b)

Fig. 6. (a) Is the spatial coherence coefficient of 10 IGSO satellites, and (b) is the theoretical 3D deformation retrieval accuracy.

Raw data verification According to Table 2, the satellites and experimental time are selected for the 3D deformation retrieval. The image of Beidou-3 IGSO3 at 9:30 is shown in the Fig. 7. Record the actual resolution and elevation angle, then carry out 3D deformation retrieval processing, the results can be obtained as shown in the table below. Comparing Table 3 with Table 2, it can be found that the resolution change trend is same, but due to the influence of noise, filter selection and measurement error, the actual resolution deteriorates to a certain extent. The satellite elevation angle is almost the same. And the 3D deformation retrieval accuracy deteriorates to a greater extent, which is caused by the incomplete compensation of channel phase error, atmospheric phase error, and elevation error [10]. However, it can be seen that the accuracy ratio

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Time

Satellites selected

Resolution (m2 )

Elevation angle (°)

Theoretical 3D deformation accuracy (mm)

9:30

Beidou-3 IGSO1

142.8

72.3

5.17

Beidou-3 IGSO3

51.3

56.9

Beidou-2 IGSO2

89.8

72.2

Beidou-2 IGSO5

68.2

63.3

Beidou-3 IGSO1

54.3

66.8

Beidou-3 IGSO2

139.2

83.9

Beidou-2 IGSO3

99.0

74.1

Beidou-2 IGSO6

71.6

76.7

16:00

5.63

Imaging Result 1000 225

220

800

215

600 210

North(m)

205

400 200

200

195

190

0 185

180

-1200

-1000

-800

-600

-400

-200

0

200

East(m)

Fig. 7. Imaging results of Beidou-3 IGSO3.

of the two experimental times is basically the same as that of the theoretical accuracy, which can prove the correctness of the algorithm. In addition, since the algorithm does not require prior trajectory information as input, the required storage space is reduced by more than 99% compared with the traditional algorithm [7], and the calculation speed is increased by more than 50%, realizing the ability to quickly select configurations, as shown in Table 4. Therefore, the algorithm can be well applied to the 3D deformation monitoring experiment of the actual scene. The cost of performance improvement is that there is a baseline error of 20 km, which is relatively small compared to the distance from the satellite to the scene. Therefore, this baseline error can be tolerated.

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Table 3. Results of raw data Time

Satellite selected

Resolution (m2 )

Elevation angle (°)

Actual 3D deformation accuracy (mm)

9:30

Beidou-3 IGSO1

173

70.4

23.68

Beidou-3 IGSO3

80

54.6

Beidou-2 IGSO2

121

70.1

Beidou-2 IGSO5

95

65.4

Beidou-3 IGSO1

92

65.3

Beidou-3 IGSO2

162

84.9

Beidou-2 IGSO3

134

74.9

Beidou-2 IGSO6

108

77.5

16:00

26.52

Table 4. Configuration selection results Required storage space (KB)

Processing time (s)

Traditional algorithm

157139

70.40

Proposed algorithm

39

32.46

5 Conclusion Based on the 3D deformation monitoring experiment in the disaster area, this paper proposes a fast configuration selection algorithm based on GNSS-based InBSAR system to solve the problem that the traditional configuration selection algorithm consumes a lot of computing resources and does not have rapid deployment and monitoring. First, the satellite trajectory is fitted by polynomial fitting of azimuth and elevation angles, then the experimental time and experimental configuration that meet the monitoring requirements are selected by calculating the resolution, elevation angle, and theoretical 3D deformation accuracy. Finally, experiments are carried out based on the above methods to verify the correctness of the algorithm. This algorithm can greatly increase the optimization speed of the experimental configuration while reducing the amount of data storage and lays the foundation for the subsequent application of 3D deformation monitoring in disaster areas.

References 1. Cherniakov M (2002) Space-surface bistatic synthetic aperture radar-prospective and problems. Radar, IET, pp 22–25 2. Zeng Z, Antoniou M, Zhang Q et al (2013) Multi-perspective GNSS-based passive BSAR: preliminary experimental results. In: 2013 14th international Radar symposium, vol 1. IEEE 3. Liu F, Fan X, Zhang T et al (2018) GNSS-based SAR interferometry for 3-D deformation retrieval: algorithms and feasibility study. IEEE Trans Geosci Remote Sens 56(10):5736–5748

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4. Wang Z, Liu F, Shang R et al (2023) A novel multiangle images association algorithm based on supervised areas for GNSS-based InSAR. IEEE Geosci Remote Sens Lett 20:1–5 5. Sharp I, Yu K, Guo Y (2009) GDOP analysis for positioning system design. IEEE Trans Veh Technol 58(7):3371–3382 6. Zhang R, Tu R, Liu J et al (2018) Impact of BDS-3 experimental satellites to BDS-2: service area, precise products, precise positioning. Adv Space Res 62(4):829–844 7. Wang Z, Liu F, Lv R et al (2022) Data acquisition of GNSS-based InSAR: joint accuracyefficiency optimization of 3-D deformation retrieval. IEEE J Sel Topics Appl Earth Observ Remote Sens 15:7886–7898 8. Wang Z, Liu F, Zhang L et al (2019) Full-time resolution analysis and path determination for air borne forward-looking SAR with opportunistic illuminator. In: 2019 IEEE international conference on signal, information and data processing. IEEE 9. Zeng T, Cherniakov M, Long T (2005) Generalized approach to resolution analysis in BSAR. IEEE Trans Aerosp Electron Syst 41(2):461–474 10. Wang Z, Liu F, Zeng T et al (2021) Interferometric phase error analysis and compensation in GNSS-InSAR: a case study of structural monitoring. Remote Sensing 13(15):3041

GNSS Carrier Tracking via a Variational Bayesian Adaptive Kalman Filter for High Dynamic Conditions Song Li, Chunjiang Ma, Pengcheng Ma, Honglei Lin, Xiaomei Tang, and Feixue Wang(B) National University of Defense Technology, Changsha 410073, China [email protected]

Abstract. Under high dynamic conditions, a robust carrier tracking approach is essential for global navigation satellite system (GNSS) receivers. In this paper, the powerful Kalman filter (KF) technique is adopted in GNSS carrier tracking. The correlation signals are used as system measurements to discard the discriminator restricted by linear region. Then, a linear measurement equation is established based on the error-state, so that the system model is linear. Hence the KF can be used instead of the nonlinear KF which requires more computational costs. Furthermore, to exploit the potential of the KF under different conditions, an adaptive KF (AKF) based on the variational Bayesian approach is proposed. The proposed filter has accurate and robust estimation performance, especially under high dynamic conditions. Simulation results verify the applicability of the proposed system model and the superiority of the proposed filter compared with the traditional KF and existing AKFs. Keywords: GNSS receiver · Carrier tracking · Adaptive Kalman filter · High dynamic conditions

1 Introduction Carrier synchronization is fundamental in any communication or positioning system’s receiver side. The traditional phase-locked loop (PLL), although simple to tune and widely used, its applicability is severely limited in harsh propagation environments, particularly under high dynamic conditions. This is because the PLL requires a large enough noise bandwidth to tolerate the dynamic hence the noise performance of the loop deteriorates accordingly [1]. In the future, the communication and navigation integration signal might be transmitted by low earth orbit satellites and applied at Ka-band (26.5–40 GHz). As the satellite dynamics and carrier frequency are extremely high, the signal dynamics are increased accordingly. Therefore, the high dynamic carrier tracking problem will be a common problem for receivers. The inertial navigation system can be used to provide dynamic information, reducing the noise bandwidth of the PLL under high dynamic conditions. However, it increases the cost and only works for dynamic users. As an alternative approach, the Kalman filter © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 379–389, 2024. https://doi.org/10.1007/978-981-99-6932-6_31

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(KF), a powerful estimation technique, can be used in carrier tracking to provide better tracking accuracy and dynamic performance than the PLL. The KF can replace the loop filter by using the phase discriminator output as system measurements [2]. However, the phase estimate accuracy is limited to the nonlinearity of the discriminator. To address this issue, the correlation signals can be adopted directly as the measurements of the KF, so that the discriminator is not required [1, 3, 4]. In addition, to overcome the negative impact of the data bit sign transition (DBST) on the phase estimation, the correlation signals are squared rather than used immediately [5]. However, there are still two problems that have not been concerned about enough in the previous work. On the one hand, the measurement equation is nonlinear due to the usage of correlation signals as system measurements. So, the nonlinear KF, such as the extended KF (EKF) or the unscented KF, is needed. It imposes a large computational burden on the receiver. On the other hand, the filter tuning of the KF is not discussed sufficiently in the previous work. In reality, the filter tuning is critical to the KF for the expected performance. This problem hinders the usage of the KF to some extent. Therefore, it is common to use the adaptive KF (AKF) technique to make the filter have the ability to tune itself adaptively under different conditions. The covariance matching methods, including the Sage-Husa AKF (SHAKF) [6] and the innovation-based AKF (IAKF) [7], are widely used, but have the risk of filtering divergence. The strong tracking filter (STF) [1] and the forgetting factor-based AKF (FFAKF) [8] have been successfully applied in the field of carrier tracking. However, these filters still have shortcomings in terms of the balance between filter robustness and estimation accuracy. The contribution of this paper is twofold: (1) A linear measurement equation using the correlation signals directly as system measurements is proposed based on the errorstate. Thus, the nonlinear KF with more computation is not required in this situation. (2) A novel AKF using the powerful variational Bayesian (VB) approach is proposed and adopted in the carrier tracking problem. It is more robust and more accurate than existing filters, especially under high dynamic conditions. This paper is organized as follows Sect. 2 briefly introduces the signal model Sect. 3 presents the system model and the proposed filter. Section 4 performs simulations and analyzes the results. Finally, conclusions are drawn in Sect. 5.

2 Signal Model The received intermediate-frequency signal of a global navigation satellite system (GNSS) receiver can be modeled as s(t) = A · D(t − τ ) · c(t − τ ) · cos(2π(fIF t + fd t + θ )) + n(t)

(1)

where t is the time, A is the signal amplitude, D(·) is the navigation data bit, c(·) is the pseudo-random noise code, τ is the signal delay, fIF is the intermediate frequency, fd is the carrier Doppler frequency, θ is the initial carrier  phase, and n(t) is the Gaussian white noise with two-sided power spectral density N0 2. Then, after correlation, the in-phase (I) and quadrature-phase (Q) correlation signals are obtained as IP,k = Ak · Dk · R(δτk ) · sin c(δfk · T ) · cos(2π · δθk ) + nI,k QP,k = Ak · Dk · R(δτk ) · sin c(δfk · T ) · sin(2π · δθk ) + nQ,k

(2)

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where “P” stands for “prompt”, T is the coherent integration time, k is the time index corresponding to T, δ denotes the error terms, R(·) is the code auto-correlation function, sin c(x) = sin(πx) πx, and nI,k and nQ,k are Gaussian white noise terms.  Assume that the code has already synchronized and when δfk · Tc  1 2 then the signal amplitude attenuation due to δfk can be ignored. Then, (2) can be rewritten as IP,k = Ak · Dk · cos(2π · δθk ) + nI,k QP,k = Ak · Dk · sin(2π · δθk ) + nQ,k

(3)

Based on (3), the phase or the frequency error can be extracted by some parameter estimation methods. In this paper, the KF-based approach is adopted.

3 Proposed Technique In this section, the system model is first established and then a novel AKF is proposed. 3.1 System Model State Equation The state is used to describe the dynamic behavior of the carrier phase, and in this paper, the carrier phase, Doppler frequency, Doppler frequency rate, and Doppler frequency second-order rate are selected: Xk = [θ, f , f˙ , f¨ ]Tk

(4)

where [·]T denotes the transpose operation. The linear propagation equation of Xk is ⎡

1T ⎢0 1 =⎢ ⎣0 0 00

Xk = F · Xk−1 + B · uk−1 + ηk−1 ⎡ ⎤ ⎡ ⎤   ⎤ ηθ T T 2 2 T 3 6 ⎢ ⎥ ⎢ ⎥ ⎢ ηf ⎥ 0⎥ T T2 2⎥ ⎢ ⎥Xk−1 + ⎢ ⎢ ⎥ · fIF + ⎢ ⎥ ⎥ 1 T ⎦ ⎣ 0⎦ ⎣ ηf˙ ⎦ 0 1 0 ηf¨

(5)

k−1

where F is the state transition matrix, B is the input matrix, uk−1 is the input vector, ηk = [ηθ , ηf , ηf˙ , ηf¨ ]Tk is the Gaussian process noise vector with zero mean vector and covariance matrix Qk as    ⎤ ⎡ 7 T 252 T 6  72 T 5 30 T 4 24 ⎢ T 6 72 T 5 20 T 4 8 T 3 6 ⎥     ⎥ (6) Qk = q⎢ ⎣ T 5 30 T 4 8 T 3 3 T 2 2 ⎦    T T 4 24 T 3 6 T 2 2 where q denotes the one-sided power spectral density of ηf¨ .

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The error terms of Xk are chosen as state variables: δXk = [δθ, δf , δf˙ , δf¨ ]Tk

(7)

where the notation δX indicates the error-state. So, the state equation is obtained as δXk = F · δXk−1 + ηk−1

(8)

Note that the state vector estimate is obtained by adding the error-state vector estimate as follows: ˆk Xk+1 = F · Xk + B · uk + δX

(9)

After that, the corresponding terms of Xk+1 are used to generate the local replica signals for the next time correlation processing. Measurement Equation In order to eliminate the influence of the DBST on the estimation of the carrier phase, the squaring operation is applied in (3) as follows [5]:  2  2

A · cos(2π · 2 · δθ ) ξI IP − QP2 = + (10) 2 2IP · QP k ξQ A · sin(2π · 2 · δθ ) k

k

2 + Q2 . where A2k can be estimated as A2k = IP,k P,k So, (10) can be rewritten as 

Zk = h(δXk ) + ξk where ξk denotes the measurement noise vector, and  2 Ak · cos(L · δXk ) h(δXk ) = A2k · sin(L · δXk ) L = 2π · [2, 0, 0, 0]

(11)

(12) (13)

The measurement equation is nonlinear with respect to the state variables, thus the Jacobian matrix is obtained as ⎡ ⎤  2

ˆ · sin L · δ X −A k  ∂h(δXk ) k ⎥ ⎢

 ⎦·L  (14) Hk =⎣

∂δXk δXk =δXˆ ˆ A2k · cos L · δX k k ˆ − denotes the a priori estimate of the error-state. where δX k Since the process model (see (8)) is an error-state model, the a posteriori estimate of the error-state should be reset to zero at the end of each filtering process. Based on this, substituting (13) into (14) obtains

 0000 Hk = 2π · A2k · (15) 2000

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As can be seen in (15), the first row of Hk is all zero, which means that the first term of the measurement vector is redundant. Thus, the measurement model can be further simplified as   2IP,k · QP,k = 2π · A2k · 2 0 0 0 δXk + ξQ,k (16)       Zk

Hk

So far, the measurement model has been established. Different from the nonlinear measurement model in (11), the proposed measurement model is linear and only onedimensional. Therefore, the computational burden is obviously lower. In the subsequent simulation, the validity of the proposed measurement model will be confirmed. 3.2 Proposed AKF Fine filter tuning is demanded by the KF, but it is usually not simple. To solve this problem, many AKFs are being developed in a wide range of application fields. Reference [9] proposed the VBAKF for linear systems, which aims to infer xk together with Pk|k−1 and Rk using the VB approach. Inspired by the VBAKF, it is preferred to estimate xk while tuning Rk only to obtain more robust filtering performance. As a result, the VBAKF is adapted accordingly. The proposed filter is referred to as the VBAKF-R, whose implementation pseudocode is summarized in Table 1. In Table 1, m is the dimension of the measurement, ρ ∈ [0, 1] is a forgetting factor, ˆ k−1|k−1 can be respectively initialized as N is the number of iterations, uˆ k−1|k−1 and U ˆ 0|0 = τ R ˜ 0 , uˆ 0|0 = m + 1 + τ , where τ ≥ 0 is a tuning parameter, and R ˜0 follows: U represents the initial nominal measurement noise covariance matrix which is selected based on engineering experience. More details are referred to [9].

4 Simulation Results The high dynamic condition chosen for performance validation in this work is defined by the American Jet Propulsion Laboratory [10]. One GPS L1 C/A signal is generated using a software signal generator. Simulations are conducted in terms of two aspects. First, the effectiveness of the proposed system model under DBST is verified. Then, the performance of the proposed filter is tested under different scenarios. 4.1 Validity of the Proposed System Model In this simulation, the validity of the proposed system model is confirmed. The process model is chosen as shown in (8), and several different types of measurement information are considered, including M1: [IP , QP ]T , M2: [IP2 − QP2 , 2IP · QP ]T (see (10)), and M3: 2IP · QP (proposed, see (16)).

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Algorithm implementation Inputs: ˆ k−1|k−1 , m, ρ, N xˆ k−1|k−1 , Pk−1|k−1 , Fk−1 , Hk , zk , Qk−1 , uˆ k−1|k−1 , U Prediction: 1. xˆ k|k−1 = Fk−1 xˆ k−1|k−1 T 2. Pk|k−1 = Fk−1 Pk−1|k−1 Fk−1 + Qk−1 Update: (0)

(0)

3. xˆ k|k = xˆ k|k−1 , Pk|k = Pk|k−1 , uˆ k|k−1 = ρ(ˆuk−1|k−1 − m − 1) + m + 1, ˆ k|k−1 = ρ U ˆ k−1|k−1 U for i = 0 : N − 1 (i)

(i)

(i)

(i)

4. k = (zk − Hk xˆ k|k )(zk − Hk xˆ k|k )T + Hk Pk|k HkT (i+1)

ˆ (i+1) = (i) + U ˆ k|k−1 = uˆ k|k−1 + 1, U k|k k  ˆ (i+1) = U ˆ (i+1) (ˆu(i+1) − m − 1) 6. R k k|k k|k 5. uˆ k|k

(i+1)

7. Kk

(i+1) −1 )

ˆ = Pk|k−1 HkT (Hk Pk|k−1 HkT + R k

(i+1)

= xˆ k|k−1 + Kk

(i+1)

= Pk|k−1 − Kk

8. xˆ k|k

9. Pk|k

(i+1)

(zk − Hk xˆ k|k−1 )

(i+1)

Hk Pk|k−1

end for (N ) (N ) (N ) ˆ ˆ (N ) 10. xˆ k|k = xˆ k|k , Pk|k = Pk|k , uˆ k|k = uˆ k|k , U k|k = Uk|k Outputs: ˆ k|k xˆ k|k , Pk|k , uˆ k|k , U

Several tracking schemes are tested, which are listed below. • the traditional third-order PLL (50 Hz noise bandwidth) • the EKF (M1/M2) • the KF (M2/M3) The simulation parameters are as follows. The carrier-to-noise ratio (C/N 0 ) of the GPS signal is set to 40 dB-Hz. The coherent integration time T is 1 ms. To the different tracking schemes using the KF (or other KF variants), the parameters of the filters are ˜0 = given by: xˆ 0|0 = [0, 0, 0, 0]T , P0|0 = diag([10, 10, 108 , 108 ]), qT = 1002 , R diag([(107 )2 , (107 )2 ]) (for M2), and R˜ 0 = (107 )2 (for M3). Figure 1 shows the carrier tracking errors of different models. It is clear that the KFbased tracking loop with original measurements (M1) loses lock on the signal quickly due to the filtering divergence caused by DBST. However, the other three methods are able to track the signal. In addition, the PLL-based tracking loop suffers from significant tracking errors. This is because the PLL-based tracking loop requires a large noise

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bandwidth to track the high dynamic signal, which increases the tracking error. In contrast, the KF- and EKF-based tracking loops with modified measurements (M2/M3) achieve the smallest tracking error as expected. And the performance of these methods is exactly the same, confirming the validity of the proposed measurement model (M3). In addition, the proposed measurement model has the advantage of being linear and only one-dimensional, indicating that it is more cost-effective.

(a) Carrier phase error

(b) Doppler frequency error

Fig. 1. Carrier tracking errors of different models

4.2 Performance of the Proposed Filter In the previous simulation, only the traditional KF is adopted for state estimation. However, the traditional KF has the inherent defect of not being able to adjust itself to adapt to different conditions, e.g., different C/N 0 and filter parameter conditions. To overcome this problem, the proposed filter (VBAKF-R) is adopted in this simulation. Two simulation scenarios are conducted to test the proposed filter under different conditions. First, different C/N 0 conditions are tested, and typically, the C/N 0 is set to 35, 40, and 45 dB-Hz, respectively. Second, different filter parameter conditions are tested, and specifically, three cases are considered: A1: R˜ 0 = (106 )2 , A2: R˜ 0 = (107 )2 , and A3: R˜ 0 = (108 )2 . Note that for the sake of simplicity, A1, A2, and A3 will be used to represent the different filter parameters in the following. In addition to the traditional KF and the proposed filter, the following existing filters are tested for comparison: the SHAKF [6], the IAKF [7], the STF [1], and the FFAKF [8]. All filters are run on the basis of the proposed system model. In the proposed filter, the parameters are set as follows: the tuning parameter τ = 3, the forgetting factor ρ = 0.99, and the number of iterations N = 10. The parameters for the other filters are chosen according to related papers, and the common parameters of all filters are set to the same value for a fair comparison. Unless specifical instruction, the simulation parameters are the same as in the previous simulation. Note that the IAKF and the SHAKF are always found filtering divergence, so their simulation results are not shown in the subsequent simulation.

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Figures 2, 3, 4 and 5 show the carrier tracking errors of the STF, the FFAKF, and the proposed filter, respectively. The STF suffers from the same problem as the KF, and it can be deduced that its adaptive logic that adopts a time-variant fading factor is not suitable under high dynamic conditions. The FFAKF shows robustness under different filter parameter conditions when C/N 0 is high, but diverges under low C/N 0 conditions. This is because it uses the most recent information and discards the previous information, thus reducing the negative effect of the old, inaccurate predicted information, at the cost of reducing the estimation accuracy. In contrast, the influence of different filter parameters on the proposed filter is negligible. Moreover, it achieves smaller estimation errors than existing filters under different C/N 0 and dynamic conditions, indicating that it has the expected self-tuning ability to adapt to different environments. In other words, the proposed filter can achieve more robust performance and better estimation accuracy compared with existing filters.

(a) Carrier phase error

(b) Doppler frequency error

Fig. 2. Carrier tracking errors of the KF

GNSS Carrier Tracking via a Variational Bayesian Adaptive

(a) Carrier phase error

(b) Doppler frequency error

Fig. 3. Carrier tracking errors of the STF

(a) Carrier phase error

(b) Doppler frequency error

Fig. 4. Carrier tracking errors of the FFAKF

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(a) Carrier phase error

(b) Doppler frequency error

Fig. 5. Carrier tracking errors of the proposed filter

5 Conclusion In this paper, the GNSS carrier tracking using the KF technique under high dynamic conditions is studied. The proposed technique involves two aspects. First, based on the error-state, a linear system model is established using the correlation signals as system measurements. Based on the linear system model, the KF can be used instead of the nonlinear KF to save computational costs. Second, a novel AKF is proposed and adopted in GNSS carrier tracking. The proposed filter has the expected ability to tune itself adaptively according to different conditions, so it outperforms existing filters in terms of both robustness and accuracy. The proposed technique is expected to exploit the full potential of the KF technique to provide receivers with a more robust and accurate carrier tracking capability. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant No. U20A0193).

References 1. Ge Q, Shao T, Chen S et al (2017) Carrier tracking estimation analysis by using the extended strong tracking filtering. IEEE Trans Ind Electron 64(2):1415–1424 2. Niu X, Li B, Ziedan NI et al (2017) Analytical and simulation-based comparison between traditional and Kalman filter-based phase-locked loops. GPS Solut 21(1):123–135 3. Psiaki ML, Jung H (2002) Extended Kalman filter methods for tracking weak GPS signals. In: Proceedings of the 15th international technical meeting of the satellite division of the institute of navigation (ION GPS 2002), Portland, OR, pp 2539–2553 4. Ziedan NI, Garrison JL (2004) Extended Kalman filter-based tracking of weak GPS signals under high dynamic conditions. In: Proceedings of the 17th international technical meeting of the satellite division of the institute of navigation (ION GNSS 2004), Long Beach, CA, pp 20–31

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5. Han S, Wang W, Chen X et al (2010) Design and capability analyze of high dynamic carrier tracking loop based on UKF. In: Proceedings of the 23rd international technical meeting of the satellite division of the institute of navigation (ION GNSS 2010), Portland, OR, pp 1960–1966 6. Sage AP, Husa GW (1969) Adaptive filtering with unknown prior statistics. In: Joint automatic control conference, Boulder, CO, USA, pp 760–769 7. Mohamed AH, Schwarz KP (1999) Adaptive Kalman filtering for INS/GPS. J Geodesy 73(4):193–203 8. Tang X (2005) Carrier recovery and carrier to noise estimation in high-quality navigation receiver. Master’s thesis, National University of Defense Technology 9. Huang Y, Zhang Y, Wu Z et al (2017) A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices. IEEE Trans Automat Control 63(2):594–601 10. Vilnrotter VA, Hinedi S, Kumar R (1989) Frequency estimation techniques for high dynamic trajectories. IEEE Trans Aerosp Electron Syst 25(4):559–577

BOC Signal Spoofing Detection Based on Multi-correlator Signal Quality Monitoring Method Mingxuan Liang, Zhengkun Chen, Zhijian Zhou, Xuelin Yuan, and Xiangwei Zhu(B) Sun Yat-sen University, Shen Zhen, China [email protected]

Abstract. Due to the open structure and the low receiving power of the global navigation satellite system (GNSS) signal, the receiver is vulnerable to some malicious spoofing interference. The signal quality monitoring (SQM) algorithm is favored because it can simply and effectively detect the correlation peak distortion in the spoofing interference. In this paper, we focus on the SQM metrics for BOC (1,1) component of the B1C signal, firstly introduce some existing SQM metrics of BOC (1,1) signal, then the statistical characteristics and detection threshold of the metrics are analyzed. On this basis, the metrics are merit-based selected by the receiver operating characteristic (ROC) curve and the curve of detection rate in the simulation experiment, and the metrics are verified by the mathematical modeling on the basis of the experimental spoofing scenario, which proves that the metrics participating in the combination are complementary. Finally, the metrics are combined under the condition of a low correlation. The experimental results show that compared with the existing metrics, the metrics obtained by the merit-based selection and combination have better performance in spoofing detection. Keywords: Spoofing Detection · BOC Signal · SQM · Multi-correlator

1 Introduction With the continuous improvement of China’s BeiDou satellite navigation system, the B1C signal as a new type of civil global satellite signal has been providing navigation, positioning and timing services in many fields, but due to the open structure and low receiving power of the signal, the receiver is vulnerable to some malicious spoofing signal interference, resulting in the final output of wrong results. This poses a serious threat to the safe operation of the whole system, and numerous incidents have shown that very serious consequences may occur when the receiver is controlled by spoofing signals [1–3]. In recent years, researchers have proposed many spoofing detection algorithms, one of which, SQM, is favored for its simplicity and effectiveness in spoofing detection. The SQM algorithms were originally applied to detect the distortion of correlation peaks caused by multipath effects. Since the power of the spoofing signal is similar to the © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 390–401, 2024. https://doi.org/10.1007/978-981-99-6932-6_32

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authentic signal during an intermediate spoofing interference, the correlation peaks produce severe distortion when the two meet and superimpose, so the SQM algorithms can also be applied in such spoofing detection. The SQM algorithms have the advantage that the detection metrics generally have a simple structure with low complexity and can effectively reflect whether the correlation peaks are symmetrical, deformed, etc. At present, there are many SQM algorithms for spoofing detection: the Delta metric uses the ratio of the difference between the output of the early and late correlators and the output of the prompt correlator to reflect the symmetry of the correlation peaks [4]; the Ratio metric uses the ratio of the output of the early or late correlators to the output of the prompt correlator to reflect the deformation of the correlation peaks [5]; Sun proposed to use the moving variance of Delta and Ratio metrics as a new type of spoofing detection metric [6]. However, the above SQM algorithms are all directed to the traditional BPSK signal. Due to the correlation peak characteristics of BOC signal are very different from those of BPSK signal. Some other scholars have studied the SQM algorithm for BOC signal. Wang [7] used the squared subpeak difference of the BOC (1,1) correlation peak as a detection metric, which was able to detect forwarded spoofing interference well, but the algorithm failed when the main peak of the authentic signal correlation peak is deformed. Jahromi [8] proposed various detection metrics such as , symmetry and asymmetry metrics for the E1 band signal of the Galileo satellite navigation system, which can detect the presence of asymmetry or deformation of BOC signal correlation peaks, but they did not consider the complementarity between the detection metrics. In this paper, based on the existing BOC (1,1) SQM metrics, we analysis the performance of their ROC curves and detection rate curves, and the correlation coefficients between them are considered, finally the metrics are merit-based selected and combined to obtain a new metric. And the simulation experiments show that the performance of the combined new metric is significantly better than that of existing metrics. The subsequent sections of the paper are organized as follows: Sect. 2 introduces the signal model, Sect. 3 presents the spoofing detection algorithm, Sect. 4 shows the merit-based selection and combination of metrics and the experimental simulation results, and Sect. 5 is the conclusion.

2 Signal Model When spoofing is present, the receiver receives the authentic signal, spoofing signal and noise at the same time. If each authentic signal has a spoofing signal corresponding to it, then the received signal can be expressed as follows: x(t) =

N 

(xia (t) + xis (t)) + n(t)

(1)

i=1

x(t) denotes the received satellite navigation signal, xia (t) and xis (t) are the i-th authentic signal and the spoofing signal, respectively, n(t) is the Gaussian thermal noise. In order to successfully spoof the tracking loop of the receiver, the structure of the authentic

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signal and the spoofing signal is approximately the same. Thus the i-th authentic signal and the spoofing signal can be expressed as:  a/s a/s a/s a/s a/s a/s xi (t) = Pi Di (t − τi )Ci (t − τi ) a/s

a/s

× sci (t − τi

)ej(2π fi

a/s

a/s

t+φi )

(2)

Where P, τ , f and φ correspond to the power, code phase, carrier frequency and carrier phase, respectively, and D is the navigation data bits, C is the pseudo-random code, sc is the subcarrier, the subscripts represent the i-th signal, and the superscripts a/s represent the authentic signal and the spoofing signal respectively. The subcarrier in BOC modulation is usually divided into two types: sine subcarrier and cosine subcarrier, where the expression of the sine subcarrier is shown below: sc(t) = sign(sin(2π fsc t))

(3)

sign(·) is the sign function, fsc is the subcarrier frequency, consider the BOC (1,1) signal, then the subcarrier frequency and PRN code rate are numerically equal. In the tracking loop, the receiver generates a carrier locally and multiplies it with the received signal for carrier demodulation. Then, it performs correlation and coherent integration with the locally generated PRN code to obtain the correlator output. When the tracking loop is locked to the authentic signal, the carrier and the PRN code of the authentic signal are completely stripped off, so the output of correlator I in the n-th coherent integration epoch can be expressed as follows [9–11]:  I Ii,dI (n) = Pia Dia (n)R(dI Tc ) + ηi,d I  s,L s + Pis Di (n)R(dI Tc − τi )

φis,L

× sin c(fis,L Tcoh ) cos(φis,L )

(4)

  Tcoh t1 + + θis,L 2

(5)

= 2π fi

s,L

R(·) is the autocorrelation function of the BOC (1,1) signal, dI Tc denotes the code phase interval between the correlator I and the prompt correlator, where dI is the dimensionless unit, Tc is the width of the pseudo-random code without the subcarrier, τ is,L , f is,L , φ is,L and θ is,L denotes the code phase difference, carrier frequency difference, carrier phase difference and carrier initial phase difference between the spoofing signal and the local signal respectively, t1 is the start time of the n-th coherent integration, Tcoh I is the Gaussian thermal noise. is the coherent integration period, and ηi,d When spoofing is not present, the correlator output obeys a Gaussian distribution with the following mean and variance [8]:  μI = 2 · (C/No ) · Tcoh · R(dI Tc ) σI2 = 1

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  σI21 ,I2 = R dI1 − dI2 Tc

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C/N0 is the signal carrier-to-noise ratio, Tcoh is the coherent integration time of the tracking loop, R(·) is the autocorrelation function of the BOC (1,1) signal, dITc is the code phase interval from correlator I to the prompt correlator, and dI1 − dI2 Tc is the code phase interval between the correlators I1 , I2 .

