China Satellite Navigation Conference (CSNC 2021) Proceedings Volume I [1] 9789811631375, 9789811631382

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Lecture Notes in Electrical Engineering 772

Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume I

Lecture Notes in Electrical Engineering Volume 772

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

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More information about this series at http://www.springer.com/series/7818

Changfeng Yang Jun Xie •

Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume I

123

Editors Changfeng Yang China Satellite Navigation Engineering Centre Beijing, China

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

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-16-3137-5 ISBN 978-981-16-3138-2 (eBook) https://doi.org/10.1007/978-981-16-3138-2 © Aerospace Information Research Institute 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

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

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

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

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Preface

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

Organization

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

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

Vice-chairman Dun Wang Shuangcheng Zhang Caicong Wu Weiqiang Li

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

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

Beijing Satellite Navigation Center, Beijing, China

Vice-chairman Shaojun Feng Changhui Xu Taosheng Wang

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

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Baoguo Yu Yang Gao

Organization

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

Topic: S03: GNSS and Their Augmentations Chairman Rui Li

Beihang University, Beijing, China

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

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

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

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

Vice-chairman Jianwen Li Jianghui Geng Bofeng Li Xiaolin Meng

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

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

National Institute of Metrology, Beijing, China

Vice-chairman Liang Wang

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

Organization

Lijun Du Xiaohui Li Patrizia Tavella

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

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

Shanghai Jiao Tong University, Shanghai, China

Vice-chairman Haihong Wang Wenbin Gong

Yuxin Zhao Caibo Hu Naser EI-Sheimy

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

Topic: S07: GNSS Signal Processing Chairman Xiaochun Lu

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

Vice-chairman Yang Li

Zheng Yao Xiaomei Tang Sherman Lo

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

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Organization

Topic: S08: GNSS User Terminals Chairman Hong Li

Tsinghua University, Beijing, China

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

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

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

Beijing University of Posts and Telecommunications, Beijing, China

Vice-chairman Jiangning Xu Jinsong Ping

Dongyan Wei Jinling Wang

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

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

Beihang University, Beijing, China

Vice-chairman Miao Tian

China Satellite Navigation Office International Corporation Center, Beijing, China

Organization

Huiying Li

Yuxia Zhou

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

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

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

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

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

Organization

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

Chairman Changfeng Yang

China Satellite Navigation System Committee, Beijing, China

Vice-chairman Yuanxi Yang Shiwei Fan

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

Executive Chairman Jun Xie Lanbo Cai

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

Organization

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

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

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

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Zhijie Chen Zhonggui Chen

Jinping Chen Baojun Lin

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

Organization

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

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

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

Organization

Xiaochun Lu Hong Li Zhongliang Deng Junlin Yang

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

Organizing Committee Director Chengqi Ran

China Satellite Navigation Office, Beijing, China

Deputy Director Jun Yang Xiaohua Qu Yun Xiao

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

Secretary-General Haitao Wu

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

Deputy Secretary-General Weina Hao

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

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

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

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Organization

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

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

Contents

Professional GNSS Applications Application of Human-Machine Collaboration Algorithm for Mine Pile Weight Estimation Based on Beidou High-Precision Location Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bin Chai, Yaozhong Chen, Junming Zhou, Qiang Huang, Changchun Pan, and Shanshan Zhan

3

Train Localization Environmental Scenario Identification Using Features Extracted from Historical Data . . . . . . . . . . . . . . . . . . . . . . . . Tao Zhang, Baigen Cai, Debiao Lu, Jian Wang, and Yu Xiao

12

Research on the Method of Precisely Removing Open Water in the Retrieval of Soil Moisture by Spaceborne GNSS-R . . . . . . . . . . . Wentao Yang, Tianhe Xu, Nazi Wang, Fan Gao, and Yunqiao He

22

Model Establishment of Atmospheric Weighted Mean Temperature in Chongming Eco-Island and Its Application During Typhoon Lekima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaojing Xu, Yu Peng, Wen Chen, Danan Dong, and Chenglong Zhang

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Analysis of COSMIC-2 Atmospheric Boundary Layer Detection Ability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhen Zhang, Tianhe Xu, Fan Gao, Shuaimin Wang, and Song Li

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Soil Moisture Retrieval Based on Satellite-Borne GNSS-R Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiangyang Li, Yongchao Zhu, Tingye Tao, and Juntao Wang

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A New Grid Model for the Vertical Correction of Zenith Hydrostatic Delay for China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ge Zhu, Liangke Huang, Junyu Li, Wei Zhou, Si Xiong, Lilong Liu, Bolin Fu, and Hongchang He

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Contents

Design of Power Inspection System Based on BeiDou Short Message and UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yineng Li, Qinghua Zeng, Jianye Liu, Zhiyu Tian, Rui Xu, and Yizhou Zhang

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Performance Assessment of Bridge Modal Frequency Identification Using High-Rate GNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhao Ren, Wenkun Yu, Wujiao Dai, and Zhaozhe Li

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Deformation Measurement Based on the Phase of Reflected Signals of Beidou GEO Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yan Li, Songhua Yan, and Qinsheng Ma

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Multi-path Error Correction Method for Slope Monitoring Based on BP Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Mengfei Lei, Xiaodong Liang, Jinyi Tang, and Junhua Zhou Application of a Fusion Communication System Based on Beidou Short Message Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Lei Xing, Shuyan Li, and Yangming Wang Simulation Research on ICAO Model Parameters Based on BDS . . . . . 123 Zhimei Yang, Lingling Chen, Qibing Xu, Han Liu, and Lixin Zhang GNSS-IR Soil Moisture Inversion Method Based on Random Forest . . . 133 Yuhua Zhang, Lili Jing, Yanmin Zhao, Hongliang Ruan, Lei Yang, and Bo Sun Tropospheric Delay Modeling Based on Multi-source Data Fusion and Machine Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Song Li, Tianhe Xu, and Nan Jiang Research on Nonlinear Inversion of Vegetation Water Content Based on Multiple Ground-Based GPS-IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Jiyang Li, Yueji Liang, Jiajia Ma, Sidan Xie, and Zhe Wen Investigation of the Characteristics of Tropopause Height Over China Using Recent RO Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Jiaqi Shi, Minghao Zhang, Laga Tong, Erjiang Fu, and Kefei Zhang Research on Train Integrity Monitoring Using Multi-constellation Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Jialei Li, Yongqiang Liu, Wei Jiang, Baigen Cai, and Jian Wang GNSS-R Interpretation of Soil Moisture Scattering Characteristics Simulation Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Zhongmin Ma, Shuangcheng Zhang, Qi Liu, Jilun Peng, Xinyu Dou, Yiming Xue, Boyuan Ma, and Xingtong Chen

Contents

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Research on Digital Elevation Model Using GNSS-IR Technology . . . . . 204 Xin Zhou, Shuangcheng Zhang, Qi Liu, Jilun Peng, Lixia Wang, and Bo Shao Research and Application of Deformation Monitoring Algorithm for Single-Frequency GNSS Low-Cost Monitoring Equipment . . . . . . . . 213 Bin Zhou, Weixin He, Xintong Xu, and Hui Liu Probing the Oceanic Precipitable Water Vapor Evolution Characteristics During the 2020 Tropical Cyclone Maysak Using the GNSS Radio Occultation and Satellite Microwave Radiometry Data . . . 224 Shiwei Yu and Zhizhao Liu Infrared Night Vision UAV Intelligent Patrol System with BDS Flight Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Xianyu Wu, Zhaobao Fang, and Jinbo Rao A Fusion Processing Method for Satellite Detection Data by Beidou Short Message System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Bing Li, Xiao Yu, Xiaojuan Sun, Yuxin Hu, Haiyan Wu, Tao Shi, and Ling Chen Design a Border Management and Control System Based on BD-3 RDSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Lili Zhang, Pengyong Zhang, Wei Hou, Hanxiao Zhou, and Huizi Li New Method of GNSS-R Wind Speed Retrieval Based on Empirical Orthogonal Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Jianming Wu, Yanling Chen, Peng Guo, Xiaoya Wang, Xiaogong Hu, and Mengjie Wu Commercial Vehicle Road Collaborative System Based on 5G-V2X and Satellite Navigation Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Bo Wang, Chunqiang Chen, and Tianchen Zhang GNSS Applications for the Mass Market A TOA-AOA Hybrid Localization Method in 5G Network with MIMO Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Lu Bai, Chao Sun, Hongbo Zhao, Joon Wayn Cheong, Andrew G. Dempster, and Wenquan Feng PDR/GNSS Fusion Positioning Based on Multipath Mitigation . . . . . . . 296 Qiang Liu, Zhendong Dai, Jiuchao Qian, Rendong Ying, and Peilin Liu The Validation and Performance Assessment of the Android Smartphone Based GNSS/INS Coupled Navigation System . . . . . . . . . . 310 Wenlin Yan, Qiuzhao Zhang, Yudong Zhang, Aisheng Wang, and Changsheng Zhao

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Initial Assessment of BeiDou-3 B1I/B1C/B2a Triple-Frequency Signals with Android Smartphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Weikai Miao, Bofeng Li, Guang’e Chen, and Zhong Li Research on Multi-sensor Integration Algorithm Based on the Multi-source Data of Smart-Phone . . . . . . . . . . . . . . . . . . . . . . . 333 Jiawei Chen, Junyao Kan, and Zhouzheng Gao Research on Dynamic Positioning of Android Smartphone Based on Doppler Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Qi Liu, Chengfa Gao, Hua Zou, Yongsheng Liu, and Wu Zhao Modeling of Ambiguity Fixed Multi-GNSS PPP Tightly Coupled with INS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Zhenqiang Du, Hongzhou Chai, Minzhi Xiang, Fan Zhang, Chunhe Liu, and Mingchen Shi Research on Precise Point Positioning Method of BDS-2/BDS-3 Mixed-Frequency Based on Low-Cost u-blox . . . . . . . . . . . . . . . . . . . . . 367 Qiang Li, Liang Li, Fuxin Yang, Xiaosong Liu, and Lin Zhao Intelligent Driving BDS High-Precision Navigation System Performance Requirements and Verification . . . . . . . . . . . . . . . . . . . . . 379 Liduan Wang, Zuohu Li, Xijiang Wang, and Jun Mao Low-Cost Dual-Antenna GNSS Precision Heading Determination Method with Baseline Length Constraint . . . . . . . . . . . . . . . . . . . . . . . . 389 Yang Li, Lin Zhao, Chun Jia, Liang Li, and Bin Ji Indoor Fingerprint Positioning Method with Standard Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Jingxue Bi, Hongji Cao, Guobiao Yao, Zhe Chen, Jingchun Cao, and Xinru Gu The Constrained Algorithm of Tightly Coupled GPS/SINS in Case of Insufficient Number of Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Mingchen Shi, Hongzhou Chai, Minzhi Xiang, Zhenqiang Du, and Chunhe Liu Analysis of Triple-Frequency Multiple Combination Differential Positioning of BDS-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Huichao Shao, Xiangxin Guo, Yanbai Liu, Zhen Tu, and Jian Liu A Real-Time Indoor Positioning System Based on Wi-Fi RTT and Multi-source Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Lu Huang, Baoguo Yu, Jun Li, Heng Zhang, Shuang Li, and Haonan Jia

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Satellite Orbits and Precise Positioning Accuracy Analysis of the Calibration Satellite Orbit Determination Based on Onboard BDS Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Chong Wang, Jun Zhu, Jie Li, Kai Guo, Yanan Fang, Han Lei, and Ying Ci Assessment of GPS/BDS Precise Point Positioning Performance with BDS-3 New Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 Zan Liu, Zengke Li, Chengcheng Wang, Zhehua Yang, and Xiangsheng Yang BDS-3 Triple Frequency Satellite Inter-frequency Clock Bias Estimation and Its Effects on Precise Point Positioning . . . . . . . . . . . . . 473 Sijie Lyu, Yan Xiang, Wenxian Yu, and Wei Wang A Method of Switching the Different Responding Beams Smoothly of RDSS in the BDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Xiaojie Li, Qinghui Tang, Rui Guo, Chengpan Tang, Shuai Liu, Hui Ren, Jie Xin, Jinglei Guo, Yijun Tian, and Yukuan Wu Research on the Influence of Pseudo-range Biases on Precise Orbit Determination and Clock Error Calculation for Beidou Navigation Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Chengeng Su, Gong Zhang, and Jun Lu Satellite Laser Links Pointing Accuracy Analysis Methods . . . . . . . . . . 502 Zheng Song, Ping Wang, Chengbin Kang, Jianxin Guo, and Huichao Zhou An Optimal Stations Network Method for Precise Orbit Determination of BDS2/BDS3 Heterogeneous Constellations . . . . . . . . . 511 Kun Li, Huicui Liu, Bing Ju, Qianxin Wang, and Jianfeng Cao Navigation Performance Analysis of LEO Augmented BDS-3 Navigation Constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 Xing Su, Hanlin Chen, Junli Zhang, Tao Geng, Zhimin Liu, Xin Xie, and Qiang Li A Method of Satellite Precise Clock Corrections Prediction Based on SSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Qingbo Zhao, Lin Zhao, Fuxin Yang, Jie Zhang, and Liang Li Research on Real-Time Precise Point Positioning Method Based on Short Message Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 Runxi Yang, Liang Li, Fuxin Yang, Jie Zhang, and Lin Zhao A Whole-Net Positioning Method Based on Baseline Optimization Selection in Multi-vehicle Cooperative System . . . . . . . . . . . . . . . . . . . . 560 Shan Hu, Hongbo Zhao, Chen Zhuang, and Yuli He

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Hardware-In-the-Loop Simulation of Real-Time Precise Orbit Determination for Differential InSAR Satellites Using BDS-3 B1C/B2a Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 Lun Ai, Wanwei Zhang, Bin Zhong, Fuhong Wang, Xuewen Gong, and Ruwei Zhang The AR Model with Trend Item and the Corresponding Algorithm of AO Detection and Satellite Clock Error Prediction . . . . . . . . . . . . . . 584 Songhui Han, Yisong Gong, Jianwen Li, Guozhong Li, Xinna Li, and Jie Guo The ERP Prediction Method Based on Phase Space Reconstruction Theory and Volterra Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Hailong Xu, Shubo Qiao, and Jiale Lin Performances Analysis of Tightly-Combined Multi-system RTK Positioning with BDS-3/GPS/Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 Song Zhu and Wei Li A Super-Long-Term Prediction Method of Earth Polar Motion Based on Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619 Weitao Lu, Lue Chen, Zhijin Zhou, Songtao Han, and Tianpeng Ren Availability and Prediction Performance Evaluation of BDS-3 Satellite Clock Error Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 Guo Chen, Yaping Gao, Wenju Fu, Xi Chen, and Jiali Yang Comparative Analysis of Beidou Single and Dual Frequency Positioning Accuracy Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 Lei Chen, Hongliang Cai, Ling Pei, Yinan Meng, Wei Zhou, and Tianlin Zhu Augmenting GNSS PPP Accuracy in South China Using Water Vapor Correction Data from WRF Assimilation Results . . . . . . . . . . . . . . . . . . 653 Yangzhao Gong, Zhizhao Liu, Pak Wai Chan, and Kai Kwong Hon The Precise Point Positioning Algorithm and Its Performance Evaluation Using Combined BDS-3 and BDS-2 . . . . . . . . . . . . . . . . . . . 671 Lun Ai, Jie Wu, Binbin Wang, Ruwei Zhang, and Wei Li Research on Orbital Position Adjustment Control Strategy of Beidou IGSO Satellite Based on Differential Evolution Algorithm . . . . . . . . . . . 681 Ying Zhang, Dingwei Wang, Quanjun Li, Lei Shi, and Yingying Zhang Performance Analysis of Real-Time PPP-RTK with Multi-scale Enhancement Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690 Lihua Wan, Xiaomeng Wu, Peng Zhang, Qi Zeng, Huijun Guo, Renpan Wu, and Yue Xu

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The Median Method of Gross Error Elimination in Multi-satellite Precise Orbit Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Yufei Yang, Chong Li, Maolei Wang, Zhixue Zhang, Shuxin Jin, Liwei Zhang, and Linze Li Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715

Professional GNSS Applications

Application of Human-Machine Collaboration Algorithm for Mine Pile Weight Estimation Based on Beidou High-Precision Location Service Bin Chai1, Yaozhong Chen1, Junming Zhou1, Qiang Huang2,4, Changchun Pan2,4(&), and Shanshan Zhan3 1

MCC Baosteel Technology Services Co., Ltd., No. 1 Baoquan Road, Baoshan District, Shanghai, China 2 Shanghai Key Laboratory of Navigation and Location Based Services, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Minhang District, Shanghai, China [email protected] 3 Shanghai Real Estate School, No. 588, Gaojing Road, Xujing Town, Qingpu District, Shanghai, China 4 Automation Department and Shanghai Key Laboratory of Navigation and Location Based Services, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Minhang District, Shanghai, China

Abstract. The terminal yard is a site used to stack bulk mineral materials. When users need, they need to estimate the weight of the mineral material pile before loading. If there is too much or insufficient mineral material, short barge trucks need to be used for stacking, allocating, and clearing to increase the field capacity and transfer efficiency of the yard. Accurate pile quality estimation can effectively reduce the use times of short-distance trucks and reduce yard operating costs. Unlike traditional yard weight estimation, which requires accurate measurement of the volume of the pile, we use comprehensive processing technology based on Beidou high-precision positioning and UAV (Unmanned Aerial Vehicle) shooting high-precision image, combined with open source software (OpenDroneMap) to quickly obtain the rough volume. Then a SVM (Support Vector Machine) high-precision quality estimation model with 8 variables including volume will be established by manually inputting 7 variable factors of pile proportion, moisture content, ore pile height, iron ore form, month, and stacking time. Through actual data verification and analysis, the estimation error is less than 4.5%. Compared with the 20% error of manual experience, it greatly reduces the labor burden and the management cost caused by the inaccurate estimation. Besides, it also improves the management level of the material yard estimation. Keywords: Yard estimation
Beidou high-precision positioning variable selection
SVM modeling


Multi-

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 3–11, 2021. https://doi.org/10.1007/978-981-16-3138-2_1

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1 Introduction Majishan Port is a distributed terminal of large deep water port in China, with an annual operation volume of more than 60 million tons. Due to the limitation of the area of the pileyard, the uncertainty of the quantity of the cargo of the client each time, and the inability of changing the belt conveyors at will, it is necessary to estimate the quality of the material in the pileyard from time to time and use the short barge truck with a load of 20 tons to stack, allocate, and empty the material in the pileyard in order to improve the utilization rate of the dockyard. For example, a cargo ship needs to carry 5000 tons of certain mineral materials. The on-site management personnel of the storage yard estimates that the material pile is 4000 tons according to the area and height of the material pile, and then transfers 1,000 tons from other material storage vehicles. The actual quality of the mineral material loaded on the ship is finally determined by the commodity inspection based on the depth of the ship’s waterline. It is easy to cause estimation error due to manual experience, resulting in more or less of the mineral material that is being transported on the pileyard. Through historical data analysis, compared with the commodity inspection value, the error estimated by manual experience is about 20%, causing a lot of waste of labor, machine damage, fuel costs and other resources. The mass calculation of the pile is the volume multiplied by the specific gravity of the pile without considering the moisture content of the pile. If the moisture content of the pile is considered, the mass of moisture must be subtracted. Because the shape of the pile is not a standard cone or cube, and the volume of general minerals is relatively large, some piles can stretch for several kilometers in length, and the specific gravity of the pile will vary depending on the type of minerals, even the same material type will change due to the quarterly time difference. More importantly, the bottom of the mineral material is heavily affected when the mineral materials are piled together. The gap between the mineral materials is squeezed, resulting in uneven distribution of the heap proportion. Therefore, in the traditional calculation formula, volume acquisition and heap specific gravity error correction are difficult problems that restrict the accuracy of estimation. In view of how to improve the accuracy of pile quality estimation, domestic scholars have proposed some practical methods with reference value. By comparing the traditional visual inspection method, weighing measurement method, total station triangulation surface fitting method, digital close-range photogrammetry, etc., it is pointed out that the use of photogrammetry for material estimation is the mainstream of development [1]. At the same time, some researchers further elaborated on processing principles like digital image matching and three-dimensional model [2]. In the past few years, with the development of the application of UAV and 3D lidar, there were researches on using lidar to estimate the volume of piles [3] and using UAVs to obtain 3D models of piles based on image control point layout [4]. Most of these studies focused on estimating the mass of the pile with the volume of the pile as the core, but lacked analysis of the influence of factors such as moisture, pile proportion, and natural settlement on the quality of the pile.

Application of Human-Machine Collaboration Algorithm

5

This paper uses low-cost Beidou high-precision UAV image acquisition without image control points. Open source software is used to extract image point cloud information and build a three-dimensional model of the pile body, then establish a calculation grid of the pile body aerial triangulation network to obtain high-precision pile body volume information. Using machine learning to integrate factors such as volume, moisture, pile proportion, natural settlement and the final commodity inspection value recognized by the customs, an intelligent quality estimation model is established to reduce measurement errors. 1.1

Volume Calculation of Piles Based on Beidou High Precision and UAV Photography

1.1.1 Yard UAV Image Collection Through comparative analysis, the UAV has the advantages of low cost and simple operation in data collection at the pileyard. In this paper, the purchased DJI Hexa-rotor UAV M600 Pro is used as the carrier platform for the image collection of the pile. The M600 Pro has problems such as the camera lens that supports automatic zoom, the poor positioning accuracy of the meter-level GPS (Global Positioning System) positioning module, and the short remote control distance of the remote control hand using an omnidirectional antenna, which cannot meet the high-precision data collection requirements of the stockpile. Therefore, the UAV carrier platform needs to be modified. The UAV hand remote control adds a signal enhancement amplifier to ensure good communication signal quality without obstruction within 10 km. Install antennas and receivers that support the reception of Beidou observation data, and add support for fixed-focus lens mounting on the UAV mounting platform according to the bracket. The multi-mode and multi-frequency satellite signal receiver uses the u-blox M8 series, which supports Beidou/GPS/GLONASS (Global Navigation Satellite System) multimode and multi-frequency satellite signal acquisition. It can receive more satellite signals and can receive data from more than 6 satellites at the same time to ensure the quality of the original observation data from the received satellites. The camera lens is SONY, set to fixed focus mode, equivalent focal length 35 mm, image resolution 6000 * 4000, meeting the needs of high-definition data collection. According to the parameters of the UAV lens, flight speed, etc., according to formula (1), set the UAV flight altitude. HðmÞ ¼ f ðmmÞ 

GSDðmÞ aðmmÞ

ð1Þ

In the formula (1), H is the relative measured ground flying height, f is the focal length of the camera lens, GSD is the ground resolution of the image, and a is the pixel size. According to the requirements of measurement accuracy, the ground resolution of the stack is selected to be 0.05 m–0.1 m, so the maximum available flying height is limited to 500 m. Combined with auxiliary facilities such as the storage yard’s maximum height of 13 m and the surrounding 30 m high light racks, the flying height of the drone is set to 60 m.

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The images collected by UAV need a certain degree of overlap to ensure the quality of image stitching. The degree of overlap is divided into standard overlap degree and heading overlap degree. The relevant low-altitude photography specifications require: heading overlap greater than 53%; side overlap greater than 8%. If in areas with high floors and complex building structures, the degree of overlap should be appropriately increased. In this paper, when the UAV collects images, the heading overlap and the side overlap are set to 70%, to ensure that the camera can still get high-precision data even when the pile is partially obscured by the stacker (Fig. 1).

Fig. 1. Modified UAV(left) and on-site operation(right)

1.1.2 UAV Image Location Calibration and Volume Calculation Based on Beidou PPK The GPS single-point positioning accuracy of the DJI M600 Pro is at the meter level. If the GPS single-point positioning accuracy is directly used, the images taken by the UAV will have serious image distortion problems when stitching and calibration, which cannot meet the application requirements. Therefore, the conventional method is to select landmark corners or intersections in the ground area photographed by the drone, and use the RTK (Real-Time Kinematic) integrated machine to survey and map the three-dimensional coordinates of the image control points. In order to avoid setting up measurement image control points, reduce cost investment, and reduce UAV load, this paper uses UAV PPK (Post-Processing Kinematic) post-processing technology to obtain high-precision image position information. Through the fusion and processing of UAV flight position data and ground base station data, PPK can improve the accuracy and efficiency of 3D position data acquisition of UAV without setting up image control points. It can obtain high-precision positioning with plane accuracy of ±5 cm and elevation accuracy of ±10 cm, as shown on the left in Fig. 2. After obtaining high-precision position data, use the captured pictures, camera position and posture, and internal calibration scenes to generate a 3D point cloud of the storage yard. Then use MVS (MultiView-Stereo, mesh density reconstruction) to encrypt and calculate the 3D point cloud data produced by SFM (Structure From Motion) to produce a textured mesh model. Finally, OBJ files, corresponding MTL and texture files are obtained. According to the required conditions such as the number of processed photos, processing time, and Meshroom computing performance, we built the hardware

Application of Human-Machine Collaboration Algorithm

7

platform required for computing: Inter 9900K for CPU, 2080 Ti for GPU computing platform, 64G memory, 1T SSD M.2. The calculation result is shown on the right in Fig. 2. Through experimental comparison in Table 1, the calculation volume error between 0.1 m and 0.05 m is less than 0.5%, while the calculation time for 0.05 m is about 10 times that of 0.1 m. Because the calculation error is relatively small and the calculation speed is relatively large, the 0.1 m grid is selected for calculation. Table 1. Mesh density and volume accuracy error statistics Heap Nu. 0.1 m mesh volume (m3) H15/23 6584 G12/24 12874 B78/98 20983

0.1 m mesh volume (m3) 6613 12923 20892

Absolute error 0.44% 0.38% 0.43%

Fig. 2. PPK processing principle diagram (left) and 3D model of storage yard (right)

1.2

Volume Calculation of Piles Based on Beidou High Precision and UAV Photography

1.2.1 A Model for Estimating the Mass of Piles Based on Machine Learning SVM can use historical data for learning, so that the model can continuously improve its own performance and achieve infinitely close to real behavior. This paper adopts the machine learning method of SVM, which is based on the principle of structural risk minimization, which can improve the generalization ability of the learning machine and can obtain smaller errors [5, 6]. SVM is proposed for classification problems, but it can also be used for regression analysis after modification. When SVM is used for regression analysis, it is also called SVR (Support Vector Regression), which is an important application branch in SVM. When SVM is used for regression analysis, there is only one type of data points, and the optimal hyperplane is to minimize the total deviation of the data points from the

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Fig. 3. SVM model of pile

hyperplane, instead of separating different types of data points as much as possible during classification. In the heap mass estimation model, the input is 8 important variable factors, namely proportion, volume, ore form, water content, air humidity, height, month and storage time, which are recorded as X ¼ fx1 ; x2 ; x3 ; x4 ; x5 x6 ; x7 ; x8 g. The output result is the mass of the pile Y. The model function is denoted as Y ¼ f ðXÞ (Fig. 3). Given a sample fXi ; Yi gði ¼ 1; 2. . .8Þ, N is the sample size. Since it is uncertain whether it is a linear model, it is treated as a nonlinear model. Each sample point is mapped to a high-dimensional space using a nonlinear function u, thereby performing linear regression. The function f is: f ðXÞ ¼ xT uðX Þ þ b

ð2Þ

In the formula (2): x is the weight vector and b is a constant. Both x and b are unknown, which are mainly confirmed by the following function: 8 1 1X min RðCÞ ¼ kxk2 þ C Le ½Yi ; f ðXi Þ 2 8 i¼1

( Le ½Yi ; f ðX i Þ ¼

jYi  f ðX i Þj  e; j Yi  f ðX i Þj  e 0; j Yi  f ðX i Þj\e

ð3Þ ) ð4Þ

In the formulae (3) and (4): C is a constant, used to balance model generalization ability and training error; Le is an insensitive loss function; e is a precision parameter. In order to reduce the model error, slack variables ni and ni* are introduced: 8  X   1  ni þ ni ; C [ 0 min L x; ni ; ni ¼ kxk2 þ C 2 i¼1

ð5Þ

Application of Human-Machine Collaboration Algorithm

 s.t

Y i  f ð X i Þ  e þ ni ; ni [ 0 f ðX i Þ  Yi  e þ ni ; ni [ 0

9

ð6Þ

Introducing Lagrangian multipliers, Lagrangian function can be obtained: 8  8  X  X  1 L ¼ kxk2 þ C ni þ ni  gi ni þ gi ni 2 i¼1 i¼1



8 X

ai ðe þ ni  Yi þ f ðX i ÞÞ

i¼1

8 X

ai



e þ ni

 þ Yi  f ð X i Þ

ð7Þ

i¼1

In the formula (7): ai [ 0; ai [ 0; gi [ 0; gi [ 0. Using the dual problem to solve, the final function f can be written as: f ðX Þ ¼

8  X

 ai  ai K ðX i ; X Þ þ b

ð8Þ

8  X  ai  ai K ðXi ; X Þ

ð9Þ

i¼1

b = Yi þ e 

i¼1

  In the formulae (8) and (9): K Xi ; Xj is the kernel function satisfying     K X i ; Xj ¼ uðX i ÞT u Xj . 1.2.2 Actual Application Effect It can be seen from the above model that the main factors affecting SVM are the kernel function K, the accuracy parameter e, and the parameter C. In the choice of kernel function, the commonly used RBF kernel is used:   ! Xi X j 2   K X i ; X j ¼ exp   ð10Þ 2r2 The corresponding parameter is r. Therefore, in this model, the parameters that need to be manually set are (r, e, C). By modifying the parameter combination for experimental comparison, it is found that the effect is better when the parameter is (0.125, 0.2, 0.9), so the parameter is selected as (0.125, 0.2, 0.9). In the construction of the algorithm model, the sklearn machine learning library in Python is mainly used. For model verification, a 5-fold cross-validation method is used. The size of the test set used to detect the effect of the model is 40, including 13 kinds of mineral materials, the heap proportion is between 2.3–2.8t/m3, the moisture content is between 3%–8%, and the quality range of commodity inspection is 20070t– 116986t. The artificial experience of the detection model and the statistical results of the error estimated by the model are shown in Table 2. The final quality verification

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B. Chai et al. Table 2. Test verification human experience and model estimation error statistics

Type

Proportion (t/m3) OCL-S 2.4 OCS-S 2.7 OFG-N 2.4 OFK-S 2.45 ONM-N 2.44 ORU-S 2.55 OCL-S 2.4 OFW-S 2.12

Water Official content (%) value (t) 3.66 39940 8.1 50136 7.42 34282 3.0 2500 3.0 54459 3.0 24729 3.0 59921 3.0 20070

Human value (t) 33000 57900 41000 2000 64000 21000 69000 16000

Model value (t) 38655 48038 32930 2426 55640 23665 61802 19351

Human error (%) − 16.10 15.50 19.60 −20.00 17.52 −15.08 15.15 −20.28

Model error (%) −3.22 −4.18 −3.94 −2.97 2.17 −4.3 3.14 −3.58

error of the pile is less than 4.5%, which is 4 times higher than the artificial error of 20%. According to the principle of the algorithm model, as time goes by, when the accumulated model learning samples are more, the accuracy of the SVM estimation model will be higher, so the estimation error of the future pile quality will become smaller and smaller. At present, the algorithm has been put into the actual test stage and achieved good results, as shown in Fig. 4 below.

Fig. 4. Web service interface of piles intelligent estimation system (left) and practical scenarios (right)

Application of Human-Machine Collaboration Algorithm

1.3

11

Conclusion

In this paper, the Beidou PPK and UAV aerial photogrammetry technology is used to realize the accurate calculation of the stack volume of the terminal yard. By establishing the SVM estimation model method for the seven variable parameters of the stack, the estimation accuracy of the stack quality is about 4.5%. Which greatly improves the accuracy of pile quality estimation, effectively reduces the operation and management costs caused by manual experience estimation errors, and improves the intelligent management level of the pileyard. Because the use of UAV to collect image data of the pile still has the problem of weather and environmental factors and the response speed is not real-time, the next step can be to install video + lidar on the surrounding infrastructure of the pileyard to achieve all-weather monitoring of the pileyard., Real-time quality management. Combined with the current BDS global service capacity improvement [7], satellite error accuracy further reduction [8], mobile BDS positioning accuracy improvement [9] and other technologies, in the future, more convenient and higher estimation accuracy of the stockpile estimation service can be realized in the dock yard. Acknowledgements. The paper was partially supported by the National key research and development program #2019YFB1705800.

References 1. Lv, G., Yanchao, X., Liu, X.: Method of measuring material weight in concentrate Bin in Miaogou iron ore mine. Min. Eng. 10(04), 66–67 (2012) 2. Wang, L.: Theoretical Research and Practice of Digital Close Range Photogrammetry Technology. Information Engineering University (2002) 3. Yang, D.: The Research of Key Technology on the Volume Measurement of Large and Medium Bulk. Dalian Maritime University (2017) 4. Lei, Y.: Aerial Photogrammetry of Multi-Rotor Unmanned Aerial Vehicle Stacking measurement. Xi’an University of Science and Technology (2017) 5. Zhao, D., Wang, H., Yin, H., et al.: Person re-identification by integrating metric learning and support vector machine. Signal Process. 166, 107277 (2020) 6. Ludwig, B., König, D., Kapusta, N.D., et al.: Clustering suicides: a data-driven, exploratory machine learning approach. Eur. Psychiatry 62, 15–19 (2019) 7. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 8. Yan, X., Li, W., Yang, Y., Pan, X.: BDS satellite clock offset prediction based on a semiparametric adjustment model considering model errors. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-019-0007-z 9. Xia, Y., Meng, X., Yang, Y., Pan, S., Zhao, Q., Gao, W.: First results of BDS positioning for LBS applications in the UK. Satell. Navig. 2(1), 1–19 (2021). https://doi.org/10.1186/s43020021-00035-1

Train Localization Environmental Scenario Identification Using Features Extracted from Historical Data Tao Zhang1(&), Baigen Cai2, Debiao Lu1, Jian Wang1, and Yu Xiao3 1

Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transport, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China [email protected] 2 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China 3 Department of Communications and Networking, School of Electrical Engineering, Aalto University, Espoo, Finland

Abstract. The application of Global Navigation Satellite System (GNSS) on the railway greatly reduces the cost on train localization. However, the railway environment is complex and changes with the train movement, buildings, trees, railroad cuts and mountains will block and reflect the GNSS signals, which will bring errors to the GNSS-based train position estimation. This paper proposes a railway scenario identification method based on historical GNSS receiver observation data to identify scenarios along the railway. Firstly, a railway environment scenario parameter model library is established according to Feature of Sky Occlusion (FSO) of typical scenarios, apply historical GNSS observation data along the railway to establish the FSO models of scenario segments, and generate FSO feature sequences. The dynamic time warping algorithm (DTW) is used to match the FSO parameter model of the scenario segment with the FSO model library. This paper collected data from field experiments at Beijing Sanjiadian station to verify the algorithm. The scenario identification results showed that the scenario identification method based on DTW can effectively identify the railway scenarios. Keywords: Train localization
GNSS
Feature of sky occlusion time warping algorithm
Scenarios identification


Dynamic

1 Introduction China railway network covers a wide range of the country and the train operation environment is complex. Real-time and accuracy train location performances are the guarantee for safe train operation. With the modern development of train operation control system, higher requirements are put forward for the positioning performance. GNSS has high accuracy / reliability and has been introduced into the railway field for train positioning, timing, and track survey etc. [1].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 12–21, 2021. https://doi.org/10.1007/978-981-16-3138-2_2

Train Localization Environmental Scenario Identification

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In open environments, satellite navigation signal reception is good, GNSS positioning can meet the railway positioning requirement. However, during the operation of the train, through various scenarios, including forests, valleys, road cuts, urban canyons, tunnels, etc., which lead to limited satellite navigation signal propagation, resulting in different degrees of degradation or even failure of GNSS-based train positioning [2]. Different degradation degrees of satellite positioning can be described by quantitative methods through parametric modelling of railway scenarios, and establishing environmental scenario models based on Feature of Sky Occlusion (FSO), using satellite azimuth, altitude and signal observation parameters such as intensity describe the occlusion boundary of the sky [3]. Identify the railway scenario according to the FSO parameter model and evaluate the satellite positioning performance. This paper classifies railway scenarios according to FSO, proposes a satellite positioning environment scenario identification method in train operation scenarios, establishes a railway environment scenario FSO parameter model library and a railway scenario segment parameter model, and uses historical railway receiver observation data to this method authenticating.

2 FSO Model of Railway Scenarios 2.1

Railway Scenarios Classification

The environmental scenarios along the railway mainly include plains, mountains, cities, forests, etc. Due to varying degrees of occlusion and reflection of satellites, the positioning performance are different in each type of environmental scenario. According to the FSO of the railway environment scenario, the satellite positioning scenarios along the railway can be categorized into 5 kinds: Unobstructed scenario (S1): No objects on both sides of the track block the satellite signals, and the positioning performance is good. Shallow occlusion on both sides scenario (S2): There are low mountains, buildings, and other occlusions on both sides of the track, which will occlude satellites with low elevations, and will reduce the number of visible satellites and reduce the satellite positioning performance. One side is deep and the other side is shallowly occluded scenario (S3): One side of the track is blocked by mountains or tall buildings, and the other side of the track is obscured by a low target. Depth occlusion on both sides scenario (S4): There are high slopes, mountains, tall buildings and other targets on both sides of the strand, he receiver can only receive high-elevation satellites. Fully obscured scenario (S5): The tunnel scenario, in which the satellite signal is fully occluded, and the satellite positioning is invalid. As shown in Fig. 1, skyplot of the S1–S5 scenarios covered by the occlusion degree is presented. The grey part represents the occluded sky.

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S1

S2

S3

S4

S5

Fig. 1. Skyplot with occlusion for designated 5 railway scenarios

2.2

Construct FSO Model Library

The FSO parameter model is a 360-dimensional discrete sequence that parameterizes the sky occlusion boundary of the railway environment scenario [4]. The FSO of different types of railway environment scenarios have their own distinct characteristics. To accurately identify the railway environment scenarios, this paper idealizes the FSO of the S1–S5 scenarios. The sky occlusion boundary of scenario S2–S4 contains linear boundary as an assumption, so the parameters of geometric model are ideally set as linear boundary for more compliable model libraries. As shown in Fig. 2, l represents the distance from point O to boundary AB, R represents the radius of sky plot, and h represents Azimuth. The scenario parameter model sequence is sampled with the azimuth resolution at 1°, and the formula (1) represents the relationship between elevation and azimuth of the straight-line boundary of the sampling sequence. The value range of h is in the range of 0° to 90°, and FSO parameter models of S2–S4 scenarios are constructed through symmetry. elei ¼ 90  ð1 

x Þ R
cos hi

Where, hi ¼ ð0; 1;


; ½arccosð1  Rx ÞÞ. A

R

O

l

B

Fig. 2. Model of sky occlusion line boundary description

ð1Þ

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The FSO parameter models of the S1–S5 scenarios constitute the FSO parameter model library ϒ = (H1, H2, …, H5), where H = (h1, h2, …, h360). The FSO parameter of each scenario is a 360-dimensional discrete sequence, representing the elevation of the sky occlusion boundary corresponding to 360 azimuths. 2.3

FSO Modeling of Scenarios Along the Railway Based on Observation Data

The scenario along the railway can be ideally regarded as composed by S1–S5 scenario segments alternately. The idea of differentiation between S1 to S5 can be used to divide the railway scenario into several short scenario segments, and the scenario type of each scenario segment is identified, finally the scenario composition is determined for the entire trajectory. According to the digital track map (DTM) the scenarios along the railway are segmented into scenario segments at equal intervals S = {seg1, seg2, …, segn}, as shown in Fig. 3. seg n

2

seg n

seg1

1

seg n seg 2

seg3

Fig. 3. Schematic diagram of the division of scenarios along the railway

According to the observation data, the satellite information of all epochs in each scenario segment is extracted [5]. Extract the total number of visible satellites in the current epoch, visible satellite pseudo-random noise (Pseudo-Random Noise, PRN), elevation, azimuth, signal-to-noise ratio. Assuming that a total of n scenario segments is divided, i denote the ith scenario segment, and j denote the jth visible satellite in the ith scenario segment. In the ith scenario segment, the number of visible satellites is SVij, and the elevation ELij, azimuth AZij, and signal-to-noise ratio SNRij corresponding to the jth visible satellites are extracted. Each scenario segment can be described using a set of parameter vector as Xi ¼ fSVi ; fELij ; AZij ; SNRij jj ¼ 1; 2;


SVi gg. Due to the inclination of the satellite trajectory, the receiver can only receive satellites with high elevations in the range of 0°–30° azimuth and 330°–360°, so only satellites within 30°–330° are considered for identification in this paper. The algorithm flow of FSO model sequence construction is shown in Table 1. The FSO parameter model of each scenario segment is a 300/k-dimensional elevation sequence, k is the azimuth resolution.

