China Satellite Navigation Conference (CSNC) 2020 Proceedings: Volume II (Lecture Notes in Electrical Engineering, 651) 9811537100, 9789811537103

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Lecture Notes in Electrical Engineering 651

Jiadong Sun Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC) 2020 Proceedings: Volume II

Lecture Notes in Electrical Engineering Volume 651

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

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Jiadong Sun Changfeng Yang Jun Xie •

•

Editors

China Satellite Navigation Conference (CSNC) 2020 Proceedings: Volume II

123

Editors Jiadong Sun China Aerospace Science and Technology Corporation Beijing, Beijing, China

Changfeng Yang China Satellite Navigation Engineering Center Beijing, Beijing, China

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

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-15-3710-3 ISBN 978-981-15-3711-0 (eBook) https://doi.org/10.1007/978-981-15-3711-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

BeiDou Navigation Satellite System (BDS) is China’s global navigation satellite system which has been developed independently. BDS is similar in principle to the 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 11th China Satellite Navigation Conference (CSNC 2020) is held during November 22–25, 2020, Chengdu, China. The theme of CSNC2020 is “GNSS, New Global Era,” 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 S09 S10 S11 S12 S13

Satellite Navigation Applications Navigation and Location-based Service Satellite Navigation Signal and Signal Processing Satellite Orbit and System Error Processing Spatial Frames and Precise Positioning Time Primary Standard and Precision Time Service Satellite Navigation Augmentation Technology Test and Assessment Technology User Terminal Technology PNT System and Multi-source Fusion Navigation Anti-interference and Anti-spoofing Technology Policies, Regulations, Standards and Intellectual Properties Technologies for Navigation of Autonomous Systems

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Preface

The proceedings (Lecture Notes in Electrical Engineering) have 201 papers in thirteen topics of the conference, which were selected through a strict peer review process from 493 papers presented at CSNC2020. In addition, another 219 papers were selected as the electronic proceedings of CSNC2020, 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 278 referees and 57 session chairmen who are listed as members of the editorial board. The assistance of CNSC2020’s organizing committees and Springer editorial office is highly appreciated.

Editorial Board

Topic: S01: Satellite Navigation Applications Chairman Shuanggen Jin

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

Vice-chairmen Dangwei Wang Shuangcheng Zhang Wu Chen

Beijing UniStrong Science & Technology Co., Ltd., Shaanxi, China Chang’an University, Shaanxi, China Hong Kong Polytechnic University, Hong Kong, China

Topic: S02: Navigation and Location-Based Service Chairman Yamin Dang

Chinese Academy of Surveying and Mapping, Beijing, China

Vice-chairmen Baoguo Yu Wenjun Zhao Fuping Sun Kefei Zhang

The 54th Research Institute of China Electronics Technology Group Corporation, Hebei, China Beijing Satellite Navigation Center, Beijing, China Information Engineering University, Henan, China RMIT University, Melbourne, Australia

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Editorial Board

Topic: S03: Satellite Navigation Signal and Signal Processing Chairman Xiaochun Lu

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

Vice-chairmen Yang Li

Zheng Yao Yubai Li Tianxing Chu

The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China Tsinghua University, Beijing, China University of Electronic Science and Technology of China, Sichuan, China Texas A&M University-Corpus Christi, Corpus Christi, Texas, USA

Topic: S04: Satellite Orbit and System Error Processing Chairman Xiaogong Hu

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

Vice-chairmen Hui Yang Geshi Tang Li Liu Zhiguo Deng

China Academy of Space Technology, Beijing, China Beijing Aerospace Control Center, Beijing, China Beijing Satellite Navigation Center, Beijing, China German Research Centre for Geosciences, Potsdam, Germany

Topic: S05: Spatial Frames and Precise Positioning Chairman Qile Zhao

Wuhan University, Hubei, China

Editorial Board

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Vice-chairmen Jianwen Li Anmin Zeng Yanming Feng

Information Engineering University, Henan, China Xi’an Institute of Surveying and Mapping, Shaanxi, China Queensland University of Technology, Brisbane, Australia

Topic: S06: Time Primary Standard and Precision Time Service Chairman Lianshan Gao

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

Vice-chairmen Chunhao Han Xiaohui Li Pascal Rochat

Beijing Satellite Navigation Center, Beijing, China National Time Service Center, Chinese Academy of Sciences, Shaanxi, China SpectraTime, Neuchatel, Switzerland

Topic: S07: Satellite Navigation Augmentation Technology Chairman Rui Li

Beihang University, Beijing, China

Vice-chairmen Qun Ding

Shaojun Feng Yansong Meng Liwen Dai

The 20th Research Institute of China Electronics Technology Group Corporation, Shaanxi, China Imperial College London Qianxun Positioning Network, Co., Ltd., Shanghai, China Xi’an Branch of China Academy of Space Technology, Shaanxi, China John Deere, Torrance, CA, USA

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Editorial Board

Topic: S08: Test and Assessment Technology Chairman Xiaolin Jia

Xi’an Institute of Surveying and Mapping, Shaanxi, China

Vice-chairmen Jianping Cao Wenxiang Liu Yang Gao

Air Force Equipment Institute, Beijing, China National University of Defense Technology, Hunan, China University of Calgary, Alberta, Canada

Topic: S09: User Terminal Technology Chairman Mingquan Lu

Tsinghua University, Beijing, China

Vice-chairmen Dun Wang Zishen Li Sang Jeong Lee

Space Star Technology Co., Ltd., Beijing, China Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Chungnam National University, Daejeon, South Korea

Topic: S10: PNT System and Multi-source Fusion Navigation Chairman Zhongliang Deng

Beijing University of Posts and Telecommunications, Beijing, China

Vice-chairmen Hong Yuan Yongbin Zhou Chengjun Guo Jinling Wang

Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing, China Institute of Aerospace Engineering, Beijing, China University of Electronic Science and Technology of China, Sichuan, China University of New South Wales, Australia

Editorial Board

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Topic: S11: Anti-interference and Anti-spoofing Technology Chairman Hong Li

Tsinghua University, Beijing, China

Vice-chairmen Wei Wang

Xiaomei Tang Lidong Zhu

The 20th Research Institute of China Electronics Technology Group Corporation, Shaanxi, China National University of Defense Technology, Hunan, China University of Electronic Science and Technology of China, Sichuan, China

Topic: S12: Policies, Regulations, Standards and Intellectual Properties Chairman Huiying Li

Electronic Intellectual Property Center, Ministry of Industry and Information Technology, PRC Beijing, China

Vice-chairmen Junlin Yang Daiping Zhang Yonggang Wei

Beihang University, Beijing, China China Defense Science and Technology Information Center, Beijing, China China Academy of Aerospace Standardization and Product Assurance, Beijing, China

Topic: S13: Technologies for Navigation of Autonomous Systems Chairman Naser El-Sheimy

University of Calgary, Alberta, Canada

Vice-chairmen Xingqun Zhan Haihong Wang

Shanghai Jiao Tong University, Shanghai, China General Design Department of Beijing Space Vehicle, Beijing, China

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Wenbin Gong

Editorial Board

Shanghai Institute of Micro-satellite Innovation, Chinese Academy of Sciences, Shanghai, China

Scientific Committee Chairman Jiadong Sun

China Aerospace Science and Technology Corporation, Beijing, China

Vice-chairmen Rongjun Shen Qisheng Sui Changfeng Yang Zuhong Li Shusen Tan

China Satellite Navigation System Committee, Beijing, China China Satellite Navigation System Committee, Beijing, China China Satellite Navigation System Committee, Beijing, China China Academy of Space Technology, Beijing, China Beijing Satellite Navigation Center, Beijing, China

Executive Chairmen Jingnan Liu Yuanxi Yang Shiwei Fan Jun Xie Lanbo Cai

Wuhan University, Hubei, China China National Administration of GNSS and Applications, Beijing, China China Satellite Navigation Engineering Center, Beijing, China China Academy of Space Technology, Beijing, China China Satellite Navigation Office, Beijing, China

Committee Members (By Surnames Stroke Order) Xiancheng Ding Qingjun Bu Quan Yu

China Electronics Technology Group Corporation, Beijing, China China National Administration of GNSS and Applications, Beijing, China Peng Cheng Laboratory, Shenzhen, China

Editorial Board

Wei Wang Liheng Wang Yuzhu Wang

Xiaoyun Wang Lihong Wang Guoxiang Ai Lehao Long Shuhua Ye Chengqi Ran Weimin Bao Daren Lv Yongcai Liu Zhaowen Zhuang Qifeng Xu Houze Xu Tianchu Li Jiancheng Li Minlin Li Yirong Wu Weiqi Wu Haitao Wu Manqing Wu Guirong Min

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China Aerospace Science and Technology Corporation, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China China Mobile Communications Group Co., Ltd., Beijing, China Legislative Affairs Bureau of the Central Military, Beijing, China National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Technology Corporation Shanghai Astronomical Observatories, Chinese Academy of Sciences, Shanghai, China China Satellite Navigation Office, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China The Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China National University of Defense Technology, Hunan, China PLA Information Engineering University, Henan, China Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Hubei, China National Institute of Metrology, Beijing, China Wuhan University, Hubei, China China Society for World Trade Organization Studies, Beijing, China The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Xichang Satellite Launch Center, Sichuan, China Satellite Navigation Headquarters, Chinese Academy of Sciences, Beijing, China China Electronics Technology Group Corporation, Beijing, China China Academy of Space Technology, Beijing, China

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Jun Zhang Xixiang Zhang

Lvqian Zhang Junyong Chen Benyao Fan Dongjin Luo Zhixin Zhou Jiancheng Fang Huilin Jiang Guohong Xia Shuren Guo Peikang Huang Huikang Huang Chong Cao Faren Qi Rongsheng Su Yi Zeng Ziqing Wei

Editorial Board

Beijing Institute of Technology, Beijing, China The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China China Aerospace Science and Technology Corporation, Beijing, China National Administration of Surveying, Mapping and Geo-information, Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China Space Engineering University, Beijing, China Beihang University, Beijing, China Changchun University of Science and Technology, Jilin, China China Aerospace Science and Industry Corporation, Beijing, China China Satellite Navigation Engineering Center, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China Ministry of Foreign Affairs of the People’s Republic of China, Beijing, China China Research Institute of Radio Wave Propagation (CETC 22), Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China China Electronics Corporation, Beijing, China Xi’an Institute of Surveying and Mapping, Shaanxi, China

Executive Members (By Surnames Stroke Order) Zhongliang Deng Xiaochun Lu Hong Li Rui Li Huiying Li

Jun Shen

Beijing University of Posts and Telecommunications, Beijing, China National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Tsinghua University, Beijing, China Beihang University, Beijing, China Electronic Intellectual Property Center, Ministry of Industry and Information Technology, PRC Beijing, China Beijing UniStrong Science & Technology Co., Ltd., Beijing, China

Editorial Board

Mingquan Lu Shuanggen Jin Xiaogong Hu Qile Zhao Xiaolin Jia Yamin Dang Lianshan Gao

Naser El-Sheimy

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Tsinghua University, Beijing, China Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Wuhan University, Hubei, China Xi’an Institute of Surveying and Mapping, Shaanxi, China Chinese Academy of Surveying & Mapping, Beijing, China The 203th Research Institute of China Aerospace Science & Industry Corporation, Beijing, China University of Calgary, Alberta, Canada

Organizing Committee Director Chengqi Ran

China Satellite Navigation Office, Beijing, China

Deputy Directors Shigang Jing Xiaobin Ding Hongbing Xu Jun Yang

Science and Technology Department of Sichuan Province, Sichuan, China Chengdu Science and Technology Bureau, Sichuan, China University of Electronic Science and Technology of China, Sichuan, China China Satellite Navigation Office, Beijing, China

Secretary-General Haitao Wu

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

Deputy Secretary-General Weina Hao

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

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Editorial Board

Deputy Secretaries Zhong Tian

Wenhai Jiao Mingquan Lu Jun Lu Zhaoyang Ding

Hong Nie

Research Institute of Electronic Science and Technology, University of Electronic Science and Technology of China, Sichuan, China China Satellite Navigation Engineering Center, Beijing, China Tsinghua University, Beijing, China China Satellite Navigation Engineering Center, Beijing, China High-Tech Department of Science and Technology Department of Sichuan Province, Sichuan, China Cooperation Office of Chengdu Science and Technology Bureau, Sichuan, China

Committee Members (By Surnames Stroke Order) Li Wang An Deng Ying Liu Shaoqian Li

Zhiwei Tang Xiuwan Chen Lu Chen Xu Chen Jianqiao Yang Haiguang Yang

Jun Shen Di Xiao

International Cooperation Research Center, China Satellite Navigation Office, Beijing, China Mianyang Economic Cooperation Bureau, Sichuan, China China Satellite Navigation Engineering Center, Beijing, China National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology, Sichuan, China Office of University of Electronic Science and Technology, Sichuan, China Peking University, Beijing, China Beijing Institute of Space Science and Technology Information, Beijing, China Chengdu Science and Technology Bureau, Sichuan, China 29 Institute of China Electronics Technology Group Corporation, Sichuan, China Office of Scientific Research and Development University of Electronic Science and Technology of China, Sichuan, China Beijing UniStrong Science & Technology Co., Ltd., Beijing, China Beidou Union Technology Co., Ltd., Beijing, China

Editorial Board

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Jinjun Zheng

China Academy of Space Technology, Beijing, China Beijing Shunyi District Economic and Information Commission, Beijing, China Beijing Satellite Navigation Center, Beijing, China Wuhan University, Hubei, China Chengdu hi tech West Zone Science and Technology Bureau, Sichuan, China The National Remote Sensing Center of China, Beijing, China High Tech Department of Science and Technology Department of Sichuan Province, Sichuan, China

Dongning Lin Wenjun Zhao Qile Zhao Qingjun Zu Min Shui Weizheng Pei

Contents

Satellite Orbit and System Error Processing Modeling of BDS Positioning Errors Due to Ionospheric Scintillation and Its Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dun Liu, Xiao Yu, Jian Feng, and Weimin Zhen

3

A BDSPHERE Solar Radiation Pressure Model for BDS GEO Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rui Guo, Xiaojie Li, Jie Xin, Shan Wu, and Shuai Liu

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Test and Evaluation of the Distributed Autonomous Orbit Determination with the BDS Inter-satellite Ranging Data . . . . . . . . . . . Jie Xin, Ziqiang Li, Xiaojie Li, Rui Guo, Dongxia Wang, and Shuai Liu

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DTM2013 Model Parameter Inversion and Correlation Analysis Between Its Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wenhui Cui, Wei Qu, Haiyue Li, Ning Chen, Nan Ye, and Zhenyu Sun

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A Method of Combined Orbit Determination of Multi-source Data with Modified Helmert Variance Component Estimation . . . . . . . . . . . . Laiping Feng, Rengui Ruan, and Anmin Zeng

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The Influence of Station Distribution on the BeiDou-3 Inter-satellite Link Enhanced Orbit Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . Yufei Yang, Yuanxi Yang, Rui Guo, Chengpan Tang, and Zhixue Zhang

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Initial Results of BDS3 GEO Orbit Determination with Inter-satellite Link Measurements . . . . . . . . . . . . . . . . . . . . . . . . . Zongbo Huyan, Jun Zhu, Yanrong Wang, and Xia Ren

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Evaluation and Analysis of Orbit Determination Accuracy of BDS Satellite Under Clock Offset Constraint . . . . . . . . . . . . . . . . . . . Shuai Liu, Rui Guo, Xiaojie Li, and Qian Chen

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A Combined RDSS/RNSS Orbit Determination Method to Improve the Service Performance of RDSS . . . . . . . . . . . . . . . . . . . . Xiaojie Li, Rui Guo, Chengpan Tang, Shuanglin Huang, Shuai Liu, Jie Xin, Junyu Pu, and Jianbing Chen

97

Error Analysis and Strategy Optimization of East-West Control for BEIDOU GEO Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Xiaoying Wei, Lei Shi, Quanjun Li, Lusha Wang, and Donglin Li Estimation of BeiDou Satellites Antenna Phase Center Offsets . . . . . . . . 116 Yanan Fang, Jie Li, Chong Wang, and Jiasong Wang Influence Analysis of Multi-LEO Augmentation MEO Satellite Orbit Determination Under Regional Station Layout . . . . . . . . . . . . . . . . . . . . 126 Tian Zeng, Lifen Sui, Laiping Feng, and Xiaolin Jia A New Ambiguity Resolution Method Applied to Uncombined Precise Orbit Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Tian Zeng, Xiaodong Qin, Lifen Sui, Rengui Ruan, Xiaolin Jia, and Guorui Xiao Study on Operation Safety of RNSS and Long-Term Evolution of Disposal Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Jing Zhou and Hui Yang An Angular Momentum Allocation Strategy to Extend the Available Time of GEO Navigation Satellites . . . . . . . . . . . . . . . . . . 160 Zhen Cui, Bin Chen, Jiajia Feng, Ye Ji, and Weijie Liu Quality Analysis of Multi-GNSS Observation Data Based on IGMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Houzhe Zhang, Kai Shao, Defeng Gu, and Xiaojun Duan Orbit Residual Analysis of BDS Satellite Based on Ranging Information and Telemetry Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 186 Xu Zhang, Hui Yang, Qiuli Chen, and Chen Wang Spatial Frames and Precise Positioning Modeling and Assessment of BDS/GPS Triple-Frequency Precise Point Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Jie Lv, Zhouzheng Gao, and Junhuan Peng Baseline-Constrained GNSS Single-Frequency Single-Epoch Attitude Determination Based on Attitude Domain Search . . . . . . . . . . . . . . . . . 211 Hongtao Wu, Yu Jiao, and Longnan Bao Estimation of GLONASS Carrier Phase Inter-frequency Biases . . . . . . 223 Wei Yang, Qinggen Yi, Zhuoshan Wu, and Guoli Lin

Contents

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An Improved Clock Jump Detection Method in Real - Time PPP . . . . . 234 Kaidi Jin, Hongzhou Chai, Changjian Liu, and Chuhan Su Functional Model Compensation of Residual Systematic Errors in GNSS Precise Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Zhetao Zhang, Bofeng Li, Yunzhong Shen, and Xiufeng He The Detection and Repair of BDS Triple-Frequency Cycle-Slip of Weakening the Influence of Ionosphere . . . . . . . . . . . . . . . . . . . . . . . 255 Jiale Lin, Shubo Qiao, Ke Yan, and Xi Zhang First Implementation and Evaluation of Five Systems Network RTK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Xiyang He and Jinpei Chen Analysis and Modeling of the Inter-system Bias Between BDS-2 and BDS-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Ziyuan Song, Junping Chen, Bin Wang, and Chao Yu Single-Frequency GNSS-Based Measurement-Domain Attitude Determination Algorithm with Inter-system Bias Calibration . . . . . . . . 290 Jingze Li, Liang Li, Jiachang Jiang, Chun Jia, and Lin Zhao Phase Multipath Detection and Its Effect on Positioning Based on Multi-GNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Zhiwen Ren, Cuilin Kuang, and Zhetao Zhang Postseismic Deformation of the MS 8.1 Nepal Earthquake in 2015 from GPS Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Xiaoning Su, Lianbi Yao, and Guojie Meng Performance Assessment of Real-Time Precise Point Positioning Using SSR Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Ruijin Qiu, Zheyu Feng, Chenzhong Gu, Zhimin Yuan, and Jianwen Li Comparative Analysis of Velocity Estimation Methods for GNSS Coordinate Time Series in Southwest China . . . . . . . . . . . . . . . . . . . . . 346 Chunqiao Xie, Cuilin Kuang, and Jiugang Xie Research on Position-Domain GNSS Multipath Error Modelling Method Based on Sidereal Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Shangwei Han, Beiping Wu, Guangxing Wang, and Zhihao Yin Score Test Method of Real-Time Cycle Slip Detection Considering the Influence of Gross Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Lei Xia, Yufeng Yang, Chenxin Qing, Changsong Mei, and Xiong Pan Precision Analysis of Terrestrial Reference Frame Parameters Based on EOP A-Priori Constraint Model . . . . . . . . . . . . . . . . . . . . . . . 378 Jiao Liu, Junping Chen, and Bin Wang