3 The Spoofing Detection Algorithm 3.1 Multi-correlator SQM Detection Metrics Compared with the BPSK signal, the autocorrelation function of the BOC signal is a multi-peak structure, the main peak is narrower and contains negative peaks, so more correlators need to be used to characterize the correlation peak characteristics when using SQM for BOC signal. To be able to more fully characterize the correlation peaks of BOC (1,1) signal, the literature [8] set the position of the correlators according to Fig. 1, and on this basis, three types of metrics, symmetry, asymmetry and , are constructed to reflect whether the correlation peak is symmetrical or deformed. Symmetry metrics : mi =

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A in Eq. (7) is the Jacobi matrix, and the elements are the partial derivatives of each metric with respect to each correlator output, for the convenience of representation, all correlator outputs are represented in a vector as: I = I−1.0 , I−0.5 , I−0.1 , I−0.05 , I0 , I0.05 , I0.1 , I0.5 , I1.0 , then the element in the i-th row and

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Fig. 1. BOC (1,1) Correlator branches

 j-th column in A can be expressed as aij 14×9 = ∂I∂m(j)i , where i = 1, 2, …13, 14, j = 1,2, …8, 9. D(I ) is the covariance matrix of the correlator outputs, and the element in the i-th row and j-th column can be expressed as dij 9×9 = σI (i),I (j) , where i, j = 1, 2, 3…, 8, 9. The correlation coefficient of the metrics can be obtained from D(m) as follows: σmi mj (11) ρmi ,mj = σmi σmj Although the metric is constructed by dividing two Gaussian variables, which can no longer be regarded as a Gaussian variable in theory, in the case of the input signal with a high carrier-to-noise ratio, the noise in the output of the prompt correlator can be ignored, which means that the output of the prompt correlator can be regarded as a constant, so the metric can still be considered as obeying the Gaussian distribution [12], and the mean value is the combination of the combined correlators output means, the variance is as follows [8]: ση2i =

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The probability distribution of each detection metric is fitted in the absence of spoofing, and the fitting result of the m13 is taken as an example. The simulation output histograms and the theoretical probability density function (PDF) of the m13 are shown in Fig. 2a, and the normal probability curve is shown in Fig. 2b. As can be seen from Fig. 2, the histogram and the PDF are well matched and the linearity of the normal probability curve behaves well, which demonstrates that the probability distribution and statistical properties of the metric are basically as expected. 3.3 Detection Threshold Analysis As analyzed before, the metrics can be regarded as obeying Gaussian distribution in the absence of spoofing interference, thus for the certain thresholds, the probability of false

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4 Merit-Based Selection and Combination of Metrics On the basis of the existing SQM metrics m1 –m14 , the process of the merit-based selection and combination are roughly as follows: firstly, we select the metric mr , which has the best performance of ROC curve among m1 –m14 , then select the metrics md that are

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complementary to the mr in detection rate, and removed md which has high correlation coefficient with mr , finally combine the metric mr and md to obtain the new metric. And in order to verify the feasibility of the method, a mathematical model of the detection metrics was built based on the experimental spoofing scenario, through which can derive the estimated value of the selected metrics to verify the complementarity between the metrics used in the combination. 4.1 Spoof Generation Experimental Scenario In order to test the performance of previously discussed method, BOC (1,1) data component of the B1C signal is generated by Matlab for experimental simulation of the spoofing scenario, and some specific experimental conditions are as follows: the coherent integration time is 10 ms, the Pfa is set to 10−5 , the C/No is 46 dB-Hz.

Fig. 3. The variation of the correlation function in the spoofing process

Total length of the signal is 20 s, and there is only authentic signal in 0–2 s, the spoofing signal is added at t = 2 s, its carrier is consistent with the authentic signal, its power is 3.6 dB higher than the authentic signal, and the relative delay of spoofing signal with respect to authentic signal changes linearly from −2Tc to +2Tc in 2–20 s, which makes the receiver tracking loop gradually locked to the spoofing signal. The overall process is shown in Fig. 3, as we can see, the receiver locked to the lower power authentic signal in the first several seconds, as the spoofing signal was added and the relative delay was gradually aligned, the receiver locked to the higher power spoofing signal in the last several seconds. 4.2 The Theoretical Basis of Merit-Based Selection and Combination To verify the complementarity among the subsequently merit-based selected metrics, the mathematical model of the metrics based on the current spoofing scenario was built. To simplify the analysis, 2 assumptions are proposed: 1. Since the effect of noise on the correlator output is relatively stable throughout the spoofing process, and the distortion effect is negligible compared to that produced by the superposition of correlation peaks, the noise is ignored in the analysis; 2. The tracking loop of the receiver stably locked to

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the authentic signal before the relative delay is aligned, and after that stably locked to the spoofing signal. Since the relative delay of spoofing signal with respect to authentic signal changes linearly from −2Tc to +2Tc in 2-20 s, the power of the spoofing signal is 1.44 times that of the authentic signal (3.6 dB), and the tracking loop locked to the authentic signal before the relative delay is aligned (t = 11 s), so the output of the correlator Ik with code phase interval kTc to prompt correlator can be expressed as: Ik (t) = 1.2R(k − a(t − 2) + 2) + R(k), 2 < t < 11

(16)

Where R(·) is the autocorrelation function of the BOC (1,1) signal, and since the relative delay of spoofing signal with respect to authentic signal changes linearly from −2Tc to +2Tc in 2–20 s, so it is easy to obtain a = 29 . When the tracking loop locked to the spoofing signal, the authentic signal should be considered as the moving side, thus Ik in t = 11–20 s can be expressed as: Ik (t) = R(k + a(t − 2) − 2) + 1.2R(k), 11 < t < 20 Therefore, the estimated value of the metric mi can be expressed as:  bk Ik (t) mi (t) = I0 (t)

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(18)

The value of bk depending on the composition of the metric mi in Eqs. (7–9). 4.3 Merit-Based Selection of Metrics In the previously described spoofing scenario, we get the output of metrics m1 –m14 and their corresponding detection thresholds as shown in Fig. 4a, where the blue solid line and red solid line are corresponding to the period 0–2 s with no spoofing and 2–18 s with spoofing, respectively. Figure 4b shows the ROC curves for m1 –m14 . From the ROC curves, we can see that the metric m11 has the best detection performance, and the detection rate can reach about 83% when the false alarm rate is 10%, it can also be seen from Fig. 4a that there is a prominent response throughout the process in 2–20 s, so we choose m11 as the aforementioned mr . Figure 5 shows the detection rate curves of metrics m1 –m14 . The detection rate here is computed within a moving window of 2 s, which means that the detection rate at t =n s actually represents the detection rate in n − 2 − n s. As we can see in Fig. 5: for m11 , although the detection rate is high for most of the time, it decreases significantly in 10–16 s, so the metrics that perform better in this period is selected as the previously mentioned md to complement with m11 . Table 1 gives the highest detection rate and the corresponding detection metric for each time period in Fig. 5. According to Table 1, we choose the m7 (the highest DR metric at t = 10 s), m6 (the highest DR metric at t = 12 s), m9 (the highest DR metric at t = 14 s) as md . The theoretical output value of m11 , m7 , m6 , m9 which were calculated by Eqs. (16– 18) and the corresponding actual output value are shown in Fig. 6. It can be seen from

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metrics are indeed complementary. However, there is a large difference between the actual output value and the theoretical output value for m6 in 9–13 s. This is because the output value of m6 contains the output of late correlator (+0.05Tc ), which will be constantly adjusted during the tracking process. However, the overall period that exceeds the detection thresholds is in line with expectations.

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4.4 Combination of Metrics After the merit-based selection, the correlation coefficients between the metrics were calculated as shown in Fig. 7, and the correlation coefficient below 0.8 is considered as low correlation [8]. According to the figure, the correlation coefficients between the detection metrics involved in the combination are all below 0.8, meeting the low correlation requirements. ⎧ 1 ⎪ m15 = m11 + ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎨ m16 = m11 + 3 1 ⎪ ⎪ ⎪ m17 = m11 + ⎪ ⎪ 3 ⎪ ⎪ ⎪ ⎪ ⎩ m = 1m + 18 11 4

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Fig. 7. Correlation coefficients for merit-based selected metrics

metrics, but the peak value decreases at the same time. And it can be seen from the m15 –m18 that: the more metrics involve in the combination, the more samples exceed the detection threshold, and the peak value become lower. It illustrates that the detection rate is improved with the cost of the peak value getting smoothed. It can also be seen from the ROC curve performance in Fig. 8b that the ROC curve performance of the combined metrics has improved compared with that of the existing metrics, and the detection rate of the combined metric m17 has reached more than 90% when the false alarm rate is 10%. Although the detection metric m18 is composed of four metrics, the detection performance is not as good as m17 , indicating that the more the metrics involved in the combination is not the better. If there are too many metrics participating in the combination, the smoothing effect of the peak value will be obvious, even make the peak value lower than the detection thresholds, resulting in a poor detection performance. 100

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5 Conclusion The characteristics of BOC signal, such as multiple correlation peaks, narrow main peak and negative sub-peak, make it quite different from the traditional BPSK signal when using SQM for spoofing detection, and the existing detection metrics of BOC signal don’t consider the mutual complementarity. In this paper, based on the BOC signal SQM

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detection metrics m1 –m14 , new SQM detection metrics are obtained through the meritbased selection and combination. The experimental simulation shows that, compared with the existing detection metrics, the detection performance of the combined metrics is more excellent. It also shows that the more detection metrics involved in the combination is not the better. When there are too many metrics involving in the combination, the detection performance may even become worse because the peak value of the detection metrics is smoothed excessively. The method proposed in this paper can be used not only for spoofing detection, but also for multi-path signal detection in complex environments. Acknowledgement. This work was financially supported by the Shenzhen Science and Technology Program (Grant No.JSGG20201102163400002, 20201026143857003).

References 1. Zhijun W, Yun Z, Yiming Y et al (2020) Spoofing and anti-spoofing technologies of global navigation satellite system: a survey. IEEE Access 165444–165496 2. Jones M (2017) Spoofing in the Black Sea: what really happened. GPS World 3. Psiaki ML, Humphreys TE (2016) GNSS spoofing and detection. In: Proceedings of the IEEE, pp 1258–1270 4. Yang Y, Li H, Lu M (2015) Performance assessment of signal quality monitoring based GNSS spoofing detection techniques. In: Proceedings of the 6th China satellite navigation academic annual conference. Springer, Heidelberg, pp 783–793 5. Manfredini EG, Dovis F, Motella B (2014) Validation of a signal quality monitoring technique over a set of spoofing scenarios. In: Proceedings of the 2014 7th ESA workshop on satellite navigation technologies and European workshop on GNSS signals and signal processing (NAVITEC), pp 1–7 6. Sun C, Cheong JW, Dempster AG et al (2018) Moving variance-based signal quality monitoring method for spoofing detection. GPS Solut 22(5):1–13 7. Zhiying W, Yucen L, Menglan W (2020) Symmetry detection algorithm to detect forwarded spoofing interference signals of BOC modulation receivers. In: IOP conference series: materials science and engineering 8. Jahromi AJ, Broumandan A, Daneshmand S et al (2016) Galileo signal authenticity verification using signal quality monitoring methods. In: Proceedings of the 2016 international conference on localization and GNSS (ICL-GNSS) 9. Gao Y, Lv Z, Zhang L (2020) Asynchronous lift-off spoofing on satellite navigation receivers in the signal tracking stage. IEEE Sens J 15(20):8604–8613 10. Xie G (2017) GPS principle and receiver design. Electronic Industry Press 11. Zhou W, Lv Z, Deng X et al (2022) A new induced GNSS spoofing detection method based on weighted second-order central moment. IEEE Sens 22(12):12064–12078 12. Huang J, Presti LL et al (2016) GNSS spoofing detection: theoretical analysis and performance of the ratio test metric in open sky. ICT Express 2(1):37–40 13. Benachenhou K, Bencheikh ML (2021) Detection of global positioning system spoofing using fusion of signal quality monitoring metrics. Comput Electr Eng 92:107159

A GNSS Spoofing Detection Method Based on CNN-DOA Chuhan Huang, Zhengkun Chen, Xinzhi Peng, Jianjun Lu, Xuelin Yuan, and Xiangwei Zhu(B) Sun Yat-Sen University, Shenzhen, China [email protected]

Abstract. GNSS is an essential source of information for daily life, providing positioning and timing data. However, due to the low power of satellite navigation information at the receiving end, the open signal structure, as well as with the development of spoofing technology, the problem of spoofing and jamming at the receiving end has become increasingly severe. The GNSS spoofing detection technology based on DOA offers robust detection performance, which can adapt to various scenarios. To address the issues of low angular resolution and poor detection performance in a low SNR environment, we propose a CNN-DOAbased spoofing detection method. Firstly, we use the Toeplitz matrix reconstruction algorithm to estimate the DOA of the coherent signal. Then, we use the DOA spectrum generated by random angle distribution and random SNR as samples, with the DOA value and authenticity of the signal used as labels for CNN network training. When the power ratio of the spoofing signal to the authentic signal is greater than 1 dB (SNR = 0 dB), the detection accuracy of the spoofing signal is nearly 90%. Compared to the PI algorithm and the ADBF algorithm, the proposed model has higher resolution and robustness. Keywords: GNSS · Anti-deception · DOA estimation · Toeplitz matrix reconstruct

1 Introduction The Global Navigation Satellite System (GNSS) is a critical technology for both military and civilian use. In 2018 and 2020, the United States passed bills to fund resilience enhancement work and improve the comprehensive capabilities of GPS, highlighting the importance of spoofing detection and suppression algorithms [1]. Spread spectrum code verification and navigation information verification technology have been used to encrypt and authenticate navigation signals in [2, 3], but practical implementation can be challenging. The authors in [4] achieve spoofing detection by establishing new detection quantities of signal component power and noise level, which still performs well even when the authentic and spoofing signal powers are similar. However, this method cannot suppress multipath effects. In [5], two low-cost antennas are used to find the baseline vector by combining carrier phase difference and ephemeris data to achieve the detection of spoofing interference. However, it is not adaptable to dynamic © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 402–414, 2024. https://doi.org/10.1007/978-981-99-6932-6_33

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scenarios. The authors in [6] detect spoofing interference using the Direction of Arrival (DOA) of the received signal of the array antenna and suppress the interference using the complementary orthogonal space of the spoofing signal. However, it is ineffective when the spoofing source is not fixed. In [7], spatial spectrum estimation techniques are used in combination with adaptive array processing techniques for spoof detection. However, the angular resolution for detecting spoof is low. In recent years, deep learning has been applied to DOA estimation to improve angular resolution and detection performance. In [8], a fully connected deep neural network is used to perform bi-target DOA estimation, which is excellent for DOA estimation at high SNR but ineffective for low SNR. The DeepMUSIC framework proposed in [9] divides the estimated angular interval into several parts and uses parallel convolutional neural networks for estimation. This framework significantly improves the problem of poor estimation performance at low SNR. The authors in [10] construct a CNN-LSTM model for sound source localization, which eliminates the dependence of traditional DOA estimation on the spatial structure of the array. To address the problems of spoofing detection mentioned above, this paper proposes a CNN-DOA based spoofing detection method. The method utilizes a high angular resolution DOA estimation algorithm to detect spoof signals. The CNN network is used to solve the DOA estimation problem in low SNR environment and provides the possibility of spoof interference detection. In this study, we first use the Toeplitz matrix reconstruction algorithm for DOA estimation of coherent signals. Then the CNN network is built to learn the spatial-features containing the authentic signal and the spoofing signal, forming a spoofing detection model with good detection performance in a highresolution, low SNR environment. The trained network can output the incoming angle of the spoofing signal and the authentic signal.

2 Spoofing Interference Characteristics Spoofing interference can be classified into two categories: generative spoofing and forwarding spoofing, based on the form and characteristics of the spoofing signal. Generative spoofing involves the use of public navigation information to generate spoofing signals that are similar to real satellite signals, for the purpose of jamming. Forwarding spoofing, on the other hand, involves the use of spoofing sources to receive real satellite signals, which are then amplified and delayed in time before being forwarded to the target receiver to achieve the desired spoofing effect. Due to its simple implementation and low cost, forwarding spoofing is widely used. The schematic diagram of forwarding spoofing is shown in Fig. 1. We have identified the characteristics of forwarding spoofing interference, which involves the sum of the transmission distance d2 from the satellite signal to the spoofing source and the transmission distance d3 from the spoofing source to the receiver is greater than the transmission distance d1 from the satellite signal to the receiver, i.e., d1 < d2 +d3 , and the corresponding propagation time also satisfies t1 < t2 +t3 . From the airspace perspective, the authentic signal and the spoofing signal incident to the receiver are θ1 and θ2 , respectively, and the DOAs of both are different, which creates conditions for forwarding spoofing detection.

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Fig. 1. Forwarding spoofing interference model

Considering that the receiver receives the authentic signal from L GPS satellites and the spoofing signal from J GPS satellites, the signal received by the array antenna of the target receiver contains both the authentic signal and the spoofing signal, and is down-converted and digitized, which can be expressed using the IF signal, as shown in Eq. (1) S(t) =

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3 Decoherent DOA Estimation Algorithm Based on the spatial characteristics of spoofing signals and authentic signals, it is known that DOA can effectively detect spoofing interference. However, when the signals are coherent, as is often the case in spoofing environments, traditional algorithms such as the MUSIC algorithm are ineffective in detecting coherent signals with different incoming directions. Therefore, this section focuses on the Toeplitz matrix reconstruction algorithm, which is a DOA estimation algorithm that can mitigate the effects of coherence.

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The signal model of a one-dimensional L element uniform array antenna receiving K signal sources is: x(t) = As(t) + n(t) The covariance matrix of x(t) can be expressed as Rxx ∈ CL×L   Rxx = E x(t)xH (t) = ASAH + σ 2 IL

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To verify the decoherence performance of the Toeplitz matrix reconstruction algorithm, we carried out experiments in which the receiver received two coherent L1 C/A signals with incidence angles of −20◦ and 45◦ , and an SNR of 5dB. The number of snapshots and array element are 128 and 8 respectively. The DOA estimation results are shown in Fig. 2, where the MUSIC-DOA algorithm only shows a small peak near 45◦ , which means the DOA estimation fails.

4 CNN-Based DOA Estimation Algorithm Although the Toeplitz algorithm is effective in estimating the incoming angle of coherent signals, its performance is unsatisfactory in low SNR environments. To address this issue, we introduce a CNN-based algorithm for high-resolution DOA estimation in this subsection.

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Fig. 2. DOA estimation of coherent signals by Toeplitz and MUSIC

4.1 Sample Generation In this subsection, we introduce a CNN-based framework for DOA estimation that is based on the Toeplitz-DOA estimated spectrum, which is a typical classification method. The received signal can be quantized into a number of P angles with equally spaced sampling, where φ = π/(P − 1). = {φ1 , φ2 , . . . , φP }

(10)

Where the signal comes from to:

= {θ1 , θ2 , . . . , θK }

(11)

The quantified signal is substituted into the Eq. (4) to obtain P    x(t) = α φp sp (t) + n(t)

(12)

p=1

Therefore, the covariance matrix Rxx ∈ CL×L of the received snapshot vector of the array antenna can be expressed as:     Rxx = E x(t)xH (t) + σ 2 IL = AE s(t)sH (t) AH + σ 2 IL (13) where IL is the unit matrix of L × L. The matrix reconstruction can be completed using Eqs. (6) and (7), and the estimation of the quantization angle can be completed with the maximum likelihood estimation [12]. To generate appropriate training samples, we first quantize the DOA estimation interval of the received signal to [−π/2, π/2]. Next, we generate two coherent L1 C/A signals with random angles and SNR, as specified in Table 1. To simplify the CNN model, we select the distinctive Toeplitz-DOA estimation spectrum as the sample features and mark +1 at the index corresponding to the incident angle as the sample labels. Each sample contains of the spatial-feature η ∈ CP×1 with the incident angle information y ∈ CP×1 . The training set contains 90,300 samples, while the test set contains 30,100 samples.

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Table 1. Array antenna setting parameters Setting

Value

Number of array elements

8

Snapshot

512

SNR

[−10:20] dB

Number of signals

2

Incidence angle

[−90◦ :90◦ ]

4.2 Network Construction Figure 3 illustrates the algorithm flow for the CNN-based DOA estimation algorithm. The framework employs an adaptive momentum (Adam) optimizer with the mean square error (MSE) between the actual vector and the output vector as the cost function. The optimizer is set to achieve an accuracy of 10−4 and the activation function used is ReLU. The network comprises five convolutional layers with four pooling layers, and the convolution kernel size is 3 × 1. To simplify the network model further, fully connected layers are not used in the output because they increase the number of training parameters exponentially. Therefore, the final convolutional output is used, and the total number of convolution neurons in the network is 547. The network output is a vector of CP×1 with vector values restricted to [0,1].

Fig. 3. Flow chart of CNN-DOA algorithm

4.3 Simulation Results To evaluate the performance of the CNN network, we set the incident signal to be two coherent L1 C/A signals with an SNR of −10 dB and incident angles of 24◦ and 30◦ . The

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results of the two DOA estimation algorithms are presented in Fig. 4. The CNN-DOA spectrum exhibits two peaks that correspond to the incident angles, whereas the Toeplitz algorithm shows only one peak, which indicates that CNN-DOA has better estimation performance and higher angular resolution.

Fig. 4. Comparison of DOA estimation of Toeplitz and CNN

5 Spoofing Interference Detection Process The CNN model described above can only perform non-differentiated DOA estimation of authentic and spoofing signals, which is not capable of detecting signal spoofing. Therefore, the training model needs to be adjusted. After receiving the input data, the network can mark the authenticity and deception of the incoming signals based on the spectral characteristics. 5.1 Simulation Settings According to the spoofing signal characteristics in Sect. 2, we added code time delay and adjusted the power of the spoofing signal during sample generation. The parameters used in the sample generation are specified in Table 2 (PSA = Pspoof /Pauthentic means the power ratio of the spoofed signal to the authentic signal). The incidence angle of the spoofing signal in the training sample label is set to −1. A total of 90,300 training samples are generated, one of which is shown in Fig. 5. The blue and red lines represent sample characteristics and sample label, respectively. Each sample contains the spatial spectrum feature η ∈ CP×1 and the incident angle information y ∈ CP×1 . The TensorFlow framework in Python is used to train the samples and evaluate the performance.



5.2 CNN Performance Analysis To evaluate the spoofing detection performance of the network, this subsection measures the performance of the neural network model using the confusion matrix. The evaluation metrics can be divided into the following four categories: 1. Correct recognition of

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Table 2. Input signal parameters Parameter setting

Value

Spoofing signal code time delay

[1:3] Tc

Number of signals

[2:4]

Angle of incidence

[−90◦ :90◦ ]

PSA

[2:5] dB

SNR

[−10:20] dB

Fig. 5. Characteristics and labels of the sample

authentic signals (True Positive, TP); 2. Incorrect recognition of authentic signals (False Negative, FN); 3. Incorrect recognition of spoof signals (False Positive, FP); 4. Correct recognition of spoof signals (True Negative, TN). Recognition is considered correct if the peak or zero trap is detected in the corresponding incoming angle of the authentic signal and spoofing signal. Otherwise, it is considered a detection error. As discussed in Sect. 4, the network performance is affected by the SNR, the number of array antennas, and the power of the spoofing signal. Therefore, this subsection will analyze the effects of SNR and spoofing signal power on the network performance. Additionally, in the confusion matrix, 00, 01, 10, and 11 represent TP, FN, FP, and TN, respectively. (1) The SNR range of [−10:10:20] dB is used, with PSA is 3 dB, whose confusion matrix is shown in Fig. 6. As the SNR increases, the detection probability of both the authentic signal and the spoofing signal increases. However, when the SNR is low, the detection accuracy of the spoofing signal is higher than that of the authentic signal, reflecting the network’s susceptibility to spoofing signals. (2) PSA is varied from [1:1:5] dB, while the SNR is set to 0 dB, The resulting confusion matrix is shown in Fig. 7. As the power of the spoofing signal increases, the detection

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probability of both the authentic signal and the spoofing signal also increases. When the power ratio of the spoofing signal to the authentic signal exceeds 2 dB, the detection accuracy of the spoofing signal reaches more than 90%, which demonstrates that the network still has good detection performance for weak spoofing signals.

Fig. 6. Confusion matrix with different SNR

Fig. 7. Confusion matrix with different PSA

5.3 CNN Performance Analysis In the previous subsection, the confusion matrix is used to analyze the spoofing detection performance of CNN with varying SNR and power of the spoofing signals. However, the display of performance is still not intuitive enough. Therefore, compared with PowerInversion (PI) and Adaptive Digital Beamforming (ADBF) algorithms, four simulation experiments are conducted in this subsection. PI algorithm is a commonly used and efficient adaptive anti-interference method [13] with low computational complexity. When the interference power decreases, the performance becomes poor and a part of the useful information is lost. The ADBF output is obtained by coherent superposition of array elements, which can adaptively change the weighting factors of each array element according to the change of the signal environment, forming an aggregation gain in the receiving direction of the array, and forming a null in the interference angle [7].

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To reflect the network model performance, four scenarios are set up as shown in Table 3. A uniform array of 8 array elements is used to receive the signal with a snapshot of 128. Both the spoofing signal and the authentic signal are GPS L1 C/A PRN. And the signal is characterized by Python for feature identification and spoofing detection. Table 3. Scenario setting parameters Scenario

PSA (dB)

SNR (dB)

Number (spoofing signal sources)

Incidence angle

1

10

10

1

−10◦ ;20◦

2

3

0

1

−10◦ ;20◦

3

5

0

3

−10◦ ;[−20◦ , 0◦ , 20◦ ]

4

5

0

1

15◦ ;20◦

Scenario 1: The authentic signal in the received signal is an incident angle of − 10◦ , the spoofing signal is an incident angle of 20◦ . The simulation results are shown in Fig. 8. When the spoofing signal power is high enough, the CNN algorithm, PI algorithm and ADBF algorithm all form a zero trap at the spoofing signal incoming angle of 20◦ . However, the PI algorithm cannot gather gain at the incoming angle of the authentic signal. Compared with the ADBF algorithm, the CNN exhibit higher angular resolution and lower suppression of the side lobes.

Fig. 8. Detection performance of scenario 1

Scenario 2: The authentic signal in the received signal is incident angle of −10°, the spoofing signal is incident angle of 20°. Simulation results are shown in Fig. 9. As the power of the spoofing signal is reduced, the spatial spectrum formed by the PI algorithm tends to be whitened. However, the CNN and ADBF algorithms still maintain robust spoofing detection performance, forming a zero trap at the incoming angle of the spoofing signal and gaining a zero trap at the incoming angle of the authentic signal.

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Fig. 9. Detection performance of scenario 2

Scenario 3: The authentic signal in the received signal is the incident angle of 10°, the spoofing signals incident angle are −20°, 0°, 20°. The simulation results are shown in Fig. 10. The CNN exhibits higher angular resolution, lower zero trap gain, and significant gain only at the incoming angle of the authentic signal. These results demonstrate that the detection performance of the CNN network framework for multiple spoofing sources remains stable.

Fig. 10. Detection performance of scenario 3

Scenario 4: The authentic signal in the received signal is the incidence angle of 15°, the spoofing signal incidence angle of 20°. Simulation results are shown in Fig. 11. When the power of the spoofing signal is sufficiently high, both the CNN and ADBF algorithms form a zero trap at the incoming angle of the spoofing signal (20°). However, the beam clustering direction of the ADBF algorithm deviates from the angle of the authentic signal, indicating that the CNN exhibits higher angular resolution and more robust performance in detecting spoofing signals.

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Fig. 11. Detection performance of scenario 4

6 Conclusion In this paper, CNN networks are built for spoofing detection. Firstly, the Toeplitz matrix reconstruction algorithm is used for DOA estimation of the coherent signal. Then the CNN network is built to learn the spatial spatial-features containing the authentic signal and the spoofing signal, forming a spoofing detection model with high-resolution performance in a low SNR environment. The CNN model is capable of discriminating the authenticity of the incoming signal and outputting the angles of both the spoofing and authentic signals. When the power ratio of the spoofing signal to the authentic signal is greater than 1 dB (SNR = 0 dB), the detection accuracy of the spoofing signal is nearly 90%. The proposed method can be integrated into the receiver software for spoofing detection without hardware changes and does not depend on other navigation data sources. However, the detection performance of the method is poor when the power of the spoofing signal is lower than that of the authentic signal, which will be analyzed subsequently to enhance the robustness of the algorithm. Acknowledgements. This work was financially supported by the Shenzhen Science and Technology Program (Grant No.JSGG20201102163400002, 20201026143857003).