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T. Zhang et al. Table 1. Railway environmental feature parameters construction algorithm Input: a set of segment information of a given line scenario, Γ= {Ω1, Ω2, …, Ωn} Output: FSO parameter model collection of scenario segment, Ψ= {φ1, φ2, …, φn} 1. Set the azimuth division range; 2. Divide the azimuth range of the skyplot from 30° to 330° into α regions;； 3. For i=1 to n do 4. Eliminate low elevation and low signal-to-noise ratio satellites to get the set Γ′Γ′； 5. For m=1 to α do 6. Traverse Γ′ and get the satellite elevation set {ELim} according to (m-1)⋅300/α≤ AZ > > Xi ¼ X  X  2  1 > max min > > < Yi  Ymin 0 Yi ¼ 21 > Ymax  Ymin > > > > Z  Zmin > : Zi0 ¼ i 21 Zmax  Zmin

ð4Þ

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Xi ; Yi ; Zi is the ith monitoring result, Xmin ; Ymin ; Zmin is the minimum value of monitoring result, Xmax ; Ymax ; Zmax is the maximum value of monitoring result, Xi0 ; Yi0 ; Zi0 is the normalized monitoring result. (3) Network topology structure determination method: according to the results of sample data training, we calculate the root mean square error rmse, adjust the number of neurons and network weights in different hidden layers, and then recalculate rmse. After repeating several times, we select the minimum number of neurons and network weights in rmse as the optimal network topology structure; vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u X u1 n ðp j  o j Þ2 rmse ¼ t n j¼1

ð5Þ

In formula 5, n is the predicted number of points, o is the expected output of the network, and p is the actual output of the network.

3 Experimental Analysis The monitoring data comes from a project in Wangcheng District of Changsha from June 29, 2020 to August 11, 2020 of. In the example, Fourier transform, BP neural network and Kalman filter algorithm are implemented by MATLAB, and the monitoring results in the north direction were used for testing. (1) The original monitoring results of this period are shown in the figure below:

Fig. 2. Time series of original monitoring results

As can be seen from the Fig. 2, the fluctuation of the original results of monitoring point is about ±5 mm, and the displacement of the monitoring point is about −10 mm from July 9, 2020 to August 11, 2020. Due to the large fluctuation of the monitoring results, the specific displacement cannot be directly seen.

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Fig. 3. The ratio value of monitoring results

As can be seen from the Fig. 3, the value of ratio can reflect the reliability of the integer ambiguity resolution in the calculation process. The fluctuation of the original results of the monitoring point is about ±5 mm, and the displacement of the monitoring point is about −10 mm from July 9, 2020 to August 11, 2020. Due to the large fluctuation of the monitoring results, the specific displacement cannot be directly seen.

Fig. 4. The number of satellites in monitoring results

As can be seen from Fig. 4, the number of satellites at the monitoring point is at least 14, at most 24, and the average value is about 19. The number of satellites shows a relatively strong periodic change. (2) Polynomial is used to interpolate the original data in Fig. 2 to complete the missing data, and then Fourier transform is carried out for the monitoring data to draw the spectrum diagram as follows (Fig. 5):

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Fig. 5. Spectrum diagram of monitoring results

It can be seen from the spectrum figure that the amplitude of low-frequency signals is large. The period and amplitude information of periodic signals with large amplitude in the spectrum figure are extracted, and the specific values are shown in the table below: Table 1. The results of spectrum analysis Frequency (Times/Hour) Amplitude (mm) Period (h) 0.047 1.24 21.27 0.092 0.615 10.86 0.175 0.238 5.71 0.267 0.263 3.74

As can be seen from Table 1, among the four relatively obvious periodic signals, the signal amplitude of 21.27h is larger, so only the signal with a period of 21.27h is considered in the model correction in this paper. (3) Sample data are used for training and the prediction of multi-path error model. Since the period of the signal is 21.27h and the time interval of the monitoring results is 0.5h, so there are about 42 results for a period. The first 420 results are selected as training samples, and the 421–504 results are taken for prediction verification.

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Fig. 6. Comparison of model results with monitoring results

Fig. 7. Monitoring results after correction

As can be seen from the prediction results in Fig. 6, the change curve of predicted multi-path error model has a high coincidence with the actual monitoring results. As can be seen from Fig. 7, except for the fluctuation of about 5 mm at some time points, the fluctuation of other time points is less than 2 mm, and the correction effect is obvious. (4) Established model is adopted to correct the data of June 29, 2020 to August 11, 2020, and then the Kalman filter algorithm is used to filter the corrected results. The processed results are as follows:

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Fig. 8. Time series of monitoring results after correction

As can be seen from Fig. 8, most periodic errors of the original monitoring results have been eliminated after error correction and filtering. Both accuracy and the fluctuation of the monitoring curve are well improved, and the mean square error is reduced from 3.2 mm to 1.4 mm,. It can be seen from the corrected time series that the monitoring point began to move around July 9th, and the overall displacement situation and values are consistent with those before data processing. The processed monitoring data can reflect the deformation situation of the monitor more accurately, and provide assistance for the technical personnel to judge the status of the monitoring point. Fourier transform is carried out for the corrected result, and the spectrum diagram is shown as follows (Fig. 9):

Fig. 9. Spectrum of the corrected result

As can be seen from the spectrum diagram, the signal of 0.047 frequency has been greatly weakened in the corrected monitoring results, the signal amplitude has been reduced from 1.24 mm to 0.32 mm, and other relatively high frequency signals, such as 0.092, 0.175, 0.267 have been effectively improved after BP neural network correction and Kalman filtering algorithm.

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4 Conclusion In this paper, Fourier transform is used for spectrum analysis of monitoring data to extract the multi-path error of the displacement of monitoring points. Then, BP neural network is used to model, predict and correct the multi-path effect. After that, Kalman filter is used for the corrected monitoring results to filter out the high-frequency errors. Through the experiment of measured data, the periodic fluctuation of the corrected coordinate time series of the monitoring station is significantly improved compared with the original data, the periodic error is effectively suppressed, and the long-term trend displacement of the monitoring object is well retained, which improves the accuracy and stability of deformation monitoring to a certain extent. Acknowledgements. Thanks to Hunan Lianzhi Technology Co., Ltd for providing the observation data of monitoring points and the broadcast ephemeris data provided by IGMAS Analysis Center of Wuhan University.

References 1. Liu, Z., Zhang, X.: Analysis of observational data of BDS-3 in-orbit test satellite. JGG Geodyn. 40(07), 741–745 (2020) 2. Han, J.: Research on high-precision BDS real-time landslide deformation monitoring technology and environmental modeling analysis. Acta Geod. et Cartogr. Sin. 49(03), 397 (2020) 3. Wu, H., Liu, Chao., Zhao, X.: BDS deformation information recognition and early warning based on improved cumulative and control chart. Geomat. Inf. Sci. Wuhan Univ. 10(02), 1–10 (2019) 4. Sardón, E., Zarraoa, N.: Estimation of total electron content using GPS data: how stable are the differential satellite and receiver instrumental biases. Radio Sci. 32(5), 1899–1910 (1997) 5. Deng, Y.: Research on Feature Extraction and Prediction Method of BDS Deformation Series. Anhui University of Science and Technology (2018) 6. Ma, X., Shen, Y.: Multipath error analysis of COMPASS triple frequency observations. Positioning 5(1), 12–21 (2014) 7. Zhang, C.: Research on Multi-path Error Elimination Technology in BDS Multi-system Dynamic Deformation Monitoring. Anhui University of Science and Technology (2017) 8. Li, P.: BDS/GPS Multi-path Error Modeling and Its Application in High Precision Deformation Monitoring. Wuhan University (2016) 9. Wang, J., He, X.: Error correction method of BDS satellite pseudo-range multipath system and its influence analysis on single-frequency PPP. Acta Geod. et Cartogr. Sin. 46(07), 841– 847 (2017) 10. Yuan, B., et al.: Deformation monitoring of BDS dam considering multi-path error correction. Navig. Position. Timing 3(01), 53–59 (2016) 11. Xiao, G., et al.: A method for detection and repair of BDS tri-frequency cycle slip by correcting pseudo-range multipath errors. J. Geodesy Geodyn. 35(04), 671–675 (2015) 12. Wu, F.: Research on GPS Dynamic Deformation Monitoring Data Processing Model. China University of Mining and Technology (2014)

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13. Wanninger, L., Beer, S.: BeiDou satellite-induced code pseudorange variations: diagnosisand therapy. GPS Solutions 19(4), 639–648 (2015). https://doi.org/10.1007/s10291-0140423-3 14. Hauschild, A., et al.: A multi-technique approach for characterizing the SVN49 signal anomaly, part 1: receiver tracking and IQ constellation. GPS Solututions 16(1), 19–28 (2012) 15. Xu, H., Cui, X., Lu, M.: Satellite-induced multipath analysis on the cause of BeiDou code pseudorange bias. In: Sun, J., Liu, J., Yang, Y., Fan, S., Yu, W. (eds.) China Satellite Navigation Conference (CSNC) 2017 Proceedings: Volume II, CSNC 2017, Lecture Notes in Electrical Engineering, vol. 438, pp. 11–21. Springer, Singapore (2017). https://doi.org/ 10.1007/978-981-10-4591-2_2 16. Liu, M.K.: Pseudo noise code tracking performance analysis of Beidou B2 frequency band navigation signal. Telecommun. Eng. 58(1), 25–29 (2018) 17. Guo, W., et al.: A new FFT acquisition scheme based on partial matched filter in GNSS receivers for harsh environments. Aerosp. Sci. Technol. 61, 66–72 (2017) 18. Wang, Q., et al.: Topological structure selection of BP neural network for day length variation prediction. Annual Review of Shanghai Astronomical Observatories, Chinese Academy of Sciences (00), 23–29 (2007) 19. Liu, L., et al.: Research of GPS elevation conversion based on least square support vector machine and BP neural network. In: Applied Mechanics and Materials, 2974 (2014)

Application of a Fusion Communication System Based on Beidou Short Message Technology Lei Xing(&), Shuyan Li, and Yangming Wang Fengqi East Street, Xi’an 710100, Shaanxi, China

Abstract. In this paper, a fusion communication system based on Beidou short message technology, which can well solve the problem of direct communication between people and ordinary mobile phones when they are working in areas with no signal or weak signal. The fusion communication technology can allow the command center or family to directly receive the Beidou short messages through ordinary mobile phones in the first time, so as to get the status and continuous location information or coordinates of outside personnel timely. The method used in this article is to adopt the design of gateway software and hardware, through the host computer software, to realize the short message data transmission between the Beidou short message terminal and ordinary mobile phone. At the same time, multi-channel command server can realize and support the load balancing of massive concurrent response from the Beidou short messages. Compared with satellite phone, this method has the advantages of low price, low cost, easily to sending and receiving the short messages, no need to borrow mobile phone application software, and can be realized to send short messages each other between the Beidou short message terminal and ordinary mobile phone. The result of this research solves the problem well that the Beidou short message can communicate directly with ordinary mobile phone through the short messages. Keywords: Fusion communication


Beidou short message
SMS

1 Introduction The BeiDou Navigation Satellite System (BDS) ranks among the four major navigation systems in the world, it is another more mature satellite navigation system after the GPS of the United States, GALILEO of the European Union, and GLONASS of Russia. The BDS is widely used in ship transportation, road transportation, railway transportation, sea operations, fishery operations, forest fire prevention, environmental monitoring, landslides, field operations and other fields, covering government, public security, customs, border defense and other department for special command and dispatch, which has produced significant economic and social effects. With the continuous improvement and improvement of the functions and performance of the BDS, the application scale and scope of the BDS will gradually expand and have a promising prospect. The short message communication service, with its integration and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 111–122, 2021. https://doi.org/10.1007/978-981-16-3138-2_12

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convenience, is still the unique difference between China's navigation system and other satellites. It transfers data by Beidou space station and has the advantages of wide coverage, no communication blind zone and encryption of data transmission. It can be used as a communication tool in emergency situations. The Beidou Satellite has the function of two-way communication. First of all, users can know their location and tell others where they are. Secondly, it can send a message by point-to-multi-point, and users can send a message to multiple people, which provides great convenience for various platform applications. Especially in the fields of sea rescue and disaster area rescue, it meets the development needs of modern satellite navigation system. The Beidou short message can solve the current needs of some special places and special moments, and with the support of the government and organizations, the products based on Beidou short message function has the advantages of low price and convenient use. In the future, this technology will be applied in more fields.

2 Demand Analysis When people work outdoors, they often encounter no signal or weak signal. If an accident occurs, it becomes a difficult problem to contact the outside world. At present, the satellite phone price is high and cannot send the user's location for a long time. With the help of the ordinary mobile phones and Beidou handheld user machine to send short messages each other, it has become a good application solution, which enables the command center or home to get the first-hand information and continuous position coordinates in the first time. In order to realize the fusion communication between the Beidou short message and mobile phone short message, the method about algorithm of software are proposed, which solves the two-way communication function of the Beidou short message and ordinary mobile phone short message in the area of no signal or weak signal, including location tracking, short message, etc. This method has the advantages of low price, easily to sending and receiving the short messages, no need mobile phone application software, and can be realized to send short messages each other between the Beidou short message terminal and ordinary mobile phone. As a space-based communication mode, the Beidou short message has all the advantages of satellite communication, such as all-weather, wide coverage and high reliability. With the opening of the global network of BDS-3 (see [1]), based on the original technical system, it has further expanded user resources, reduced terminal power, increased system capacity, and expanded the length of single message capabilities, which is more conducive to the potential application needs of civil services. At the same time, it provides a strong technical foundation for the development of fusion communication system based on Beidou Short Message Technology [2] (Fig. 1).

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Beidou Satellite Beidou SatelliteBeidou Satellite

Beidou Ground Station

Computer Room

Operator

Beidou RNSS/RDSS Terminal

No Signal Area

Fig. 1. Network topology

3 System Design The overall requirement is that the Beidou handheld user machine sends short messages to the ordinary user's mobile phone through the Beidou satellite. Similarly, the ordinary user's mobile phone is sent to the Beidou handheld user machine through the mobile base station. The software compilation platform is VS2010, and the operating system is Windows 7, Windows 10 or Windows Server 2008 and above. 3.1

Overall Design

Based on interface protocol and gateway protocol of short message data, the short message data transmission between the Beidou handheld user machine and ordinary mobile phone is realized through the host computer software (Fig. 2).

Beidou Satellite Network Beidou handheld user machine

SP

SP TCP Protocol Beidou Gateway Server Beidou CommunicaƟon Unit

Ordinary User Mobile Phone

Internet

Short message data service area

SMS Gateway

Wireless CommunicaƟon Network

Plaƞorm SoŌware

Fig. 2. Principle of system flow

When the commander machine receives the Beidou short message, it send a request to the SMS gateway through the TCP/IP protocol. If accepts, sends the message. If don’t accept, stop sending. The details are as follows: 1. The communication scheme adopts the long connection mode, and the both communication establish a TCP connection in a client-server mode for mutual submission of information between the parties.

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2. Login operation. The client registers with the server as a legal client identity. If the registration is successful, the application layer connection is established, after that, the client can receive and send messages with the server. 3. After the Beidou handheld user machine sends the message data to the ordinary mobile phone, the Beidou gateway server submits the message data to the short message gateway server. 4. The short message gateway sends a short message to the Beidou gateway. 5. Link detection is used for keep-alive connections for long-connection mode. 3.2

Technical Process

3.2.1 The Beidou Communication Unit The hardware of Beidou positioning communication unit is composed of antenna, RDSS module, BD/GPS low noise amplifier, Beidou protocol processing unit, power supply module and battery. Among them, the antenna is the integrated antenna of Beidou transceiver and RNSS BD/GPS receiving; The RDSS module includes Beidou receiving channel and transmitting channel, Beidou protocol processing board is composed of Beidou short message protocol processing circuit, BD/GPS module, watchdog and IC card; The power module includes a DC/DC module and a rechargeable battery (Fig. 3). RDSS Module

Antenna Beidou receiving antenna

LNA

downconversion mixer amplifier

Beidou Protocol Processing Unit

baseband signal processing Positioning, communication, area alarm, business management, power state management, one-key alarm, display and control module, data exchange and other functions.

PLL

Beidou transmitting antenna

Information processing

PA

BPSK modulator

BD/GPS Antenna

Inbound baseband signal shaping

IC card BD/GPS Module

RS232

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BD/GPS LNA

Power Module Battery

9-36V

Display Control

Fig. 3. Principle of Beidou RDSS communication unit

After receiving satellite signals, the antenna of Beidou positioning communication unit will send the signals directly to module for processing after filtering and amplification. The module will complete the navigation and positioning calculation based on satellite constellation, and output its navigation and positioning information data in NMEA-0183.

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The Beidou protocol processing board mainly completes the analysis and splicing of inbound and outbound signals, realizes the formatting, encryption, and decryption of Beidou navigation information, and realizes the serial interface for the processing board. In addition, it realizes the functions of positioning data packaging, communication, alarm, management, power state management, one-key alarm, display and control unit, data exchange by the Beidou handheld user machine. In order to prevent the battery from deeply discharging, the charging circuit analyzes that the power reaches 25% of the rated power and starts to charge the battery. If the battery power is 25% and there is no external power supply, the Beidou positioning communication unit should automatically shut down before the battery runs out. The above description is an explanation of the working principle of the Beidou positioning communication unit [3, 4]. 3.2.2 External Links Data forwarding software, the customer data used mainly includes short message data, SOS data, instruction feedback data, etc.; Server data includes terminal configuration information, query information, etc. (Fig. 4).

Data forwarding soŌware Beidou CommunicaƟon Unit

Data receiving Serial port

Data decoding/encoding

Gateway Server Internal network

Data transmission OperaƟon control and display

Fig. 4. Connection relationship between data forwarding software and external systems

3.2.3 Data Forwarding Design To establish communication with the Beidou command machine through serial port, and to establish communication with the server through in long connection mode, data forwarding software mainly realizes two functions respectively: 1. Pack the data from the Beidou command machine and send it to the server in the format of short message gateway protocol; 2. The data from the server will be decoded in accordance with the format of the short message gateway protocol, and the data part will be sent to the Beidou command machine (Fig. 5).

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coding

Short Message Protocol Short Message Gateway Protocol

decoding

Data Processing

decoding

Middleware

Display

coding

SMS Gateway Server

Fig. 5. The technical process of data forwarding

1. Data receiving and sending (1) Capable of receiving data from Beidou command machine, mainly including short message data, SOS data, instruction feedback information, etc.; (2) Capable of receiving data from the server, mainly including login feedback information of the Beidou handheld user machine, and submit short message feedback information of the Beidou handheld user machine, etc. 2. Data decoding and encoding (1) The function of format data encoding for login (Table 1). Table 1. Description of the main fields of the login Name

Field

Required parameters

Client ID Authenticator Client LoginMode TimeStamp ClientVersion

Length (bytes) 8

1

Data type Octet String Octet String Integer

4 1

Integer Integer

16

Description The user account used by the client to log in to the server Client authentication code, used to verify the legitimacy of the client The login type used by the client to log in to the server Timestamp Protocol version number supported by the client

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(2) The function of format data decoding for Login_Resp (Table 2). Table 2. Description of the main fields of the login_resp Name

Field

Required parameters

Status Authenticator Server Server Version

Length (bytes) 4 16 1

Data type Integer Octet String Integer

Description Request to return results Authentication code returned by the server to the client The highest version number supported by the server

(3) The function of format data encoding for Submit (Table 3). Table 3. Description of the main fields of the submit Name Field Required MsgType parameters NeedReport Priority MsgFormat ValidTime AtTime SrcTerm ID MsgLength Reserve

Length (bytes) Data type 1 Integer 1 Integer 1 Integer 1 Integer 17 Octet String 17 Octet String 21 Octet String 1 Integer 8 Octet String

Description SMS type Does the SP require a status report Short message sending priority SMS format Short message effective time Time to send short messages SMS sender number Short message length Keep

(4) The function of format data decoding for Submit_Resp (Table 4). Table 4. Description of the main fields of the submit_resp Name Field Length (bytes) Data type Description Required MsgID 10 Octet String SMS serial number parameters Status 4 Integer Request to return results

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(5) The function of format data decoding for Deliver (Table 5). Table 5. Description of the main fields of the deliver Name Field Required MsgID parameters IsReport MsgFormat RecvTime SrcTermID DestTermID MsgLength Reserve

Length (bytes) Data type Description 10 Octet String SMS serial number 1 Integer Is it a status report 1 Integer SMS format 14 Octet String SMS receiving time 21 Octet String SMS sending number 21 Octet String SMS receiving number 1 Integer Short message length 8 Octet String Keep

(6) The function of format data encoding for Deliver_Resp (Table 6). Table 6. Description of the main fields of the deliver_resp Name Field Length (bytes) Data type Description Required MsgID 10 Octet String SMS serial number parameters Status 4 Integer Request to return results

(7) The function of format data encoding for Active_Test. (8) The function of format data decoding for Active_Test_Resp. 3. Operation control and display (1) The function for Active_Test (2) The function for display and control of terminal connection status (3) The function for display and control of server connection status 3.3

Design of Software Platform

The fusion communication service platform realizes the information exchange between Beidou handheld user machine and ordinary mobile phones through the connection with the Beidou satellite network and the ground mobile network; and realizes the sending and receiving, processing and storage of network information data, and realizes distribution to various service function servers according to data types for distributing

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data, and finally completes the fusion communication and monitoring and management services between Beidou short messages and ordinary mobile phone short messages (Fig. 6).

Fig. 6. Location monitoring of service platform

Through the information encoding and decoding between the Beidou Short Message Gateway and Short Message Gateway, the message information can be monitored and recorded in mutual communication (Fig. 7).

Fig. 7. Data gateway information monitoring

The test results are shown in the figure below, the left side is the information interface of the Beidou short message user machine, and the right side is the information interface of an ordinary mobile phone. The application of this method can well solve the problem of communication each other between ordinary mobile phones and the outside world when working in the area of no signal or weak signal (Fig. 8).

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Fig. 8. Test results

4 Key Techniques 4.1

Load Balance and Message Priority Techniques

The transmission of Beidou short message is limited by the frequency of the Beidou IC card, the platform requires the design of the message sending buffer queue design and the message sending priority configuration design. The Beidou communication unit establishes a buffer queue for waiting messages, saves 10 messages to be sent for waiting and extra messages will be automatically ignored. Emergency alarm or one-key alarm is the first priority. When an emergency alarm or one-key alarm arrives, it will be sent immediately or placed at the front of the queue, Emergency alarm or one-key alarm will be sent first; If the buffer queue for waiting messages is full, the last one is cleared and the waiting message is moved backwards one by one. The area alarm is the second priority, in the absence of emergency alarms and one-key alarms, the area alarms are sent immediately or placed at the front of the queue. If the buffer queue for waiting messages is full, the last one is cleared and the waiting message is moved backwards one by one, and area alarm is be send first (Fig. 9).

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Middleware Data receiving Data decoding/encoding

Data transmission Beidou Server Array

Data Gateway Server

Operation control and display

Softwareimplemented load balancing array Middleware Data receiving Data decoding/encoding

Data transmission Data gateway server

Data Gateway Server Operation control and display

Fig. 9. Connection relationship between data forwarding software and external systems for array of load balance

4.2

Multicast/Broadcast Random Delay Response Technology

In order to better manage a large number of Beidou handheld user machine, a large number of terminals use the same broadcast address currently. Because multicast instructions will cause a large number of terminals to basically respond at the same time, the inbound capacity of Beidou short message can’t meet the response for a lot of information, resulting in a large number of communication loss. In order to solve this problem well, the platform uses random response technology in the processing of broadcast instructions, so that after receiving the broadcast instruction, the terminal will send messages of the largest uniform distribution in a response frequency according to the required random algorithm, so that the inbound information of a large number of terminals can be evenly distributed in the time range of the delay threshold for Multicast/ broadcast. 4.3

Middleware Technology

The information service platform is a distributed application system, and its scale will become larger and larger. At the same time, there are a large number of data transmission and interactive operations between systems, and these operations are mixed with specific business logic, and the application level is not clearly divided, which brings great difficulties to software updates, upgrades, maintenance and reuse. Therefore, this platform adopts layered technology to build a distributed application-based, universal, easy-to-extensible data transmission middleware DDTM (distributed data transmission middleware) with communication capabilities to solve such problems. Middleware is the core technology in the current field of software development. In the information service platform, middleware realizes data transmission, filtering, and data format conversion between hardware equipment and application systems. A lot of data information of the terminal is extracted, decrypted, filtered, formatted, and imported into the platform's application through the middleware, which reflected on the user interface through the application system for users.

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DDTM uses XML as the standard format for data transmission, which solves the problem of data standardization in data transmission. Data transmission only requires simple data format definition to facilitate seamless data transmission. DDTM divides the system into interface layer, which deals with data transmission request layer, navigation layer, transport transaction control layer and system management layer, and expounds the cooperation relationship between each layer and related interface design. DDTM builds a data transmission logic network, provides navigation functions at the application level according to the relationship between applications, and shields the complexity of TCP/IP layer communication for specific applications.

5 Conclusions Compared with GPS, BDS has a short message function since its birth, this unique technological innovation create a broad space for its subsequent applications and market development. Today, with the opening of the “Global Era’ of China’s Beidou, a global search and rescue system and emergency communication system based on short messages are being established. People can use Beidou short messages to communicate with ordinary mobile phone short messages anytime, anywhere, and everything is within reach.

References 1. Yang, Y., Mao, Y., Sun, B.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020019-0006-0 2. Yuan, J.: Multi-source information fusion technology and application development status. Ind. Econ. Forum 4(5), 42–47 (2017) 3. Zou, L.: Research on Key Technologies of Beidou Second Generation Software Receiver. Xi'an University of Electronic Technology (2014) 4. Hui, D., Zhao, H., Yao, J.: Design and implementation of emergency communication command system based on Beido. Wirel. Commun. Technol. 28(04), 35–38 (2019)

Simulation Research on ICAO Model Parameters Based on BDS Zhimei Yang(&), Lingling Chen, Qibing Xu, Han Liu, and Lixin Zhang Xi’an Institute of Space Radio Technology, Xi’an 710100, China

Abstract. With the promotion of the new navigation system by the International Civil Aviation Organization (ICAO), BDS must provide satellite navigation signal abnormal fault models and parameters to join ICAO. The article establishes an equivalent ICAO model with BDS. According to the actual faults that may occur during the navigation signal generation process, the methods are respectively proposed to simulate the digital circuit failure (TMA) caused by the code control clock abnormality of the spread spectrum code, and to simulate the analog circuit failure (TMB) caused by the deterioration of the transmission channel amplitude and group delay when a certain 1–2 bit of the simulation predistortion filter parameter is overturned by space single particle. Finally, the fault model parameters of the BDS are provided, which provides technical support for BDS to join the international civil aviation standards. Keywords: ICAO


BDS
Threat model

1 Introduction Providing services for international civil aviation is also one of the important development strategies of BDS satellite navigation system. However, minor malfunctions in satellite hardware may cause abnormal satellite signals. The most typical example of satellite failure is the SV-19 satellite signal abnormal event in 1993 [1]. When the Federal Aviation Administration used differential navigation to achieve assisted landing, it was discovered that the C/A code and the P code were seriously out of synchronization, with a deviation of about 6 m [2]. Subsequently, various effective navigation signal anomaly models have been proposed. The most representative one is the 2OS (Second-Order Step) model proposed by Phlts [3]. It is considered by ICAO as a standard signal anomaly model and has been used until now. Literature [2] analyzes the influence of abnormal signal on ranging performance, and concludes that a larger analog distortion parameter value and a smaller digital distortion will weaken the influence on ranging performance. The asymmetry of navigation signal waveform and its influence on users from three aspects of timedomain waveform in literature [4]. The error between FPGA distortion waveform and MATLAB simulation waveform is within 0.5% through FPGA implementation method in literature [5]. The above literature analyzes the impact of signal distortion on user ranging or the hardware implementation, but the acquisition of BDS satellite fault model parameters has rarely been reported. ICAO has parameterized the abnormal © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 123–132, 2021. https://doi.org/10.1007/978-981-16-3138-2_13

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waveforms of GPS, Galileo and GLONASS in time domain and written them into the International Civil Aviation Convention. If BDS wants to join ICAO, it must provide abnormal fault models and parameters of satellite navigation signals. Therefore, this paper carries out the parameter analysis and demonstration of BDS satellite signal abnormal fault model, which lays the foundation for BDS to join the international civil aviation standard and apply in the civil aviation field.

2 BDS Navigation System Fault Model Integrating the navigation transmission channel models of major navigation systems, the general mathematical model [6] of the navigation signal generated by the payload transmission can be summarized as shown in Fig. 1. NDU outputs navigation data, C/A code and P(Y) code baseband signal. The analog processing includes frequency upconverter, medium power amplifier and high power amplifier (IPA and HPA), antenna beamforming (RABF), and finally the antenna.

Fig. 1. The general model of the payload transmitted signal.

According to the location of the fault, the causes of signal abnormalities are divided into three categories [7]: TMA (Threat Model A), TMB (Threat Model B), and TMC (Threat Model C). (1) TMA (Threat Model A) TMA failure Occurs in the navigation digital signal generation stage [8]. TMA model can be modeled as the sum of a normal sequence and a D sequence. which can be expressed as: xTMA ðtÞ ¼ xðtÞ þ xD ðtÞ  max½xðt  DÞ  xðtÞ; 0 D  0; xD ðtÞ ¼ min½xðt þ DÞ  xðtÞ; 0 else:

ð1Þ ð2Þ

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(2) TMB (Threat Model B) The TMB failure occurs in the process of signal modulation and amplification [9]. The damped oscillation frequency fd (MHz) and the attenuation factor r (Mnepers/second) are modeled as ‘ringing’, and the ringing is described as a damped second-order response, It can be described by the unit step response of the second-order system:  hðr;fd Þ ðtÞ ¼

0 1  ert ½cos wd t þ

r wd

t0 sin wd t t  0

wd ¼ 2pfd

ð3Þ ð4Þ

The TMB model can be expressed by a second-order system response xTMB ðtÞ ¼ xðtÞ
hðr;fd Þ ðtÞ

ð5Þ

(3) TMC (Threat Model C) The is TMC fault model cascaded by the TMA fault model and the TMB fault model, adjusted by D, f d and r, which can be expressed as: xTMC ðtÞ ¼ ½xðtÞ þ xD ðtÞ
hðr;fd Þ ðtÞ

ð6Þ

The generation process of the BDS-3 downlink navigation signal is shown in Fig. 3. The BDS navigation system is similar to the general mathematical model in Fig. 1. It can be seen that the BDS is also adapted to the classic ICAO mentioned above. The model is consistent with the GPS, Galileo, and GLONASS. Therefore, the BDS fault model can also adopt the ICAO model (Fig. 2).

Fig. 2. ICAO model parameters.

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Digita l predistor tion filter

Digit al IF mod ulati on

D/A

upc onve rter

TMA

Anal og filter

TW TA

com bine r

TMB TMC

Fig. 3. Flow diagram of BDS navigation system downlink navigation signal generation.

3 System Fault Model Parameter Analysis Annex 6, Volume 10 of the International Civil Aviation Convention provides the ICAO model parameters as shown in Table 1. Table 1. ICAO model parameters of GPS, Galileo and GLONASS. ICAO parameters TM-A Galileo E1C Galileo E5a GPS L1C/A GLONASS TM-B Galileo E1C Galileo E5a GPS L1C/A GLONASS TM-C Galileo E1C Galileo E5a GPS L1C/A GLONASS

D (chip)

r(Mnepers/s) fd (MHz)

[−0.12 0.11] [−1.2 1.2] [−0.12 0.12] [−0.11 0.11] /

/

/ / [0 55] [0 23] / [0.8 8.8] / [2 8] [−0.12 0.11] [0 55] [−1.2 1.2] [0 23] [−0.12 0.12] [0.8 8.8] [−0.11 0.11] [2 8]

/ / / [0 20] [0 18] [4 17] [10 20] [0 20] [0 18] [7.3 13] [10 20]

The three GEO satellites broadcast SBAS signal at two frequency points, B1C and B2a [10]. The status is shown in Table 2. Table 2. BDS B1C and B2a signals. Signal Center frequency (MHz) Signal system Code rate (MHz) B1C 1575.42 BPSK(1) 1.023 B2a 1176.45 QPSK(10) 10.23

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Obtain D Parameter of TMA Model

TMA occurs in the digital waveform generation stage, and the parameter D is mainly considered to be the failure caused by the abnormal code control clock that generates the spreading code of B1C and B2a signals. When the main clock is abnormal, consider one more clock cycle or less one clock cycle. The code rate of the B1C signal is 1.023M chips/s and the 85.932 MHz clock is used as the main control clock, the chip length will be more or less (1/85.932 MHz) cycle, that is, the parameter range of D is [−0.012chip, 0.012chip]. The code rate of the B2a signal is 10.23M chips/s and the 61.38 MHz clock is used as the main control clock, and the chip length will be more or less (1/61.38 MHz) The period, that is, the parameter range of D is [−0.17chip, 0.17chip]. 3.2

Obtain the Fd\r Parameter in the TMB Model

TMB occurs in the radio frequency link. In order to compensate for the deterioration of signal quality caused by the non-ideal characteristics of the transmitting channel, a digital pre-distortion filter is designed [11]. Taking frequency B1 as an example, the actual transmit channel is shown in Fig. 4 and the pre-distortion is shown in Fig. 5.

Amplitude frequency characteristics

Group delay characteristics

Fig. 4. Actual transmit channel characteristics.

Amplitude frequency characteristics

Group delay characteristics

Fig. 5. Pre-distortion filter characteristics.

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The following failure possibilities are mainly considered in the TMB model: • Since the filter and triplexer are passive components, there is almost no such risk, so do not consider; • When the active stand-alone machine fails to shut down, the receiver cannot receive the signal, so it is not considered; • When the characteristics of the channel change due to the aging of the device, but this fault is a slow-changing fault, and can be eliminated through regular on-board pre-distortion parameter adjustments, so do not consider; • When there is a large jump in power or group delay and exceeds the alarm threshold, the monitor will alarm, and The downlink signal message will be set as unavailable, and the receiver will not use this signal, so regardless of it; but when the power or group delay jump is small, it will cause signal distortion and no monitor alarm will be generated. • Affected by the electromagnetic environment in space, a certain 1–2 bit of the predistortion filter parameter is overturned by a single particle, which may cause the deterioration of the pre-distortion filter characteristics, and the transmission channel cannot be compensated normally, which causes the transmission signal to be distorted. This situation cannot be ruled out. Therefore, the simulation is divided into two parts to obtain fd and r parameters: (1) The pre-distortion filter works normally, that is, the normal state on the satellite; (2) A certain 1–2 bit of the pre-distortion filter parameter is overturned, causing the amplitude and group delay characteristics of the on-board transmission channel to deteriorate, thereby simulating the state when the on-board analog channel is transmitting failure. 3.2.1 Parameters in Normal State In order to be consistent with the actual state of the satellite, the baseband signal is first modulated to the intermediate frequency in the simulation, after the pre-distortion filter, and then through the actual channel characteristics collected on the satellite. The obtained time-domain chip waveforms of B1C and B2a are shown in Fig. 6 and Fig. 7.

Fig. 6. Time-domain chip waveform of B1C.

Fig. 7. Time domain chip waveform of B2a.

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The relevant calculation of the unit step response of the fd second-order system can obtain fd and r, and the simulation can obtain different fd and r parameters through different receiving filter bandwidths as shown in Table 3: Table 3. The fd and r parameters under different receiving filter bandwidths. Signal Unilateral receive bandwidth (MHz) fd(MHz) 10.16 B1C 10 15.15 15 19.24 20 22.24 30 10.50 B2a 10 15 14.86 20 17.18 30 17.41

r(Mnepers/s) 3.76 5.29 7.52 9.08 2.84 4.13 6.85 7.15

Through the analysis of the simulation results in Table 3, it can be concluded that: ① fd is related to the minimum filter bandwidth of the entire transmit and receive link. ② The attenuation factor r characterizes the convergence speed of the signal oscillation, the larger the value of r is, the faster the convergence will be; the higher the signal code rate is, the smaller the value of r will be. 3.2.2 Parameters in Abnormal State Based on the normal state, the abnormal state of the digital filter is simulated. There are 32 digital filter parameters, and each parameter occupies 16 bits, which is 512 bits overturned by simulation traversal A certain 1–2 bit can get different amplitude frequency and group delay characteristics. According to the simulation traversal results, when the 16th and 17th parameters are overturned, the characteristics change the worst as shown in Fig. 8. When the lowest bits of the 1st and 32nd parameters are overturned, the characteristics change the least as shown in Fig. 9.

Amplitude frequency characteristics

Group delay characteristics

Fig. 8. When the highest bit of the 16th and 17th parameters is overturned.

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Amplitude frequency cha racteristics

Group delay characteristics

Fig. 9. When the highest bit of the 1th and 32th parameters is overturned.

As we discussed, when the signal has an amplitude change or delay deviation that exceeds the warning threshold, the integrity monitoring will alert, so there is no need to consider the degradation of amplitude frequency and group delay characteristics. When the TMB is too large, the main consideration is to change the characteristics of the transmission channel, which makes the transmitted signal distorted but does not warn. At this time, the receiver can still receive the signal but the error is too large, that is, the fd and r parameters we require are at the critical point. According to the indicators of integrity monitoring and simulation results, when the 6th bit of the 16th and 17th parameters is knocked over, the integrity monitoring will not alarm and the receiver can receive the boundary condition of the distorted signal. The corresponding characteristic curve is shown in Fig. 10.

Amplitude frequency characteristics

Group delay characteristics

Fig. 10. When the middle position of the 16th and 17th parameters is overturned.

Other simulation conditions are the same as in Sect. 3.2.1, and the corresponding fd and r parameters can be obtained by simulation, as shown in Table 4. Through the comparative analysis of Table 4 and Table 3, it can be seen that: ① The change of analog channel amplitude and group delay characteristics will not affect the value of fd, which is related to the minimum bandwidth of the filter in the entire link. ② The value of r will become smaller as the parameters of the predistortion filter are reversed, that is, the amplitude frequency and group delay characteristics of the transmitting channel deteriorate.

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Table 4. The fd and r parameters under different receiving filter bandwidths. Signal Unilateral receive bandwidth (MHz) fd(MHz) 10.53 B1C 10 15.60 15 19.41 20 22.63 30 10.76 B2a 10 14.92 15 17.39 20 17.51 30

3.3

r(Mnepers/s) 0.57 3.55 6.08 7.42 0.32 3.09 5.81 6.19

TMC Model

Combining the simulation results and analysis of TMA and TMB, try to give the ICAO model parameters of BDS as shown in Table 5. Table 5. Beidou's ICAO model parameters. ICAO parameters TM-A B1C B2a TM-B B1C B2a TM-C B1C B2a

D(chip)

r(Mnepers/s) fd (MHz)

[−0.012 0.012] / [−0.17 0.17] / [0 10] [0 8] [−0.012 0.012] [0 10] [−0.17 0.17] [0 8]

/ [4 [0 [4 [0

23] 18] 23] 18]

The parameter range of D refers to the TMA model. fd is related to the minimum bandwidth of the filter in the entire link, and is not affected by changes in channel amplitude and group delay characteristics. In the actual simulation result, the maximum fd is 22.63. Therefore, the upper limit of the fd of B1C is 23M; the lower limit of fd is 4M, because the lower frequency will affect the military signal, and the military signal It is more strictly monitored than the C/A code [5]. In the same way, the upper limit of the B2a signal fd is set to 18, and the lower limit is set to 0 because there is no military signal on the B2 branch, so the impact on the military signal is not considered. r characterizes the convergence speed of the oscillation. The higher the code rate, the worse the amplitude-frequency and group delay characteristics of the transmitting channel, and the smaller r. Combining the actual simulation results in Table 3 and Table 4, and referring to the ICAO model parameters of GPS, Galileo and GLONASS in Table 1. B1C is taken as 10, B2a is taken as 8; the lower limit of r is taken as 0, because r < 0 will bring unstable oscillation, and there is no such situation in reality.