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Time Primary Standard and Precision Time Service Research on Main Kinds of Frequency Biases of Optically-Pumped Cesium Beam Frequency Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Weibin Xie, Xuan He, Shengwei Fang, Nan Chen, Jiachen Yu, Qing Wang, Xianghui Qi, and Xuzong Chen Key Parameters Control of Optically Pumped Cesium Beam Atomic Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 Xuan He, Weibin Xie, Shengwei Fang, Nan Chen, Qing Wang, Xianghui Qi, and Xuzong Chen Considering Receiver Clock Modeling in PPP Time Transfer with BDS-3 Triple-Frequency Un-combined Observations . . . . . . . . . . . 410 Shuo Ding, Yulong Ge, Peipei Dai, WeiJin Qin, Xuhai Yang, and Ye Yu Performance Evaluation and Analysis of Galileo Satellite Clock in Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 Yufeng Yang, Changsong Mei, Chenxin Qing, Lei Xia, and Xiong Pan A Method for Evaluating BDS Real-Time Satellite Clock Offset Based on Satellite-Specific Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Zhimin Yuan, Changsheng Cai, Yanjie Li, and Guang Liu Controlling the Microwave Power in Optically Pumped Cesium Beam Frequency Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Nan Chen, Qing Wang, Xuan He, Weibin Xie, Shengwei Fang, Zezheng Xiong, Xianghui Qi, and Xuzong Chen Performance Analysis of the On-board Atomic Clocks for BeiDou-3 Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Yunfeng Sun, Yansong Meng, Erwang Du, Guanwen Huang, and Wei Xie New Research Progress in Active Hydrogen Maser in BIRMM . . . . . . . 463 Tiezhong Zhou, Mengzhi Wang, Shiqing Ren, Qiong Wu, Xiumei Wang, Chenyuan Zhang, Chunyan Cao, Yaxuan Liu, Liang Wang, and Lianshan Gao A Method of Remote Nanosecond Time Reproduction . . . . . . . . . . . . . . 472 Pan Du, Longxia Xu, Ya Liu, Xiaohui Li, and Feng Zhu Research on Time-Frequency Synchronization Technology of Multistatic Joint Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 Ya Liu, Duo-sheng Fan, Jia-chen Wang, Rui-qiong Chen, and Xiao-hui Li Research on BDS/GPS Carrier Phase Time and Frequency Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 Xiang-lei Wang, Feng-feng Shi, Fang-jun Yan, and Jia-min Fang

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A Rubidium Clock Taming Algorithm Based on Modified Grey Model and PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Jingyan Zhao, Xinyu Miao, and Yaojun Qiao The Method of BDS PPP Time Transfer Considering Clock Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 Yulong Ge, Shuo Ding, Peipei Dai, Xuhai Yang, WeiJin Qin, and Ye Yu The Long-Term Performance and Life Test of the Spaceborne Rubidium Atomic Clock Under Vacuum on the Ground . . . . . . . . . . . . 536 Feng Xu, Jia Yu Hu, Ke Liang He, Min Cheng, Ruo Feng Cao, Wei Zhang, Chang Liu, Tao Yang, Chun Bo Zhao, Er Wang Du, and Yu Ling He Discrete GM (1,1) Based on Sequence of Stepwise Ratio in the Application of the BDS Satellite Clock Bias Prediction . . . . . . . . 544 Changsong Mei, Yufeng Yang, Chenxin Qing, Lei Xia, and Xiong Pan Progress Towards a Miniaturized Mercury Ion Clock for Space Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Hao Liu, Yihe Chen, Bibo Yan, Ge Liu, and Lei She Research on a New On-orbit Control Strategy of Onboard Atomic Clock of Navigation Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 Maolei Wang, Jun Lu, Shenghong Xiao, Shichao Wang, and Sijia Yang BDS PPP Ambiguity Resolution and Its Application on Time and Frequency Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 Daqian Lv, Fangling Zeng, Yijing Han, and Xiaofeng Ouyang Satellite Navigation Augmentation Technology Non-Gaussian Carrier-Derived Doppler Integrity FDE for Multiple GNSS Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Wenying Lei, Hong Han, Wenshan Liu, Fei Ling, and Yansong Meng Analysis of Ionospheric Grid Model Performance for China Area . . . . . 598 Dun Liu, Xiao Yu, Liang Chen, and Weimin Zhen Type B Fault Integrity Monitoring for BDS Broadcast Ephemeris . . . . 611 Liang Li, Yuanyuan Liu, Chun Cheng, and Hui Li Design and Analysis of Beidou Global Integrity System Based on LEO Augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 Yizhe Jia, Lang Bian, Yueling Cao, Yansong Meng, and Lixin Zhang Method of GNSS Security Augmentation Based on LEO Satellite . . . . . 634 Tao Yan, Ying Wang, Xiao Liu, Lang Bian, and Yansong Meng

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Performance Analysis of a Navigation System Combining BeiDou with LEO Communication Constellation . . . . . . . . . . . . . . . . . . . . . . . . 643 Xing Li, Xia Guo, Bing Zhu, and Shumin Geng Error Modeling and Integrity Risk Analysis in SPP . . . . . . . . . . . . . . . 651 Yuan Song, Qingsong Li, Yi Dong, Wanli Jian, Dingjie Wang, and Jie Wu Research on Software Defined Payload Reconstruction Technology Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 Guochun Wu, Lei Wang, and Fei Ling Sparse Reconstruction of Regional Ionospheric Tomography Based on Beidou Ground Based Augmentation System . . . . . . . . . . . . . 673 Yun Sui, Haiyang Fu, Denghui Wang, Shaojun Feng, Zonghua Ding, Feng Xu, and Yaqiu Jin Un-difference PPP Method and Performance Assessment Based on Regional Ionospheric Model . . . . . . . . . . . . . . . . . . . . . . . . . . 684 Han Wang, Yun Sui, Denghui Wang, Haiyang Fu, and Shaojun Feng Online Integrity Alert Limit Determination Method for Autonomous Vehicle Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696 Qian Meng, Li-Ta Hsu, and Shaojun Feng Analysis of GBAS Integrity Requirements Based on Single Frequency Beidou Supporting CAT III . . . . . . . . . . . . . . . . . 707 Congbing Su, Anshi Wang, and Bin Li Analysis of the Spatial Correlation of Ionosphere in the Middle Latitude Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Zheng Yuan, Letao Zhou, Yinghao Zhao, and Huchao Xu Derivation of Integrity Allocation for Satellite Based Augmentation System Ionosphere Monitors . . . . . . . . . . . . . . . . . . . . . . 727 Yan Zhang, Xiaomei Tang, Yangbo Huang, Long Huang, and Gang Ou A Statistical Study of the Ionospheric Anomalies Affecting SBAS Safety Detected over China Area in 2015 . . . . . . . . . . . . . . . . . . . . . . . . 739 Yaxi Liu, Rui Li, Junjie Bao, and Yutong Liu Applicability Analysis of Kriging Methodology for China . . . . . . . . . . . 751 Junjie Bao, Rui Li, and Zhigang Huang Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

Satellite Orbit and System Error Processing

Modeling of BDS Positioning Errors Due to Ionospheric Scintillation and Its Application Dun Liu(&), Xiao Yu, Jian Feng, and Weimin Zhen No. 22nd Research Institute, CETC, Qingdao 266107, Shandong, China [email protected]

Abstract. In this work, efforts are made to develop models of BDS positioning errors due to ionospheric scintillation. Two aspects are specially considered in the modeling work, namely the lose-of-lock on signals and the range errors under scintillation. Analysis with scintillation data from China shows that the possibility of signal loss of lock follows a Weibull Distribution. With this in mind, a method is developed to determine the signal-locking statue based on the scintillation index. The theoretical model on range errors is improved to expand the range of input parameters. Errors arising from scintillation related ionospheric irregularity are also accounted for. Then, BDS positioning performance is analyzed with the constructed models for typical scintillation scenarios with the output of GISM (Global Ionospheric Scintillation Model). The Results show the rationality of the models. Keywords: Ionospheric scintillation error
Scintillation index


Possibility of loss-of-lock
Ranging

1 Introduction Ionospheric scintillation describes the rapid fluctuations in phase and amplitude of navigation signals that pass through the ionosphere caused by electron density irregularities along the signal propagation path [1–3]. Ionospheric scintillation causes deep fading in amplitude of received signal, leading to loss-of-lock of the signal under serious conditions. At the same time, when rapid fluctuation in phase of the received signal exceeds bandwidth of the receiver’s tracking loop, cycle slip or loss-of-lock will also occur. These effects of scintillation are hard to be corrected with models, as that could be done for ionospheric delay error. Additionally, scintillation can affect the whole L band in which GNSS system operates, making it impossible to compensate these impacts even with dual-frequency observations. As the result, scintillation remains to be the most severe ionospheric impact for modernized GNSS [2, 4, 5]. As one of the countermeasures, scintillation monitoring or forecasting could be used to draw up working plans beforehand, or make assessment afterwards. As an example, service has being provided by ESA with the Scintillation Quickmaps product [6]. Similar products are also served by NASA [7]. Additionally, FAA has taken scintillation impact into account in its regular assessment on WAAS performance [8, 9]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 3–15, 2020. https://doi.org/10.1007/978-981-15-3711-0_1

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There are two issues should be dealt with reasonably in scintillation products service. Firstly, relation between scintillation monitoring results and its impacts on system performance should be addressed reasonably. In their products, severity of scintillation effect described by loss-of-lock of GNSS signals, like Quickmaps from ESA, or determined with ROT (Rate of TEC) or ROTI (Index of Rate of TEC) as that of NASA [6, 7]. These products, however, cannot give a clear picture on the available system performance under scintillation. Secondly, the existing theoretical models, such as the one developed by Conker et al., has limitation when it deals with real observations. These tracking error models require an input scintillation index of less than 0.7 [8, 9], while in practice it usually observes scintillation events with index greater than 0.7. As the result, the signal with scintillation index greater than 0.7 has to be treated as a lost one mandatorily in analysis. This generally leads to an overestimated result. Our work in this paper, therefore, is to construct more reasonable models to examine GNSS positioning performance under scintillation. The modeling efforts are concentrated on the loss-of-lock of signal link and the measurement error of GNSS receiver under scintillation. The works laid the foundation for future BDS ionospheric scintillation monitoring and forecasting service. The paper is organized as follows. In Sect. 2 we focus on the tracking model of GNSS signal link under scintillation. In Sect. 3, we further consider the ranging error model of receiver impacted by scintillation. With the models, in Sect. 4 we show the application of performance assessment of BDS under scintillation in a service rating way. Our conclusion is summarized finally.

2 Modeling for Signal Tracking Under Scintillation 2.1

Model of GNSS Signal Loss-of-Lock Possibility Under Scintillation

The most serious impact of scintillation on GNSS positioning performance is the disruption of signal tracking. Therefore, a rational method to determine the status of GNSS signal link is critical to analysis of ionospheric scintillation effect. To this end, statistical analysis was carried out on scintillation observations with GPS from 2012 to 2014 in Haikou, Guangzhou and Kunming in south of China. The observations are made with the dedicated NovAtel receiver for scintillation monitoring [10]. Figure 1 shows the cumulative probability of GPS signal loss-of-lock with scintillation index (amplitude scintillation index S4 hereafter) for Haikou in March 2012. Similar results are achieved also with the other data set. It can be seen that even with a small scintillation index (0.2), satellite signal still has a possibility of losing lock, and under a severe scintillation condition with index greater than 1, satellite signal loses lock almost certainly. Phase locked loop (PLL) in GNSS receiver is more susceptible to scintillation. Theoretical analysis shows that the mean time of losing lock of the GNSS signal is depended on the loop tracking error [11]. Amplitude fade arising from scintillation will cause the received signal strength to decrease, increasing the loop tracking error and reducing the mean time of losing lock [12]. At the same time, the prolonged fading duration of intensity will increase the probability of signal loss-of-lock [12]. Therefore, for receiver under lengthy scintillation impact, even a weak event could make the signal losing.

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5

Cumulative Percentage of losing signal

100 90 80 70 60 50 40 30 20 10 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Scin. index

Fig. 1. Cumulative probability of signal losing under scintillation (Haikou, March 2013)

The statistical result from all the data shows that the probability of signal link outage follows a Weibull distribution. The figure below shows this result from measurement and the fitted Weibull distribution. It can be seen that the statistical result, blue squares in the figure, is consistent with the theoretical fitting one, red curve in the figure. It also can be seen that the loss-of-lock probability reaches the maximum when S4 is about 0.7. As the value of S4 increases, the signal could still be locked instead of total disruption, contradicting to the theoretical analysis way. In theory, the input S4 with values larger than 0.7 (the exact value is 0.707) will make the model nonsense. This is can be seen clearly from Eq. (1). Therefore, the signal link with index S4 larger 0.7 is to be treated as a losing one, leading to an overestimated result. To address the issue, a method is put forward to determine the GNSS signal link status in a statistical way. It also can be seen from Fig. 2 that the scintillation index appears to be much larger than 1, but theoretically its value should be smaller than 1 [2, 3]. Scintillation index is generally calculated with signal intensity data of one minute length. In practice, strength of a signal reduced to be zero when interrupted by scintillation. To calculate the index S4, raw data has to be preprocessed with these zero values eliminated or interpolated. Here in the work, we pay more attention to signal interruption caused by scintillation. If the zero value in the original data is processed beforehand, the result is consistent with the theory, but the information on signal interruption therein will be lost. Therefore, in actual analysis, the index S4 is calculated in the usual way, but with the zero value maintained. Although such data processing strategy will lead to scintillation index larger than one, information on signal interruption has been reserved. The resulting scintillation index will benefit the following modeling work.

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Probability

0.1 0.08 0.06 0.04 0.02 0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

S4 index

Fig. 2. Probability of signal losing w.r.t scintillation index S4, (blue squares for real data, red line for fitting result)

2.2

Analysis Procedure for GNSS Signal Loss-of-Lock Under Scintillation

With the probability model of signal loss-of-lock, we can predict the GNSS signal link status with Monte Carlo simulation [13]. The main process is as follows • Random number generation Generate a uniformly distributed random number between zero and one. • Loss-of-lock possibility estimation Probability of losing the signal is estimated with the empirically determined Weibull distribution with index S4 for the signal link as input. • Signal loss-of-lock judgment When the losing probability from Weibull estimation is greater than the random number generated, the signal is judged to be disrupted. • Signal link availability determination Repeat the simulation many times and count the possibility of signal link interruption. The satellite signal will be treated as unavailable when the resulting possibility is greater than a preset threshold. Figure 3 shows the BDS measurement under scintillation at Kunming station on April 18, 2014 (108th day of year). The figure includes the number of actual observed BDS satellites, and the associated HDOP and VDOP values. It can be seen that under strong scintillation, the number of BDS satellites actually tracked by receiver changed frequently, with 2–3 satellites lost simultaneously. With the reduced satellites, the DOP values increased sharply.

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Fig. 3. Viewed BDS SVs (up), and the resulting HDOP (mid) and VDOP (below) (Kunming, 18th April, 2014)

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Figure 4 shows the analysis results with observation from GPS. As only GPS scintillation measurement has been made in Kunming, here we made the examination with GPS observation to reproduce the typical features in BDS measurements. It can be seen that with the signal link tracking model, we realistically reproduced the receiver’s frequently loss-of-lock on multiple satellites. The variation of the corresponding DOP values in the case of signal loss-of-lock is further shown in Fig. 5. It can be seen that the results truly reproduces the repeating increase in DOP values under scintillation, especially the sporadic ‘spike’ ones.

Fig. 4. Viewed GPS SVs and available GPS SVs under scintillation obtained with signal loseof-locking model (Kunming, 18th April, 2014)

Fig. 5. HDOP and VDOP for GPS user under scintillation, obtained with signal loss-of-lock model (Kunming, 18th April, 2014)

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3 Modeling for Ranging Errors Under Scintillation 3.1

Ranging Errors from Scintillation Effects

In Ref. [13], the ranging error under scintillation is modeled statistically, but without a reasonable explanation. We explored ways to model ranging error with the hope to find explicit dependency of the error on various parameters. The results show ranging error changes with elevation angle. The following figure, with data from Kunming on April 18 2014, shows the trend significantly (Fig. 6). The discrete points with larger values in the figure are wild values when receiver tracking loop was in critical condition. After removing these wild values, the ranging error is about 20–30 m at low elevation angles. Ranging error for B1 signal under scintillation can also be estimated with the tracking error model established by Conker et al. [9] (Fig. 7). It can be seen that under strong scintillation with S4 value of 0.7, the ranging error can reach 20 m, the similar level to the actual data. Therefore, the tracking error model established by Conker et al. could still be used, but the limitation on input had to be removed. In the work, Conker’s tracking model is used in the following ways. For signal links with scintillation index smaller than 0.7, the error is estimated with tracking model normally, while for links with index greater than 0.7, the errors are estimated using the model with fixed values of 0.7.

Fig. 6. Ranging error w.r.t elevation angle under scintillation

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Fig. 7. Theoretical ranging error under scintillation

Here, we give the error models constructed by Conker as follows [9]:
Bn d 1 þ r2s ¼

 1 gðc=n0 Þð12S24 Þ

  2ðc=n0 Þ 1  S24

ð1Þ

Where Bn is the bandwidth of tracking loop, g is the receiver pre-detection integration time, and d is the correlator spacing in code chips, c=n0 is fractional forms of signal-to-noise ratio (C=N0 ), c=n0 ¼ 100:1C=N0 . The ranging error rs in meters is: rbs ¼ WB1I rs

ð2Þ

Where WB1I = 146.526 m is the chip length of the B1I code of BDS. 3.2

Total Ranging Errors Under Scintillation

In our work, total errors of range measurement is estimated with the model as that in WAAS system [14]. r2PR ¼ r2Eph þ F 2 r2Ion þ r2Rvr þ

r2Trop r2Mul þ 2 2 tan ðEÞ sin ðEÞ

ð3Þ

Among them, r2Eph is ephemeris error, including satellite positioning error and satellite clock error; r2Ion is ionospheric delay error but will be modified to include errors from scintillation effects, r2Rvr is receiver measurement error, r2Mul is multipath error, and r2Trop is tropospheric residual error, F is the mapping function, and E is the elevation angle. One can refer to the Ref. [14] for more details.

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Two kinds of error sources are taken into account for scintillation effect. One is the ranging error caused by signal fading, as that described in Sect. 3.1, the other is the delay error from ionospheric electron density irregularity triggering the scintillation. The irregularity is generally 10–20% of the background ionospheric electron density [15]. In the analysis, background ionosphere is obtained with GIM ionospheric map product. The overall ionospheric delay error accounted for in the analysis is then r2Ion ¼ r^2s þ r2Irreg

ð4Þ

4 Analysis of Scintillation on BDS Performance 4.1

Analysis Procedure

When regional scintillation condition has been known, either by monitoring or by forecasting, then the impacted GNSS system performance can be analyzed with scintillation error models for the area. Here in the paper, we make an examination of BDS system performance under scintillation with GISM (Global Ionospheric Scintillation Model). The GISM is a long-term statistical model for scintillation study recommended by ITU [15]. The work is made for the area of 60° E–150° E and 10° S–50° N, which covers China’s low-latitude area effected most seriously by scintillation. The area is divided into 1°  1° grids, and each grid point is treated as a virtual user. For each virtual user, the observing geometry is calculated with ephemeris to find the visible satellites. For each visible satellite, scintillation index is estimated with GISM model at the ionosperhic pierce point (IPP) where satellite signal intersects the shell model. Whether a visible satellite is available for positioning is then determined using the method in Sect. 2.2 with the estimated scintillation index. For the available satellite, its ranging errors can be calculated with the models in Sect. 3.2. With the observing geometry and ranging errors, the positioning error for each virtual user can then be determined. In the analysis, the delay error from the background ionosphere is corrected with GIM TEC maps. In doing so, we can make the analysis especially focusing on the effects arising from ionospheric scintillation, including the impacts from signal link disruption, signal ranging error, and delay error from the scintillation-triggered electron density irregularity. 4.2

Analysis Results of Scintillation on BDS Performance

Scintillation index maps were obtained in advance with the GISM model, with the date set on September 22, 2012, the autumn equinox at a high solar activity year, and F10.7 value 120, indicating a strong scintillation scenario. Input time could be selected between 10:00–21:00 UT (corresponding to 18:00 LT to 5:00 LT next day) as scintillation generally emerges after sunset and lasts until midnight local time. Scintillation index maps were generated with a spatial resolution of 1°  1° and a temporal resolution of 15 min. Analyzed frequency was set to 1561.098 MHz for the BDS public service signal.