References 1. Wu J, Tang X, Li Z, Li C, Wang F (2019) Cascaded interference and multipath suppression method using array antenna for GNSS receiver. IEEE Access 7:69274–69282 2. Wu Z, Zhang Y, Liu R (2020) BD-II NMA&SSI: an scheme of anti-spoofing and open BeiDou II D2 navigation message authentication. IEEE Access 8:23759–23775 3. Guo J, Sun J, Li D (2020) Analysis and design of a new GNSS encryption authentication scheme. Telecom World 27(6):125–136 4. Hu Y, Bian S, Cao K et al (2018) GNSS spoofing detection based on new signal quality assessment model. GPS Solut 22(1):1–13 5. Chen J, Xu Y, Yuan H, Yuan Y (2020) A new GNSS spoofing detection method using two antennas. IEEE Access 8:110738–110747

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6. Hu Y, Bian S, Li B, Zhou L (2018) A novel array-based spoofing and jamming suppression method for GNSS receiver. IEEE Sens J 18(7):2952–2958 7. Gu N, Tao C, Xing F et al (2022) Research on anti-satellite navigation spoofing jamming technology based on ESPRIT+GSSMI algorithm. Air Space Defense 5(1):78–85 8. Kase Y, Nishimura T, Ohgane T, Ogawa Y, Kitayama D, Kishiyama Y (2018) DOA estimation of two targets with deep learning. In: 2018 15th Workshop on positioning, navigation and communications (WPNC). IEEE, pp 1–5 9. Elbir AM (2020) DeepMUSIC: multiple signal classification via deep learning. IEEE Sens Lett 4(4):1–4 10. Li Q, Zhang X, Li H (2018) Online direction of arrival estimation based on deep learning. In: 2018 IEEE international conference on acoustics, speech and signal processing (ICASSP). IEEE, pp 2616–2620 11. Liu K, He L (2020) Research progress of GNSS spoofing and anti-spoofing technology. J Jiangsu Ocean Univ 29(4):77–85 12. Zhao H, Cai M, Liu H (2017) Two-dimensional DOA estimation with reduced-dimension MUSIC algorithm. In: 2017 International applied computational electromagnetics society symposium (ACES). IEEE, pp 1–2 13. Ren B, Ni S, Chen F, Wu J, Gao L (2021) Anti-spoofing performance analysis of GNSS zeroing anti-jamming antennas. Glob Position Syst 46(6):30–36

Analysis of Anti-Repeater-Spoofing Performance of GNSS Nulling Anti-Jamming Receiver Binbin Ren(B) , Shaojie Ni, Feiqiang Chen, Zukun Lu, and Yifan Sun National University of Defense Technology, Changsha Hunan 410073, China [email protected]

Abstract. To analyze the anti-spoofing performance of the adaptive nulling antijamming satellite navigation receiver in response to direct meaconing attrack, this paper derives the theoretical formula for the power inversion (PI) algorithm used in nulling anti-jamming receiver to suppress real satellite signal and meaconing signal in the case of limited number of snapshots. Through the two indicators of signal absolute power and carrier to noise ratio, analyzes the impact of repeated signal input power on the suppression effect. It is found that the PI algorithm has good suppression effect on direct forwarding, making the receiver not spoofed. Finally, using the antenna array software receiver for simulation, the conclusion is validated according to the capture code phase and carrier-to-noise ratio. Keywords: GNSS nulling anti-jamming receiver · The direct repeater spoofing · Anti-spoofing performance · Power inversion algorithm

1 Introduction Global navigation satellite systems (GNSS) can provide all-weather position, navigation and timing service information for users, and play an irreplaceable role in many aspects of national production [1, 2]. With the development of software radio technology, the cost of GNSS jamming is becoming lower and lower, and the means of attack are becoming more diverse, which brings considerable security threats to military and civilian navigation terminals [3]. Direct repeater spoofing can delay, amplification and repeat received satellite signals without knowing the signal structure, which can pose a security threat to military receivers [4], the repeat principle is shown in Fig. 1. At present, there are many algorithms about spoofing detection and recognition have been proposed. Signal characteristics in time-frequency domain and spatial domain, such as signal arrival angle [5], signal power [6], carrier phase [7], doppler frequency [8], location result [9], spatial correlation [10], and comparison consistency with other autonomous sensor location results [11], can be used as detection quantities. However, there are relatively few researches on spoofing suppression, mainly through signal cancellation [12] and spatial nulling [13, 14]. In contrast, the antenna array has excellent anti-jamming capability [15–19]. The PI algorithm is widely used in radar, navigation and other strong interference & weak signal environments [20], because it is simple to implement and does not require any prior © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 415–427, 2024. https://doi.org/10.1007/978-981-99-6932-6_34

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5HDOVLJQDO

5))URQW (QG GHOD\DPSOLI\ 6SRRILQJ 5HSHDWHU

7DUJHW UHFHLYHU

Fig. 1. Schematic diagram of repeater spoofing

information. Presently, the analysis of the PI algorithm’s performance in suppressing various types of interference is relatively complete [21, 22], but the performance of PI algorithm in spoofing scenarios is rarely considered [23]. Analyzed the suppression performance of the adaptive nulling anti-jamming receiver against the noise free purified repeater spoofing. However, the implementation of purified repeater is very complex, at present, the common repeater spoofing is mainly direct repeater spoofing. Therefore, this paper deeply studies the anti-repeater-spoofing performance of GNSS nulling anti-jamming receiver, and analyzes the power and carrier-noise-ratio (CNR) of the spoofing signal and the real signal from the antenna array quantitatively. Through research and analysis, the following conclusions are drawn, the meaconing signal power output by the anti-interference antenna is always much lower than the power of the real satellite signal, nulling anti-jamming receiver can effectively suppress low delay direct direct repeater spoofing.

2 Signal Model K satellites and L repeater spoofing incident on the antenna array from the far field of space as plane waves. The repeated spoofing signals are composed of delayed repeater navigation satellite signals and repeater noise. As shown in Fig. 2. Assuming the repeater signal comes from the same direction, the signal received by the antenna array can be expressed in this formula form: x(t) =

K  k=1

αk sk (t) + β[

L 

jl (t) + nj (t))] + n(t)

(1)

l=1

where, sk (t) is the k th real satellite signal received by reference array element, jl (t) is the l th repeater spoofing. nj (t) is the noise part of the meaconing signal, with mean value 0, and variance σn2j , n(t) is the noise vector, which is composed of the noise of each array element channel ni (t) (i = 1,2,…,N). ni (t) is independent and identical distribution with

Analysis of Anti-Repeater-Spoofing Performance

417

Z

6SRRILQJ6LJQDO

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X

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Fig. 2. Antenna array receiving real and spoofing signals

variance σn2 , mean value 0. Each row of x(t)=[x1 (t), x2 (t), ..., xN (t)]T represents the mixed signal received by an array element, [·]T represents the transposition operation. αk is the steering vectors of the real signal and β is the steering vectors of meaconing signal, and take αk as an example, its expression is: ⎡ j(2π p e(θk ,φk )/λ) ⎤ 1 e ⎢ ej(2π p2 e(θk ,φk )/λ) ⎥ ⎢ ⎥ (2) αk =⎢ ⎥, k = 1, 2, ...K .. ⎣ ⎦ . ej(2π pN e(θk ,φk )/λ) In the above formula, θk is the pitch angle of the k th signal and φk is the azimuth angle. e(θk , φk )=[cos θk cos φk , cos θk sin φk , sin φk ]T is the unit propagation vector of the plane wave, λ is the signal wavelength, pn (n = 1,2,…,N) is the position coordinate of the n th array element. An important property of the steering vector is: αkH αk = N

(3)

where [·]H represents conjugate transposition. In order to facilitate analysis, this paper considers only a single real satellite signal and a single spoofing signal exist, then Eq. (1) can be expressed as: x(t) = αs(t) + βj(t) + βnj (t) + n(t) = s(t) + j(t) + nj (t) + n(t) = s(t) + v(t)

(4)

s(t) = αs(t)

(5)

j(t) = βj(t)

(6)

nj (t) = βnj (t)

(7)

v(t) = βj(t) + βnj (t) + n(t)

(8)

where,

Here, v(t) is the mixed-signal vector that only contains noise and spoofing.

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3 Representation of Weight Vector Under Limited Snapshots After the anti-jamming receiver receipts the mixed signal, the anti-jamming algorithm will generate a series of corresponding antenna array weights multiplied by the input signal. The PI criterion takes the output of an array element (usually the array element at the origin) as the reference signal, ensures that the weighting coefficient of the output power of this channel signal is constant, and adjusts the array values of other channels to minimize the power of the array output signal. The optimization goal can be expressed as:

2 min{Pout = E[ wH x ]} (9) s.t. wH c1 = 1 where, c1 = [1, 0, ..., 0]T . Equivalent to fixing the weight value of the first array element as 1, adjust [w1 , w2 , ....wN ]H to minimize the output power. The purpose of the constraint is to avoid getting meaningless all zero solution, that is, w1 = w2 = ... = wN = 0. By solving the above equation, we can get the expression of the optimal weight value as: wPI =

R−1 x c1 H c1 R−1 x c1

(10)

In the above formula, Rx = E[x(t)xH (t)] is the covariance matrix of the mixed-signal received by the array. With the limited of snapshot numbers, Rx should be expressed as:  ˆx = 1 x(ti )xH (ti ) R m m

i=1

= Rˆ s + Rˆ j +Rˆ n + Rˆ nj + αˆrH + ˆrα H

(11)

ˆ = σˆ s2 αα H + αˆrH + ˆrα H + Q where m is the number of snapshots, ˆr is the sample cross-correlation between the real signal and spoofing plus noise, which is an N-dimensional vector, σˆ s2 is the sampling ˆ s Rˆ j Rˆ nj and Rˆ n are the autocorrelation matrices mean square power of the real signal, R ˆ is the of the desired signal, repeater spoofing, repeater noise and noise, respectively. Q sampled autocorrelation matrix of spoofing plus noise. The calculation formulas are: 1 s(ti )sH (ti ) = σˆ s2 αα H Rˆ s = m

(12)

1 j(ti )jH (ti ) = σˆ j2 ββ H Rˆ j = m

(13)

1 nj (ti )nH ˆ n2j ββ H Rˆ nj = j (ti ) = σ m

(14)

m

i=1 m

i=1 m

i=1

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419

1 n(ti )nH (ti ) = σˆ n2 I Rˆ n = m

(15)

 ˆ = 1 v(ti )vH (ti ) Q m

(16)

m

i=1

m

ˆr =

1 m

i=1 m 

s∗ (ti )v(ti )

(17)

i=1

where σˆ j2 σˆ n2j and σˆ n2 in Eqs. (13), (14) and (15) are the sampling mean square power of repeater spoofing, repeater noise and noise respectively. Substituting Eq. (12) into Eq. (11), the expression is: w ˆ PI =

1 M

−1 Rˆ x c1

ˆ −1 cH 1 Rx c1

=

ˆ −1 c1 Q ˆ −1 cH 1 Q c1

− [I −

ˆ −1 α Q ˆ −1 cH 1 Q c1

−1

ˆ ]Q

ˆr

(18)

ˆ Q = E[Q] ˆ = When m and N meet m  3N , Q can completely replace Q, M  E[v(ti )vH (ti )], because most of the limited snapshot effect is reflected in the i=1

sample correlation vector ˆr. Equation (18) is finally expressed as: w ˆ PI =

Q−1 c1 α H Q−1 c1 − Q−1 α −1 − [ ]Q ˆr −1 −1 cH cH 1 Q c1 1 Q c1

(19)

Equation (19) shows that w ˆ PI can be divided into two parts under the limited number of snapshots: the weight vector part (the first item on the right of the formula) determined only by the repeater spoofing and noise, and the relevant disturbance part (the second item on the right of the formula) caused by the correlation between the meaconing signal and the real satellite signal and the limited snapshots.

4 The Influence of Spoofing Power on Algorithm Performance In order to analyze the suppression effect of PI algorithm on spoofing signal, this paper studies the influence of the input spoofing signal power on the output power of real satellite signal and meaconing signal under PI algorithm. 4.1 The Influence of Spoofing Power on the Real Satellite Signal The array signal output y(t) after PI algorithm processing is:  y(t) = w ˆH ˆH ˆH ˆH PI x(t) = w PI αs(t) + w PI βj(t) + w PI βnj (t) + n (t)

(20)

wherein, n (t) = wH PI n(t) is the noise of antenna array output. The output power of real signal is:

2

2

Q−1 c

α H Q−1 c1 − Q−1 α −1 H 1

H



ˆ αs(t) ] = E[ ( H −1 − [ ]Q ˆr) αs(t) ] (21) Ps = E[ w H −1

c1 Q c1

c1 Q c1

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Substituting Eqs. (3), (16), (17), we can get:

2 σs2 σn2 + (σj2 + σn2j + σs σj ρ)N (1 − α)

Ps =

2 σn2 + (σj2 + σn2j + σs2 )(N − 1) + 2σs σj ρ(1 − N α)

(22)

 wherein α = α1H α2 |α1 ||α2 | is the spatial correlation coefficient  of the steering vectors of the desired and spoofing signals, and ρ = E[s∗ (t)j(t)] σs σj is the correlation coefficient of the desired and meaconing signals. It can be seen from Eq. (22) that the power of the output real satellite signal is related to the input satellite signal and the repeat spoofing signal, which is a complex multivariate function. When the spoofing-to-signal ratio (SSR) is low, namely σs2 < σj2  σn2 < σn2j , the above formula can be approximated as:

2 σs2 σn2 + σn2j N (1 − α) σs2 [N + (1 − N α)]2 Ps ≈

2 ≈ N2 σn2 + σn2j (N − 1)

(23)

 When 1 − N α > 0, that is, −1 < α < 1 N , the numerator is greater than the denominator, and the output real signal power will be greater than the input power; At that time, the result was just the opposite. When the SSR is high, namely σs2  σn2  σj2  σn2j , the terms σs2 and σn2 in the formula can be ignored, and the above formula can be approximated as:

2 σs2 (σj2 + σn2j )N (1 − α) σs2 [N (1 − α)]2 Ps ≈

2 = [(N − 1)]2 (σj2 + σn2j )(N − 1)

(24)

The output power will be increased compared with the low SSR. It will be demonstrated in the simulation analysis section. 4.2 The Influence of Spoofing Power on the Output of the Spoofing Signal This section derives the expression of the PI algorithm’s response to the spoofing signal, and analyzes its influence quantitatively. The spatial response in the spoofing direction after PI weighting can be expressed as: 



H 2 ˆ PI β

(25) Gj = E w Substituting Eqs. (3), (12), (16), (17), we can get: 2  2 σn + σs2 N 2 (1 − |α|2 ) + σs σj ρN (α − 1)

GPI =

2 σn2 + (σj2 + σn2j + σs2 )(N − 1) + 2σs σj ρ(1 − N α)

(26)

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421

Naturally, the power of repeater spoofing Pj and repeater noise Pnj is: Pj =

GPI σj2

 2 σj2 σn2 + σs2 N 2 (1 − |α|2 ) + σs σj ρN (α − 1)

=

2 σn2 + (σj2 + σn2j + σs2 )(N − 1) + 2σs σj ρ(1 − N α)  2 σn2j σn2 + σs2 N 2 (1 − |α|2 ) + σs σj ρN (α − 1) 2 Pnj = GPI σnj =

2 σn2 + (σj2 + σn2j + σs2 )(N − 1) + 2σs σj ρ(1 − N α)

(27)

(28)

When the spoofing signal is directly repeated, the noise andsatellite signal in the repeat spoofing signal are amplified simultaneously, namely σj2 σn2j = A is satisfied, and A is the original signal-to-noise ratio (SNR). When the SSR is low, that is, σs2 < σj2  σn2 < σn2j , the above equation can be approximated as: Pj ≈

 2 σj2 σn2 σn2 + σn2j (N − 1) Pnj =

2 ≈

σj2 σn4 σn4 [1 + (N − 1)]2

=

σj2 N2

σj2 1 Pj ≈ A AN 2

(29)

(30)

However, with the increase of the spoofing ratio, the increase of σn2j in the denominator will make the overall trend smaller. When the spoofing confidence ratio is high, i.e. σs2  σn2  σj2  σn2j , Eqs. (27) and (28) can be approximated as:  2 σj2 σs σj ρN (α − 1) σs2 [AρN (α − 1)]2 Pj ≈

2 = [(1 + A)(N − 1)]2 (σj2 + σn2j )(N − 1) Pnj =

1 Aσs2 [ρN (α − 1)]2 Pj ≈ A [(1 + A)(N − 1)]2

(31)

(32)

It can be seen that when the spoofing delay is more than one chip, ρ ≈ 0, indicating that the power of the spoofing signal will always be reduced; When the spoofing delay is less than one chip, the spoofing signal power tends to a value independent of the input spoofing signal power.

5 Simulation and Analysis 5.1 Simulation of Signal Flow In order to verify the conclusions in Sect. 4, this section generates data streams and sets two scenarios for analysis and comparison. The simulation antenna array is set as shown in Fig. 3, which is a 7-element central circular array, and the array element spacing is half wavelength. The sample mean of 300 Monte Carlo runs is used to replace the expected operator, and the data samples for each run are 20,000. The signal settings in the scene are shown in Table 1.

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0.5λ

x/m

Fig. 3. Schematic diagram of array element layout

Table 1. Simulation parameter settings Parameter type

Parameter value

True signal power

−160dBW

Pure spoofing power

−160— −70dBW

Power step progress

1dB

Spoofing DOA (scene 1)

(30°, 60°)

Spoofing DOA (scene 2)

(53°, 10°)

Spoofing delay (scene 1)

1 chip

Spoofing delay (scene 2)

0.5 chip

Power spectral density of noise

−205 dBW/Hz

Receiver bandwidth

20 MHz

Under the above parameters, the calculated correlation coefficient is ρ1 = 0.038, ρ2 = 0.504. In the experiment, the output power of the real satellite signal, repeater spoofing and repeater noise in the two scenarios with the change of the SSR is simulated respectively. The results are shown in Figs. 4, 5 and 6.

Fig. 4. The output real signal power varies with SSR

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Output power of pure spoofing/dBW

-160 Theoretical Results (Scenario 1) Simulation Results (Scenario1) Theoretical Results (Scenario2) Simulation Results (Scenario2)

-180

-200

-220

-240

-260

-280 0

10

20

30

40

50

60

70

80

90

Input SSR/dB

Fig. 5. The output repeater pure spoofing power varies with SSR

tput power of repeater noise/dBW

-140 Theoretical Results (Scenario 1) Simulation Results (Scenario 1) Theoretical Results (Scenario 2) Simulation Results (Scenario 2)

-160

-180

-200

-220

-240

-260 0

10

20

30

40

50

60

70

80

90

Input SSR/dB

Fig. 6. The output repeater noise power varies with SSR

Through the above simulation, it can be seen that the simulation results are very close to the theoretical analysis curve. It can be seen from Fig. 4 that the output power of real signal first increases with the increase of the SSR and then tends to a stable value, according to the analysis in the previous section, in this scenario, the real signal power output in both scenarios will be greater than the input spoofing power, and when the SSR is high, it will be stable at: Ps1 ≈ 10 lg Ps2 ≈ 10 lg

σs2 [N (1 − α1 )]2 [(N − 1)]2 σs2 [N (1 − α2 )]2 [(N − 1)]2

= −158.26dBW

(33)

= −158.42dBW

(34)

It is consistent with the simulation results. For the repeater spoofing signal, in Figs. 5 and 6, the power of the repeater spoofing and noise in both scenarios decreases first, then increases, and finally tends to be stable.

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In this scenario, the power output by the repeater spoofing is less than the output power of the real signal when the SSR is 0dB, and the power of the repeater noise is slightly greater than the power of the real signal. When the SSR is is high, the values of Eqs. (31) and (32) are: Pj1 ≈ 10 lg Pj2 ≈ 10 lg Pnj1

σs2 [Aρ1 N (α1 − 1)]2

= − 242.7dBW

(35)

= − 220.4dBW [(1 + A)(N − 1)]2 1 = 10 lg Pj1 = −214.7dBW A

(36)

[(1 + A)(N − 1)]2 σs2 [Aρ2 N (α2 − 1)]2

Pnj2 = 10 lg

1 Pj = −192.4dBW A 2

(37) (38)

The theoretical calculation and simulation results are consistent, it indicates that the theoretical analysis is correct. 5.2 Simulation of Antenna-Array Receiver To further verify whether the above analysis is correct when the antenna array receiver processes real satellite signals, this section generated four BDS satellites synthetic signals and verified the analysis by the antenna-array software receiver processing. The parameter settings are shown in Table 2, the repeated 4 satellite signals are all set to be delayed by 1 chip, and the SSR is from 0dB to 50dB in steps of 5dB, all from the same direction (15°, 15°). Table 2. Parameter setting of real satellites PRN number

AOA (pitch, azimuth)

CNR (dBHz)

Code phase (chip)

1

(45°,126°)

43

30

2

(66°,93°)

44

25

3

(53°,135°)

45

20

4

(72°, 79°)

46

15

The parameter settings of the software receiver are shown in Table 3, and the antenna array structure is the 7-element central circular array as shown in Fig. 2. After PI algorithm processing, the code phase and CNR changes of the four satellites are shown in Fig. 7. It can be seen that after the PI algorithm processing, the code phase captured by the receiver is the code phase of the real satellite signal, and the CNR of the received signal keeps floating in a small range, which indicates that the direct repeater spoofing signal from a single direction cannot cheat the adaptive-nulling anti-jamming antenna array receiver.

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Table 3. Parameter setting of antenna array receiver Parameter

Value

Number of array elements

7

Power spectral density of noise

−205 dBW/Hz

Receiver bandwidth

20 MHz

Sampling rate

20.48 MHz

30

prn 1 prn 2 prn 3 prn 4

50

Output CNR/dBHz

Code phase/Chip

52

prn 1 prn 2 prn 3 prn 4

35

25

20

48 46 44

15 0

10

20 30 Input SSR/dB

a)

40

50

42 0

10

20 30 Input SSR/dB

40

50

b)

Fig. 7. Receiver processing results (a Captured code phase; b the CNR of real signal)

6 Summary In this paper, the performance of adaptive-nulling anti-jamming receiver against direct repeater spoofing is analyzed, the mathematical model of antenna array receiving and repeater spoofing is established, and the expressions of real signal, repeater spoofing and repeater noise output power after PI algorithm processing are derived. According to the quantitative analysis, it is found that the direct repeater spoofing in a single direction is processed by the PI algorithm, the power of spoofing signal is always far less than the power of real satellite signal, so the receiver cannot be successfully deceived. The correctness of the conclusion is verified by data flow simulation and signal flow simulation. This paper proves that PI anti-jamming algorithm has the ability of anti-spoofing, which guidances for anti spoofing strategy selection in the field of navigation countermeasure. Acknowledgement. Thanks to the support of 62003354&U20A0193 from the National Natural Science Foundation of China, and thanks to the teachers and students of the anti-jamming group for their help in the experiment.

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References 1. Lu Y, Zhang G, Chen G (2020) Development status and prospect of satellite navigation system. Spacec Eng 29(4):1–10 (Ch) 2. Liu J, Gao K (2020) Role, path, and vision of “5G + BDS/GNSS.” Satell Nav 1(1):1–8 3. Hein GW (2020) Status perspectives and trends of satellite navigation. Satell Nav 1(1):245– 256 4. Peng J, Ni S, Nie J (2016) Research on GNSS spoofing jamming technology. Fire Comm Control 41(7):1–4 (Ch) 5. Bhamidipati S, Gao GX (2020) GPS spoofing mitigation and timing risk analysis in networked PMUs via stochastic reachability, 33rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2020), P3920–3937 6. Hegarty C, O’Hanlon B (2019) Spoofing detection in GNSS Receivers through crossambiguity function monitoring, 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), pp 920–942. Miami, Florida, USA 7. Gao Y, Li H, Lu M (2013) Intermediate spoofing strategies and countermeasures. Tsinghua Sci Techn 18(6):599–605 8. Wen J, Li H, Wang Z (2019) Spoofing discrimination using multiple independent receivers based on code-based Pseudorange measurements, 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), pp 3892–3903. Miami, Florida, USA 9. Wang F, Li H, Lu M (2017) GNSS spoofing detection based on power monitoring of twoantenna, China Satellite Navigation Conference (CSNC), pp 843–852. Beijing, China 10. Fan G, Huang Y, Zhang G (2016) The GPS spoofing detection based on the Joint WSSE of DOA and pseudorange, China Satellite Navigation Conference (CSNC), pp 643–652. Changsha, Hunan, China 11. Jahromi JA (2013) GNSS signal authenticity verification in the presence of structural interference. University of Calgary, pp 12–15 12. Humphreys TE, Ledvina BM, Psiaki ML (2008) Assessing the spoofing threat: development of a portable gps civilian spoofer, The 21st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS ’08), pp 2314–2325. Savannah, Ga, USA 13. Ni S, Ren B, Chen F (2022) GNSS spoofing suppression based on multi-satellite and multichannel array processing. Front Phys 10 14. Zhang Y, Wang L (2014) Spoofing Jamming Suppression Techniques for GPS Based on DOA Estimating, China Satellite Navigation Conference (CSNC), Nanjing, Jiangsu, China 15. Chen F (2017) GNSS antenna array receiver interference suppression and measurement deviation compensation technology, Changsha. National University of Defense Science and Technology (Ch) 16. Dai X, Nie J (2017) Distortionless space-time adaptive processor based on MVDR beamformer for GNSS receiver. IET Radar Sonar Navig 11(10):1488–1494 17. Lu Z, Nie J, Chen F (2017) Adaptive time taps of STAP under channel mismatch for GNSS antenna arrays. IEEE Trans Instrum Meas 11:1–12 18. Nie J (2012) Research on anti-jamming algorithm and performance evaluation technology of GNSS antenna array. Changsha, National University of Defense Technology (Ch) 19. Ren B, Chen F, Ni S (2022) Performance analysis of repeater spoofing suppression based on GNSS multi-beam receiver. Front Phys 10 20. Tian Y, Yi X (2016) Performance analysis and simulation of power inversion adaptive antijamming algorithm. Elect Inf Counterm Technol 31(5):66–70 (Ch) 21. Sang H, Li Z, Wang F (2003) Performance of power inversion array using RLS algorithm. J Nat Univ Def Technol 25(3):36–40 (Ch)

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22. Sang H (2015) Anti jamming performance analysis of globally optimal space-time antijamming GNSS receiver using power inversion array. Surv Map Sci Eng 35(3):64–68 (Ch) 23. Ren B, Ni S, Chen F (2021) Anti spoofing performance analysis of GNSS zero adjustment anti-jamming antenna. Global Posit Syst 46(6):30–36 (Ch)

Design and Performance Assessment of a Time-Varying Channel Simulator for High-Mobility Satellite Navigation Scenarios Shun Zhou(B)

, Shiyun Yu, Wei Shi, and Yongyang Hu

The Sixty-Third Research Institute, National University of Defense Technology, Nanjing 210007, China [email protected]

Abstract. With the development of high-mobility satellite navigation systems such as LEO satellite navigation enhancement system, the ability of traditional fixed channel models to simulate channel characteristics has been widely challenged. This work focuses on the background theory, time-varying emulator design, and performance assessment application for the necessity of a channel simulator to enable the propagation modeling from LEO satellite to mobile receiver in the high-mobility satellite navigation scenario. The concept of satellite Doppler effect, separation of satellite Doppler shift, and local Doppler shift are discussed in this work, along with the sampling criteria for time-varying channel modeling. The time-varying simulator based on the model of the time-varying satellite navigation channel is provided, and it is used to assess the tracking loop performance of the navigation software receiver. The results show that the rapidly updating time-varying channel will subject the receiver to severe fluctuations and may possibly result in the tracking loop losing lock. In general, the rapidly time-varying channel scenario is more challenging to track and produce stable output than the general multipath channel scenario. Keywords: Satellite navigation channel · High-Mobility · Time-Varying · Simulator · Performance assessment

1 Introduction Global navigation satellite systems (GNSS) have become one of the most important security and economic development infrastructures in the world [1]. The growth of the low earth orbit (LEO) constellation and recent advancements in GNSS in medium orbit have put the Beidou navigation satellite system on the verge of a new wave of modifications. As a result, the LEO satellite navigation enhanced GNSS system has drawn a lot of interest in the satellite navigation community. When compared to GNSS in medium and high orbit, the LEO satellite propagation signal has the advantages of high landing power, speedy operation, and rapid geometric configuration change, all of which can significantly improve the performance of GNSS. The high dynamic properties of LEO satellites in particular will cause a significant Doppler impact to the © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 428–437, 2024. https://doi.org/10.1007/978-981-99-6932-6_35

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signal reception, which is significantly bigger than that of conventional medium and high orbit satellite signals, lengthening the signal search time and complicating receiver processing. Hence, in order to satisfy the criteria of the new system signal design for LEO satellite navigation enhancement, it is important to simulate the rapidly moving time-varying satellite navigation channel. An abstract mathematical description of the intricate satellite-earth radio channel is necessary in order to develop and assess a new generation of satellite navigation systems in high, medium, and low Earth orbit [2, 3]. For new navigation and location scenarios, channel models must also be enabled, including propagation odelling from low-earth orbit satellites to mobile receivers. The capacity of classic fixed channel models to reproduce channel characteristics has been severely tested by the development of high-mobility wireless systems like LEO. In addition, in order to assess the locating capabilities of satellite navigation multifrequency signals in actual scenarios, it is necessary to address the issues of high field test costs, numerous interference elements, and difficulties in odelling the specifics of the electromagnetic environment. This work focuses on the high-mobility satellite navigation scenario and gradually introduces some parts, including background theory, time-varying simulator design, and performance assessment analysis, in order to address the aforementioned issues. The concepts of satellite Doppler shift and local Doppler shift are abstracted through the discussion and analysis of the satellite Doppler effect, a two-segment time-varying multipath Doppler effect model is established, and the sampling criteria for time-varying channel simulation are highlighted. The time-varying channel simulator design can be guided by the aforementioned conclusions; Second, a time-varying simulator based on a channel model for satellite navigation is provided. Third, the tracking loop of a GNSS software receiver is assessed using the time-varying simulator.

2 Time Varying Channel Principle of Satellite Navigation 2.1 Satellite Doppler Effect The Doppler effect, a fundamental principle of electromagnetic wave propagation, has been useful in many applications, including ranging, location, and radio navigation [4, 5]. We explore the Doppler effect caused by the relative velocity of the transceiver in the section that follows. It is assumed that there is simply a specular reflection multipath signal and the line-of-sight (LOS) signal in this simplified example. In fact, the derivation process is not restricted by the idea of a specularly reflected multipath signal and is just as possible if numerous reflected signals are replaced. The following analysis fulfills the plane wave hypothesis that for all points along the moving path, the ranging signal from the satellite remains parallel. The situation when LOS signals and multipath signals are both present throughout is then examined. As depicted in Fig. 1, the geometrical configuration of the satellite transmitter to the ground mobile receiver and reflector is discussed. If the satellite transmitter approaches the mobile receiver at speed V. V is the satellite transmitter velocity vector projected in the radial (line-of-sight) velocity of the satellite transmitter and mobile receiver. If the mobile receiver moves away from the reflector at

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Satellite TX Reflection Point

θ θ1

Mobile RX

Fig. 1. Geometry of satellite to ground fixed receiver

velocity V 1 , V 1 is the velocity vector of the mobile receiver at the point of reflection and the velocity projected radially by the mobile receiver can be written as V1 = vu  · cos θ1

(1)

where, vu is the velocity vector of the mobile receiver, and θ1 is the included angle between the moving direction of the mobile receiver and the connecting direction of the reflector-receiver. At the same time, if the mobile receiver approaches the satellite transmitter at the speed V 0 , V 0 is the radial projection speed of the mobile receiver and satellite transmitter, which can be written as V0 = vu  · cos θ

(2)

Then, if the Doppler shift caused by the motion of satellite transmitter relative to mobile receiver, the motion of mobile receiver relative to satellite transmitter and the motion of mobile receiver relative to the point of reflection are respectively set as, and, it can be proved that fD =

V V0 V1 , fd 0 = , fd 1 = λ λ λ

(3)

The equivalent low pass of the received signal is shown as follows rL (t) =a0 exp(j2π (fD + fd 0 )t) + a1 exp(j2π (fD + fd 1 )t)

(4)

According to Eq. (4), the first sum represents the low-pass equivalent of the LOS signal, and the second sum represents the equivalent low-pass representation of the multipath signal. We can infer a few important facts from the formula above: ( f D + f d0 ) is the Doppler shift brought on by the relative motion of the satellite and the receiver, which is referred to in this paper as the satellite Doppler shift; f d1 is the Doppler shift brought on by the movement of the ground receiver relative to the reflector, which is referred to in this paper

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as the local Doppler shift. These two kinds of Doppler shifts will be handled differently in this paper. Because the satellite’s speed in relation to the ground receiver won’t change considerably in a short amount of time, the former is typically approximated as a fixed frequency offset; The primary cause of the “time-varying” properties of satellite ground time-varying multipath channels is the local Doppler shift, which is tied to the scenario and changes rapidly in a variety of diverse situations. 2.2 Time Varying Channel Sampling Conditions The channel simulation parameter update cycle T CIR , referred to as the channel sampling interval in this article, is crucial for time-varying channel simulation systems. To distinguish the time-varying process with Doppler shift, a minimum sampling rate must be guaranteed, that is, the channel simulation sampling rate must be greater than or equal to twice the maximum Doppler frequency of the channel fm : fCIR ≥ 2fm

(5)

1 TCIR

(6)

and fCIR = as well as Vmax (7) λ In Eq. (7), Vmax is the maximum moving rate of the receiver. Put Eqs. (6) and (7) into both sides of Eq. (5), then TCIR needs to satisfy the upper bound: fm =

λ (8) 2Vmax On the other hand, T CIR must be greater than the maximum delay spread of the channel τmax , otherwise the channel impulse response (CIR) of different Channel “snapshots” will be aliased, that is TCIR ≤

TCIR ≥ τmax

(9)

Based on the above derivation, considering Eq. (8) and (9), we obtain τmax ≤ TCIR ≤

1 2fm

(10)

Equation (10) is the sampling condition of time-varying channel simulation. Section 2 investigates the theoretical models and physical effects associated with time-varying multipath channels for satellite navigation, and two conclusions are obtained as follows: first, the concepts of satellite Doppler shift and local Doppler shift are given, and a satellite Doppler model with two Doppler effects is established, with satellite Doppler shift modeled as a fixed frequency offset and local Doppler shift as the main modeling object for time-varying channels; second, it is pointed out that the time-varying channel simulation sampling condition of Eq. (10) needs to be satisfied. The above conclusions can be used to guide the design of the time-varying channel simulator discussed in Sect. 3.