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4 Conclusion In this paper, firstly, though analysis we got the conclusion that the BDS navigation system fault model should adopt the classic ICAO model. Then we analyze the actual failures, simulating the digital circuit failure (TMA) caused by the abnormality of the control clock. By simulating 1–2 bit overturned by space single particle of the predistortion parameters, which can cause the deterioration of the transmission channel amplitude and group delay, to simulate the resulting analog circuit failure (TMB).At the same time, combined with the ICAO model parameters of the other three satellite systems, we obtain the fault model parameters of BDS. The research provides technical support for BDS to join the international civil aviation standards and lays a foundation for BDS 's application in the field of civil aviation.

References 1. Edgar, C., Czopek, F., Barker, B.: A Co-operative Anomaly Resolution on PRN-19. In: Proceedings of the 2000 13th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS-2000. Proceedings of ION GPS 2000, vol. 2 (2001) 2. He, C.Y., Lu, Y., Guo, J., et al.: Generation mechanisms of GNSS navigation signal distortions and influence on ranging performance. Syst. Eng. Electron. 37(7), 1611–1620 (2015) 3. Phelts, R.E., Akos, D.M.: Effects of signal deformations on modernized GNSS signals. J. Global Positioning Syst. 5(1 & 2), 2–10 (2006) 4. He, C.Y., Lu, X.C., Guo, J.: Evil waveform evaluating method for new GNSS signals. J. Electron. Inf. Technol. 41(5), 1017–1024 (2019) 5. Luo, X.Z., Xie, J., Gao, D.B., et al.: Simulation and FPGA-implementation of waveform distortion in time domain for satellite navigation signals . GNSS World China 02, 17–20 (2015) 6. Phelts, R.E., Multicorrelator techniques for robust mitigation of threats to GPS signal quality. Ph.D. Dissertation, Stanford University, pp. 1–345 (2001) 7. Jakab, A.J.: An approach to GPS satellite failure detection. In: Proceedings of the Institute of Navigation, pp. 1029–1038 (1999) 8. Andrew, J.J.: Quality monitoring Of GPS signals. University of Calgary, Alberta (2001) 9. Phelts, R.E., Akos, D.M.: Nominal signal deformation: limits on GPS range accuracy (2004) 10. Guo, S.R., Liu, C., Gao, W.G., et al.: Construction and development of satellite navigation augmentation system. GNSS World China 44(2) (2019). https://doi.org/10.13442/j.gnss. 1008-9268.2019.02.001 11. Liu, H., Yang, Z.M., Xu, Q.B., et al.: A piecewise pre-distortion optimization method based on spaceborne digital filter. Acta Geodaetica et Cartographica Sinica 49(9), 1235–1242 (2020)

GNSS-IR Soil Moisture Inversion Method Based on Random Forest Yuhua Zhang1, Lili Jing3, Yanmin Zhao1, Hongliang Ruan4, Lei Yang1,2, and Bo Sun1(&) 1

College of Information Science and Engineering, Shandong Agricultural University, Taian, China [email protected] 2 School of Electronic and Information Engineering, Beihang University, Beijing, China 3 Chinese Association of Remote Sensing Applications, Beijing, China 4 Jinhua Vocational and Technical College, Beijing, China

Abstract. Soil moisture is a key factor affecting crop growth, and accurate monitoring soil moisture is of great significance for agriculture. GNSS-IR is a low-cost remote sensing technology, using the interference of GNSS direct and reflected signals to obtain environmental parameters, which can realize noncontact, large-scale, real-time and continuous soil moisture monitoring. In this paper, a random forest algorithm is proposed to conduct soil moisture inversion using SNR frequency, amplitude, phase observables of GPS L1, L2 respectively, and the processing flow and soil moisture inversion model are presented. Taking the inversion results of PRN 4 as an example, the R2 of L1 single frequency parameter inversion result is improved by 0.56% and 4.25% compared with the inversion results of amplitude and phase, RMSE decreases by 6.49% and 29.65% respectively. The R2 of L2 single frequency parameter inversion result is improved by 5.76% and 6.21% compared with the inversion results of amplitude and band single parameter, and the RMSE is reduced by 29.55% and 37.10% respectively. The results show that the random forest algorithm used in frequency inversion is more effective than the amplitude and phase. Keywords: Soil moisture
Remote sensing system
Random forest
Inversion model


Global navigation satellite

1 Introduction Soil moisture is not only the main source of water absorbed by plants, but also an indispensable medium for chemical, biological and physical processes in soil. It is an important factor of soil fertility [1], therefore, accurate measurement of soil moisture is crucial in agriculture. At present, the most direct and standard method for measuring soil moisture is oven drying method for its high accuracy [2].However, it is not suitable for detecting soil moisture in a large area. Microwave remote sensing technology can realize contactless

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 133–144, 2021. https://doi.org/10.1007/978-981-16-3138-2_14

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and continuous soil moisture detection for large area. A novel remote sensing approach GNSS-R technology receives more and more attention in recent years. In 1988, Hall and Cordey proposed the possibility of ultlizing GNSS reflected signals as an opportunity of ocean remote sensing [3]. In 2018, Jean-Christophe Calvet used GNSS-IR technology and collected L2C and L5 signals, successing invert the surface soil mositure from SNR (Signal-to-noise Ratio) [4]. Xu Xiaoyue extracted parameters from the multi-path signal components of SNR and proved that there is a strong correlation between SNR’s amplitude and soil moisture [5]. In 2019, Feng Qiulin used BP (Back Propagation) neural network and support vector regression machine algorithms to build GNSS-IR soil moisture inversion model respectively, and compared with linear regression model and the in-situ measured data, proved that machine learning method can effectively improve the inversion accuracy [6]. In 2020, Chen Kun proposed GNSS-IR soil moisture inversion method based on deep confidence network and compared it with linear regression and BP neural network, and verified that this method can effectively improve the accuracy of inversion [7]. Ren Chao et al. proposed a GNSS-IR inversion model based on GA-BP neural network, aiming at the problem that GNSS-IR could not realize continuous detection in space, and achieved good modeling effect [8]. However, most of the above soil moisture inversion methods based on GNSS-IR technology [4–8] only verified that GNSS signals could be used for soil moisture inversion, and only adopted the single satellite and single frequency band, ignoring the data’s differences between different frequency bands and different satellites. Therefore, in this paper, a GNSS-IR soil moisture inversion method based on random forest is proposed, which adopts the data of two frequency bands, GPS L1 and L2. And the observables of SNR measurement data of GPS L1, L2 are analyzed, and be divided into training set and test set. Then the inversion model is built on the training set through random forest regression algorithm. Finally, the inversion results are obtained by using the test set data and verified by comparison with the in-situ value of soil moisture.

2 Principle of GNSS-IR Soil Moisture Inversion The GNSS-IR technology uses a single RHCP (Right-handed Circular Polarization) antenna to receive both the direct and reflected GNSS signal simultaneously. In the scenario of in-situ observation with low antenna height, the difference of Doppler shift between direct and reflected signal can be ignored and in the same time the transmit path’s difference is less than one chip, so that the two signals are coherent, then the two signals are interfering each other at the phase center of antenna. The scenario of interference’s generation is demonstrated as Fig. 1, and the corresponding SNR record by receiver is demonstrated as Fig. 2.

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Fig. 2. Interference phenomenon of SNR data

Fig. 1. Single antenna observation mode

As the reflected signal contains more RHCP component in low elevation angle scenario, so that the interference is more significant in that case. Following article [9], The SNR can be expressed by Eq. (1): SNR2 ¼ A2d ðhÞ þ A2m ðhÞ þ 2Ad ðhÞAm ðhÞ cos w

ð1Þ

where Ad , Am is the amplitude of direct and reflected signal respectively; w is the phase difference between the direct and reflected signal; h is elevation angle of GNSS satellite. Assuming that the antenna height is h, the angle between the reflecting surface is b, the angle between the reflecting surface and the soil surface is c, d is the path difference between the direct and reflected signal, which can be expressed by Eq. (2) [10]: d ¼ 2h sinðjh  cjÞ w¼

2p d k

ð2Þ ð3Þ

where k is the wavelength of carrier wave. The SNR is determined by the geometry relationship among the reflector surfaces, satellite and antenna. In the application of soil moisture monitoring, the angle between the reflector and the ground is negligible, so we can assume c  0.Then Eq. (4) can be derived as: w¼

4ph sin h k

ð4Þ

From Eq. (4), the frequency of multipath oscillation can be obtained as Eq. (5): f ¼

dw 4ph dh 4ph dh ¼ cos h þ sin h dt k dt k dt

ð5Þ

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dh where dh dt and dt is the change rate of elevation angle and equivalent antenna height to time respectively. And dh dt can be ignored in a short period of observation. Let x ¼ sin h, then f can be expressed by Eq. (6):

f ¼

4ph k

ð6Þ

According to Eq. (6), the oscillation frequency has a linear relationship with the antenna equivalent height. From Eq. (1)–(6), the SNRm is the reflected interference signal after depriving the direct component from SNR, which can be expressed by Eq. (7): SNRm ¼ A cos

  4ph sin h þ u k

ð7Þ

where A is amplitude; u is phase. Since the change of SNR with sin h is nonlinear, the oscillation frequency can be derived by Lomb-Scarge spectrum analysis, and then the antenna equivalent height can be obtained. Finally, the A and u can be derived by least-square fitting method. Equation (7) is the basis for the soil moisture inversion by GNSS-IR technology, and the three parameters of h, A and u are the key for the soil moisture inversion. The study of Zavorotny and Chew proved that these three parameters have a linear relationship with soil moisture and they can all be used for soil moisture inversion.

3 GNSS-IR Inversion Model Based on Random Forest 3.1

Experimental Study Area and Data Acquisition

3.1.1 Experimental Study Area The experimental field is a farm land which located in Lamasquere, Toulouse, southern France (43 29 14.45N, 1 13 44.11E). The experimental land is bare soil and flat without shelter, which can ignore the influence of topography, vegetation cover and roughness of land as shown in Fig. 3. The GNSS data were collected from on Feb. 4th to Mar. 21st, 47 d in total.

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direct signal

Reflect signal

Soil surface

Soil moisture detecƟon

Fig. 3. Reality of experimental site

Experimental parameters are shown below: the antenna is pointing zenith with 1.70 m height. The receiver is Leica GR25, and the frequency of 1 Hz is used to sample SNR. Two ML3 Theta Probe soil moisture sensors were buried 2 m away from the antenna for to collecting soil moisture in every 10 m. The depth of the sensors are 2 cm and 5 cm, respectively, with an accuracy of 1%. In this paper, the daily average soil moisture at a depth of 2 cm was taken as the reference truth value of soil moisture. 3.1.2 Experiment Data Processing The data processing process is shown in Fig. 4:

Fig. 4. Flow of data processing

The signals of different frequency bands contain different information. In this paper, both GPS L1 and L2 are used for data processing. Defined SNR1 and SNR2 are the SNR of the L1 and L2 respectively. Then SNR sequence was divided into ascending and descending segment. The time series of SNR1 and SNR2 were transformed into   function of the sine of the elevation angle. Then select the low elevation (0 –30 ) angle data for further processing. Using a second-order polynomial to deprived the direct

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component to obtain the SNRm1 and SNRm2 reflection component respectively. The spectrum of the equivalent height of antenna and frequency can be derived by LombScargle spectrum analysis. Then take the equivalent height with maxim amplitude in the spectrum as the estimated value of the equivalent height of antenna. Finally, according to Eq. (7), the amplitude and phase observation quantity can be derived by least-square fitting of the reflection component. 3.2

Soil Moisture Inversion Based on Random Forest Regression

Random forest (RF) is composed by multiple decision trees, and there is no connection between any decision trees. It utilize Bootstrap re-sampling method and is represented by fhðX; Hk Þ; k ¼ 1;


g, where X is the input vector and fHk g is the independent identically distributed random vector [11], which can be interpreted as the effect of multiple independent variables ðX1 ; X2 ;


; Xk Þ on dependent variable Y. The random forest regression model has been used in the inversion of grassland vegetation coverage [12], but there is almost no application in the soil moisture inversion. When inverse soil m, taking soil moisture value as the dependent variable Y, and frequency, amplitude and phase parameters as independent variables respectively. Random forest regression (RFR) is a key application types of random forest theory, with advantages such as high prediction accuracy, rapid converging, few adjustable parameters, and none over-fitting [13]. In the regression model of decision tree, each leaf node in the decision tree is a learning and training subset. The original data starts from the root node. The final leaf node and the classification rules are unique, which enables the prediction function in decision making [14]. When the random forest algorithm deals with the regression problem, the final result is the average of decision trees’ output. In nature, soil moisture inversion is a regression problem, which is suitable for random forest algorithm processing.

Fig. 5. Soil moisture inversion based on random forest regression

The modeling process is as follows: first of all, training samples are randomly and repeatedly extracted from the training data by using Bootstrap method, and the rest of the sample set is called outside the bag [15]. Then frequency, amplitude and phase

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observables are randomly selected to establish the decision tree respectively. Repeating it n times, and generating random forests of n decision tree model. According to the data processing process in Sect. 3.1.2, the frequency, amplitude and phase observables of 31 satellites in L1 and L2 frequency bands were respectively taken as the input independent variable and the soil moisture as the output dependent variable. In this paper, frequency, amplitude and phase random forest soil moisture regression models were established respectively and then compared them with traditional linear regression model (as shown in Fig. 5).

4 Data Processing and Result Analysis

Number of PRN

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Fig. 6. R2 of traditional methods on GPS L1

Fig. 7. RMSE of traditional methods on GPS L1

Figure 6 shows the statistical results of model R2 modeled by frequency, amplitude and phase characteristic parameters. Figure 7 shows the RMSE of the model modeled by frequency, amplitude and phase characteristic parameters. According to the model established by integrating the above three observation parameters, the effect is not ideal. Table 1. Comparison results of traditional regression methods on GPS L1 R2 of frequency Average 0.3169

R2 of amplitude

R2 of phase

RMSE of frequency

RMSE of amplitude

RMSE of phase

0.1768

0.1732

1.6158%

1.6948%

1.7548%

Table 1 shows the inversion results of L1 band using the traditional regression method [16]. The average R2 of frequency, amplitude and phase are 0.3169, 0.1768, 0.1732 respectively. The mean RMSE are 1.6158% m3/m3, 1.6948% m3/m3, 1.7548% m3/m3 respectively. And the accuracy of the model based on frequency is slightly higher.

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Results of Random Forest Regression

In this paper, the frequency, amplitude and phase data of L1 and L2 frequency band are divided into training set and test set with a ratio of 2:1. Then are calculated the R2 and RMSE of inversion results. Taking the inversion results of PRN 4 as an example, and obtained the average value for analysis. The PRN4 experimental results of L1 frequency, amplitude and phase are shown in Fig. 8, 9 and 10.

Fig. 8. Frequency observation of GPS L1

Fig. 9. Amplitude observa- Fig. 10. Phase observation of tion of GPS L1 GPS L1

Figures 8, 9 and 10 shows the frequency, amplitude and phase prediction result of the random forest model on GPS L1. The R2 were 0.9373, 0.9321, 0.8991, respectively. The RMSE were 0.5070% m3/m3, 0.5421% m3/m3, 0.7207% m3/m3 respectively. Compared with the inversion results of amplitude and phase, the R2 increases 0.56% and 4.25% respectively, and the RMSE decreases 6.49% and 29.65% respectively. It can be seen that the result of frequency observable is better than that of amplitude and phase. The PRN4 experimental results of L2 frequency, amplitude and phase are shown in Fig. 11, 12 and 13.

Fig. 11. Frequency observation of GPS L2

Fig. 12. Amplitude observation of GPS L2

Fig. 13. Phase observation of GPS L2

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Figure 11, 12 and 13 is the frequency, amplitude and phase prediction result of the random forest model on GPS L2. The R2 were 0.9622,0.9098,0.9059 respectively. The RMSE were 0.4120% m3/m3, 0.5848% m3/m3, 0.6550% m3/m3 respectively. Compared with the inversion results of amplitude and phase, the R2 increases 5.76% and 6.21% respectively, and the RMSE decreases 29.55% and 37.10% respectively. It can be seen that the result of frequency parameter fitting is also better than that of amplitude and phase.

Fig. 14. R2 of random forest methods on GPS L1

Fig. 15. RMSE of random forest methods on GPS L1

Figure 14 shows the statistical results of model R2 modeled by frequency, amplitude and phase characteristic parameters. Figure 15 shows the RMSE of the model modeled by frequency, amplitude and phase characteristic parameters. According to the model established by integrating the above three observation parameters, the results of SNR characteristic parameters in L1 processed by random forest method are greatly improved compared with those processed by traditional methods in L1 frequency band. Table 2. Comparison of average inversion results of random forest method on GPS L1 R2 of frequency Average 0.8135

R2 of amplitude

R2 of phase

RMSE of frequency

RMSE of amplitude

RMSE of phase

0.8077

0.8080

0.5573%

0.5910%

0.6371%

Table 2 shows the frequency, amplitude and phase prediction result of the random forest model on GPS L1. The average R2 of all satellite predictions were 0.8135, 0.8077, 0.8080 respectively, which increased by 156.71%, 356.84%, 366.51% compared with the traditional method on GPS L1. The mean RMSE were 0.5573% m3/m3, 0.5910% m3/m3, 0.6371% m3/m3 respectively, which decreased by 65.51%, 65.13%, 63.69% compared with the traditional method. The average R2 of the L1 frequency model is increased by 0.72% and 0.68% compared with the amplitude and phase parameter, respectively. The average RMSE decreased by 5.70% and 12.53%

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compared with the amplitude and phase parameters, respectively. Therefore, it can be seen that the random forest method has the highest accuracy for the L1 frequency band model.

Fig. 16. R2 of random forest methods on GPS L2

Fig. 17. RMSE of random forest methods on GPS L1

Figure 16 shows the statistical results of model R2 modeled by frequency, amplitude and phase characteristic parameters. Figure 17 shows the RMSE of the model modeled by frequency, amplitude and phase characteristic parameters. According to the model established by integrating the above three observation parameters, the results of SNR characteristic parameters in L2 processed by random forest method are greatly improved compared with those processed by traditional methods in L1 frequency band.

Table 3. Comparison of average inversion results of random forest method on GPS L2 R2 of frequency Average 0.8519

R2 of amplitude

R2 of phase

RMSE of frequency

RMSE of amplitude

RMSE of phase

0.7465

0.7906

0.5694%

0.8784%

0.6634%

Table 3 shows the frequency, amplitude and phase prediction result of the random forest model on GPS L2. The average R2 of all satellite predictions were 0.8519, 0.7465,0.7906 respectively, which increased by 168.82%, 322.23%,356.47% compared with the traditional method on GPS L1. The mean RMSE were 0.5694% m3/m3, 0.8784% m3/m3, 0.6634% m3/m3 respectively, which decreased by 64.76%, 48.17%, 62.20% compared with the traditional method. The average R2 of the L2 frequency model is increased by 14.12% and 7.76% compared with the amplitude and phase parameter, respectively. The average RMSE decreased by 35.18% and 14.17% compared with the amplitude and phase parameters, respectively. Therefore, it can be seen that the random forest method has the highest accuracy for the L2 frequency band model.

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Conclusion

This paper proposes GNSS-IR soil moisture inversion method based on random forest regression, Then the general flow of data processing is also given, and experiments are carried out to verify the method. The experimental results show that:   Under the condition of low elevation Angle (0 –30 ), the predicted soil moisture by using random forest method has a good correlation with the in-situ soil moisture, and the R2 can reach 0.8519, which can better inverse the soil moisture in the experimental field. Compared with the traditional processing results, the average R2 of L1 is increased by 156.71%, 356.84%, 366.51% respectively. The mean RMSE is decreased by 65.51%, 65.13%, 63.69% respectively. The average R2 of L2 is increased by 168.82%, 322.23%, 356.47% respectively. The mean RMSE is decreased by 64.76%, 48.17%, 62.20% respectively. Showing that the random forest can effectively improve the accuracy of soil moisture inversion of frequency, amplitude and phase parameters. Compared with the traditional method, the average R2 of L1 frequency is increased by 0.71% and 0.68%, and the mean RMSE is reduced by 5.70% and 12.53% respectively. The average R2 of L2 frequency is increased by 14.12% and 7.76%, and the mean RMSE is reduced by 35.18% and 14.17%, respectively. Showing that the random forest is more effective for soil moisture inversion of frequency parameter. Acknowledgements. Thanks to Jose Darrozes of the Third University of Toulouse for the experimental data.

References 1. Department of Climate Monitoring and Application Management. National Meteorological Administration. Guidance on meteorological instruments and observation methods 6th (edn.), pp. 211–221. China Meteorological Press, Beijing (1996) 2. Cheng, L., Yang, G., Chen, H., et al.: Analysis of sampling error for soil water measured by drying and weighing method. Meteorol. Environ. Sci. 32(2), 33–36 (2009) 3. Yang, D., Zhang Q.: The basis and practice of GNSS reflected signal processing. Publishing House of Electronics Industry, Beijing, p. 196 (2012) 4. Zhang, S., Calvet, J.C., Darrozes, J., Roussel, N., Frappart, F., Bouhours, G.: Deriving surface soil moisture from reflected GNSS signal observations from a grassland site in southwestern France. Hydrol. Earth Syst. Sci. 22(3), 1931–1946 (2018) 5. Xu, X., Zheng, N., Tan, X.: Monitoring of Soil Moisture Fluctuation in Mining Areas Based on GPS-R. J. Zhengzhou Inst. Surv. Mapp. 32(5), 465–468 (2015) 6. Feng, Q.: Study on GNSS reflected signal soil moisture retrieval method based on machine learning. China University of Mining and Technology, Jiangsu (2019) 7. Kun, C., Fei, S., Xinyun, C., Yifan, Z.: GNSS-IR soil moisture inversion based on deep confidence network. Bull. Surv. Mapp. 09, 100–105 (2020) 8. Pan, Y., Ren, C., Liang, Y., Zhang, Z., Shi, Y.: Inversion of surface vegetation water content based on GNSS-IR and MODIS data fusion. Satell. Navig. 1(1), 1–15 (2020). https://doi.org/ 10.1186/s43020-020-00021-z

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9. Larson, K.M., Small, E.E., Gutmann, E., Bilich, A., Axelrad, P., Braun, J.: Using GPS multipath to measure soil moisture fuctuations: initial results. GPS Solut. 12(3), 173–177 (2008) 10. Bilich, A., Larson, K.M., Axelrad, P.: Modeling GPS phase multipath with SNR: case study from the Salar de Uyuni, Boliva. J. Geophys. Res. Atmos. 2008, 113(4) 11. Chen, Y., Song, Y.Q., Wang, W.: Grassland Vegetation Cover Inversion Model Based on Random Forest Regression: A Case Study in Burqin County, Altay, Xinjiang Uygur Autonomous Region. Acta Ecol. Sin. 38(7), 2384–2394 (2018) 12. Chew, C.C.: Soil Moisture Remote Sensing Using GPS-Interferometric Reflectometry. University of Colorado, Colorado (2009) 13. Zhang, B., Zhou, B., Shi, M., Wei, J.: Feedback analysis of water temperature in front reservoir of dam based on distributed optical fiber. Water Resour. Power 2017(04), 209–213. 14. Zhao, B., Tan, Z., Deng, K.: Calculation of the tangent of major influence angle based on random forest regression model. Metal Mine 000(003), 172–175 (2016) 15. Cao, Z.: Study on optimization of random forests algorithm. Capital University of Economics and Trade (2014) 16. Jing, L.L.: Retrieval of surface soil moisture using GNSS-IR dual-frequency data fusion (2019)

Tropospheric Delay Modeling Based on Multi-source Data Fusion and Machine Learning Algorithms Song Li1,2, Tianhe Xu3(&), and Nan Jiang2,3 1

3

School of Geological and Surveying Engineering, Chang’an University, Xi’an 710054, China 2 Key Laboratory of Marine Environmental Exploration Technology and Application, Ministry of Natural Resources, Beijing, China Institute of Space Sciences, Shandong University, Weihai 264209, China

Abstract. Machine learning algorithms have been widely applied in various fields, including the research of the tropospheric delay of Global Navigation Satellite System (GNSS) signal. In this paper, back-propagation neural network (BPNN), radial basis function (RBF) neural network, and least square support vector machine (LSSVM) algorithm are applied to develop the regional zenith troposphere delay (ZTD) models by merging International GNSS Service ZTD products (GNSS-ZTD) and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over North America throughout 2020. Among them, two data-fusion strategies are designed with different input parameters of modeling, including the fusion of ERA5 meteorological parameters with GNSS-ZTD and the fusion of ZTD estimations from ERA5 data (ERA5-ZTD) and GNSS-ZTD. With ZTD derived at 77 IGS stations, the accuracy of regional ZTD models is verified by month, as well as the stability and efficiency. The results show that the effect of RBF is best when modeling ZTD with small-size training samples. Among them, the average RMSE of the ZTD models with RBF is 20.8 mm and 20.1 mm for two data-fusion strategies, respectively. The accuracy of RBF is improved by 40.4% and 38.5% over the BPNN in modeling ZTD. The result of the model using the LSSVM is close to the RBF. Moreover, the BPNN has an obvious advantage in modeling ZTD with large-size training samples. Keywords: ZTD
BP neural network
RBF neural network support vector machine
ERA5
GNSS


Least square

1 Introduction The refraction of the troposphere causes propagation delays of GNSS code and phase signals, namely troposphere delay. It is one of the main error sources of GNSS and is expressed as the product of the zenith troposphere delay (ZTD) and the mapping function. For illustrating the non-linear characterize of ZTD spatiotemporal change, machine learning algorithms have been applied to model tropospheric delay.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 145–158, 2021. https://doi.org/10.1007/978-981-16-3138-2_15

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In 2009, Katsougiannopoulos.S et al. used multi-layer perceptron to predict ZTD with the bias of 2–3 cm [1]. Based on GNSS stations in Hong Kong, the backpropagation neural network (BPNN) was adopted for fitting ZTD and gradient values in 2013, the temporal-spatial ZTD model was established with an RMS of 4.7 cm [2]. In 2016, a genetic algorithm (GA) was introduced to optimize initial weights and thresholds of BPNN to build a regional tropospheric delay model, which estimated ZTD at millimeter level in some CORS stations of the Anhui Power System [3]. Suparta et al. adopted an adaptive neural fuzzy reasoning system (ANFIS) to predict ZTD values by inputting meteorological parameters from 2013 to 2016 [4, 5]. The Radial basis function (RBF) neural network was applied to establish a regional tropospheric delay interpolation model in 2017 [6]. In 2018, the initial parameters of BPNN were fixed to build a regional tropospheric delay model based on 1000 GNSS stations in Japan [7]. Two fusion models of BP-Hopfield and GA-BP-EGONS were established using error compensation technology in 2019, and the accuracy of fusion models was improved by 33% and 58% over the Hopfield model and EGONS model respectively [8]. In 2020, Zhang et al. combined the BPNN and long short-term memory (LSTM) network to derive an hourly high-accuracy ZTD prediction model in West Antarctica [9]. The aforementioned tropospheric delay models are concentrated on artificial neural networks (ANN), especially the BPNN. Also, the current research on ERA5 reanalysis data is mainly the evaluation of meteorological parameters and the estimation of ZTD with the physical model [10–12]. Given these two aspects, based on the International GNSS Service (IGS) ZTD data and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over North America throughout 2020, we design two data-fusion strategies and establish regional ZTD models by adopting three machine learning algorithms, namely BPNN, RBF neural network and least squares support vector machine (LSSVM).

2 Data and Methodology 2.1

Data Sources

Two different data are from the IGS-ZPD file and ERA5 reanalysis. Among them, the IGS-ZPD file contains the required geodetic coordinates of the stations and ZTD estimations (GNSS-ZTD) with a sampling rate of 5 min. The ERA5 reanalysis offers single-layer meteorological grid data with a spatial resolution of 0.25° and a temporal resolution of 1 h, including the required pressure, temperature, dew point temperature and geopotential. Besides, the hourly GNSS-ZTD values are retained to keep the same temporal resolution with ERA5 data. We select GNSS-ZTD values at 77 IGS stations in North America from January 1, 2020 to December 11, 2020. The distribution of stations is shown in Fig. 1. Figure 2 illustrates how the average GNSS-ZTD values vary with the coordinate of available stations. It can be seen that the distribution of IGS stations is uneven and sparse in the research region. Moreover, GNSS-ZTD values change linearly with elevation but nonlinearly over latitude and longitude.

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Fig. 1. Distribution diagram of the experimental base stations

Fig. 2. GNSS-ZTD change over latitude, longitude, and altitude

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Methodology of Modeling ZTD

2.2.1 Calculating ZTD Using ERA5 Data ERA5 grid data is extended to the ZTD estimations at IGS stations based on the Saastamoinen model. Specific calculation steps are as follows [13]: (1) Data pre-processing. The geopotential q at the grid point is converted into the ellipsoid height with the EGM2008 model. (2) Bilinear interpolation. According to the longitude h and latitude u of the targeted IGS station, the four nearest grid points are selected in the ERA5 grid. The pressure Ps , 2-m temperature Ts and 2-m dew point temperature Tds of targeted IGS station are calculated at height HS by linear interpolation twice. (3) Elevation correction. The meteorological elements at height HS are corrected to the targeted IGS station height H. The specific correction formulas are as follows:

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ERA5-T ¼ Ts  6:5  dh

ð1Þ

ERA5-Td ¼ Tds  6:5  dh

ð2Þ

ERA5-P ¼ Ps  ð1 

6.5  dh)5:2559 ERA5-T

dh ¼ HS  H

ð3Þ ð4Þ

(4) Calculating water vapor pressure. The water vapor pressure ERA5-e at the targeted IGS station is derived based on ERA5-T and ERA5-Td . ERA5-RH 

eðERA5-Td Þ eðERA5-TÞ

 R3 ðERA5-Td  273:16Þ ERA5-Td  R4   R3 ðERA5-T  273:16Þ eðERA5-TÞ ¼ R2 exp ERA5-T  R4

ð5Þ



eðERA5-Td Þ ¼ R2 exp

ð6Þ ð7Þ

ERA5-e ¼ ERA5-RH
 exp 34:2465 þ 0:213166  ERA5-T  0:000256908  ERA5-T2 ð8Þ Among them, ERA5-RH represents relative humidity. In the case of ERA5-T [ 0  C,R2 ¼ 6:112 hpa; R3 ¼ 17:502 K; R4 ¼ 32:1 K: (5) Estimating ZTD value. ERA5-ZTD is derived at the targeted IGS station by the Saastamoinen model, which is expressed as follows [14]: ERA5-ZTD ¼ 0.002277

1255 [ERA5-P þ ð ERA þ 0.05)ERA5-e] 5-T

1  0.00266cosð2uÞ  0.00028H

ð9Þ

2.2.2 Data-Fusion Using Machine Learning Algorithms Machine learning algorithms simulate the mapping rules between input parameters and output parameters by learning pairs of known data. Two data-fusion strategies are designed based on different parameters. One is the fusion of ERA5 meteorological parameters and GNSS-ZTD products at IGS stations. Another is to merge the ERA5 - ZTD estimations with the GNSS - ZTD products at IGS stations. Figure 3 shows the structure of ZTD models based on two data-fusion strategies respectively.

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Fig. 3. Structure of ZTD models based on two data-fusion strategies

In the case of Strategy 1, the single input vector ~ x and the corresponding output parameter y are (b, l, h, ERA5-P, ERA5-T, ERA5-e) and GNSS-ZTD at an IGS station, respectively. In the case of Strategy 2, the single input vector ~ x is (b, l, h, ERA5-ZTD), and the output parameter y is the same as Strategy 1. For a given training sample, the modeling process of BPNN, RBF neural network and LSSVM algorithm are elucidated, respectively. BPNN involves two processes of learning: the forward calculation of data signals and the back propagation of error signals. The specific process is detailed in Fig. 4. Among them, the initial weights matrix Wij and Wjk are assigned randomly. Table 1 lists the initial parameters in the experiment. Table 1. The setting of initial BPNN parameters Parameter Number of hidden layers Number of neuron in a hidden layer The activation function of the input layer The activation function of the hidden layer Maximum number of iterations Learning rate Training error threshold Maximum times of gradient descent failure

Value 1 7 ‘tansig’ ‘purelin’ 100 0.1 0.001 8

RBF neural network is a feedforward neural network with a single hidden layer. Different from BPNN, RBF only adjusts the weight between the hidden layer and the output layer. Figure 4 shows the topological structure of the RBF neural network. Wherein, the input parameters are converted to the parameters in the hidden layer by radial basis function, the output parameter is the linear combination of the parameters in the hidden layer with weights Wjk . The training error threshold of the RBF neural network is set to 0.001 in the experiment. The least squares support vector machine (LSSVM) is developed from SVM, which maps nonlinear input data into high dimensional space by the kernel function. With the

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Fig. 4. The topological structure of BPNN and RBF

quadratic function of error as a constraint, the least squares method is adopted to solve hyperplane problems in high-dimensional space. In this paper, the parameters and methods of the LSSVM are listed in Table 2. Table 2. Initial LSSVM parameters setting Parameter Value The tradeoff between equation size and training error 10000 Kernel function factor 2 The method of optimization Grid search Kernel function ‘RBF kernel’ The method of verification Cross-validation

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Method of Verifying the ZTD Models

Due to the poor GNSS-ZTD data integrity of some IGS stations in a long period, we adopt the segmentation modeling and verification method by dividing the entire observation period (2021.1.1–2021.12.11) into 12 periods by month. In the experiment, about 50 stations with continuous GNSS-ZTD data are available per month, and 10 stations without participating in model training are selected as test stations. With the reference of GNSS-ZTD at 10 test stations, the monthly bias and the monthly root mean square error (RMSE) of the ZTD estimations are calculated to evaluate the accuracy of ZTD models.

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3 Results 3.1

Analysis of Accuracy

Figure 5, 6, 7 and 8 statistic the monthly bias and monthly RMSE of 10 test stations in 2020, the mean value are listed in Table 3 and Table 4. Among them, the results of 10 test stations per month are defined as one group. For the box diagram of Fig. 5, 6, 7 and 8, the red line is the median reflecting the mean level. The blue box lines respectively represent the upper quartile Q1 and lower quartile Q3 of this set of data, and 50% of the data is contained in the range of Q1 and Q3. The width of the box reflects the dispersion degree of each group result. Q1 + 1.5(Q1 – Q3) and Q3 – 1.5(Q1 – Q3) are taken as the upper and lower limits. The black lines extending above and below the box respectively represent the maximum and minimum values of each group within the range of limits. The data over the upper or lower limits are considered outliers and represented by a symbol with the red cross.

Fig. 5. The monthly bias of ZTD models based on Strategy 1

Fig. 6. The monthly bias of ZTD models based on Strategy 2

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The statistical results of monthly bias in Fig. 5 and Fig. 6 show that the results of BPNN fluctuate greatly over the month and contain most outliers. For the results of RBF and LSSVM, the variation amplitude within a year is slight, the discretization degree of each group results of the RBF is smaller than that of the LSSVM in most months. As can be seen from Table 3, the mean monthly bias of BPNN is the smallest with the value of 1.1 mm and 1.2 mm for two data-fusion strategies respectively, followed by RBF and LSSVM algorithm. From the higher monthly bias in most months, ERA5-ZTD has obvious systemic bias with GNSS-ZTD, which are weakened significantly after fusing ERA5 data with GNSS-ZTD by three machine learning algorithms. Table 3. The average monthly bias of different ZTD models at ten test stations (Units: mm) ERA5-ZTD BP Strategy1 Jan 1.2 1.3 Feb 1.3 −0.7 Mar 0.2 1.8 Apr −4.6 3.0 May −3.8 3.1 Jun 0.0 4.2 Jul −5.8 0.6 Aug −7.8 1.0 Sept −5.3 −0.1 Oct 1.0 0.7 Nov 3.2 −0.7 Dec 7.3 −1.2 Mean −1.1 1.1

RBF LSSVM Strategy2 Strategy1 Strategy2 Strategy1 Strategy2 1.0 1.5 1.0 2.3 1.2 0.7 0.7 0.9 0.4 0.2 2.5 3.6 3.2 3.7 3.6 2.7 3.4 3.2 3.6 3.2 3.2 3.9 2.5 3.6 3.7 5.4 4.8 5.4 5.1 5.4 0.6 1.8 0.9 3.3 2.6 1.8 1.3 0.6 4.3 3.5 −1.2 2.7 1.1 0.8 −0.8 1.2 3.3 2.8 1.5 1.4 −0.7 0.5 −0.7 0.2 0.4 −2.2 −0.9 −1.6 −1.7 −1.7 1.2 2.2 1.6 2.3 1.9

Fig. 7. The monthly RMSE of ZTD models based on Strategy 1

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Fig. 8. The monthly RMSE of ZTD models based on Strategy 2

In Fig. 7 and Fig. 8, the monthly RMSE of BPNN is larger than that of RBF and LSSVM. The dispersion of RBF is slightly bigger than LSSVM, especially from May to October. For Strategy 2, the results of the three algorithms have fewer outliers with the comparison of Strategy 1. As can be seen from Table 4, the monthly RMSE of BPNN is greater than that of ERA5-ZTD in 2020. The monthly RMSE of RBF is not much different from that of LSSVM, the mean values are smaller than that of BPNN and ERA5-ZTD. In addition, the maximum RMSE of all ZTD models appears in the summer from June to August, and the dispersion degree of results is relatively large. Table 4. The average monthly RMSE of different ZTD models at ten test stations (Units: mm) ERA5-ZTD BP Strategy1 Jan 21.1 28.0 Feb 18.6 23.2 Mar 20.6 25.1 Apr 23.3 28.5 May 26.3 35.6 Jun 30.9 42.0 Jul 34.9 41.1 Aug 33.0 48.4 Sept 31.7 46.1 Oct 26.4 38.1 Nov 22.1 33.1 Dec 25.5 29.3 Mean 26.2 34.9

Strategy2 25.7 24.9 23.4 24.9 32.2 38.0 40.4 44.4 42.1 39.0 28.5 29.1 32.7

RBF Strategy1 14.3 12.3 14.4 16.4 21.0 28.7 29.5 27.6 27.3 23.7 18.2 16.6 20.8

Strategy2 14.6 12.4 14.4 16.1 19.6 25.7 28.7 26.9 26.1 21.5 17.7 17.1 20.1

LSSVM Strategy1 12.9 11.6 13.8 16.6 20.9 28.4 29.5 27.8 27.3 22.5 17.8 16.8 20.5

Strategy2 13.4 12.2 14.3 16.9 20.9 27.7 30.5 28.2 27.5 21.5 18.7 18.3 20.8

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In summary, the overall accuracy of ZTD models using the BPNN is lower than that of ERA5-ZTD, while the ZTD model based on RBF is similar to the LSSVM with higher accuracy. Moreover, all ZTD models work worse in summer (June to August) owing to the rich water vapor and high temperature. 3.2

Analysis of Efficiency and Stability

Table 5 lists the cost time for modeling ZTD by different algorithms under the same conditions. The results show that the efficiency of RBF is highest, followed by BPNN. The LSSVM takes the longest time for modeling ZTD. RBF maps data from the input layer to the hidden layer through radial basis function, which has the characteristics of local approximation and fast convergence. For BPNN, the weight of each neuron is adjusted by back-propagation error signals. It is a global approximation with a long convergence time. The grid-research method leads to a larger computational burden for modeling with LSSVM. Moreover, three algorithms are used to conduct ZTD models with the same training samples for 5 times to verify the stability. As shown from the average RMSE of ZTD models in Fig. 9 and Fig. 10, the results of the BPNN have obvious differences for the same training sample, while that of the LSSVM varies slightly in sub-millimeter level, and the RMSE of ZTD models using RBF is stable and unchanged.

Table 5. Cost time of models based on different algorithms (Units: s) BP Strategy1 Jan 122.2 Feb 109.4 Mar 115.7 Apr 118.9 May 120.9 Jun 116.3 Jul 119.3 Aug 118.7 Sept 113.2 Oct 120.9 Nov 113.5 Dec 41.7 Mean 110.9

RBF Strategy2 Strategy1 120.7 55.9 113.1 48.7 122.7 53.2 118.6 52.3 123.5 55.0 120.4 56.8 124.0 58.5 125.4 56.2 120.0 54.1 123.8 55.7 118.9 51.8 44.3 19.6 114.6 51.5

LSSVM Strategy2 Strategy1 53.5 646.2 45.7 633.2 52.8 716.7 51.9 688.0 55.1 678.0 56.7 655.7 58.4 679.0 55.9 687.8 54.3 652.6 55.5 716.4 51.8 616.9 19.9 240.1 51.0 634.2

Strategy2 668.7 629.0 683.4 652.4 674.9 653.0 672.9 672.6 649.6 670.3 607.5 239.2 622.8

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Fig. 9. The average RMSE of ZTD models based on Strategy 1

Fig. 10. The average RMSE of ZTD models based on Strategy 2

With comprehensive consideration of the accuracy, efficiency, and stability of modeling ZTD with three machine learning algorithms, it is concluded that the RBF neural network has the best effect for the above training samples. The accuracy and stability of the LSSVM are roughly similar to the RBF but efficiency is lower.