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In the analysis, BDS ephemeris was used to get the observing geometry of visible satellites. Height of the shell model was set at 350 km, and the scintillation index at IPP was determined with the nearest grid in scintillation index maps. Others in the analysis, the ephemeris error was taken as that of the fast products of IGS precise ephemeris and clock correction, r2Mul was 0.5 m, and r2Trop 0.1 m. The electron density irregularity was taken as 20% of the background ionosphere, which was given by GIM TEC map. Three-tiers of service level was adopted in the analysis to illustrate the result, namely standard performance service (SPS), moderately declined performance service (MPS), and degraded performance service (DPS). The following criteria were used to divide various services [16, 17] (Table 1). Table 1. Service performance level for BDS Service level Positioning accuracy (2r) SPS ErrHozi \5 m and ErrVert \8 m MPS 5m  ErrHozi \9 m or 8m  ErrVert \15 m DPS ErrHozi  9 m and ErrVert  15 m

Figure 8 shows the results for the time of 13:00 UT. The figure includes the scintillation index map, ionospheric delay distribution, and horizontal and vertical positioning error for BDS single-frequency user. It can be seen that at 13:00 UT, strong scintillation mainly covered the area of 10° S–20° N, 110° E–180° E, with the maximum S4 exceeding 0.7, while the large ionospheric delay was located primarily over the African region. The service was degraded moderately or seriously in the area of 5° N–20° N, 125° E–160° E, which was affected by strong scintillation. At this time, ionospheric delay in this area was generally less than 5 m. Since the delay from background ionosphere has been corrected with GIM model, the residual ionospheric error was mainly from the irregularity, which is about 20% of the background values. Consequently, the ionospheric delay’s contribution to the positioning error will not exceed 1 m. Therefore, the decreased accuracy of BDS service originated from the serious ionospheric scintillation impacts. The work shows that with the available ionospheric scintillation conditions and the positioning error models, BDS service performance under scintillation could be analyzed. Although the service division is not in a strict way, the results show the impacted system performance in a clear way even with a glimpse.

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a) Iono. Delay (in m) for UT 13.0 80

11 10

60

9

Latitude (Deg)

40

8

20

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0

6 5

-20 4 -40

3

-60

2 1

-80 -150

-100

-50

0

50

Longitude (Deg)

100

150

b)

c)

Fig. 8. Analysis results with GISM and positioning error models. (a) scintillation index map, (b) ionospheric delay map, (c) horizontal positioning error, (d) vertical positioning error.

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Fig. 8. (continued)

5 Conclusion System performance evaluation under scintillation is need as one of future BDS public services. To this end, modeling efforts have been made on the availability of signal links and tracking errors of pseudorange under scintillation. Statistical analysis on the loss of lock on GPS signal has been conducted for scintillation events observed in south of China. It was found that the probability of signal disruption with scintillation index S4 follows a Weibull distribution. Based on this finding, we develop a method to predict the signal tracking conditions. The new method makes the determination on whether a signal link is available in a statistic way instead of a fixed threshold. As the result, the method gives a more reasonable estimation on scintillation impacts. Furthermore, the theoretical models for ranging errors are examined with comparison to measured data. With the outliers removed, the error in measurements is at the same order with theoretical model. With this in mind, the theoretical model is still adopted in the work, but its applicability is extended with proposals put forward. Errors originating from irregularity are also taken into account in the analysis. At last, we demonstrate the application of errors model with GISM scintillation model. The performance for static positioning user under scintillation is analyzed and illustrated in various service levels. The results could be act as the preliminary foundation for future public services. Acknowledgements. This research was supported by the National Key R&D Program of China (No. 2018YFB0505100).

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References 1. Knight, M.F., Finn, A.: The impact of ionospheric scintillations on GPS performance. In: ION GPS, pp. 555–564, September 1996 2. Knight, M.F.: Ionospheric effects on global positioning system receivers. The University of Adelaide (2000) 3. Doherty, P.H., Delay, S.H., Valladares, C.E., Klobuchar, J.A.: Ionospheric scintillation effects in the equatorial and auroral regions. In: ION GPS, pp. 662–671, September 2000 4. Humphreys, E., Psiaki, M.L., Kintner, P.M.: Modeling the effects of ionospheric scintillation on GPS carrier phase tracking. IEEE Trans. Aerosp. Electron. Syst. 46(4), 1624–1637 (2010) 5. Liu, D., Feng, J., Deng, Z., Zhen, W.: Study of ionospheric scintillation effects on GNSS positioning performance. Chin. J. Radio Sci. 25(4), 702–710 (2010) 6. ESA, Scintillation quickmaps: Quickmaps and history of the effects of ionospheric scintillation on GPS/GLONASS signals. http://swe.ssa.esa.int/TECEES/sda/ scintillationquickmaps/index.html 7. NASA, Latest Global RTI. http://iono.jpl.nasa.gov/scint_demo.html 8. Hegarty, C., El-Arini, M.B., Kim, T., Ericson, S.: Scintillation modeling for GPS/WAAS receivers. In: ION GPS, pp. 799–807 (2000) 9. Conker, R.S., El-Arini, M.B., Hegarty, C.J., Hsiao, T.: Modeling the effects of Ionospheric scintillation on GPS/satellite-based augmentation system availability. Radio Sci. 38, 1 (2003) 10. Liu, D., Yu, X., Chen, L., Zhen, W.M.: Characterization of positioning errors for BDS/GPS receiver under ionospheric scintillation. In: The 10th China Satellite Navigation Conference (CSNC 2019), Beijing, May 2019 11. Gardner, F.M.: Phaselock Techniques, 3rd edn. Wiley, Hoboken (2005) 12. Simon, M.K., Alouini, M.: Digital Communications over Fading Channels. Wiley, New York (2000) 13. Carrano, C.S., Groves, K.M., Griffin, J.M.: Empirical characterization and modeling of GPS positioning errors due to ionospheric scintillation. In: Ionospheric Effects Symposium, Alexandria, VA, May 2005 14. RTCA Special Committee 159, Minimum Operational Performance Standards for Airborne Equipment Using Global Positioning System/Wide Area Augmentation System, RTCA/DO229C, November 2001 15. Beniguel, Y.: GIM: a global ionospheric propagation model for scintillation of transmitted signals. Radio Sci. 37(3), 1032–1044 (2002) 16. European Commission, and ESA. GALILEO Mission High Level Definition, September 2002 17. Li, Z.H.: Research on monitoring and assessment of satellite navigation system performance. PLA Information Engineering University (2012)

A BDSPHERE Solar Radiation Pressure Model for BDS GEO Satellites Rui Guo(&), Xiaojie Li, Jie Xin, Shan Wu, and Shuai Liu 32021 Troops, Beijing 100094, China [email protected]

Abstract. The precision of BDS navigation message based on global satellite laser ranging (SLR) analysis is about 60 cm for geostationary earth orbit (GEO) satellites. There is an obvious gap between the POD accuracy of GEO satellites and IGSO & MEO satellites. The reason being that the GEO satellites lie in high and geostationary orbits. Also, the mature GPS solar radiation pressure (SRP) model is used as a reference in orbit determination for GEO satellite. We uses traditional spherical SRP model as background model and estimates the SRP parameters of a 2-yr precise GEO satellite ephemeris with dynamic smoothing method, and builds a continuous SRP parameter sequence. Thoughts on “Fourier series overlaid linear term” modeling are proposed and an empirical SRP model for BDS GEO satellite (BDSPHERE for short) comes into being. We verify the model based on observation data and the results show that: (1) the signal-in-space range error (SISRE(ORB)) of GEOs based on BDSPHERE model amounts to 0.63 m, while the orbital SISRE(ORB) for 8 h, 12 h and 24 h prediction is 0.79 m, 1.24 m and 1.65 m respectively; (2) compared to traditional spherical SRP model, there is an increase of 56.55%, 65.81%, 63.31% and 58.33% with the BDSPHERE model. The precision of radial orbit by global SLR analysis is 0.597 m, an increase of 70.06%. Keywords: BDS
GEO
SRP model
Precise orbit determination
Dynamic smoothing
Fourier series

1 Introduction BDS is China’s self-developed satellite navigation system and GEO satellite is an important component of the BDS constellation. Therefore, the POD and prediction accuracy of GEO satellites provide a fundamental guarantee for the navigation system services [1]. Unlike MEO satellites of GPS, the orbit determination of BDS GEO satellites proves both a hot topic and a challenge in the field of satellite navigation and POD. Based on SLR evaluation, the radial orbit accuracy obtained from BDS GEO satellite navigation message is 60 cm, while in the case of IGSO and MEO satellites, the precision values amount to 20–30 cm [2, 3]. There is an obvious gap between the GEO satellites and the IGSO/MEO satellites in terms of POD, the first reason being that GEO satellites lie in high and geostationary orbits, which limits the length of ground tracking network, worsens geometric conditions for orbit determination, causes high © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 16–26, 2020. https://doi.org/10.1007/978-981-15-3711-0_2

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correlation between clock errors and orbital parameters and therefore makes the orbit determination equation become morbid. Secondly, the SRP error by the single-satellite precise orbit determination (SPOD) can hardly be precisely modeled. Its changing patterns are closely related to satellite attitude control mode, solar radiation intensity, exposed areas of satellites, optical properties of surfaces and the geometric relationship between the sun and the satellites. Currently, the orbit determination of BDS GEO satellites is mainly based on the SRP model of GPS satellites, while the two types of satellites differ in platforms, surface properties and satellite attitude control mode [4]. What’s more, BDS does not own independent intellectual proprietary rights of the SRP model for BDS GEO satellites and the current mechanics model has incompatible issues in the POD process. Both scholars at home and abroad have started investigations into the precision of the SRP model since 1980 s and three types of SRP models [6–10], i.e., analytical, empirical and semi-empirical SRP models, which have been constructed based on GPS satellites. When Arnold was trying to use global IGS stations to conduct experiments on geophysical parameter based on GPS/GLONASS satellite observation data in 2015, he managed to reconstruct the original ECOM model, which later became known as ECOM-2 model [11]. In 2016, the POD accuracy evaluation of Galileo satellites was conducted with the ECOM-2 model and Cuboid Box-Wing model by Montenbruck and Steigenberger [12]. Compared to the traditional SRP model of ECOM 5, the precision of radial orbit by SLR evaluation can be improved to 10 cm from 20 cm [13]. Zhao [14] established two simplified Box-Wing models based on the characteristics of BDS satellite platform and Feng [15] established the SRP models for the BDS IGSO satellites based on the ray tracing technique. These two types of models are both analytical models. As satellite surface materials are affected by space environment and other factors, the long-arc changes in the analytical models will lead to the increase of model errors. Therefore, physical modeling has its limits. Based on the above analysis, we focus on the reconstruction of the SRP models for GEO satellites and construct a 2-yr precise satellite ephemeris based on the long-arc observation data obtained from in-orbit satellites. With the traditional spherical SRP model as the background model, we conduct evaluations on the SRP parameters by the long-arc precision ephemeris smoothed by the dynamic smoothing method and build a 2-yr SRP parameter time series. Based on the characteristic analysis of the time series, the BDSpherical SRP model is built as “Fourier series overlaid linear term”. The model is verified by measurement data obtained from the BDS GEO satellites and it can greatly improve the POD accuracy and ensure the continuity and stability of the signal in space accuracy (SISA).

2 Spherical SRP Model Different methods are used to calculate the radial pressure of sphere-shaped satellites and complicatedly shaped satellites. To calculate the SRP of complexly shaped satellites, the satellites need to be divided into different planes; as for spherically shaped

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satellites, the calculation can be performed by referring to the sphere-shaped SRP model, the calculation formula is shown below: Ds A ~ S~ RP ¼ Ps a2u Cr ð Þc m Ds 8 1 in sunshine > < c¼ 0 in shadow > : 0\c\1 in semi  shadow Ashadow c ¼ 1 Aall

ð1Þ

In (1), Ps refers to the SRP on the black body which is one astronomical unit away from the sun; ~ Ds ¼ ~ R~ Rs , ~ R and ~ Rs refer to the position vectors of the satellite and the sun in the earth-centered inertial coordinate system respectively; au is the astronomical unit; A=m is the face value ratio; c is the earth shadow factor; Cr represents the SRP scaling parameter of the satellite surface which is used for parameter resolution in orbit determination; Ashadow is the visual area of solar eclipse; Aall is the visual solar area. For more information about the model, please refer to the attached references [15].

3 BDS Satellite Attitude Control Mod The yaw steering mode is used for in-orbit attitude control of the BDS GEO satellite, i.e. the Z axis points to the earth center, the Y axis is orthogonal to the motor level of orbit, the X axis is orthogonal to the Y/Z axis, and the yaw steering angle remains 0. As showed in Fig. 1, the direction of the X axis is in line with the direction of velocity.

Fig. 1. Illustration of yaw steering for BDS GEO Satellite

Currently, the SRP model used in BDS Satellites is mainly based on the GPS satellite model. It is worth noting that dynamic biasing model and continuous and dynamic biasing models are applied in GPS satellites, which have the same control model with BDS IGSO/MEO satellites, but there exists difference from BDS GEO satellites. Therefore, the SRP model used by GPS satellites will create more errors in

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analyzing GEO satellite than IGSO/MEO satellites. It can be seen from Table 1 that the POD SISRE(ORB) of the IGSO/MEO satellite is approximately 0.4 m, while the SISRE(ORB) of GEO satellite is 1.41 m, which is 1 m lower. Therefore, it’s necessary to reconstruct the SRP model of BDS GEO satellites to improve the service performance of BDS GEO satellites. Table 1. POD accuracy of BDS satellites based on spherical SRP model (unit: m) Satellite C01 C04 C08 C10 C11

Radial direction 1.31 1.34 0.38 0.41 0.33

Along-track direction 4.02 4.14 0.74 0.17 0.22

Normal direction 3.65 3.12 0.89 0.32 0.12

Positioning accuracy 5.59 5.35 1.22 0.55 0.41

SISRE (ORB) 1.40 1.42 0.39 0.41 0.33

4 Construction Method of BDSPHERE Model for BDS GEO Satellites 4.1

Time Series Construction of SRP Parameter Based on Dynamic Smoothing

The long-arc time series of SRP parameter can reflect the adaptability and regularity of the SRP model in POD and provides the foundation for the reconstruction of the SRP model for GEO satellites. The following paragraphs will show you how to construct time series of long-arc SRP parameter based on dynamic smoothing. The BDS precise ephemeris is the result of continuous long-arc POD, while the long-arc precise orbit is made by patching-up the short arcs. We use the middle day orbit (taken from daily BDS POD results) as the precise orbit and patch up a 2-yr longarc precise orbit, which is dispersed and lacks uniform dynamic orbit characteristics. On this basis, it’s suggested to smoothen the dispersed orbit with an orbital dynamic method to get the dynamic high-precision parameters and produce the continuous satellite orbit via orbit integral. The orbit determination differs from orbit dynamic smoothing in that orbit determination corrects the dynamic parameters and preliminary orbit via actual observations, while orbit dynamic smoothing just needs satellite state vectors instead of actual observations and solves the orbit parameters by treating the vectors as virtual observations. To eliminate the short-period variation of the SRP model, we set the smoothing length as 3 days and the frequency is set as 1 day, which means smoothing is conducted 365 * 2 times. The dynamic smoothing strategy is shown in Table 2. The orbit smoothness precision is generated by calculating the difference between smoothened orbit and original precise orbit. The 3-day fitting result of orbit precision for C01 and C04 satellites are shown in Table 3. It can be seen that 3-day dynamic smoothing SISRE(ORB) is 0.42 m, which can support centimeter-level SRP modeling.

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Observations Parameters to be estimated Arc/sampling interval/smoothing times Parameter estimation method

Long-arc precise ephemeris Preliminary orbit, system error of measurement model and SRP model parameter Cr 3 days/5 min/365 * 2 times

Least squares estimation batch

Dynamic model

Earth’s gravitational field: 10  10 step JGM-3 model Planetary ephemeris: parameter JPL DE405 Earth tide: IERS96 Model nutation: IAU80 model SRP: sphere-shaped

Table 3. Dynamic smoothing accuracy of GEO satellites (unit: m) Satellite

C01 C04 Average

3-day fitting result Radial Along-track direction direction 0.40 0.73 0.41 0.71 0.41 0.72

Normal direction 0.12 0.09 0.11

Positioning accuracy 0.84 0.83 0.84

SISRE (ORB) 0.41 0.42 0.42

The orbit smoothing is conducted once a day and a set of SRP model parameters will be gathered. If we extend the period up to two years, then the 2-yr SRP model parameter Cr will be generated. Below shown is the SRP model parameter sequence of C01 and C04 satellites generated via dynamic smoothing in 2013 and 2014. Also, the time series of parameter Cr is produced via SPOD based on original pseudorange observations as a comparison.

Fig. 2. Time series of parameter Cr for C01 and C04 Satellite (the left: C01, the right: C04, as to each satellite, top: results of dynamic smoothing method, bottom: results of SPOD resolution based on original observations)

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It can also be seen from Fig. 2 that: 1. The parameter Cr generated vis dynamic smoothing of C04 satellite ranges between 0.08 and 0.18, while the parameter Cr resolved via SPOD based on original pseudorange observations range between −0.06 and 0.05. It’s the same case in C01 satellite. The ephemeris accuracy of BDS GEO satellite remains stable throughout the year, and the SISRE(ORB) acquired via dynamic smoothing based on virtual observations is 0.42 m. 2. There exists a linear change item in the parameter Cr which will increase with time, as orbital maneuver will be conducted every 30 days and the maneuver will consume satellite fuels. Therefore, the satellite area-to-mass ratio will increase gradually. However, it remains fixed in orbit determination, being reflected in the reflection coefficient Cr and increasing in long-arcs as a result. 3. The noise of the Cr parameter series via SPOD based on original pseudorange observations are relatively loud. Also, the Cr parameter resolution during certain periods (from January to April 2013) is not stable, which has to do with the lowquality observation data during these periods. Therefore, the dynamic parameter precision via orbit determination will be easily affected by the quality of observation data. 4. The dynamically smoothened parameter Cr contains a linear term and has a halfyear period features, starting form summer or winter solstice each year. With the linear term deducted, the parameter Cr follows the similar changes in Fourier polynomials. 4.2

Construction of BDSpherical SRP Model

Based on the results of the above-mentioned analysis, one can use the periodic Fourier polynomials and linear term to fit and predict the SRP parameter Cr model. According to the experimental analysis, the use of Fourier polynomials will create a better fitting result. Thus, the “Fourier series overlaid linear term” is proposed. Therefore, the BDSpherical SRP model for BDS GEO satellites can be created by inserting parameter Cr in the spherical SRP model. The formula is listed below: Ds A ~ S~ RP ¼ Ps a2u Cr ð Þc m Ds Cr ¼ px þ a0 þ a1
sin

    2p 2p ðx  hÞ þ b1
cos ð x  hÞ T T

ð2Þ

In (2), Cr refers to the satellite surface reflection coefficient and is used as resolution parameter in SPOD; p and a0 are the linear parameters; a1 and b1 are the Fourier polynomial coefficients; x is time, day is the unit; T is the change cycle of periodic term, i.e., 183 days; ðx  hÞ ranges between 0–183 days. As the periodic term of sin and cos starts at summer or winter solstice every year, h refers to the summer or winter solstice of the year. Suppose the starting date of x parameter sequence is January 22, 2014, then the starting date of the periodic term of sin and cos would be the winter solstice of 2013, ðx  hÞ would mean the duration between January 22, 2014 and the

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winter of 2013, i.e., a total of 31 days. The fitting is conducted on the time series of SRP parameter Cr during 2013 and 2014 based on “Fourier series overlaid linear term”. The fitted parameter Cr based on dynamic smoothing for C01 and C04 satellites is listed in Table 4 and Fig. 3. As can been seen from the above results of C01 and C04 satellites, the modeling method of “Fourier series overlaid linear term” can better describe the time series of the parameter Cr. The original value is consistent with fitted value when it’s neither at vernal and autumn equinox periods. There will be more fitted errors at these periods. However, the Cr fitted errors of C01 satellite tend to be smaller. It can be inferred that the use of the reconstructed BDSpherical SRP model during normal periods (excluding vernal and autumn equinox) can improve the POD accuracy. Table 4. Fitting results of coefficient parameters for parameter Cr model a1 b1 Satellite p a0 C01 0.00005 0.1619 0.0014 0.0284 C04 0.00002 0.0231 0.0023 0.0372