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3 Time-Varying Channel Simulator Real-time channel model simulation requires the creation of a sample trace that implements the fading characteristics of the channel model [6]. A combination of the timevarying multipath channel model and actual simulation technology is used in this section to conduct application research and design.

Parameter Input

Shaping Filter

Channel Sample Ratre fCIR

CIR

GNSS Baseband Signal Generator Data & PN Code Generator

Channel Model

fs

TDL FIR Filter

DDC

D/A

RF Front

Receiver Under Test

(a) Dynamic Scenario Deduction Module MPS Scenario Building Module

Velocity Interpolation

Channel Simulation Module Input

Velocity Decomposition

Velocity Integration

Coordinate Update

CIR Generation Module Channel Resampling

TDL

CIR Calculation

Propagation Path Delay Calculation

Output

(b)

Fig. 2. Block diagram of time-varying channel simulator: (a) basic form; (b) simulator based on time-varying scenario channel model

Figure 2(a) shows a block diagram of the basic structure of the time-varying multipath channel simulator for satellite navigation [7]. In the simulator, there is a GNSS baseband signal generator, a test receiver, a channel model, and a tapped-delay-line (TDL) finite impulse response (FIR) filter. The GNSS baseband signal generator generates signal samples at the sampling rate and the receiver under test receives all samples at the end of the simulated channel chain. The simulated signal chain operates in parallel in distinct channels if multiple navigation satellites are to be simulated. The channel model is suitable for a variety of scenarios. The simulator based on time-varying scenario channel model is shown in Fig. 2 (b), including multiple point-scatterers (MPS) scenario building, dynamic scenario deduction, CIR generation and channel simulation module [8]. The MPS building module uses the MPS model to build a time-varying virtual simulation scenario, sets multiple point scatterers around the receiver, sets the direct signal to be completely blocked, and the signal energy at the mobile receiver is all contributed by the scattered signal from the MPS. The dynamic scenario deduction module includes velocity interpolation unit, velocity decomposition unit, velocity integration unit and

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coordinate update unit. The CIR generation module includes a propagation path length and delay calculation unit and a CIR calculation unit. The propagation path length and delay calculation unit is used to calculate the propagation path length of the multipath component combined with the geometric relationship of the time-varying virtual simulation scene of the MPS model; the CIR calculation unit is used to calculate the response at the receiver and output it. A TDL unit and a channel resampling unit make up the channel simulation channel module. Channel resampling unit converts CIR parameters over the continuous-time delay domain into discrete-time form with uniform sampling intervals [9]; The TDL unit is implemented using a FIR filter, which is characterized in that the delay interval between the N-taps of the filter is uniform, comprising a set of transversely arranged delay elements, a set of weighting coefficients, a set of multipliers and adders.

4 Performance Assessment In this section, we use the simulator based on the channel model to make a preliminary application assessment to assess the partial performance of GNSS software receiver. Try to explain how to use our channel model or standard channel model to implement the performance assessment task. 4.1 Assessment Configuration In Fig. 3, the assessment block diagram shows the basic structure of the channel simulator. In addition, the signal acquisition and code tracking loop, which are core components of GNSS software receivers, are additionally attached for receiver performance assessment. The channel model provides time-varying CIR parameters for the simulator.

Channel Model (Replacable)

Parameter Input

Channel sampling rate fCIR

CIR GNSS SDR GNSS Baseband Signal Generator

fs

Channel Convolution

Signal Capture

Code Tracking Loop

Fig. 3. Block diagram of receiver performance assessment

The first satellite navigation channel model configured in the assessment is the Deutsches Zentrum für Luft-und Raumfahrt (DLR) multipath channel model listed in Table 1 [10]. Time-varying channel CIRs are generated using the DLR multipath channel model in the assessment. Channel sampling rate is set to 100 Hz for 5 s of simulation. As a result, 500 sets of CIR parameters are produced during simulation time. In the channel model, the receiver is positioned on the vehicle at a speed of 20 km/h in an urban setting.

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The second satellite navigation channel model configured in the assessment is the satellite navigation channel model with time-varying scenarios under non-line-of-sight (NLOS) proposed in [8]. During the assessment, the model generates a time-varying channel CIR. Channels are sampled at 1000 Hz and the simulation takes 4 s. Thus, 4000 sets of CIR parameters are generated during simulation. The receiver moves at a variable speed. The GNSS L1 BPSK baseband signal is generated by the GNSS baseband signal generator. The assessment object is the core part of the GNSS software receiver, including signal acquisition and delay locked loop code tracking loop. Real-time operation channel has a signal sampling rate of 20 MHz. Table 1 summarizes the configuration of main parameter. Table 1. Configuration of main parameters Model

Channel type

Speed (km/h)

Channel sampling rate (Hz)

Number of CIRs

DLR

Time-varying

20

100

500

NLOS

Time-varying

Variable Speed

1000

4000

4.2 Results

LOS path Multipath

-20

Power (dB)

Normalized Magnitude

Using the DLR multipath channel model, two types of CIR parameters are produced for simulation. Fig. 4 (a) and (b) display a set of fixed CIR parameters as well as timevarying CIR parameters. Overall, there are 500 time-varying CIR parameters. In static time-invariant channel conditions, a set of fixed CIR parameters is selected to evaluate the performance of software receivers.

-30 -40

0

0.5

1

1.5

2

Delay (s)

(a)

2.5

3

3.5

4 10-7

Delay(ns)

Time (ms)

(b)

Fig. 4. CIR parameters generated by the DLR multipath channel model: (a) a set of fixed CIR parameters (b) time-varying CIR parameters.

With a fixed set of CIR parameters, Fig. 5 shows the partial output of the code tracking loop using the DLR multipath channel model. In this case, the correlation interval set in

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Fig. 5 (a) is 0.5 chips, while the correlation interval shown in Fig. 5 (b) is 0.1 chips. In the static time-invariant channel conditions, the tracking results of the software receiver are therefore fairly smooth and stable.

(a)

(b)

Fig. 5. Partial output results of the code tracking loop using the DLR multipath channel model with fixed CIR parameters: (a) correlation interval of 0.5 chips; (b) correlation interval 0.1 chip.

Using the DLR multipath channel model, Fig. 6 illustrates the partial output results of the code tracking loop using the time-varying CIR parameters. Where in Fig. 6(a) the correlation interval is 0.5 chips, whereas in Fig. 6(b) the correlation interval is 0.1 chips. In line with the previous description, some output results of the code tracking loop are consistent. In Fig. 6, it can be seen that, with a time-varying channel, the tracking results of the software receiver are no longer smooth, and the outcomes also fluctuate significantly. Compared with Fig. 6 (a) and (b), It is also found that the output of smaller correlation intervals is more stable.

(a)

(b)

Fig. 6. Results of the code tracking loop using the DLR channel model: time-varying CIR parameters: (a) correlation interval of 0.5 chips; (b) Correlation interval 0.1 chip

By using the time-varying NLOS channel model, Fig. 7 illustrates the partial output results of the code tracking loop. Where in Fig. 7(a) the correlation interval is 0.5 chips, while in Fig. 7(b) it is 0.1 chips. Some output results of the code tracking loop are

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consistent with the previous description. According to Fig. 7, software receiver tracking results fluctuate dramatically with NLOS channel conditions, and Fig. 7(a) shows a trend of lock loss as well. In Fig. 7(b), the correlation interval is smaller, improving the quality of the output results.

(a)

(b)

Fig. 7. Partial output results of code tracking loop using time-varying NLOS channel model: time-varying CIR parameters: (a) correlation interval 0.5 chips; (b) Correlation interval 0.1 chip

5 Conclusion The principle of satellite Doppler analysis, identifying satellite and local Doppler shifts, and the sampling criteria for time-varying channel simulation are covered in this work. A preliminary assessment to assess the performance of the GNSS software receiver with the simulator is made after the presentation of the simulator design, which is based on the time-varying satellite navigation channel model. The results indicate that the rapidly updating time-varying channel will cause significant fluctuations in the GNSS receiver and even cause the tracking loop to lose lock. The time-varying NLOS channel scenario makes tracking and achieving stable results more challenging than the multipath channel scenario in general. A practical application example is provided to show how to execute the performance assessment task using the standard channel model, as well as to provide indirect support for the usefulness of the time-varying satellite navigation channel model.

References 1. Zhou S, Lin H, Wang M, Tang X, Ou G (2020) A survey of satellite navigation channel models. Chinese J of Radio Science 35(4):504–514 2. Zhang X, Ma F (2019) Review of the development of LEO navigation-augmented GNSS. Acta Geod et Cartogr Sin 48(9):1073–1087 3. Gao W et al (2021) Research and simulation of LEO-based navigation augmentation. Sci Sin-Phys Mech Astron 51(1):019506 4. Guier W, Weiffenbach G (1958) Theoretical analysis of doppler radio signals from earth satellites. J Nature 181(4622):1525–1526

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5. Guier W, Weiffenbach G (1960) A satellite doppler navigation system. Proc IRE 48(4):507– 516 6. Ghiaasi G, Blazek T, Ashury M, Santos RR, Mecklenbräuker C (2018) Real-time emulation of nonstationary channels in safety-relevant vehicular scenarios. Wirel Commun Mob Comput 2018(2423837):1–11 7. Schubert FM, Prieto-Cerdeira R, Robertson P, Fleury BH (2009) SNACS-the satellite navigation radio channel signal simulator. In: Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), pp. 1982–1988. ION, Savannah USA 8. Zhou S, Ou G, Tang X, Mou W (2022) Time-varying non-line-of-sight (NLOS) satellite navigation channel modelling and simulation using multiple point-scatterers. IET Radar Sonar Navig 16(5):775–785 9. Cullen P, Fannin P, Garvey A (1994) Real-time simulation of randomly time-variant linear systems: the mobile radio channel. IEEE Trans Instrum Meas 43(4):583–591 10. Lehner A, Steingass A (2005) A novel channel model for land mobile satellite navigation. In: Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), pp 2132–2138. ION, Long Beach USA

Research on Receiving and Processing Technology of Short-Time Burst Spread Spectrum Signal Yaohui Chen, Qijia Dong(B) , Dun Wang, Shenyang Li, Zhenxing Xu, Shangna Zhang, Guoji Zou, and Yali Liu Space Star Technology Co, Ltd, Beijing 100095, China [email protected]

Abstract. Short time burst spread spectrum signal has attracted extensive attention in the field of LEO satellite navigation because of its strong anti-interference and good concealment. However, due to the short duration of the short-time burst spread spectrum signal, the acquisition and tracking of the signal is more demanding. The closed-loop tracking algorithm widely used in the navigation field is no longer suitable, and the open-loop carrier synchronization algorithm is needed, which means that the received signal needs to be cached, frequency offset estimation and compensation, which brings great difficultly to the signal receiving and processing. In addition, the traditional L&R carrier frequency offset estimation algorithm is difficulty to balance the estimation range and accuracy. Aiming at the above problems, an improved L&R algorithm is proposed in this paper, which considers the estimation accuracy and greatly expands the estimation range. At the same time, a complete signal receiving and processing framework is designed, and the influence of different parameters on signal receiving preference is fully analyzed in the process of signal receiving, which provides guidance for receiver design and reference for short-time burst spread spectrum signal system design. Through theoretical analysis and simulation verification, the results show that the proposed method can effectively expand the estimation range of frequency offset without affecting the accuracy of frequency offset estimation. Keywords: Short-time burst · Spread spectrum · L&R · Frequency offset estimation

1 Introduction With the development of Global Navigation Satellite System (GNSS), the applications based on GNSS have been gradually applied to all aspects of national economic life and become an indispensable national space infrastructure. However, because the satellite signal reached by the ground is very weak (for example, the minimum power of the L1 Supported by the “Outstanding Engineer” Growth Plan of Beijing Association of Science and Technology. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 438–452, 2024. https://doi.org/10.1007/978-981-99-6932-6_36

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C/A code of GPS satellite signals is approximately –158.5 dBW, which is even weaker 20 ~ 30 dB than the receiver thermal noise) [1], it is susceptible to various types of radio frequency interference. Therefore, it is very necessary to study the enhancement or supplementary backup methods of GNSS. Low Earth Orbit (LEO) satellite has attracted extensive attention in the field of satellite navigation due to its unique constellation and signal advantages. LEO satellite constellation can not only broadcast satellite navigation signals as enhancement and supplement of GNSS, but also broadcast independent ranging signals of the compatible communication signals as backup of GNSS, providing independent positioning and navigation functions. For example, the Satellite Time and Location (STL) service launched by the Iridium satellite system of the United States has become a backup and supplement of the GPS system [2]. Iridium satellite STL signal is a spread spectrum pulse signal transmitted through the communication channel [3]. This independent ranging signal of the compatible communication signal broadcasts in the allocated time slot, which belongs to short burst pulse signal. Thus, the time available for the signal acquisition, tracking ranging, and positioning solution is short, which makes the signal processing and positioning solution methods commonly used in the satellite navigation difficult to apply. Generally, the burst signal is captured by matched filtering, which can quickly obtain the coarse synchronization information, such as frequency offset and phase offset of the signal carrier. Further, open-loop tracking can be carried out to improve the signal synchronization accuracy. The receiver uses the Doppler measurement value to realize the position calculation based on Doppler. Therefore, the Doppler measurement accuracy directly affects the positioning accuracy of the receiver. Frequency offset estimation has long been a hot issue owing to its wide applications in communications, navigation [3], etc. The open-loop carrier synchronization algorithm can be divided into data assisted carrier synchronization algorithm and non-data assisted carrier synchronization algorithm according to whether the training sequence is used or not. According to the different ways of removing data modulation, it can be divided into the following three types: data assisted algorithm (DA) [4], decision guidance algorithm (DD) [5] and non-data assisted algorithm (NDA) [6]. Due to large Doppler variation range and large Doppler variation rate of the LEO satellites, and the existing open-loop carrier frequency offset estimation algorithm is difficult to consider both the frequency offset estimation range and estimation accuracy, it is urgent to study the carrier frequency offset estimation algorithm that can consider both. Therefore, this paper focuses on the above difficulties in the process of receiving short-time burst signals and carries out researching on the signal receiving method and implementation architecture. This paper is structured as follows: Sect. 1 is the introduction; Sect. 2 introduces the short burst spread spectrum signal model and signal processing architecture; Sect. 3 introduces the signal receiving algorithm; Sect. 4 introduces the improved algorithm; In Sect. 5, the performance of the algorithm is analyzed and verified by simulation with theoretical data as an example; Sect. 6 summarizes the full text. The improved L&R algorithm and signal processing architecture proposed in this paper can effectively receive short-time burst signals.

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2 Received Signal Model and Signal Processing Architecture This section mainly introduces the received signal model and signal processing architecture. 2.1 Received Signal Model The short-time burst spread spectrum signal is usually composed of three parts: continuous wave (CW), unique word (UW) and modulated data, as shown in Fig. 1, BPSK modulation is adopted. To facilitate the following description, the received signal model is first given. When the signal exists, the IF signal output by the receiver can be expressed as √   (1) s(t) = 2PC(t)D(t)cos 2π (fI + fd )t + θ0 + n(t) where, P is the received signal power, C(t) is the spread spectrum code, D(t) is the modulation data, fI is the intermediate frequency carrier frequency of the received signal, fd is the received signal Doppler, θ0 is the initial phase of the received signal carrier, n(t) is Narrow band Gaussian noise.

CW

UW

Modulated Data

Fig. 1 Signal structure

2.2 Signal Processing Architecture The overall architecture of short burst signal reception processing is shown in Fig. 2, mainly including antenna, RF, AD, acquisition (including signal detection and time synchronization), tracking (including carrier frequency offset estimation and compensation, carrier phase offset estimation and compensation), etc.

Fig. 2 Short-time burst signal reception and processing overall architecture

First, the signal is converted into digital IF signal by antenna, RF and AD sampling; Secondly, signal acquisition is carried out. The signal detection module uses the parallel

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frequency search method to obtain the carrier Doppler, and the time synchronization module uses the obtained Doppler information to down convert the digital IF signal obtained by AD and to reduce the carrier frequency offset. Here, the parallel code phase search method is used to obtain the time synchronization information to complete symbol synchronization; Then, the carrier frequency offset is estimated and compensated by using the symbols obtained after synchronization; Finally, the compensated symbols are used for carrier phase offset estimation and compensation to obtain symbol information.

3 Signal Receiving Algorithm This section mainly includes acquisition and tracking. 3.1 Capture Algorithm According to the characteristics of short-time burst signals, the acquisition process needs to meet two requirements: First, it is to meet the requirements of Doppler search range; Second, the frequency resolution should meet the requirements of the subsequent carrier frequency offset estimatiozzzn algorithm for the frequency offset range. Common spread spectrum signal acquisition algorithms include linear search, parallel frequency search and parallel code phase search [1]. In this paper, the capture process is divided into signal detection and time synchronization. Signal detection The signal detection is mainly completed by CW. Since CW does not modulate the spread spectrum code and message, it only needs to search in the frequency dimension. Parallel frequency search is adopted, as shown concretely in Fig. 3.

Fig. 3 Parallel frequency search flow

At this time, the received signal shown in Eq. (1) can be expressed as √   s(t) = 2Pcos 2π (fI + fd )t + θ0 + n(t)

(2)

The baseband signal after down conversion by the mixer is    S(t) = s(t)e−j2π fI t = P/2 ej(2π fd t+θ0 ) + e−j[2π (2f I +fd )t+θ0 ] + n˜ (t)

(3)

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Fig. 4 Parallel code phase search flow

where, the real part and imaginary part of the noise component n˜ (t) = n(t)e−j2π fI t are independent of each other and meet the Gaussian distribution with mean value of 0 and variance of σn2 respectively. The result after integration can be expressed as xn =

1

t0 +(n+1)T  coh

Tcoh

S(t)dt ≈ an ej(2π nfd Tcoh +θc ) + nn

(4)

t0 +nTcoh

where, t0 is the initial time, Tcoh is the coherent integration time, an is the signal amplitude, the real part and imaginary part of nn are independent of each other, and are respectively Gaussian white noise sequences with mean value of 0 and variance of  σn2 / Bpd T coh , Bpd is the noise bandwidth before integration. Here, an =

nn =



P/2sinc(fd Tcoh )

1 Tcoh

(5)

t0 +(n+1)T  coh

n˜ (t)dt

(6)

t0 +nTcoh

θc = π fd Tcoh + θ0 + π/2

(7)

The integral result xn is ped by N -point Fourier transform, and the result is expressed as Xk =

N −1

2π

xn e−j N

nk

, k = 0, 1, · · · , N − 1

(8)

n=0

For frequency domain signal Xk after Fourier transform, search the k corresponding to the amplitude exceeding the preset threshold TH to obtain the capture results k=

max {|Xk |}

k,max>TH

The Doppler frequency offset acquired after successful signal detection is fk, k < N2 fd = f (k − N ), k ≥ N2

(9)



(10)

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where, f = fs /N is the frequency resolution, fs = 1/Tcoh is the sampling frequency. The Doppler search range is [–fs /2, +fs /2]. Time synchronization Time synchronization is mainly achieved through UW. Since UW does not modulate the message, the message can be considered to be equal to 1. Assuming the Doppler obtained by signal detection is accurate enough, it is only necessary to search in the code phase dimension, and using the parallel code phase search method. The search process is shown in Fig. 4. According to the Doppler obtained by signal detection, the baseband signal after down-conversion processing of the received signal can be expressed as

 −j2π fI +f d t 

S(t) = s(t)e =



⎡

  ⎤ −j 2π 2f I +fd +f d t+θ0 

P/2C(t)D(t)⎣e

j(2π fe t+θ0 )

+e

⎦ + n˜ (t)

(11)



−j2π fI +f d t 

where, the real part and imaginary part of the noise component n˜ (t) = n(t)e are independent of each other and meet the Gaussian distribution with mean value of 0 and variance of σn2 respectively. Set the code phase search step as tbin = Tc /D, Tc is the chip time length, and D is the number of search segments for each chip. Slide by search step tbin , coherent integration time Tcoh = Tc . Then, the nD + d integral result can be expressed as xn,d

1 = Tc

t0 +(n+1)T  c +dtbin

S(t)dt

(12)

t0 +nTc +dtbin

where, d = 0, · · · , D − 1 is the search sequence number in each chip. Take the N point Fourier transform of the integral result xn,d . The results can be expressed as. (m)

Xk,d =

N −1

2π

xn+m,d e−j N

nk

, k = 0, 1, · · · , N − 1

(13)

n=0

Where, the superscript (m) represents the number of the whole chips of searching for slide, m = 0, 1, · · · . The Fourier transform of the local code {cn } can be expressed as Ck =

N −1

2π

cn e−j N

nk

(14)

n=0 (m)

Multiply Xk,d and the conjugate of Ck , and the result can be expressed as (m)

(m)

Yk,d = Xk,d Ck∗

(15)

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Carry out inverse Fourier transform on Yk,d to obtain time-domain correlation result. (m) yn,d

N −1 1 (m) j 2π nk = Yk,d e N , n = 0, 1, · · · , N − 1 N

(16)

k=0

For the time domain correlation results, search m, d , n corresponding to the correlation results exceeding the preset threshold th to obtain the capture results. The search process is shown as follows     (m)  (17) [m, d , n] = max max max yn,d  m,max>th

d

n

After the successful capture, the values of m and d are determined. Under the condition of no confusion, m, d and t0 are omitted. The synchronized chip integration results can be expressed as 1 xn = Tc

(n+1)T  c

S(t)dt = an ej(2π nfe Tc +θc ) + nn

(18)

nTc



where, fe = fd − f d is carrier frequency offset, an is the signal amplitude, the real part and imaginary part of nn are independent of each other, and are respectively Gaussian  white noise sequences with mean value of 0 and variance of σn2 / Bpd T c , Bpd is the noise bandwidth before integration. Here,  an = P/2Cn Dn sinc(fe Tc ) (19) 1 nn = Tc

(n+1)T  c

n˜ (t)dt

(20)

π 2

(21)

nTc

θc = π fe Tc + θ0 +

Considering that the code phase search step is tbin = Tc /D, x τ  < tbin /2, the code phase deviation will be smaller after fine search. After obtaining the time synchronization information, the chip integration results will be accumulated correlatively to obtain symbol information, and symbol synchronization will be completed. Namely, yk =

K−1

Ck∗K+m xk∗K+m = Ak Rk (τ )ej(2π kfe Ts +θs ) + Nk

(22)

m=0

where, Ak is the signal amplitude, Rk (τ ) is the autocorrelation function of the spread spectrum code, Ts = KTc is the symbol time length, K is the number of chips corresponding to each symbol, θs is the initial phase of the - symbolic carrier, the real part

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and imaginary part of Nk are independent of each other, and are respectively Gaussian  white noise sequences with mean value of 0 and variance of Kσn2 / Bpd T c . Here, Ak =

 sin(π fe Ts ) P/2Dk sinc(fe Tc ) sin(π fe Tc )

Nk =

K−1

Ck∗K+m nk∗K+n

(23)

(24)

n=0

θs = π fe Ts + θ0 + π/2 When 2π fe Ts  1, Eq. (23) can be approximated as  Ak = P/2Dk sinc(fe Tc )K

(25)

(26)

It can be seen that the performance of the received signal is affected by the captured Doppler frequency offset, the coherent integration time (here is the chip time), and the code phase deviation. 3.2 Tracking Algorithm Consideringthe characteristics of short-time burst signal, it is difficult to adopt the traditional closed-loop tracking algorithm, so the open-loop carrier synchronization algorithm is needed. There are many open-loop carrier synchronization algorithms, such as M&M algorithm [4], Kay algorithm [5], Fitz algorithm [6], L&R algorithm [7], etc. This paper focuses on the analysis of L&R algorithm and M-L&R algorithm. Carrier frequency offset compensation Since the captured frequency resolution is f , the acquired Doppler estimation error fe is within the range of [– f / 2,  f / 2]. Therefore, fe needs to be further estimated. Carrier frequency offset estimation Jiang Wen Bing [8] gives the approximate solution of carrier frequency offset estimation of MPSK modulation obtained by [7] when SNR is good and Doppler frequency offset is small (for convenience of description, it is called M-L&R algorithm in this paper)  L 

1 fe = arg RM (k) , L < N (27) M π Ts (L + 1) 

k=1

where, arg[·] is the argument angle, M is the exponent of MPSK, N is the length of symbols, and the autocorrelation operation result RM (k) after demodulation is N  ∗

1 M yiM yi−k RM (k) = N −k i=k+1

where, “*” means taking conjugate, M is the exponent of MPSK.

(28)

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The estimation range of carrier frequency offset is |fe |
1, we find the second cluster in the same way, and the object number is denoted as N (2) . If M − N (1) = 1, N (2) = 1. If M − N (1) = 0, there is no second cluster, then N (2) = 0.

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Step 3: Positioning Calculation The signals corresponding to the first cluster participate in positioning calculation. Step 4: Spoofing Detection It is judged whether N (2) is greater than 1. If yes, the detection result is that there is spoofing interference. If not, spoofing interference is considered nonexistent. 3.2 Method Feasibility Analysis The proposed GNSS anti-spoofing method based on signal transmission time density clustering uses the signals corresponding to the first cluster to perform positioning calculation, and judges whether there is spoofing interference according to the object number of the second cluster. The feasibility of the method is analyzed below. Generally speaking, the probability of two authentic signals appearing anomalies at the same time is extremely low. Ignoring this situation, this paper assumes that at any time, there is at most one authentic signal with abnormal transmission time. Based on this assumption, when there is no spoofing interference, the object number of the second cluster satisfies that N (2) is less than or equal to 1, and the detection result is that there is no spoofing interference. In addition, the signal with large abnormal degree can be directly eliminated, so as to get correct positioning results. When there is spoofing interference, if the abnormal degree of spoofing signals is small, this method cannot detect spoofing interference. However, both spoofing signals and authentic signals will participate in positioning calculation. Since they generally do not meet the consistency, RAIM method can detect anomalies [14]. If the abnormal degree of spoofing signals is large, it is highly probable that N (2) is greater than 1, and this method will be able to give an alarm to spoofing interference. From the above analysis, it can be concluded that when the degree of anomaly is large, the proposed anti-spoofing method can eliminate abnormal signals when there is no spoofing interference, and give an alarm when there is spoofing interference.

4 Experimental Results In this chapter, the feasibility of the proposed method will be verified by testing experiments. B1I signals are used for the test. The experimental devices include GNSS receiver, signal source simulator, antenna, signal synthesizer, etc. The signal source simulator can generate spoofing signals according to ephemeris information and preset receiver state and time. The longitude of the experimental site is about E104.75°, the latitude is about N31.52°, and the altitude is about 500 m. 4.1 Signal Transmission Time Test In this section, the transmission time of B1I signals is tested. Table 1 shows the three groups of signal transmission times tested in the environment without spoofing interference. Their corresponding test times are 9:00, 15:00 and 20:00 Beijing time respectively.

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In Table 1, PRN numbers are marked black for MEO satellites and red for GEO/IGSO satellites. The three groups of signal transmission time in Table 1 are unified, and the corresponding maximum transmission time difference is obtained statistically, as shown in Table 2. Table 1. Three sets of signal transmission time. The first group

The second group

The third group

PRN

Transmission time (s)

PRN

Transmission time (s)

PRN

Transmission time (s)

3

349277.8769

39

370875.8799

46

388871.9259

1

349277.8733

30

370875.9182

1

388871.8727

38

349277.8781

2

370875.8761

2

388871.8760

39

349277.8666

3

370875.8766

3

388871.8763

5

349277.8713

4

370875.8683

5

388871.8710

7

349277.8741

8

370875.8800

6

388871.8801

8

349277.8786

6

370875.8808

7

388871.8767

10

349277.8771

9

370875.8768

9

388871.8769

11

349277.9198

16

370875.8799

10

388871.8745

13

349277.8776

13

370875.8809

16

388871.8785

14

349277.9274

20

370875.9197

19

388871.9264

27

349277.9115

23

370875.9236

20

388871.9210

28

349277.9245

27

370875.9132

22

388871.9192

33

349277.9270

29

370875.9152

30

388871.9113

40

349277.8726

32

370875.9252

36

388871.9241

41

349277.9184

37

370875.9210

39

388871.8783

Table 2. Maximum unified transmission time difference. Minimum unified Transmission time (s)

Maximum unified Transmission time (s)

Maximum time Difference (s)

The first group

349277.9115 (PRN 27)

349277.9274 (PRN 14)

0.0159

The second group

287946.9132 (PRN 27)

287946.9285 (PRN 13)

0.0153

The third group

388871.9113 (PRN 30)

388871.9277 (PRN 6)

0.0164

Assuming that the altitude of the receiver is equal to 500 m, the maximum unified transmission time difference of BDS can be calculated as about 0.02 s by Eq. (11). According to the analysis in Sect. 2.2, the density clustering threshold can be set to 0.02 s. As can be seen from Table 2, the three maximum unified transmission time differences are 0.0159, 0.0153 and 0.0164 s respectively, which meet the requirements of less than

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or equal to T e . It means that the signal transmission times of each group belong to the same cluster, which is consistent with the actual situation. The test results show that the analysis of density clustering threshold selection in this paper is reliable. 4.2 Ability Test for Eliminating Abnormal Signals This section tests the ability of the proposed method to eliminate abnormal signals. Since the probability of satellite fault or errors in ephemeris calculation is very small, this section chooses to simulate the abnormal situation by tampering with the signal transmission time. In the test process, the transmission time of PRN 3 signal is reduced by 0.03 s, and the density clustering threshold is set to 0.02 s. The test results are shown in Fig. 3. In the figure, the left half of subgraph (a) is the unified signal transmission time corresponding to each channel, and the right half is the result of sorting from small to large and density clustering. Subgraph (b) shows the satellite number, locking mark and carrier-to-noise ratio corresponding to each channel. The locking mark E0 indicates that the signal is locked but does not participate in positioning calculation, and E1 indicates that the signal is locked and participates in positioning calculation. Subgraph (c) is the distribution of satellites participating in positioning and the results of positioning calculation.