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Moreover, the BP neural network algorithm works worse in modeling ZTD, especially the accuracy. 3.3

Discussion of Applicability

For exploring the advantages of machine learning algorithms, we further discuss the applicability of the three algorithms. Small-size training samples (about 50 stations) are adopted for modeling ZTD per month in the above experiment. Based on the existed researches, insufficient learning is one of the reasons why the BPNN has low accuracy for modeling ZTD. Therefore, we add three parameters (year, day of year, and seconds) in the input layer to expand the size of the training samples matrix. The number of available training samples is increased from about 50 to about 23,000 per month. The ZTD models are established and verified based on this sample matrix in this section. The larger sample matrix makes the equation singular in the calculation process of the LSSVM, which leads to failure to establish the ZTD model. Therefore, only the average monthly RMSE values of BPNN and RBF are listed in Table 6. For the modeling ZTD with BPNN, the accuracy is better than the results of modeling with fewer samples. Simultaneously, the efficiency of modeling is improved since the time information is learned as the input parameter. However, the accuracy of RBF is lower than that of modeling ZTD with fewer samples, and the memory of the program increases sharply during calculation. Therefore, we conclude that the BPNN is more suitable for modeling variables with a large number of training samples, and the RBF algorithm and LSSVM algorithm have better effects when fewer training samples are available.

Table 6. The average RMSE of different ZTD models with large-size training samples based on BPNN and RBF (Units: mm) BP Strategy1 Jan 16.1 Feb 15.4 Mar 17.2 Apr 18.9 May 21.6 Jun 28.6 Jul 30.4 Aug 28.5 Sept 26.4 Oct 23.4 Nov 22.3 Dec 18.5 Mean 22.3

Strategy2 16.6 15.5 17.3 18.6 22.3 27.9 31.0 29.2 29.1 24.9 20.1 19.9 22.7

RBF Strategy1 16.7 15.7 18.1 20.5 24.3 28.3 31.3 31.6 31.1 26.9 29.9 21.2 24.7

Strategy2 17.0 15.7 18.6 20.6 24.6 29.8 31.9 32.1 30.8 27.4 26.2 22.2 24.7

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4 Conclusion With two data-fusion strategies, ERA5 data and GNSS data are fused by three machine learning algorithms to model the zenith tropospheric delay (ZTD) in North America. Through the analysis of the ZTD models with a small-size training sample, the accuracy and stability of ZTD models adopting the RBF are comparable to that of LSSVM, and both of them are better than BPNN. Owing to different methods of optimizations, RBF has the highest modeling efficiency, followed by BPNN and LSSVM. Moreover, BPNN has obvious advantages in modeling massive training data, while RBF and LSSVM are more suitable for modeling small-size training samples. Simultaneously, the accuracy of modeling ZTD by integrating ERA5 meteorological parameters and GNSS-ZTD value is similar to that of models fusing ERA5 ZTD and GNSS ZTD, but the ZTD models adopting Strategy 2 are more stable. Besides, the systemic bias of the ZTD estimations based on machine learning algorithms and data fusion is smaller than that of ZTD estimations from ERA5 and Saastamoinen models (ERA5-ZTD), in which the average RMSE value of RBF and LSSVM is reduced by about 6 mm. Acknowledgement. Thanks to European Centre for Medium-Range Weather Forecasts (ECMWF) and international GNSS service (IGS). This project is supported by the National Key Research & Development Program of China (2016YFB0501701), the National Natural Science Foundation of China (Grant No. 41874032), the Natural Science Foundation of Shandong Province, China (ZR2020QD046 and ZR2020MD045), and the Open Fund of the Key Laboratory of Marine Environmental Exploration Technology and Application, Ministry of Natural Resources, China (No. : MESTA-2020-B013).

References 1. Katsougiannopoulos, S., Pikridas, C.: Prediction of zenith tropospheric delay by multi-layer perceptron J. Appl. Geodesy (2009). https://doi.org/10.1515/JAG.2009.022 2. Li, J., Wu, L., Hu, W., et al.: Calculation of tropospheric wet delay based on BP neural network algorithm. J. Southeast Univ. (Nat. Sci. Edn.) (2013). https://doi.org/10.3969/j.issn. 1001-0505.2013.S2.030 3. Yin, W., Tao, T., Deng, Q., et al.: Interpolation algorithm of GPS tropospheric delay based on GA-BP. Science of Surveying and Mapping (2016) 4. Suparta, W., Alhasa, K.M.: Application of ANFIS Model for prediction of zenith tropospheric delay. In: Proceedings of 2013 3rd International Conference on Instrumentation, Communications, Information Technology, and Biomedical Engineering (ICICI-BME), Bandung, November 7–8, pp. 172–177 (2013) 5. Suparta, W., Alhasa, K.M.: Modeling of tropospheric delays using ANFIS. SpringerBriefs Meteorology (2016). https://doi.org/10.1007/978-3-319-28437-8 6. Ma, J., Tao, T., Yin, W.: Interpolation model of GPS tropospheric delay based on RBF neural network. Metal Mine (2017). https://doi.org/10.19614/j.cnki.jsks.2017.10.007 7. Xiao, G., Ou, J., Liu, G., et al.: Construction of a regional precise tropospheric delay model based on improved BP neural network. Chin. J. Geophys.-Chin. Edn. (2018) https://doi.org/ 10.6038/cjg2018L0565

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8. Yang, H., Feng, K., Xie, S., et al.: Improved GPT2w model based on BP neural network and its global precision analysis. Syst. Eng. Electron. (2019) 9. Zhang, Q., Li, F., Zhang, S., et al.: Modeling and forecasting the GPS zenith troposphere delay in West Antarctica based on different blind source separation methods and deep learning. Sensors (Basel) (2020) https://doi.org/10.3390/s20082343 10. Albergel, C., Dutra, E., Munier, S., et al.: ERA-5 and ERA-interim driven ISBA land surface model simulations: which one performs better? Hydrol. Earth Syst. Sci. (2018). https://doi. org/10.5194/hess-22-3515-2018 11. Sun, Z., Zhang, B., Yao, Y.: An ERA5-based model for estimating tropospheric delay and weighted mean temperature over China with improved spatiotemporal resolutions. Earth Space Sci. (2019). https://doi.org/10.1029/2019ea000701 12. Wang, S., Xu, T., Nie, W., et al.: Evaluation of precipitable water vapor from five reanalysis products with ground-based GNSS observations. Remote Sens. (2020). https://doi.org/10. 3390/rs12111817 13. Jiang, C., Xu, T., Wang, S., et al.: Evaluation of zenith tropospheric delay derived from ERA5 data over CHINA using GNSS observations. Remote Sens. (2020). https://doi.org/10. 3390/rs12040663 14. Saastamoinen, J.: Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging Satellites. Use of Aritificial Satellites for Geodesy (1972)

Research on Nonlinear Inversion of Vegetation Water Content Based on Multiple Ground-Based GPS-IR Jiyang Li1, Yueji Liang1,2(&), Jiajia Ma1, Sidan Xie1, and Zhe Wen1 1

2

College of Geomatics and Geoinformation, Guilin University of Technology, Guilin, China [email protected] Research Center of Precise Engineering Surveying, Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin, China

Abstract. It is of great significance to timely and accurately monitor the vegetation water content (VWC) for the study of plant growth status, drought assessment, and fire risk forecasting. Global Positioning System Interferometric Reflectometry (GPS-IR) is a new type of remote sensing technology. The signalto-noise ratio recorded by the measurement receiver can be used to retrieve VWC effectively. Although studies have fully proved that the change of VWC can be effectively reflected by the normalized microwave reflectance index (NMRI), the NMRI based on a single ground-based GPS-IR cannot achieve spatial continuity. This paper makes full use of the advantages of multiple ground-based GPS-IR combined with vegetation index, weather, topography and other related elements, and a nonlinear inversion method of high spatial resolution VWC based on multiple ground-based GPS-IR is proposed. Firstly, First, various elements are acquired through Google Earth Engine, and the resolution is unified through ArcGIS; Then, the relationship model between the multiple ground-based GPS-IR and related elements is established through the least square support vector machine (LS-SVM), and the modeling effects of different model input variables are compared and analyzed, and the best modeling solution is selected; Finally, after model testing, the accurate inversion of VWC is realized. Taking a certain area of the United States as the research object, experiments show that: 1) Different fac-tors have different influences on modeling accuracy. Three vegetation indices of NDVI, GPP and LAI > topography > longitude and latitude of the station > daily average rainfall and daily average temperature. Among them, NDVI is a key element that affects modeling accuracy. 2) Using LS-SVM can effectively integrate multiple groundbased GPS-IR and related elements, and the model fitting process is relatively stable; the 16Day/500 m resolution NMRI image obtained by model inversion can better reflect regional VWC changes. 3) The model inversion error is relatively stable. The maximum error is only 0.031, and the root mean square error is only 0.040. Keywords: Vegetation water content
GPS interferometric reflectometry
Environmental elements
Least squares support vector machine
Precision analysis

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 159–172, 2021. https://doi.org/10.1007/978-981-16-3138-2_16

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1 Introduction The water content of the vegetation canopy is an important biophysical parameter for climate research and drought monitoring. Accurately monitoring the Vegetation Water Content (VWC) is of great significance to the study of plant growth status, drought analysis, fire risk assessment, etc. [1]. In recent years, with the rapid development of remote sensing technology and imaging spectroscopy technology, the Normalized Differential Vegetation Index (NDVI) with high spatial resolution can be obtained through optical remote sensing. Since NDVI is largely considered to measure the greenness of plants, it can be used to estimate biomass, Leaf Area Index (LAI), VWC and vegetation coverage [2]. However, factors such as plant types, plant water conditions and water climate conditions have different effects on VWC and “greenness”, resulting in a weak relationship between NDVI and VWC [3]. Moreover, optical remote sensing is easily affected by clouds and fog, leading to loss of information. In addition, although VWC obtained by microwave remote sensing is not affected by clouds and fog, its spatial resolution is low, and it is difficult to accurately represent small and medium-sized VWC information. Although some scholars have tried to combine optical remote sensing and microwave remote sensing to invert VWC, the large difference in spatial resolution between the two causes more uncertainty in the model inversion results. In recent years, the use of GPS reflected signals to monitor geophysical parameters has become a new remote sensing monitoring method, which has the advantages of high efficiency, all-weather, and high temporal and spatial resolution. Among them, the Global Position System-Interferometric Reflectometry (GPS-IR), which is developed based on measurement receivers, uses the direct and reflected signals of satellites to superimpose interference at a single antenna to achieve environmental parameters of the station. The measurement of its changes has been effectively verified in terms of snow thickness, sea level height, soil moisture, and vegetation index [3–567].For vegetation water content inversion, Small et al. first used GPS noise statistics MP1 rms to qualitatively estimate vegetation growth, indicating that the reflected signal in the Signal to Noise Ratio (SNR) can affect the vegetation growth status Respond [8]; Larson et al. showed that the amplitude of the reflected signal interferogram depends on the VWC, and defined a daily vegetation index dependent on the reflection amplitudeNormalized Microwave Reflection Index (NMRI), which can be more Reflect the changes of VWC well, and compile the NMRI time series database of more than 300 stations [9]; Wan et al. showed that when the moisture content of grassland is 0– 0.5 kg/m2, there is a strong linear relationship between VWC and reflected signal amplitude [10]; Zheng Nanshan et al. showed that GPS reflected signal amplitude and NDVI have significant annual periodicity And seasonal characteristics. Although these existing studies can obtain high-precision VWC through a single ground-based GPSIR, they cannot achieve continuous spatial monitoring of VWC [11]. In order to obtain regional VWC, Yuan et al. realized the effective integration of ground-based GPS-IR and MODIS data and rainfall through machine learning methods, indicating that machine learning methods can better learn the correlation between NMRI and input VWC related indexes, and the cross-validated R value is 0.71–0.83 [12]. Pan et al. built

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a high-altitude resolution VWC inversion model based on genetic BP neural network and showed that the correlation coefficients between NMRI estimates and reference values are all greater than 0.87, and RMSE is less than 0.049 [13]. However, there is a close relationship between VWC and surface environmental information. Existing studies have not considered comprehensively the factors related to VWC, and lack effective evaluation of model input variables, which affects the stability and reliability of VWC inversion results to a certain extent. In summary, this article aims at the problem of the inability to achieve spatial continuity in a single ground-based GPS-IR monitoring VWC, and makes full use of the advantages of multi-base GPS-IR integration to study the construction of a joint multi-base GPS-IR and related elements. Resolution VWC nonlinear inversion method. Firstly, various elements are acquired through Google Earth Engine (GEE), and then based on the principle of Least Squares Support Vector Machine (LS-SVM) [14], the establishment of joint multiple ground-based GPS-IR and Non-linear relationship between relevant elements, and compare and analyze the modeling effects of different model input variables, discuss the important elements that affect modeling, select the best modeling plan, obtain spatially continuous NMRI images, and better represent VWC changes.

2 Principles and Methods 2.1

Ground-Based GPS-IR Principle

SNR is an index that characterizes the signal quality of a receiver antenna, and is mainly affected by antenna gain parameters, multipath effects, and random noise in the receiver. The signal acquired by a survey GPS receiver often includes direct satellite signals and signals reflected on the earth's surface, as shown in Fig. 1.

Fig. 1. Geometric model of ground multi-path error

In Fig. 1, h represents the priori reflection height, b represents the angle between the satellite signal and the slope, and c represents the satellite incident height angle.

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Existing studies have shown that the use of multipath reflection signals in SNR can realize the monitoring of geophysical parameters [3]. Moreover, there is a sine or cosine relationship between the SNR observation value and the multipath interference phase. The SNR multipath reflection component after the direct component is removed by low-order polynomial fitting and a fixed frequency sine (or cosine) function still exists between Relationship [8, 9]. The interferogram of the signal-to-noise ratio can be expressed by the following formula: SNR ¼ Acos

  4ph sin h þ u k

ð1Þ

In the formula, h represents the priori reflection height, k is the carrier wavelength, h represents the satellite incident altitude angle, A and u represent the amplitude and phase respectively, which can be calculated by the least square estimation method. NMRI is used as an index to evaluate the change of the reflected signal amplitude, and its core is to calculate the root mean square value of the pseudo range multipath index MP1 on the L1 carrier. The calculation process of MP1 is shown in literature [9]. Then, the calculation formula of NMRI can be expressed as [9]: NMRI ¼

ðRMSMP1  maxðRMSMP1 ÞÞ maxðRMSMP1 Þ

ð2Þ

In the formula, RMSMP1 is the root mean square of MP1 on a single day, and maxðRMSMP1 Þ is the average value of the top 5% of RMSMP1 after sorting the value of RMSMP1 from large to small. 2.2

High Spatial Resolution VWC Nonlinear Inversion Method

Considering the time and space complexity of ground-based GPS-IR and various vegetation indices, weather, topography and land cover types, in this paper, the widely used LS-SVM with strong generalization ability, fast calculation speed, high nonlinear fitting accuracy, small samples, is used to construct a nonlinear relationship model between multiple ground-based GPS-IR and various elements, to achieve accurate inversion of high spatial resolution VWC. Suppose the input variable set of the model composed of various elements is x, and the output variable set corresponding to x is y, and the samples in the input space are mapped to a higher-dimensional feature space through a nonlinear transformation /ðxÞ, thereby converting the input space The nonlinear problem in is transformed into a linear problem in the feature space, and then LS-SVM is used to fit the sample points in the feature space[14]. The detailed process can be found in literature [14]. In order to make better use of the performance of

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LS-SVM, this paper selects the Radial Basis Function (RBF), which can reflect the complexity of the model well and has good universality, as the kernel function of LSSVM. At the same time, the grid search method [15] is used to optimize the selection of kernel parameters and regularization parameters. 2.3

Inversion Process

1) Experimental area setting. Combining the distribution of ground-based GPS stations and the characteristics of various elements, the area of this experiment is set up reasonably. 2) Data acquisition and preprocessing. Considering that the minimum time and space resolution of the experimental data is 16Day and 500 m respectively, the resolution of all data needs to be unified to 16Day/500 m; Use GEE platform to write language programs to download various image data corresponding to the experimental area, and use ArcGIS software to unify the temporal and spatial resolution to extract NDVI, LAI, Gross Primary Productivity(GPP), elevation, slope, aspect, hillshade, daily average rainfall, daily average temperature and land cover type, a total of 10 elements. 3) Data set construction. According to the latitude and longitude information of each GPS station, the 10 elements of the corresponding location are extracted separately, and the latitude and longitude of each station and the 10 elements are randomly combined to obtain the model training input variable set of various modeling schemes, and the corresponding location The NMRI is used as the model training output variable set. 4) Selection of the optimal modeling plan. Establish an LS-SVM training model based on the training input variable set designed in step 3) and the corresponding training output variable set; Compare and analyze the modeling accuracy of different model training input variables, select the best modeling plan to obtain the required model building Input variables. 5) Model testing and accuracy verification. According to the best modeling plan, input the model input variable set corresponding to all pixels with a spatial resolution of 500m in the experimental area into the trained LS-SVM model to obtain a spatially continuous NMRI, and pass the foundation that is not involved in the modeling The GPS station performs accuracy statistical analysis. The specific inversion process is shown in Fig. 2.

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Fig. 2. Experimental flowchart

3 Experimental Area and Data Source The U.S. Plate Boundary Observatory (PBO) is currently the only observation network that operates continuously based on GPS-IR principles. The daily vegetation water content, soil moisture and snow depth obtained based on GPS-IR can be downloaded for free from the website http://xenon.colorado.edu/portal. As can be seen from Fig. 3, ground-based GPS stations cover almost all of the continental United States located at 32° * 49 °N latitude and 102° * 125 °W longitude. In order to better verify the feasibility and effectiveness of this method, and considering the impact of the diversity of terrain and the diversity of vegetation coverage. The yellow area in the Fig. (40° to 45° north latitude, 110° to 122° west longitude) is selected as the experimental area. The digital elevation model (DEM) and the type of surface vegetation cover corresponding to the experimental area are shown in Fig. 4 and Fig. 5, respectively.

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Fig. 3. Distribution of ground-based GPS stations

Fig. 4. Digital elevation model of the experimental area

Fig. 5. Land cover types of the study area

It can be seen from Fig. 4: the ups and downs of the area are more obvious, the minimum altitude is 41m, and the maximum is 4143 m; The selected 71 ground-based GPS stations have different distribution locations and densities. They are distributed in low, medium and high-altitude areas. Among them, 71 circles represent stations participating in the modelling, the 6 triangles represent stations that are not involved in modelling. Combined with Fig. 5 analysis found, among the 71 ground-based GPS stations, 66 ground-based GPS stations are located in the grassland environment. For the 6 GPS stations for model verification, three are located in a grassland environment, two are located in a savanna, and one is located in a mixed forest, the distribution of these stations is conducive to the verification of model inversion accuracy. Combined with the analysis of Fig. 4 and Fig. 5, The terrain on the left half of the experimental area is relatively flat, and the surface is covered with a variety of different vegetation; The topography on the right half is more obvious, and the land cover type is more complicated, there is the famous Great Salt Lake in the United States (the light blue area in the lower right corner). Visible, considering the experiment area different topography and land cover types, is conducive to fully verify the feasibility and effectiveness of this method.

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Therefore, the selected elements mainly include: NDVI, GPP and LAI three vegetation indices, as well as daily average rainfall, daily average temperature, elevation, slope, aspect, hill shade and land cover type. Through the GEE platform (https:// developers.google. com/earth-engine/datasets/), by writing related data download programs, batches of various product data in the experimental area are obtained, the detailed information can be seen from Table 1 Considering that NDVI has the lowest time resolution. Therefore, the spatial and temporal resolution of the experimental data is set to 16 Day/500m.The time corresponding to the effective modeling data in the selected time period of the experiment is: 2012–06-25, 2012–07-11, 2012–07-27, 2012–08-12, 2012–08-28, 2012–09-13 and 2012–09-29, 7 days in total. Through ArcGIS software, the daily NMRI and related elements of 71 stations in the study area can be extracted in batches. Among them, DEM can provide elevation, slope, aspect and hill shade elements. Table 1. Detailed information of each product Elements NMRI NDVI GPP LAI DEM Average daily rainfall Average daily temperature Land cover type

Resolution Daily/station 16Day/500 m 8Day/500 m 4Day/500 m 500 m Daily/500 m Daily/500 m Year/500 m

Product PBO H2O MOD13A1 MOD17A2H MCD15A3H SRTMG L1 AN81d -ppt AN81d-team MCD12Q1

Date 2012.6.25–2012.9.29 2012.6.25–2012.9.29 2012.6.25–2012.9.29 2012.6.25–2012.9.29 2000.02 2012.6.25–2012.9.29 2012.6.25–2012.9.29 2012.1.01

4 Experiment Analysis In order to select the best modeling input variables and discuss the key elements that affect modeling, the original training input variable set is divided into four types. The longitude and latitude information of the station (lon, lat) is the location element of the station; NDVI, LAI and GPP are vegetation elements; daily average rainfall (ppt) and daily average temperature (tmean) are meteorological elements; elevation (ele), slope (slope), aspect (aspect) and shadow (h) are the topographic features; Land cover type (f) is the land cover element. There are 15 modeling schemes designed for comparison and analysis, as shown in Table 2 Suppose the model input variable set of each scheme is x, the formula is as follows: x ¼ ½x1 ; x2 ; . . .; xi ði¼1; 2; . . .; 6Þ xi ¼ ½w1 ; w2 ; . . .; wb ðb ¼ 1; 2; . . .; 71Þ

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Table 2. Modeling training program design Scheme 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Variables of model training input lon + lat + GPP + NDVI + LAI + ppt + tmean + aspect + ele + h + slope + f GPP + NDVI + LAI + ppt + tmean + aspect + ele + h + slope + f lon + lat + ppt + tmean + aspect + ele + h + slope + f lon + lat + GPP + NDVI + LAI + aspect + ele + h + slope + f lon + lat + GPP + NDVI + LAI + ppt + tmean + f lon + lat + NDVI + ppt + tmean + aspect + ele + h + slope + f lon + lat + GPP + ppt + tmean + aspect + ele + h + slope + f lon + lat + LAI + ppt + tmean + aspect + ele + h + slope + f lon + lat + NDVI + LAI + ppt + tmean + aspect + ele + h + slope + f lon + lat + GPP + NDVI + ppt + tmean + aspect + ele + h + slope + f lon + lat + GPP + LAI + ppt + tmean + aspect + ele + h + slope + f lon + lat + GPP + NDVI + LAI + ppt + aspect + ele + h + slope + f lon + lat + GPP + NDVI + LAI + tmean + aspect + ele + h + slope + f lon + lat + NDVI + ppt + aspect + ele + h + slope + f lon + lat + NDVI + tmean + aspect + ele + h + slope + f

wb ¼ ½a1 ; a2 ; . . .; an ðn ¼ 1; 2; . . .; mÞ

ð3Þ

In the formula, wb represents the model training input variable of the pixel where the b-th GPS station is located on the i-th day; an represents the n-th element, and m represents the number of elements. In the experiment, each scheme was modeled and trained 100 times. For each modeling process, 497 columns of variables in 426 columns are randomly selected as model training input, and the corresponding NMRI is used as model training output to establish LS-SVM training model, and use grid algorithm to optimize model parameters; the remaining 71 columns of variables are input into the established model, and the NMRI inversion results of 71 stations are output. At the same time, obtain the correlation coefficient (r) between the output result of each modeling test and the reference value, and calculate the maximum correlation coefficient (r_max) and average phase relationship (r_mean) of 100 runs as well as the maximum root mean square error of the test error (RMSE_max) and the mean root mean square error (RMSE_mean). The results are shown in Table 3 At the same time, r is divided into four different levels for statistics, as shown in Fig. 6.

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Modeling accuracy statistics of each scheme Scheme

r_max

r_mean

RMSE_max

RMSE_mean

1

0.856

0.764

0.030

0.022

2

0.848

0.703

0.034

0.024

3

0.813

0.645

0.036

0.027

4

0.895

0.791

0.028

0.022

5

0.838

0.675

0.038

0.026

6

0.882

0.761

0.033

0.023

7

0.882

0.758

0.031

0.023

8

0.840

0.710

0.034

0.024

9

0.884

0.740

0.036

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10

0.864

0.761

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11

0.870

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0.034

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12

0.862

0.750

0.023

0.023

13

0.913

0.781

0.029

0.022

14

0.848

0.728

0.031

0.024

15

0.888

0.757

0.030

0.023

Fig. 6. Correlation coefficients of different levels of each scheme

It can be seen from Table 3 and Fig. 6 that when 12 factors are involved in the modeling, the mean r is 0.764, the mean RMSE is 0.022, and r less than 0.70 accounts for 17%. Comparing Schemes 2 to 5, when vegetation elements are removed, the average r is only 0.645, and r less than 0.60 accounts for 20%; When the meteorological elements are eliminated, the average r value is 0.791, the maximum value of r reaches 0.895, and the r less than 0.7 is only 6%; when the station location elements or terrain elements are removed, r less than 0.60 accounts for 8% and 17%, respectively. Compared with scheme 1, the influence degree of the four groups of elements on improving the modeling accuracy is: vegetation element > topography element > station location element > meteorological element. It can be seen that the vegetation element is the main element that affects the modeling effect, and the meteorological element is not conducive to the improvement of the modeling accuracy. In order to further explore the key elements of vegetation and meteorological elements that affect the modeling effect, combining the analysis of options 6 to 15 it can be obtained: 1)Analysis of the influence of vegetation elements. Comparing schemes 6 * 8, it is found that when only a certain vegetation element is considered, NDVI has the greatest impact on model performance. The maximum and average values of r are 0.88 and 0.761 respectively. The value of r is mainly concentrated between 0.7 and 0.8, and the mean RMSE is only 0.023. Compared with NDVI and GPP, LAI is less effective in participating in modeling. It can be seen from Schemes 9–11 that two vegetation elements are randomly selected to participate in the modeling, and the inversion results are not much different. It can be further compared with scheme 3 that if one or two vegetation elements are involved in the modeling, the accuracy of the model is improved. This shows that all three vegetation elements can improve the accuracy of the model, and NDVI is the key one that affects the modeling effect. 2) Impact analysis of meteorological elements. Comparing schemes 1, 12 and 13, It can be got that the daily average temperature participating in the modeling is improved relative to the daily average rainfall. The average r is 0.781, and the maximum is 0.913,

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however, selecting only the daily average temperature to participate in the modeling is more conducive to the improvement of modeling accuracy. Compared with scheme 4, the model with the removal of meteorological elements improves r-mean and RMSE compared with the selection of daily average temperature or daily average rainfall. At the same time, a comparative analysis with schemes 14 and 15 found that the key vegetation element NDVI is modeled with daily average temperature and daily average rainfall respectively, and the mean r value is reduced. It can be seen that the effect of selecting daily average temperature to participate in modeling is better than that of daily average rainfall, and the modeling effect after removing meteorological elements is better. Based on the above analysis, four schemes with higher modeling accuracy are selected, and the correlation coefficient changes of the four schemes running 100 times are statistically analyzed, as shown in Fig. 7.

Fig. 7. Comparative analysis of correlation coefficient

Combined with the analysis of Fig. 6 and Fig. 7, the r values of scheme 4 and scheme 13 between 0.70 and 0.80 accounted for 55% and 53%, respectively, and greater than 0.80 accounted for 43% and 39%, respectively. It can be seen that the modeling accuracy of scheme 4 is better, and the variation range of the correlation coefficient is small, indicating that the modeling process is relatively more stable. To sum up, Option 4 is selected as the best modeling solution and the trained model is input the test input variable sets corresponding to all pixels on the 7th day of the experimental area to obtain an NMRI image with a resolution of 16Days/500m, see Fig. 8(a). The NDVI, GPP and LAI at the time corresponding to the NMRI are shown in Fig. 8(b), (c) and (d). It can be seen from Fig. 8 that the spatial distribution of NMRI is basically consistent with the corresponding overall trend of NDVI, GPP, and LAI. The NMRI value in the western part of the experimental area is higher, and the NMRI value in the eastern area is lower, which is consistent with the geographical characteristics of the experimental area. Further analysis of Fig. 8(a) shows that the NMRI inversion effect is basically the same for areas covered by grassland, such as the central area, which is mainly affected by the grassland environment in 94% of the modeling stations. For the

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(a) NMRI

(b)NDVI

(c) GPP

(d)LAI

Fig. 8. Comparative analysis of model inversion results

northwestern region (44°* 45°N, 115°* 121°W), there is a certain deviation. This may be due to the sparse distribution of ground-based GPS stations in this area, which leads to the inversion accuracy of NMRI Lower. At the same time, comparing and analyzing the distribution of the Great Salt Lake, the model inversion results still have certain deviations. It can be seen that although the inversion results of NMRI in some areas are somewhat deviated, the spatial distribution characteristics of NMRI are consistent with NDVI, GPP, and LAI on the whole, which indicates that the inversion results of the method in this paper are feasible in terms of spatial distribution. Table 4. Model inversion accuracy statistics Station ceda p369 p373 p457 p736 p739

Err RMSE r1 r2 r3 0.001 0.040 0.944 0.879 0.916 0.002 0.014 0.020 0.031 0.005

In order to comprehensively evaluate the effectiveness of the model, three indicators of inversion error (Err), root mean square error and correlation coefficient are used for evaluation. The results are shown in Table 4. In the table, r1, r2, and r3 represent the correlation coefficients between the inversion results of 6 stations and NDVI, GPP, and LAI, respectively. It can be seen that although the 6 stations that did not participate in the modeling are distributed at different altitudes and different land

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cover types, the inversion errors between their NMRI inversion values and the reference values are all relatively small. The maximum error is only 0.031, and the RMSE is only 0.04. However, the r between the NDVI, GPP, and LAI inversion values is greater than 0.879, and the maximum r reaches 0.944. Therefore, there are no gross errors in the model inversion results, and the inversion accuracy is reliable and accurate in local areas.

5 Conclusion In this paper, on the basis of making full use of multi-base GPS-IR and combining various elements, according to the principle of LS-SVM, a high-spatial resolution vegetation water content nonlinear inversion method combining multi-base GPS-IR and related elements is proposed. The theoretical analysis and experimental results show that: 1) For the various selected elements, their importance to the modeling effect is: vegetation elements (NDVI, GPP, and LAI) > topography elements (elevation, slope, aspect and mountain shadow) > station location (latitude and longitude) > weather Elements (daily average rainfall and daily average temperature), and vegetation elements are the main elements that affect the modeling effect. Among them, NDVI is a key element that affects modeling accuracy. 2) The LS-SVM can be adopted to realize the effective fusion of multi-ground GPS-IR and related elements, and the modeling process is relatively stable; the 16Days/500m resolution NMRI image obtained by the model inversion is basically the same as the overall trend of NDVI, GPP and LAI Consistent. However, for areas with sparsely distributed stations and water areas, the inversion accuracy of NMRI is reduced. 3) The model has relatively stable NMRI inversion accuracy for local areas. The maximum inversion error between the inversion results of the 6 GPS stations that are not involved in the modeling and the reference value is only 0.031, and the RMSE is only 0.04. The r between the inversion results and NDVI, GPP, LAI is greater than 0.879, and the maximum is 0.944. Therefore, the method proposed in this paper is feasible and effective, and NMRI based on multi-ground GPS-IR joint inversion can better represent the changes of regional VWC. It is necessary to carry out further research on the influence of the distribution characteristics and distribution density of different ground-based GPS stations on the VWC inversion results. At the same time, whether the removal of non-essential land cover types (such as rivers, lakes, residential areas, etc.) is conducive to the improvement of inversion accuracy, this requires more in-depth research. Acknowledgements. In this experiment, NMRI comes from PBO H2O (https://gnss-h2o.jpl. nasa.gov/index.php), and the products corresponding to various elements come from the Google Earth Engine platform. Thanks for the PBO H2O observation network and the GEE platform, as well as the anonymous reviewers for their valuable comments. Funding. This work was supported by the National Natural Science Foundation of China (No. 41901409; 42064003); Basic Ability Improvement Project for Young and Middle-Aged Teachers in Guangxi Universities (No.2018KY0247).

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References 1. Kramer, P.J., Boyer, J.S.: Water Relations of Plants and Soils, p. 495. Academic Press, San Diego (1995) 2. Chen, D., Huang, J., Jackson, T.J.: Vegetation water content estimation for corn and soybeans using spectral indices derived from MODIS near- and short-wave infrared bands. Remote Sens. Environ. 98(2–3), 225–236 (2005) 3. Ceccato, P., Stéphane, F., Jean-Marie, G.: Designing a spectral index to estimate vegetation water content from remote sensing data: part 2. validation and applications. Remote Sens. Environ. 82(s 2–3), 198–207 (2002) 4. Shuanggen, J., Estel, C., Feiqin, X.: GNSS Remote Sensing, Theory, pp. 241–249. Springer, Methods and Applications. Amsterdam (2014) 5. Ban, W., Yu, K., Zhang, X.: GEO-Satellite-Based Reflectometry for Soil Moisture Estimation, Signal Modeling and Algorithm Development. IEEE Trans. Geosci. Remote Sens. 56(3), 1829–1838 (2017) 6. Zhang, S.C., Dai, K.N., Nan, Y., et al.: Preliminary Research on GNSS-MR for Snow Depth. Geomatics and Information Science of Wuhan University 43(02), 234–240 (2018). (Chinese) 7. Wang, X., Zhang, Q., Zhang, S.: Water levels measured with SNR using wavelet decomposition and Lomb-Scargle periodogram. GPS Solutions 22(1), 1–10 (2018) 8. Small, E.E., Larson, K.M., Braun, J.J.: Sensing vegetation growth with reflected GPS signals. Geophys. Res. Lett. 37(12), 1–5 (2010) 9. Larson, K.M., Small, E.E.: Normalized microwave reflection index: a vegetation measurement derived from GPS networks. IEEE J. Selected Topics Appl. Earth Observ. Remote Sens. 7(5), 1501–1511 (2014) 10. Wan, W., Larson, K.M., Small, E.E., Chew, C.C., Braun, J.J.: Using geodetic GPS receivers to measure vegetation water content. GPS Solutions 19(2), 237–248 (2014). https://doi.org/ 10.1007/s10291-014-0383-7 11. Zheng, N., Feng, Q., Liu, C., et al.: Correlation between signal to noise ratio and NDVI of GPS reflection signal. J. Wuhan Univ. (Information Science Edition) 44(10), 1423–1429 (2019). (Chinese) 12. Yuan, Q., Li, S., Yue, L., et al.: Monitoring the variation of vegetation water content with machine learning methods: point–surface fusion of MODIS Products and GNSS-IR Observations. Remote Sens. 11(12), 1440 (2019) 13. Pan, Y., Ren, C., Liang, Y., Zhang, Z., Shi, Y.: Inversion of surface vegetation water content based on GNSS-IR and MODIS data fusion. Satellite Navigation 1(1), 1–15 (2020). https:// doi.org/10.1186/s43020-020-00021-z 14. Yueji, L., Chao, R., Yibang, H., et al.: Rolling estimation model of soil moisture based on multi satellite fusion. Chin. J. Remote Sens. 23(04), 648–660 (2019). (Chinese) 15. Xianglou, L.I.U., Dongxu, J.I.A., Hui, L.I., et al.: Research on Kernel parameter optimization of support vector machine in speaker recognition. Sci. Technol. Eng. 10(7), 1669–1673 (2010)

Investigation of the Characteristics of Tropopause Height Over China Using Recent RO Measurements Jiaqi Shi1, Minghao Zhang1,2, Laga Tong1,2, Erjiang Fu2, and Kefei Zhang1(&) 1

2

School of Environment Science and Spatial Informatics, CUMT, Xuzhou 221116, China {shijq,profkzhang}@cumt.edu.cn Bei-Stars Geospatial Information Innovation Institute, Nanjing 210000, China [email protected]

Abstract. The Global Navigation Satellite Systems (GNSS) radio occultation (RO) is a relatively new effective technique for atmospheric sounding and has been routinely used in operational numerical weather prediction models run by major world forecasting centers. The key advantages of using RO data include global coverage, high precision, high vertical resolution, long-term stability and all-weather operation capability and capacity. The latest development in GNSS RO makes it possible to use RO technology for researches on extreme weather events including tropical cyclones and ENSOs phenomena etc. This study is to use the widely used RO processing package (Radio Occultation Processing Package, ROPP) to investigate the tropopause height (TPH) over the Chinese region (70°E–140°E, 0°N–60°N). The data used were from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) during the period 2015–2016, and the algorithm was the temperature lapse rate tropopause (LRT). Results showed that the distribution of the TPH is latitude-dependent. The TPH mainly concentrated in the 15.5–18 km altitude range in the southern part of China (latitude range: 0°N–33°N), whilst the TPH mainly concentrated in the 7–12.5 km altitude range in the northern part of China (34°N–60°N). The TPH did not show the characteristic of variation with longitude. The knowledge on the characteristics of the regional TPH is beneficial for a better understanding of the tropopause in China, and even beyond. Keywords: GNSS radio occultation processing package (ROPP)


Tropopause height
Radio occultation

1 Introduction In recent years, as a new and effective technique for atmospheric sounding, Global Navigation Satellite Systems (GNSS) radio occultation (RO) technology has been widely used in atmospheric sciences. It contrasts with traditional atmospheric sounding methods which are high cost, uneven distribution of data, low vertical resolution, unavailability of long-term stable observations in all weather conditions [18]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 173–181, 2021. https://doi.org/10.1007/978-981-16-3138-2_17

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The principle of RO is to use radio signals transmitted from GNSS satellites collected by receivers aboard Low Earth Orbit (LEO) satellites, which are refracted when traveling through the ionosphere and neutral atmosphere. From the refracted amount of the signals during a short period of time, some atmospheric parameter profiles can be obtained from the inversion algorithms [17]. Currently, RO data from several missions such as COSMIC [9], CHAMP (Challenging Minisatellite Payload) [13], METOP (Meteorological Operational) [3], and GRACE (Gravity Recovery and Climate Experiment) [14] etc. have been widely used in scientific research. With the development of Chinese satellite navigation technology, Fengyun-3C and Fengyun-3D were successfully launched in 2013 and 2017 respectively. The network of Fengyun-3C and Fengyun-3D satellites facilitate the research on the detection of the atmosphere and space environments, and their RO data have been used for the quality evaluation of RO [16], ionospheric parameter comparison [15], the tropopause height (TPH) analysis and other researches [6]. In 2019, the second-generation COSMIC-2 satellite system was put into use, providing more occultation data with higher resolution and stronger stability [10]. The tropopause is the transitional area between the troposphere and stratosphere in the earth's atmosphere. Since the changes in temperature, humidity, pressure, and circulation in the tropopause directly affect weather and climate; it can be used as an indicator for the process of atmospheric changes [2]. The TPH is an important parameter of the tropopause and current methods for determining the TPH include the Cold Point Tropopause (CPT) and Lapse Rate Tropopause (CPT) algorithms. Zhang et al. [19] studied atmospheric temperature over Australia using data from CHAMP, COSMIC and radiosonde stations, and found that the temperature profiles derived from RO had high temporal and spatial resolution. Schmidt et al. [8] used CHAMP and GRACE data to study the relationship between the change in the TPH and temperature in the troposphere and stratosphere. Xu et al. [17] used COSMIC bending angle data to analyse the structural changes of the tropopause in China, and stated that the TPH, temperature, pressure, and other parameters vary with latitude. Shan et al. [12] used COSMIC refractivity data to study the temporal and spatial characteristics of the TPH over the land area of China, and concluded that the average TPH in this area is usually the highest in summer and lowest in winter. RO data processing involves complex physics and mathematics, thus it requires dedicated and sophisticated software packages. The Radio Occultation Processing Package (ROPP) is a modular RO data processing toolkit developed by the Radio Occultation Meteorology Satellite Application Facility (ROM SAF), which is the department responsible for occultation data processing in the European Organisation for The Exploitation of Meteorological Satellites (EUMETSAT). Compared with the traditional RO data processing software End-to-end GNSS Occultation Performance Simulator (EGOPS) [11], the biggest advantage of the ROPP is its open source, which makes it possible for users to integrate their own code into the ROPP code or run any single module selected for processing the part needed [20]. Currently, the ROPP can process not only COSMIC, GRACE, CHAMP, and Metop data, but also Fengyun-3C RO data, although some functions are yet to be completed.