Fig. 3. Time series and model fitting results of parameter Cr for GEO Satellites (the blue curve represents the discrete values of parameter Cr time sequence based on dynamic smoothing, while the red curve represents the fitted value of parameter Cr model based on the “Fourier series overlaid linear term”)

5 Analysis of Orbit Determination Experiments The orbit determination experiment based on BDSpherical SRP model is proposed with L-band pseudorange which is obtained from the BDS monitoring receivers. In SPOD resolution, the original observational data are pre-processed with all sorts of errors corrected. There exists an obvious gap between the sphere model and BDSPHERE model. As to the sphere model, the parameter Cr is resolved in orbit determination, while it is a forecast value provided by Eq. (2) for BDSPHERE model. We use C01 and C04 satellites as experiment subjects. The C01 satellite is situated beyond the center of China’s latitude area while C04 satellite is beyond one side of the homeland. The orbit determination is conducted based on data collected from January 27 to February 17, 2014 (a total of 21 days) with smoothing method. The orbit determination arc is 1 day

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long, and the orbit determination frequency is 1-hs. The POD and prediction accuracy based on sphere model and BDSPHERE mode respectively is estimated with the precise BDS ephemeris and global SLR data as criteria. 5.1

Inner Evaluation Results of Orbital Accuracy

With the precise BDS ephemeris as reference orbit, we calculate the error of overlapped arc between the reference orbit and the orbit obtained from sphere model or BDSpherical SRP model respectively. The SISRE(ORB) result is the orbital inner precision. The calculating method of SISRE(ORB) within predicted n-hr is to compare the in-arc orbit determination and n-hr prediction accuracy with the precise ephemeris of the same epoch and calculates the errors in the directions of radial ðDRi Þ, along-track ðDTi Þ and normal ðDNi Þ and SISREi for each epoch i within the overlapped arc. m is the total number of orbital epoch points on certain or predicted orbital arc. SISRERMS is the RMS value of SISREi , meaning the final precision at the end of the hour. The 24-h RMS value will be calculated and used as the orbital accuracy of the day. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðDRi Þ2 þ ð0:09DTi Þ2 þ ð0:09DNi Þ2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m P SISRERMS ¼ SISREi2 =m

SISREi ¼

ð3Þ

i¼1

Table 5. POD and Prediction accuracy for GEO Satellites based on different SRP Models (unit: m) Satellite

POD 8 h prediction 12 h prediction 24 h prediction Sphere BDSPHERE Sphere BDSPHERE Sphere BDSPHERE Sphere BDSPHERE

C01 C04 Average Improvement

1.66 1.24 1.45 0.82

0.57 0.68 0.63

2.46 2.15 2.31 1.52

0.83 0.74 0.79

4.08 2.68 3.38 2.14

1.43 1.05 1.24

4.79 3.12 3.96 2.31

1.69 1.61 1.65

As can been seen from the results of Table 5, the SISRE(ORB) of POD and 8 h, 12 h and 24 h prediction for GEO satellites is 0.63 m, 0.79 m, 1.24 m and 1.65 m based on BDSpherical SRP model. Compared to the spherical SRP model, the accuracy has an improvement of 0.82 m, 1.52 m, 2.14 m and 2.31 m, an increase of 56.55%, 65.81%, 63.31% and 58.33% respectively. Therefore, the BDSpherical SRP model performs extremely well both in orbit determination and prediction arc. The advantages will get more and more obvious as the prediction arc length increases and the model will be as precise as precise BDS ephemeris. 5.2

Accuracy Evaluation in Orbit Radial Based on Global SLR Data

SLR is the only high-precision measurement means which is independent of radio carrier phase measurement for navigation satellite. Thus, it is an important means of

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orbit precision evaluation. BDS satellites have now become the subjects of global SLR tests. Large amounts of SLR observation data for one GEO (C01) satellite, two IGSO (C08, C10) satellites and one MEO (C11) satellite have been accumulated since 2012. The international laser ranging service (ILRS) currently consists of around 40 survey stations. The accuracy verification of C01 satellite orbit determination will be conducted based on data collected from February to March 2014. The accuracy of atmospheric delay correction via SLR checking is related to the observed vertical angle (20°). In the below paragraphs, a detailed analysis of the orbit precision of BDSpherical SRP model and spherical SRP model are conducted respectively. Please see the distribution diagram of SLR residuals in Fig. 4.

Fig. 4. Global SLR residuals distribution of C01 satellite based on different SRP models

As can been seen from the Fig. 4, the orbital RMS of SLR residual via spherical SRP model and BDSpherical SRP model is 1.994 m and 0.597 m respectively, meaning the later accuracy of satellite orbit determination in radial direction improved by 1.397 m, an increase of 70.06%.

6 Summary We propose a modeling method for BDS GEO satellite based on the traditional SRP modeling, builds the BDSpherical SRP model and verifies the results by using BDS long-arc measured data. The main conclusions are as follows: 1. Propose a BDS SRP modeling method based on a precise ephemeris. Use highprecision orbit as the virtual observation data and the spherical SRP model as background model to estimate the parameters of SRP model and build a parameter Cr model based on “Fourier series overlaid linear term” through dynamic smoothing. Then, the SRP parameter series is analyzed to build the BDSpherical SRP model further. 2. Conduct the orbit determination experiments based on BDS long-arc measured data. Compared to the spherical SRP model, the SISRE(ORB) of orbit determination is 0.63 m and the SISRE(ORB) of 8 h, 12 h and 24 h prediction is 0.79 m, 1.24 m and 1.65 m. Compared to the spherical SRP model, the SISRE(ORB) has increased by 0.82 m, 1.52 m, 2.14 m and 2.31 m respectively.

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3. Analyze the POD accuracy based on BDSpherical SRP model. The orbit accuracy in radial direction by global SLR data is 0.597 m, an increase of 70.06% compared to that of spherical SRP model (1.994 m), which helps greatly to improve the POD accuracy of the BDS GEO satellites. Acknowledgements. This research is supported by the National Natural Science Foundation of China (project No: 41874043, 41704037, and 61603397).

References 1. Guo, R., Zhou, J., Hu, X., et al.: Precise orbit determination and rapid orbit recovery supported by time synchronization. Adv. Space Res. 55(12), 2889–2898 (2015) 2. Zhao, Q., Guo, J., Li, M., Qu, L., Hu, Z., Shi, C., Liu, J.: Initial results of precise orbit and clock determination for COMPASS navigation satellite system. J. Geodesy. https://doi.org/ 10.1007/s00190-013-0622-7 3. Zhao, G., Zhou, S., Zhou, X., Wu, B.: Orbit accuracy analysis for BeiDou regional tracing network. In: Proceedings of China Satellite Navigation Conference, vol. 5, pp. 235–244 (2016) 4. Guo, R., Hu, X.G., Li, X.J., Wang, Y., Tang, C.P., Chang, Z.Q., Wu, S.: Application characteristics analysis of the T20 solar radiation pressure model in orbit determination for COMPASS GEO satellites. In: China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume I, pp. 131–141. Springer (2016) 5. Li, X., Zhou, J., Hu, X., Liu, L., Guo, R., Zhou, S.: Orbit determination and prediction for Beidou GEO satellites at the time of the spring/autumn qeuinox. Sci. China Phys. Mech. Astron. 58(8), 089501 (2015) 6. Dach, R., Brockmann, E., Schaer, S., et al.: GNSS processing at CODE: status report. J. Geodesy 83, 353–365 (2009) 7. Springer, T.A., Beutler, G., Rothacher, M.: A new solar radiation pressure model for GPS satellites. GPS Solutions 2(3), 50–62 (1992) 8. Bar-Sever, Y.E., Kuang, D.: New empirically derived solar radiation pressure model for global positioning system satellites, pp. 42–159. Interplanetary Network Progress Report, Pasadena, California (2004) 9. Ziebart, M., Dare, P.: Analytical solar radiation pressure modeling for GLONASS using a pixel array. J. Geodesy 75, 587–599 (2001) 10. Rodriguez-Solano, C.J., Hugentobler, U., Steigenberger, P.: Improving the orbits of GPS block IIA satellites during eclipse seasons. Adv. Space Res. 52, 1511–1529 (2013) 11. Arnold, D., Meindl, M., Beutler, G., et al.: A CODE’s new solar radiation pressure model for GNSS orbit determination. J. Geodesy 89(8), 775–791 (2015) 12. Montenbruck, O., Steigenberger, P., Hugentobler, U.: Enhanced solar radiation pressure modeling for Galileo satellites. J. Geodesy 89(3), 283–297 (2015) 13. Steigenberger, P., Montenbruck, O.: Galileo status: orbits, clocks, and positioning. GPS Solutions (2016). https://doi.org/10.1007/s10291-016-0566-5 14. Zhao, Q., Wang, X., He, B., et al.: The solar radiation pressure modeling on high-altitude earth orbit satellite. In: Proceedings of China Satellite Navigation Conference (CSNC), vol. 302, pp. 214–217 (2014)

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15. Feng, W., Guo, X., Qiu, H., et al.: A study of analytical solar radiation pressure modeling for BeiDou navigation satellites based on ray tracing method. In: Proceedings of China Satellite Navigation Conference (CSNC), vol. 304, pp. 425–435 (2014) 16. Huang, C.: Precise determination of the earth’s rotation parameters based on lageos laser ranging data. Shanghai Astronomical Observatory, Chinese Academy of Sciences, 30–40 (1985)

Test and Evaluation of the Distributed Autonomous Orbit Determination with the BDS Inter-satellite Ranging Data Jie Xin1(&), Ziqiang Li2, Xiaojie Li1, Rui Guo1, Dongxia Wang1, and Shuai Liu1 1

32021 Troops, Beijing 100094, China [email protected] 2 Wuhan University, Wuhan, China

Abstract. The new generation satellites of the BeiDou navigation satellite system (BDS) all carry the inter-satellite payload in Ka band, which can support the realization of the inter-satellite ranging and information interaction. Firstly, we propose the process of the distributed orbit determination algorithm, develops a ground testing software and propose a strategy for the autonomous orbit determination. Secondly, we analyze the constellation geometry and the inter-satellite ranging error of the 18 Medium Earth Orbit (MEO) satellites in BDS-3 constellation. Finally, the 60 days results of the autonomous orbit determination are given based on the actual inter-satellite ranging data and compared with the precision orbit. The results demonstrate that the inter-satellite status of BDS is rather stable and the constellation geometry can support the autonomous orbit determination for the distributed navigation constellation with 18 MEO satellites; the simulation accuracy of the autonomous orbit determination is 0.80 m, which confirms the validity of the proposed method and establish a firm foundation for the engineering implementation of the autonomous navigation for the BDS. Keywords: BeiDou navigation satellite system (BDS) determination
Inter-satellite ranging data


Autonomous orbit

1 Introduction The BDS-3 baseline system with 18 MEO satellites has begun providing initial services to global users on December 27, 2018 [1]. As all the satellites are equipped with Kaband loads, two-way measurements are conducted every 3 s which effectively verifies the application of the inter-satellite technology and lays a foundation for the realization of the distributed autonomous navigation with the inter-satellite ranging data [2]. The autonomous orbit determination technology of the distributed navigation constellation is a technology that obtains prior information and relevant configuration parameter information based on the inter-satellite ranging data and the interactive messages and then realizes the autonomous orbit determination by the on-board processor combined with various filtering methods [3]. Some domestic scholars has used various of data processing and autonomous navigation models based on the simulated © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 27–35, 2020. https://doi.org/10.1007/978-981-15-3711-0_3

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inter-satellite ranging data and estimated the precision and usability of the autonomous navigation service [4–6], laying a theoretical basis for the autonomous navigation service for the BDS. Song [7] thoroughly analysed the autonomous orbit determination algorithm and conducted some experiments with simulated data in his doctoral thesis. Chen [8] mainly verified the affection of the inter-satellite ranging error with the simulated inter-satellite data of the whole BDS-3 constellation. Tang [9] promoted a centralized autonomous orbit determination method and estimated its feasibility with the measured data of the experimental BeiDou satellites. However, the space environment is rather complex and exists uncertain ranging noise and disturbance, bringing unpredictable differences in simulation and on-board testing results. The differences mainly reflect in the following aspects: • As to the space segment, the physical performance of the in-orbit BDS satellites clock is affected by the space environment, the device differences and other factors. The actual observation ability of the constellation can hardly be simulated, limiting the restraining ability of the integral rotation of the constellation. What’s more, there exists various visual relationships between the BDS-3 satellites. Therefore, the constellation configuration in each linking cycle, the efficiency of the two-way measurements and the successive rate of the interactive message are all the limiting factors to the autonomous filtering of each satellites. Currently, there is no relevant study based on the actual measurements. • As to the ground segment, the algorithm of the on-board operation unit needs to be started with the initial parameters injected by the ground segment, such as the initial configuration parameters, the initial orbit and the propagation delay of the transmission and receiving links between satellites. Usually, the propagation delay can be precisely determined by the ground segment to support the autonomous orbit determination. Based on the above analysis, we firstly research on the algorithm of the autonomous orbit determination with the inter-satellite measurement. Secondly, we analyse the ranging error of the inter-satellite links (ISLs) and the constellation geometry in each linking cycle based on the actual ranging data of the 18 BDS MEO satellites. Finally, we conduct the accuracy estimation of the autonomous orbit determination with the precise orbit as reference, verifying the efficiency of the algorithm.

2 Algorithm of the Autonomous Orbit Determination Currently, the Extended Kalman Filter (EKF) is the main filtering method for the distributed autonomous orbit determination. In terms of the filtering algorithm, the filtering accuracy and convergence rate of the state estimation are mainly affected by the model parameters and the initial conditions. Therefore, we should build a proper measurement equation with the preprocessed inter-satellite observation date and a state equation which can describe the filtering process.

Test and Evaluation of the Distributed Autonomous Orbit Determination

2.1

29

Data Processing of the Inter-satellite Observation Date

The inter-satellite ranging data of the BDS satellites is a two-way ranging with the time division, meaning that the two-way ranging is conducted in different time. According to the application experience of the two-way measurement, the orbit information can be obtained by adding the ranging values at the same as the satellite clock error is eliminated [10]. Therefore, the data processing can be showed as Fig. 1 showed.

Fig. 1. Data processing of the inter-satellite observation date

2.2

Algorithm of the Distributed Autonomous Orbit Determination

We assume that the ranging time of two satellites can be unified to the same time t0 , then the orbit parameters can be described as: qOrb ðt0 Þ ¼

qA;B ðt0 Þ þ qB;A ðt0 Þ 2

¼ jRA ðt0 Þ  RB ðt0 Þj þ c 

sSend þ sRev sSend þ sRev eBA þ eAB A A B þc  B þ ð1:1Þ 2 2 2

In the equation, qA;B ðt0 Þ and qB;A ðt0 Þ refer to the ranging data received by satellite A and satellite B respectively at time t0 ; RA ðt0 Þ and RB ðt0 Þ are the position of the satellite A and satellite B at time t0 ; c refers to the speed of time; sSend and sRev refer to the sending and receiving channel delay of each satellite; eAB and eBA are the error correction parameters, such as the correction of the satellite antenna phase, tropospheric delay, the relativistic effect correction, which can be precisely modeled in one-way measurement. See the reference [9] for detail.

30

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Strategy of the Autonomous Orbit Determination

Before the starting of the distributed autonomous orbit filtering, the configuration items of the software should be configured and necessary data should be set accordingly. The main configuration parameters include: • The initial parameters and their residuals of the satellite orbit and clock error. • The inter-satellite channel delay parameters of all satellites involved in the autonomous orbit determination. • The earth orientation parameters. • The orbital integral parameter. The detail strategies adopted by the autonomous orbit determination is showed in Table 1. Table 1. Strategies of the autonomous orbit determination Parameters Models Sampling interval of the ISLs measurement 3 s Relativistic correction Only general relativity error Tidal correction Only solid tide Gravitational field model 12 step EGM2008 model Solar radiation model ECOM model Filtering interval 60 s Gravitation Only lunar and solar perturbations Orbit parameters Broadcast ephemeris with 18 parameters

3 Realization Analysis of the BDS ISLs The BDS ISLs adopt the concurrent spatial time division duplexing technology based on the phased array antenna, which can realize the two-way communication between satellites though a single link worked in semi-duplex mode and provide a feasible way for the distributed autonomous navigation. Nevertheless, it greatly depends on the network transmission protocol and the information transfer rates. Therefore, it’s necessary to reasonably build the inter-satellite relationship and properly analyze the effectiveness of the ISLs. 3.1

Effective Number of the ISLs

Each inter-satellite ranging frame contains two processes of the signal transmission and reception, namely, the forward ranging is carried out in the first 1.5 s and the reverse ranging is carried out in the second 1.5 s. After the signal transmission and reception processing of a ranging frame is completed, the inter-satellite pseudo-distance ranging values generated by the current ranging frame will be propagated to the relevant satellites [11]. As the increase of the effective links, the accuracy of the distributed autonomous orbit determination will also be improved. When the number of effective

Test and Evaluation of the Distributed Autonomous Orbit Determination

31

links exceeds 5, it can basically meet the requirement of autonomous orbit determination for 60 days [8]. There are three visual relationships between the MEO satellites: continuous visibility, non-continuous visibility and non-visibility. The effective number of the ISLs construction is related to the orbital position of the satellites and the slot planning. By analyzing the inter-satellite ranging values of the 18 satellites, we can know that the ISLs are mostly stable from February 26 to March 27, while there is a lack of ranging data sometimes. As shown in Fig. 2, C23 can make connection with up to 13 satellites and basically maintain about 9 two-way ranging links.

Fig. 2. ISLs number between C23 satellite and other satellite under the scene of 18 satellites

3.2

Consatellation Geometry Analysis

For the autonomous operating satellites, the constellation geometry formed by the ISLs in each linking cycle is an important factor to the accuracy of the autonomous orbit determination, that is, the visibility of the satellites in the constellation and the geometric relationship should be considered when the autonomous navigation processing of distributed constellation is conducted. Usually, we can use the dilution of the position (POD) factor to describe the constellation geometry. The smaller the DOP value is, the higher positioning accuracy it represents. Seen from the Table 2, the average of the DOP is 1.05, meeting the requirements of the distributed autonomous navigation. What’s more, the DOP values exist beep points with the interrupt and recovery of the ISLs. 3.3

Inter-satellite Ranging Error Analysis

As to the inter-satellite ranging error, the residuals of the quadratic polynomial fitting result can directly reflect the abnormal variation of the ranging values [11]. We choose the inter-satellite ranging data on February 11 to 17, 2019 to evaluate the inter-satellite ranging error. In order to ensure the accuracy of the inter-satellite link distance measurement, we consider the forward and backward ranging can be paired only if the twoway ranging is completed within 3 s. The Table 3 gives the results of the inter-satellite ranging error.

32

J. Xin et al. Table 2. DOP value and links number of the ISLs PRN 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 Average

Least value of DOP Maximum value of DOP Average value of DOP 0.72 4.80 0.99 0.74 4.97 1.07 0.73 5.00 1.02 0.75 5.00 1.09 0.73 4.90 1.08 0.75 4.97 1.07 0.74 4.34 1.02 0.74 4.85 1.03 0.75 4.97 1.08 0.72 4.99 1.01 0.75 4.93 1.08 0.71 4.91 1.02 0.72 4.95 1.05 0.74 4.98 1.06 0.74 4.67 1.04 0.72 5.00 1.06 0.75 4.99 1.08 0.74 4.98 1.05 0.74 4.90 1.05

Table 3. Statics results of the inter-satellite ranging error (unit: cm) PRN RMS 19 1.72 20 1.57 21 1.62 22 1.68 23 3.62 24 1.48 25 2.38 26 2.40 27 2.41 Average

PRN 28 29 30 32 33 34 35 36 37

RMS 2.43 2.42 2.39 2.20 1.73 2.09 2.06 1.64 1.34 2.05

As can be seen from the above result: • The series of the inter-satellite ranging error are rather stable, which have no significant change with time. • The RMS of the inter-satellite ranging error is within 3 cm, except the C23 satellite. • Combined with the high-precision calibration method of the inter-satellite time synchronization, BDS has realized the inter-satellite ranging with high accuracy.