Unified Signal Transmitting Time

The Second Cluster

Sorting and Density Clustering

The First Cluster

Latitu de Longitude Altitud e

(a) PR N

Loc kin g Mark

C/ N0

X PR N

Loc kin g Mark

C/ N0

Y Z V VX

VY VZ Pos itioning Satellite N um ber

(b)

(c)

Fig. 3. Experimental results in abnormal signal scene.

From the subgraph (a), we can see that the unified transmission time of PRN 3 signal belongs to the second cluster, N (2) = 1. Since N (2) = 1, the spoofing detection result is no spoofing interference, which means that the positioning calculation results are credible. The test results show that only PRN 3 signal does not participate in positioning, and the positioning calculation results are correct, which is consistent with the analysis results, which proves that the proposed method can eliminate signals with abnormal transmission time.

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4.3 Anti-spoofing Ability Test This section tests the ability of the proposed method to detect deception interference. In the test process, the receiver receives and processes the authentic signals and a group of spoofing signals generated by the signal source simulator. The signal source simulator sets the longitude, latitude and altitude of the receiver as E116.00°, N40.00° and 100 m, respectively. The power of spoofing signals is adjusted to be close to the authentic signals, and the density clustering threshold is set to 0.02 s. The test results are shown in Fig. 4, where the contents are consistent with those in Fig. 3. From the subgraph (a), we can see that the unified transmission time of PRN 1, PRN 8, PRN 27, PRN 19 and PRN 20 signals belongs to the second cluster, N (2) = 5. Since N (2) > 1, the spoofing detection result shows that there is spoofing interference, which means that the positioning calculation results are not credible. The test results show that PRN 1, PRN 8, PRN 27, PRN 19 and PRN 20 signals do not participate in positioning, and the positioning calculation results are the receiver position set by the signal source simulator, which is consistent with the analysis results. It is proved that the proposed method can detect spoofing interference.

Unified Signal Transmitting Time

The Second Cluster Sorting and Density Clustering

The First Cluster Latitu de Longitude Altitud e

(a) PR N

Loc kin g Mark

C/ N0

X PR N

Loc kin g Mark

C/ N0

Y Z V VX

VY VZ Pos itioning Satellite N umber

(b)

(c)

Fig. 4. Experimental results in spoofing interference scene.

5 Conclusion Based on the fact that the transmission time difference between any two authentic signals without anomalies is within a certain range, this paper proposes a GNSS anti-spoofing method based on signal transmission time density clustering, and verifies the feasibility of the method by testing experiments. The analysis and test results show that the proposed method can eliminate the abnormal signal when there is no spoofing interference and

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give an alarm when there is spoofing interference. In addition, this paper also analyzes the selection of density clustering threshold of signal transmission time in detail, and reduces the density clustering threshold of BDS by unifying the signal transmission times. The ability of the proposed method to eliminate abnormal signals and detect spoofing interference is further improved.

References 1. Grant A, Williams P, Ward N, Basker S (2009) GPS jamming and the impact on maritime navigation. J Navig 62(2):173–187 2. Ioannides T, Pany T, Gibbons G (2016) Known vulnerabilities of global navigation satellite systems, status, and potential mitigation techniques. Proc IEEE 104(6):1174–1194 3. Humphreys T (2012) Statement on the vulnerability of civil unmanned aerial vehicles and other systems to civil GPS spoofing. Technical Report, University of Texas at Austin 4. Warner J, Johnston R (2002) A simple demonstration that the Global Positioning System (GPS) is vulnerable to spoofing. J Secur Adm 25(2):19–27 5. Ouyang X, Zeng F, Hou P, Guo R (2015) Analysis and evaluation of spoofing effect on GNSS receiver. In: Proceedings of UIC-ATC-ScalCom, pp 1388–1392 6. Shepard D, Humphreys T, Fansler A (2012) Evaluation of the vulnerability of phasor measurement units to GPS spoofing attacks. Int J Crit Infrastruct Prot 5(3–4):146–153 7. Schmidt D, Radke K, Camtepe S (2016) A survey and analysis of the GNSS spoofing threat and countermeasures. ACM Comput Surv 48(4):1–31 8. Kaplan E, Hegarty C (2006) Understanding GPS: principles and applications. Artech House Publishers, Boston, USA 9. Rao A, Liu B, Li Q, Zhang L (2016) Characteristics and calculation method of GLONASS ephemeris’s message. J Chin Inert Technol 24(3):355–360 10. Yang Y, Li H, Lu M (2015) Performance assessment of signal quality monitoring based GNSS spoofing detection techniques. In: Proceedings of China satellite navigation conference, pp 783–793 11. Sander J (2011) Density-based clustering. In: Encyclopedia of machine learning. Springer US 12. Hao D, Wu X, Yu L (2022) Review of clustering algorithm based on density. Commun Technol 55(2):135–142 13. Xie G (2013) Principles of global navigation satellite systems: GPS. GLONASS and Galileo. Publishing House of Electronics Industry, Beijing 14. Tao H, Wu H, Li H, Lu M (2019) GNSS spoofing detection based on consistency check of velocities. Chin J Electron 28(2):218–225

Research on Spoofing Detection Based on C/N0 Measurements for GNSS Array Receivers Jinyuan Liu , Yuchen Xie , Feiqiang Chen , Shaojie Ni , and Guangfu Sun(B) College of Electronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China [email protected]

Abstract. In recent years, Global Navigation Satellite System (GNSS) spoofing detection techniques have attracted wide attention. Compared with jamming, spoofing which always hides in the shadows has stronger concealment leading to more threat to the security of receivers. Carrier-to-noise ratio (C/N0 ) is one of the important measurements of receiver. Spoofing may cause abnormal changes in the C/N0 , but the variations of the C/N0 are not obvious in most cases, and it is liable to cause false alarm in the presence of jamming. Based on antenna arrays, this paper theoretically derives the effective C/N0 model of array receivers as spoofing successfully or unsuccessfully captures tracking loop. And we demonstrate that the C/N0 single difference (CSD) between satellites can be the testing statistic for spoofing detection. Simulation results show that the proposed method can detect the abnormal C/N0 features of counterfeit signals after anti-jamming for the antenna array. This method does not require modifications to the hardware configuration of conventional receivers and can provide an effective defense for array receiver in the combination of jamming and spoofing attacks. Keywords: GNSS · Spoofing detection · Antenna array · C/N0

1 Introduction 1.1 A Subsection Sample The Global Navigation Satellite Systems (GNSS) have become a critical in-frastructure to provide time and position information. With the development of the Internet of Things, unmanned platforms, mobile communication base stations and other systems, more and more devices will rely on GNSS to provide secure and reliable position and timing services. However, GNSS signals are weak-power (with a landing level of about –163 dBW), which are naturally vulnerable to unintentional and intentional interference [1]. Intentional interference can be divided into two categories: jamming and spoofing. Spoofing is highly concealed and threatening, which seriously affects the security and availability of GNSS and prevents receivers from obtaining trusted position and/or timing information. Especially, with the rapid development of software-defined radio (SDR) technology, the © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 556–566, 2024. https://doi.org/10.1007/978-981-99-6932-6_46

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cost and difficulty of spoofing attack will be significantly reduced by combining relevant RF platforms with open source signal simulators [2]. At present, the spoofing attack is mainly in the form of single station i.e., multiple counterfeit signals are sent by the same source. This feature can be exploited to distinguish the authentic signals from the spoofed signals. The carrier-to-noise ratio (C/N0 ) is widely used to evaluate the quality of GNSS signals. In an open area with good observation, the C/N0 measurements vary smoothly which are generally only related to the platform dynamic changes and ionospheric errors. The C/N0 measurement for defender is easy to obtain and the method is simple, while the spoofing attacker is difficult to precisely control the signal power reaching the defender’s antenna. Therefore, monitoring the abnormal variation of C/N0 is known to be an effective means to detect spoofing. A joint detection method of C/N0 and AGC is proposed in [3] to give the C/N0 and AGC characteristics of receiver under authentic signals and spoofing, respectively. This method requires the receiver to have an additional AGC and the C/N0 measurements to be stable. A difference method in C/N0 is utilized in [4] for spoofing detection, which requires two antennas with different patterns, such as a monopole antenna and a patch antenna. This method requires significant difference between two patterns of antenna, while the difference between common GNSS antenna is small, which will result in high false alarm rate. Jahromi et al. proposed a method based on the prior power information of GNSS signals [5]. Since the C/N0 of the real satellites in a certain area is usually known in advance within a certain range, any inconsistency with this prior information could indicate the presence of spoofing. The performance of spoofing detection is heavily dependent on the the prior threshold, making it susceptible to improve the missed alarm if the spoofer modulates the signal power. Another approach, as presented in reference [6], exploits the difference in correlation coefficients between the real and spoofed signals when the receiver or antenna is in motion. This method essentially uses the spatial movement to introduce the variation of received power which is always be small, and the performance is influenced by the distance and velocity of movement, resulting in a limited practical application. With the increasing threaten of interference, the use of antenna array combined with space-time processing (STAP) or space-frequency processing (SFAP) technology is the most common and effective means for current GNSS receivers [7, 8]. The above methods based on C/N0 are mainly applied for single-antenna receiver which still have been difficult to use in receivers equipped with anti-jamming antenna arrays. It is well known that C/N0 of antenna array receiver depends on the processing gain, which depends on the relative power spectral densities of the signal of interest (SOI), interference and noise [9]. The unpredictable variation of C/N0 in the presence of jamming and spoofing attack will introduce degradation in the performance of spoofing detection. In recent years, more and more civil and military platforms are reported to affected by spoofing [10, 11]. In the actual scenario, the combination of jamming and spoofing attack has become increasing, such as jamming the victim’s instrument first and then dragging the victim off the original correlation function unnoticed [12]. To solve this problem, this paper proposes a spoofing detection method based on single difference (SD) of C/N0 between satellites after mitigating jamming by the adaptive antenna array.

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The remainder of this paper is organized as follows. In Sect. 2, the theoretical model of antenna array and the effective C/N0 when the jamming and spoofing exist simultaneously are given. The inter-satellite single difference measurement of C/N0 is introduced in Sect. 3, and based on this, a spoofing detection method is designed. The Sect. 4 gives the simulation results to verify the theoretical analysis. Finally, the conclusion is given in Sect. 5.

2 Signal Model 2.1 Array Signal Model We consider that the array is composed of M elements and satisfies the narrowband assumption. It is assuming that counterfeit signals forged by spoofer are transmitted from the same direction. The received signal of the antenna array can be expressed in the complex baseband as:

x(t) =

P  p=1

apau sp (t) + asp

Q 

sq (t) +

q=1

J 

aji i(t) + n(t)

(1)

j=1

where the superscript au, sp and i represent the authentic signal, spoofing and jamming, respectively, which P, Q and J are the number of the corresponding signal component. The steering vector of p-th real satellite signal, q-th spoofing and j-th jamming are shown as:   2π T au 2π T au 2π T au apau = e−j λ p1 ep , e−j λ p2 ep , . . . , e−j λ pM ep   2π T sp 2π T sp 2π T sp asp = e−j λ p1 e , e−j λ p2 e , . . . , e−j λ pM e   2π T i −j p e −j 2π pT ei −j 2π pT ei aji = e λ 1 j , e λ 2 j , . . . , e λ M j

(2)

In (2), pm is the position vector of m th (m = 1, 2, . . . M ) array element. The unit propagation vector of plane wave is determined by the elevation angle θ and azimuth angle ϕ, that is to say, e = [sin θ cos ϕ, sin θ sin ϕ, cos θ ]T . The STAP is considered, which is the most widely used in array receivers [13, 14]. The output of the STAP can be given as: y[n] = wH x[n]

(3)

where x[n] denotes the digital signals output by analog to digital converter (ADC), and the complex weight vector is w = [w1,1 , ...w1,N , w2,1 , ...w2,N , ..., wM ,1 , ...wM ,N ]T

(4)

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where wmn is the weight at the n th tap of the m th array element. Based on different requirements, various weight calculation methods have been proposed. The power inversion (PI) criterion uses the covariance matrix of the received signal to form a nulling in the direction of the incoming signal with strong power [15]. PI have been widely used in GNSS antenna array because it is easy to implement without any prior information of the received signal [16]. The weight is calculated as follows:

wPI =

Rx−1 bn

−1 bH n Rx bn

= μRx−1 bn

(5)

where μ is a normalization constant, bn is the M ×N dimensional vector with 0 elements except for 1 at the reference tap. Since the power of real signal component and spoofed signal component is well below the noise, (5) can be simplified as: i

Rx = E[x(t)x (t)] ≈ Ri + Rn ≈ H

N 

Pj aji (aji )H + σ 2 I

(6)

j=1

2.2 Effective C/N0 Model The effective C/N0 model of the array receiver in the presence of both jamming and spoofing is derived below. The adaptive antenna array can be regarded as a digital filtering system consisting of M antenna elements, and the frequency response of the system can be expressed as [9]:

Hsys (f , θ, ϕ) =

M 

Am (f , θ, ϕ)Fm (f )Wm (f )e−j

2π λ

pTm e(θ,ϕ)

m=1

=

M  N  m=1 n=1

(7) T −j 2π λ pm e(θ,ϕ)

Am (f , θ, ϕ)e  

Generalized steering vector

∗ −j2π(n−1)fTs F (f )wmn e  m







Array Pattern

where Am (f , θ, ϕ), Fm (f ) and Wm (f ) denote the response of the m th antenna element for the signal incident from the (θ, ϕ), the response of the RF channel behind the element and the response of STAP filter, respectively. Assuming that the normalized power spectral density of the real signal is Gs (f ) ( Gs (f )df = 1) and the signal power is Cs , the power spectral of the p-th authentic signal at the output of the adaptive antenna array is

2



Spau (f ) = Cs Hsys (f , θpau , ϕpau ) Gs (f )

(8)

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It can be assumed that the power spectral density of spoofing with the power Csp , and all counterfeit signals are incident from the direction (θ sp , ϕ sp ), the power spectral of the q-th spoofing at the output of the adaptive antenna array is

2

sp Sq (f ) = Csp Hsys (f , θ sp , ϕ sp ) Gs (f )

(9)

If the power of the j-th jamming is Cj , and the normalized power spectral density is Gj (f ) ( Gj (f )df = 1), the power spectral of the j-th jamming at the output of the adaptive antenna array is

2



Sji (f ) = Cji Hsys (f , θji , ϕji ) Gji (f )

(10)

The noise component in the received signal can be modeled as the Gaussian white noise with zero mean, and its power spectral density at the array output is

Sn (f ) = Cn

M 

|Fm (f )Wm (f )|2

(11)

m=1

where Cn is the total noise power before the signal enters the RF front-end filter. Firstly, considering that the spoofing fails to capture the tracking loop and does not affect the correlation peak of the real signals. In this case, the spoofing is equivalent to a type of matched-spectrum interference. Due to the cross-correlation between pseudocodes, the spoofing may improve the noise floor after STAP filtering [5]. Referring to [17], (7)–(11) can further give the theoretical model of effective C/N0 as



Cs N0

=

β

2

2r



au au

Cs βr Hsys (f , θp , ϕp ) Gs (f )df

−2

eff



βr 2 − β2r

(12)

Gw (f )Gs (f )df

where βr is RF front-end bandwidth, Gw (f ) is the sum of power density of interference and noise components after filtering by the adaptive antenna array as

2

Gw (f ) = QCsp Hsys (f , θ sp , ϕ sp ) Gs (f ) J

2 



Cji Hsys (f , θji , ϕji ) Gji (f ) + Sn (f ) + j=1

(13)

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Secondly, when the spoofing successfully captures the tracking loop of the receiver, the theoretical model of effective C/N0 can be expressed as: 

Cs N0

=

β

2

2r



sp sp



Cs βr Hsys (f , θ , ϕ ) Gs (f )df

−2

eff

βr 2 − β2r

(14)

Gw (f )Gs (f )df

where the output power of the jamming and noise components after filtering by the adaptive antenna array sums up to Gw (f )

=

J 



2



Cji Hsys (f , θji , ϕji ) Gji (f ) + Sn (f )

(15)

j=1

3 Spoofing Detection In the previous section, the theoretical model of effective C/N0 under successful and unsuccessful spoofing are given, respectively. In this section, the C/N0 single difference (CSD) metric and a spoofing detection method are further discussed. 3.1 C/N0 Single Difference Supposing that the set of satellites that can be stably tracked within the observation time is . The C/N0 measurement of the h th and l th (h, l ∈ , h = l) satellite is Ch and Cl , respectively. When the PRNs are real satellites, the CSD between the two satellites can be obtained according to (12) au Ch,l

=



2 β

2 

β2r

2r

au au au au



Cs βr Hsys (f , θh , ϕh )Gs (f )df − βr Hsys (f , θl , ϕl )Gs (f )df

−2 −2

βr 2 − β2r

(16)

Gw (f )Gs (f )df

It can be seen that the CSD model in the nominal case is quite complex, and it is determined by the array response to the different signal components. It is obvious that this indicator will have significant values introduced by the adaptive pattern variation under the jamming. Furthermore, if the receiver tracks the signals incident from the same direction, the CSD between different satellites is theoretically zero, which can be expressed as sp

Ch,l = 0

(17)

That is to say, the actual value of the CSD under the spoofing condition is mainly determined by the C/N0 measurement noise which is related to the C/N0 estimation method used by the receiver.

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3.2 Spoof Detection Based on C/N0 Single Difference The CSD deduced in the previous section shows significant difference between real signal and spoofing, so it can be applied as a detection statistic. Let H 0 represents the hypothesis in case of the authentic signals and H 1 represents the hypothesis in case of spoofing. The hypothesis testing model can be established as 

au H 0 Ch,l = Ch,l + nau h,l sp

H 1 Ch,l = nh,l

(18)

where nh,l is the SD in the noise of C/N0 measurement. In the case of H 0 , it is difficult to accurately determine the distribution on the CSD because the adaptive pattern of antenna array varies randomly in the presence of interference. However, in the case of H 1 , the statistics satisfy the following distribution Ch,l ∼ N (0, 2σn2 )

(19)

where σn2 is the variance of the C/N0 measurement error. Thus, we can set a fixed detection threshold in advance empirically based on the theoretical value of the C/N0 measurement error. The common methods of C/N0 estimation in receivers include Narrow-Wideband Power Ratio Method (NWPR) [18], Variance Summing Method (VSM) [19], Moments Method (MM) [20] and other methods. Researchers have studied the above-mentioned C/N0 estimation algorithms in detail, so the theory of specific algorithms will not be repeated here. The method of moment estimation and its estimation error have been introduced in [21]. The simulation analysis in the next section will take the moment estimation method as an example and use the upper limit of the theoretical value of the C/N0 estimation error as the detection threshold to establish a hypothesis test. Therefore, if the detection statistic is greater than the threshold value γ , the hypothesis test H0 is determined to be valid, and there is at least one real signal between the two signals. On the contrary, the hypothesis test H 1 should be made, where the two signals are both counterfeit signals.

4 Simulation Results In this section, the proposed spoofing detection method based on CSD metric is simulated and verified. In the simulation model, the antenna array is selected as a four-element circular array with the half-wavelength spacing, of which an element locates in the central. And the number of tap in STAP algorithm is chosen to be 5. According to (7), the impact of antenna element patterns on the effective C/N0 cannot be ignored. In order to simulate the actual characteristics of antenna element patterns, this paper models a dual-feed point microstrip patch antenna commonly used by GNSS receivers in CST Microwave Studio (as shown in Fig. 1) [22]. Noted that, the broadband impact brought by antenna elements is not considered in the simulation. That is to say, the gain and phase pattern of the antenna are the same at each frequency point.

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Fig. 1. Microstrip patch antenna simulated in this study

We have built a GNSS array signal simulator based on MATLAB software developed in [23], which can generate mixed signals including the authentic signals, jamming and spoofing. The main signal parameters are shown in Table 1. Two scenarios are set. One set of signal includes the authentic signals and three high-power broadband jamming, and the other set contains spoofing incident from the same direction and three highpower broadband jamming. The length of each scenario is 2s, where three wideband jamming signals begin at 0, 1 and 2 s, respectively. The signals generated by the array signal simulator are fed into the STAP module for anti-jamming processing. The output by the STAP filter will be processed by the software-defined receivers (SDR) and test the proposed metric to detect the spoofing. The sampling rate is set to 62 MHz and the IF frequency is 46.52 MHz. Table 1. The main parameters of simulation The type of signal

PRN

Authentic signal

2 4

Elevation (°)

Azimuth (°)

SNR (dB)

5

310

−28

15

220

−28

8

25

48

−28

11

35

80

−28

15

45

270

−28

Spoofing

2,4,8,11,15

75

0

−18

Jamming 1

/

80

120

35

Jamming 2

/

85

45

40

Jamming 3

/

75

0

40

The simulation results considered as an example of CSD detector is reported in Fig. 2. And PRN 02 is chosen to be the reference satellite. It can be clearly seen that the CSD metrics under the spoofing condition are much lower than those in the case of authentic signals. The simulation results verify the previous theoretical analysis that the CSD metric under the adaptive antenna array model can discriminate between the authentic signals and counterfeit signals in the presence of jamming.

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(a)

(b)

Fig. 2. CSD metrics in simulation under a authentic signal and b spoofing

The receiver operating characteristic (ROC) curves are commonly used to evaluate the performance of detection methods. Figure 3 shows the ROC curves of the proposed method under different numbers of jamming. Obviously, the performance of the detection method in the present of high-power jamming is significantly better than that in the absent of jamming. This is due to that, if there is no high-power jamming, the adaptive pattern of antenna array will introduce slightly difference towards different directions. It should be noted that, the spoofing in the absent condition can be detected by other methods using single antenna such as introduced in Sect. 1, which are out of the scope in this paper.

Fig. 3. ROC curves under different numbers of jamming

5 Conclusion This paper proposes a new CSD metric for spoofing detection by measuring the abnormal energy introduced in the process of anti-jamming by the adaptive antenna array. We derived theoretical model and further verified the performance of CSD metric by

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a simulation platform based on the software-defined receiver. The simulation results demonstrate that the method can effectively detect spoofing especially in the presence of jamming. The idea in this paper significantly decreases the computational complexity for spoofing detection, which depends on the raw measurements in receivers and does not require additional modifications to the conventional GNSS array receivers. Acknowledgments. This study is supported by National Nature Science Foundation of China U20A0193.

References 1. Xie G (2009) Principles of GPS and receiver design[M]. Publishing House of Electronics Industry (in Chinese) 2. Semanjski S, Semanjski I, Wilde WD, et al. (2020) Use of supervised machine learning for GNSS signal spoofing detection with validation on real-world meaconing and spoofing data: part I[J]. Sensors (4) 3. Manfredini EG, Akos DM, Chen YH, et al. (2018) Effective GPS spoofing detection utilizing metrics from commercial receivers[C]. 2018 International Technical Meeting of The Institute of Navigation 4. Zhang Z, Trinkle M, Qian L, et al. (2013) Quickest detection of GPS spoofing attack[C]. Military Communications Conference. IEEE 5. Jahromi AJ, Broumandan A, Nielsen J et al (2012) GPS spoofer countermeasure effectiveness based on signal strength, noise power, and C/N0 measurements[J]. Int J Satel Commun Netw 30(4):181–191 6. John, Nielsen, Ali, et al. (2011) GNSS spoofing detection for single antenna handheld receivers[J]. Navigation 58(4):335–344 7. Chen FQ (2017) Interference mitigation and measurement biases compensation for GNSS antenna array receivers[D]. National University of Defense Technology, (in Chinese) 8. Daneshmand S (2013) GNSS interference mitigation using antenna array processing[D]. PhD dissertation, University of Calgary 9. O’Brien AJ, Gupta IJ (2010) Comparison of output SINR and receiver C/N0 for GNSS adaptive antennas[J]. IEEE Trans Aerosp Electron Syst 45(4):1630–1640 10. Psiaki ML, Humphreys TE (2016) GNSS spoofing and detection[J]. Proc IEEE 104(6):1258– 1270 11. Schmidt D, Radke K, Camtepe S et al (2016) A survey and analysis of the GNSS spoofing threat and countermeasures[J]. ACM Comput Surv 48(4):1–31 12. Broumandan A, Jafarnia-Jahromi A, Daneshmand S et al (2016) Overview of spatial processing approaches for GNSS structural interference detection and mitigation[J]. Proc IEEE 104(6):1–12 13. Zukun Lu, Junwei Nie, Feiqiang Chen, Huaming Chen, Gang Ou (2017) Adaptive timetaps of STAP under channel mismatch for GNSS antenna arrays [J]. IEEE Transactions on Instrumentation & Measurement 14. Marathe T, Daneshmand S, Lachapelle G (2016) Assessment of measurement distortions in GNSS antenna array space-time processing[J]. Int J Anten Propag 2016(2):1–17 15. Compton RT (1979) The power-inversion adaptive array: concept and performance[J]. IEEE Trans Aeros Elect Syst AES-15(6):803–814 16. Chen FQ, Nie JW, Ni SJ, et al. (2017) Improved least mean square algorithm for powerinversion global navigation satellite system antenna array[J]. J Nat Uni Def Technol 6, 39(3):47–51 (in Chinese)

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17. Betz JW, Kolodziejski KR (2009) Generalized theory of code tracking with an early-late discriminator part I: lower bound and coherent processing[J]. IEEE Trans Aerosp Electron Syst 18. Bradford W Parkinson, James J Spilker (1996) Global positioning system: theory and applications[M]. Am Inst Aeronaut Astron 12 19. Psiaki ML, Akos DM, Thor J (2003) A comparison of “direct RF sampling” and “down convert & sampling” GNSS receiver architectures [C]. Proc ION GPS/GNSS 2003:9 20. Pauluzzi DR, Beaulieu NC (2000) A comparison of SNR estimation techniques for the AWGN channel. IEEE Trans Commun 48(10):1681–1691 21. Emanuela Falletti, Marco Pini, et al. (2008) Assessment on low complexity C/No estimators based on MPSK signal model for GNSS receivers[C]. Position, Location and Navigation Symposium, IEEE/ION 2008: 167–172 22. Li LX (2016) Research on antenna technique for high accuracy navigation receiver [D]. National University of Defense Technology, (in Chinese) 23. Liu J, Li L, Lv Z et al (2019) Impact of element pattern on the performance of GNSS power-inversion adaptive arrays[J]. Electronics 8(10):1120

A Fast C/N0 Estimation Method Based on the Ratio of Acquisition Correlation Value Yimin Ma(B) , Hong Li, Ziheng Zhou, Zhenyang Wu, Wenhao Li, and Mingquan Lu Tsinghua University, Beijing 100084, China [email protected], [email protected]

Abstract. The carrier-to-noise ratio (C/N0 ) is widely recognized as a vital measurement in Global Navigation Satellite System (GNSS) as it serves as a common indicator of signal power. Its significance is apparent in numerous scenarios such as receiver tracking loop operation, spoofing detection, satellite signal quality monitoring, positioning and system state evaluation. Thus, research on estimating C/N0 has gained importance in practical applications. Most existing C/N0 estimation methods rely on the tracking process as a premise, leading to poor accuracy in specific scenarios where the signal is sporadic, intermittent or data is relatively short. Moreover, the signal tracking process limits the response speed and accuracy of existing methods, making them impractical for emergency scenarios requiring rapid estimation. To address these limitations and expand the applicability of C/N0 estimation, this paper proposes a fast C/N0 estimation method based on the acquisition correlation ratio (ACR). This approach estimates C/N0 in the acquisition stage using only millisecond observation information. Simulation and experimental results indicate that the proposed method can significantly enhance the estimation accuracy of C/N0 in short data scenarios compared to existing methods, achieving an estimation error of 0.52 dBHz with 50ms data. Keywords: C/N0 · Acquisition correlation value · Short data · Fast

1 Introduction The carrier-to-noise ratio, C/N0 , is a normalized measure of the signal-to-noise ratio. It is a key measurement output of the Global Navigation Satellite System (GNSS) receiver, which directly reflects the quality of satellite signals. Moreover, C/N0 can be used for various application scenarios, such as weighted least squares positioning [1], signal acquisition threshold setting [2], multipath error correction of carrier phase [3], and spoofing detection using power information [4]. Therefore, it is of great practical significance to do research on C/N0 estimation. Various estimation methods have been proposed so far. The most commonly used method is the Wideband-Narrowband Power Ratio (NWPR) [5], which is considered as the benchmark method for C/N0 estimation due to its high estimation accuracy [6]. The Correlator Comparison Method (CCM) has low computational complexity and needs to occupy additional asynchronous correlator resources [7]. The Variance Summation © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 567–577, 2024. https://doi.org/10.1007/978-981-99-6932-6_47

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Method (VSM) and Moment Estimation Method (MM) is simple to understand but its computational complexity is high, and the accuracy is poor in the case of low carrier-tonoise ratio [8]. Additionally, some scholars apply the Extended Kalman Filter to improve the estimation rate and robustness [9]. However, the above methods all depend on the tracking I/Q integral values to directly estimate the signal power and noise power, thereby obtaining the C/N0 estimation. But due to the errors in the tracking initialization parameters obtained by acquisition, the tracking loop needs continuous operation to converge to a stable state. Unstable tracking results can lead to non-ideal signal and noise power estimates. The existing methods require continuous data on the order of seconds to obtain reliable estimation results. In some practical application scenarios, the signal is sporadic, discontinuous and short, making it difficult to estimate C/N0 rapidly and accurately. These scenarios include using the signal power information to fast detect spoofing in the acquisition stage [10, 11], adaptively adjusting the tracking loop parameters in the initialization stage according to the fast estimation results of C/N0 [12, 13], and mitigating the impact of signal occlusion in urban canyons [14], etc. To address the aforementioned issues, this paper proposes a fast C/N0 estimation method based on the ratio of acquisition correlation values, called the Acquisition Correlation Ratio Method (ACR), which can rapidly estimate C/N0 and solve the problem that the existing methods are not applicable in the above application scenarios. The rest of the paper is organized as follows. Section 2 describes the GNSS signal processing and C/N0 calculation model. Section 3 presents the principle and derivation of the proposed ACR method in detail. Section 4 simulates and analyzes the ACR method and compares its performance with existing methods. Section 5 presents the actual test results and the last section is the summary and prospect part.