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China has a vast territory mainly located in subtropical and temperate regions, and has complex climatic characteristics. Different regions have different climatic characteristics, which closely related to the troposphere. The analyses of the spatial characteristics of the TPH in China have significance for studying regional climate change in China. In this study, COSMIC RO data during the 2-year period from 2015 to 2016 and the temperature lapse rate tropopause (LRT) algorithm contained in the ROPP were used to determine the TPH in China. The TPH was validated using the TPH obtained from ERA-Interim data interpolated to the location of the COSMIC RO profiles. The characteristics of the spatial distribution of the TPH in China were analysed.

2 Data and Method 2.1

Data Description

The data used in this study were wet profile data (wetPrf) processed from the ROPP and the aforementioned 2-year COSMIC data and ERA-Interim data interpolated to the position of the COSMIC RO profiles (bgnPrf) at the ROM SAF. Both wetPrf and bgnPrf data were provided by the European Center for Medium-Range Weather Forecast (European Center for Medium-Range), and the data contain the average position of the RO profiles, the TPH, and the quality control parameters of the TPH. There were 27225 and 17903 RO profiles in 2015 and 2016, respectively, and the numbers of the RO profiles that met the quality control standards were 27127 and 17838, respectively. 2.2

Introduction to ROPP

The ROPP was developed based on the Linux system using Fortran programming language, and can be downloaded from the website of the ROM SAF (https://www. romsaf.org/). As a modular software package, its main modules and corresponding functions are given in Table 1. The ropp_io module provides general format support for RO data, e.g., converting occultation data from different data centers into the format required by the ROPP. Geometric optics or wave optics methods can be used in the ropp_pp module for obtaining bending angle profiles on the L1 and L2 bands from the phase information. The neutral bending angle profile can be obtained with an ionospheric correction. The refractivity profile and dry temperature can be obtained from the Abel transform algorithm. The ropp_app module can calculate the TPH and planetary boundary layer height (PBLH) from the bending angle, refractivity, and temperature profiles. The function of the ropp_fm module provides a forward operator for calculating the vertical refractivity and bending angle profile from the background data in the vertical grid of the mixed Numerical Weather Prediction (NWP) model based on pressure and height. The ropp_1dvar module provides a one-dimensional variational program for obtaining pressure, temperature and humidity profiles from refractivity or bending angle profiles. The ropp_utils module provides utility functions for height, date, and coordinate conversion, as well as other general library functions.

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2.3

Function Format conversion of RO data, input and output Pre-process of RO data Applications of RO data (TPH and PBLH) Forward operators 1D-Var routines Height and date conversion, other general library functions

Method for Determining TPH

The LRT algorithm was used to obtain the TPH in this study. According to the definition of the TPH given by the World Meteorological Organization (WMO) in 1957, it is the lowest altitude that satisfies the following conditions: the temperature lapse rate is less than or equal to 2 °C/km and the mean of the temperature lapse rates within the 2 km above this altitude is not greater than 2 °C/km [7]. The procedure for obtaining the TPH from the LRT algorithm is as follows. (1) The bending angle is obtained from the phase information; (2) The neutral bending angle after an ionospheric correction is used to obtain the refractivity index through the Abel integral transform; (3) The refractivity index is converted to refractivity; (4) Dry temperature and dry pressure are obtained by hydrostatic integration which neglects water vapor; (5) The TPH is obtained from temperature and pressure. The procedure for RO data processing is shown in Fig. 1 and Fig. 2 is mainly for the process of using the LRT method to obtain the TPH [4, 5].

Fig. 1. Procedure for RO data processing

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Fig. 2. Procedure for obtaining the TPH from the LRT algorithm

In this study, the area from 70°E to 140°E, and from 0°N to 60°N was divided into 2°  2° grid first, then all those RO profiles that were co-located with each grid point (defined as under a 300 km horizontal distance) were identified and used to calculate the weighted mean TPH for the grid point using the following inverse-distance weighting method [1]: TPHi  D2 i TPH ¼ Pn 2 i¼1 Di

ð1Þ

where i is the index of the RO profile, n is the number of all RO profiles co-located with the grid point; Di is the distance from the i th RO profile to the grid point.

3 Results 3.1

TPH and Validation

Before the investigation for the spatial characteristics of the TPHs over China was carried out, the TPHs obtained from the LRT algorithm adopted in the ROPP from the COSMIC data were validated by comparing them with the ones obtained from ERAInterim data (as the reference). The original ERA-Interim data need to be interpolated in both the temporal and spatial domains for obtaining the values at the grid points that were closest to the position of the RO profile being compared. As previously discussed, the whole area was divided into 2°  2° grid, and the weighted mean TPH over each grid point was calculated using Eq. (1). Figure 3(a) and Fig. 3(b) show the relationship between the TPH obtained from two types of data along the longitude and latitude directions. The results showed a good agreement between the TPH obtained from the COSMIC data and that from the ERA-Interim data in both longitude and latitude

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Fig. 3. Two-year mean of TPHs from both COSMIC and ERA-Interim data during the period of 2015–2016 along longitude (a) and latitude (b)

directions. Figure 4 shows the frequency distribution histogram for the value of the difference between the two sets of TPHs, which indicates that the difference values basically conform to a normal distribution. Moreover, 43895 profiles have a under 2 km difference value, accounting for 97.62% of the total; 42188 profiles have a under 1 km difference value, accounting for 93.82% of the total; 38,665 profiles have a under 0.5 km difference value, accounting for 85.99% of the total. Overall, the TPH obtained from the two data sources were reasonably consistent, suggesting that the TPH obtained from the LRT algorithm adopted in the ROPP can be used to analyse the spatial characteristics of the TPH over China.

Fig. 4. Frequency histogram for the difference of the TPHs obtained from RO and ERA-Interim in the period of 2015–2016

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Spatial Distribution of TPH

The annual mean TPH over China in 2015 and 2016 are calculated and results are shown in Fig. 5(a) and Fig. 5(b), respectively for investigation of their spatial characteristics. We can see that, generally, the TPH is latitude-dependent, and it significantly decreases with the increase in latitude. The TPH mainly concentrated in the 15.5–18 km altitude range in the southern part of China (latitude range: 0°N–33°N), whilst the TPH mainly concentrated in the 7–12.5 km altitude range in the northern part of China (34°N–60°N). The largest variations in the TPH occurred in the range between 30°N and 35°N, roughly. However, the TPH did not show any feature of variation with longitude.

Fig. 5. Spatial distribution of annual mean TPH over China in 2015 (a) and 2016 (b)

Fig. 6. TPH in different longitudes (a) and latitudes (b) in 2015 (red dots) and 2016 (blue dots)

For more clear comparisons, the TPH in different latitudes and longitudes are shown in Fig. 6 (a) and Fig. 6 (b), respectively in the form of scatter plots, where the red and blue dots represent the TPHs in 2015 and 2016, respectively. It is clear that the TPH is latitude-dependent whilst its variation in the longitude direction is insignificant. Since the number of the RO profiles from which the TPHs obtained were in the altitude

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range of 12.5–15.5 km is small and the distribution of global RO profiles is uniform, it is likely that the area where the TPH values are in the altitude range of 12.5–15.5 km is also small, and the area where the TPH varies greatly is in the latitude range of 25°N– 40°N.

4 Conclusion This study investigated the spatial distribution of the TPH over China in 2015 and 2016 and the TPH was obtained from the LRT algorithm adopted by the ROPP and the COSMIC RO data. The TPH was validated using the TPH from ERA-Interim data interpolated at co-location. Results showed both sets of TPH agreed well, and more than 90% of the difference values were under 1 km. From the spatial distribution of the annual mean TPH in the two years tested over China, it was found that the TPH is latitude-dependent, and its value decreases with the increase in latitude; However, it did not show the tendency of variation with longitude. The TPH values over China mainly concentrated in the altitude ranges of 7–12.5 km and 15.5–18 km. Acknowledgements. We are grateful for the ROPP software and RO data provided by the ROM SAF department. This research was supported by the National Natural Science Foundation of China (41730109), the National Natural Science Foundation of China (41874040), the Xuzhou Key Research and Development Plan (KC19111) and the Jiangsu Dual Creative Talents and Jiangsu Dual Creative Teams Programme Projects.

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8. Schmidt, T., Wickert, J., Beyerle, G., Reigber, C.: Tropical tropopause parameters derived from GPS radio occultation measurements with CHAMP. J. Geophys. Res. 109, D13105 (2004). https://doi.org/10.1029/2004JD004566 9. Schreiner, W., Sokolovskiy, S., Hunt, D., et al.: Analysis of GPS radio occultation data from the FORMOSAT-3/COSMIC and Metop/GRAS missions at CDAAC. Atmosph. Measur. Tech. 4(10) (2011). https://doi.org/10.5194/amtd-4-2433-2011 10. Schreiner, W., Weiss, J.P., Anthes, R.A., et al.: COSMIC‐2 radio occultation constellation: First results. Geophys. Res. Lett. 47, e2019GL086841 (2020). https://doi.org/10.1029/ 2019GL086841 11. Schweitzer, S., Pirscher, B., Pock, M.: End-to-end Generic Occultation Performance Simulation and Processing System EGOPS: Enhancement of GPS RO data processing and IR laser occultation. J. Pharmacol. Exp. Ther. 288(2), 858–865 (2006) 12. Shan, Y., Xia, P., et al.: Spatial-Temporal characteristics of the tropopause height over land area of China with COSMIC radio occultation refractivity. J. Geom. Sci. Technol. 36(5) (2019) 13. Wickert, J., Reigber, C., Beyerle, G., et al.: Atmosphere sounding by GPS radio occultation: First results from CHAMP. Geophys. Res. Lett. (2001). https://doi.org/10.1029/ 2001GL013117 14. Wickert, J., Beyerle, G., Koenig, R., et al.: GPS radio occultation with CHAMP and GRACE: a first look at a new and promising satellite configuration for global atmospheric sounding. Ann. Geophys. 23(3), 653–658 (2005). https://doi.org/10.5194/angeo-23-6532005 15. Wang, H., Luo, J., Xu, X.: Ionospheric peak parameters retrieved from FY-3C radio occultation: a statistical comparison with measurements from COSMIC RO and Digisondes Over the Globe. Remote Sens. 11(12), 1419 (2019). https://doi.org/10.3390/rs11121419 16. Wei, J., et al.: An evaluation of Fengyun-3C radio occultation atmospheric profiles over 2015–2018. Remote Sens. 12(13), 2116 (2020). https://doi.org/10.3390/rs12132116 17. Xu, X., Gao, P., Zhang, X.: Structure and variation of the tropopause over China with COSMIC radio occultation bending angles. Chin. J. Geophys. 56(8), 2531–2541 (2013). https://doi.org/10.6038/cjg20130804 18. Xu, X., Liu, S., Luo, J.: Analysis on the variation of global ABL top structure using COSMIC radio occultation refractivity. Geomat. Inf. Sci. Wuhan Univ. 43(1), 94–100 (2018). https://doi.org/10.13203/j.whugis20160183 19. Zhang, K., Fu, E., Silcock, D., Wang, Y.:An investigation of atmospheric temperature profiles in the Australian region using collocated GPS radio occultation and radiosonde data. Atmosph. Measur. Techn. 4(10) (2011). https://doi.org/10.5194/amt-4-2087-2011 20. Zhran, M., Mousa, A., et al.: Utility of GNSS Radio occultation technique for tropopause height investigation over Egypt. NRIAG J. Astron. Geophys. 8(1), 45–54 (2019). https://doi. org/10.1080/20909977.2019.1617559

Research on Train Integrity Monitoring Using Multi-constellation Measurements Jialei Li1, Yongqiang Liu1,3, Wei Jiang1,2(&), Baigen Cai1,2, and Jian Wang1,2 1

School of Electronic and Engineering, Beijing Jiaotong University, Beijing 100044, China [email protected] 2 Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transportation, State Key Laboratory of Rail Traffic Control and Safety, School of Electronic and Engineering, Beijing Jiaotong University, Beijing 100044, China 3 General Technology Branch of CETC Northwest Group, Software Products Department, Xian 710068, China

Abstract. Train integrity monitoring is the key to ensure the safe operation of trains. Traditional train integrity monitoring is based on ground equipment. However, with the development of satellite positioning technology, and in order to meet the needs of the next generation train control system (NGTC), the demand for ground equipment should be minimized. The application of satellite positioning technology in train positioning is more and more. Its principle is to calculate the length of the moving-baseline between the head and end antennas of the train by satellite positioning, and monitor the integrity status of the train according to the length change. The multi-constellation positioning has more visible satellites and better geometric distribution of satellites compared with the single constellation system. Especially, the advantages of the multi-constellation system are more prominent in the limited satellite signals scenes. Therefore, this paper proposes a train integrity monitoring method based on multi-constellation moving-baseline solution. The first step is to unify the time and space systems, then make full use of the multi constellation carrier phase measurements, and finally eliminate the propagation path error and satellite clock error by double difference carrier phase. The moving-baseline length between two antennas is calculated in real time by Kalman filter algorithm, and then compared with the actual train length to realize the train integrity monitoring. Keywords: Multi-constellation
Train integrity monitoring
NGTC
Kalman filter
Moving-baseline

This work was supported in part by the National Key Research and Development Program of China under Grant 2018YFB1201500, and the National Natural Science Foundation of China under Grant U1934222 © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 182–191, 2021. https://doi.org/10.1007/978-981-16-3138-2_18

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1 Introduction Train integrity is one of the important factors affecting the safe operation of trains. The traditional train integrity monitoring function is mainly realized by checking the occupation of track circuit. To reduce the installation and maintenance costs of equipment, improve the availability of train operation control systems, the next generation train control system (NGTC) requires that the train integrity monitoring function should be completed by on-board equipment [1]. At present, train integrity monitoring methods include the following three methods: the train brake pressure tube, the movement state of the train head and end, and the change of the train length [2]. The last method is simple in principle, which only needs to locate the position of the head and end of the train and calculate the train length in real time to reflect the integrity of the train. At present, with the further development of satellite positioning technology, its positioning accuracy and reliability have been continuously improved, which has gradually become an important support of train control system [3]. Some scholars have shown that in single constellation system, the result error can reach within 1.5 m through moving-baseline solution [4]. Due to the increase of the number of visible satellites, the multi-constellation positioning can further improve positioning accuracy compared with single constellation system in theory. In February 2020, European Global Navigation Satellite System Administration (GSA) released the third edition of global navigation satellite system (GNSS) User Technical Report, which emphasized that the new situation of GNSS is multi-constellation, multi-frequency and multi-signal development [5]. At the same time, supporting multi-constellation has become the standard of receivers, which shows that multi-constellation positioning has become a trend of satellite navigation system development in future. With successful construction of Beidou Navigation Satellite System (BDS) and its enhancement system [6], GPS and BDS combined positioning can make full use of the global satellite resources, increase the number of visible satellites, and optimize the geometric distribution of satellites, which can effectively improve the reliability and stability [7]. Therefore, this paper proposes a train integrity monitoring method based on multiconstellation moving-baseline solution. The moving-baseline refers to the baseline vector installed between the head and end antennas of the train. After unifying the time system and space system of different constellations, the error in the propagation process and the satellite clock error are eliminated by double difference carrier phase. The double difference carrier phase of different constellations is combined with equal weight. Then the moving-baseline length is solved by Kalman filter algorithm, and the train integrity monitoring is realized by comparing with the actual train length.

2 Multi-constellation System Combination Method For different satellite positioning systems, the time system and space system are different. Therefore, it is significantly important to unify the time and space system.

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Multi-constellation Time and Space System Combination

In BDS/GPS positioning, it is necessary to change the time system. GPS uses Global Positioning Time (GPST) and BDS uses Beidou Time (BDST). Although both of them belong to atomic time (AT) [8], their starting times are different. The former starts at 0:00:00 on January 6, 1980, but the latter starts at 0:00:00 on January 1, 2006. Because of leap second, the time relationship between BDS and GPS can be expressed as: GPSweek ¼ BDSweek þ 1356

ð1Þ

GPSsec ¼ BDSsec þ 14

ð2Þ

Where GPSweek and BDSweek is the integer weeks of GPST and BDT, GPSsec and BDSsec is the seconds of GPST and BDT. BDS adopts 2000 Chinese Geodetic Coordinate System (CGCS2000), and GPS adopts American Geodetic Coordinate System (WGS84), which are consistent with the definition of International Earth Reference System (ITRS) and the parameter deviation is small [9]. Table 1 is the parameter comparison between GPS and BDS coordinate system. Table 1. Fundamental earth parameters of GPS and BDS coordinate system Reference frame WGS-84 CGCS2000

Origin of coordinate Earth centroid Earth centroid

Semi-major axis (m) 6378137.0

Gravity constant of the earth (m3/s2) 398600.5  109

1/298.257223563

6378137.0

398600.441  109

1/298.257222101

Oblateness

The coordinate origin and major axis of the two coordinate systems are same, and from the current measurement accuracy, the difference between the two coordinate systems due to the parameter difference can be ignored [10]. 2.2

Double Difference Carrier Phase Model

The key to calculate the length of moving-baseline is to calculate the relative position of two antennas. At present, there are two basic positioning models, pseudo-range positioning and carrier phase positioning. Carrier phase positioning is realized by measuring the phase change. The error of this method is smaller than pseudo-range positioning. Thus, it is more suitable for high-precision positioning scenes. The carrier phase observation equation can be written as: / ¼ k1 ðqb  Ib þ Tb Þ þ f ðdtR  dtS Þ þ Nb þ eb

ð3Þ

Where / represents the carrier phase measurement; k represents the wavelength of the carrier signal; q represents the geometric distance between the satellite and the receiver; N represents the integer ambiguity; dtR represents the clock difference of the receiver; dtS represents the clock difference of the satellite; e represents the residual error[11].

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According to the carrier phase equation, when two antennas receive the ith satellite at the same time, the observation equation of inter-station difference can be written as: i /iEH ¼ /iE  /iH ¼k1 qiEH þ f ðdtRE  dtRH Þ þ NEH þ eiEH

ð4Þ

Where /iEH represents the carrier phase difference between two receivers; qiEH is the i is the ambiguity distance difference between two receiver antennas and satellites; NEH i result of single difference and eEH is the single difference of error. Similarly, if the jth satellite is selected as the reference satellite, the inter-satellite carrier phase difference is based on inter-station difference. The double-difference carrier phase observation equation is as follows: j ij /ijEH ¼ /iEH  /EH ¼k1 qijEH þ NEH þ eijEH

ð5Þ

ij Where rEH represents the double difference result of the real distance between ith and ij is the double difference result of the ambiguity, eijEH is jth , head and end antennas; NEH the double difference of the error, and superscript ij indicates the difference between the ith satellite and the jth satellite. It is necessary to fuse carrier phase of different constellations for multi-constellation systems. When the time system and coordinate system are unified, each constellation system performs inter-satellite difference and inter-station difference independently, and then combines the double-difference carrier phases of different constellations with equal weight to form the carrier phase difference result of multi-constellation system.

3 Solution of Multi-constellation Moving-Baseline Based on Kalman Filter According to the double-difference carrier phase observation equation, the doubledifference ambiguity and relative position coordinates are unknown, which need to be estimated by Kalman filter. Combined with the calculation results of the previous epoch and the measurement results of the current epoch, the state estimation is updated by recursive operation, and through iterative correction to obtain more accurate solution results. Kalman filter predicts the current state through the system model and corrects the predicted state through the measurement model. The system model is: Xk ¼ AXk1 + Wk

ð6Þ

Where Xk is the state vector of the system; A is the state transition matrix; Wk  Nð0; QÞ is the process noise of the system. The multi-constellation system needs a more accurate motion model to describe the moving-baseline motion state. Thus, the motion state of the moving-baseline is made as first-order Markov acceleration model. The estimated state includes nine parameters (three-dimensional relative position, three-dimensional relative velocity and

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three-dimensional relative acceleration) and double-difference integer ambiguity of different constellations. The state matrix of the system can be expressed as: h _ x Dv _ y Dv _ z XTk ¼ Dx Dy Dz Dvx Dvy Dvz Dv Gðn 1ÞGj

G1Gj G2Gj NHE NHE


NHE G



Bðn 1ÞBj

B1Bj B2Bj NHE NHE


NHE B

i

ð7Þ

  Where Dvx ; Dvy ; Dvz represents the relative velocity in three directions and  _ y ; Dv _ z represents the relative acceleration in three directions,G and B cor_ x ; Dv Dv

respond to GPS system and BDS system respectively; nG and nB represent the number of satellites of GPS and BDS respectively; Assume that GPS selects jth satellite as reference satellite and BDS selects k th satellite as reference satellite,   Gðn 1ÞGj

G1Gj G2Gj NHE


NHE G NHE

is the matrix composed of double difference integer   Bðn 1ÞBk B1Bk B2Bk NHE


NHE B ambiguity corresponding to GPS system; NHE is the matrix G1Gj composed of double difference integer ambiguity corresponding to BDS system; NHE indicates the whole cycle ambiguity after GPS double difference. State transition matrix can be written as:

2 6 6 A¼6 4

3

I33 033

DT  I33 I33

033 DT  I33

03½ðnG 1Þ þ ðnB 1Þ 03½ðnG 1Þ þ ðnB 1Þ

033 0½ðnG 1Þ þ ðnB 1Þ3

033 0½ðnG 1Þ þ ðnB 1Þ3

I33 0½ðnG 1Þ þ ðnB 1Þ3

03½ðnG 1Þ þ ðnB 1Þ I½ðnG 1Þ þ ðnB 1Þ½ðnG 1Þ þ ðnB 1Þ

7 7 7 5

ð8Þ Where DT is the time interval, I is unit matrix. The noise matrix of the system can be written as:  Qk ¼ diag 013 013

2DT 2 s

2DT 2 s

2DT 2 s

 w1ðnG 1Þ w1ðnB 1Þ

ð9Þ

Where s is the correlation time, and w is the random walk process corresponding to the double difference ambiguity. The measurement model of Kalman filter system is: Zk ¼ Hk Xk þ Vk

ð10Þ

Where Zk is the observation vector of the system; Hk is the measurement matrix; Vk  N ð0; RÞ is white noise with Gaussian distribution, and the corresponding covariance matrix is R. The observation matrix of the system composed of carrier phase double difference results of different constellation systems is as follows:

Research on Train Integrity Monitoring Using Multi-constellation Measurements

h Zk ¼  /G1Gj EH

/G2Gj EH

Gðn 1ÞCj

/EH G

:::

/B1Bk EH

/B2Bk EH

:::

Bðn 1ÞBk

/EH B

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iT

ð11Þ

Measurement matrix of the system is as follows: 2

aG1Gj aG2Gj .. .

6 6 6 6 6 6 aGðnG 1ÞGj Hk ¼ 6 6 aB1Bk 6 6 aB2Bk 6 .. 6 4 . aBðnB 1ÞBk

bG1Gj bG2Gj .. .

bGðnG 1ÞGj bB1Bk bB2Bk .. . bBðnB 1ÞBk

cG1Gj cG2Gj .. .

cGðnG 1ÞGj cB1Bk bB2Bk .. . cBðnB 1ÞBk

3

0ðnG 1Þ9

0ðnB 1Þ9

7 7 7 kG
IðnG 1ÞðnG 1Þ 7 7 7 7 ð12Þ 7 7 7 7 7 kB
IðnB 1ÞðnB 1Þ 5

If the head antenna is selected as the main antenna, a; b; c in the measurement matrix are the coefficient parameters of Taylor expansion when Kalman filter is linearized: as ¼

xs  xH s ys  yH s z s  z H ; b ¼ ; c ¼ rHs rHs rHs

ð13Þ

In which xS ; yS ; zS is the three-dimensional coordinate of satellite, xH ; yH ; zH is the three-dimensional coordinate of train head antenna, rHs is the distance between satellite and the approximate position of train head antenna. After the system model and measurement model are determined, recursive operation needs to be realized through time update and measurement update. The relative position between two antennas in each epoch can be calculated in real time, so the moving-baseline length can be expressed as: L¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dx2 þ Dy2 þ Dz2

ð14Þ

The calculated moving-baseline length L is compared with the real distance between the two antennas, and the current train integrity status can be judged.

4 Results Analysis In order to verify the performance of the proposed train integrity resolution method, a real experiment was carried out on the Beijing-Shenyang high-speed railway in June 2018. The data not only includes the train running process, but also includes the train inbound and outbound scenes. In this scene, the number of visible satellites and vehicle speed change greatly, which can verify the accuracy and stability of the algorithm. The train absolute length is 186.9 m between the head and the end antennas centers. Therefore, the absolute distance between the two antennas in the static state is used as a reference to compare with the calculation results.

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Fig. 1. Changes in the number of visible satellites

Figure 1 shows the change of the visible satellites number of different constellation system. Because the train enter Xinminbei Station and Shenyangxi Railway Station for a short stop between epoch 6738–8459 and epoch 15670–17650. Due to the shelter ceiling in the station, the number of visible satellites decreases a lot.

Fig. 2. Satellite DOP value of GPS

Figure 2 shows the GNSS geometry change during the experimental period, where the position dilution of precision (PDOP), the horizontal dilution of precision (HDOP), and the vertical dilution of precision (VDOP) are plotted. PDOP directly reflects the geometric distribution of satellites. Before epoch 6000, the PDOP value is less than 5,

Fig. 3. Moving-baseline calculation result of single constellation

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between epoch 6738–8459 and epoch 15670–17650, the PDOP value obviously increases and some PDOP values reach 15 because the train enters the station. The result of moving-baseline solution in single GPS system is shown in Fig. 3. After the train enters Xinminbei Railway Station, the number of satellites decreases because the signal in the station is blocked, and the number of visible satellites in some epochs is less than four, so the error of moving-baseline solution results increases, and the maximum error reaches more than 1 m.

Fig. 4. Moving-baseline calculation results of multi-constellation

Figure 4 is the calculation result of moving-baseline based on multi-constellation. Compared with the single GPS moving-baseline results, the solution accuracy is obviously higher than single constellation system, and the error is kept within 0.3 m. After 6000 epochs, the multi-constellation moving-baseline solution results are obviously better than the single constellation system. Especially when the satellite observation conditions deteriorate between 6738–8459 and 15670–17650 epochs, the multiconstellation system moving-baseline solution results are more stable and the overall availability of the system is improved.

Fig. 5. Comparison of error cumulative distribution functions

The error cumulative distribution function diagram(CDF) of the moving-baseline solution results is shown in Fig. 5. The single GPS solution error is all less than 1.2 m, while the multi-constellation positioning solution error is all less than 0.43 m.

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Table 2. Error comparison of single constellation and multi-constellation moving-baseline solution results Maximum(m) Mean(m) RMS(m) STD(m) GPS 1.20 0.49 0.65 0.42 GPS + BDS 0.43 0.18 0.20 0.09

Table 2 shows the comparison of the maximum error, mean error, root mean square error and standard deviation error between single constellation system and multiconstellation system. The multi-constellation system solution result is obviously better than single constellation system.

5 Conclusions This paper proposes a train integrity monitoring method based on multi-constellation moving-baseline solution. GPS and BDS are combined and carrier phase double difference model is used to eliminate the errors and satellite clock errors in the propagation path. The moving-baseline length is solved in real time by Kalman filtering algorithm and compared with the actual train length to get the train integrity status. The mean error of multi constellation moving-baseline is only 0.18 m, which improves the positioning accuracy compared with single constellation. The root mean square error is reduced from 0.65 meters to 0.2 m. The multi constellation combined measurement solution increases the number of satellites in the limited scene, improves the accuracy of train integrity monitoring.

References 1. Cui, J.: Research on method of autonomous train integrity detection for next generation train control system. Railway Commun. Signal Eng. Technol. 16(11), 10–12 (2019) 2. Guo, J.: Overview and application prospect of train integrity inspection technology. Railway Commun. Signal Eng. Technol. 17(07), 84–87 (2020) 3. Guo, X.: Application of satellite positioning technology in next generation of train control systems. Railway Commun. Signal Eng. Technol. 14(02), 42–45 (2017) 4. Jiang, W., Liu, Y., Liu, D., et al.: Train integrity monitoring based on GNSS movingbaseline approach. In: The 11th International Conference on Modelling, Identification and Control (ICMIC 2019), vol. 582, pp. 653–662 (2019) 5. Cao, C.: The advent of multi-satellite and multi-frequency era: the third edition of GNSS user technical report was released. Satell. Appli.n 2020(11), 55–58 (2020) 6. Li, R., Zheng, S.Y., Wang, E.S., et al.: Advances in BeiDou navigation satellite system (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1, 12 (2020) 7. Rodolinski, P.J., Teunissen, G., Odijk, D.: Combined GPS + BDS for short to long baseline RTK positioning. Measur. Sci. Technol. 26(4) (2015) 8. Qiao, L.: Research on multi-constellation and multi-frequency combined high-precision baseline resolution and software development (2017)

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9. Ning, J., Yao, Y., Zhang, X.: Rev. of the development of global satellite navigation system. J. Navigat. Position. 1(01), 3–8 (2013) 10. Li, H., Bian, S., Li, Z.: Chinese geodetic coordinate system 2000 and its comparison with WGS84[J]. Appl. Mech. Mater. 580(3), 2793–2796 (2014) 11. Zhen, J.: A study and design of dual-antenna GPS/SINS integrated navigation system. (2017)

GNSS-R Interpretation of Soil Moisture Scattering Characteristics Simulation Research Zhongmin Ma1, Shuangcheng Zhang1,2(&), Qi Liu1, Jilun Peng1, Xinyu Dou1, Yiming Xue1, Boyuan Ma1, and Xingtong Chen1 1

2

College of Geology Engineering, Chang’an University, Xi’an 710054, China [email protected] State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China

Abstract. Soil moisture has always been a surface physical quantity that people pay attention to. It is an indicator of the global surface water cycle, and it is the focus of research in the fields of agriculture, meteorology, and hydrology. Traditional soil moisture monitoring methods generally have disadvantages such as high cost and low temporal and spatial resolution. GNSS-R technology is an emerging remote sensing technology that uses navigation satellite signals and forward scattering signals as signal sources to carry out large-scale surface physical parameter analysis and inversion. With many advantages, it has been widely used in sea surface wind fields, sea ice detection and soil moisture inversion. The existing GNSS-R soil moisture retrieval methods have certain limitations. In this paper, the forward model SCoBi (The Signals of Opportunity Coherent Bistatic scattering model and simulator) based on generalized full polarization released by Mississippi State University is used in the bare or vegetation-covered terrain. By changing the vegetation coverage type of soil surface, the reflectivity of soil under different parameter configurations or their combinations is obtained. It provides a reference for improving the existing GNSS-R soil moisture retrieval algorithm and analyzing and determining the best parameter configuration in different GNSS-R scenes. Keywords: GNSS-R


Soil moisture
Scattering characteristics
Simulation

1 Introduction Soil moisture, as a basic parameter in the study of the formation, transformation and consumption process of land water resources, is a key parameter to describe the energy and moisture exchange between the surface and the atmosphere, and plays a very important role in agricultural environmental monitoring, weather forecasting, research of land energy balance and so on. Therefore, it is urgent to carry out effective monitoring of the spatial and temporal distribution of soil moisture and related physical parameters, and explore its internal mechanism and existing rules. However, the soil moisture has a strong heterogeneity in time and space, so the traditional monitoring method based on ground combined with meteorological stations is difficult to meet the application requirements. The development of satellite remote sensing technology provides a new method for soil moisture monitoring, but visible light and thermal © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 192–203, 2021. https://doi.org/10.1007/978-981-16-3138-2_19

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infrared remote sensing are easily limited by weather conditions. Although microwave remote sensing can achieve all-weather and all-day observation, the time resolution (repeated global coverage every three days) is far from meeting the scientific needs of monitoring [1, 2]. The emergence of GNSS-R remote sensing provides a new opportunity for ground feature monitoring. Its main work is in the penetrating L-band, which is suitable for soil moisture monitoring. At the same time, this remote sensing method has unique advantages that other remote sensing methods do not have, such as low cost, low power consumption, wide coverage, and high spatial and temporal resolution. At present, GNSS-R technology has become increasingly mature in the retrieval of sea surface parameters, such as sea surface wind field, wave height, sea ice detection and so on [3–5]. In terms of land surface parameter inversion, soil moisture, snow cover and vegetation biomass estimation are all research hotspots in recent years [6, 7]. However, compared with the inversion of sea surface parameters, the research on the inversion of land surface parameters is far from enough. Especially in the context of soil moisture retrieval, which has a high degree of attention, the GNSS-R method still has several important and difficult problems to be solved. For example, the existing GNSS-R soil moisture retrieval algorithms seldom consider the influence of vegetation on the upper surface of soil, the influence of roughness of reflecting surface and the influence of different parameter configuration of receiver antenna, etc. [8–10]. Therefore, in order to effectively carry out soil moisture inversion, eliminate the influence of surface roughness and vegetation, and improve the accuracy of soil moisture inversion, it has become a research hotspot in GNSS-R field in recent years to use various simulators to simulate the land surface scattering characteristics of GNSS remote sensing and provide reference for inversion algorithm and parameter configuration. At present, domestic and foreign scholars have launched a series of ground-based, airborne, and spaceborne observation experiments for GNSS-R soil moisture monitoring. A series of related studies have been carried out in the inversion mechanism and inversion algorithm, which proved that the use of reflected signals can obtain soil moisture data, showing the strong potential of using GNSS-R technology to obtain land surface features [11–13]. However, in terms of software development, there are few simulators specifically designed for dual-base GNSS-R configurations. In terms of the type of dual-base model they use, the existing simulators can be divided into two categories: with incoherent or simulator of coherent bistatic scattering model. The former type uses a model based on radiation transfer theory and only provides amplitude information, while the latter type uses a model based on analytical wave theory, which provides both amplitude and phase information. An example of the first category is Bi-MIMICS (Bi-static Michigan Microwave Canopy Scattering Simulator), which is used for linearly polarized forest biomass estimation in the X, C, and L bands [14]. The second example is the Tor Vergata model, which is used to monitor biomass in various frequency ranges with circular or linear polarization [15, 16]. The third example is SAVERS (Soil and Vegetation Reflection Simulator), which is developed based on the Tor Vergata model and is used for GNSS bare and vegetation cover soil reflection [17]. There are few simulators with coherent bistatic models. MPSIM (Multipath Simulator) is a GPS multipath simulator in this category, developed in Matlab/Octave environment. It is a forward model based on the near-surface reflection

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method, which can generate signal-to-noise ratio, carrier phase and code pseudorange output at GPS L1 and L2 frequencies [18]. WAVPY (waveform simulation in Python) is also a simulator in the second category. Its difference is that it is not only a simulator, but also an open source GNSS-R software library for separate simulation purposes [19]. In other words, it provides many categories, which can be used for different tasks or combined together. In addition, there is a model called COBISMO (Coherent Biological Static Scattering Model), which focuses on the analysis of the canopy scattering coefficient of P-band linear polarization [20]. Although it has been used for simulation, there is no publicly published literature using the COBISMO simulator. Through the above research status, it can be found that the existing simulation simulators are not comprehensive enough when simulating the ground scattering process of GNSS-R, for example, they fail to analyze the full polarization by combining linear and circular polarization, antenna direction, beam width, sidelobe effect, cross polarization coupling, beam divergence and interference measurement effect. Therefore, this paper adopts the forward model SCoBi (the signals of opportunity coherent bistatic scattering model and simulator) based on generalized polarization released by Mississippi state university and the scattering characteristics of GNSS-R land surface remote sensing are analyzed on bare or vegetation-covered terrain, focusing on the influence of representative vegetation-covered soil and surface roughness on soil moisture retrieval, and simulating the scattering characteristics of soil moisture retrieval by GNSS remote sensing. The second part of the article is an introduction to the SCoBi simulation platform, and the third part is the simulation results. The conclusion is given in the fourth part.

2 SCoBi Simulation Platform and Parameter Settings 2.1

SCoBi Simulation Platform

In essence, GNSS-R is a type of Signals of Opportunity (SoOP). Due to the potential of signal of opportunity in providing cost-effective global remote sensing for land applications, Mississippi State University released a forward model SCoBi based on generalized full polarization in 2018. The modified model hopes to use the fully coherent scattering model framework of the Information Processing and Sensing (IMPRESS) Laboratory through a user simulation interface to conduct a comprehensive analysis of the dual-base SoOP configuration for land applications. The simulator can analyze the complex scattering of GNSS-R on the ground, and can create an analysis environment for researchers, scientists, and users without a background in electromagnetics [21]. The SCoBi framework can currently perform GNSS-R scattering analysis on bare or vegetation-covered terrain, under which the soil can be modeled as a single-layer or multilayer dielectric. The software is free and open source under the GNU General Public License (GPL) and is compatible with the MATLAB development environment. In use, SCoBi can obtain multiple inputs for dual-base configuration through a set of graphical user interface (GUI) windows, such as simulation type, transmitter and receiver antenna characteristics, ground layering information, and cover vegetation

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information, etc. After running the simulator, it can generate simulated direct reception field and power, as well as specular reflection coefficient and reflectivity output. Using the SCoBi simulation platform, you can study the GNSS-R land surface remote sensing scattering characteristics under different ground environments, vegetation conditions, and antenna conditions [22, 23]. 2.2

SCoBi Simulation Platform Parameter Settings

Figure 1 shows the graphical user interface (GUI) of the current version of the SCoBi simulation platform.

Fig. 1. SCoBi simulation platform GUI

As shown in Fig. 1, the current SCoBi graphical user interface provides 5 types of optional input parameters and 1 type of custom input parameters. The upper left side of the GUI interface is the simulation scene selection, showing a total of 8 types of simulation scenes: Forest, Agriculture, Soil, Root-zone, Snow, Topography, Permafrost, and Wetlands, but the current version can only run the first four simulation scenarios, the emulators suitable for the last four scenarios will be launched in future versions. What needs to be pointed out here is that when the user selects a simulation scenario, it does not mean that the user can only conduct simulation research in that scenario. For example, if a user wants to study the influence of the multi-layer soil model under the agriculture cover on the reflected signal, he can first select the Agriculture simulation scene, and then add the multi-layer soil model in the parameter selection to obtain the desired simulation results. As this paper mainly explores the application potential of SCoBi in GNSS remote sensing, we define the transmitter frequency as 1575.42 MHz(L1A) and the polarization mode as right-handed circular polarization (RHCP). Similar to the definition of transmitter parameters, here we choose the polarization mode of receiver as left-handed circular polarization (LHCP). Since we want to explore the impact of forest on GNSS-R signals, the receiver height is defined as 20 m (tower base).

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The current SCoBi version (v1.0.0) has the following functions: (1) It can be combined with the full polarization analysis function of linear and/or circular polarization; (2) It can be analyzed in combination with antenna characteristics, including antenna direction, antenna pattern and cross-polarization coupling, etc.; (3) It can analyze the interference effect caused by complex voltage and beam; (4) It can analyze the geometric effect caused by the height, direction and distribution loss on the vegetation depth and soil moisture profile. This article is to use the powerful simulation function of the SCoBi simulation platform to study the scattering characteristics of soil moisture inversion by GNSS remote sensing.

3 Simulation Research on the Influence Factors of Soil Reflectance 3.1

The Influence of Satellite Elevation Angle on Reflectivity Under Different Dielectric Constant Models

The idea of dual-antenna GNSS-R soil moisture retrieval is to calculate the soil dielectric constant by using reflectivity, and then to link the dielectric constant with soil moisture, so as to reverse the soil moisture. Soil dielectric constant model mainly describes the relationship between soil dielectric constant and soil water content. Because the relationship between them is complex, empirical model or semi-empirical model is often used. The commonly used empirical and semi-empirical soil dielectric constant models are Dobson semi-empirical model, Mironov semi-empirical model and Wang empirical model. (1) Dobson dielectric constant model Dobson et al. gave a semi-empirical model. This dielectric model characterizes the relationship between soil dielectric constant, incident signal frequency and soil characteristics, including volume water content, component content, bulk density and temperature. The model is shown below ð1Þ 0

In formula (1), e is the real part of the soil dielectric constant; mv is the soil volumetric water content; qb is the soil bulk density; qs is the soil matrix density, usually qs = 2.66 g/cm3; es is the soil matrix dielectric constant; a is the empirical 0 constant, the optimal value is 0.65; b is the parameter affected by the soil; efw is the real part of the free water dielectric constant, which is usually calculated by the Debye formula. (2) Mironov dielectric constant model The analytical formula of Mironov’s dielectric constant is mainly a function of soil moisture (mv, mvt) and temperature (t) variables.