Test and Evaluation of the Distributed Autonomous Orbit Determination

33

4 Test and Evaluation With the actual inter-satellite ranging data of the BDS 18 MEO satellites and the method mentioned above, we conduct the autonomous orbit determination for 60 days, and analyze the differences of the autonomous orbit determination. As to the accuracy evaluation, we compare the autonomous results with the precise orbit products obtained with overlapping arc method and evaluate the SISURE (signalin-space user ranging error) which only contains orbit error information. For MEO satellite, the SISURE of the autonomous orbit determination can be expressed as follows when the error caused by clock error is not considered: SISUREMEO ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:96
dR2 þ 0:04
ðdA2 þ dC2 Þ

SISURERMS

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n X ¼ SISUREi2 =n1

ð1:2Þ ð1:3Þ

i¼1

In the equation, dR, dA and dC refer to the orbit determination residuals in R, A and C direction respectively; SISURERMS refers to the root-mean-square statistic. With June 1, 2019 as the starting time, the autonomous orbit fixing results of the 18 MEO satellites are conducted for 60 consecutive days with the BDS inter-satellite ranging data, including the initial position error variance of 0.1 m and the filtering interval of 60 s. The accuracy of the autonomous orbit determination is conducted with the precision orbit results as reference. Table 4 and Fig. 3 shows the Accuracy statistic of the autonomous orbit determination. Table 4. Statics results of the inter-satellite ranging error (unit: cm) SCID

R

T

N

Position URE

19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 Average

0.087 0.138 0.14 0.093 0.667 0.095 0.146 0.157 0.128 0.198 0.142 0.172 0.633 0.101 0.18 0.134 0.131 0.103 0.253

2.022 1.971 1.947 1.992 2.325 2.077 2.115 2.157 3.431 3.521 3.477 3.439 2.009 1.907 3.459 3.519 2.21 2.146 2.626

3.177 3.114 3.182 3.167 2.356 2.58 2.491 2.593 2.527 2.571 2.599 2.557 3.09 3.144 2.659 2.659 2.6 2.529 2.77

3.766 3.688 3.733 3.743 3.376 3.313 3.271 3.376 4.263 4.364 4.343 4.289 3.739 3.678 4.367 4.412 3.415 3.319 3.825

0.758 0.749 0.759 0.754 0.93 0.669 0.669 0.692 0.861 0.893 0.879 0.873 0.963 0.742 0.89 0.892 0.694 0.671 0.803

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Fig. 3. Average accuracy of the autonomous orbit determination for C23 satellite in different directions (60 days)

The evaluation results show that: • For distributed constellations that are cross-linked over the whole network and whose inter-satellite ranging residuals meet the conditions of autonomous filtering, the three-dimensional position errors of all satellites are basically consistent with the SISURE variation trend. • The results of autonomous orbit determination based on EKF filter are basically in a stable state after convergence, and the radial direction can maintain a good accuracy, but the tangential direction and normal direction show a trend of gradually increasing. The SISURE of the whole constellation for 60 days is better than 0.80 m. • The fluctuation range of the residuals in A and C direction is significantly greater than the result in R direction. The reason is that there is no reference for the constraint of the orbit surface and the accuracy of the selected solar radiation pressure model should be improved. What’s more, we count the measurement residuals after each filtering process and analyze the residuals RMS of each echo as shown in Fig. 4. The result shows that the relative residuals are rather stable, while the change of the absolute residuals in A and C direction is rather obvious. This is also due to the lack of the orbit reference. It reflects the problem of the unobservable constellation rotation in autonomous orbit determination, which cannot be distinguished and eliminated by the constellation itself.

Fig. 4. Orbit determination residuals of C23 satellite after each filtering echo (60 days)

Test and Evaluation of the Distributed Autonomous Orbit Determination

35

5 Conclusion Based on the ranging data of the 18 BDS satellites, we analyze the inter-satellite ranging error and the configuration of the ISLs, and then we conduct the autonomous orbit determination for 60 days and obtain the SISURE results for the whole constellation, which is better than 0.80 m. The results show that: • The inter-satellite ranging data is stable and reasonable, which can support the autonomous orbit determination effectively. • The SISURE results of the distributed autonomous is better than 0.80 m with the processing strategy mentioned above. It can provide some references for the engineering application of the autonomous navigation. • In the case of a lack of the ground reference, there exists the problem of the unobservable constellation rotation, which cannot be distinguished and eliminated on the basis of inter-satellite ranging. • The research on the anchor station will be conducted further to solve the problem of the unobservable constellation rotation. Acknowledgements. This research is supported by the National Natural Science Foundation of China (project No: 41874043, 41704037, 41804030, 41874039, and 61603397).

References 1. Yang, Y., Mao, Y., Sun, B.: Basic performance and future development of BeiDou global navigation satellite system. Satell. Navig. 1, 1–8 (2020) 2. Wang, D., Xin, J., Xue, F., Guo, R., Xie, J., Chen, J.: Development and prospect of GNSS autonomous navigation based on inter-satellite link. J. Astronaut. 37(11), 1279–1287 (2016) 3. Wang, H., Chen, Z., Chu, H., Wu, X., Zheng, J.: On-board autonomous orbit prediction algorithm for navigation satellites. J. Astronaut. 33(8), 1019–1026 (2012) 4. Xu, H., Wang, J., Zhang, X.: Autonomous broadcast ephemeris improvement for GNSS using inter-satellite ranging measurements. Adv. Space Res. 49, 1034–1044 (2012) 5. Han, S., Gui, Q., Li, J.: On new measurement and communication techniques of GNSS intersatellite links. Sci. China Technol. Sci. 55, 285–294 (2012) 6. Liu, L., Zhu, L.F., Han, C.H., et al.: The model of radio two-way time comparison between satellite and station and experimental analysis. Chin. Astron. Astrophy 33, 431–439 (2009) 7. Song, X.: Study on the orbit determination of COMPASS navigation satellites. University of Changan, Xi’an (2008) 8. Chen, Y., Hu, X., Zhou, S., et al.: A new autonomous orbit determination algorithm based on inter-satellite ranging measurements. Sci. Sin.-Phys. Mech. Astron. 45, 079511 (2015) 9. Tang, C.P., Hu, X.G., Zhou, S.S., et al.: Centralized autonomous orbit determination of BeiDou navigation satellites with inter-satellite link measurements: preliminary results. Sci. Sin. Phys. Mech. Astron. 47, 029501 (2017). (in Chinese) 10. Guo, R., Hu, X.G., Tang, B., et al.: Precise orbit determination for geostationary satellites with multiple tracking techniques. Chin. Sci. Bull. 55, 687–692 (2010) 11. Yang, Y., Yang, Y., Hu, X., et al.: Comparison and analysis of two orbit determination methods for BDS-3 satellites. Acta Geod. et Cartogr. Sin. 48(7), 831–839 (2019)

DTM2013 Model Parameter Inversion and Correlation Analysis Between Its Accuracy Wenhui Cui1(&), Wei Qu2, Haiyue Li1, Ning Chen3, Nan Ye1, and Zhenyu Sun1 1

State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China [email protected] 2 Aerospace Engineering University, Beijing 101416, China 3 Xi’an Satellite Control Center, Xi’an 710043, China

Abstract. The framework and the amendment terms of DTM2013 atmospheric model are derived based on the historical DTM series model algorithms. The Legendre polynomial coefficients are derived based on the high-order associated Legendre polynomials algorithm. The long term optimal mean of F30 proxy is derived based on fitting polynomial of the F30 proxy historical measured data. The construction of the DTM2013 model algorithm was completed by integrating the inversion parameters. The correctness of the model is verified by comparing the calculation results of the parameter inversion DTM2013 model with that of the ATMOP DTM2013 model. The DTM2013 model and the MSIS00 model calculation accuracy are calculated based on GOCE atmospheric measured data, and the high correlation between the solar radiation proxy deviations and the model accuracies are derived. The solar radiation proxy factors of the model accuracy of the atmospheric models are explained, which proves that F30 proxy has better application value in atmospheric models. Keywords: DTM2013 atmospheric model atmospheric model
GOCE


Parameter inversion
MSIS00

1 Introduce Due to the influence of external factors such as solar flux and geomagnetic, it is very difficult to model the atmospheric density with high precision [1]. The error between the early atmospheric models and measured data often reach 15%–30% or even as high as 100% in some years [2, 3]. Therefore, various atmospheric models have been summarized and iterated from various perspectives. Currently, the atmospheric models that commonly used in the space field include CIRA series, Jacchia series, DTM series, MSIS series and other atmospheric models [4–11]. Among them, the CIRA series and the Jacchia series are the most widely used atmospheric models in early space systems. With the continuous improvement of observation accuracy and measurement methods, as well as the continuous change of space atmospheric density distribution with the solar activity cycle and time, several kinds of new measurement data have been added to the verification and innovation of the atmospheric model theory. With the operation of CHAMP, GOCE, and other measurement projects, a large number of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 36–46, 2020. https://doi.org/10.1007/978-981-15-3711-0_4

DTM2013 Model Parameter Inversion and Correlation Analysis

37

measured atmospheric density data at the 400 km altitude space and below were used for space atmospheric density modeling. Based on this, the United States Naval Research Laboratory (NRL) proposed NRLMSISE-00 atmospheric model in 2000 (The following text is abbreviated as the MSIS00 model) [7]. International Space Science Committee proposed JB2006 model in 2006, and further upgraded to JB2008 model in 2008 [8]. Solar proxies such as F10.7, M10.7, S10.7, Y10.7 and geomagnetic proxies such as Ap, Dst were used in the above models. F10.7 and Ap could predict accurately, while the other parameters could only use the measured data of SOHO (Solar and Heliospheric Observatory) and other institutions. The MSIS00 atmospheric model which used F10.7 and Ap were more widely used. F10.7 and Ap proxies were also continuously used in DTM series models until the DTM2013 model replaced F10.7 solar radiation proxy with F30 solar radiation proxy [9].

2 The Common Algorithm of DTM2013 Atmospheric Model DTM atmospheric model originated from Drag Temperature Model 1978, and DTM94 model [10], DTM2000 model [11] were proposed on this basis subsequently. At present, the latest official version of DTM models proposed by ATMOP (Advanced Thermosphere Model and Orbit Prediction project) is the DTM2013 model. Though the DTM2013 model is the latest atmospheric model released with the highest accuracy, ATMOP has not disclosed its specific algorithm, which brings a lot of problems to the application of the model. The general algorithm of the DTM model is: (1) Obtain or calculate the required parameters, including date, time, longitude, latitude, altitude, and consult the table to obtain the values of solar radiation proxy and geomagnetic activity proxy for the corresponding date and time (generally UTC time); (2) Calculate the value of Legendre polynomials according to the solar incidence angle; (3) Calculate the atmospheric density. The formula of atmospheric density calculation is: qðzÞ ¼

X i

qi ð120 kmÞfi ðzÞ expðGi ðLÞÞ

ð2:1Þ

Where qðzÞ is total atmospheric density, the qi ð120 kmÞ is the density of components i (include O, O2 , H, He, N and N2 ) of the atmosphere at 120 km altitude and 120 km is the minimum height limit of the DTM model. Gi ðLÞ is the atmospheric density correction of components i based on periodic and non-periodic factors in the region. The non-periodic terms include latitude term, solar activity term, and geomagnetic activity term. The periodic terms include annual term, semi-annual term, diurnal term, semidiurnal term, and diurnal term.

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fi ðzÞ ¼ ðT120 =TðzÞÞ1 þ a þ ci expðrci fÞ

ð2:2Þ

Where T120 is the temperature at 120 km altitude and TðzÞ is the temperature at the height z. TðzÞ¼T1  ðT1  T120 Þ expðrfÞ

ð2:3Þ

Where T1 is the outer boundary temperature of the thermosphere, a is the thermal diffusion coefficient of H and He; f is geopotential altitude, f¼

ðh  120ÞðRa þ 120Þ Ra þ h

ð2:4Þ

Ra ¼ 6356:770 km, r is the relative temperature gradient, r ¼ Sþ

1 Ra þ 120

ð2:5Þ

S is the temperature gradient parameter, S ¼ 0:02. ci ¼

mi g120 rRT1

ð2:6Þ

mi is the molecular weight of each component of the atmosphere; g120 is the gravitational acceleration at altitude of 120 km, g120 ¼ 9:446626 m=s2 ; R is the gas constant, R ¼ 8:31432 [10, 12]. In the document [10], Berger et al. discussed the specific algorithm of the DTM94 model in detail and gave the specific expression of fi ðzÞ and Gi ðLÞ. In the document [11], Bruinsma et al. gave a variety of DTM2000 improvements based on DTM94, including the additional items in the expressions of association and Legendre polynomials, and the additional items in the fitting coefficients of periodic and non-periodic terms and atmospheric components. In the document [9], Bruinsma explained the improvement of DTM2013 based on the DTM series historical models, mainly the solar radiation proxy changed from F10.7 to F30. Besides, the reference data of the model added a variety of earth measurement data from the satellites that launched after 2000, such as CHAMP (2001–2010), GRACE (2003–2011) and GOCE (2009–2012). Therefore, the non-periodic terms in DTM2013 algorithm should be expressed as follows: Latitude: a2 P20 þ a3 P40 þ a37 P10 þ a77 P30 þ a78 P50 þ a79 P60 Solar:
30 Þ þ a5 ðF30  F
30 Þ2 þ a6 ðF
30  avgF30 Þ þ a38 ðF
30  avgF30 Þ2 þ a85 ðF
30  avgF30 ÞP20 a4 ðF30  F
30  avgF30 ÞP30 þ a87 ðF
30  avgF30 ÞP40 þ a86 ðF

DTM2013 Model Parameter Inversion and Correlation Analysis

39


p þ a65 K
p P20 þ a68 Kp P40 Magnetic activity: ða7 þ a8 P20 ÞKp þ a39 Kp2 þ a64 K Periodic terms should be expressed as follows: Symmetrical annual: ða9 þ a10 P20 Þ cos½Xðd  a11 Þ Symmetrical semi-annual: ða12 þ a13 P20 Þ cos½2Xðd  a14 Þ Asymmetrical annual (seasonal): ða15 P10 þ a16 P30 þ a17 P50 Þ cos½Xðd  a18 Þ Asymmetrical semi-annual: a19 P10 cos½2Xðd  a20 Þ Diurnal: ða21 P11 þ a22 P31 þ a23 P51 þ ða24 P11 þ a25 P21 Þ cos½Xðd  a18 ÞÞ cos xt þ ða26 P11 þ a27 P31 þ a28 P51 þ ða29 P11 þ a30 P21 Þ cos½Xðd  a18 ÞÞ sin xt

Semidiurnal: ða31 P22 þ a32 P32 cos½Xðd  a18 ÞÞ cos 2xt þ ða33 P22 þ a34 P32 cos½Xðd  a18 ÞÞ sin 2xt þ a88 P32 cos 2xt þ a89 P32 sin 2xt þ a90 P52 cos 2xt þ a91 P52 sin 2xt þ a92 P62 cos 2xt þ a93 P62 sin 2xt

Terdiurnal: a35 P33 cos 3xt þ a36 P33 sin 3xt Pnm is the result of high-level associated Legendre polynomials according to the solar incidence angle. F30 is the value of F30 Solar radiation proxy on the previous day,
30 is the mean of F30 over three solar rotations (81 days) before the required day, Kp is F the three-hourly geomagnetic proxy taken with a delay based on latitude (3 h at the pole, 6 h at the equator with a linear interpolation), d is the number of days in the year. 2p X ¼ 365 , x ¼ 2p 24 . In the case of leap years, the X by the formula is not totally correct, but the error is too small to be worth creating a step function to deal with. All the periodic terms are to be multiplied by (1 + terms of solar activity) when adding to the DTM series model except for H and He [9].

3 The Legendre Polynomial and the Long-Term Mean of F30 in DTM2013 In the documents [9–11], specific expressions of Pnm in Gi ðLÞ are not given. The specific expression of Legendre polynomials applicable to the DTM94 model was given in the document [12], but the Pnm expression of the DTM2000 model and subsequent models have not been published. According to the document [13], the relationship between Pnm and the solar incidence angle u can be derived as follows: P10 ¼ sin u

ð3:1Þ

1 P20 ¼ ð3 sin2 u  1Þ 2

ð3:2Þ

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1 P30 ¼ ð5 sin2 u  3Þ sin u 2

ð3:3Þ

1 P40 ¼ ð35 sin4 u  30 sin2 u þ 3Þ 8

ð3:4Þ

1 P50 ¼ ð63 sin4 u  70 sin2 u þ 15Þ sin u 8

ð3:5Þ

P60 ¼

1 ð231 sin6 u  315 sin4 u þ 105 sin2 u  5Þ 16 P11 ¼ cos u

ð3:7Þ

P21 ¼ 3 sin u cos u

ð3:8Þ

3 P31 ¼ ð5 sin2 u  1Þ cos u 2

ð3:9Þ

1 P51 ¼ ð315 sin4 u  210 sin2 u þ 15Þ cos u 8

ð3:10Þ

P22 ¼ 3 cos2 u

ð3:11Þ

P32 ¼ 15 sin u cos2 u

ð3:12Þ

15 ð7 sin2 u cos2 u  cos2 uÞ 2

ð3:13Þ

105 ð3 sin3 u cos2 u  sin u cos2 uÞ 2

ð3:14Þ

P42 ¼ P52 ¼ P62 ¼

ð3:6Þ

 1 3465 sin4 u cos2 u  1890 sin2 u cos2 u  105 cos2 u 8

ð3:15Þ

P33 ¼ 15 cos3 u

ð3:16Þ

F30 proxy replaced F10.7 proxy as the representation of the solar activity in the DTM2013 model. Therefore, 150 as the long term mean of F10.7 is no longer applicable in the expression of solar term, and the long-term mean of F30 must be given in the algorithm. The F30 proxy has been measured by Nobeyama since 1957. According to historical solar radiation data released by NOAA (National Oceanic and Atmospheric Administration) [14] and other agencies, F10.7 and F30 proxies were recorded from 1971 to 2013 were as follows:

DTM2013 Model Parameter Inversion and Correlation Analysis

41

400 F10.7 F30

350

Solar radiation proxy(sfu)

300 250 200 150 100 50 0 1971

1980

1990 Time(year)

2000

2010

Fig. 1. The measured data of F10.7 and F30 from 1971 to 2013

As can be seen from Fig. 1, a large number of extreme values of F10.7 proxy and F30 proxy appeared in high solar activity years, but the overall performance of F30 proxy was more stable than that of F10.7 proxy. Through variance analysis of the two proxies, it can be obtained that the variance of the F10.7 proxy is 51.0535, and the variance of the F30 proxy is 31.3736. The variance of F30 proxy is far smaller than that of F10.7 proxy, and the stability of the F30 proxy is much higher than that of the F10.7 proxy. To eliminate the influence of extreme values and measurement errors on the calculation of the mean of the F30 proxy in high solar activity years, the mean of the F30 proxy can be calculated through the appropriate fitting of the F30 proxy according to the error analysis theory. Since the revised data of the DTM2013 model is mainly collected after 2000, F30 proxy during the solar activity cycle from 2002 to 2013 was used for modeling. F30 proxy from 2002 to 2013 were fitted multiple times in high order (4 order, 8 order and 16 order) according to the timing sequence, and the fitting error matrix was calculated by the least-squares. After the error analysis of each order fitting function and F30 measurement data, the 8-order fitting of F30 data is the best approximate function. In one year, the variance of the 8-order fitting was 61.003, lower than that of the 16-order fitting of 74.23 and the 4-order fitting of 89.33. According to this fitting polynomial, its optimal mean in a solar activity cycle is about 68.9941. To simplify the calculation avgF30 can be evaluated as 69. The atmospheric density of 250 km altitude above the Xi’an area was calculated and compared according to the parameter inversion model and ATMOP model. The time sampling was from January 2011 to October 2012, and the first day of each quarter was 08:00:00.000 (UTC 00:00:00.000). The coordinates are longitude 108.942° and latitude 34.261°. As shown in Table 1, the maximum single-point error is 1.94%, the minimum single-point error is 0.93%, and the average multi-point error is 1.56%.