2 Signal Model Taking the GPS C/A signal as an example, the RF signal broadcast by the mth satellite is received by the antenna the receiver. After down-conversion, quantization and ADC sampling, the intermediate frequency signal is obtained, which can be expressed as [8]     (m) (m) sIF (tn ) =AIF D(m) tn − τa(m) P (m) tn − τa(m)     (m) (m) cos 2π fi + fd tn + θ (m) + wIF (tn ) (1) (m)

where tn represents the sampling time, AIF represents the signal amplitude, P (m) (·) represents the pseudo random noise (PRN) code, D(m) (·) represents the navigation message, τa(m) represents the signal delay, fi represents the intermediate frequency of the (m) signal, fd represents the Doppler frequency, θ (m) represents the initial carrier phase, (m) and wIF (·) represents the signal noise. The signal is multiplied by a set of local quadrature signals to obtain the I/Q signal. For convenience, the satellite number m is omitted from the expression below sI (tn ; f ) = AD(tn − τa )P(tn − τa ) cos(2π δfe tn + δθe ) + wI (tn )

(2)

A Fast C/N0 Estimation Method Based

sQ (tn ; f ) = AD(tn − τa )P(tn − τa ) sin(2π δfe tn + δθe ) + wQ (tn )

569

(3)

where f represents the local carrier frequency, δf e = f − fd and δθe represent the frequency difference and initial phase difference between the local carrier and the signal. Respectively, wI (tn ) and wQ (tn ) are the I/Q noise which can be assumed as independent Gaussian white noise N (0, σ 2 ). Further, correlating sI (tn ; f ) and sQ (tn ; f ) with the local pseudocode, the I/Q coherent integral value can be obtained Ik (f , τ ) =

N −1 1  AD(tn − τa )P(tn − τa )P(tn − τ ) cos(2π δfe tn + δθe ) N

+ Qk (f , τ ) =

1 N +

n=0 N −1 

1 N

P(tn − τ )wI (tn )

(4)

n=0 N −1 

AD(tn − τa )P(tn − τa )P(tn − τ ) sin(2π δfe tn + δθe )

n=0 N −1 

1 N

P(tn − τ )wQ (tn )

(5)

n=0

where k = 1, 2, . . . , K represents the index of the I/Q integral value,R(·) represents the normalized pseudocode autocorrelation function, τ represents the local code phase, N = fs Tcoh , fs is the sampling rate and Tcoh is the coherent integration time. To avoid the impact of navigation message bit flip on coherent integration, the duration of Tcoh is often less than one message bit, so it can be considered that D(·) = 1 in a coherent integration time. Ik (f , τ ) = AR(τa − τ )sinc(δfe Tcoh ) cos(ϕk ) + wI,k

(6)

Qk (f , τ ) = AR(τa − τ )sinc(δfe Tcoh ) sin(ϕk ) + wQ,k (7)  where ϕk = 2π fe t k + Tcoh + δθ e , t k represents the initial moment of coherent integration, and the noise wI,k and wQ,k obeys the Gaussian distribution N (0, σ12 ), in which √ σ = N σ1 . When the tracking loop converges to a stable state, the local pseudocode and carrier are precisely aligned with the signal, that is, τ = τa , f = fd , and δθe = 0, the above formula can be further simplified as 



Ik (fd , τa ) = A + wI,k Qk (fd , τa ) = wQ,k . According to the definition of C/N0 , it can be calculated as follows 2

 A 2 Pc 2 A = 10 lg C/N0 =10 lg fs Pw 2σ 2

2  A2 A fs = 10 lg =10 lg 2σ 2 2σ12 Tcoh Equations (6) to (9) are the basis of the C/N0 estimation methods.

(8)

(9)

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3 Method Based on the potential correspondence between the ratio of the acquisition correlation values and the signal power, this paper proposes a fast C/N0 estimation method based on the ratio of acquisition correlation values, the ACR method. In order to ensure that the acquisition result is not affected by the initial phase difference of the carrier, the acquisition correlation value is generally constructed by the I/Q correlation value [15], and its expression is as follows Vk (f , τ ) = Ik (f , τ )2 + Qk (f , τ )2 .

(10)

According to the formula above, maximum Vkm and the corresponding  the global carrier frequency and code phase fd,k , τ k is defined as  Vkm = max(Vk (f , τ )) fd,k , τk = argmax(Vk (f , τ )). (11) f ,τ

f ,τ

The same-frequency large correlation value Vks represents the maximum of the other correlation values with the same carrier frequency and a distance of more than one chip as Vkm and τ k denotes the corresponding code phase     Vks = max Vk fd,k , τ τˆk = argmax Vk fd,k , τ . (12) 

|τ −τk |>1

|τ −τk |>1

 Assuming sinc(δfe Tcoh ) ≈ 1, R(τa − τk ) ≈ 1 and R τa − τ k = p, we can get   Ik fd,k , τk = A cos(ϕk ) + wI,k Ik fd,k , τˆk = pA cos(ϕk ) + wI,k (13) 

  Qk fd,k , τk = A sin(ϕk ) + wQ,k Qk fd,k , τˆk = pA sin(ϕk ) + wQ,k .

(14)

Using σ1 to normalize the noise of Vkm and Vks , we have V˜ km = Vkm /σ1 V˜ ks = Vks /σ1 .

(15)

2 with 2 degrees of freedom For V˜ km , it obeys the non-central chi-square distribution X2,λ 1 and non-central parameter λ1 , and λ1 is shown in Eq. (17)

λ1 =

C/N0 A2 A2 A2 cos2 (ϕk ) + 2 sin2 (ϕk ) = 2 = 2Tcoh 10 10 . 2 σ1 σ1 σ1

(16)

For V˜ ks , it is equivalent to the maximum value of Ny independent and identically dis2 tributed non-central chi-square distribution X2,λ random variables, which is approxi2 mately equal to the number of p in the normalized self-correlation function R(·). The non-central parameter λ2 can be expressed as 

C/N0 A 2 λ2 = p = 2p2 Tcoh 10 10 . σ1

(17)

A Fast C/N0 Estimation Method Based 2 , F(x; n, λ) = Using f (x; n, λ) to represent the PDF of Xn,λ 2 , we can know [16] represent the CDF of Xn,λ

f (x; n, λ) = e

− λ2

x

0 f (x; n, λ)dx

n +∞ i  x 1 λ xi+ 2 −1 n i+ n e− 2 (x > 0) i! 2 + 1 2 2

i=0

571

to

(18)

2

Further we can get   E V˜ km = 2 + λ1

(19)

+∞  s ˜ vNy f (x; 2, λ2 )(F(x; 2, λ2 ))Ny −1 dv. E Vk =

(20)



0

In order to reduce the randomness of single measurement, we can take the K measurements of Vkm and Vks , and define the acquisition correlation value ratio rk as   1 K 1 K m m E V˜ km ˜ V V k k = K1 k=1 ≈  . rk = K1 k=1 (21) K K s s ˜ V V E V˜ ks k=1 k k=1 k K K The relationship between rk and C/N0 can be obtained rk = g(C/N0 ; Tcoh ) =

2 + λ1 . +∞ ∫0 vNy f (x; 2, λ2 )(F(x; 2, λ2 ))Ny −1 dv

(22)

The above formula establishes the correspondence between rk and C/N0 . rk can be obtained by observation, and therefore C/N0 can be estimated as follows C/N0 = g −1 (rk ; Tcoh ).

(23)

Since g −1 (rk ; Tcoh ) is difficult to be expressed, C/N0 can be estimated by interpolation or look-up method in practical applications.

4 Simulation Analysis This section describes the simulation experiments carried out to evaluate the impact of the model parameters Ny , p and Tcoh on the results and to compare the performance of the ACR method with existing methods. The intermediate frequency and sampling frequency of the simulation signal are 4.13 MHz and 16.37 MHz. 4.1 Influence of N y and p Taking the GPS C/A code signal as the example, the magnitude of the normalized autocorrelation function has three possible values besides 1, namely 65/1023, 63/1023

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and 0. Considering the small difference between the first two values, we assume that they have the same effect on the Vks . For formula (20), the simplest assumption is to ignore the influence of the possible value of p = 0, and given p = 65/1023, Ny = 250, where 250 is approximately equal to the number of values of non-ideal correlation peaks p = 65/1023. However, this assumption introduces substantial error when C/N0 is low as the difference between the correlation peak and 0 becomes insignificant under strong noise conditions. To overcome this limitation, based on the assumption of independent and identical distribution of Vks , we choose the fixed p = 65/1023, and map the influence of p = 0 to Ny . 2 , and Assuming that the random variable X1 obeys the chi-square distribution X2,0 2 , where λ is shown in formula (17), it can X2 obeys the chi-square distribution X2,λ 2 2 be obtained that under different C/N0 , the probability P(X1 > X2 ) can be calculated as follows +∞ P(X1 > X2 ) = (1 − F(x; 2, 0))f (x; 2, λ2 )dx.

(24)

0

The larger P(X1 > X2 ), the greater the influence of p = 0 relative to the influence of the non-ideal correlation peak. Figure 1 shows the values of P(X1 > X2 ) corresponding to different C/N0 when Tcoh = 1ms. It can be observed that P(X1 > X2 ) increases as C/N0 decreases and displays a gradual “slow-fast-slow” increasing trend. Ny = 2P(x1 > x2 )Ny2 + Ny1 .

(25)

Therefore, we can use P(X1 > X2 ) to adjust Ny , assuming Ny1 = 250, Ny2 = 1022− 250 = 772, and use the formula (25) to adjust Ny . 10,000 Monte Carlo simulations are performed on the ACR method. The results are shown in Fig. 2. The blue curve represents the ACR method with fixed Ny , and the red curve represents the ACR method with adjusted Ny . It can be clearly seen from the figure that the latter is more correspond to the simulation results. In addition, Fig. 2 also shows the simulation results of three different PRN satellites. The difference between the results of different satellites is not significant, which represents the rationality of neglecting the small difference between different satellites.

Fig. 1. The relationship between P(X1 > X2 ) and C/N0

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Fig. 2. The influence of two different Ny value to ACR and simulation result of satellites with different PRN

4.2 Influence of T coh When C/N0 is low, the acquisition correlation peak Vkm does not correspond to the true position of the signa l(fd , τ a ) shown in Eq. (13), so the acquisition correlation ratio value r k defined by Eq. (21) is greater than 1, and its theoretical value rk is less than 1, the estimation result of the ACR method does not correspond to the carrier-to-noise ratio, and a large estimation error will occur. Therefore, we define the lowest C/N0 that makes the theoretical acquisition correlation value ratio rk greater than 1 as the cut-off carrier-to-noise ratio (C/N0 )T of Tcoh , as shown in the following equation 

(C/N0 )T = min{C/N0 |rk = g(C/N0 ; Tcoh ) > 1}.

(26)

Table 1 lists the values of (C/N0 )T under different Tcoh . It can be clearly seen from the results that increasing Tcoh can significantly expand the range of C/N0 accurately estimated by the ACR method. Table 1. The relationship between Tcoh and (C/N0 )T Tcoh /ms

1

2

3

4

(C/N0 )T /dBHz

38.26

35.25

33.49

32.24

Figure 3 shows the theoretical relationship between C/N0 and rk under different Tcoh values and the Monte Carlo simulation results. It can be seen that the simulation results are consistent with the theoretical formula. 4.3 Performance Comparison To comprehensively measure the deviation and fluctuation degree of the estimated results compared with the real value, we choose the Root Mean Squared Error (RMSE) as the evaluation standard of the estimation effect of different methods. Figure 4 shows the estimation results of different methods. The first four curves in the legend represent the estimation results of the ACR method when only 50 ms data is

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Fig. 3. The theory and simulation results of ACR under different Tcoh

used, the NWPR-long and NWPR-short represent the calculation results of the NWPR method using 1 s and 50 ms stable I/Q integral value, which can be used as the standard to measure the estimation results of the ACR method. The NWPR-init represents the NWPR method using 50 ms initial I/Q integral value. The conclusions that can be obtained are as follows.

2 1.5 1 0.5 0 36

38

40

42

44

Fig. 4. RMSE comparison of different estimation methods

Firstly, as the real carrier-to-noise ratio (C/N0 )real decreases, the estimation error of the ACR method initially increases, then decreases and then increases. In this process, the error initially increases due to the limited estimation accuracy of the ACR method, which is affected by the noise power. The reason it decreases and then increases is that the estimation result is influenced by (C/N0 )T . When (C/N0 )real approaches (C/N0 )T and ultimately becomes smaller than the theoretical value, rk will gradually approach and be smaller than 1, but the measured value will be infinitely close to 1 and will never be smaller than 1. This causes the above change of error, and when (C/N0 )real is lower than (C/N0 )T , the error of the ACR method starts to increase linearly. As evident from Fig. 4, when Tcoh = 1 and(C/N0 )real starts from 39 dBHz, for every 1 dB decrease, the RMSE of the ACR method increases by approximately 1 dB. Comparing the results under different Tcoh laterally, it can be observed that with the increase of Tcoh , the (C/N0 )T decreases. Secondly, as compared with NWPR-long and NWPR-short, the ACR method can achieve the same level of accuracy as NWPR-long in cases of high (C/N0 )real . When

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(C/N0 )real > (C/N0 )T , the accuracy of the ACR method is superior to that of the NWPR-short method that uses 50ms accurate tracking results. Thirdly, NWPR-init reflects the real situation when the tracking loop is unable to enter the stable state in a timely manner in cases involving short data. It can be observed that the error gradually increases with the increase of (C/N0 )real . It is particularly noticeable in cases where the noise ratio is high. The reason is that even though the signal with higher (C/N0 )real can enable the loop to enter the steady state more quickly, the I/Q integral value in the initial stage of the tracking loop is unstable, and the result calculated by the integral value is low. Consequently, the performance of the estimation is more obviously affected for higher (C/N0 )real . If the influence of the bit flip of the navigation message is taken into consideration, NWPR-init generates a larger error.

5 Experiment Results To verify the effectiveness and accuracy of the ACR method, we carried out real-world experiment, and compared the estimation results of the ACR method with the NWPR method. The parameter settings is shown in Table 2 and the satellite positions are depicted in Fig. 5. Table 2. Parameters of the real-world experiment Parameter

Settings

Time

2020-5-15 22:40 UTC

Place

N 40.0016° E 116.3301°

IF frequency

46.42MHz

Sample frequency

20MHz

Satellites

3 14 16 22 26 29 31 32

The estimation result of the NWPR-long method with the highest estimation accuracy is used as the standard. The estimation results of the ACR method using 50 ms data and the NWPR-init and NWPR-short methods are compared. The experimental results in Table 3 reveals that the RMSE of NWPR-init reaches 4.39 dBHz due to the unstable initial I/Q integral value of the tracking loop and the inability to achieve message bit synchronization. However, the RMSE of the ACR method is only 0.52 dBHz, and it outperforms the NWPR-short method which has an RMSE of 0.80 dBHz. These experimental outcomes are consistent with the simulation results obtained in the previous subsection. In comparison with existing methods, the ACR method can rapidly and accurately estimate the carrier-to-noise ratio using short data.

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30°

60°

03

270°

26

22

29

31

90°

90°

14

16

32

180°

Fig. 5. Skyplot

Table 3. The RMSE of real data test results/(dBHz) PRN

Standard C/N0

ACR

NWPR-init

NWPR-short

3

44.25

0.67

4.07

0.77

14

46.36

0.70

6.44

0.79

16

44.04

0.79

2.72

0.68

22

42.54

0.60

4.41

0.89

26

51.19

0.26

6.11

0.89

29

46.37

0.36

4.98

0.68

31

49.55

0.36

4.29

0.71

32

41.07

0.41

2.13

0.97

Mean

–

0.52

4.39

0.80

6 Conclusion In this paper, a fast carrier-to-noise ratio estimation method based on the ratio of acquisition correlation values, the ACR method, is proposed. This method can use millisecondlevel data to fast complete high-precision estimation of C/N0 in the signal acquisition stage. Compared with the existing methods, the ACR method avoids the influence of instability in the initial stage of the tracking loop by constructing the relationship between the ratio of the acquisition correlation value and C/N0 . It greatly improves the estimation accuracy of C/N0 in the case of short data. In the case of using only 50 ms of data, the RMSE of ACR method is only 0.52 dBHz, while the RMSE of NWPR method calculated using the I/Q value of the tracking initial stage exceeds 4 dBHz. Therefore, this method can be applied to application scenarios with sporadic, discontinuous or short data, and can quickly and accurately estimate C/N0 . In the future, this method can also be combined with incoherent accumulation to analyze the quantitative impact of data length, and reduce algorithm complexity to improve performance.

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References 1. Zhou Z, Li H, Chen Z, et al (2022) GNSS spoofing discrimination based on doppler residual monitoring. In: Proceedings of the 2022 international technical meeting of the institute of navigation, pp 168–181 2. Liu S, Li S, Zheng J et al (2020) C/N0 estimator based on the adaptive strong tracking kalman filter for GNSS vector receivers. Sensors 20(3):739 3. Rost C, Wanninger L (2009) Carrier phase multipath mitigation based on GNSS signal quality measurements 4. Dehghanian V, Nielsen J, Lachapelle G (2012) GNSS spoofing detection based on receiver C/N0 estimates. In: Proceedings of international technical meeting of the satellite division of the institute of navigation 5. Sayre MM (2003) Development of a block processing carrier to noise ratio estimator for the global positioning system. Ohio University 6. Muthuraman K, Borio D (2010) C/N0 estimation for modernized GNSS signals: Theoretical bounds and a novel iterative estimator. Navigation 57(4):309–323 7. Groves PD (2005) GPS signal-to-noise measurement in weak signal and high-interference environments. Navigation 52(2):83–94 8. Sliarawi MS, Akos DM, Aloi DN (2007) GPS C/N0 estimation in the presence of interference and limited quantization levels. IEEE Trans Aerosp & Electron Syst 43(1):227–238 9. Issa H, Stienne G, Reboul S et al (2021) A probabilistic model for on-line estimation of the GNSS carrier-to-noise ratio. Signal Process 183(4):107992 10. Zhang X, Li H, Yang C et al (2020) Signal quality monitoring-based spoofing detection method for global navigation satellite system vector tracking structure. IET Radar Sonar Navig 14(6):944–953 11. Jahromi AJ, Broumandan A, Nielsen J et al (2012) GPS spoofer countermeasure effectiveness based on signal strength, noise power, and C/N0 measurements. Int J Satell Commun Netw 30(4):181–191 12. Cheng Y, Chang Q (2020) A carrier tracking loop using adaptive strong tracking Kalman filter in GNSS receivers. IEEE Commun Lett 24(12):2903–2907 13. Won JH (2013) A novel adaptive digital phase-lock-loop for modern digital GNSS receivers. IEEE Commun Lett 18(1):46–49 14. Tabatabaei A, Mosavi MR (2017) Robust adaptive joint tracking of GNSS signal code phases in urban canyons. IET Radar Sonar Navig 11(6):987–993 15. Kaplan ED, Hegarty C (2005) Understanding GPS/GNSS: principles and application, 3rd edn. Artech House 16. Wei L (2015) Mathematical statistics. Science Press, Beijing

Development and Evaluation of GPS L2C Software Receiver Baseband Signal Processing Module Zhenyang Wu(B) , Hong Li, Ziheng Zhou, Yimin Ma, Lingtao Wang, and Mingquan Lu Tsinghua University, Beijing 100084, China [email protected], [email protected]

Abstract. GPS L2 civil (L2C) signal adopts time-division multiplexed CM and CL code for spread spectrum modulation, which makes the design of replica code one of the crucial factors that determine the implementation complexity and system performance in GPS L2C baseband signal processing. Firstly, this paper introduces several commonly used replica codes in the acquisition of L2C CM code. Through theoretical analysis, the performances of these methods are compared from the perspectives of sensitivity and complexity. Furthermore, simple CM and CL tracking methods are compared based on discriminator performances. Then, a GPS L2C software baseband signal processing module with multiple optional replica code shapes which can be implemented for acquisition and tracking schemes as required is developed in this paper. The module is utilized to evaluate the impact of the above replica code designs on acquisition and tracking performance in realworld experiments. The research results provide a test and evaluation platform for users to optimize the design of L2C receiver according to their requirements of complexity and signal processing performance. Keywords: L2C · Replica code · Receiver · Signal acquisition

1 Introduction Since GPS satellite first broadcast L2 civil (L2C) signal at L2 frequency point (1227.6 MHz) in 2005, the signal has been widely used by various users. Compared with the traditional L1 coarse acquisition (C/A) signal modulated at L1 frequency point, L2C signal has better performance in weak signal acquisition performance, tracking performance and message demodulation bit error rate [1–3]. These improvements benefit from the time division multiplexing (TDM) based spread spectrum modulation mode adopted by L2C. Data channel with message bits and pilot channel without message are broadcasted in interlaced timeslots, so that users may use various local replica code shapes for better reception performance [4]. The modulation of L2C signal is divided into the following three levels: first, navigation message information with original data rate of 25 bps is convolutionally encoded © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 578–589, 2024. https://doi.org/10.1007/978-981-99-6932-6_48

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to obtain message data bit with data rate of fb = 50 bps; Then, the message data is modulated by civil medium length (CM) code and “chip by chip multiplexed” with civil long length (CL) code in TDM mode, forming L2C base band signal with fc = 1.023 Mbps. Finally, the baseband signal is upconverted by a L2C carrier [2, 4]. The periods of CM and CL codes are NCM = 10230 chips and NCL = 75NCM = 767250 chips respectively. Figure 1 illustrates the baseband modulation of L2C signal in one CM code period. The code segment index l takes 0 to 74, indicating the position of CM chip segment in a CL code cycle; Dm is the message bit carried by this CM cycle, where m indicates its position in navigation message.

Fig. 1. Schematic diagram of L2C baseband signal modulation in a single CM code cycle

TDM spread spectrum modulation structure provides a rich design space for replica code shape. Three commonly used code shapes are return-to-zero (RZ) [4–7], nonreturn-to zero (NRZ) [6–9] and extended return-to-zero (ERZ) [6, 7]. The schematic diagram of the above code types in one CM period is shown in Fig. 2.

Fig. 2. Three common local copy code configurations in baseband signal processing

The following chapters of this paper are arranged as follows: Sect. 2 introduces the overall block architecture of the baseband processing module; Sects. 3 and 4 analyse the characteristics of different local replica code shapes in the acquisition and tracking stages respectively; Sect. 5 verifies the feasibility and performances of the algorithm through real-world data.

2 Design of Baseband Signal Processing Module The overall design of the L2C baseband signal processing module implemented in this paper is shown in Fig. 3. The module consists of three functional modules: CM code delay and carrier Doppler frequency acquisition, CL code position acquisition, and tracking loops. Structures related to the design of the copied code are marked in red in the figure: including the zero-padding width control in CM code phase acquisition module and discriminator design in carrier frequency or phase locking loop.

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Fig. 3. Overall design diagram of L2C baseband signal processing module

3 L2C Signal Acquisition Algorithm A traditional L2C receiver usually estimates the code phase of CM code with shorter period first, and then search the CL code phase from 75 possible positions. Compared with direct acquisition of CL code, this strategy has better performance under typical signal quality conditions, and can greatly reduce the computational overhead. Therefore, this chapter will mainly introduce the strategy in CM code acquisition [4]. 3.1 L2C Signal and Correlator Model Considering the L2C signal transmitted by a specific satellite received by the receiver, the if signal obtained after down-conversion can be modeled as √ (1) r(t) = 2P · B(t) cos((ωIF + ωd )t + φ) + w(t), where P is the signal power, ωIF = 2π fIF is the center frequency of if signal obtained by down conversion, ωd = 2π fd is the doppler frequency to be determined, φ is the unknown carrier phase, and w(t) is white gaussian noise with variance σ 2 , the baseband signal B(t) can be expressed as B(t) = CM(t) ⊕ D(t), during CM timeslot; CL(t), during CL timeslot Use the local correlator to multiply the sampled if signal by the local carrier of different frequencies ejωn , local replica code C [n − τ ] with different code phases point by point, and then have the product accumulated coherently within Ncoh = fs Tcoh points, where fs is the sampling rate, Tcoh is the coherent integration time. The envelope of the integration result is calculated as the detection statistic of signal acquisition. Assuming that no message bit reversal occurs during the coherent integration period, the above process can be written as follows:     Ncoh    √     jwn ˆ    ˆ r[n] C[n − τ ] e  ≈ ( 2P/2) sin c(Ncoh ω)Rcˆ (τ ) + wcˆ  (2) AEnv  =   n=1    





where τ indicates the code phase difference between the replica code C [n − τ ] and the actual pseudo code C[n]; digital angular frequency ω = ω − (ωIF + ωd ) indicates 

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the difference between the frequency of local digital carrier and the received signal carrier; w denotes the total noise when C [n − τ ] is taken as the replica; the normalized C correlation value is defined as 



R (τ ) = C 

N coh



B[n] · C [n − τ ]/Ncoh .

(3)

n=1

3.2 Influence of Replica Code Shape on Acquisition Performance Correlation Properties of Local Replica Codes. Shapes of replica codes in Fig. 2 Can be parametrically described with shape factor α in the following form: 



C [n] = C α [n] = CM[n], 0 ≤ {nfc /2fs } < α/2; 0, Otherwise

(4)

where {x} represents the fractional part of x, and CM[n] is the sampling of the output of CM code generator with a code rate of 0.5115 Mbps at time n. For RZ, NRZ and ERZ CM code, α takes 1, 2 and 1.5 respectively [6, 7]. Take the spread spectrum code of PRN 8 as an example when fs = 5.115 (MHz), Fig. 4 shows the relation between the normalized correlation value of these replica CM codes and the L2C code in the received signal and the code phase delay.

Normalized Env. Amp.

0.6 RZ CM Full-rate NRZ CM Full-rate ERZ CM Full-rate RZ CM Chip-rate, worst situation NRZ CM Chip-rate worst situation ERZ CM Chip-rate, worst situation

0.5

0.4 0.3 0.2 0.1 0 -3

-2

-1

0

1

2

3

Code Phase Delay(chip)

Fig. 4. The relationship between the normalized correlation value and the code phase delay

Detection Probability of Acquisition. A basic evaluation metric of an acquisition algorithm is the single acquisition probability. Assume the frequency of local replica carrier and the code phase of the pseudo-noise code are consistent with those of the received signal, and accumulating period is Tcoh , then pick a decision threshold Vt to maximize the detection probability PD under a given false alarm probability PFA [1, 7, 10, 11]. Under signal hypothesis H1 and non-signal hypothesis H0 , the distribution of coherent integral amplitude z obtained from observation can be written as [1]:        H1 : p1 (z) = z/σn2 exp z 2 + A2Env /2σn2 I0 AEnv z/σn2 ,     H0 : p0 (z) = z/σn2 exp z 2 /2σn2 , (5) where I0 (·) is a Bessel function of order 0.

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√ Set false alarm probability to PFA , the judgment threshold is Vt = σn −2lnPFA , and the corresponding probability of detection would be +∞

+∞

PD = ∫ p1 (z)dz = √ ∫

−2 ln PFA

Vt

    ζ exp ζ 2 + C/N I0 2C/N ζ dζ

(6)

where C/N represents the power ratio of signal to noise. Note that with the increase of NRZ segments in coherent integration, more noise from CL time-slots will be introduced into the coherent accumulation of CM code timeslots, which will increase the total noise energy. The relationship is given by the following formula [6]: η



C

= ηα = α · N0 Tcoh /8,

(7)

where N0 /2 is the power spectral density of the double sideband noise.

Fig. 5. PD when using the three types of replica code under different C/N0 , , obtained through theoretical calculation and simulation (PFA = 10−3 , Tcoh = 20ms)

Therefore, under given signal power C, compared to code shape with α = 1.0, using α = 1.5 and√α = 2 will √ lead to 1.5 times and 2 times of extra noise power, and Vt has to increase 1.5 and 2 times respectively to maintain consistent PFA . Figure 5 shows that when PFA = 10−3 , Tcoh = 20ms is taken, the functional relationship between PD of three types of replica codes and carrier to noise ratio C/N0 = CTcoh /N , obtained through theoretical calculation and simulation. Probable Maximum Signal-to-Noise Ratio Loss. When the search step is not significantly shorter than the width of a chip, the SNR loss related to the start time of coherent integration is also assignable [6–9]. It consists of two parts: correlation peak value loss (λ) maxLcorr = maxR1 (τ )/Rα (τ ), and extra noise power Kα = ηα /η1 introduced by the replica code shape. Figure 4 has shown that all three replicas can achieve the maximum correlation value after alignment. However, the correlation peak loss of the three code types varies except when a significantly small search step is taken [6–9]. Table 1 shows the probable maximum SNR loss and its compositions when α varies. Due to the flat correlation curve near 0, ERZ and NRZ CM replica has no loss in correlation peak regardless of the start time of correlation integration when using a larger search step, but these shapes also reduce estimation accuracy [6].

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Table 1. Maximum loss of correlation between local replica code and received code Step length

α

 f1 c

1

0

0

0

1.5

1.5

0

1.5

2

3

0

3

1

0

2.5

2.5

1.5

1.5

0

1.5

2

3

0

3

1

0

6

6

1.5

1.5

2.5

4

2

3

0

3

Semi-chip

Chip

Kα (dB)

maxLcorr (dB)

maxLSNR (dB)

3.3 Implementation of L2C CM Acquisition Module Based on the above discussion, the L2C CM code phase parallel acquisition module implemented in this paper is shown in Fig. 6: the grey part of the module works as correlators using FFT and IFFT technique; changeable parameter α controls the proportion of CM and 0 in the replica code. Then, by changing the chip width to Tc = 1/fc or half chip width Tc /2, the sampled signal multiplied by the local carrier are accumulated point by point to greatly reduce complexity at the cost of accuracy of code phase estimation under some replica code configurations [8, 10].

Fig. 6. Architecture of L2C CM code phase parallel acquisition

4 L2C Signal Tracking Algorithm There are three common methods for simple L2C signal tracking: tracking CM code directly [6, 9]; tracking CL code while replicating CM code for message demodulation [6, 9]; merging discrimination results of CM and CL loops for combined tracking [12, 13]. This section will focus on the first two basic tracking methods. To reduce additional noise and multi-path effects, RZ code shape should be used [4]. 4.1 Discriminators in L2C Tracking Tracking Correlation Model. when tracking L2C signals, a receiver still uses a correlator structure similar to that in acquisition stage, but cares about both correlation values

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of in-phase (I) and quadrature (Q) branch rather than I 2 + Q2 . Ignoring the Noise, real and imaginary parts of the k th coherent integration can be expressed as: kNcoh−1



Ik + jQk =

n=(k−1)Ncoh

P ˆ + φˆ k )) √ Dk Cn (ωn + φk )Cˆ n exp(j(ωn 2

(8)

= ADk Rcˆ (τk ) · sin c(θk ) exp (j(kθk + φk )) √ where A = Ncoh · 2P/2, Dk is the message bit during the correlation integration period (when tracking CL, i.e., pilot channel, Dk is independent of k, so it can be assumed that Dk ≡ 1), θk = Ncoh ωk . Note that when A is constant and τk ≡ 0, the normalized amplitude of correlation value can be defined as [9]: ˜ k = Dk exp(j(kθk + φk )) I˜k + j Q

(9)

The correlation value above can be used as the measurements for the digital frequency error of the local carrier ωk and phase error φk estimation. Frequency Discriminator for Pilot Channel and Data Channel. There are three typical frequency discrimination methods as follows: cross product (CP), four-quadrant arc tangent (ATAN2) for pilot tracking, and point product (DP) for message tracking [1, 9]. The First two frequency discrimination methods are applicable to CL code tracking, I.E., pilot channel tracking; the latter is suitable for tracking CM code with message bit data. frequency difference estimation are expressed as: 

CROSS Ncoh ·(2π/fs ) = sin c(2θk )fk ,CROSS) k ),cos(2θk )) f ATAN2,k = atan2(DOT = atan2(sin(2θ fk Ncoh ·(2π/fs ) θk sgn(DOT )·CROSS f DP,k = Ncoh ·(2π/fs ) = sgn(cos(2θk )) · sin c(2θk )fk 

fCP,k =

(10)



˜ k−1 , CROSS = I˜k−1 Q ˜ k − I˜k Q ˜ k−1 , θk = 2π Tcoh fk . ˜ kQ Where DOT = I˜k−1 I˜k + Q Introduce frequency discrimination gain as Kdf (fk Tcoh ) = f /f [9]. DP method is a Costas frequency discriminator insensitive to flipping of message; CP and ATAN2 are universal frequency discriminators. However, DP method halves in the frequency discrimination range: When |f |Tcoh > 0.25, Kdf < 0; for ATAN2 and CP methods, negative Kdf only occurs when |f |Tcoh > 0.5. Negative Kd may result in a positive feedback loop which is not able to track the signal received. Figure 7 shows the functional relationship between discrimination gain Kdf and f · Tcoh . 