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pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2d ðl; t; f Þ  1 ½mv þ ðmvt  mvÞH ðmv  mvtÞ 2s ðl; t; f ; mvÞ ¼ 2d ðl; tÞ þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2Þ þ 2v ðl; t; f Þ  1 ðmv  mvtÞH ðmv  mvtÞ

In formula (2), , , are the dielectric constants of dry soil (dry), bound water (bound) and free water (unbound) respectively; l, f , t are soil texture parameters, microwave frequency and soil temperature, respectively; mv are soil moisture, mvt is the soil moisture at the wilting point; H ð xÞ is a step function, and the value is 1 at the x [ 0 time and 0 at the x  0 time. (3) Wang dielectric constant model The Wang dielectric constant model expresses the dielectric constant as a quadratic function of soil moisture. The specific formula is as follows: 2 ¼ 3:1 þ 17:36 mv þ 63:12 m2v

ð3Þ

By simulating the above three soil dielectric models, the relationship between soil dielectric constant and soil moisture is obtained, as shown in Fig. 2.

Fig. 2. Three kinds of soil dielectric constant simulation diagram

It can be seen from the figure that as the soil moisture increases, the soil dielectric constants obtained by the three models all show a monotonous increase, but the upward trend of the three models has certain differences. Therefore, when conducting GNSS-R soil moisture inversion experiments, researchers need to select an appropriate soil dielectric constant model according to the actual situation. Figure 3 shows the influence of satellite elevation angle on reflectivity under different dielectric constant models (PHI = 15°, RMSH = 1 cm, VSM = 0.15 cm3/cm3). In order to show the effect of vegetation cover more clearly, agriculture (corn fields) are added to the bare soil during the simulation in this example. Vegetation information

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Fig. 3. The influence of satellite elevation angle on reflectivity under different dielectric constant models

will be given in Sect. 3.3. At the same time, in order to illustrate the influence of the receiver parameters on the reflected signal strength, we also give the reflectivity obtained by the receiving antenna in the ideal state and the reflectivity obtained by the receiving antenna in the actual state. As shown in the figure, from top to bottom are the Dobson model, Mironov model and Wang model.

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It can be seen from the figure that, in an ideal state, as the elevation angle of the satellite increases, the cross-polarization (RL, hereinafter referred to as RL) component of either bare soil or vegetation coverage under each model will increase accordingly. The co-polarization component (RR, hereinafter referred to as RR) of the corn field increases first and then decreases, reaching the maximum at 30°, while the RR component of bare soil has been decreasing. The changing trends under different dielectric constant models show good consistency. In actual conditions, when the satellite elevation exceeds 60°, the RR component of bare soil will increase. The differences among different dielectric constant models are mainly reflected here. It can be seen from the figure that when the satellite elevation angle exceeds 60°, the bare soil RR component of Mironov model and Wang model changes similarly. The main difference between the two models and the Dobson model is that they do not decline in segments under the Dobson model. The reason for the difference in reflectivity between the ideal state and the actual state is that when the satellite runs to a high elevation angle, the polarization crosstalk of the receiving antenna in the actual state may cause a part of the signal to enter the opposite port (polarization leakage). Unless otherwise specified, Dobson dielectric constant model is used for simulation by default. 3.2

The Influence of Soil Moisture on Reflectivity

Fig. 4. Influence of soil moisture on reflectivity

Figure 4 shows the influence of soil moisture on reflectivity under bare soil conditions. As shown in the figure, when the soil moisture rises from 0.05 cm3/cm3 to 0.4 cm3/cm3, the RR and RL components in the reflected signal both show an upward trend, with increase is about 15 db and 10 db, respectively. This is consistent with the actual situation, that is, when the soil moisture increases, the soil dielectric constant increases, the reflected signal strength increases, and the reflectivity increases.

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The Effect of Vegetation Cover on Reflectivity

Fig. 5. The relationship between soil moisture and reflectivity under different vegetation coverage conditions (left: forest/right: crops)

Figure 5 shows the relationship between soil moisture and reflectivity under different vegetation coverage conditions (TH = 75°, PHI = 0°, RMSH = 1.5 cm). Among them, the measured forest data comes from the active/passive remote sensing soil moisture retrieval experiment conducted by the US Department of Agriculture in Maryland in 2006 [24]. The covered vegetation in the experimental area is a paulownia forest with a height of 11 m–13 m, and the ground surface root mean square height (RMSH) is about 0.5 cm, which can be considered as flat. The measured crop data comes from the joint radar radiometer field experiment conducted by the United States Department of Agriculture in Maryland in 2012 [25, 26]. The covered vegetation in the experimental area is a corn crop with an average height of about 2.2 m in the early stage of maturity. The root mean square height of the ground surface is about 1 cm, which can also be considered to be flat. As shown in the figure, whether it is under forest cover or crop cover, as the soil moisture increases, the reflectivity components show an upward trend, and the reflectivity of bare soil decreases significantly after vegetation cover. The left side of Fig. 5 shows the change of soil reflectivity before and after forest cover. It can be seen from the figure that after forest cover, the RR component of bare soil reflectivity has dropped by about 10 db, and the RL component has dropped by about 7 db. The impact is very obvious. The right side of Fig. 5 shows the change of soil reflectivity before and after crop coverage. From the figure, it can be seen that after crop coverage, the RR component of bare soil reflectivity is not different from the RR component of soil reflectivity with crop coverage at low soil moisture. But as the soil moisture increases, the two begin to separate, with a difference of about 5 db. At the same time, it can be found that the presence or absence of crop coverage has a more significant impact on the RL component of the soil reflectivity. After crops are covered, the RL component decreases by about 10 db.

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It can be seen from this example that different kinds of vegetation have different effects on the reflection signal, but the reflectivity of soil covered with vegetation is significantly lower than that of bare soil, and the influence of specific parameters such as vegetation height and vegetation water content (VWC) on the inversion results will be further considered in the follow-up study. 3.4

The Effect of Surface Roughness on Reflectivity

Fig. 6. The effect of surface roughness on reflectivity

Figure 6 shows the effect of surface roughness on reflectivity (TH: 40°, PHI: 0°, VSM = 2.5 cm3/cm3). Same as Example 3.1, this example also adds agriculture (corn field) coverage in the simulation process. The left picture shows the change of RL component of bare soil and corn field, and the right picture shows the change of RR component of bare soil and corn field. As shown in the figure, as the surface roughness (RMSH) increases, the RR and RL components both show a rapid downward trend, and there is no sign of convergence. Therefore, when conducting GNSS-R soil moisture inversion experiments, we should choose as much as possible an experimental area with a flat surface and good observation conditions. When the surface of the experimental area cannot meet the flat condition, we should add the topographic effect correction to the algorithm as much as possible.

4 Conclusion The continuous development of GNSS-R technology has brought a new efficient and cheap detection method to the field of remote sensing. Although GNSS-R technology has become increasingly mature in the field of ocean remote sensing, there are still many problems in its application in the field of land surface remote sensing, which urgently need to be studied by researchers. These studies include a series of theoretical analysis to experimental verification. In this process, the research on the simulator can play a good role as a bridge and help us carry out a series of complex and

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comprehensive theoretical verification work before experimental observation. In this paper, the influence of geophysical parameters, such as surface roughness, soil moisture and vegetation, on the intensity of different polarization components of GNSS reflection signals is introduced by using SCoBi simulator released by Mississippi State University, and the scattering characteristics of soil moisture retrieved by GNSS remote sensing are studied through measured vegetation data. The main work in the next step is to optimize the algorithm of soil moisture retrieval by GNSS-R combined with the simulation results of the simulator and the measured data of GNSS stations, and analyze and determine the best parameter configuration under different scenarios and tasks of GNSS-R. Acknowledgments. Thanks to the SCoBi simulation platform provided by the IMPRESS laboratory of Mississippi State University. Thanks to the experimental data provided by the USDA. Sincerely thank the editorial department and anonymous reviewers of your journal for their valuable comments and suggestions for this article! This work has been supported by State Key Laboratory of Geo-Information Engineering(SKLGIE2019-Z-2-1); National Key R&D Program of China (2020YFC1512000,2019YFC1509802, 2018YFC1505102); Natural Science Foundation of China projects (NSFC) (42074041,41731066); ZFS (ZFS19001D-ZTYJ08, Y9E0151M26) and CETC Industrial development fund project “BDSBAS International Standards Research” (20201121); Shaanxi Natural Science Research Program (2020JM-227); Fundamental Research Funds for the Central Universities (No. 300102269201, 300102299206).

References 1. Wu, X.R., OuYang, X.Q., Wang, F., Ma, W.X.: Bare soil circular polarization scattering properties for GNSS-R applications. J. Beijing Univ. Aeronaut. Astronaut. 46(10), 1883– 1889 (2020) 2. Yan, S.H., Gong, J.Y., Zhang, X.X., Li, D.X.: Ground-based GNSS-R observations for soil moisture. Chin. J. Geophys. 54(11), 2735–2744 (2011) 3. He, X.F., Wang, J., Wang, X.L., Song, M.F.: Retrieval of coastal typhoon storm surge using multi-GNSS-IR. Acta Geodaetica Cartogr. Sin. 49(09), 1168–1178 (2020) 4. Zhu, Y.C., Zou, J.G., Yu, K.G.: A new sea ice distribution detection method using GNSS reflected signals. Geomat. Inf. Sci. Wuhan Univ. 43(10), 1472–1477 (2018) 5. Zhang, S.C., Nan, Y., Li, Z.Y., Zhang, Q., Dai, K.Y., Zhao, Y.H.: Analysis of tide variation monitored by GNSS-MR. Acta Geodaetica Cartogr. Sin. 45(09), 1042–1049 (2016) 6. Zheng, N.S., Feng, Q.L., Liu, C., Zhou, X.M.: Relationship analysis between GPS reflection signal SNR and NDVI. Geomat. Inf. Sci. Wuhan Univ. 44(10), 1423–1429 (2019) 7. Bian, S.F., Zhou, W., Liu, L.L., Li, H.P., Liu, B.: GNSS-IR model of snow depth estimation combining wavelet transform with sliding window. Acta Geodaetica Cartogr. Sin. 49(09), 1179–1188 (2020) 8. Wan, W., Chen, X.W., Peng, X.F., et al.: Overview and outlook of GNSS remote sensing technology and applications. J. Remote Sens. 20(05), 858–874 (2016) 9. Liu, J.N., Shao, L.J., Zhang, X.X.: Advances in GNSS-R studies and key technologies. Geomat. Inf. Sci. Wuhan Univ. 11, 955–960 (2007) 10. Yang, D.K., Zhang, Q.S.: GNSS reflected signal processing basics and practice. Publishing House of Electronics Industry (2012)

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11. Li, W., Cardellach, E., Fabra, F., et al.: Lake level and surface topography measured with spaceborne GNSS reflectometry from CYGNSS mission: example for the lake Qinghai. Geophys. Res. Lett. (2018) 12. Jin, S.G., Zhang, Q.Y., Qian, X.D.: New progress and application prospects of global navigation satellite system reflectometry(GNSS + R). Acta Geodaetica Cartogr. Sin. 46(10), 1389–1398 (2017) 13. Pan, Y.L., Ren, C., Liang, Y.J., et al.: Inversion of surface vegetation water content based on GNSS-IR and MODIS data fusion. Satell. Navig. 1, 21 (2020). https://doi.org/10.1186/ s43020-020-00021-z 14. Liang, P., Pierce, L.E., Moghaddam, M.: Radiative transfer model for microwave bistatic scattering from forest canopies. IEEE Trans. Geosci. Remote Sens. 43(11), 2470–2483 (2005) 15. Ferrazzoli, P., Guerriero, L., Pierdicca, N., Rahmoune, R.: Forest biomass monitoring with GNSS-R: theoretical simulations. Adv. Space Res. 47(10), 1823–1832 (2010) 16. Guerriero, L., Pierdicca, N., Pulvirenti, L., Ferrazzoli, P.: Use of satellite radar bistatic measurements for crop monitoring: a simulation study on corn field. Remote Sens. 5(2), 864–890 (2013) 17. Pierdicca, N, Guerriero, et al.: SAVERS: a simulator of GNSS reflections from bare and vegetated soils. Geosci. Remote Sens. (2014) 18. Nievinski, F.G., Larson, K.M.: An open source GPS multipath simulator in Matlab/Octave. GPS Solutions 18(3), 473–481 (2014) 19. Fabra, F., Cardellach, E., Li, W., Rius, A.: Wavpy: a GNSS-R open source software library for data analysis and simulation. In: IEEE International Geoscience Remote Sensing Symposium (IGARSS), Fort Worth, Texas, pp. 4125–4128 (2017) 20. Wu, X.R., Jin, SH.G.: GNSS-reflectometry: forest canopies polarization scattering properties and modeling. Adv. Space Res. 54(5), 863–870 (2014) 21. Kurum, M., Deshpande, M., et al.: SCoBi-Veg: a generalized bistatic scattering model of reflectometry from vegetation for signals of opportunity applications. IEEE Trans. Geosci. Remote Sens. (2019) 22. Eroglu, O., Boyd, D.R., Kurum, M.: The signals of opportunity coherent bistatic scattering simulator: a free, open source simulator framework. IEEE Geosci. Remote Sens. Mag. PP (99), 1 (2020) 23. Eroglu, O., Boyd, D., Kurum, M.: Open-sourcing of a soop simulator with bistatic vegetation scattering model. In: IEEE Geoscience and Remote Sensing Symposium (IGARSS). IEEE (2018) 24. Kurum, M., Lang, R.H., O’Neill, P.E., Joseph, A.T., Jackson, T.J., Cosh, M.H.: A first-order radiative transfer model for microwave radiometry of forest canopies at L-band. IEEE Trans. Geosci. Remote Sens. 49(9), 3167–3179 (2011) 25. O’Neill, P., et al.: L-band active/passive time series measurements over a growing season using the ComRAD ground-based SMAP simulator. In: Proceedings of IEEE International Symposium on Geoscience Remote Sensing, pp. 37–40 (2013) 26. Orhan, E., Mehmet, K., John, B.: Response of GNSS-R on dynamic vegetated terrain conditions. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 12(5), 1599–1611 (2019)

Research on Digital Elevation Model Using GNSS-IR Technology Xin Zhou1, Shuangcheng Zhang1,2(&), Qi Liu1, Jilun Peng1, Lixia Wang1, and Bo Shao3 1

2

School of Geological Engineering and Geomatics, Chang’an University, Xi’an 710054, China State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China 3 The 20th Research Institute of CETC, Xi’an 710068, China

Abstract. With the continuous in-depth research on the emerging technology of GNSS remote sensing, GNSS-IR technology is widely used in various environmental remote sensing. It is a new attempt to use this technology to interpret digital elevation models. This article explains the theoretical mechanism of using GNSS-IR technology to interpret digital elevation models., The signal-to-noise ratio data of different azimuths and elevation angles, calculate the difference between the reflection height parameter and the height of the station, and calculate the first Fresnel reflection zone (FFZ) corresponding to different signal-to-noise ratio (SNR) reflection component sequences), and finally assign the value to the corresponding grid to interpret the digital elevation model of the site. In order to verify the feasibility of the theory, this paper selects a flat bare ground as the experimental site, and uses different receivers for analysis. The experimental results show that the height of the station retrieved by GNSS-IR technology is slightly different from the actual height of the station. The preliminary research results verify the feasibility of using GNSS-IR technology to interpret digital elevation models, and provide an important reference for the subsequent use of GNSS-IR technology to interpret digital elevation models of complex terrain. Keywords: GNSS-IR


SNR
Digital elevation model

1 Introduction Digital Elevation Model is abbreviated as DEM, which is a digital model that describes the landform information of the earth’s surface [1]. Because it can truly reflect the characteristics of topography and geomorphology in the study of surface terrain, and has the characteristics of constant accuracy, high resolution, and convenient update, it has become a research hotspot in various fields such as geographic information system, geological analysis, surveying and mapping, remote sensing and virtual reality [2]. The establishment of high-precision, high-temporal-spatial resolution, and high-efficiency digital elevation models has become an urgent need in various fields [3].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 204–212, 2021. https://doi.org/10.1007/978-981-16-3138-2_20

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GNSS-IR remote sensing technology is an emerging remote sensing technology that realizes monitoring and inversion of environmental parameters on the earth’s surface by analyzing the interference signals received by geodetic antennas [4]. At present, GNSS-IR is widely used in many fields such as soil moisture, vegetation water content, sea level changes, snow depth and volcanic activity detection [5] due to its low cost, all-weather use, high accuracy, and high spatial and temporal resolution [6]. The application of GNSS-IR technology to the interpretation of digital elevation models has not yet been carried out at home and abroad, and many technical issues need further exploration and research. This article will use GNSS-IR technology for the first time to conduct research and analysis on interpreting digital elevation models to verify the feasibility of GNSS-IR technology for terrain inversion, so as to discover the greater potential of GNSS-IR technology and make it more widely used.

2 GNSS-IR Interprets the Principle of Digital Elevation Model The signal received by the GNSS receiver is not unique. While receiving the direct signal transmitted by the satellite, it also receives the signal reflected by the ground [7]. Figure 1 is a schematic diagram of using GNSS-IR technology to detect high reflection.

Fig. 1. Schematic diagram of high reflectance detected by GNSS-IR

In Fig. 1, H represents the height of the antenna from the ground, that is, the vertical distance from the antenna phase center of the receiver to the ground; h represents the reflection distance from the receiver antenna phase center to the undulating surface, which is called the reflection height. The amplitude of the direct signal and the reflected signal are represented by Ad and Am respectively. E is the angle between the direct signal and the horizontal plane where the reflection point is located, and it is also the satellite altitude angle. For conventional receiver antennas, because of the influence of antenna gain, the amplitude of the direct signal and the reflected signal has a large difference[8], and their relationship is as follows: Ad  Am

ð1Þ

From formula (1), it can be concluded that the overall change trend of the composite signal is determined by the direct signal Ad , and the reflected signal Am appears

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as a local periodic oscillation in the curve of the composite signal [9]. Since the influence of the multipath effect on the SNR increases with the decrease of the satellite altitude angle, the periodic oscillation becomes larger in the low altitude angle range. SNR has the following relationship with the amplitude of direct and reflected signals [10]: SNR2 ¼ A2c ¼ A2d þ A2m þ 2Ad Am cos w

ð2Þ

In Eq. (2), Ac is the amplitude of the composite signal, and w is the angle between the direct signal and the reflected signal. Generally, the method of quadratic polynomial fitting is used to separate the direct signal and the reflected signal, and the residual sequence of the SNR value after the overall trend term is removed in the low altitude range can be obtained. The amplitude of the reflected signal in the multipath can be fitted with the following formula [11, 12]: Am ¼ A cos


 4ph sin E þ w k

ð3Þ

In the formula: k is the wavelength of the carrier, and sin E is recorded as t, and 2h=k is recorded as f , then the formula (3) can be simplified to a standard cosine function expression: Am ¼ A cosð2pft þ wÞ

ð4Þ

Perform L-S (Lomb-Scargle) spectrum analysis on the SNR residual sequence to obtain the frequency f of the multipath reflection signal [13]. Refer to the formula f ¼ 2h=k to obtain the vertical reflection distance from the antenna phase center to the ground surface at the reflection point. Zhang Shuangcheng, Wang Xiaolei et al. (2017) proposed the principle of planar gridding. The specific implementation method is to select the N-segment SNR sequence that the receiver receives within a certain period of time and oscillates at a specific altitude and azimuth angle, and obtain the effective reflection high parameter hn corresponding to the SNRn sequence; at the same time, according to the interference characteristics between the received direct signal and the reflected signal, the first Fresnel zone FFZn corresponding to the middle moment of the SNRn sequence is inferred.

Fig. 2. Schematic diagram of planar grid inversion

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In the Fig. 2, the two focal points of the first Fresnel reflection zone FFZn are C1n and C2n respectively. The coordinates of the two focal points are ðxc1n ; yc1n Þ and ðxc2n ; yc2n Þ respectively. The major axis and focal length of the ellipse are 2an and 2cn respectively. In this grid mode, the corresponding value of the reflection height at any point gridði; jÞ on the ground is: hði; jÞ ¼ PN

XN

1

n¼1

n¼1

wn

w n
hn

ð5Þ

In the formula, wn is the weight of hn with respect to gridði; jÞ. When point gridði; jÞ is at the center of FFZ, wn is 1. If point gridði; jÞ is at the boundary of FFZ, wn is s. The weight should be inversely proportional to the distance. The calculation formula is as follows[14]: wn ¼ 1 

1s ðR  2cn Þ; ð0\s\1; wn [ 0Þ 2an  2cn

ð6Þ

In formula (6), s is the threshold and R is the sum of the distances from point gridði; jÞ to the focal point. By subtracting the height of the antenna from the ground from the corresponding reflection height parameter value in the FFZn of the first Fresnel zone, the relative height hr of the grid elevation in the inversion area relative to the site elevation can be obtained, thereby interpreting the DEM map of the site, the calculation formula is as follows: hr ¼ hði; jÞ  H ¼ PN

XN

1

n¼1

wn

n¼1

wn
hn  H

The flowgraph of GNSS-IR for digital elevation model is shown in Fig. 3.

Fig. 3. Flowgraph of GNSS-IR for digital elevation model

ð7Þ

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3 Analysis of Calculation Examples of Research on Digital Elevation Model Using GNSS-IR Technology In order to verify the feasibility of the above theoretical methods, the experimental station is located in Chang’an District, Xi’an City, Shaanxi Province (34°8′25″N, 109° 2′13″E). The terrain around the station is flat and open, and there is no vegetation on the surface. The terrain around the station is flat and open, and there is no vegetation on the surface. It is an ideal test site for ground GNSS interpret site DEM. In the experiment, LEICA receiver and low-cost receiver were used to collect experimental data, and finally analyze the data. Figure 4 shows the station environment and experimental equipment (the left one is the LEICA receiver, the right one is the lowcost receiver).

Fig. 4. The observation environment and experimental equipment around the station

The observation data on the 302th day of 2020 were collected using LEICA and low-cost receivers respectively. Then perform the derivation calculation of GNSS-IR interpret site DEM according to the steps of the flowchart. Set the elevation angle range of LEICA and low-cost receivers to extract SNR data to 15–0° and 5–20° respectively. Figure 5 and Fig. 6 respectively show SNR variations and L-S results of all satellites received by the LEICA receiver and low-cost receiver. The abscissa value at the peak of the L-S spectrum amplitude corresponding to the SNR sequence in Fig. 6 is the effective detection vertical reflection distance. It can be seen from the figure that the effective detection vertical reflection distance calculated by each SNR sequence is slightly different, indicating that the vertical distance from the ground surface in each inversion area grid to the antenna phase center is approximately the same, because the selected experimental site is relatively flat, which is in line with the actual terrain. When interpreting site DEM, the corresponding value in each inversion area grid is the difference between the calculated effective vertical reflection height and the station height. Because the station height is fixed, therefore, the accuracy of the vertical reflection distance detected by GNSS-IR technology will affect the accuracy of the interpretation of the digital elevation model of the site.

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Fig. 5. SNR variations of all satellites received by the LEICA receiver (a) and low-cost receiver (b) (DOY302)

Fig. 6. L-S results for SNR variations of all satellites received by the LEICA receiver (a) and low-cost receiver (b) (DOY302)

Because the inversion area of the entire experimental site is relatively flat, this paper compares the average vertical reflection distance obtained by L-S spectrum analysis of all SNR sequences in the entire inversion area with the antenna height of the actual station to verify the accuracy of the vertical reflection distance detected by GNSS-IR technology. The antenna height of the LEICA receiver is corrected to 1.4664 m. After processing all the SNR reflected signal data received by the receiver, the average value of the vertical reflection distance is 1.4624 m. The difference between the two is 0.004 m and the standard deviation is 0.066 m. The result is shown in Fig. 7(a). The antenna height of the low-cost receiver is 1.6271 m, the average height after processing the experimental data is 1.6132 m, the difference between the two is 0.008 m, and the standard deviation is 0.0514 m. The result is shown in Fig. 7 (b). Comparing the experimental results of the two receivers, it is shown that the inverted station height by GNSS-IR is in good agreement with the actual station height, which further proves that the use of SNR reflection signal to detect the vertical reflection distance has high accuracy, and furthermore, it provides a favorable basis for using GNSS-IR technology to interpret digital elevation models.

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Fig. 7. Error analysis of measuring station height with LEICA receiver (a) and low-cost receiver (b)

In this paper, through planar grid processing, perform L-S spectrum analysis on the SNR reflection data of all satellites received by the receiver on the day, and the vertical distance hði; jÞ from the ground surface to the antenna phase center in each grid is obtained, and the vertical distance between the receiver antenna phase center and the ground is H, according to formula (9), the relative height between each grid and the receiving point can be obtained, so as to interpret the digital elevation model of the site. Figure 8(a) and Fig. 8(b) are respectively the DEM diagrams of the sites where the LEICA receiver and the low-cost receiver are interpreted by GNSS-IR technology. It can be seen from Fig. 8 that the size of the area monitored by the two receivers is different. This is because for ground observations in single antenna mode, the effective detection area can be approximated by the area of the first Fresnel reflection zone [15], and the size of the Fresnel reflection area is related to the altitude of the satellite and the height of the receiver antenna. Due to the azimuth of the satellite, there is no FFZ in the small area north of the azimuth of the two receivers, so the relative height value in the corresponding area is lacking.

Fig. 8. DEM obtained using LEICA receiver (a) and low-cost receiver (b)

4 Discussion In this paper, based on the basic principle of GNSS-IR technology to calculate the reflection height, combined with Zhang Shuangcheng and others proposed the principle of plane gridding, to conducted experimental analysis to calculate DEM, and verifies the feasibility of the GNSS-IR technology in the interpretation site DEM. GNSS-IR technology has shown great potential in inverting terrain, effectively expanding the

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application range of GNSS multipath signals. Undoubtedly, for the preliminary research results obtained by GNSS-IR technology in interpreting digital elevation models, there are the following issues that need to be studied: 1. Analysis of the impact of different receiver antenna types on interpretation accuracy; 2. The DEM diagram interpreted in this experiment is a grid diagram that differs from the actual DEM diagram. 3. This experiment is only a study on the flat surface, and it did not analyze the influence of the undulating and complex terrain on the interpretation accuracy. According to theoretical analysis, improving the spatial resolution of this method requires more signal-to-noise ratio data around the site. When interpreting complex terrain, in order to improve the inversion accuracy, the long-time sequence SNR data of GNSS multi-system satellites should be integrated to interpret the digital elevation model; 4. The penetration ability of electromagnetic waves varies with the change of soil moisture, so this method has seasonal deviations. In the later research, we can consider establishing a corresponding model to weaken and eliminate errors. Acknowledgement. This work has been supported by State Key Laboratory of Geo-Information Engineering(SKLGIE2019-Z-2-1); National Key R&D Program of China (2020YFC1512000, 2019YFC1509802,2018YFC1505102); Natural Science Foundation of China projects (NSFC) (42074041,41731066); ZFS (ZFS19001D-ZTYJ08, Y9E0151M26) and CETC Industrial development fund project “BDSBAS International Standards Research” (20201121);Shaanxi Natural Science Research Program (2020JM-227); Fundamental Research Funds for the Central Universities (No. 300102269201, 300102299206). The authors gratefully acknowledge UNAVCO for providing experimental data; Kristine Larson, Carolyn Roesler, Berkay Bahadur, and many others who have provided open access to MATLAB code. Three anonymous reviewers are thanked for their constructive review of this manuscript.

References 1. Shuaitang, H., Jianbo, C., Yalikun, A., Yuan, Y., Yangang, X., Fangfang, N.: Study on landforms of south tianshan based on digital elevation model. Plateau Earthq. Res. 30(03), 17–24+6 (2018) 2. Changlong, H., Yan, Y.: Digital elevation model (DEM) and methoda of display. J. Heilongjiang Univ. Sci. Technol. 04, 233–236 (2004) 3. Li, H.: Contents and methods of quality control of digital elevation model production using point cloud. Geomat. Spat. Inf. Technol. 43(9), 183–185. (2020) 4. Wan, W., Li, H., Hong, Y., Chen, X.W., Peng, X.F.: Definition and application of GNSS-R observation patterns. J. Remote Sens. 19(6), 882–893 (2015). https://doi.org/10.11834/jrs. 20154304 5. Wang, L.X., Wang, T., Zhang, S.C., Zhang, J.J., Zhao, G.S., Peng, J.L.: Soil moisture retrieval based on long-term SNR data. In: Paper presented at the 11th China Satellite Navigation Conference, Chengdu, Sichuan, China (2020)

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6. Pan, Y.L., Ren, C., Liang, Y.J., et al.: Inversion of surface vegetation water content based on GNSS-IR and MODIS data fusion. Satell. Navig. 1, 21 (2020). https://doi.org/10.1186/ s43020-020-00021-z 7. Kristine, M.L., Felipe, G.N.: GPS snow sensing: results from the EarthScope Plate Boundary Observatory. GPS Solutions 17(1) (2013) 8. Shuangcheng, Z., et al.: Preliminary research on GNSS-MR for snow depth. Geomat. Inf. Sci. Wuhan Univ. 43(02), 234–240 (2018) 9. Zhang, J., Zhang, S., Guo, L.: Retrieval of snow depth using ground-based GPS. Meteorol. Sci. Technol. 48(01), 46–51 + 67 (2020) 10. Nagai, T., Ogawa, H., Terada, Y., et al.: GPS buoy application to offshore wave, tsunami and tide observation. Coastal Engineering 2004:(In 4 Volumes) (2015) 11. Larson, K.M., Small, E.E., Gutmann, E., Bilich, A., Axelrad, P., Braun, J.: Using GPS multipath to measure soil moisture fluctuations: initial results. GPS Solutions 12(3), 173–177 (2008) 12. Larson, K.M., Small, E.E., Gutmann, E.D., Bilich, A.L., Braun, J.J., Zavorotny, V. U.: Use of GPS receivers as a soil moisture network for water cycle studies. Geophys. Res. Lett. 35 (24). (2008) 13. Jiang, L.M., Wang, P., Zhang, L.X., et al.: Improvement of snow depth retrieval for FY3BMWRI in China. Earth Sciences, Science China (2014). https://doi.org/10.1007/s11430-0134798-8 14. Zhang, S., Wang, X., Zhang, Q.: Avoiding errors attributable to topography in GPS-IR snow depth retrievals. Adv. Space Res. 59(6) (2017) 15. Katzberg, S.J., Torres, O., Grant, M.S., Masters, D.: Utilizing calibrated GPS reflected signals to estimate soil reflectivity and dielectric constant: results from SMEX02. Remote Sens. Environ. 100(1) (2005)

Research and Application of Deformation Monitoring Algorithm for Single-Frequency GNSS Low-Cost Monitoring Equipment Bin Zhou1(&), Weixin He1, Xintong Xu2, and Hui Liu2 1

Wuhan Navigation and LBS, Inc., Wuhan, China [email protected] 2 Wuhan University, Wuhan, China

Abstract. GNSS precision positioning technology has been widely used in earth surface subsidence monitoring, engineering building displacement monitoring and other directions. It has the advantages of global, all-weather, high precision, no intervisibility between stations and so on. In this paper, Aiming at the problems of low-cost GNSS equipment, such as single frequency, large observation noise and frequent cycle slips, a complete set of real-time and highprecision deformation monitoring algorithm is designed and verified in the actual projects such as power facilities deformation monitoring, tailings settlement monitoring and geological disasters monitoring. The results show that the algorithm and software can achieve the precision of millimeter/sub-millimeter level, and can realize the fast response to the actual deformation. Keywords: GNSS


Deformation monitoring
Low-cost
Single frequency

1 Introduction With the full completion of Beidou Navigation Satellite System (BDS), the positioning related applications have been widely promoted in the national economic construction. There are many advantages of GNSS in comparison to the traditional measurement methods, such as high precision, all-weather, continuous, no intervisibility required between stations and easy to automate. BDS has been used in tailings settlement monitoring, dam and bridge engineering buildings displacement monitoring, and landslides and debris flows geological disasters monitoring, and good results have been achieved [1–3]. Traditional multi-system multi-frequency GNSS monitoring equipment suffers from multiple disadvantages such as high cost, bulky volume, high power consumption, and complexity in project implementation. While the low-cost monitoring equipment based on multi-system and single frequency GNSS chip avoid these problems. However, due to the complex application environment of actual deformation monitoring projects, occlusion and interference often occur, which result in the poor quality of GNSS observations and low monitoring precision, which restrict the wide application of low-cost monitoring equipment in deformation monitoring field.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 213–223, 2021. https://doi.org/10.1007/978-981-16-3138-2_21

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At present, the research on GNSS deformation monitoring mainly focuses on multisystem and multi frequency joint positioning [4], multi-path error processing [5], multisensor fusion monitoring and system integration [6], while the research on single frequency low-cost application is less. So, this paper designs a set of deformation monitoring algorithm suitable for low-cost single frequency GNSS equipment and develops a deformation monitoring software by analyzing the data of practical application scenarios.

2 A Mathematical Model for GNSS Deformation Detection Algorithm and Data Quality Control 2.1

The Mathematical Model

According to the error characteristics of GNSS satellite observation, the doubledifference observation equations of pseudorange and carrier phase can be obtained by station-satellite double-differences: ij ij DrPijAB ¼ DrqijAB þ DrIAB þ DrTAB

ð1Þ

ij ij ij þ DrTAB  kDrNAB kDruijAB ¼ DrqijAB  DrIAB

ð2Þ

In the equations, DrPijAB is the pseudorange double-difference observation, DruijAB is the carrier phase double-difference observation, DrqijAB is the double-difference ij distance between user and satellite, DrIAB is the double-difference ionosphere delay, ij ij DrTAB is the double-difference troposphere delay, DrNAB is the double-difference ambiguity, k is the wavelength. In the actual deformation monitoring project, the distance between the monitoring station and the reference station is usually several hundred meters to several kilometers, generally no more than 5 km. The double-difference ionosphere and the troposphere delay can be eliminated and ignored. So, the actual double-difference observation models are as follows: DrPijAB ¼ DrqijAB

ð3Þ

ij kDruijAB ¼ DrqijAB  kDrNAB

ð4Þ

The key problem of the mathematical model in Eq. (3) and Eq. (4) is to solve the ^ This paper uses double-difference ambiguity DrN, and fix DrN as an integer DrN. the extended Kalman filter to improve the fixed rate of ambiguity, and then improves the usability and reliability of the deformation algorithm. The quality of the filtering solution depends on the quality of the observations of the monitoring equipment. However, deformation monitoring equipment is usually deployed in a bad environment sheltered by trees or slopes. Gross errors and cycle slips

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are inevitable. In order to avoid the filtering divergence, effective quality control methods must be used in filtering algorithms. 2.2

DIA Quality Control Method in the Filtering Process

Low-cost deformation equipment can only output single frequency observations, and it is difficult to detect and repair cycle slips effectively. So, cycle slips are also treated as gross errors in this algorithm. The RAIM algorithm based on the traditional least squares method can only judge whether there is an abnormality in the solution process based on the post-test residual and its variance information, but cannot effectively judge and identify which observation is abnormal. Therefore, this paper introduces the DIA (Detection-Identify-Adjust) processing strategy [7] for the Kalman filter algorithm to detect and identify gross errors, and then dynamically adjust the filtering process according to the specific conditions. The implementation of the algorithm is divided into the following three steps: (1) System detection. Innovation vector establishes the relationship between system state prediction and observation equation, which is an important information in Kalman filter. The expressions of innovation vector and its variance are as follows: ~t Vt ¼ Zt  Ht X

ð5Þ

~ t HtT þ Rt Qv ¼ Ht P

ð6Þ

Because the Rt matrix already contains the weight of pseudorange and carrier phase, the whole detection variable can be constructed: T ¼ VtT Q1 v Vt

ð7Þ

The innovation vector Vt follows the Gaussian normal distribution, while the detection variable T follows the v2 distribution with n (number of independent observations) degrees of freedom. Under the assumption of no gross error, the confidence interval is calculated as the detection threshold TD according to the false alarm probability PFA (generally 0.01 or 0.05). When T is less than TD, it is consistent with the hypothesis, and it is considered that there is no gross error in the system. When T is greater than TD, the hypothesis is not tenable, and it is considered that there is gross error in the system. (2) Gross error identification. When there is gross error in the system, the innovation vector VT should be checked one by one to determine the position of gross error. First, assume that there is no gross error in the i-th observation, construction statistics variable:

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Ci Q1 v Zt ffi Wi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T Ci Q1 v Ci

ð8Þ

Where Ci is the unit vector with the i-th position value of 1, and Wi follows Gaussian normal distribution. Assuming that there is no gross error in the observation, the confidence interval is calculated according to the false alarm probability PFA/n as the detection threshold WD. When Wi is less than WD, it is consistent with the hypothesis, and it is considered that there is no gross error in the observation. When Wi is greater than WD, the hypothesis is not tenable, and it is considered that there may be gross error in the observation and it is marked. By checking the innovation vector Vt one by one, a group of problematic statistical vectors W are obtained: W ¼ fW 1 ; W 2 ;


W i


g

ð9Þ

There may be one or more gross errors at same time in the system, so iterative processing is needed. Each time, only the observation value of the satellite corresponding to the maximum value in the statistical vector W is taken as the gross error. (3) Adjustment control. Firstly, according to Eq. (10), the calculated state parameters are brought back to the ~t : equation to calculate the residual vector V ~t ¼ Vt  HXt V

ð10Þ

The type of observation corresponding to Wi is judged and it’s residual value is extracted, and then the pseudorange and carrier phase are processed separately in the adjustment process. ① Processing of pseudorange. ~i is larger than VPD, the satellite will be set The residual threshold VPD is set, if V ~ elimination mark; else if Vi is smaller than VPD, the Rt matrix will be adjusted, the ~i 2, and diagonal element corresponding to the observation value will be added with V the weight reduction mark will be set, and then the filter will be performed again. If the observation is still marked abnormal in the subsequent checking process, it will be removed. ② Processing of carrier phase. ~i is larger than VLD, the satellite will be set The residual threshold VLD is set, if V elimination mark. If it is smaller than VLD, the cycle slip mark will be set. Adjust the ambiguity parameter and filter again, if the observed value is still marked abnormal in the subsequent checking, it will be removed (Fig. 1).

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Fig. 1. Quality control flow of Kalman filter

3 Design of Deformation Monitoring Algorithm Traditional deformation monitoring schemes usually adopt the method of solving the baseline afterwards at intervals. If the deformation occurs, the response is too long to meet the actual application requirements, which limits the scope of its application. In this paper, an adaptive deformation monitoring algorithm adopts different methods to detect slow deformation and sudden displacement, and responds to deformation events rapidly while ensuring high precision. 3.1

Estimation of Displacement

After Kalman filter is used to estimate the ambiguity floating-point solution and lambda algorithm is used to fix the integer ambiguity of each observation, the double-difference carrier phase observation can be restored to high-precision range observation: DrPLijAB ¼ DrqijAB þ DreiLAB

ð11Þ

According to the above equation, the carrier phase observation equation of each satellite is linearized and expressed in matrix form: DrPLt ¼ Drq0t þ Ht dX

ð12Þ

Lt ¼ DrPLt  Drq0t

ð13Þ

Vt ¼ Ht dX  Lt

ð14Þ

Where dX is the position parameter to be estimated and is considered to be invariant in a solution period. The equation of carrier phase observation of all epochs in the solution period is reconstructed, and the high-precision monitoring station position is obtained by using the least squares adjustment algorithm, and then the displacement change of the monitoring point can be obtained by processing the coordinate sequence.

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2

3

2

3

2

Lt1

3

0 6 7 Vt1 Ht1 Pt1 6 Lt2 7 6 7 6 .. 7 6 .. 7 B 4 . 5 ¼ 4 . 5dX  6 . 7; Pw ¼ @ 6 .. 7 4 5 0 Vtn Htn Ltn

..

0 .

1 C A

ð15Þ

Ptn

Vw ¼ Hw dX  Lw

ð16Þ

dX ¼ ðHwT Pw Hw Þ1 ðHwT Pw Lw Þ

ð17Þ

In the equations, PW is the weight matrix. In the adjustment solution, the weight of observation is adjusted according to the time interval to present epoch time, which can speed up the response to deformation. As shown in the Fig. 2, the overall solution process of the algorithm adopts the way of real-time sliding window. The length of the solution period is indicated in curly brackets, which determines the precision of the monitoring results. In the actual project, it needs to be adjusted according to the precision requirement and response time requirement.