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Table 1. The results of atmospheric density calculation by the two models above Xi’an area Index

Date

1 2 3 4 5 6 7 8

2011-01-01 2011-04-01 2011-07-01 2011-10-01 2012-01-01 2012-04-01 2012-07-01 2012-10-01

ATMOP model/ 1011 kg=m3 3.050330 6.600020 4.103406 7.120990 6.055830 6.032320 6.390770 9.280960

Parameter inversion model/ 1011 kg=m3 3.078698 6.699020 4.1756259 7.199321 6.173313 6.145124 6.505804 9.429455

Error rate (%) 0.93 1.50 −1.76 −1.10 1.94 −1.87 1.80 1.60

Fig. 2. Parameter inversion model calculation error above the land of China

The atmospheric density error rate calculated by the parameter inversion model in August 2011 is shown in Fig. 2. The area of longitude range is 73°−135° and latitude range is 19°−53°, and mainly covered the land of China at 260 km altitude. The average error rate between the results of the parameter inversion model and the ATMOP model is about 1.6%, which is less than the basic error rate range of the ATMOP model. Therefore, the parameter inversion model framework and its coefficients conform to the implementation method of the DTM2013 model.

4 Correlation Analysis of Solar Radiation Proxy with the Accuracy of DTM2013 Model GOCE (Gravity field and steady-state Ocean Circulation Explorer) was the ESA’s earth exploration satellite that launched in March 2009 with an orbital inclination of 96.5°. The eccentricity of GOCE was 0 and the orbital period was about 1.6 h. Its scientific exploration mission lasted from November 2009 to October 2013, and its orbit remained at the altitude of 255 km until July 2012. ESA released GOCE satellite measurement data as public products of the high-altitude precise atmospheric model [15].

DTM2013 Model Parameter Inversion and Correlation Analysis

43

According to document [9] and document [7], the most important improvement of DTM2013 compared with the MSIS00 model is that the F30 proxy is used instead of F10.7 proxy, while the fitting coefficients of other atmospheric components, the nonperiodic terms and the periodic terms of Gi ðLÞ, temperature profile forms and geomagnetic proxy are same. Since solar activity not only brings change in solar radiation proxy but also affects the geomagnetic proxy significantly [16, 17], the selection of solar radiation proxy is of great significance for the atmospheric models [18, 19]. The calculation accuracy of the two models can be obtained by comparing the atmospheric density calculation results of the DTM2013 model and MSIS00 model based on the GOCE measured atmospheric density data in 2011. The GOCE measured area is mainly delimited by the space of satellite orbit. The local time and geodetic coordinates corresponding to the ground are also determined by the satellite space trajectory. To analyze the atmospheric density data presented in time series, a fixed region must be selected for measurement and calculation. In this manuscript, the space 258–272 km altitude over Xi’an area is selected as the target space for atmospheric density calculation and comparison. The longitude of this area was about 108 ± 0.5° and the latitude of it was about 34 ± 0.5°. -11

5.5

x 10

200 F10.7 F30

5

4

Solar radiation (sfu)

atmospheric density(kg/m3)

4.5

3.5 3 2.5

150

100

2 1.5 1 Jan 2011

Apr

July Time

Oct

Jan 2012

Fig. 3. The measured atmospheric density of GOCE above Xi’an area in 2011

50 Jan 2011

Apr

July Time

Oct

Jan 2012

Fig. 4. The measured data of F30 and F10.7 proxies in 2011

The atmospheric density measured by GOCE of the space above the Xi’an area in 2011 is shown in Fig. 3. The F30 proxy and F10.7 proxy in the same period are shown in Fig. 4. According to the statistics of Pearson’s correlation criterion, the correlation between the F10.7 proxy and the GOCE measured atmospheric density data in 2011 is shown in Fig. 5, and the correlation between the F30 proxy and the GOCE measured atmospheric density data in 2011 is shown in Fig. 6. The high correlation between the atmospheric density and the solar radiation proxies are analyzed by the statistical results. The correlation coefficients are both more than 80%. The correlation coefficient between F10.7 and atmospheric density is 81.35%, and that between F30 and atmospheric density is 84.76%.

44

W. Cui et al. -11

-11

x 10

GOCE measured atmospheric density(kg*m-3)

GOCE measured atmospheric density(kg*m-3)

x 10

5

4

3

2

1 80

5

4

3

2

1

90

100

110 120 130 140 F10.7 measured data(sfu)

150

160

Fig. 5. The correlation between the F10.7 proxy and GOCE atmospheric measured data

60

70

80 90 100 F30 measured data(sfu)

110

Fig. 6. The correlation between the F30 proxy and GOCE atmospheric measured data

45 DTM2013 DTM2013 MSIS00 MSIS00

40 35

Deviation rate(%)

30 25 20 15 10 5 0 -5 0

50

100

150 200 Time(day of year)

250

300

350

Fig. 7. The calculation deviation rate of the DTM2013 model and the MSIS00 model

The deviation rate of atmospheric density calculated by the DTM2013 model and the MSIS00 model for the target area in 2011 were shown in Fig. 7. The longitude range of the target space is from 107.676°−108.422°. The latitude range of the target space is 33.51°−34.425°. The altitude range of target space is 258.819–272.439 km. The DTM2013 model and the MSIS00 model used F30 proxy and F10.7 proxy as the characterization data of solar radiation respectively. The average deviation rate of the DTM2013 model in this period is 11.07%, and that of the MSIS00 model in this period is 17.02%. The correlation between the DTM2013 model deviation rate and F30 proxy deviation and the correlation between the MSIS00 model deviation rate and F10.7 proxy deviation were both higher than 80%. In the period of large solar radiation proxy deviation, the atmospheric model deviation rate was relatively large, up to 40–50%; in the period of small solar radiation proxy deviation, the model deviation rate was about 5–10%.

DTM2013 Model Parameter Inversion and Correlation Analysis

45

5 Conclusion In the manuscript, the long-term mean of the F30 proxy is derived by fitting the measured data of the F30 proxy from 1971 to 2013, and the high-order Legendre polynomial coefficients are derived by the algorithm analysis. The parameter inversion DTM2013 model is established based on the DTM historical models algorithm and the derivation of various parameters. The correctness of the parameter inversion model is confirmed by the calculation results comparison between the parameter inversion DTM2013 model and the ATMOP DTM2013 model. The correlation between F10.7 and F30 solar radiation proxies and the GOCE measured atmospheric density over the Xi’an area in 2011 is derived, and the high correlation between solar radiation proxy and atmospheric density is deduced. The correlation between the DTM2013 model deviation rate and F30 proxy deviation, and the correlation between the MSIS00 model deviation rate and F10.7 proxy deviation are derived. The solar radiation proxy factors of the calculation deviations of the atmospheric models were explained. The study established a reliable correlation between the accuracy of the atmospheric model and the deviations of the solar radiation proxies from a statistical sense, which could provide a reference for the selection and improvement of the solar radiation proxy in subsequent atmospheric models. Solar radiation proxies from 1971 to 2013 were analyzed in this study, and the solar radiation proxies after 2013 are not included in the manuscript. At the same time, the time interval studied in this paper is relatively limited, so the following research will adopt the new solar radiation data in the study, and the correlation between solar radiation proxy deviations and atmospheric model accuracy will be studied in low and high solar activity years, which will makes the conclusions of this manuscript more universal. Acknowledgments. I would like to thank Dr. Stuart Grey of the University of Strathclyde for providing part of the original data for this article, and Prof. Massimiliano Vasile for his help in writing this article.

References 1. Guo, Z., Li, W., Zhang, H.: Analysis of time-varying spatial characteristics for atmospheric density of Earth edge. J. Astronaut. 33(8), 1177–1184 (2012). (Ch) 2. Marcos, F., Bass, J., Baker, C., Boner, W.: Neutral density models for aerospace applications. In: 32nd Aerospace Sciences Meeting and Exhibit, Reno, New York, 10–13 January (1994) 3. Rhoden, E., Forbes, J., Marcos, F.: The influence of geomagnetic and solar variabilities on lower thermosphere density. J. Atmos. Solar-Terr. Phys. 62, 999–1013 (2000) 4. Jacchia, L.G.: New static models of the thermosphere and exosphere with empirical temperature models. Technical report 313, Smithsonian Astrophysical Observatory (1970) 5. Hedin, A.: MSIS-86 thermospheric model. J. Geophys. Res. 92(A5), 4649–4662 (1987) 6. Kallmann-Bijl, H., Boyd, R.L.F., Lagow, H., et al.: CIRA 1961: COSPAR International Reference Atmosphere 1961. North-Holland Publishing Company, Amsterdam (1961)

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7. Picone, J., Hedin, A., Drob, D., et al.: NRLMSISIE-00 empirical model of the atmosphere: statistical comparisons and scientific issues. J. Geophys. Res. 107(A12), SIA–SIA15 (2002) 8. Bowman, B.R., Tobiska, W.K.: A new empirical thermospheric density model JB2008 using new solar and geomagnetic indices. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii (2008) 9. Bruinsma, S.: The DTM-2013 thermosphere model. J. Space Weather Space Clim. 5(A1) (2015) 10. Berger, C., Biancale, R., Barlier, F., et al.: Improvement of th empirical thermosphere model DTM: DTM-94-a comparative review of various temporal variations and prospects in space geodesy applications. J. Geodesy 72(3), 161–178 (1998) 11. Bruinsma, S., Thuillier, G., Barlier, F.: The DTM-2000 empirical thermosphere model with new data assimilation and constraints at lower boundary: accuracy and properties. J. Atmos. Solar-Terr. Phys. 65, 1053–1070 (2003) 12. Li, J.: Satellite Precision Orbit Determination, pp. 178–183. PLA Press, Beijing (1995) 13. Boyd, J.P., Petschek, R.: The relationships between Chebyshev, legendre and jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. J. Sci. Comput. 59(1), 1–27 (2014) 14. Wang, H.B., Xiong, J., Zhao, C.Y.: The mid-term forecast method of solar radiation index F10.7. J. Astronaut. 55(4), 302–312 (2014) 15. Bruinsma, et al.: Validation of GOCE densities and thermosphere model evaluation. Adv. Space Res. 54, 576–585 (2014) 16. Li, X., Xu, J.Y., Tang, G.S., et al.: Processing and calibrating of in-situ atmospheric densities for APOD. Chin. J. Geophys. 61(9), 3567–3676 (2018) 17. Xue, B., Cang, Z.: Optimizing the NRLMSISE-00 model by a new solar EUV proxy. Chin. J. Space Sci. 37(3), 291–297 (2017) 18. Miao, J., Liu, S., Li, Z., et al.: Correlation of thermosphere density variation with different solar and geomagnetic indices. Manned Spaceflight 18(5), 24–29 (2012) 19. Huang, M., Wang, D., Feng, H., et al.: Method and application of atmosphere density retrieving based on measured data. J. Astronaut. 39(12), 1419–1424 (2018)

A Method of Combined Orbit Determination of Multi-source Data with Modified Helmert Variance Component Estimation Laiping Feng1,2(&), Rengui Ruan1,2, and Anmin Zeng1,2 1

2

National Key Laboratory of Geographic Information Engineering, Xi’an, China [email protected] Xi’an Research Institute of Surveying and Mapping, Xi’an, China

Abstract. The application of inter-satellite link technology, the rise of loworbit satellite enhancement constellation and the maturity of on-borne GNSS orbit determination technology provide a new method for precise orbit determination different from the traditional ground monitoring station. The method can use a variety of observation data to achieve precise orbit determination under the condition of regional monitoring station. Due to the differences among inter-satellite link, low-orbit satellite-borne GNSS and ground monitoring station data, the reasonable weighting of all kinds of data in joint orbit determination is conducive to improving the accuracy of orbit determination. So this paper proposed a multi-source weighted method of orbit determination data based on Helmert variance component estimation. Meanwhile, it proposed a data processing method of joint orbit determination parameter classification, to solve the limitation of parameter quantity constraint in the process of orbit determination by the rigorous variance component estimation method. The simulation experiment shows that, compared with the weighting strategy based on different observation data accuracy, the Helmert variance component estimation method increases the average RMS of orbital accuracy from 0.073 m to 0.058 m, about 21% up, 31.8%, 13.6%, and 20.4% in R, T, and N directions respectively, by reasonably adjusting the weight allocation of three types of orbital data. Keywords: Inter-satellite link
Ground monitoring station
Space-based monitoring station
Combined orbit determination
Helmert variance component estimation

1 Introduction In order to improve the accuracy of orbit determination, the ground monitoring stations of the BDS navigation satellite system need global distribution. But in fact, it is hard to carry out due to geographical factors. Space-based monitoring stations provide a new method to enhance the orbit determination of regional monitoring stations [1, 2], based on LEO-low Earth Orbit satellites and inter-satellite links. It includes space-based monitoring stations augmentation and inter satellite link orbit determination © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 47–57, 2020. https://doi.org/10.1007/978-981-15-3711-0_5

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augmentation. In the former, the LEO satellites are regarded as moving monitoring stations, obtained the high precision pseudo-distance and carrier observation data by its on-board receiver, together with the ground monitoring station data, it can calculate the precise orbit of the navigation satellite [3–8]. The latter is a method to obtain the precise orbit of a satellite by the combined processing of two-way pseudo-range observation and ground monitoring station data [9]. Therefore, all kinds of observation data from ground, space-based monitoring station and inter-satellite link constitute the basic observation quantity of joint orbit determination. However, the three types of data employed to jointly determine the orbit are quite different. For example, It causes the difference between ground and space-based data because of the different receivers and signal propagation paths, and inter-satellite data difference for its way of frequency, signal modulation and measuring systems. Due to the different equipment delays, it will influence the joint results on orbit determination in the form of system errors [10, 11]. It’s a concern of combined orbit determination. Therefore, this paper proposed a multisource weighted method of orbit determination data based on Helmert variance component estimation. And proposed a data processing method of joint orbit determination parameter classification, breaking through the parameter quantity constraint in the process of orbit determination by rigorous variance component estimation method.

2 Summary of Problems in Determining the Weights of Observation for Orbit Determination 2.1

Mathematical Model to Determine the Orbit

The observation model of the combined orbit determination, using ground monitoring station data, LEO satellite onboard data and inter satellite link data, can be simply expressed as follows.
 8 1 ¼ G ð x ; x ; x ; t Þ þ n ; n 2 0; P L sta s sta o > sta sta sta <
 Lleo ¼ Fðxs ; xleo ; xo ; tÞ þ nleo ; nleo 2 0; P1 leo >
 : Lisl ¼ Rðxs ; xo ; tÞ þ nisl ; nisl 2 0; P1 isl

ð1Þ

Where, Lsta , Lleo respectively represent the observation data (BDS) from ground station and on-borne GNSS, Lisl (isl: inter-satellite link) represents the inter-satellite link data, nsta ; nleo ; nisl are the corresponding measurement errors, Psta ; Pleo ; Pisl are the corresponding weight matrix, t is the time parameter. xs and xleo are the set of orbit parameters for GNSS satellite and LEO satellite, xsta is a set of the monitoring station parametes, such as the station’s coordinates, tropospheric delay etc., and xo corresponds to the measurement parameters, such as carrier phase ambiguity, clock error, equipment delay of inter-satellite link, etc. [12]. The above observation equation is linearized and transformed into the following form.

A Method of Combined Orbit Determination of Multi-source Data

3 2 dx 3 2 3 s vsta lsta @xs 6 7 dx 6 7 leo 7 4 vleo 5 ¼ 4 @F @F 4 5 0 56 @xs @xleo 4 dxsta 5  lleo @R visl lisl 0 0 @xs |fflfflffl{zfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl |fflfflffl{zfflfflffl} o ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflffldx ffl {zfflfflfflffl ffl } v l 2

3

2 @G

@G @xsta

0

@G @xo @F @xo @R @xo

A

49

ð2Þ

dx

Where 8
0 0 0  > < lsta ¼ Lsta  G
xs ; xsta ; xo ; t  lleo ¼ Lleo  F x0s ; x0leo ; x0o ; t >
 : lisl ¼ Lisl  R x0s ; x0o ; t xðÞ0 represents the initial value of the parameter, dðÞ represents correction to the parameter. The corresponding least squares solution can be expressed as:
1 d^x ¼ AT PA AT Pl

 ^ x ¼ AT PA 1 ¼ AT Psta Asta þ AT Pleo Aleo þ AT Pisl Aisl 1 Q sta leo isl

ð3Þ

Where 2 P¼4

Psta

3 Pleo

5 Pisl

^x Asta , Aleo and Aisl are the first, second and third rows of matrix A in formula (2). Q is the covariance matrix for estimating unknowns. Obviously, compared to the simplistic technique for determining the orbit parameters of ground monitoring stations alone, it’s conducive to improving the accuracy of parameter estimation by adding lowsatellite and inter-satellite link data. 2.2

Weight Determination Method for Observation Data

There are usually three ways of determining the weight ratio of any kind of observation data [13]. In the first, weight is determined based on the empirical model for processing long-term observation data [14]. The second is to determine the weight ratio from standard deviation of known observation data. The third is to adjust the weight ratio by using variance component estimation and posterior residual analysis. The standard deviation of the observed values is just the internal coincidence precision. Empirical weighting can not objectively reflect the actual deviation of observed data. In case of multi-source data with a large amount of complex-type observations, improper weight ratio determination will lead to a decline in processing accuracy of data. Helmert variance component estimation is widely used in the field of data processing, because it can reweight observation values according contribution to global solution, by utilizing adaptive iteration in the calculation process for posterior variance component estimation.

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Helmert Variance Component Estimation

It is assumed that the linear system containing k kinds of observation data can be expressed as [15]: Li ¼ Ai X i þ Di X X ¼ ¼ r20;i QDi ¼ r20;i P1 i D L i

ð4Þ

i

Where Li is the type i observation value of dimension mi  1, Ai is a coefficient matrix of mi  n, X is the coefficient matrix of n  1, Di is the random error vector of P mi  1, r20;i is the unit weight variance of type i observations, i is the covariance matrix of Di , and Pi is the weight matrix of Di . Its normal equation is: k X

!

k X

^¼ Ni X

i¼1

ð5Þ

Ui

i¼1

Where N i ¼ ATi Pi Ai , Ui ¼ ATi Pi Li . The above formula is based on the same variance factor. Normally variance factors of different types of observations are not the same and can be adjusted in accordance with the variance component. The basic principle of the Helmert variance component ^20;i of the class parameter, based on estimation is to estimate the posterior unit weight r ^ i obtained by adjustment. the correction vector Vi ¼ Li  Ai X 2.3.1 Rigorous Formula of Helmert Variance Component Estimation The rigorous formula of Helmert variance component estimation is: ^2 ¼ W S
r

kk k1

ð6Þ

k1

Where, 2

s1;1 6 s1;2 6 S¼6 . 4 ..

s1;2 s2;2 .. .

s1;k

s2;k

 2 ^0;1 ; ^2 ¼ r r

^20;2 ; r

3


s1;k


s2;k 7 7 .. 7 .. . 5 .


sk;k

 W ¼ V T1 P1 V 1 ; V T2 P2 V 2 ;




;

^20;k r

ð7Þ

T




; V Tk Pk V k



2 si;i ¼ mi  2tr N 1 N i þ tr N 1 N i
 si;j ¼ tr N 1 N i N 1 N j

ð8Þ T

ð9Þ ð10Þ

A Method of Combined Orbit Determination of Multi-source Data

51

Solution of (6): ^2 ¼ S1 W r

ð11Þ

In data processing of the joint orbit determination on various observations, there are large data volume from ground monitoring stations, inter-satellite link and on-borne BDS. On this condition, the estimation with rigorous formula would be a heavy work. The following is an improved method for faster calculation. 2.3.2 Simplified Formula of Helmert Variance Component Estimation In (8), let ^20;1 ¼ r ^20;2 ¼


¼ r ^20;k ¼ r ^20;i ð6¼ r ^20 Þ r

ð12Þ

We have: V Ti Pi V i ¼






mi  2tr N 1 N i þ tr N 1 N i N 1

k X

!! Nj

j¼1




 2 ^0;i ¼ mi  2tr N 1 N i þ tr N 1 N i N 1 N 1 r

1  2 ^0;i ¼ mi  tr N N i r

^20;i r ð13Þ

The above formula is a simplified version of the Helmert variance component estimation. At the start of the iteration, formula (12) is not valid, the valuation being biased. After several iterations; though, the formula will prove satisfactory, the final result would be unbiased. Omit the trace section in Eq. (13), then ^20;i ¼ r

V Ti Pi V i mi

ð14Þ

The sum of (14) is known to have biased valuation, so is called the approximate formula of Helmert variance component estimation. If Pi is true, then Eq. (12) is true, and ^20 ^20;i ¼ r r

ð15Þ

So we know from (13) that: k X

V Ti Pi V i ¼

i¼1

k
X


 2 ^0;i mi  tr N 1 N i r

i¼1

¼

m  tr N

1

k X i¼1

¼ ðm 

nÞ^ r20

!! Ni

^20 r

ð16Þ

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That is: k P

^20 r

¼

i¼1

V Ti Pi V i ð17Þ

mn

Usually when given the weight, this formula can be used to calculate the unit weight variance valuation. In adjustment calculations, the off-diagonal elements of the coefficient matrix N and N i of the normal equation are usually smaller than the main diagonal elements, so a better approximation can be obtained by omitting them. Let N i from which remove the off-diagonal element be: N i ¼ ATi Pi Ai ¼ diagð ½paai ; ½pbbi ;


;

½pbbi Þ

ð18Þ

So: k
 X N fi ; f ¼ a; b; c;


; n tr N 1 N i ¼ Nf i¼1




2

tr N 1 N i N 1 N j ¼

k X N fi N fj i¼1

ð19Þ

Nf

By using formula (19) to obtain the trace, the calculation can be simplified and faster. 2.3.3 Bäumker Variance Component Estimation Formula Estimation proposed by Bäumker in 1984 [16] is: ^20;i ¼ r

V Ti Pi V i gi

ð20Þ

mi t m

ð21Þ

Where: gi ¼ mi 

Where m is the number of all observations, mi is the number of observed values of class i, and n is the number of all unknown parameters. Compared with the original method, it improved the calculation efficiency greatly in multi-type and mass data processing, avoiding the complex matrix calculation.