Phase Discriminator for Pilot Channel and Data Channel. Similarly, three typi∼

cal normalized quadrature integral (Q), four-quadrant arc tangent

phase

discriminators:  ∼ ∼ ∼ ∼ atan2 Q, I and unsigned quadrature integral (Q ·sgn I ), can be used to estimate the phase deviation between local replica carrier and the carrier of received signal. their phase discrimination gain characteristics exactly correspond to those of CP, ATAN2 and

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Fig. 7. Relationship between Kdf and f · Tcoh

Fig. 8. Relationship between Kdp and φ

DP methods, so these abbreviations are used as the subscript [1]: 

˜ ϕ  CP,k  = Q = sinc(ϕk )ϕk ˜ I˜ = (atan2(cos(ϕk ), sin(ϕk ))/ϕk )ϕk ϕ ATAN2,k = atan2 Q,   ˜ · sgn I˜ = sgn(cos(ϕk ))sinc(ϕk )ϕk ϕ DP,k = Q 

(11)



The relationship between phase discrimination gain Kdp and ϕk is shown in Fig. 8. It can also be concluded that compared with general phase discriminator (±180◦ ), the frequency discrimination range of Costas phase discriminator is only ±90◦ . Tracking Threshold for Pilot and Data Channel. When using phaselock loop (PLL) for carrier tracking, the 3σ range shall not exceed half of the single-side phase detection range according to the empirical design law. considering the relationship between PLL thermal noise power as the main noise source of PLL tracking measurement error and carrier-to-noise ratio C/N 0 σ PLL ≈ σ t,PLL ∝ (C/N 0 )−1/2 [1]. If the requirement for σ PLL is Doubled in value, the requirement for C/N 0 will be reduced by 4 times equivalently. Thus, the CL code tracking threshold carrier-to-noise ratio (C/N 0 )th is 6 dB lower than CM code tracking. The conclusion holds for frequency lock loop, too. 4.2 Implementation of L2C Tracking Module The L2C tracking module implemented is shown in Fig. 9. δ = 0.5 chip is taken as the phase difference of early/prompt/late integration in code loop, which is equivalent to δNc = δfc /fs clocks. In addition, the carrier frequency correction multiplied by ratio coefficient 1/1200 is added to the code frequency correction [1].

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Fig. 9. Architecture of L2C tracking loop submodule

5 Real-World Signal Test In order to verify the acquisition and tracking algorithm discussed in this paper, we collected a sequence of GPS satellite signal, and used the L2C software receiver developed on the MATLAB platform to process baseband signal. 5.1 Real-World Signal Acquisition Set the doppler frequency search range to [−5, 5)(kHz), then take number of frequency search points NAcq,freq = 256, and coherent integration duration Tcoh = 20 ms; RZ, ERZ and NRZ are used as replica codes with search step of 0.5, 0.5 and 1 chip. The results are shown in Figs. 10, 11 and 12. Note that a correlation value close to the maximum value appears with the same fd and the adjacent code phase when RZ CM is used as replica codes, which indicates that this shape is likely to be influence by an adverse initial coherent integration position.

Fig. 10. RZ CM semi-chip-step acquisition

Fig. 11. ERZ CM semi-chip-step acquisition

To achieve accuracy of ±0.25 chip, 75 or 150 possible CL positions are searched. When Tcoh = 20 ms is taken, the search results are shown in Figs. 13 and 14.

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Fig. 12. NRZ CM chip-step acquisition pattern

Fig. 13. CL code position search result (CM search step 0.5 chip)

Fig. 14. CL code position search result (CM search step 1 chip)

5.2 Real-World Signal Tracking Take coherent duration Tcoh = 2 (ms) and a 2nd-order FLL with Bn,FLL = 1.5 (Hz). DP and ATAN2 frequency discriminator are used to track CM and CL code respectively. After Tpull = 1.0(s), FLL is replaced with a 2nd-order PLL with Bn,PLL = 15 (Hz). In both stages, a 2nd-order loop filter with Bn,DLL = 4(Hz) is taken in DLL. The correlation results of early, prompt and late codes of the two tracking modes (CM/CL) and in-phase (I ) down-conversion reach a ratio of approximately 1:2:1 after convergence, which reflects the autocorrelation characteristics of RZ replica.

Fig. 15. The correlation result of Early/Prompt/Late I/Q channels

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Figure 16 compares the outputs of frequency discriminator and phase discriminator (f , ϕ ) in the carrier tracking loop. It could be found that after both loops are locked, the deviations of CM code and CL code tracking are close in absolute value. However, the output of frequency and phase discriminators when tracking CM codes should be considered more significant due to the discriminating range of Costas loop. 



Fig. 16. Frequency discriminator and phase discriminator output in carrier tracking loop

6 Conclusion In this paper, different replica code shapes used in L2C signal acquisition and tracking and their impacts are studied, and a baseband signal processing module of L2C software receiver with multiple duplicate codes is implemented. In CM acquisition stage, RZ shape provides the best noise suppression, while NRZ shape minimize complexity when relatively long code phase search step is used. Besides, using RZ CL code in tracking can achieve a sensitivity gain of 6 dB compared to RZ CM. Finally, the baseband processing algorithm module implemented in this paper is used to verify the above conclusions with real environment signals. Acknowledgement:. Supported by the National Natural Science Foundation of China (61973181).

References 1. Kaplan ED, Hegarty CJ (2021) Understanding GPS/GNSS: principles and applications, 3rd edn. Publishing House of Electronics Industry, Beijing, p 2021 2. Fontana RD, Cheung W, Novak PM, Stansell TA (2001) The new L2 civil signa. Proceedings of the 14th International Technical Meeting of the Satellite Division of the Institute of Navigation, Salt Lake City, UT, pp 617–631 3. IS-GPS-200N (2022) NAVSTAR GPS space segment/ navigation user segment interfaces [EB/OL].(2022–08–01)[2022–11–17]. https://www.gps.gov/technical/icwg/IS-GPS200N.pdf 4. Dempster AG (2006) Correlators for L2C: Some considerations[J]. Inside GNSS 1(7):32–37 5. Mariappan S, Babu SR, Rao SB (2011) Acquisition and tracking strategies of modernised GPS L2C signal[C]//2011 International Conference on Recent Trends in Information Technology (ICRTIT). IEEE,pp 281–285 6. Tran M (2004) Performance evaluations of the new GPS L5 and L2 Civil (L2C) signals[J]. Navigation 51(3):199–212

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7. Qaisar SU, Dempster AG (2012) Assessment of the GPS L2C code structure for efficient signal acquisition[J]. IEEE Trans Aerosp Elect Syst 48(3):1889–1902 8. Li H, Lu M (2015) Double-chipwise correlation technique for efficient L2C signal acquisition. IEEE Trans Aeros Elect Syst 51(2):1575–1582 9. Muthuraman K, Shanmugam KS, Lachapelle G (2007) Evaluation of data/pilot tracking algorithms for GPS L2C signals using software receiver[C]. Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation, Fort Worth, TX, pp 2499–2509 10. Psiaki ML (2004) FFT-based acquisition of GPS L2 civilian CM and CL signals. Proceedings of the 17th International Technical Meeting of the Satellite Division of the Institute of Navigation, Long Beach, CA, 457–473 11. Li C, Lu M, Feng Z (2010). Study on GPS L2C acquisition algorithm and performance analysis. J Elect Inf Technol 32(2):296–300 (Ch) 12. Liu Y (2014) Research on acquisition and tracking algorithm of GPS L2C signal based on joint data and pilot channel[D]. Beijing: Tsinghua University, (Ch) 13. Zhu X, Shen F, Chen J, et al (2015) Combined tracking strategy based on unscented Kalman filter for Global Positioning System L2C CM/CL Signal[J]. Defence Sci J 65(5):395–402 14. Xie G (2009) Principles of GPS and receiver design. Beijing: Publishing House of Electronics Industry, (Ch)

Algorithm Optimization and Terminal Validation of BDSBAS Ionospheric Correction Ang Liu(B) , Ningbo Wang, Zishen Li, Liang Wang, Zhiyu Wang, and Hong Yuan Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China [email protected]

Abstract. The BeiDou Satellite Based Augmentation System (BDSBAS) achieved Initial Operating Capability (IOC) from 2020, which is embedded into BDS as a component. The ionospheric enhancement corrections provided by BDSBAS protects users from threats generated by ionospheric disturbances. This paper addresses the ionospheric algorithm applied in BDSBAS, which consist of the Grid Ionospheric Vertical Delay (GIVD), its corresponding error bound called Grid Ionospheric Vertical Error (GIVE) and the processors used in BDSBAS ionospheric solution. The performance of BDSBAS ionospheric enhancement service is analysed, focusing on service coverage, ionospheric delay correction accuracy and corresponding integrity risk. Results shows that the BDSBAS ionospheric enhancement service basically cover all airspaces over China and surrounding area, with a satellite cut-off angle of 15 degrees at the boundary. Compared to the rapid Global Ionospheric Map (GIM), the accuracy of BDSBAS GIVD is about 2.0–3.0 TEC unit (TECU) during Day of Year (DOY) 130–160, 2021. No misleading information appeared during the test period which indicates that the probability of hazardously misleading information of BDSBAS ionospheric correction is limited below 10–7 per approach. Keywords: BeiDou satellite based augmentation system (BDSBAS) · Grid Ionospheric vertical delay (GIVD) · Grid Ionospheric vertical error (GIVE) · Adjusted spherical harmonics adding KrigING method (SHAKING)

1 Introduction Global Navigation Satellite System (GNSS) have attracted interest from the aviation field to render GNSS position estimates safe and reliable for aircraft navigation [1]. The Satellite Based Augmentation Systems (SBASs) have been developed to ensure the accuracy, integrity, availability and continuity of user position estimates derived from GNSS measurements [2–4]. Currently, several SBASs have been implemented for civil aviation and approved by the Required Navigation Performance (RNP) following the L1 SBAS Minimum Operational Performance Standards [5], including wide-area augmentation system (WAAS) of the USA [6, 7], European Geostationary Navigation Overlay Service (EGNOS) [8], GPS aided geo augmented navigation (GAGAN) of India [9], Multi-functional Satellite Augmentation System (MSAS) of Japan [10], BeiDou © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 590–604, 2024. https://doi.org/10.1007/978-981-99-6932-6_49

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Satellite Based Augmentation System (BDSBAS) of China [11]. With an accelerated rise in the use and development of GNSS technologies, the modifications to SBASs have touched all aspects of the system including adding reference stations, improving the ionospheric algorithms, refreshing the hardware such as reference receivers and antennas and enhancing communications networks [12]. The largest source of positioning errors comes from ionospheric activity and ionospheric disturbances cause the ionospheric errors for GNSS signal to increase dramatically [13, 14]. Real-time (RT) regional ionospheric correction and safety-critical integrity bound is provided by SBASs as one of the major factors of SBAS corrections [15, 16]. SBAS Ionospheric grid points information, including Grid Ionospheric Vertical Delay (GIVD) and its corresponding error bound called Grid Ionospheric Vertical Error (GIVE), are transmitted to users in Message Type 18 and 26 [17]. As an ionospheric integrity parameter, GIVE refers to the reliability and trustworthiness of the ionospheric correction information provided by the SBASs and to the ability to deliver timely alerts when the ionospheric correction should not be used for navigation [18]. GIVEs, which are designed to protect the user from the effects of delay estimation error due to ionospheric irregularity (both sampled and undersampled), are derived from inflated and augmented values of the formal estimation error [19]. Inverse distance weighting (IDW) combined with a Klobuchar time-delay model and incorporating integrity monitoring is employed as a prelude for the advent of SBAS ionosphere monitoring [20]. In initial operating capability (IOC) version of WAAS, a receiver network consisted of 25 reference stations is used and a planar-fit model with implementing a mechanism of storm detector is adopted [7]. This method didn’t meet the requirement of WAAS due to its limited coverage, i.e., only most of Conterminous United States (CONUS) not all of the airspace. So that in WAAS Follow-On Release 3, the kriging grid-model algorithm first appeared to extend its coverage of services [18]. For other SBASs, the Triangular Interpolation (TRIN) model is used as the ionospheric algorithm of second operational SBAS, i.e., EGNOS [21] and ISRO GIVE Model Multi-Layer Data Fusion (IGM-MLDF) is developed by GAGAN [9]. The ionospheric algorithm of MSAS is based on the planar-fit ionospheric algorithm where zeroth order and quadratic fits is introduced [22]. Currently, the IOC version of BDSBAS adopted IDW method to supply ionospheric services over China and surrounding areas. Among them, there are two key factors that need to be considered. The first is the coverage of ionospheric services. The observed ionospheric information search domain radius of IDW or planar-fit method is about 600 km. Under the premise of limited station distribution, it may not be able to guarantee the service coverage (for BDSBAS is 70o–140oE, 5o–55oN). The second key point is the correction accuracy. The China and surrounding areas belong to mid- and low- latitude regions where the ionosphere is characterized by large spatial gradients, with a frequently apparition of non-planar ionospheric spatial gradients during geomagnetic storms [23]. In this paper, an adjusted Spherical Harmonic and Kriging (SHAKING) approach [24] is adjusted to be used for estimating grid ionospheric vertical delay and error for BDSBAS. The algorithm of SHAKING for BDSBAS is described in detail at first, followed by the analysis of BDSBAS broadcast ionospheric information. Summary and conclusions are finally given.

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2 Ionospheric Estimation of BDSBAS 2.1 GIVD in BDSBAS BDSBAS uses the RT data stream provided by the self-built 27 GNSS monitoring stations, so an ionospheric method with a larger search radius is needed to cover all required airspaces. Considering that the ionospheric TEC consists of both deterministic and stochastic components as well as the remaining noises [25], the SHAKING method is updated to be used in BDSBAS ionospheric monitoring, shown in Eq. (1).   ˜ λ˜ + IIGP−KRIGING (ϕ, λ) (1) GIVDBDSBAS (ϕ, λ) = IIGP−ASH ϕ, where GIVDBDSBAS (ϕ, λ)denotes  the GIVD of the IGPs with geographic latitude ϕ ˜ λ˜ and IIGP−KRIGING (ϕ, λ) denote the adjusted Spherical and longitude λ, IIGP−ASH ϕ, Harmonic (ASH) based deterministic vertical total electron content (VTEC) and Krigingbased stochastic VTEC, respectively, which can be derived from Eq. (2). ⎧   ⎨ IIGP−ASH ϕ, ˜ λ˜ = AX (2) ⎩I (ϕ, λ) = λI IGP−KRIGING

R

where A is the coefficient vector of current IGP which is determined by the ASH, which ˜ · (A˜ nm cos(mλ˜ ) + B˜ nm sin(mλ˜ )), P˜ nm is the normalized associated consists P˜ nm (sin ϕ) Legendre function of degree n and order m; X is the coefficients vector of the established ASH model; λ = [ λ1 λ2 · · · λN ]T is the vector of corresponding weighting value λ, which is estimated by Kriging, N denotes the number of ionospheric pierce points (IPPs) within a certain range around individual IGPs; IR is the vector of ionospheric residuals; ϕ˜ and λ˜ are the adjusted-latitude and cap-longitude of the IPP, shown in Eq. (3). ⎧ π π π ⎪ ϕ ˜ = − − arccos[sin ϕ · sin ϕ + cos ϕ cos ϕ cos(λ − λ )] ⎪ 0 0 0 ⎨ 2 θmax 2 

(3) sin(λ − λ0 ) · cos ϕ ⎪ ⎪ ˜ ⎩ λ = arcsin arccos(sin ϕ0 · sin ϕ + cos ϕ0 cos ϕ cos(λ − λ0 )) where (ϕ0 , λ0 ) and θmax denotes the geographic coordination of the new pole and the half-angle for the spherical cap established by ASH, respectively. The ASH model is constructed from the ionospheric information obtained from the BDSBAS real-time data stream, and the model coefficients are estimated using the Least-Squares (LS) method, as shown below. X = (BT PB)−1 BT PL

(4)

where B is a matrix of the same form as A, but determined by IPPs; P is the weight matrix of observations; L is the observation vector. Ordinary kriging method is adopted

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Fig. 1. Ionospheric semi-variance based on Gaussian variogram

to estimate the VTEC stochastic component, in which the weight calculation is shown in Eq. (5). ⎤⎡ ⎡ ⎤ ⎡ ⎤ r11 r12 · · · r1n 1 λ1 r10 ⎥ ⎢ r r ⎢ ⎥ λ2 ⎥ ⎢ 21 22 · · · r2n 1 ⎥⎢ ⎥ ⎢ r20 ⎥ ⎥⎢ ⎢ . . ⎢ ⎢ ⎥ . . . ⎢ .. .. . . .. .. ⎥⎢ . ⎥ = ⎢ . ⎥ (5) ⎥⎢ . ⎥ ⎢ . ⎥ ⎢ .. ⎥ ⎥⎣ ⎢ ⎣ ⎦ ⎦ ⎣ rn1 rn2 · · · rnn 1 ⎦ λn rn0 φ 1 1 1 ··· 1 0 where φ is Lagrange multiplier; rij (j = 0) represents the semi-variance between a pair of IPP-IPP and ri0 represents the semi-variance between a pair of IPP-IGP, which can be obtained from Gaussian variogram, as shown in Fig. 1 and Eq. (6). ⎧ COV (d ) = γ (∞) − γ (d ) ⎪ ⎪ ⎪ ⎧ ⎨ d =0 ⎨ C0 (6) √ −d 2 /a2 ) 0 < d ≤ 3a ⎪ γ (d ) = C + C ∗ (1 − e ⎪ 0 ⎪ √ ⎩ ⎩ d > 3a C0 + C where d denotes the distance between different IPP points; COV (d ) is the spatial covariance with distance d ; γ (d ) represents the semi-variance from Gaussian variogram; C0 , C0 +C and a represents nugget, sill and range, respectively; C is partial sill which √ equal sill minus nugget. It should be pointed that the radius of fit domain is set as 3a while 1 − e−3 ≈ 0. The 9-bit broadcasted IGP vertical delays have a 0.125m resolution, for a 0–63.750m valid range. Thus, the broadcasted GIVD values are rounded to the nearest specified quantized vertical delay value. 2.2 GIVE in BDSBAS The estimation variance of GIVD is defined as follows: ⎧ 2 2 2 ⎪ ⎪ σIGP = σASH + σKriging ⎨ 2 σASH = A(BT PB)−1 AT ⎪ ⎪ ⎩σ2 = λT Rλ − 2λT R + C +C + λT Nλ Kriging

0

0

(7)

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2 2 where σASH and σKriging are the variances of the deterministic and stochastic parts, respectively; R and R0 are vectors which consist the semi-variance rij (j = 0) and ri0 , respectively; and N is covariance of the measurement noise. The above variance is obtained from the model established by the sampled information which will be too optimistic, that is, the value significantly underestimates the actual error [26]. An inflation factor is introduced to account for ionospheric and statistical uncertainty, which is parameterized by the number of degrees of freedom of estimation, i.e., the number of measurements minus the number of necessary observations in the model, as shown in Eq. (8). 2 /χP2md R2irreg (Pfa , Pmd ) = χ1−P fa

(8)

where χ 2 is the inverse of the cumulative density function, Pfa and Pmd are false alarm rate and missed detection probability respectively (set to 10–3 and 10–1 for BDSBAS). Since the ionospheric model is established over the whole region, the number of IPPs found around IGP is taken as the degree of freedom of the point approximately. The inflation factor for different degrees of freedom is shown in Table 1. The integrity requirement for BDSBAS vertical guidance is an upper bound (10–7 ) on the probability of broadcasting hazardously misleading information (MI) that use precision approach with vertical guidance. The fault tree of BDSBAS allocates to GIVE Monitor an upper limit of 2.25*10–8 on the probability of MI. Therefore, BDSBAS GIVE is provided by the Eq. (9). GIVE = KGIVE

KHMI− GIVE  2 2 + σ2 Rirreg ∗ σIGP Undersampled KHMI

(9)

in which KGIVE is 3.29 which with a confidence interval with a confidence level of 99.9%; KHMI− GIVE and KHMI are 5.529 and 5.33, respectively, i.e., the constant that defines 1–2.25*10–8 and 1–10−7 confidence interval; σUndersampled denotes the spatial threat model that protects the user from undersampled irregularities [27]. The computed GIVE at each IGP is rounded upward to the next larger quantized GIVE value. Table 1. R2irreg for different degrees of freedom, with Pfa = 10−3 and Pmd = 0.1 (from 5 to 14). Freedom

2 χ0.999

2 χ0.1

R2irreg

Freedom

2 χ0.999

2 χ0.1

R2irreg

5

20.51

1.61

12.74

10

29.59

4.87

6.08

6

22.45

2.20

10.19

11

31.26

5.58

5.61

7

24.32

2.83

8.58

12

32.91

6.30

5.22

8

26.12

3.49

7.49

13

34.53

7.04

4.90

9

27.88

4.17

6.69

14

36.1

7.79

4.64

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2.3 Ionospheric Parameter Setting When calculating the GIVD and GIVE, the search domain is determined by a circle centered upon the IGP, whose radius is measured by the spherical distance between the location of the IGP and the points on the circle, shown in Fig. 2. The step-by-step search method is used to retrieve the IPP location. The first search circle is determined by the minimum distance Rmin . If the number of eligible measurements is less than Ntarget , the new search radius is expended by a step RStep until the eligible number exceeds the Ntarget . Importantly, if the search radius exceeds the Range of variogram (RKriging ) and the eligible number less than Nmin , the current IGP GIVE will be marked as Not Monitored (NM).

RStep RMIN Rkriging

Ionospheric Grid Points (IGP)

Ionospheric Pierce Points (IPP)

Fig. 2. Selection of IPPs for GIVD and GIVE calculation.

Fig. 3. The coverage under different parameter configurations in established ASH coordinate system.

From the ionospheric algorithm adopted by BDSBAS, its coverage is related to the established adjusted spherical harmonic coordinate system, that is, the half angle of the spherical cap and the new pole coordinates. Figure 3 shows the coverage under different

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coordinate system parameter configurations. The yellow area in the figure is the effective service area, and the blue area is beyond the coverage area of the ionospheric algorithm. It can be seen that if the half-angle of the spherical cap is too small, the coverage cannot cover the entire airspace, but if it is too large, the boundary that lacks the input of observational information cannot provide integrity information. Therefore, the selection of coordinate system parameters is a trade-off between coverage and availability. The relevant parameter settings are shown in Table 2. Table 2. Ionospheric parameter settings in BDSBAS Half Angle

Pole Lat

Lon

MIN

R(km)

35°

32.5°N

105°E

500

MAX √ 3a

Nmin

Ntarget

Pmd

Pfa

5

30

0.1

10–3

Step 100

2.4 BDSBAS Ionospheric Procedure Figure 4 provides a depiction of the overall architecture of BDSBAS ionospheric model, which including Quality Monitoring and Mistake Rejection processor (QMMR), Observation File Generation (OFG); Carrier to Code Leveling processor (CCL); Differential Code Biases Estimation and Smoothed (DCBES); Bias-Free Ionospheric observation extraction and Check processor (BFIC); Ionospheric GIVD and GIVE Processor (IGEP); Ionospheric Information Broadcast (IIB). RT GNSS data stream are transported with the same antenna and three differentiated receivers at each station in the monitoring stations network of BDSBAS. The QMMR processor performs an initial screening of the data to identify and reject mistakes. The processor also performs a unified evaluation of the three data streams, selects the best quality one and maintains the consistency of the monitoring network. Two operations are performed on the data passing the inspection, i.e., the generation of the observation file and the input into the CCL processor. The CCL processor is used to extract the line-of-sight ionospheric information with Differential Code Biases (DCB). Due to the influence of the continuous arc length in RT smoothing process of CCL, the first 10 min data of the new arc is discarded. In the whole program, CCL plays two important roles. One is receiving RT data provided by QMMR to extract ionospheric information by forward filtering and fed into BFIC filter. The other is using a bidirectional cross-filtering to extract the Slant TEC (STEC) from OFG and fed into DCBES processor. DCBES processor is used to estimate the receiver and satellite DCB and then fed into BFIC to get the Bias-Free (BF) VTEC, where the modified generalized triangular series (MGTS) function is employed to simultaneously estimate local ionospheric VTEC and satellite-plus-receiver DCB parameters. Satellite DCBs are fixed to CAS MGEX DCB products [28]. A smoothing filtering process with a window of 30 days for the DCB estimation results is adopted to avoid large jumps.

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GNSS Raw Code and Carrier Obs. From BDSBAS Real-Time stream

QMMR

Quality Monitoring & Mistake Rejection Carrier to Code Leveling

OFG

CCL

Observation File Generation

Ionospheric GIVD and GIVE Processor

Differential Code Biases Estimation and Smoothed

DCBES

BFIC Ionospheric Information Broadcast

IGEP

IIB

Bias-Free Ionospheric Obs. and Check

GIVDs & GIVEs to users

Fig. 4. A schematic of the major ionospheric monitors. QMMR, Quality Monitoring and Mistake Rejection; OFG, Observation File Generation; CCL, Carrier to Code Leveling; DCBES, Differential Code Biases Estimation and Smoothed; BFIC, Bias-Free Ionospheric observations Check; IGEP, Ionospheric GIVD and GIVE Processor; IIB, Ionospheric Information Broadcast processor.

The operation of BFIC is the last step of data processing before modeling, and its main functions include the calculation of BF VTEC and outlier detection within set search domain at each grid point based on Pauta Criterion [29]. The IGEP processor is the core, and the ionospheric GIVD and GIVE calculation methods described in this article are also used here. The resulting output is fed into IIB processor to encode the information that needs to be broadcast. The predefined IGP locations must be stored permanently by the user. If the IGP masks in BDSBAS is 1, it indicates that the IGP is effective, and corresponding ionospheric delay information will be broadcast in Message Type 26 [30].

3 Discussion The real-time GNSS data streams with a sampling rate of 1 Hz (including GPS, BDS-2, BDS-3 and GLONASS) are used to generate the real-time regional GIVD and GIVE for BDSBAS, with an interval of 240 s. As the safety-critical integrity bound, if the GIVE levels Index (GIVEI) is equal to 15 (GIVE > 45m), the corresponding grid point is regarded as service unavailable. Figure 5 shows the available BDSBAS GIVD and GIVEI maps in DOY 129 2021. The dark green dots mark lower levels of GIVEI ≤ 10 (GIVE ≤ 3.6 m), while the pink dots indicate a much higher GIVE at 45 m (GIVEI = 14). The turquoise dots show areas that are not monitored (NM). When no IPP is available in the fitting domain, the grid point is marked as unavailable. Considering that the ionospheric TEC variogram is generally characterized by linear growth on the spatial scale of the fit domain and discontinuity at the origin, the fit range in BDSBAS is set as 1900–2100 km. Since the neutral gas molecules in the ionosphere gradually ionize with the enhancement

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Fig. 5. The BDSBAS ionospheric GIVD (left panel) and GIVEI (right panel) map based on the SHAKING method at DOY 129, 2021.

of solar intensity, the number of electrons in low latitude areas (10o N-30o N, 120o E140o E) increases continuously and GIVD is significantly larger than other grid points. The GIVEI available grid points are mainly distributed in the north of China, which is determined by the multi-GNSS observation IPPs location, among which BDS, GPS, and GLONASS are marked in red, blue, and black respectively. In the GIVEI map, most of the GIVEI in the central area of the region is within 10 (GIVE < 3.6m), while the marginal area is larger. Figure 6 shows the time series of BDSBAS IGPs GIVEI on DOY 129, 2021. It can be seen that the variation of BDSBAS GIVEI was relatively steady and mainly ranged between 9 (GIVE < 3.0 m) and 12 (GIVE < 6.0 m) in the middle and high latitude bands. This trend occurs in a magnetically moderate activity without any detection of ionospheric irregularity. In addition, the figure shows significant stratification in low longitude and high longitude areas (70°E and 140°E), which is due to the poor density of IPPs around the concerned IGP. The lack of TEC measurements degrades the interpolation performance and consequently GIVE values are incremented to face the possible large errors in GIVD estimation. In most cases, GIVEI is marked as unavailable in low latitude areas. The Fig. 7 shows BDSBAS ionospheric information coverage when the satellite cut-off angle set as 15° at China border on DOY 129 of 2021, in which the IGPs is divided into four types, including not needed and not broadcasted (gray points), needed but not broadcasted (red points), not needed but broadcasted (purple points), needed and broadcasted (green points). Obviously, the red dots are our focus, which indicates the ionospheric model at that points should be improved. It turns out that there are only 3 points that need further adjustment (in fact, the two points, i.e., 5o N-125o E and 0o N120o E, can be ignored because there are 3 available points around them where the user can perform triangular interpolation). Probability distribution with GIVEI equal to 15 calculated by BDSBAS is shown in Fig. 8, where blank area indicates that GIVEI does not appear to be NM. Low availability points appear in the edge regions, represented by the southwest and southeast regions. This is mainly due to the IPPs provided by the BDSBAS station, although the search

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Fig. 6. Time series of BDSBAS GIVEI on DOY 129 of 2021.