Fig. 2. Algorithm flow of deformation monitoring

3.2

Sudden Displacement Monitoring

The linearization of Eq. (2) can be expressed as follows: kDrut1 ¼ Drq0t1 þ Ht1 dXt1  DrIt1 þ DrTt1  kDrNt1

ð18Þ

kDrut2 ¼ Drq0t2 þ Ht2 dXt2  DrIt2 þ DrTt2  kDrNt2

ð19Þ

Where the interval between t1 and t2 is small and the same initial position parameter is used when the equation is linearized, Ht1 and Ht2 are the coefficient matrices of the two epochs, dXt1 and dXt2 are the offsets relative to the initial position to be estimated, and ddX is the position offset between epochs, so:

Research and Application of Deformation Monitoring Algorithm

dXt2 ¼ dXt1 þ ddX

219

ð20Þ

In the case of no cycle slip, the ambiguity parameter can be eliminated by making a difference between Eqs. (18) and (19), and the variation between the ionosphere and troposphere delay can be ignored. According to Eq. (20), three-difference observation equation can be obtained: kDrDut1;t2 ¼ DrDq0t1;t2 þ ðHt2  Ht1 ÞdXt1 þ Ht2 ddX

ð21Þ

When the interval between t1 and t2 is small enough and the initial position is accurate, the variables related to the coefficient difference between epochs in the equation can be ignored [8]. In this case, the three-difference observation equation can be written as follows: kDrDut1;t2 ¼ DrDq0t1;t2 þ Ht2 ddX

ð22Þ

The equation only includes the inter epoch displacement parameters, and only using the single epoch carrier phase observation, the inter epoch displacement can be obtained by the least squares solution. Because of the high precision of carrier phase, the displacement change calculated by Eq. (22) can reach millimeter level, and the position sudden offset above centimeter level can be detected in real time. 3.3

Slow Displacement Monitoring

When the location of the monitoring point changes small, but at a fast speed, the sudden displacement detection algorithm cannot detect and identify because of the small change between epochs. It needs a solution period to reflect the actual displacement change. In this paper, a method of using short period checking long period is designed to reduce the response time.   dPost ¼ Post;tm  Post;tn  ð23Þ In the Eq. (23), m and n are the length of the short solution period and long solution period respectively. Post;tm and Post;tn are the positions of the monitoring points calculated by using m and n epochs observation according to Eq. (17). The RMS is counted by the long and short solution period coordinate difference in a period of time and the detection threshold TD is given below: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u tn uX RMSt ¼ t dPos2ti =ðn  1Þ

ð24Þ

t1

TD ¼ 4  RMSt

ð25Þ

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When dPost is larger than TD, the system considers that the displacement exceeds the limit, issues a warning and initializes the long period.

4 Case Verification Analysis 4.1

Verification of Deformation Monitoring Algorithm

The GNSS module of low-cost single frequency GNSS deformation monitoring equipment used in this paper is MXT906AM of Wuhan Mengxin technology company (GPS L1, BDS BI1 and GLONASS R1, three systems single frequency). 4.1.1 Precision Analysis of Deformation Algorithm In order to verify the feasibility of deformation monitoring and the precision of the algorithm, this paper uses the actual data of a baseline in a disaster monitoring project (the baseline length is 235 m), and analyzes the precision that the monitoring software can achieve under several different solution periods.

Fig. 3. Result of long-periodic of 2 h, 4 h, 8 h, 12 h and 24 h

It can be seen from the results in the Fig. 3 that with the increase of the long period solution time, the precision of displacement monitoring is greatly improved. When the period is 2 h or 4 h, the monitoring precision can reach the level of 2 mm in horizontal direction and 5 mm in elevation direction. When the period is more than 8 h, the precision is below mm in horizontal direction. In actual application, the reasonable long period solution time can be set according to the observation environment, precision requirements, deformation detection time and other specific factors. 4.1.2 Displacement Detection Effect of Deformation Algorithm In order to verify the detection effect of deformation algorithm and software on the displacement change of monitoring points, a group of short baseline experiments are designed. Two antennas with a distance of about 10 m are arranged on the company’s roof, one of which is installed on a three-dimensional movable adjustable platform. The position of the antenna can be moved to simulate the deformation scene.

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After collecting a section of static data, turn the knob of the movable platform at 05:42:00 (GPST), let the antenna to move up 5 cm (the antenna adjustment process lasts for about 10 s). Because of the short baseline and good observation environment in this experiment, RTK can also obtain high-precision positioning results and accurately detect the movement of the antenna. Therefore, this paper uses the results of the RTK to indicate the movement time of the antenna. The RTK effect is shown by the gray curve in Fig. 4.

Fig. 4. Experiment scene(left) and Comparison of different process strategies(right)

The long period solution time of the monitoring software is 2 h and the short period solution time is 15 min. The monitoring effects of the following three treatment strategies were compared and analyzed. (1) Long period strategy only. The mode of using long period strategy only is similar to the traditional post-processing mode. It can be seen from the green curve in Fig. 4 that although the deformation curve is gradually approaching the actual displacement change, it is not until 07:30 (GPST) that the displacement change is fully displayed. (2) Short period checking long period strategy. As can be seen from the blue curve in Fig. 4, the deformation was detected in the short period at 05:56:53 (GPST) and the long period was initialized. (3) Enable the inter epoch difference strategy (ddd strategy). As can be seen from the red curve in Fig. 4, 8 s after the deformation simulation event, the inter epoch difference algorithm detected a sudden displacement change in the U direction at 05:42:08 (GPST), which triggered the initialization of the long period solution. Compared with the previous two strategies, the inter epoch difference strategy has a faster response to deformation. In addition, compared with the results of RTK, it not

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only ensures the high-precision monitoring, but also achieves the rapid response effect similar to that of RTK. 4.2

Application of Deformation Algorithm in Actual Projects

The deformation algorithm designed in this paper has been successfully applied in many actual projects and achieved good results. For example, a copper mine deformation monitoring project (two pictures left in Fig. 5) and a disaster monitoring project in Guizhou (two pictures right in Fig. 5).

Fig. 5. Actual monitoring effect of deformation monitoring algorithm

5 Conclusions This paper discusses the theoretical model of differential GNSS technology for realtime deformation monitoring, and researches the algorithm and implementation scheme for single frequency low-cost GNSS deformation monitoring, as well as the development of real-time deformation monitoring software. The experimental results and the application in many actual projects both show that the real-time monitoring software developed in this paper can achieve the precision of millimeter/sub-millimeter level, and can response to the actual displacement change quickly. The software runs stably for a long time in the project, which proves the reliability of the algorithm and has great practical value.

References 1. Li, Z., Liu, Z., Wang, Z.: Study on dam deformation observation using GPS positioning technology. J. Wuhan Univ. Hydraul. Electr. Eng. 6, 26–29 (1996) 2. Huang, S., Liu, X., Yang, Y.: Experiment and result for measuring dynamic characteristics of large bridge using GPS. Geomatics Inform. Sci. Wuhan Univ. 29(3), 198–200 (2004) 3. Wu, H., Huang, C., Zhang, J., et al.: Deformation monitoring system for high slope in open pit mine with the integration of GNSS and GIS. Geomatics Inform. Sci. Wuhan Univ. 40(5), 706–710 (2015) 4. Ye, S., Zhao, L., Chen, D., et al.: Real-time deformation monitoring data processing based on BDS triple-frequency observations. Geomatics Inform. Sci. Wuhan Univ. 41(6), 722–728 (2016) 5. Liu, C., Wang, J., Hu, H., et al.: Research on real-time correcting model of multipath in GPS dynamic deformation monitoring. Geomatics Inform. Sci. Wuhan Univ. 35(4), 481–485, 490 (2010)

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6. Han, H., Wang, J., Meng, X.: Reconstruction of bridge dynamics using integrated GPS and accelerometer. J. China Univ. Min. Technol. 44(3), 549–556 (2015) 7. Salzmann, M.: Least Squares Filtering and Testing for Geodetic Navigation Applications (1993) 8. Liu, Z., He, X., Zhang, S., Wang, J.: Single frequency GPS dynamic three difference method for structural deformation monitoring. Beijing Surv. Map. 39(7), 1074–1078 (2011)

Probing the Oceanic Precipitable Water Vapor Evolution Characteristics During the 2020 Tropical Cyclone Maysak Using the GNSS Radio Occultation and Satellite Microwave Radiometry Data Shiwei Yu1,2 and Zhizhao Liu1,2(&) 1

Department of Land Surveying and Geo-Informatics (LSGI), The Hong Kong Polytechnic University (PolyU), Hong Kong, P.R. China [email protected] 2 Research Institute for Sustainable Urban Development, The Hong Kong Polytechnic University (PolyU), Hong Kong, P.R. China

Abstract. A tropical cyclone (TC) is a rapidly rotating storm system with complex weather phenomena, such as powerful winds, heavy rainstorms, and damaging thunderstorms. It brings enormous effects on human lives and properties over the coastal area. Moreover, the intensity of TCs is showing an increasing trend with global warming. Therefore, monitoring tropical cyclones, including the atmospheric evolution characteristics, is scientifically and practically meaningful. The Global Navigation Satellite System (GNSS) radio occultation (RO) is a powerful tool to study the atmosphere evolution during the TC period. Much more RO sounding data can be utilized than before with the completion of the new generation six-satellite Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC-2) in 2019. In this study, we analyzed the precipitable water vapor (PWV) in the upper atmosphere between 1.6 km and 40.0 km. We classified the region around the TC eye center into five bands according to the distance to the TC eye center: band 1 for the region with a radius of 0–200 km from TC eye center; band 2 for 200–400 km; band 3 for 400–600 km; band 4 for 600– 800 km; and band 5 for 800–1000 km. The PWV within the band 1 showed an evident increase from August 28 with a value of *9.5 kg/m2 to September 1, 2020 with a value of *43.6 kg/m2, when the TC became increasingly intensified. While the PWV in bands 2 to 5 showed a decreasing trend during this period. The mean PWV gradient was −2.47 kg
m2
ð100 kmÞ1 from band 1 to band 2, −.27 kg
m2
ð100 kmÞ1 from band 2 to band 3, −1.17 kg
m2
ð100 kmÞ1 from band 3 to band 4, and −1.16 kg
m2
ð100 kmÞ1 from band 4 to band 5. We also analyzed PWV data from altimetry satellites and found that symmetric spatial gradient of PWV can be apparently observed. These findings can help us further understand the atmospheric evolution characteristics over ocean during the TC period, thus improve the forecast reliability and accuracy. Keywords: Precipitable water vapor satellite
Tropical cyclone


GNSS radio occultation
Altimetry

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 224–234, 2021. https://doi.org/10.1007/978-981-16-3138-2_22

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1 Introduction A tropical cyclone (TC) is a complex storm system characterized by a low-pressure center, powerful winds, and a spiral arrangement of thunderstorms [1]. TCs are one of the weather disasters with a destructive nature during and after the landfall. TC landfall accompanying strong winds and intense rainfall poses severe risks to the lives and properties of coastal regions. The annual global damage from TCs is approximately US $ 26 billion [2], and the annual global fatalities from TCs is around 8,000 on average [3]. Moreover, researchers have found that the intensity of TCs is showing an increasing trend due to global warming [4]. Therefore, a good understanding of TC’s mechanism can help to improve the TC forecasting accuracy and reduce property and life losses. The meteorological parameters, such as temperature, atmosphere pressure, and relative humidity, play a fundamental role in the TC forecasting models [5]. The primary observation source of these parameters is remote sensing meteorological satellites, such as Fengyun meteorological satellites of the National Satellite Meteorological Center (NSMC) of China [6]. However, the main drawbacks of this technique are the low temporal resolution, e.g. *12 h, and the low spatial resolution e.g. 0.25º  0.25º [7]. In addition, remote sensing satellites seldom provide meteorological observations in a vertical profile. The global navigation satellite system (GNSS) radio occultation (RO) provides us with an opportunity to understand atmospheric dynamics from the vertical aspect. For instance, Healy et al. [8] utilized GNSS RO data to study zonal winds in the tropical stratosphere at different pressure levels. In addition, numerous studies showed that GNSS RO data can help to improve the accuracy of TC forecasts [9, 10]. With the completion of the second-generation Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC-2) mission in 2019, *5,000 sounding can be observed every day globally, more than *3 times compared with the first-generation COSMIC, i.e. *1,500 soundings [11]. Besides the GNSS RO technique, MWR instrument onboard altimetry satellites is another powerful tool to facilitate atmospheric dynamics research. Different from the MWR instrument onboard the remote sensing satellites, the MWR onboard altimetry satellites can measure the precipitable water vapor (PWV) in the atmosphere at the nadir points with high spatial and temporal resolutions, e.g. 20 km and 1 s intervals between sounding points in Sentinel-3 mission [12]. Taking advantage of these RO and altimetry satellite techniques, we studied the atmospheric dynamics during the 2020 tropical cyclone Maysak in the western North Pacific Ocean. The data and methodology are introduced in Sect. 2. In Sect. 3, the PWV variations observed by the GNSS RO soundings and MWR soundings from altimetry satellites is presented. The conclusions are summarized in Sect. 4.

2 Data and Methodology In this section, the TC information and PWV retrieval method from GNSS RO and altimetry satellites are introduced.

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The 2020 TC Maysak

Maysak formed as a tropical depression over the western North Pacific about 1,050 km east-northeast of Manila, Philippines, on the afternoon of August 28, 2020. It intensified into a typhoon on August 30 and moved northward. It further intensified into a super typhoon on the night of August 31 and passed through the Ryukyu Islands, Japan. Maysak reached its peak intensity on the morning of September 1. The sustained wind speed near its center was estimated to be *195 km/h. Maysak then moved northnortheastward and swept across the East China Sea. It made landfall over the south of the Korean Peninsula on the afternoon of September 2 [13]. The track of the Maysak is presented in Fig. 1, based on the data retrieved from the International Best Track Archive for Climate Stewardship (IBTrACS) of the National Oceanic and Atmospheric Administration (NOAA) [14].

Fig. 1. Track of the 2020 TC Maysak, for which the TC center positions were presented every 3 h, and the date marked beside the track denotes the TC position at 00 UTC of that given day. The color denotes different TC categories according to the 1-min maximum sustained surface wind speed defined by the National hurricane center of the NOAA (https://www.nhc.noaa.gov/pdf/ sshws.pdf)

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PWV from GNSS RO Sounding

To investigate the PWV variation during the TC period, we calculated the PWV based on the atmospheric parameters from each GNSS RO profile. The PWV can be expressed as [15]: PWV ¼

1 Z Pt qdP g Pb

g ¼ 9:784
ð1  0:00266
cos2u  0:00028
H Þ q¼

0:62198
e P  e
ð1  0:62198Þ

ð1Þ ð2Þ ð3Þ

where g is the gravitational acceleration in m/s2. It can be expressed as a function of latitude u in the unit of radians and height H in the unit of km. Pb and Pt in the unit of Pa are the pressure at the bottom and top of the atmosphere profile. q is the specific humidity. The specific humidity q at a pressure level of P in the unit of Pa can be calculated from the water vapor pressure e in the unit of Pa at the corresponding pressure level. In this study, data from multiple GNSS RO missions are used, including (1) COSMIC-2 jointly developed by the Nation Space Organization (NSPO) of Taiwan, China, and the NOAA and the United States Air Force (USAF); (2) meteorological operational satellites such as Metop-A, Metop-B, and Metop-C developed by the European Space Agency; (3) Korea Multi-Purpose Satellite-5 (KOMPASAT5) designed by the Korea Aerospace Research Institute; (4) PAZ of the Spanish National Earth Observation Programme; (5) TerraSAR-X (TSX) and TanDEM-X (TDX) managed by the German Aerospace Center. 2.3

PWV from Altimetry Satellites

Altimetry satellites were often equipped with MWR instrument to remove the atmospheric delay caused by the water vapor in the range measurement [16]. From the other aspect, the MWR measurements can be utilized to study the water vapor variation. In this study, we analyzed the PWV variation from four altimetry satellites, including SARAL, Jason-3, Sentinel 3A, and Sentinel 3B.

3 Results In this section, we investigated the PWV retrieved from both the GNSS RO missions and altimetry satellite missions during the TC Maysak. 3.1

PWV Variation Based on GNSS RO Soundings

PWV of the GNSS RO sounding profiles can be calculated by integrating specific humidity from the bottom to top sounding points. Due to the low signal power and the

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Fig. 2. The distribution of GNSS RO sounding points within a radius of 1,000 km from the TC center during the period from August 28 to September 2, 2020. The center of each plot represents the TC center

terrain features [11], the penetration depths are different in different GNSS RO sounding profiles. Zhu et al. [17] found that the PWV in the lower troposphere (0– 1.6 km) has almost no change during the whole life cycle of TC but the PWV above the altitude of 1.6 km showed a significant increase with the effect of TCs. To get a consistent comparison of PWV from all GNSS RO profiles, we calculated the PWV between altitudes of 1.6 km and 40.0 km. For every day from August 28 to September 2, PWV at each GNSS RO sounding point within a radius of 1,000 km from the TC center is shown in Fig. 2. Examining the colors of the dots, it can be seen that PWV closer to the TC center generally had a higher level than that far from the TC center. The detailed statistics of PWV on each day are listed in Table 1. The daily mean PWV was stable around *30.0 kg/m2 during the TC developing period of August 28 to September 1. On September 2, the mean PWV was much lower 15.2 kg/m2, because no RO observations within a radius of 200 km from TC center.

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Table 1. PWV daily statistics from August 28 to September 2, 2020. The 1-min maximum sustained surface wind speed at 00:00 UT on each day is shown in the last column. The numbers in parentheses denote the number of soundings from GNSS RO missions COSMIC-2, Metop-A, Metop-B, Metop-C, KOMPSAT5, PAZ, TSX, TDX Date

Max. PWV Min. PWV Mean PWV # of sounding points Max. sustained wind speed (kg/m2) (kg/m2) (km/h) at 00:00 UT (kg/m2)

August 28 40.0 August 29 39.9 August 30 43.2 August 31 44.7 September 1 39.5 September 2 39.1

22.0 13.7 22.2 23.0 19.5 7.5

31.7 31.0 29.9 30.5 31.0 15.2

29 19 25 25 15 20

(24,1,2,1,0,0,1,0) (15,0,2,1,0,0,1,0) (20,1,3,0,0,1,0,0) (22,2,0,1,0,0,0,0) (13,0,0,0,2,0,0,0) (18,0,0,0,2,0,0,0)

46.3 100.0 129.6 172.2 213.0 194.5

We defined five bands with different radii from the TC center: 1) band 1 with the distance of 0–200 km; 2) band 2 with the distance of 200–400 km; 3) band 3 with the distance of 400–600 km; 4) band 4 with the distance of 600–800 km; 5) band 5 with the distance of 800–1,000 km, as shown in Fig. 3(a). Then, the average PWV of GNSS RO sounding events located in each band during the whole TC period was calculated, and the results were shown in Fig. 3(b). The results demonstrated that the PWV with a smaller radius distance had a larger value. The average PWV for band 1 increased from *39.5 kg/m2 to *43.6 kg/m2 during the period from August 28 to August 31. Then, it suddenly decreased to *37.4 kg/m2 on September 1. Compared with the variation of average PWV in band 1, the PWV in the other four bands experienced a generally decreasing trend during the TC period. The daily mean decrease rate is 0.82 (kg/m2)⋅day−1, 1.05 (kg/m2) ⋅ day−1, 1.28 (kg/m2) ⋅ day−1, and 1.63 (kg/m2) ⋅ day−1 for band 2, band 3, band 4, and band 5, respectively. The results imply that the PWV with a larger distance from TC center had a larger PWV decrease rate. The daily mean PWV in each band was displayed in Fig. 3(c). A clear decreasing trend was observed. The PWV monotonously decreased from the band 1 (inner band closest to TC center) to band 5 (outside band furthest from the TC center). The mean PWV in the band 1 is about 41.0 kg/m2 and it decreased to about 26.5 kg/m2 in band 5. The mean slopes between each neighbor band was −2.47 kg
m2
ð100 kmÞ1 between band 1 and band 2, −2.27 kg
m2
ð100 kmÞ1 between band 2 and band 3, −1.17 kg
m2
ð100 kmÞ1 between band 3 and band 4, and −1.16 kg
m2
ð100 kmÞ1 between band 4 and band 5. This result implied that the PWV in bands closer to the TC center had a larger spatial gradient than PWV in bands far away from TC center. By the way, on September 2, the PWV showed a low level in each band when the TC intensity started to decrease.

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Fig. 3. Mean PWV in different bands during the TC period from August 28 to September 2, 2020. (a) the definition of five bands: band 1 is the region within a radius of 0–200 km from TC center; band 2 for 200–400 km; band 3 for 400–600 km; band 4 for 600–800 km; and band 5 for 800–1000 km; (b) PWV temporal variations in each band against the maximum sustained wind speed (black line with dots); (c) PWV variation in each band and the spatial change rate between two adjacent bands with respect to the PWV distance from TC center, during the TC period from August 28 to September 2, 2020. The PWV over the altitudes from 1.6 km to 40.0 km was used for the calculation

3.2

PWV Variation Based on Altimetry Satellite Soundings

During the TC period, four PWV sounding tracks of the altimetry satellites passed through the TC area, as shown in Fig. 4. The first PWV pass was from the altimetry satellite mission SARAL, as shown in Fig. 4(a). At *21:00 UT on August 30, 2020, the SARAL PWV observations had the closest distance to TC, *245 km. The second PWV pass was from the altimetry satellite mission Sentinel 3A, as shown in Fig. 4(b). The PWV was measured at *01:50 UT on August 31. The shortest distance between the sounding track and the TC center was *256 km. The altimetry satellite mission Jason-3 provided the third PWV pass at *07:30 UT on August 31, as shown in Fig. 4

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(c). The closest distance between the PWV pass and the TC center was *164 km. The last PWV pass with the closest distance of *161 km from the TC center was sounded by the altimetry satellite mission Sentinel 3B at *02:00 UT on September 2, as shown in Fig. 4(d).

Fig. 4. The PWV sounding points from different altimetry satellite missions: (a) SARAL; (b) Sentinel 3A; (c) Jason-3; (d) Sentinel 3B. The cross marker was the location of the TC eye center. The red arrow denoted the flying direction of the altimetry satellite. The background color denoted the brightness temperature, which was retrieved from the Japanese Himawari-8 satellite products

The PWV variation along the sounding tracks is shown in Fig. 5. The PWV showed a significant increase when the sounding points got closer to the TC center. The PWV started to increase from a distance of *600 km from the TC center. At such a distance, the PWV over the four passes was around 50 kg/m2 on average. The rich PWV could be observed near the TC center, i.e. *78.0 kg/m2 in the first pass, *73.4 kg/m2 in the second pass, *90.1 kg/m2 in the third pass, and *75.4 kg/m2 in the fourth pass. Furthermore, we conducted a linear regression for the PWV sounding points within a distance of 600 km from the TC center, including altimetry satellite soundings approaching to and departing from TC center. The results showed

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that the slopes of the linear regression function, f ð xÞ ¼ a
x þ b, during the approaching and departing phases were generally symmetric around the TC center in all the four passes. In detail, the slopes of the first pass during the approach and departing phases were 0.0253 kg
m2
km1 and −0.0312 kg
m2
km1 , respectively; 0.0524 kg
m2
km1 and −0.0685 kg
m2
km1 in the second pass, 0.0574 kg
m2
km1 and −0.0410 kg
m2
km1 in the third pass, and 0.0260 kg
m2
km1 and −0.0203 kg
m2
km1 in the fourth pass. It is worth noting the large slopes could be observed on August 31.

Fig. 5. Variation of PWV, denoted in blue dots, were retrieved from different altimetry satellite passes against the distance from the TC eye center: (a) PWV retrieved from SARAL during 20:56–1:03 UT on August 30, 2020; (b) PWV retrieved from Sentinel 3A during 01:47–01:54 UT on August 31, 2020; (c) PWV retrieved from Jason-3 during 07:25– 07:32 UT on August 31, 2020; (d) PWV retrieved from Sentinel 3B during 01:56–2:03 UT on September 02, 2020. The location of PWV observations approaching toward or departing from the TC center was shown with a negative or positive distance, respectively. The PWV data used for linear regression, i.e.

, was depicted as red dots

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4 Conclusions The PWV variation during the TC period was investigated based on both GNSS RO and satellite microwave radiometer data. The main findings were: 1. The PWV experienced a significant increase when the location is closer to the TC center during the TC period, while the PWV showed a decreasing trend when the location is further from the TC center. 2. In the radial direction, the PWV gradient between each 200-km-interval band was −2.47 kg
m2
ð100 kmÞ1 between band 1 (within *200 km from TC center) and band 2 (200–400 km from TC center), −2.27 kg
m2
ð100 kmÞ1 between band 2 and band 3 (400–600 km from TC center), −1.17 kg
m2
ð100 kmÞ1 between band 3 and band 4 (600–800 km from TC center), and −1.16 kg
m2
ð100 kmÞ1 between band 4 and band 5 (800–1,000 km from TC center). 3. The PWV clearly showed a spatially symmetric distribution around the TC center, as revealed from the PWV data of altimetry satellites. The PWV spatial increase gradient during the satellite approaching to TC center and spatial decrease gradient during satellite departing from TC center were 2.53 kg
m2
ð100 kmÞ1 and −3.12 kg
m2
ð100 kmÞ1 , respectively, as retrieved from SARAL PWV on August 30, 5.24 kg
m2
ð100 kmÞ1 and −6.85 kg
m2
ð100 kmÞ1 , respectively, as retrieved from Sentinel 3A PWV on August 31, 5.74 kg
m2
ð100 kmÞ1 and −4.10 kg
m2
ð100 kmÞ1 , respectively, as retrieved from Jason-3 PWV on August 31, and 2.60 kg
m2
ð100 kmÞ1 and −2.03 kg
m2
ð100 kmÞ1 , respectively, as retrieved from Sentinel 3B PWV on September 2. Acknowledgments. The grant support from the Key Program of the National Natural Science Foundation of China (project No.: 41730109) is acknowledged. The grant supports from the Hong Kong Research Grants Council (RGC) project (B-Q61L PolyU 152222/17E) are highly appreciated. The support from the project (No. 1-BBWJ) in the Emerging Frontier Area (EFA) Scheme of Research Institute for Sustainable Urban Development (RISUD) of The Hong Kong Polytechnic University is also acknowledged.

References 1. Marks, F.D.: Tropical cyclones and hurricanes|hurricanes: observation. In: North, G.R., Pyle, J., Zhang, F. (eds.) Encyclopedia of Atmospheric Sciences, pp 35–56. 2nd edn. Academic Press, Oxford (2015) 2. Mendelsohn, R., Emanuel, K., Chonabayashi, S., Bakkensen, L.: The impact of climate change on global tropical cyclone damage. Nat. Clim. Change 2, 205–209 (2012) 3. Bakkensen, L.A., Mendelsohn, R.O.: Global tropical cyclone damages and fatalities under climate change: an updated assessment. In: Collins, J.M., Walsh, K. (eds.) Hurric, pp. 179– 197. Springer International Publishing, Cham, Risk (2019) 4. Yamaguchi, M., Chan, J.C.L., Moon, I.-J., Yoshida, K., Mizuta, R.: Global warming changes tropical cyclone translation speed. Nat. Commun. 11, 47 (2020)

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5. Keclik, A.M., Evans, C., Roebber, P.J., Romine, G.S.: The influence of assimilated upstream, preconvective dropsonde observations on ensemble forecasts of convection initiation during the Mesoscale Predictability Experiment. Mon. Weather Rev. 145, 4747– 4770 (2017) 6. Lu, Q., Hu, J., Wu, C., et al.: Monitoring the performance of the Fengyun satellite instruments using radiative transfer models and NWP fields. J. Quant. Spectrosc. Radiat. Transf. 255, 107239 (2020) 7. Draper, D.W., Newell, D.A., Wentz, F.J., Krimchansky, S., Skofronick-Jackson, G.M.: The Global Precipitation Measurement (GPM) Microwave Imager (GMI): Instrument overview and early on-orbit performance. IEEE. J. Sel. Top. Appl. Earth Obs. Remote Sens. 8, 3452– 3462 (2015) 8. Healy, S.B., Polichtchouk, I., Horányi, A.: Monthly and zonally averaged zonal wind information in the equatorial stratosphere provided by GNSS radio occultation. Q. J. R. Meteorol. Soc. 146, 3612–3621 (2020) 9. Bai, W., Deng, N., Sun, Y., et al.: Applications of GNSS-RO to numerical weather prediction and tropical cyclone forecast. Atmosphere (2020). https://doi.org/10.3390/ atmos11111204 10. Mueller, M.J., Kren, A.C., Cucurull, L., Casey, S.P., Hoffman, R.N., Atlas, R., Peevey, T.R.: Impact of refractivity profiles from a proposed GNSS-RO constellation on tropical cyclone forecasts in a global modeling system. Mon. Weather Rev. 148, 3037–3057 (2020) 11. Schreiner, W.S., Weiss, J.P., Anthes, R.A., et al.: COSMIC-2 Radio occultation constellation: first results. Geophys. Res. Lett. 47, e2019GL086841 (2020) 12. Fernandes, M.J., Lázaro, C., Vieira, T.: On the role of the troposphere in satellite altimetry. Remote Sens. Environ. 252, 112149 (2021) 13. Hong Kong Observatory: Tropical Cyclones in 2020. Hong Kong Observatory, Hong Kong (2020) 14. Knapp, K.R., Kruk, M.C., Levinson, D.H., Diamond, H.J., Neumann, C.J.: The International Best Track Archive for Climate Stewardship (IBTrACS). Bull. Am. Meteorol. Soc. 91, 363– 376 (2010) 15. Böhm, J., Schuh, H.: Atmospheric Effects in Space Geodesy. Springer, New York (2013) 16. Donlon, C., Berruti, B., Buongiorno, A., et al.: The Global Monitoring for Environment and Security (GMES) Sentinel-3 mission. Sentin Missions - New Oppor Sci 120, 37–57 (2012) 17. Zhu, M., Liu, Z., Hu, W.: Observing water vapor variability during three super typhoon events in hongkong based on GPS water vapor tomographic modeling technique. J. Geophys. Res. Atmos. 125, e2019JD032318 (2020)

Infrared Night Vision UAV Intelligent Patrol System with BDS Flight Control Xianyu Wu1(&), Zhaobao Fang1, and Jinbo Rao2 1

Joint Laboratory for Geographic Information Technology of Jiangxi Normal University and HI-TARGET, Nanchang, China 2 Disaster Reduction and Preparedness Center of Jiangxi Province, Nanchang, China

Abstract. Due to overfishing, fishery resources in the Yangtze River have been in serious decline in recent years. At the mercy of the shortage of staff and backward equipment, there are still many shortcomings in the fight against illegal fishing. Therefore, the Joint Laboratory for Geographic Information Technology of Jiangxi Normal University and HI-TARGET has developed a set of infrared night vision UAV intelligent patrol system based on BDS flight control. Equipping with Beidou flight control system (BDS), infrared night vision instrument, searchlight and 5G wireless communication module, the system can not only solve the typical problems such as low patrol efficiency, poor patrol effect at night, inability to patrol remote areas and limited law enforcement, but also send back surveillance video in real time and quickly lock the evidence and criminal suspects, so that the lawbreakers has no place to hide. Keywords: UAV
BDS flight control fishing
Intelligent patrol system


Infrared night vision
Banning

1 Introduction The Yangtze River, the mother river of the Chinese nation, is an important barrier to maintain ecological security in China and promote the green development of the Yangtze Economic Belt. However, in recent decades, the overfishing of the Yangtze River has been a heavy burden, leading to the continuous decline of the biodiversity index and the serious decline of fishery resources. It is imperative to ban fishing and let the Yangtze River recuperate, which is the key to alleviate the decline of biodiversity and biological resources in the Yangtze River. In January 2020, the Ministry of Agriculture and Rural Affairs announced the implementation of the “10-year fishing ban plan on the Yangtze River” starting from 0 o ‘clock on January 1, 2020, banning the productive fishing of natural fishery resources in the natural waters of the main stream and important tributaries of the Yangtze River, except for the nature reserves for aquatic organisms and the protection areas for aquatic germplasm resources. General Secretary Xi Jinping has stressed that “at present and for a long time to come, we should give overwhelming priority to the restoration of the ecological environment of the Yangtze River, and make concerted efforts to protect it instead of pursuing further development” (Xiao and Liu 2017). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 235–242, 2021. https://doi.org/10.1007/978-981-16-3138-2_23

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However, there are still lawbreakers who use electric fishing tools to carry out illegal fishing at night in remote areas, hidden riverside beaches or shallow water inaccessible to law enforcement vessels, which seriously threaten the fishery resources of the Yangtze River and the prohibited fishing achievements. On the one hand, as these crimes are scattered sporadically in the Yangtze River valley, with limited law enforcement and inconvenient transportation, the government is often powerless. On the other hand, illegal fishing activities are often carried out at night and in remote areas, with strong concealment. In addition, due to backward law enforcement equipment, some law enforcement vessels cannot sail at night or in some specific area, it is often difficult to detect illegal fishing criminal activities in time. The UAV (unmanned aerial vehicle) has the characteristics of mobility, speed, low cost and convenient maintenance, which can effectively reduce the difficulty and improve the efficiency of banning fishing. But most drones have to patrol in well-lit conditions, which are less effective at night or in poor light conditions. In order to solve the above problems, the Joint Laboratory for Geographic Information Technology of Jiangxi Normal University and HI-TARGET developed a set of infrared night vision UAV intelligent patrol system based on Beidou flight control. Based on the Beidou flight control technology, the system can effectively solve the flight attitude control technology problems, making the night vision operation more efficient. At the same time, using infrared night vision instrument and searchlight, the system can well record illegal fishing at night or poor light conditions, and quickly lock the suspect through the face recognition system. In addition, based on 5G wireless communication module, the system can transmit real-time surveillance video and quickly lock evidence and targets, which is helpful for law enforcement personnel to respond quickly and enforce the law in time, and thus provide real-time, intuitive and accurate data support for the application of government patrol law enforcement decision-making at night in fishery law enforcement, forest protection, traffic monitoring and other industries.

2 System Components

Fig. 1. Infrared night vision UAV intelligent patrol system with BDS flight control

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The system (Fig. 1) consists of Beidou flight control system, night vision instrument, night vision instrument stabilization platform, searchlight, searchlight rotation drive steering gear, 5G wireless communication module, microprocessor and humancomputer interaction module, etc. 2.1

Beidou Flight Control System

The flight control system utilizes the HI-TARGET BX220 low-power high-precision navigation board card, with small size (71  46  8.5 mm), light weight (20 g) and low power consumption (less than 1/4 power consumption of the mainstream highprecision board cards). Meanwhile, the board supports GPS/Beidou dual star system, 72 satellite E solution channels, GPS L1, Beidou B1, and wide area differential enhancement system (SBAS). Besides, BX220 has a built-in-ertial navigation module, integrates MEMS motion sensor, and supports INS integrated navigation, enabling accurate positioning even if the satellite signal is temporarily lost. Thus, it can effectively solve multifarious problems of flight attitude control technology, making the patrol operation more efficient. 2.2

Night Vision System

On the one hand, the night vision system is equipped with an excellent night vision camera with an optical zoom of 10 times, which can capture clear video and visible light photos in a completely unlit environment and send them back to the ground data processing center in real time. On the other hand, the system is equipped with an infrared thermal imaging camera with a resolution of 640 * 512, which can detect the ground electric discharge rapidly. The system can automatically control the opening and closing of the night vision instrument. When the light of the UAV patrol environment is sufficient, it only turns on the visible light camera to realize the patrol of the surrounding environment. Whereas, when the ambient light is insufficient (patrol at night, for instance), it can automatically turn on the infrared night vision camera to realize the patrol at night aided by the searchlight. 2.3

Searchlight System

The system uses a high-brightness LED searchlight with low power consumption, good light gathering performance and a detection range of 60–100 m. It will automatically choose whether to turn on the searchlight according to the ambient light conditions. The searchlight can be turned on and off easily through the searchlight switch. 2.4

Unmanned Flight Platform

An unmanned flight platform with stable performance is the basic guarantee of the system (Li and Li 2014; Sun et al. 2003). The flight platform selected by this system has the advantages of good wind resistance, excellent waterproof performance, strong load expansion capacity, large refit space, collapsible arm, telescopic leg, convenient

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transportation, long image transmission distance up to 7 km. Therefore, it is especially suitable to fly over the river, lake at night, on light rainy days and other harsh and complex environments. 2.5

5G Wireless Communication Module

The 5G wireless communication module comprises a signal transmitter and a signal receiver. On the one hand, the system can receive 5G control signals through a signal receiver, and then use a microprocessor to operate the night vision device controller. On the other hand, the system can also transmit the patrol information to the ground data processing center through the signal transmitter, and display the obtained information in real time on the remote control of the UAV or the screen of the ground data processing center, achieving the most intuitive observation of UAV patrol. 2.6

Software System

In order to realize the basic functions of the UAV intelligent patrolling system, a professional software integrating route planning, flight control and data processing has been designed and developed. The actual flight verifications have proved that the software system has the advantages of simple operation and high reliability. 2.6.1 Flight Control Software Based on HI-TARGET iFly C2–a flight control module integrating high-precision IMU and remote data link, a special flight control software (Fig. 2) has been developed. iFly C2 uses military grade manufacturing process and follows GJB150A & GJB151B reliability environment test standards. Owing to the advanced nonlinear high precision GPS/SINS/AHRS algorithm and total energy control algorithm, iFly C2 module can realize aircraft precision of attitude control and high precision positioning function.

Fig. 2. Screenshot of flight control software

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Experiments proved that the flight control software based on the iFly C2 flight control module is robust, which can not only adapt to the influence of high wind speed and wind direction change on the open water or in the valley, but also can realize the forward photography flight, strip flight and 360 panoramic flight, making patrol and law enforcement operations more efficient. 2.6.2 Sensor Data Processing Software The system is equipped with a variety of sensors such as visible light camera, infrared camera, POS system, etc. In view of the characteristics of the unmanned aircraft, such as small image amplitude, unstable attitude, large degree of overlap, and nonprofessional cameras, high degree of overlap, data processing system for each sensor are specially developed. Moreover, the system has several aerial photogrammetry processing technologies, such as intelligent adjustment technology, stereo matching technology for images with large height difference and deviation angle, point-cloud acquisition technology at pixel level, multi-form DSM filtering technology, etc. With the advantages of advanced algorithm, perfect function, flexible configuration, high efficiency, and accurate results, it can realize high-precision geometric processing of various sensor data. 2.6.3 Coordinate Calculation Software of Illegal Points Although ordinary infrared cameras can find illegal points, their pictures cannot be associated with coordinate information. Through secondary development, the system can automatically assign high-precision Beidou positioning information to the photos and videos. After the orthophoto mosaic, the coordinates of the illegal points can be quickly and accurately calculated to help the law enforcement to take targeted measures. 2.6.4 UAV Night-Vision Intelligence Expert System On this basis, according to the characteristics of illegal fishing, the UAV night-vision intelligence expert system was developed. With the help of the expert system, artificial intelligence, pattern recognition, and a variety of visualization technology, illegal fishing can be quickly and accurately located, and thus the criminal suspects can be locked efficiently. Hence, this system makes important influence on improving the night patrol efficiency of the government and fighting against illegal fishing.