A Method of Combined Orbit Determination of Multi-source Data

53

3 Improved Formula of Variance Component in Combined Orbit Determination In formula (21), different types of observations correspond to the same batch of unknown parameters, while in the joint orbit determination of the three types of observation data, the corresponding parameters to be estimated are not the same. As shown in Table 1, the information of the parameters to be estimated in the ground receiver data, the satellite-borne receiver data and the inter-satellite link data are different. Table 1. Parameter types of data processing in combined orbit determination Parameter types

Observation station coordinates, clock difference and troposphere parameter Carrier phase ambiguity parameter Low-orbit satellite orbit and clock difference parameters Satellite navigation orbit and clock difference

Ground receiver data √

Satelliteborne data –

Intersatellite link data –

√ –

√ √

– –

√

√

√

The table above shows that the unknown parameters of different types of observed quantities are different. Data from satellite-borne or inter-satellite link is of no use for observation station coordinates, clock difference and troposphere parameter. So it is not adequate to calculate directly according to Eq. (21). An improved formula is proposed: gi ¼ m i 

n X mj i

j¼1

mj

ð22Þ

Where mij is the number of i-class observation quantities related to the parameter j, and m j is the total number of observations related to the parameter j. This formula describes more finely the contribution of observation to unknowns.

4 Experimental Verification 4.1

Experimental Data

In order to verify the effectiveness of the improved Helmert variance component estimation method and combined orbit determination weight, three types of data including ground, low orbit and inter-satellite link are simulated, and 3GEO + 3 IGSO + 24MEO (walk24/3/2) [17] are adopted. The Ka bean angle range of intersatellite link is 15–60°. The low orbit constellation is the Walker6/6/2 configuration.

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The measurement accuracy of ground and satellite-borne receivers is 0.3 m in pseudorange, and 0.002 m in the carrier phase. The measurement accuracy of inter-satellite link data is 0.1 m and the system deviation is 0.1 m. Three schemes are adopted to conduct orbit determination experiments. 4.2

Experimental Schemes

The studies show that during the process of orbit determination, ground station and satellite-borne data do not need to undergo different processing [13]. While it’s hard to assign weights to the inter-satellite link data for the system errors. To compare the influence of weight size on results, and that of variance component estimation on combined orbit determination, there are three methods listed in the scheme below, mainly based on the assignment of large and small weights to inter-satellite link data. Scheme 1: Assign weights according to the magnitude of the noise of the observed values (single-frequency, pseudo-range, phase of ground station and space-borne data is 0.3 m and 0.2 m respectively, while inter-satellite data is 0.1 m). Scheme 2: Utilize artificial methods to reduce or increase inter-satellite weight values, and assign them according to the multiple relationships of the original weights p=5:0, p=10:0, 5p and 10p (respectively corresponding to IIA, IIB, IIC, IID). Scheme 3: Estimate posterior variance using the improved Helmert variance component estimation method, and improve weight ratio. 4.3

Results and Analysis

The weight correction factors of the three observed quantities, obtained by posterior variance component estimation, are respectively: 3.8:5.6:0.38. This means that on the basis of weighting in accordance with the accuracy of observation, the weight of ground monitoring station data and low-orbit satellite-borne data is increased, while the weight of inter-satellite link data is decreased. Table 1 shows the 3-dimensional position errors of the orbit determination results of each navigation satellite corresponding to the three schemes. It can be seen that in scheme 1, the average 3d orbit determination accuracy of the satellites is 0.073 m, obtained by weighing the accuracy of the observed values. In scheme 2, the orbit determination accuracy is 0.067 m, 0.075 m and 0.080 m respectively of the 4 kinds of weights, which indicates that weight assignment has a definite influence on orbit determination accuracy. In scheme 3, variance component estimation is used to determine the orbit, with the average accuracy of the satellite’s 3-D orbit being 0.058 m, which is the highest accuracy in comparison with other strategies. This shows that variance component estimation is effective for the determination of combined orbits in this paper. Furthermore if comparing the results of schemes 3 and 2, we can see the results in scheme 3 are more consistent with the P/10/0. In fact, the weight ratio of all 3 types of data is 10:10:1, compared with other schemes, is much closer to posterior variance component estimation. That confirmed the effectiveness of the Helmert variance component estimation method. Compared with scheme 1, which relies on the traditional weighting strategy based on the accuracy of observed data, scheme 3 improves the accuracy from 0.075 m to 0.058 m, about 21% up.

A Method of Combined Orbit Determination of Multi-source Data

55

Table 2 shows the orbital errors of the above schemes in radial (R), tangential (T) and normal (N) directions, and the results are basically consistent with previous ones. The Helmert variance component estimation was valid in R, T and N directions, when the variance components were weight adjusted, obtaining better orbit determination accuracy than other methods. Orbit determination accuracy in the R direction was 0.015 m, 0.038 m in T and 0.039 m in N, increasing by 31.8%, 13.6% and 20.4% respectively compared to scheme 1 (Table 3). Table 2. 3D orbit determination accuracy of different weighted strategies according to satellite number statistics (unit: m) PRN

Scheme 1 Scheme 2 p IIA: p=5:0 01 0.044 0.041 02 0.083 0.045 03 0.164 0.085 04 0.067 0.159 05 0.096 0.053 06 0.064 0.058 07 0.035 0.089 08 0.049 0.058 09 0.096 0.040 10 0.055 0.042 11 0.075 0.091 12 0.081 0.045 13 0.037 0.068 14 0.039 0.079 15 0.044 0.040 16 0.075 0.045 17 0.065 0.038 18 0.069 0.069 19 0.050 0.062 20 0.093 0.070 21 0.046 0.053 22 0.063 0.090 23 0.170 0.043 24 0.056 0.058 25 0.047 0.162 26 0.067 0.055 27 0.040 0.052 28 0.111 0.067 29 0.132 0.034 30 0.074 0.109 Mean 0.073 0.067

Scheme 3 IIB: p=10:0 IIC: 5p IID: 10p M-Helmert 0.053 0.035 0.035 0.050 0.054 0.044 0.047 0.052 0.090 0.085 0.089 0.084 0.130 0.176 0.181 0.115 0.033 0.071 0.075 0.029 0.041 0.075 0.080 0.035 0.061 0.106 0.109 0.052 0.048 0.069 0.071 0.043 0.054 0.030 0.030 0.051 0.033 0.056 0.062 0.032 0.073 0.103 0.107 0.066 0.020 0.067 0.075 0.018 0.052 0.086 0.093 0.046 0.074 0.086 0.089 0.068 0.053 0.040 0.045 0.050 0.060 0.035 0.037 0.057 0.021 0.051 0.053 0.020 0.051 0.083 0.087 0.044 0.056 0.070 0.075 0.052 0.075 0.076 0.083 0.072 0.064 0.053 0.057 0.061 0.082 0.094 0.096 0.074 0.042 0.049 0.051 0.039 0.041 0.067 0.067 0.035 0.138 0.184 0.194 0.134 0.069 0.062 0.068 0.067 0.079 0.050 0.057 0.077 0.078 0.078 0.086 0.076 0.041 0.056 0.063 0.039 0.105 0.119 0.126 0.098 0.062 0.075 0.080 0.058

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Table 3. Statistics of orbit determination accuracy in the R/T/N direction with different weight methods (unit: m) Scheme I II-A II-B II-C II-D III

Inter-satellite values R T N P 0.022 0.044 0.049 P/5.0 0.020 0.043 0.047 P/10.0 0.016 0.041 0.043 P*5.0 0.021 0.046 0.052 P*10.0 0.023 0.051 0.057 Helmert 0.015 0.038 0.039

5 Conclusion In this study, the variance component estimation method is used in fusion weighted processing and orbit determination, on the data from ground, satellite-borne and intersatellite link. The following conclusions were obtained: 1. On the data characteristics of large differences among the various types and system errors in inter-satellite data, this paper proposed a weighted Helmert variance component estimation method. With the limitations of strict variance component estimation, propose a data processing method on parameter classification in joint orbit determination. 2. Combined orbital determination was obtained by using simulated data on the Helmert variance component estimation. By comparing the results of schemes, an orbit determination strategy based on variance component estimation is the optimum solution. The weight correction factor obtained from the three observed quantities in posterior variance component estimation are more in line with actual joint processing, and the accuracy of the solutions is the best. 3. Compared with the traditional weighting strategy based on observation data accuracy, the Helmert variance component estimation reasonably adjusted the weight allocation of multiple-source tracking data. The average RMS orbit determination accuracy increased from 0.073 m to 0.058 m, increases of 31.8%, 13.6% and 20.4% respectively in R, T and N directions. The overall accuracy increased by 21%.

References 1. Feng, L., Mao, Y., Song, X., et al.: Analysis on the accuracy of Beidou combined orbit determination enhanced by LEO and ISL[J]. Acta Geod. et Cartogr. Sin. 45(S2), 902–907 (2016) 2. Meng, Y., Bian, L., Wang, Y.: Global navigation augmentation system based on Hongyan satellite constellation. Space Int. 10, 20–27 (2018) 3. Svehla, D., Rothacher, M.: Kinematic and reduced-dynamic precise orbit determination of low earth orbiters. Adv. Geosci. 2003(1), 47–56 (2003) 4. Rothacher, M.: Precise orbit determination for low earth orbiters. In: Colloquium on Atmospheric Remote Sensing Using the Global Positioning System (2004)

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5. Zhu, S., Reigber, C., Konig, R.: Integrated adjustment of CHAMP, GRACE, and GPS data. J. Geodesy 78, 103–108 (2004) 6. Shen, D., Meng, Y., Bian, L., et al.: A global navigation augmentation system based on LEO communication constellation. J. Terahertz Sci. Electron. Inf. Technol. 17(2), 209–215 (2019) 7. Kang, Z., Tapley, B., et al.: Precise orbit determination for the GRACE mission using only GPS data. J. Geodesy 80, 322–331 (2006) 8. Geng, J., Shi, C., Zhao, Q., et al.: Precsise determination of GPS satellite orbit by combining ground and space-borne data. J. Wuhan Univ. Inf. Sci. Ed. 32(10), 906–909 (2007) 9. Zhu, J.: Research on orbit determination and time synchronization method for navigation satellites based on inter-satellite link. University of National Defense Science and Technology, Changsha (2012) 10. Xiao, Y.: Research on key technology of autonomous navigation satellites, graduate school of the Chinese academy of sciences (Shanghai Institute of Technical Physics), Shanghai (2016) 11. Rui, G., Zhou, J.H., Hu, X.G., et al.: Precise orbit determination and rapid orbit recovery supported by time synchronization. Adv. Space Res. 55(12), 2889–2898 (2015) 12. Guo, R., Chen, J., Zhu, L., et al.: Kinematic orbit determination method optimization and test analysis for BDS satellites with short-arc tracking data. Acta Geod. et Cartogr. Sin. 46(4), 411–420 (2017). https://doi.org/10.11947/j.AGCS.2017.20160361 13. Qin, X..: Research on orbit determination theory and low-orbit satellite borne GPS method. University of Information Engineering (2009) 14. Xiao, G., Sui, L., Liu, C., et al.: Weight determination method for single point positioning of polaris navigation and positioning system. Acta Surv. Mapp 43(9), 902–907 (2014) 15. Zu, A., Li, J., Wang, Y., et al. A BDS satellite orbit determination algorithm using variance component estimation. Surv. Mapp. Sci. (2009) 16. Hu, W.: Modern Adjustment Theory and its Application. PLA Press, Beijing (1992) 17. Wang, R., Ma, X., Li, M.: Optimal design of satellite clusters with regional coverage using genetic algorithm. Acta Astronaut. 23(3), 24–28 (2002)

The Influence of Station Distribution on the BeiDou-3 Inter-satellite Link Enhanced Orbit Determination Yufei Yang1, Yuanxi Yang2(&), Rui Guo1, Chengpan Tang3, and Zhixue Zhang1 2

1 Beijing Satellite Navigation Center, Beijing 100094, China Xi’an Research Institute of Surveying and Mapping, Xi’an 710054, China [email protected] 3 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China

Abstract. The basic system of the third generation BeiDou Global Satellite Navigation System (BeiDou-3 or BDS-3) has been completed by the end of 2018, and the complete system is planned to be completed by 2020. The intersatellite link technology is deployed by BDS-3, which not only can realize the autonomous navigation of the constellation, but also can be used to enhance the orbital determination under normal operating conditions. In this paper, the influence of ground monitoring station distribution on the BDS-3 inter-satellite link enhanced orbit determination is analyzed. The results show that, with the ISL, the orbital accuracy based on three monitoring stations separated by several hundred kilometers is almost equal with that based on eight domestic monitoring stations. The ISL greatly reduces the ground monitoring station number and distribution requirements of the orbit determination. Only a few ground stations are needed to constrain the positional relationship between the constellation and the earth, thereby weakening the rotation and translation of the entire constellation with regard to the earth. Keywords: BDS-3
Inter-satellite link
Orbit determination
Ground station
Station distribution

1 Introduction According to the three-step plan, the third generation BeiDou Global Satellite Navigation System (BeiDou-3 or BDS-3) will provide global services around 2020. At that time, BDS-3 will have 30 satellites in orbit, including three geostationary equatorial orbit (GEO) satellites located at 80 °E, 110.5 °E and 140 °E, respectively, three inclined geosynchronous orbit (IGSO) satellite with an orbit inclination angle of 55°, and 24 medium Earth orbit (MEO) satellites evenly distributed in three orbital planes [1, 2]. By the end of 2018, BDS-3 had completed the launch of 19 satellites (18 MEO satellites in orbital service, 1 GEO satellite in orbit test) and began to provide basic services to users around the world. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 58–70, 2020. https://doi.org/10.1007/978-981-15-3711-0_6

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High-precision satellite orbit product is one of the pre-conditions for global satellite navigation system (GNSS) to provide high-performance positioning, navigation and timing services [3, 4]. Since the Beidou monitoring stations can only be deployed in China, when a MEO satellite travels out of the monitoring range of the regional tracking stations, the tracking and monitoring of the MEO satellite is interrupt, which greatly restricts the accuracy of the Beidou satellite orbit [5–7]. Autonomous navigation of GNSS was first proposed by American scholars, in the 1980s, which is based on inter-satellite links to reduce the dependence of GPS system on ground facilities [8]. Starting in 1997, a series of GPS BLOCK IIR satellite equipped with UHF band inter-satellite link payloads were send into orbit, and the in-orbit autonomous navigation was successfully carried out. The results show that the 75-day URE is better than 3 m [9, 10]. In view of the successful experience of GPS, GLONASS and Galileo have also proposed their own inter-satellite link development plans [11, 12]. All of the BDS-3 satellite are equipped with Ka-band ISL payloads, which enable high-precision ranging and communication between satellites and satellites. ISL can not only help the ground control system to switch to the autonomous navigation mode in the event of a malfunction, but also can be used to orbit determine together with the ground monitoring station to improve the orbit accuracy under normal conditions. In addition, ISL link can also solve the problem that the overseas satellite broadcasting ephemeris cannot be timely injected and updated, and realize the domestic injection, in-orbit distribution and whole constellation update of the broadcast ephemeris, which has a great significance for shortening the satellite ephemeris data age [13–16]. In this paper, the influence of ground monitoring station distribution on the BDS-3 inter-satellite link enhanced orbit determination is analyzed. The results show that, with the ISL, the orbital accuracy based on three monitoring stations separated by several hundred kilometers is almost equal with that based on eight domestic monitoring stations. The ISL greatly reduces the ground monitoring station number and distribution requirements of the orbit determination. Only a few ground stations are needed to constrain the positional relationship between the constellation and the earth, thereby weakening the rotation and translation of the entire constellation with regard to the earth.

2 ISL Enhanced Orbit Determination Principle 2.1

Inter-satellite Ranging

The BDS-3 ISL adopts a dual-one-way ranging technology, which can obtain forward and backward ranging measurements in 3 s [17, 18]. The inter-satellite ranging measurement includes not only the distance, but also the relative clock difference between the satellites which can be decoupled by summation and difference of the two dual-oneway ranging measurements. As can be seen in Fig. 1, The process of dual-one-way ranging is as follows: Firstly, satellite A send a ranging signal on its local time t1, and satellite B receive the ~AB . And then, satellite B ranging signal at its local time t2, obtaining the ranging value q

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Fig. 1. Inter-satellite dual-one-way ranging

send a ranging signal on its local time t3, and satellite A receive the ranging signal at t4, ~BA , the two forward and backward ranging values can be obtaining the ranging value q expressed as:

AB ~AB ðt2 Þ ¼
~ RB ðt2 Þ  ~ RA ðt1 Þ
þ c
clkB ðt2 Þ  c
clkA ðt1 Þ þ c
ssend þ c
srcv q A B þ Dqcor þ n ð1Þ

BA ~BA ðt4 Þ ¼
~ q RA ðt4 Þ  ~ RB ðt3 Þ
þ c
clkA ðt4 Þ  c
clkB ðt3 Þ þ c
ssend þ c
srcv B A þ Dqcor þ n ð2Þ Where, ~ RA and ~ RB are the three-dimensional position vectors of the satellite A and rcv send and srcv satellite B, clkA and clkB are the clock offsets, ssend A , sA , sB B are the transAB mission and reception delays of the ISL payload, Dqcor and DqBA cor are corrections including satellite antenna phase center offset (PCO) correction, relativistic effect correction, etc., and also tropospheric delay correction, station PCO correction, tidal effect correction if the link is between satellite and ground anchor station. n are observing noise and other unknown systematic errors. The accuracy of the ISL ranging is about a few cm, and the ionospheric delay of Ka-band ISL is about a few cm, which is negligible. 2.2

Time Correction of ISL

The time of two dual-one-way ranging are different, so it is necessary to do time correction for ranging measurement. The Eqs. 1 and 2 can be rewritten into the following form:

~AB ðt2 Þ ¼
~ q RB ðt2 Þ  ~ RA ðt2  Dt2 Þ
þ c
clkB ðt2 Þ  c
clkA ðt2  Dt2 Þ þ c
ssend A AB þ c
srcv B þ Dqcor þ n

ð3Þ

The Influence of Station Distribution



~BA ðt4 Þ ¼
~ RA ðt4 Þ  ~ RB ðt4  Dt4 Þ
þ c
clkA ðt4 Þ  c
clkB ðt4  Dt4 Þ þ c
ssend q B BA þ c
srcv A þ Dqcor þ n

61

ð4Þ

Where Dt2 and Dt4 is the signal propagation delay, which can be calculated by iteration. Then the ranging measurement can be corrected to middle time t0 based on priori satellite orbit and clock difference information. ~AB ðt0 Þ ¼ q ~ ðt Þ þ dqAB q
AB 2
AB
¼ ~ RB ðt0 Þ  ~ RA ðt0 Þ
þ c
clkB ðt0 Þ  c
clkA ðt0 Þ þ c
ssend þ c
srcv A B þ Dqcor þ n ð5Þ ~BA ðt0 Þ ¼ q ~ ðt Þ þ dqBA q
BA 4
BA
¼ ~ RA ðt0 Þ  ~ RB ðt0 Þ
þ c
clkA ðt0 Þ  c
clkB ðt0 Þ þ c
ssend þ c
srcv B A þ Dqcor þ n ð6Þ Where dqAB and dqBA are corrections for satellite position and satellite clock error.