Fig. 7. BDSBAS ionospheric information coverage when the satellite cut-off angle set as 15°at China border on DOY 129 of 2021.

domain radius used by the algorithm is as high as 2000km. BDSBAS ensures availability of airspace dominated by mainland China. Figure 9 shows BDSBAS GIVD validation results with respect to Global Ionospheric Map (GIM) released by Center for Orbit Determination in Europe (CODE), i.e., CORG, from DOYs 130 to 160 in 2021. Results show that, compared to CORG, the accuracy

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Fig. 8. Probability distribution with GIVEI equal to 15 calculated by BDSBAS.

of BDSBAS ionospheric products is about 2.0–3.0 TEC unit (TECU), and the corresponding bias and STD are 1.06 TECU and 2.0 TECU, respectively. One peak of RMS (2.95 TECU) occurred on DOY 133 due to the sudden geomagnetic storm. Figure 9 also shows variations of Dst indexes, which are used to describe the intensity of geomagnetic storms. It shows that geomagnetic storms have occurred on DOY 133 of 2021 with the Dst index less than -60 nT. On the first stormy day (the night of DOY 132), the main phase of the storm started. The Dst index dropped to a minimum value of -61 nT and the Kp index reached the maximum value of 7.0 reflecting a strong perturbation of the geomagnetic field. This storm event was caused by the impact on the Earth’s magnetosphere of coronal mass ejections (CME) registered 129th day of 2021, which caused the formation of plasma bubbles. They propagated up to the high and mid-latitudes and leading to scintillations in GNSS signals.

Fig. 9. Comparison between BDSBAS GIVD and CORG during DOY 130–160, 2021. Top and bottom panels give the RMS and the corresponding Dst index, respectively.

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As BDSBAS GIVE is an integrity parameter, the integrity performance (the probability of integrity risk) in the user segment is also analyzed. Figure 10 shows BDSBAS User Ionospheric Vertical Error (UIVE) and GIVD residuals at different o’clock with respect to (w.r.t) CORG VTEC during DOY 130–160, 2021. The bins of UIVE and TEC residuals are divided with the resolution of 0.1TECU, and the color in each bin represents the number of occurrences of the value. The red line is the line of symmetry, and the point above the red line means that the UIVE is greater than the VTEC residual, otherwise it means that the UIVE is less than the residual. It can be seen that the distribution is relatively scattered between 3:00 and 10:00 UTC, which mainly because this period is 11:00 -18:00 local time (LT). UIVE responded ideally to the more active ionosphere which caused by the stronger sunlight.

Fig. 10. BDSBAS UIVE and GIVD residuals at different o’clock w.r.t CORG VTEC during DOY 130–160, 2021.

Figure 11 shows the distribution of BDSBAS UIVE and GIVD residuals of BDSBAS w.r.t CORG VTEC during DOY 130–160, 2021. The relationship between GIVD VTEC residuals and UIVE is divided into three types. If UIVE exceeds 45m (GIVEI = 15), the grid point is considered to be unavailable. In the case that UIVE is less than 45m and can bound safely GIVD error, the service is considered to be available. In other cases, UIVE is regarded as misleading information (MI), which may cause integrity risks. As shown in Fig. 11, it is observed that the BDSBAS UIVE was able to bound safely GIVD error during the period of this geomagnetic storm, which is the most important attribute for SBAS. According to statistics results, no MIS appear and the reliability and trustworthiness of the BDSBAS ionospheric correction satisfy the integrity requirement for precision approach guidance in the test period, which limits the probability of hazardously misleading information to below 10–7 per approach.

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Fig. 11. BDSBAS UIVE and GIVD residuals w.r.t CORG VTEC during DOY 130–160, 2021.

4 Conclusion The BeiDou Satellite Based Augmentation System is an important part of BDS and will provide the Single Frequency (SF) service through BDSBAS-B1C signal. The complex changes of the ionosphere in the mid- and low- latitudes make it difficult to represent the ionospheric VTEC in this region and protect the user from the effects of delay estimation error due to ionospheric irregularity. This paper focus on the calculation method of the ionospheric correction and the integrity parameters which used in BDSBAS. The ionospheric performance of BDSBAS, including service coverage, correction accuracy and integrity risk, is also analyzed. Considering the ionospheric stochastic component is not negligible in the ionospheric modeling requiring accuracy, the SHAKING is applied in BDSBAS to provide the TEC enhancement corrections, which estimates the deterministic and stochastic component of the ionospheric TEC based on ASH and Kriging, respectively. An inflation factor is introduced to account for ionospheric and statistical uncertainty to enlarge the variance obtained from the model established by the sampled information. The ionospheric results provided by the BDSBAS for DOY 130–160 in 2021 were evaluated against the CORG, a rapid GIM product released by CODE. Results show that, the accuracy of BDSBAS ionospheric corrections is about 2.0–3.0 TECU w.r.t CORG, with bias and STD of 1.06 and 2.0 TECU, respectively. No MIs appeared during the test period which indicates that the probability of hazardously misleading information of ionospheric correction is limited below 10–7 per approach. Additionally, the number of observation sample is crucial for the statistics of integrity risk, so the sample size will be expanded in the next study. Acknowledgments:. This work was supported by the National Key Research Program of China (2017YFGH002206), the National Natural Science Foundation of China (42074043), the Alliance of International Science Organizations (ANSO-CR-KP-2020–12), the Youth Innovation Promotion Association and Future Star Program of the Chinese Academy of Sciences.

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References 1. S. Conker R, El-Arini MB, Albertson TW et al. (1997) Description and assessment of realtime algorithms to estimate the ionospheric error bounds for WAAS [J]. NAVIGATION: J Inst Navig 44(1):77–88 2. Lim CS, Park B, So H et al (2016) Analysis on the multi-constellation SBAS performance of SDCM in Korea [J]. J Posit Navig Timing 5(4):181–191 3. Jin B, Chen S, Li D et al (2021) Performance analysis of SBAS ephemeris corrections and integrity algorithms in China region [J]. Satell Navig 2(1):15 4. Chen J, Zhang Y, Yu C et al (2022) Models and performance of SBAS and PPP of BDS [J]. Satell Navig 3(1):4 5. Arenas J, Ochoa B, RAMÍREZ ME, et al. (2014) Facing strong ionosphere in SBAS systems: comparison of different techniques for ionosphere estimation [M]. Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014). Tampa, Florida, pp 1153–1162 6. Sparks L, Altshuler E, Pandya N, et al. (2022) WAAS and the Ionosphere—a historical perspective: monitoring storms [J]. Navigation: J Inst Navig 69(1) 7. Walter T, Hansen A, Blanch J et al (2014) Robust detection of ionospheric irregularities [J]. Navigation 48(2):89–100 8. Lupsic B, Takács B (2019) Analysis of the Egnos ionospheric model and its impact on the integrity level in the central Eastern Europe region [J]. Intern Arch Photogr Remote Sens Spat Inf Sci XLII-4/W14(159–165) 9. Rao KS (2007) GAGAN - The Indian satellite based augmentation system [J]. Indian J Radio Space Phys 36(4):293–302 10. Sakai T, Kitamura M, Aso T, et al. (2017) SBAS ionospheric correction with minimalization of the ionospheric threat; proceedings of the Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, F [C] 11. Shao B, Ding Q, Wu X (2020) Estimation method of SBAS dual-frequency range error integrity parameter [J]. Satell Nav 1(1):9 12. Walter T, Shallberg K, Altshuler E et al (2018) WAAS at 15 [J]. Navigation 65(4):581–600 13. Jakowski N, Stankov SM, Schlueter S et al (2006) On developing a new ionospheric perturbation index for space weather operations [J]. Adv Space Res 38(11):2596–2600 14. Ghobadi H, Spogli L, Alfonsi L, et al. (2020) Disentangling ionospheric refraction and diffraction effects in GNSS raw phase through fast iterative filtering technique [J]. Gps Solut 24(3) 15. Rovira-Garcia A, Juan JM, Sanz J et al (2016) Accuracy of ionospheric models used in GNSS and SBAS: methodology and analysis [J]. J Geodesy 90(3):229–240 16. Kitamura M, Sakai T (2019) DFMC SBAS prototype system performance using global monitoring stations of QZSS. Proceedings of the Proceedings of the ION 2019 Pacific PNT Meeting, Honolulu, Oahu, Hawaii, F, 2019 [C] 17. RTCA-DO-229E (2016) Minimum operational performance standards for global positioning systemsatellite-based augmentation system airborne equipment [M]. RTCA Program Management Committee on TBD 18. Sparks L, Blanch J, Pandya N (2011) Estimating ionospheric delay using kriging: 1. Methodology [J]. Radio Sci 46(6):RS0D21 19. Sparks L, Blanch J, Pandya N (2011) Estimating ionospheric delay using kriging: 2. Impact on satellite-based augmentation system availability [J]. Radio Sci 46(6):RS0D22 20. Takka E, Belhadj-Aissa A, Yan J, et al. (2019) Ionosphere modeling in the context of algerian satellite-based augmentation system [J]. J Atmosp Solar-Terrest Phy 193(105092)

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21. Mannucci AJ, Wilson BD, Edwards CD (1993) A new method for monitoring the Earth ionosphere total electron content using the GPS global network [J]. Proc Inst Nav 22(2):1323– 1332 22. Sakai T, Matsunaga K, Hoshinoo K, et al. (2005) Modified ionospheric correction algorithm for the SBAS based on geometry monitor concept [J]. Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), 735–747 23. Arslan Tariq M, Yuyan Y, Shah M, et al. (2022) Ionospheric-thermospheric responses to the May and September 2017 geomagnetic storms over Asian regions [J]. Adv Space Res 70(11):3731–3744 24. Liu A, Li Z, Wang N et al (2022) Shaking: adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations [J]. Adv Space Res 71(1):67–79 25. Rino C, Yu M, Breitsch B et al (2019) Stochastic TEC structure characterization [J]. J Geophys Res Space Physics 124(12):10571–10579 26. Zhao J, Hernández-Pajares M, Li Z, et al. (2021) Integrity investigation of global ionospheric TEC maps for high-precision positioning [J]. J Geod 95(3):35 27. Jin B, Chen S, Li D et al (2020) Ionospheric correlation analysis and spatial threat model for SBAS in China region [J]. Adv Space Res 66(12):2873–2887 28. Li Z, Yuan Y, Li H et al (2012) Two-step method for the determination of the differential code biases of COMPASS satellites [J]. J Geodesy 86(11):1059–1076 29. Ding J, Cai J (2020) Two-side coalitional matching approach for joint MIMO-NOMA clustering and BS selection in multi-cell MIMO-NOMA systems [J]. IEEE Trans Wireless Commun 19(3):2006–2021 30. BDSBAS-B1C (2020) BeiDou navigation satellite system signal in space interface control document satellite based augmentation system service signal BDSBAS-B1C (Version 1.0) [M]. China Satellite Navigation Office

Research on Intelligent Navigation Algorithm of Long and Short Term Memory Network Based on Firework Algorithm Optimization in Satellite Blocking Environment Yu Rui, Rong Wang(B) , Jingxin Zhao, Zhi Xiong, and Jianye Liu Navigation Research Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210000, China [email protected]

Abstract. This paper proposes an intelligent navigation algorithm based on long and short term memory network (LSTM) optimized by the fireworks algorithm (FWA) to address the issue of low positioning accuracy of pure inertial navigation systems under satellite blocking. The LSTM network is used to provide simulated satellite navigation positioning information, and the training, predicting, and validation modes are designed to evaluate the network’s prediction accuracy and state under dynamic changes in the carrier movement environment and measurement conditions. The FWA is utilized to dynamically adjust the LSTM network parameters and maintain pseudo location availability in the shortest possible training time. In the presence of satellite rejection, the FWA-LSTM network is flexibly selected to correct the inertial navigation system and maintain network availability. Simulation results demonstrate that the FWA-LSTM method provides supplementary support for satellite navigation under complex conditions, enhancing the training efficiency and availability ratio of the navigation system. Keywords: LSTM · BP · INS/GNSS integrated navigation system · GNSS unavailable · FWA optimization

1 Introduction With the development of modern society, GNSS satellites in traditional integrated navigation may be interfered, cheated or attacked, leading to problems such as delayed update or signal interruption. When the GNSS satellite signal is interrupted and the positioning accuracy is greatly decreased, the system switches to the pure inertial navigation system. However, the inertial navigation system is affected by the accumulation of errors, and the positioning accuracy will gradually decline over time [1]. Traditional navigation methods can no longer meet the requirements of navigation accuracy under the condition of satellite blocking. Because of its powerful self-organization and learning ability, neural network can provide powerful help for inertial navigation system in the research of integrated navigation technology based on neural network by using its intelligent characteristics, and © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 605–614, 2024. https://doi.org/10.1007/978-981-99-6932-6_50

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open up new ideas and ways for the research of integrated navigation performance, increasingly become an effective method of information fusion, with good theoretical significance and practical value. Traditional neural networks, such as back propagation neural network (BP) [2], radial basis function neural network (RBF) [3] and other static neural networks, cannot analyze the timing sequence characteristics of the errors of inertial navigation system, and have problems such as slow convergence speed and easy to fall into local minimum when processing large amounts of data [4]. Therefore, the prediction of static neural network only depends on the state of the carrier at the previous time, and the prediction accuracy is not high. At present, the training inputs and outputs of the neural network are mainly based on the positioning error of the INS and the output position of INS. The above methods incorporate a variety of uncontrollable sensor errors and ranging errors into the training of the neural network [5], and there are only training and predicting modes. In practical application, the prediction accuracy only depends on the result of one-time training. Thus, the prediction accuracy and flexibility of the system are not high [6]. Therefore, this paper proposes an intelligent navigation algorithm of long and short term memory network based on the optimization of fireworks algorithm. Firstly, the prediction of long and short term memory network (LSTM) is applied to the integrated navigation system. In the case of GNSS signal failure, the optimal LSTM network model obtained by training is used. The angle and velocity increment data of the load system output by the inertial navigation system were input to predict the simulated navigation position increment information. The position information output by the simulated navigation can be obtained by integrating the position increment, so that the Kalman filter in the SINS/GNSS integrated positioning system can be measured and updated continuously. Secondly, compared with the traditional LSTM, validation mode is added to save training time and increase the flexibility of the system. In addition, the fireworks algorithm is used to optimize the LSTM network parameters adaptively to improve the prediction accuracy of LSTM network. This improves the positioning accuracy of the pure inertial navigation system when the GNSS satellite signal is interrupted, and optimizes and updates the LSTM network to further improve the positioning accuracy of the navigation system during the next interruption.

2 Intelligent Navigation Method of LSTM Network Based on Fireworks Algorithm Optimization 2.1 LSTM Network Model In order to solve the problem that static neural network cannot process time sequence information, LSTM has added gate memory compared with recursive neural network (RNN) [7]. Each LSTM unit contains a forgetting gate Ut , an input gate it and an output gate ot , in which the information output of the node at the last time can be limited by Ut , the new input information can be selectively obtained by it , and the output of the current time can be determined according to the new input information and the output of the hidden layer at the last time by ot [8]. The structure of LSTM computing cell is shown in Fig. 1.

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Fig. 1. Schematic diagram of LSTM internal structure

As can be seen from Fig. 1, for the output of the forgetting gate ft , Sigmoid activation function is adopted to map the output to the interval [0, 1] [0, 1] [9]. The formula of the forgotten door ft is ft = σ (ht−1 Wf +x(t − 1) Uf +bf )

(1)

where σ is Sigmoid activation function and ht−1 is the state of the hidden layer at the last moment. x(t − 1) is the input of the previous time. Wf , Uf is the parameter matrix, bf is the parameter vector, · represents the matrix product. The input gate it determines what input information is retained. The input information includes two parts: the input at the current time and the output of the hidden layer at the previous time. The formula of the input gate it is it = σ (ht−1 Wi +x(t)Ui +bi )

(2)

where x(t) is the input of the current time. Wi , Ui is the parameter matrix, bi is the parameter vector. The output gate ot determines what information in ht−1 and x(t) will be output. Through the output gate, the hidden state of the current moment ht can be obtained as the output. The formula is ht = ot ◦ tanh(ct )

(3)

where ct is the LSTM cell state, ◦ represents the elements product. 2.2 Fireworks Algorithm Model In the process of designing the LSTM network architecture, two important network parameters need to be adjusted: (1) the number of hidden layers of the LSTM unit, (2) the time step of LSTM network, namely the learning rate [10, 11]. At present, LSTM mostly adopts manual parameter adjustment in the intelligent correction of inertial navigation, which is inefficient and difficult to find the optimal parameters. Based on this, the fireworks algorithm (FWA) is introduced in this paper

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to optimize the number of hidden layers and learning rate of LSTM. The fitness function adopts the average value of LSTM network prediction error under corresponding parameters. The fireworks operator of FWA is designed to search for the fireworks ai with the least fitness within the optimization range, that is to give consideration to both local accurate search and global efficient search. The expression of fireworks ai in this paper is ai = [N , η]

(4)

where N represents the number of hidden layers and η represents the learning rate. Initialize ai with the number of n as the optimization input. The expression of the number of optimization operators Si and optimization radius Ai is Si = M ×

ymax − f (ai ) + ε n  (ymax − f (ai )) + ε

(5)

i=1

ˆ × Ai = A

f (ai ) − ymin + ε n  (f (ai ) − ymin ) + ε

(6)

i=1

where f (ai ) is the training framework of the memory network, ymax and ymin are the maximum and minimum optimization range, M is the constant adjusting the number ˆ is the constant adjusting the optimization radius, ε is the of optimization operators, A mechanical minimum preventing division by 0, n is the number of initial optimization operators. Random mutation strategy and selection strategy are introduced into the algorithm, and the optimization parameter results are screened according to the principle of maximum Si within the range Ai . The selection possibility of each operator is calculated, and its expression is R(ai ) RP (ai ) =  R(ai )

(7)

ai ∈K

  ai − aj  R(ai ) =

(8)

ai ∈K

where RP (ai ) is the probability that the optimization operator is selected, K is the set of all results calculated by the optimization model, and R(ai ) is the sum of distances between the current optimization operator and other optimization operators. Select the larger RP (ai ) optimization results to train the system, and finally select the parameter with the least fitness as the hidden layer number and learning rate of LSTM network.

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3 Design of Intelligent Navigation Algorithm Based on LSTM Network in Satellite Blocking Environment 3.1 LSTM Training Structure In this paper, the FWA-LSTM network training input and predicting input are X ∈ {x(t)|ti < t < ti+ }, and the expression of x(t) is  T x(t) = VXt VYt tX tY tZ

(9)

where tX is the angular increment of the carrier X axis, tY is the angular increment of the carrier Y axis, tZ is the angular increment of the carrier Z axis, VXt is the velocity increment of the carrier X axis, VYt is the velocity increment of the carrier Y axis. The FWA-LSTM network training output is Y ∈ {y(t)|ti < t < ti+ }, and the expression of y(t) is:   y(t) = PLt Ptλ (10) where PLt is the increment of longitude position and Pλt is the increment of latitude position. 3.2 Intelligent Navigation System Mode Based on LSTM Network The structure of intelligent navigation system based on FWA-LSTM network is shown in Fig. 2. It consists of three modes, the training mode represented by blue is mainly used to train the LSTM network when the satellite navigation signal is available. The predicting mode represented by red is mainly used to predict the position increment of simulated-satellite navigation output in the case of satellite rejection. The validation mode represented by green is mainly used to determine whether the LSTM network needs to continue training after the satellite navigation signal recovered. Training Mode. When GNSS is available, the output data of gyroscope and accelerometer are calculated and converted to obtain the angular velocity and acceleration of the carrier. Obtain the longitude position and latitude position of the aircraft measured by GNSS, and make the difference of the position information of adjacent moments output by GNSS to obtain the longitude and latitude increment of the aircraft. Building the LSTM network model, and optimizing the parameters of the LSTM network by FWA optimization method based on the existing training input and output data, and adaptively adjust the number of hidden layers and learning rate in the LSTM network parameters. Check the training effect of LSTM network, and stop training when the network training error is lower than the expected error. Predicting Mode. When GNSS fails, the system changes from training mode to predicting mode. The Angle and speed increment of the inertial navigation system output

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Fig. 2. Structure diagram of intelligent navigation system modes based on LSTM network

when GNSS fails are learned by the trained FWA-LSTM network, and the position increment array predicted by FWA-LSTM network is output. the position pseudo-observation information p∗GNSS calculated after GNSS signal loss is as follows: p∗GNSS = pGNSS +

m 

y∗ (t)

(11)

k=2

where y∗ (t) is the predicted output of LSTM network, pGNSS is the position of GNSS signal loss moment, and m is the duration of GNSS signal loss. Validation Mode. After GNSS recovery, the system enters the validation mode, and makes a difference between the pseudo position increment predicted by FWA-LSTM network and the position increment measured by GNSS when it returns to normal. the difference is compared with the set expected error size to determine whether it is necessary to continue training FWA-LSTM network. If the difference is greater than the set expected error, the system enters the training mode again, otherwise, the training stops.

4 Simulation Results and Analysis 4.1 Simulation Design and Simulation Results In this paper, the proposed FWA-LSTM intelligent navigation algorithm is simulated and verified by Matlab simulation platform. The simulation time of aircraft track adopted in the simulation experiment is 1500 s, among which 1 ~ 900 s and 1000 ~ 1200 s GNSS is available, during 900 ~ 1000 s and 1200 ~ 1500 s GNSS is unavailable. For pure INS, BP network prediction, LSTM network prediction and LSTM network prediction after FWA optimization, the same failure time as described above is used for testing,

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and the accuracy of navigation and positioning is compared. The comparison image of navigation curves is shown in Fig. 3. In the simulation, accelerometer first order Markov process white noise is set as 5 × 10-4g m/s2, gyroscope first order Markov process white noise is set as 0.5 deg/h.

Fig. 3. Comparison of navigation curves

4.2 Analysis of Simulation Results Figure 4 shows the comparison of navigation position error results of four different navigation methods within the failure time of 900-1000s. It can be seen from the figure that GNSS fails within 900-1000s: within 13s of GNSS failure, the navigation performance of the intelligent navigation algorithm based on LSTM network for the satellite denial environment is inferior to that of the diverging pure inertial navigation system. After 13s of GNSS failure, the navigation position error of the intelligent navigation algorithm based on LSTM network for the satellite blocking environment is smaller than that of the pure inertial navigation system. Therefore, the FWA-LSTM network in this paper can supply the simulated-satellite navigation and positioning information, improve the accuracy of the navigation system and the prediction effect is better than assisted by the traditional BP neural network. The maximum positioning error and error rate of GNSS during the first period of failure are shown in Table 1. The calculation formula of error rate is δ=

l ∗ − ltrue × 100% ltrue

(12)

where δ is the error rate, ltrue is the ideal position increment value in the failure stage, and l ∗ is the position increment value under each navigation method. The prediction accuracy of the LSTM network optimized by FWA is 97.8% higher than that of pure

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Fig. 4. Position errors of 900 ~ 1000s with different algorithms

Table 1. Max error of position and error rate when GNSS is unavailable in different algorithms Pure INS Max Position Error(m) Error Rate

BP

LSTM

FWA-LSTM

42.18

29.97

25.53

6.32

102.8%

68.9%

32.5%

5.0%

inertial navigation calculation, 63.9% higher than that of BP network, and 27.5% higher than that of LSTM network without parameter optimization. Figure 5 is a comparison of navigation position error results of four different navigation methods within 1200 ~ 1500s failure time. It can be seen from the figure that GNSS fails within 1200 ~ 1500s: within 47s of GNSS failure, the navigation performance of the intelligent navigation algorithm based on FWA-LSTM network for the satellite denial environment is inferior to that of the pure inertial navigation system with divergent properties. After 47s of GNSS failure, the navigation error of the intelligent navigation algorithm based on LSTM network for the satellite denial environment is smaller than that of the pure inertial navigation system. Therefore, the LSTM network in this paper can supply the simulated-satellite navigation and positioning information, improve the accuracy of the navigation system and the prediction effect is better than assisted by the traditional BP neural network. The maximum positioning error of GNSS during the second stage failure time is shown in Table 2. Among them, the prediction accuracy of LSTM network optimized by FWA increased by 156.1% compared with pure inertial navigation calculation, 66.6% compared with BP network, and 28.2% compared with LSTM network without parameter optimization.

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Fig. 5. Position errors of 1200 ~ 1500s with different algorithms

Table 2. Max error of position and error rate when GNSS is unavailable in different algorithms pure INS

BP

LSTM

FWA-LSTM

Max position Error (m)

247.53

77.7

48.84

15.54

Error rate

163.7%

74.2%

35.8%

7.6%

5 Conclusion In this paper, an intelligent navigation algorithm based on long and short term memory network optimized by fireworks algorithm is proposed. By predicting the position increment in the case of GNSS satellite failure, the position information output of simulatedsatellite navigation is obtained, and the INS is combined with Kalman filter to reduce the divergence error of inertial navigation. The simulation results show that the LSTM network with FWA parameter optimization has higher prediction accuracy, which can provide an effective correction for the inertial navigation system under the condition of satellite rejection, and provide a supplementary role for the satellite navigation. Therefore, the method proposed in this paper can maintain the pseudo-positioning prediction accuracy online under complex application conditions and shorten the training time according to the performance requirements, improve the adaptability of the navigation system and the navigation accuracy under the condition of satellite blocking, and is suitable for practical applications. Acknowledgements. This work was partially supported by the National Natural Science Foundation of China (Grant No. 62073163, 61703208, 61873125), the Fundamental Research Funds for the Central Universities(Grant No. NT2022009, NZ2020004, NZ2019007), the 111 Project(B20007), the Shanghai Aerospace Science and Technology Innovation Fund(SAST2020– 073, SAST2019–085), Introduction plan of high end experts(G20200010142), "Qing Lan Project" of Jiangsu Province, the Science and Technology Innovation Project for the Selected Returned Overseas Chinese Scholars in Nanjing.

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Author Index

B Ba, Xiaohui 322 Bian, Lang 179, 263, 295 C Cai, Baigen 322 Cai, Hongliang 239 Chang, Jin 154 Chen, Feiqiang 415, 556 Chen, Lei 239 Chen, Li 168 Chen, Maolin 546 Chen, Qiuli 40, 68 Chen, Si 481 Chen, Siyuan 322 Chen, Xiao 13 Chen, Yaohui 438 Chen, Ying 13 Chen, Zhengkun 390, 402 Cui, Xiaozhun 345 D Deng, Zhongliang 525 Ding, Zhenke 525 Dong, Qijia 438 Dong, Xinying 253 Dong, Yanchen 228 Du, Fengze 105 Du, Junyu 525 F Fan, Caoming 228 Fan, Liqian 239 Feng, Junhong 505 Feng, Yuan 334 G Gao, Jiahao 367 Gao, Wang 94 Gao, Weiguang 239 Ge, Yuxiang 495 Guo, Ji 464

Guo, Shan 168 Guo, Xia 200 H Han, Lin 179 Han, Xinjuan 453 He, Chengyan 464 Hou, Yuzhuo 481 Hu, Yongyang 428 Hu, Zhigang 239 Huang, Chuhan 402 Huang, Guoxian 81 Huang, Pan 516 Huang, Zhigang 28, 55 J Jia, Qiongqiong 535 Jia, YiZhe 179 Jiang, Dongfang 137 Jiang, Kun 200 Jiang, Siyuan 283 Jiang, Wei 322 Jin, Ming 283 K Kan, Haoyu

239

L Li, Hong 567, 578 Li, Jing 215 Li, Kai 505 Li, Liang 105 Li, Linyang 453 Li, Mingxia 40 Li, Ping 40, 115, 200, 345 Li, Rui 68, 190, 215 Li, Ruiji 105 Li, Shenyang 438 Li, Shi-chong 305 Li, Song 379 Li, Tian 295 Li, Tianyi 215

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1093, pp. 615–617, 2024. https://doi.org/10.1007/978-981-99-6932-6

616

Author Index

Li, Weipeng 535 Li, Wenhao 567 Li, Xin 453 Li, Xing 200, 263 Li, Xinyue 253 Li, Zengke 495 Li, Zishen 590 Lian, Xiaotang 154 Liang, Mingxuan 390 Liang, Taotao 546 Lin, Haoyu 516 Lin, Honglei 379 Liu, Ang 590 Liu, Bingjie 137 Liu, Dan 179 Liu, Dun 168 Liu, Feifeng 367 Liu, Jianye 605 Liu, Jinyuan 556 Liu, Rui 464 Liu, Shuai 283 Liu, Xuanzuo 239 Liu, Yali 438 Liu, Zan 495 Liu, Zhiquan 546 Lu, Jianjun 402 Lu, Jun 13 Lu, Junyong 505 Lu, Mingquan 567, 578 Lu, Zhiwei 81 Lu, Zukun 415 Lv, Ruihong 367 M Ma, Chunjiang 379 Ma, Fu Jian 115 Ma, Pengcheng 379 Ma, Yimin 567, 578 Meng, YanSong 179 Meng, Yansong 263 N Ni, Shaojie

415, 556

O Ouyang, Chenhao 253 P Pan, Shuguo 94

Peng, Wenjie 253 Peng, Xinzhi 402 Q Qu, Bo 295 Qu, Zhongjun 154 R Ren, Binbin 415 Rui, Yu 605 S Sha, Hai 137 Shen, Jian 94 Shen, Jun 3 Shi, Junbo 253 Shi, Wei 428 Su, Chengeng 13, 481 Sun, Guangfu 556 Sun, Rui 81 Sun, Yifan 415 T Tang, Xiaomei 200, 379 Tang, Yinyin 505 Tang, Zuping 126, 334, 345 Teng, Xianliang 94 Tian, Xiang 13 Tian, Ye 263, 295 W Wang, Chuan 546 Wang, Dun 438 Wang, Feixue 379 Wang, Jian 322 Wang, Li 137 Wang, Liang 590 Wang, Ling 464 Wang, Lingtao 578 Wang, Ningbo 590 Wang, Rong 605 Wang, Runnan 283 Wang, Weiwei 263 Wang, Xuyu 137 Wang, Yangyang 495 Wang, Yansen 190 Wang, Yaoding 481 Wang, Yifan 495 Wang, Ying 295, 357

Author Index

Wang, Yongchao 55, 190 Wang, Yuechen 3 Wang, Zhanze 367 Wang, Zhiyu 590 Wang, Zhongzhi 154 Wei, Heng 137 Wei, Jiaolong 126, 334 Wu, Chengfeng 525 Wu, Xiaojing 367 Wu, Zhenyang 567, 578 X Xa, Jingyuan 334 Xie, Jun 263 Xie, Yuchen 556 Xing, Jianping 228 Xiong, Zhi 605 Xu, Chengdong 81 Xu, Fei 305 Xu, Zhenbang 453 Xu, Zhenxing 438 Y Yan, Tao 263, 295, 357 Yang, Tiantian 190, 215 Yao, Guodong 28 Yao, Zheng 228 Ye, Qiwei 105 Yin, Kai 55, 68 Yu, Haoyuan 137 Yu, Huizhen 94 Yu, Shiyun 428 Yuan, Hong 590

617

Yuan, Wenze 516 Yuan, Xuelin 390, 402

Z Zhang, Duo 345 Zhang, Gong 115 Zhang, Hao 115 Zhang, Jian-ming 305 Zhang, Min 94 Zhang, MinShu 179 Zhang, Peng 179 Zhang, Shangna 438 Zhang, XiaLu 179 Zhang, Xinran 546 Zhang, Xinxing 28 Zhao, Jing 81 Zhao, Jingxin 605 Zhao, Yingying 137 Zhao, Yun 40 Zhao, Zishan 55, 68 Zheng, Jin Jun 115 Zhou, Chuang 126 Zhou, Hongwei 28, 345 Zhou, Quan 179, 263 Zhou, Shun 428 Zhou, Yun 263 Zhou, Yuxuan 453 Zhou, Zhijian 390 Zhou, Ziheng 567, 578 Zhu, Qinglin 168 Zhu, Xiangwei 390, 402 Zou, Guoji 438