RB ðt0 Þ  ~ RA ðt0 Þ

~ RB ðt2 Þ  ~ RA ðt2  Dt2 Þ
þ c
½clkB ðt0 Þ  clkA ðt0 Þ dqAB ¼
~  c
½clkB ðt2 Þ  clkA ðt2  Dt2 Þ þ n



RA ðt0 Þ  ~ RB ðt0 Þ

~ RA ðt4 Þ  ~ RB ðt4  Dt4 Þ
þ c
½clkA ðt0 Þ  clkB ðt0 Þ dqBA ¼
~  c
½clkA ðt4 Þ  clkB ðt4  Dt4 Þ þ n

ð7Þ

ð8Þ

Generally, the priori satellite speed is better than 0.1 mm/s, the priori clock speed is better than 1E-13 s/s, and the correction time interval is less than 1.5 s, so the calculation accuracy of dqAB and dqBA better than 1 cm can be achieved [19]. ~AB ðt0 Þ and q ~BA ðt0 Þ can eliminate the clock difference and obtain The addition of q the relative distance between the satellites. qBA ðt0 Þ ¼


ssend þ srcv ~AB ðt0 Þ

~ ~BA ðt0 Þ þ q ssend þ srcv q A B ¼ RA ðt0 Þ  ~
cþ B
cþn RB ðt0 Þ
þ A 2 2 2 ð9Þ

~AB ðt0 Þ and q ~BA ðt0 Þ can eliminate relative distance and obtain the The subtraction of q clock difference between the satellites. dclkAB ðt0 Þ ¼

~BA ðt0 Þ ~AB ðt0 Þ  q q 2

¼ c
½clkB ðt0 Þ  clkA ðt0 Þ þ

ssend  srcv ssend  srcv A A B
c B
cþn 2 2

ð10Þ

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However, it should be noted that this method requires that the observation interval of the two dual-one-way ranging measurement is about 3 s. If the time interval is too large, the correction accuracy will be reduced.

3 Characteristics of ISL Satellite links to different satellites or anchor stations at different time slots according to the link-building plan generated by the master control station (MCS) in advance. A total of 7 days of BDS-3 ISL observation data (from June 09 to 15, DOY 160 to 166, 2019) were analyzed. The results of C25 (MEO satellite), C59 (GEO satellite), and C76 (anchor station) are shown in Figs. 2, 3 and 4.

Fig. 2. Links between C25 and other satellites/anchor station

Figure 2 shows the link-building of C25 satellites and other satellites. The horizontal axis is the DOY of 2019, and the vertical axis is the pseudo-random noise code (PRN) of the satellites/anchor station link with C25. The blue points represent the linkbuilding plan, which means there should be two one-way ranging measurements at that moment. The yellow and red points represent the forward and backward ranging measurements, respectively, received by the MCS. As can be seen from the figure: (1) Except for C23, C24 and C36, all of the other satellites have links with C25. C24, C23, and C36 has the same orbit plane as C25, and are invisible to C25 because of the large nadir angle or the occlusion of the Earth. (2) There are 6 satellites, three of them in the same orbit plane as C25 and the other three in the different orbit plane, are always visible to C25, and the links between them and C25 are continuous (see C26 and C27). The other satellites are in orbit planes different from that of C25, and the links are discontinuous (see C28 and C29).

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63

(3) The entire arc of the C25 orbit is covered by the ISL, which means that the relative clock among every satellite in the constellation can be measured using a large number of ISLs.

Fig. 3. Links between C59 and other satellites

Figure 3 shows the link-building of C59 satellites and other satellites. As can be seen from the figure: (1) As C59 is a GEO satellite, the relative positional relationship between C59 and anchor station C76 is almost unchanged, and the link between them is continuous; (2) All the MEO satellites are not always visible to C59, and the links are discontinuous. The longest link duration between MEO satellites and C59 and is longer than 12 h, and the shortest one is shorter than 1 h.

Fig. 4. Links between C76 and other satellites

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Figure 4 shows the link-building of anchor station C76 and other satellites. As can be seen from the figure: (1) All the satellites have links with C76. The links with GEO satellite C59 is continuous, and all the others links are discontinuous. (2) Compared with the GEO satellite, the link duration between anchor station and MEO satellite is significantly shorter, and the longest arc is shorter than 10 h, which is because the visible relationship between the anchoring station and the MEO satellite changes more rapidly. As can be seen from Figs. 2, 3, and 4, there are some moments when one of the dual one-way ranging measurements is missing (or even both). These instances may be caused by the loss of data transmission. However, the ISL time correction requires that the time interval between two dual-one-way ranging measurement should be no longer than 3 s. If a ranging measurement cannot find a reverse measurement within three seconds, it is considered invalid. The total data amount and valid data amount are counted. The data amount of the dual one-way ranging measurements for 7 days is about 300,000, about 43,000 per day, and the valid data amount is about 38,000. The data amount of MEO satellites and GEO satellite data is basically the same, and significantly bigger than that of the anchor station, which is only about 10,000 data per day. By analyzing the link-building characteristics of GEO satellites, MEO satellites and anchor stations, it can be found that under the condition of BDS-3 19 satellites and 1 anchor station, the ISL constructs a space observation and communication network composed of more than 100 links. The tracking, monitoring and observation of the full arc of the MEO satellite are realized.

4 Orbit Determination Strategy The addition of the ISL can not only improve the accuracy of the orbit, but also reduce the dependence of the satellite navigation system on the ground monitoring station, making it possible to obtain high-precision orbit with a small number of monitoring stations. In this section, the influence of station distribution on the BDS-3 ISL enhanced orbit determination is analyzed. The experiment is divided into six schemes (as shown in Fig. 5): (1) 8 Stations (8S). The orbit determination is based only on 8 stations within China mainland. The station coordinates are fixed, and the station No. 1 is chosen as the reference of which the clock difference is fixed to zero. (2) 8 Stations & ISL (8S-ISL). The orbit determination is based on ISL and 8 stations within China mainland. The station coordinates are fixed, and the station No. 1 is chosen as the reference of which the clock difference is fixed to zero. (3) 5 Stations (5S-ISL). The orbit determination is based on ISL and 5 stations, namely No. 3, No. 5, No. 6, No. 7 and No. 8, and the station No. 8 is chosen as the reference.

The Influence of Station Distribution

(1) 8S & 8S-ISL

(3)3S-B-ISL

65

(2) 5S-ISL

(4) 3S-S-ISL

Fig. 5. Station distribution of different schemes

(4) 3 Stations for big area (3S-B-ISL). The orbit determination is based on ISL and 3 stations in a big area, namely No. 5, No. 6 and No. 8, and the station No. 8 is chosen as the reference. (5) 3 Stations for small area (3S-S-ISL). The orbit determination is based on ISL and 3 stations in a small area, namely No. 4, No. 7 and No. 8, and the station No. 8 is chosen as the reference. (6) 1 Anchor Station (1AS). The centralized autonomous orbit determination is based on ISL and 1 anchor station and the coordinates and clock of anchor station are fixed. The experiment time is from January 7 to 10, 2019. There are 18 BDS-3 MEO satellites are involved in the experiment. And the orbit based on 21 globally distributed stations and ISL is taken as the reference to evaluate the orbital accuracy of the above schemes (Table 1).

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Arc length Interval Observations

Station coordinates Satellite/receiver antenna PCO Satellite/receiver antenna PCV Ambiguities Tropospheric delay Ionospheric delay N-body Solar radiation pressure

Ground observation 3 days 30 s Undifferenced ionospheric-free code and phase combination of B1I & B3I

ISL observation 3s Ka-band pseudorange measurement

ITRF 2008 Default values Not applied Float solution Saastamoinen model for wet and dry hydrostatic delay with GMF mapping function without gradient model (Saastamoinen, 1972) The first-order ionospheric delay is eliminated by the dual frequency combinations JPL DE405 BERNESE ECOM5

Not exist

Not exist for ISLs between satellites

The observations of ground station are undifferenced ionospheric-free code and phase combination of B1I & B3I with an interval of 30 s, and the measurements of ISL are Ka-band pseudorange measurements with an interval of 3 s. There are several differences between different kinds of observation calculation: (1) The tropospheric delays of the ground station observation are corrected by the Saastamoinen model and the GMF function, while no correction is needed for the ISL observation; (2) The first-order ionospheric delays of the ground observation are eliminated by ionospheric-free combination, and the high-order effects are ignored. While there is no ionosphere delay for ISLs between satellites and no correction is needed; (3) The influences of the tide are considered for the ground measurements, while the tide effect does not exist in the ISL measurements.

5 Result and Analyze 5.1

Orbit Determination

The orbit determination results are compared with the reference orbit, and the accuracy statistics are shown in Fig. 6.

The Influence of Station Distribution

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

SatllitePRN

2.5

0.60

Orbiterrorof3S-S-ISLsolution/m

Radial Along Cross 3D

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05

(3) 5S-ISL Radial Along Cross 3D

0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

SatllitePRN

(4) 3S-B-

Radial Along Cross 3D

1.5

1.0

0.5

0.0

0.00

0.00

2.0

0.05

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

0.45

0.40

(2) 8S-ISL

0.60

0.50

0.45

SatllitePRN

(1)8S 0.55

0.50

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

SatllitePRN

Radial Along Cross 3D

0.55

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C m 37 ea n

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 m 7 ea n

0.0

Orbiterrorof3S-B-ISLsolution/m

Radial Along Cross 3D

0.55

Orbiterrorof5S-ISLsolution/m

0.9

0.60

0.60

Orbiterrorof1ASsolution/m

Orbiterrorof8Ssolution/m

1.0

SatllitePRN

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

Radial Along Cross 3D

1.1

Orbiterrorof8S-ISLsolution/m

1.2

67

(5) 3S-S-ISL

SatllitePRN

(6)1AS

Fig. 6. Accuracy statistics of determinate orbit

As seen in the figure: (1) The orbit determination accuracy of 8S solution in radial, along, cross and 3D direction are about 0.13 m, 0.53 m, 0.28 m and 0.61 m. When the ISL observations are added, the accuracy of 8S-ISL solution in radial, along, cross and 3D direction are about 0.02 m, 0.18 m, 0.18 m and 0.24 m, improved for 84%, 66%, 35% and 60% respectively. (2) The orbit determination accuracy of 8S, 5S, 3S-S solution are almost equivalent. The ISL greatly reduces the ground monitoring station number and distribution requirements of the orbit determination. Only a few ground stations are needed to constrain the positional relationship between the constellation and the earth, thereby weakening the rotation and translation of the entire constellation with regard to the earth. (3) The orbit determination accuracy of 3S-B solution are worse than the 3S-S solution. The accuracy in radial, along, cross and 3D direction are about 0.02 m and 0.36 m, 0.36 m and 0.51 m, respectively. This is because the orbit determination requires the common view of more than one monitoring stations at the same satellite, in order to estimate the satellite/station clock. When a station doesn’t have common view of any satellite with any other station, the observation is in valid. Since the distance between the three monitoring stations of 3S-B solution are too long, there are many moments that no common view is available. And the observation deficiency results in a decrease in the accuracy of the orbit. (4) The centralized autonomous orbit determination based on ISL and an anchor station is deployed, and the and the accuracy in radial, along, cross and 3D direction are about 0.04 m, 1.27 m, 1.30 m and 1.83 m, respectively. The main reason of low orbit accuracy is the big orbital in along and cross direction.

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5.2

Orbit Prediction

1.5

1.0

0.5

0.0

0.6 0.5 0.4 0.3 0.2 0.1 0.0

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C m 37 ea n

SatllitePRN

0.6 0.5 0.4 0.3 0.2 0.1 0.0

0.2 0.1 0.0

SatllitePRN

(4) 3S-B-ISL

Radial Along Cross 3D

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

SatllitePRN

Orbitpredictionerrorof1ASsolution/m

0.3

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0.4

0.8

(3) 5S-ISL

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

0.5

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

Orbitpredictionerrorof3S-B-ISLsolution/m

0.6

Radial Along Cross 3D

0.7

(2) 8S-ISL Radial Along Cross 3D

0.7

0.8

SatllitePRN

SatllitePRN

(1)8S 0.8

Radial Along Cross 3D

0.7

2.5

Radial Along Cross 3D

2.0

1.5

1.0

0.5

0.0

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

2.0

0.8

Orbitpredictionerrorof5S-ISLsolution/m

Radial Along Cross 3D

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 m ea n

Orbitpredictionerrorof8S-ISLsolution/m

2.5

C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 2 C3 3 C3 4 C3 5 C3 6 C m 37 ea n

Orbitpredictionerrorof8Ssolution/m

The 24-h orbit prediction results are compared with the reference orbit, and the accuracy statistics are shown in Fig. 7.

(5) 3S-S-ISL

SatllitePRN

(6)1AS

Fig. 7. Accuracy statistics of predicted orbit

Because of the high accuracy of the dynamic model, the reduction of the prediction orbit accuracy is slow relative to the measured orbit. As seen in Fig. 7: (1) The orbit prediction accuracy of 8S solution in radial, along, cross and 3D direction are about 0.25 m, 1.46 m, 0.35 m and 1.52 m. When the ISL observations are added, the accuracy of 8S-ISL solution in radial, along, cross and 3D direction are about 0.04 m, 0.23 m, 0.14 m and 0.27 m, improved for 84%, 84%, 60% and 82% respectively. (2) The orbit prediction accuracy of 3S-B solution are worse than the 3S-S solution as same as orbit determination. The accuracy in radial, along, cross and 3D direction are about 0.04. m, 0.23 m, 0.14 m and 0.27 m, respectively. (3) The centralized autonomous orbit prediction based on ISL and an anchor station is deployed, and the accuracy in radial, along, cross and 3D direction are 0.02 m, 1.16 m, 1.20 m and 1.67 m, respectively.

The Influence of Station Distribution

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6 Conclusion In this paper, the influence of ground monitoring station distribution on the BDS-3 inter-satellite link enhanced orbit determination is analyzed. The results show that, with the ISL, the orbital accuracy based on three monitoring stations separated by several hundred kilometers is almost equal with that based on eight domestic monitoring stations. The ISL greatly reduces the ground monitoring station number and distribution requirements of the orbit determination. Only a few ground stations are needed to constrain the positional relationship between the constellation and the earth, thereby weakening the rotation and translation of the entire constellation with regard to the earth. The centralized autonomous orbit determination and prediction based on ISL and an anchor station are deployed. The orbit determination accuracy in radial, along, cross and 3D direction are about 0.04 m, 1.27 m, 1.30 m and 1.83 m, respectively. The orbit prediction accuracy in radial, along, cross and 3D direction are about 0.02 m, 1.16 m, 1.20 m and 1.67 m, respectively. Acknowledgement. This work is sponsored by National Natural Science Foundation of China (41874039, 41804030 and 41874043).

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Initial Results of BDS3 GEO Orbit Determination with Inter-satellite Link Measurements Zongbo Huyan1,2(&), Jun Zhu1,2, Yanrong Wang2, and Xia Ren3,4 1

State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China [email protected] 2 Xi’an Satellite Control Center, Xi’an 710043, China 3 Xi’an Research Institute of Surveying and Mapping, Xi’an 710054, China 4 State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China

Abstract. Owning to some successful applications of RDSS and RNSS, keeping GEO satellites in BeiDou Navigation Constellation becomes one of the key differences between BDS and other Global Navigation Satellite Systems (GNSS). And for the first time, BDS GEO works as a node of Inter-Satellite Links. It makes precise orbit determination (POD) based on Inter Satellite Ranging (ISR) for GEO possible. Orbit, hardware delay and solar radiation pressure parameters are estimated in POD process. Mean value of estimated hardware delay is 1189.18 ns and STD is 0.15. RMS of post-fit residuals of ISR, between 10 of 18 MEO satellites and GEO satellite is less than 45 cm, and that between the other 8 MEO satellites and GEO satellite is less than 56 cm. RMS of GEO 48-h OOD is no greater than 2.4 m in position and no greater than 0.2 m in radial direction. Keywords: BDS3


Inter satellite link
GEO
Precise orbit determination

1 Introduction BDS-3 constellation is designed to be a 3GEOs + 3IGSOs + 24MEOs global navigation satellite system. Since November 5th 2017, the first pair of BDS3 MEOs was launched, 1GEO + 2IGSOs + 18MEOs have been sent into space by August 31st 2019 [1]. With observations of international GNSS monitoring assessment service (iGMAS) stations, the accuracies of the radial, tangential and normal components of the satellite orbit improved from 8.0, 34 and 37 cm in December 2018 to 1.5, 5.7 and 4.1 cm in July 2019 (Yang et al. [2]). GEO is one of the major differences between BeiDou and other GNSS. With GEO, BeiDou could provide a radio navigation satellite service (RNSS) and a radio determination satellite service (RDSS). In addition to rapid positioning, short message and precise timing services provided by RDSS, BeiDou GEOs significantly improve the Beidou-only positioning accuracy, for the height component particularly (Steigenberger et al. [3]).

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Sun et al. (Eds.): CSNC 2020, LNEE 651, pp. 71–82, 2020. https://doi.org/10.1007/978-981-15-3711-0_7

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Since the ground tracking station are relatively static to GEO satellites, the observation geometry for GEO satellites are worse than that of IGSO and MEO satellites. With the same ground stations, accuracy of GEO precise orbit determination (POD) are lower than that of IGSO and MEO POD (Guo et al. [4]). With satellite laser ranging (SLR) validation, the accuracy of GEO orbit in radial direction is *0.6 m (Guo et al. [5]) or *0.5 m (Montenbruck et al. [6]). Ge et al. [7] used 3-day arcs and nine parameter ECOM solar radiation pressure model (Beutler et al. [8]) to do POD of BDS2 satellites, the 3D root-mean-square (RMS) of overlapped orbit differences (OODs) reached 3.3 m for GEOs and 0.51 m for ISGOs. In order to improve the observation geometry for GEO satellites, Zhao et al. [9] used FengYun-3C onboard BeiDou and GPS data. With global ground stations and GPS data, the averaged 3DRMS of OODs reduced from 354.3 cm to 53.3 cm for GEO. Ge et al. [10] simulated MEO onboard GNSS data, the averaged 3D-RMS of day boundary discontinuities for 5 BDS2 GEO satellites varies from 20 cm to 120 cm with ground tracking data and the onboard MEO data. Massive use of Inter-Satellite Links (ISL) is another great feature of BDS. One big advantage is that ISL breaks the limitation of ground tracking networks. For ISL establishment, BDS-3 satellites are equipped with phased array antenna. Phased array antenna can change direction of beam without attitude control or antenna rotation. Establishment of ISL follows a time division multiple address (TDMA) structure and the time-slot for each link is 3 s. A forward link is established in first 1.5 s and a reverse link in latter 1.5 s. Besides information exchange, ISL also provides high accuracy ranging. Wang et al. [11] found that RMS of ISL ranging errors are less than 0.25 ns with random noise, hardware delay variation and satellite antenna offset modeling errors taken into consideration. Chen et al. [12] proved that ISL ranging contributes to POD and clock. Tang et al. [13] used ISL established among 2 IGSOs, 2 MEOs and 1 anchor station, got radial OODs are