3 Key Technologies 3.1

Flight Control and Navigation Technology Based on Beidou

The flight control and navigation system, the key to the UAV flight system, realizes the flight control, management and navigation of the UAV’s flight attitude and thus directly affects the patrol effect of the UAV (Li and Li 2014). In the process of patrolling, UAVs are often affected by weather conditions such as wind and rain, as well as obstacles like high buildings, trees and electric wires. In view of these situations, a good flight control and navigation system must be able to control

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the flight attitude of UAV remotely in real time. In this system, a controller based on Beidou navigation and positioning is introduced to control the deviation of the UAV. Experiments and practical applications have proved that this controller can well realize the control of UAV flight attitude. 3.2

Multi-sensor High-Precision Time Synchronization Technology

The UAV implements its patrol and law enforcement function by equipping a large number of sensors. Therefore, the data obtained by these independent sensors must be effectively connected in series. Consequently, the key to realizing this function is to establish a unified time coordinate to achieve high precision synchronization of sensor time. This UAV system is equipped with a multi-mode satellite navigation receiver, which can output positioning data and 1PPS pulse. Besides, the sensor data obtained can be correlated and synchronized by time synchronization controller. Specifically, the time of POS, CCD camera, infrared night vision and other sensors are synchronized and unified into the Beidou positioning module, which is synchronized with the time of satellite navigation. Thus, the time of multiple data sources is finally unified. 3.3

Visual Detection Technology

Visual detection technology is the most basic function of the UAV. This UAV system is equipped with high-definition camera equipment, which can capture and record the details of the inspection line, and timely return the collected information to the ground data processing center for storage. Hence, the staff of the ground data processing center can process and analyze the collected information, determine the location of the illegal event, analyze the causes of the illegal event, and quickly lock the suspect through the face recognition system. 3.4

Infrared Detection Technique

The infrared thermal camera is the key part of the UAV night vision detection module. When patrolling at night, the infrared thermal camera carried by the night vision UAV can not only collect the surface temperature information to form an infrared spectral image, but also send the image back to the ground processing data center. Then, the data center can quickly and accurately identify illegal fishing events, and further judge the incident location and lawbreakers. In the current research, we should pay special attention to the infrared image processing technology under complex background to improve the night vision inspection accuracy. 3.5

Wireless Communication Technology

On the one hand, the system can remotely control the UAV through wireless communication remote control technology, including the aircraft attitude and the switches of various airborne sensors. On the other hand, using wireless communication telemetry technology, the system can monitor and track the operation of UAV in real

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time, and realize the information transmission between the UAV and the ground data processing center. The wireless communication part of the system is composed of a ground station module, a relay module and an airborne module. These three modules cooperate with each other to realize communication and various functions. 3.6

Surface Data Processing Technology

Undoubtedly, the ground data processing technology plays an important role in the UAV. Unlike ordinary aerial photography, the UAV mostly uses small imaging and non-imaging sensors, which has many problems, such as high spatial resolution, large number of images, small image amplitude, large inclination and irregular inclination direction. In view of its special flight characteristics and image processing requirements, the UAV data post-processing method must be obviously different from the traditional photogrammetry method (Li and Li 2014; Wang et al. 2017). Therefore, the ground data processing center has adopted the self-developed remote sensing data processing system, which can carry out high-precision geometric processing on the images, videos, coordinates and attitude data acquired by various sensors such as visible light camera, infrared imager and POS system, and quickly calculate the precise position coordinates of the illegal location. On this basis, according to the characteristics of illegal fishing, the UAV nightvision intelligence expert system was developed. Through the expert system, artificial intelligence, pattern recognition and a variety of visualization technologies, the illegal fishing electrofishing incidents can be quickly identified and accurately located.

4 System Advantages 4.1

Excellent Comprehensive Performance

The system has a number of advanced indicators, such as Beidou navigation precise positioning, low power consumption and high precision navigation board card, 5G wireless communication, high-definition image transmission, 10x zoom night vision, integrated control, infrared night vision, face recognition, folding, dust and rain prevention, etc. Therefore, this system is generally at the advanced level in China. 4.2

Strong Night Vision Function

With the aid of infrared night vision intelligent equipment, the system can still effectively work under the low light condition at night. Experiments proved that, the face of the violator can be clearly seen and the real-time video forensics can be obtained from a distance of 35 m in the dark night patrol, and thus the suspect can be identified and arrested through the image recognition system.

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Quick and Accurate Positioning

Based on the precise positioning of Beidou navigation, it can calculate the accurate coordinates of the trajectory of the illegal electric fishermen at night, so as to guide the law enforcement departments to quickly strike and arrest the illegal personnel.

5 Conclusion At present, more and more advanced technology and equipment have been widely used in the work of banning fishing. UAV is a very important one, which has played a significant role in combating illegal fishing (Wang 2020). In order to provide strong scientific and technological support for the protection of the Yangtze River, the technical level of UAV should be further improved in the following aspects. (1) Flight control and navigation technology With the further application of fishing ban, the conventional linear control and single navigation method have been difficult to meet the requirements of complex flight performance in practical missions. Therefore, the nonlinear model of efficient computation and the multi-integrated navigation method of Beidou /GPS/ inertial navigation will be the important research directions of flight control and navigation technology in the future (Li and Li 2014). (2) Sensor technology Sensor is the basic equipment of the UAV patrolling system. For a long time, the design and development of various visible light, infrared, laser and radar sensors with small volume, light weight, low cost and excellent performance will be an important research target of the UAV patrolling system. (3) Data processing technology With the continuous improvement of UAV flight speed, sensor time/space/spectral resolution, sensor types and bandwidth of communication frequency, the intelligent and efficient processing of massive image data will become a new bottleneck for the application of the UAV patrolling system. Therefore, the design and development of automatic, intelligent and real-time UAV data processing system is also the top priority in future UAV research (Li and Li 2014).

References Li, D., Li, M.: Research advance and application prospect of unmanned aerial vehicle remote sending system. Geomatics Inf. Sci. Wuhan Univ. 39(05), 505–513+540 (2014) Sun, J., Lin, Z., Cui, H.: UAV low altitude remote sensing monitoring system. Remote Sens. Inf. 1, 49–50+27 (2003) Wang, K., Fu, Y., Peng, X., Zuo, Z., Yi, L., Huang, S.: Overview of UAV low altitude remote sensing technology and application in typical industries. Bull. Surv. Mapp. S1, 79–83 (2017) Wang, J.: Application status and development of UAV in forest fire prevention. Shanxi Agric. Econ. 16, 146–147 (2020) Xiao, J., Liu, T.: The Yangtze river economic belt: strategic measure for realizing ecological preference and green development. West Forum 27(01), 39–42 (2017)

A Fusion Processing Method for Satellite Detection Data by Beidou Short Message System Bing Li1,2,3,4, Xiao Yu5, Xiaojuan Sun3,4,6(&), Yuxin Hu3,4,6, Haiyan Wu7, Tao Shi3,4, and Ling Chen7 1

3

School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100149, China 2 State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China [email protected] 4 Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China 5 Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China 6 School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100149, China 7 National Space Science Center, Chinese Academy of Science, Beijing 100190, China

Abstract. With the support of Beidou terminal of short message service system, the space science satellite can transmit all-day data that are astronomical alert data such as gravitational waves and Gamma ray bursts and satellite telemetry parameters. Then Beidou message service system has become an important means for finding the space astronomical events quickly, planning the follow-up observation and monitoring the real-time health of satellite and payloads. Then the application fields of the Beidou system has expanded into space science observation and satellite emergency operation. The short message data receiving and processing in ground system has many features of near real-time and continuity which is different from the processing methods of satellite data transmitted by data channel and telemetry channel. And the multi-source satellite data of the telemetry parameters and the astronomical alert information from these three channels need to be integrated. So, the real-time processing system of satellite data based on Beidou short message transmission has great challenges. In this paper, we explored an organization method of Beidou short messages, and proposed a multisource data fusion algorithm for the ground satellite data processing system. The data processing system with this method was designed and implemented. Applying to the ground system of the satellite named gravitational wave highenergy electromagnetic counterpart all-sky monitor, the performance analysis of improved system shows that the processing delay for important telemetry © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 243–252, 2021. https://doi.org/10.1007/978-981-16-3138-2_24

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Satellite data processing processing
Space science satellites
Gamma ray bursts


Telemetry data

1 Introduction The Beidou satellite system [1] is a satellite navigation, positioning and communication system independently constructed and operated by China, which can provide global users with high precision and high reliability services including positioning, navigation and timing in all weather and all day. Beidou satellite system also can transmit the short messages. The Beidou-3 global navigation satellite system was officially launched in July 2020. The Beidou Message Service (BDMS) can transmit information through communication links composed with GEO (Geostationary Orbit) satellite, MEO (Medium Earth Orbit) satellite and the Beidou operation and control centre of the ground by combining regional short messages with global short messages [2, 3]. The Beidou short message terminal can be equipped on the low orbit spacecraft to realize data communication using the short message transmission channel of Beidou satellite radio measurement service (hereinafter referred to as “Beidou channel”) [4, 5]. The goal of space exploration is to discover and explore violent changes of celestial bodies and high-energy physical events in the universe, monitor the activity of celestial bodies all day, and study and reveal the nature and physical mechanism of cosmic phenomena such as gravitational waves and black holes. Since the launch of the first satellite, the Dark Matter Particle Explorer Satellite in 2015, the space science satellite has made a number of major scientific discoveries such as the detection of gravitational wave events [6]. The ground data processing system has rapidly completed the processing of satellite detection data, strongly supporting scientific discoveries [7, 8]. At present, the application of Beidou short message service has been extended to space science and space exploration. Three BDMS terminals were deployed on the Gravitational Wave Bursts High Energy Electromagnetic Corpses All-Sky Monitor (GECAM) satellite, which was successfully launched in December 2020. They can be used to transmit gravitational wave gamma-ray burst information and telemetry data captured by the satellite through the Beidou channel. On January 20, 2021, the ground data processing system received the first Beidou short message about 60 s after the gamma-ray Burst event triggered through the Beidou channel, automatically completed all data processing and transmission, and supported the scientific application team to quickly publish the observation announcement through the International Gamma-ray Burst Coordination Network (GCN) [9]. The astronomical explosion alarm can be transmitted to the ground in quasi-real time by Beidou channel, which can be used to quickly guide the follow-up observation, therefore the observation efficiency can be improved greatly. The Beidou channel can only obtain detection data when the satellite altitude is lower than the Beidou satellite. The receiving and processing of short message in ground system has characteristics of all day, near real time and continuity. This is different from the original data

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processing methods of satellite data transmission and telemetry data transmission. Multi-channel telemetry data and astronomical alarm data need integration. Therefore, real-time processing system based on Beidou short messages faces enormous challenges. After the analysis of Beidou channel data characteristics and processing characteristics, this paper gives the improved real-time processing system structure of Beidou short message data, and the multi-source data organizing method and the data fusion processing algorithm are proposed for astronomical alarm data and telemetry data. Then the new method is applied to the actual system. Through the performance analysis of the actual system with satellite in-orbit data, the real-time processing performance of the data processing system for space science satellite shows great improvement with the application of the Beidou short message service system.

2 Application Research of Satellite Relay System Using the data communication ability of relay satellites, the problem of discontinuous communication between ground station and low orbit satellite can be solved. Compared with land-based and sea-based measurement and control system, space-based measurement and control system which is one of the mature applications of satellite relay system, has the characteristics of wide coverage measurement, high real-time performance and high reliability of data transmission. The Beidou system can support the measurement and control of low orbit satellites, and short message transmission can be used as a backup measurement means. The research of satellite measurement and control system based on Beidou user terminal can be divided into simulation research and experiment research. Some simulation analysis in the literature [10] gives the feasibility of using BDMS to realize space-based measurement and control. In 2010, the number nine remote sensing satellite carrying the Beidou terminal completed the inorbit test for the first time. The test results in the literature show that the system has realized the telemetry receiving and processing and the correctness of data processing is verified. However, as an experimental system, there are few studies on the common data process of telemetry data in ground system, and there is also no deep discussion about how to integrate Beidou data with traditional channel data. There are also some research achievements about data communication application area by satellite relay system. Then high-performance data communication services for earth observation remote sensing satellites can be provided. In 2015 the global maritime satellite communication service system named Inmarsat which was managed by international maritime satellite organization, and Singapore addvalue innovation companies united to start a more than one year test on the small low orbit satellite named Velox-2 using the data relay communication services of inter-satellite data relay service (IDRS), and explored a new satellite data communication mode based on satellite relay system [11]. Another research project named SeeMe in the United States [12] has been planned since 2013. Consisting of a constellation of several satellites, the project can transmit remote sensing image data through satellite relay communication services, and enable soldiers to obtain high-resolution satellite images in the battlefield equiped with smart mobile phones or other hand-held devices, in order to complete efficient military assembly. However, the follow-up plans for these studies were postponed, the related

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researches have explored the initial application models, and the further research of new characteristics on ground data processing system is not mentioned. Therefore the data transmission application of satellite relay system in the field of space-based measurement and control system has been studied for a long time, it is immature in the field of satellite observed data processing system. The ground data processing system based on the satellite relay communication channel needs further research to meet the requirements of multi-source space observation data processing.

3 Multi-source Data Fusion Processing Method for Space Science Satellites 3.1

Model Definition

Because the data characteristics of various channels are quite different, the data processing is faced with great challenges. The Beidou short message data is divided into small data blocks and has diverse data format definition, and has a high frequency and presents the feature of streaming [13, 14]. The data of multiple channels is partly repeated and disordered, and can be complemented with each other. We respectively make an abstraction of the preprocessing results, the fusion processing results and the output results during the process, and correspondingly define data unit, data cluster and data set. Definition 1: Data unit. It is defined as the basic data processing element after data preprocess, including two types of telemetry parameter data unit and astronomical alarm data unit. It is composed of data generating time, data unit type, data source, priority and data entity. A data unit d is represented by a quintuple . The element t represents the satellite data generating time in the format of yyyymmddthhmmss. The element c represents the type of data unit, with the natural number n (n > 0), n = 1 represents the astronomical alarm type, and n  2 represents specific telemetry parameter type. The element s represents data source, with values from 1 to 3, 1 for Beidou channel, 2 for data transmission channel, and 3 for telemetry transmission channel. The element p represents the priority of data output, with values from 1 to 4. The priority value of the Beidou alarm data unit with serial number one is 1, the priority value of the Beidou alarm data unit with serial number two is 2, the priority value of the Beidou telemetry data unit is 3, and the priority value of other data units is 4. The element r represents the data entity. The data entity of the astronomical alarm data unit is binary format data, and the data entity of the engineering telemetry data unit is the actual value of the parameters. Definition 2: Data cluster. It is defined as the data generated by the fusion processing of all data units under certain conditions, which is composed of start time, end time, data cluster identification, integrity tag and data entity. A data cluster c is represented by a quintuple . The element st represents the data start time of the data cluster and is the minimum satellite data generating time of all data units in the data cluster. The element se represents the data end time of the data cluster, and is the maximum satellite data generating time of all data units in the data cluster. The element f stands for the data cluster identification, the astronomical alarm data identification is concatenated by “1” and data generating time, the engineering telemetry parameter identification is

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concatenated by the parameter code and the start time of data generating period. The element i represents whether the data is integral. An astronomical alarm data cluster containing 31 data units is integral, and an engineering telemetry data cluster containing continuous one-hour data units at the data detecting frequency is integral. The 0 value represents the data cluster is not integral, and the 1 value represents the data cluster is integral. The element D represents the data entity, which is a collection of all the data units contained in the data cluster, and is represented by D ¼ fd1 ; d2 ; . . .; dn g. Definition 3: Dataset. It is defined as the output data with a standardized format for a integral data cluster, which is composed of data set identification and data entity. A data set g is represented by a tuple . The element f represents the data set identification, the engineering telemetry data set identification is t_yyyyMMddThh, and the astronomical alarm data set identification is a_yyyyMMddThhmmss. The element P represents the data entity, which has a standardized format conformed to products data. 3.2

Multi-source Data Organized Method

The constructing method of multi-source data structure is shown in Fig. 2. Different channels have various constructing methods. For Beidou channel, the short message data is parsed to obtain the data type, then for the astronomical alarm type, the complete data area is taken as the data entity of the data unit, for the engineering telemetry type, the telemetry parameter value is taken as the data entity of the data unit. For data transmission channel, source packet data is extracted according to virtual channel transmission frame number and source packet synchronization code. For telemetry transmission channel, source packet data is extracted according to virtual channel transmission frame number and the position pointer of the first packet dominant head. Then, data generating time and data entity forming data unit are obtained from the coheader and the data domain in source packet. Data units are sorted according to data time. Then engineering telemetry data units fuse a data cluster according to parameter

Fig. 2. Multi-source data organizing structure

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code, astronomical alarm data units fuse a data cluster according to alarm number, and the whole data cluster with integral data convert to a data set. 3.3

Multi-source Data Fusion Algorithm

Transmission channel are preprocessed firstly, and the multi-source data fusion algorithm generates the corresponding data clusters and data sets according to the attributes of individual data units. The correctness of products is closely related to the multi-source data fusion algorithm. The algorithm has the steps of processing priorities of data units, applying the data buffer of data cluster, maintaining the data entity, sorting and de-duplicating data in accordance with the time continuity. After the previous processing steps, the data integrity is judged, and the standard product corresponding to a data set is outputted. Input: data unit d to be processed. Output: data cluster c and data set g after data fusion. Initialization: The data unit d to be processed is initialized to structure. The default buffer number of data clusters is m, and the data cluster c to be outputted is initialized to structure, with a value of 0. The data set g to be outputted is initialized to , with a value of 0.

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4 Performance Analysis Our method is applied to the ground data processing system for space science satellites, and the performance of the multi-source data fusion system is evaluated from two aspects of processing timeliness and data integrity. The experimental environment is a server cluster of high-performance computers connected by 10 GB Ethernet, consisting of one scheduling node and three computing nodes. The experimental data are actual Beidou data, telemetry data and data transmission data from the ground data processing system of GECAM satellite. The data time is from 2021-1-13 to 2021-1-31. The improved system with our fusion processing methods is compared with the existed system. Four high performance computers have two 12-core 2.93 GHz Intel Xeon X5670 CPUs, 36 GB memory, two 60G SSD disks, connected with 40G infinite-band network. 4.1

Processing Time

The data processing time is measured by the time from the data generating time on satellite to the processing completion time in the ground system. The improved system has three channels of Beidou, telemetry transmission and data transmission as input data, while the existed system has only telemetry transmission data and transmission channel data. In the experiment, engineering telemetry parameter of “satellite service +5V voltage telemetry” and astronomical alarm data were selected for comparison, and the satellite data generating time and the processing completion time of the improved system and the existed system were recorded. And the delay from the satellite data generating time to the processing completion time was calculated.

Fig. 3. Real time capability of the improved system compared with the existed system

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The test results show that the processing time of the improved system is better than that of the existed system. Due to the lack of Beidou channel, the curve of the processing completion time in the existed system shows a shape of obvious ladder (Fig. 3(a) and (c)). In terms of processing delay, the average delay of the improved system is 216 s, while the average delay of the existed system is 9.5 h, indicating that the improved system has excellent real time processing capability. However, the maximum processing delay of the improved system is 512 s, the minimum processing delay is 23 s, and the processing delay fluctuates greatly. The reason is speculated that the longer delay of Beidou short message when the GECAM satellite orbit is outside the Asia-Pacific region. 4.2

Alarm Data Integrity

The astronomical alarm data is respectively transmitted from telemetry transmission, data transmission and Beidou channels, and the integrity of astronomical alarm data is measured by the continuity of corresponding source packets. The telemetry and data transmission channel will lose frames in the transmission process between the satellite and the ground, so the experiment compares the processed amount of astronomical alarm data between the situation of using the traditional two channels and the situation of using all three channels. The integrity is calculated with hourly data. The calculation P formula is P = ( N i¼0 ðMi =31Þ)/N * 100%. And P is integrity value, Mi is the number of data slices received by the ith astronomical alarm, and N is the number of astronomical alarm triggers within this hour.

Fig. 4. Alarm data integrity of the improved system compared with the existed system

The test results (Fig. 4) show that the data integrity of the improved system using all channels and the existed system using only traditional channels is all 100%, while the integrity based on the Beidou channel data is 80%. The improved system supplements the missing data of Beidou channel after multi-source data fusion. Although there is no phenomenon of lack of data during the test period, in the long run, the data of multiple channels can complement each other through multi-source data fusion. The higher data integrity will be acquired, so as to improve the effect of space astronomical event monitoring.

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5 Conclusion The paper issued a data organizing method of Beidou short messages and a multisource data fusion algorithm for the ground data processing system, which solved the processing problems of different data from telemetry, data and Beidou transmission channels, the problems of high frequency of Beidou short messages and continuous small data blocks. Through the analysis of the in-orbit data, the application of the Beidou-3 short message service system terminal in the space science satellite can significantly improve the real-time processing of the ground system for space science satellites. In the future, the ground processing system based on Beidou short message needs to be further studied in terms of stability of real-time processing performance and the improvement of data integrity. With the subsequent application of the Beidou terminals in more scientific satellites, the Beidou sytem will help to achieve more achievements in space scientific exploration.

References 1. Beidou Navigation Satellite System Website, Introduction to Beidou Navigation Satellite System. http://www.beidou.gov.cn/xt/xtjs/201710/t20171011_280.html. Accessed 06 Mar 2017. 2. Yang, Y., Mao, Y., Sun, B.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020019-0006-0 3. Li, R., Zheng, S.Y., Wang, E.S., et al.: Advances in BeiDou Navigation Satellite System (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1, 12 (2020) 4. He, Y.F., Wang, J.S., Li, Y.P., Chen, J.R.: Space-based measurement and control technology of near-earth satellite based on Beidou 1 and its application. Geomatics Inf. Sci. Wuhan Univ. 37(04), 441–444 (2012) 5. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 6. Abbott, B.P., Abbott, R., Abbott, T.D., et al.: GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119(16), 161101 (2017) 7. Sun, X.J., Shi, T., Hu, Y.X., Tong, J.Z., Li, B., Song, Y.: Real-time processing of space science satellite data based on streaming calculation. Appl. Comput. 39(06), 1563–1568 (2019) 8. Sun, X.J., Shi, T., Li, B., et al.: Fast data processing method for space science satellite. In: 2017 National High-Performance Computing Academic Conference: CCF, pp. 438–443 (2017) 9. Centre for Particle Celestial Objects, Institute of High Energy Physics, Chinese Academy of Sciences. Beidou 3 Satellite Navigation System for Space Exploration, GECAM Quasi-realtime down transmission gamma-ray burst observation alarm. http://www.ihep.cas.cn/xwdt/ gnxw/2020/202101/t20210121_5874777.html 10. Zhu, X.P., Dang, C., Liu, T., Zhang, Z.Y., Xu, L.J.: Space-based measurement and control design of low orbit spacecraft based on Beidou message communication system . Spacecraft Eng. 29(05), 19–25 (2020)

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11. Jia, P.: National Defence Science and Technology Information Network, International Mobile Satellite Organization and Singapore Value-added Innovation Company Joint Trial of New International Satellite Data Relay Service. http://www.dsti.net/Information/News/ 103706. Accessed 28 Feb 2017 12. Li, Y.: Progress of the American “military combat space enablement” satellite project. China Aerosp. 03, 38–41 (2013) 13. Sun, X.J., Lei, B., Cheng, Z.Y., et al.: Workflow application in operation control of remote sensing data processing. Comput. Eng. 38(4), 28–30 (2012) 14. Sun, D.W., Zhang, G.Y., Zheng, W.M.: Big data streaming computing: key technologies and system example. J. Softw. 25(4), 839–862 (2014)

Design a Border Management and Control System Based on BD-3 RDSS Lili Zhang(&), Pengyong Zhang, Wei Hou, Hanxiao Zhou, and Huizi Li Harbin Aerospace Star Data System Technology Co. Ltd., Harbin 150000, China

Abstract. China’s border area has more areas, fewer people, inconvenient traffic and poor communication. Take the China-Russia border in Heilongjiang Province as an example, the border is 2,981 km long, of which the water boundary ac-counts for more than 90%. It is urgent need to use scientific and effective super-vision measures to curb illegal fishing and cross-border fishing and avoid foreign-related incidents. In addition, the coverage of the ground network is patchy in the border areas. It’s not easy to find ground markers because snow and ice cover the ground in winter, and sometimes the misery compounded by heavy snowfalls. Once the border patroller get lost, have emergencies promptly or need reinforcements, they cannot establish communication links with the command and dispatch center in time and in accurate way. This paper presents a border management and control system based on BD-3 RDSS function, using BDS-3 positioning, short-message communicating to realize real-time dynamic monitoring of patroller, vehicles, ships, patrol path navigation, border command and dispatch, command situational awareness and automatic supervision of operating fishing boats. Using PSDA algorithm to realize the optimal strategy of border patrol path and improve the patrolling efficiency. The system also introduces the concept of grid management based on BD grid code technology, which is used for the binding management of key elements of border defense, cases and locations. The method proposed in this paper safeguard the security and stability of border areas through perceived border situation real-timely, controlling patrol forces, warning border-related cases timely. Keywords: BD-3 RDSS
Command and dispatch
Optimization of datrolling route

1 Introduction China has the longest land border and the largest number of neighbors in the world, with a total length of about 22,000 km [2]. The border area has more areas, fewer people, inconvenient traffic and poor communication. The patrolling condition in the border areas in Northeast China, such as China with North Korea, China with Mongolia and China with Russia, is particularly bad, it’s urgently needed to improve border prevention and control capacity. Implement the General Secretary’s important directives such as “enhancing national defense capability in step with the economy” and “guarding the north gate of the country”. Adhere to the top-level design, seize the weak links and prominent problems facing China’s border defense under the new era © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 253–261, 2021. https://doi.org/10.1007/978-981-16-3138-2_25

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situation, and meet the needs of various business departments to deal with border business together. Taking advantage of the development opportunities of the global network of the BDS, using the unique functions of the BDS-3’positioning, navigation and the global short message communication [1, 3], intensifying the promotion of the BDS-3 terminal, building an integrated information network of the sky and the earth, integrate military, police and civilian efforts, forming an integrated multi-dimensional border prevention and control system, maintaining border security and stability. At present, the international epidemic is spreading rapidly. In this way, to awareness border situation real-timely, to control patrol forces, and to warn border-related cases timely, to safeguard the security and stability of border areas. In order to prevent illegal entry and cross-border operations of fishermen from causing the import of the epidemic and foreign-related incidents, the strengthening of border control is not only related to border security and stability, but also related to the national epidemic control condition and China’s international influence.

2 System Design 2.1

System Architecture

System architecture takes “open standards, safe and reliable, and sharing” as the principles. This paper adopts the MVC (Model View Controller) design pattern from the point of view of easy maintenance, easy expansion and practicality. By implementing the business logic layer and user layer, data service layer completely separate, and user operations, access to services, business process, data interaction of multi-layer separation to realize the high cohesion and low coupling, not only ensure the

Fig. 1. System architecture diagram

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application level of independent security, flexible and ensure that all levels of access, improve system security, efficient, flexible and open. The main functions of the system are command and dispatch, grid management, task planning, fishing boat supervision, etc. The systems are mutually independent and mutually supportive (Fig. 1). 2.2

Communications Link

BD-3 is a global satellite position system developed by China independently, the system has the advantages of good security, high positioning accuracy and strong stability [4]. It overcomes the latitude effect of BD-2 [5], and it solves the problems that regional short message has occlusions and instability of communication caused by too low elevation angle in the high latitude area of Chinese northern. In this paper, the space-based BD-3 short message communication, ground internet and mobile communication network are integrated to build a space-time integrated information network [10], so as to form a space-time continuous, safe and reliable border defense communication network with up-down linkage. Patrol personnel use BD-3 RDSS terminal short message communication and mobile 3G/4G/5G [6] network to realize information exchange with the command center to realize patrolman (vehicle, ship) status monitoring and data acquisition; The mobile phone client reports illegal cases to the command center through the mobile 3G/4G/5G network; The system share the interdata with the Gaofen Center through the Gaofen special line. Police office and fishery department can interconnect with the system by using the government private network to realize the exchange of information (Fig. 2).

Fig. 2. Communication link diagram

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2.3

Main Function

2.3.1 Scheduling Command Scheduling command mainly realize functions of the routine patrolling path planning and the emergency command and dispatch. Multi-objective optimization PSDA algorithm [8] is used to realize the routine patrolling path planning. It could realize the goal that patrol achieve high efficiency and low cost patrol and cost under the condition of limited resources. The emergency command and dispatch function receives temporary and emergency handling tasks such as external case reporting (patrol abnormal reported, public security system pushing, and people reporting) and system automatic can identification and alarm (fishing boat automatic alarm), to realize the management and control system of border guards, police and civilians working together (Fig. 3).

Fig. 3. Command and dispatch business flow chart

This is shown in the figure above about business process of the emergency command and dispatch function business, which mainly includes the process of case filing, dispatch, disposal and case closure. A urgent task trigger the process of case, the operator of the command center determine to put on record it if the case’s conditions are enough. When the condition is enough, the command center operator selects patrolman by system, nearby principle task dispatching command, the issuance of the tasks detailed information and task, with patrolman’s terminal receives the missions, went to the field investigation and verification, fill out and submit the disposal result, back to the command center (Fig. 4).

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Fig. 4. Scheduling command system diagram

2.3.2 Grid Management The grid management implements the functions of the grid company division and the grid information management functions. The way in which accomplishing integration of the grid management method with the BD grid code technology [11], establishing multi-level nested grid record to realize grid resources within the jurisdiction of transparent regulation, rapid retrieval and precise positioning, to realize the rapid perception of frontier situation and optimal allocation of resources. The grid unit division is used for grid partitioning based on the main roads, the secondary roads, streets and alleys, communities, villages, company, industries, places and etc. [12]. At the same time, the regional management introduces BD grid position code to refine the spatial dimension within the jurisdiction, and to establish a multilevel nested cell grid. The grid information management manages physical information management within their respective jurisdictions about ship tube stations, workstations, indeed, fishing boats estuary, civil air defense forces, merchants, bayonet, video monitoring and so on, using the BD grid code technology to correlate all kinds of objects, to support scheduling command, mission planning, fishing boats, regulatory and other business data can also be used for efficient query, statistics, correlation analysis, path analysis, the case of time and space heat map display and other multi-level evaluation border business. 2.3.3 Fishing Boat Supervision The fishing boat supervision completes supervised functions of the fishing operating area and the fishing boat automatic alarm, using the BD RDSS ship terminal to realize the border information automatic regulation of fishing boat, monitoring the state of the fishing boat real-timely, using electronic fence specification of fishing boat working area, avoid the fishermen go into closure of fishing areas or across the border to illegal fishing.

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The supervision of fishing operating area: Setting the reference lines for the electronic fence according to boundary river centerline extracted from high-resolution image, line field boundary and fishing area data. Setting early warning line and alarm line, for example, the early warning line far away from the reference line about 20 m, and the alarm line far away from the reference line about 10 m, and the multi-electronic fences provide data support for the multi-alarm reminders of the fishing boat automatic alarm. The fishing boat automatic alarm function: using electronic fence technology and BD terminal positioning technology, to realize multiple alarm reminder. When the fishing boat crosses the early warning line, the system will automatically send an early warning to the fishing boat terminal. When the operating fishing boat crosses the alarm line, the system will automatically send back warning to the fishing boat terminal, and the system will automatically lock and mark and track the alarm fishing boat. The commander will immediately start the emergency command and dispatch mechanism at the same time, and dispatch the nearest patrol ship to the scene according to the nearby principle. 2.3.4 Monitoring Management Monitoring and management to achieve case statistics, patrolman (car, ship) statistics. The statistics of frontier defense cases are based on the source, type, status, trend and efficiency of case settlement. Patrolman (car, boat) statistics mainly show the current patrolman’s terminal online and offline status, and count the patrolman’s current patrolman’s mileage. The statistical results can provide data support for frontier command and dispatch, patrol quality evaluation and other work.

3 Key Technology 3.1

Multi-objective Optimization PSDA Algorithm

Fig. 5. Logic diagram of objective optimization PSDA algorithm

Multi-objective optimization PSDA (Probabilistic Solution Discovery Algorithm) is a kind of improved double objective optimization method [8]. It is used to balance the

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patrol vulnerability and cost. According to the monitoring and management statistics about the occurrence of time and place distribution, working out multi-choice patrol plans, using scientific means to replace the subjective judgment of empirical, to maximize the enhancement of border security patrol network. The main implementation ideas are as above (Fig. 5). Initialize the main border set hotspots selected, setting the patrol unit number, patrol and protect the average velocity, patrol and protect cost per kilometer costs, etc., after several rounds of iteration optimization generates S , using pareto [9] analysis according to patrol and protect vulnerability and patrol and protect double objective evaluation and sorting [8], forming the optimal patrol strategy pareto set, eventually form is not the only solution. 3.2

Information Correlation Method Based on BD Grid Code Technology

The definition of BD grid location code is a grid code identification of the location of the geospatial region [11], which is applied to the output of BD terminal based on Geospatial Subdivision Model (GEOSOT). In other words, each grid has a unit space. As the unique identifier of the unit space, the grid position code can automatically and uniformly associate entities and associated events in the unit space, thus forming grid management files based on the BD grid position code technology. The realization of information association method based on BD grid code technology mainly consists of three steps, as follows: Step 1: Grid level selection of BD grid position code. In this paper, grid level selection is based on the positioning accuracy of BD RDSS terminal. The positioning accuracy of BD RDSS terminal is better than 3 m, so the eighth grid is selected, which is equivalent to 0.97 m  0.97 m grid. Step 2: Grid coding method of BD grid position code. The coding form of BD grid code adopts BD short position code, namely the reference place name + grid position offset, which should conform to the coding principles of uniqueness, nesting, compatibility, computability and practicability. Step 3: Information correlation method in unit space of BD grid position code. As the unique identification of space, grid code automatically and uniformly correlates static data, semi-dynamic data and dynamic data in space, so as to realize unified index, correlation and integration of all dynamic and static data in the same unit space. Static data mainly includes ship management station, workstation, responsibility area, fishing boats estuary, service deployment, businesses and other basic detailed information data; Semi-dynamic data mainly includes fixed-point observation dynamic change data such as bayonet and video monitoring. Dynamic data mainly includes BD-3 RDSS handheld terminal, BD-3 RDSS vehicle terminal, BD-3 RDSS boat terminal, case occurrence and other dynamic change data. The information association method based on BD grid code technology can also be used in complex multi-source data fusion systems such as digital agriculture, urban management, ecological environmental protection and spatio-temporal data management, which can fundamentally improve the ability of efficient data retrieval, multisource integration, exchange and sharing, etc. (Fig. 6).

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Fig. 6. Schematic diagram of technical information association based on BD grid code

4 Conclusion This paper propose a border management and control system based on BD-3 RDSS. First, the integrated communication network of heaven and earth (BD-3 short message + mobile Internet) is combined to realize no dead corner of communication and provide safe and reliable communication guarantee. Second, border patrol personnel (vehicles, ships) and fishing boats are equipped with BD-3 RDSS terminals to unify supervising information and forming a network of border control and command. Third, the electronic sand table is established by using remote sensing satellite and grid management method based on BD grid code technology, which provides geographic basic information support for command, dispatch and situation analysis, and forms a command and combat map. Fourth, we will build an integrated multi-dimensional border prevention and control system by pooling military, police and civilian efforts to improve the efficiency of border patrol and maintain security and stability in border areas. At the same time, we should do a good job in the promotion and application of BD-3 terminal in high-dimensional and alpine areas, and stabilize the industrial pattern and situation of “good use in the sky, good use on the ground”.

References 1. Yang, Y., Mao, Y., Sun, B.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020019-0006-0 2. Liu, S.: The State of Border Security in Northeast China. International Herald Tribune (2015) 3. Guo, S., Cai, H., Meng, Y.: Navigation and positioning technology system and service performance of BD-3. Acta Geodaetica et Cartographica Sinica (2019)

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4. Yang, Y.: The difficult challenges in the opening of BDS. Chin. J. Sci. Technol. (2020) 5. Jing, Y., Yang, Y., Zeng, A.: Latitude Effect on Positioning Performance of BD Regional Navigation Satellite System. Geomatics and Information Science of Wuhan University (2017) 6. Liu, J.N., Gao, K.F., Guo, W.F., et al.: Role, path, and vision of “5G+BDS/GNSS.” Satell. Navig. 1, 23 (2020) 7. Zhang, J., Liao, K.: Design and implementation of border guard service integrated system. Comput. Age 64–67 (2014) 8. Muaafa, M., Ramirez-Marquez, J.E.: Bi-objective evolutionary approach to the design of patrolling schemes for improved border security. Comput. Ind. Eng. 107, 74–84 (2017) 9. Muaafa, M., Ramirez-Marquez, J.: Development of patrolling schemes for improved border security performance through an evolutionary approach. In: Proceedings of 22nd annual INCOSE int. symposium (IS 2012), Rome, Italy (2012) 10. Li, R., Zheng, S.Y., Wang, E.S., et al.: Advances in BeiDou navigation satellite system (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1(1), 9 (2020) 11. BD Grid Position Code, GBT 39409-2020, P1-14 12. Hou, W., Bao, S.: Innovative research on flat grid management of smart city management in Harbin. Urban Management and Technology (2019)

New Method of GNSS-R Wind Speed Retrieval Based on Empirical Orthogonal Function Jianming Wu1,2, Yanling Chen1(&), Peng Guo1, Xiaoya Wang1, Xiaogong Hu1, and Mengjie Wu1 1

Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China [email protected] 2 University of Chinese Academy of Sciences, Beijing, China

Abstract. The geophysical model function (GMF) and the cumulative distribution function (CDF) are two main algorithms used for retrieving sea surface wind speed from GNSS-R observations. The difficulties in segment fitting and the complicity in parameter adjustment hinders the wide application of the GMF, while the wind speed retrieved by using the later renders a deviation of about –2 m/s when the wind speed is in the range of 0–3 m/s. This paper proposes a new algorithm based on the empirical orthogonal function (EOF) to retrieve wind speed from GNSS-R observations. Based on the EOF, two wind retrieval models are trained by using the delay doppler map average (DDMA) and the leading edge slope (LES) as the training set, respectively. In the training, the wind speed data (resolution: 30 km, 1 h) from European Centre for mediumrange weather forecasts (ECMWF) reanalysis V5 (ERA5) are used as the ground truth data. The DDMA and LES are 80% of the resampled NASA’s cyclone global navigation satellite system (CYGNSS) and GNSS-R data of 2019 at an interval of 10 s. The final wind speeds are calculated from the two kinds of retrieval by a minimum variance (MV) criterion. At last, the test data set (20% of CYGNSS data) are used to evaluate the accuracy of the final wind speeds. The result shows that when the reference wind speeds are below 20 m/s, the mean bias and RMSE of the retrieved wind speeds are 0.026 m/s and 1.77 m/s when using the ERA5 wind speeds as the reference, which are 0.23 m/s and 1.67 m/s when using advanced scatterometer (ASCAT) wind speeds as the reference. This proves that the EOF algorithm has a good performance in retrieving sea surface wind speed. Keywords: GNSS-R LES


EOF
Ocean surface wind speed retrieval
DDMA


1 Introduction In 1993, Martín-Neira first proposed the Global Navigation Satellite Systems Reflectometry (GNSS-R) technology for ocean altimetry application [1]. Now, it has been used to retrieval sea surface wind speed, sea surface height, significant wave height, soil moisture, sense sea ice remotely or to inverse surface vegetation water content by receiving direct GNSS signals from BeiDou, GPS, Galileo or GLONASS satellites and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 262–273, 2021. https://doi.org/10.1007/978-981-16-3138-2_26

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forward scattering signals from the earth’s surface [2–7]. GNSS-R technology has attracted increasing worldwide attention for its all-day and all-weather capabilities, high temporal-spatial resolution, low cost, low power consumption and global observation capabilities [6]. GNSS-R bistatic radar scattering model proposed by Zavorotny and Voronovich laid the basic principle for retrieval of sea surface wind speed by the spaceborne GNSSR observations [7]. In 2003 and 2014, Britain successively launched UK-DMC, TDS-1 GNSS-R satellites [8, 9] verifying the GNSS-R wind speed retrieval technology. On December 15, 2016, NASA launched the Cyclone Global Navigation Satellite System (CYGNSS) satellite constellation, the first satellite constellation dedicated to GNSS-R sea surface wind remote sensing, consisting of eight small satellite [10]. China launched the BuFeng-1 A/B twin satellites for sea surface wind remote sensing in 2019 [11]. At present, the wind speed retrieval accuracy by GNSS-R is generally around 2 m/s. Most of GNSS-R wind speed retrieval methods are based on statistical models of the relationship between the GNSS-R observations and sea surface wind speed. In 2015, Foti et al. used the normalized bistatic radar cross section measured by the TDS-1 satellite and the sea surface wind speed to establish an exponential function regression model, and the accuracy of the retrieval was 2.21 m/s [9]. In 2016, Clarizia et al. used the minimum variance (MV) method to linearly combines the two wind speed results retrieved by DDMA and LES models as the final wind speed. The RMSE of the final result is better than 2 m/s. However, as a GMF fitting method, a large number of parameters need to be empirically tuned [12]. Although many scholars have made significant improvements in the parameters tuning and data quality control in the retrieval process, the retrieval method still adopts the nonlinear regression method [13, 14]. In 2020, Clarizia et al. improved the CYGNSS wind speed inversion algorithm based on the Cumulative Distribution Function (CDF). However, this method is not suitable for strong wind retrieval [15]. In addition, Liu et al. proposed wind speed retrieval method based on neural network, which uses the whole DDM for the model training [16], but the physical meanings cannot be clearly interpreted in the network. Considering the complex modeling of the GMF and CDF methods and the limited applicable wind speed range, this paper proposes a new algorithm for retrieving the sea surface wind speed based on the empirical orthogonal function (EOF) [17]. In this algorithm, the correlation of the original data is analyzed, based on which the main characteristics of the original data are extracted by using the eigenvalue decomposition. Therefore, the original data can be described by a few independent variables. This algorithm avoids the specific basis functions, such as spherical harmonic functions, that are usually required for function decomposition. In addition, this algorithm has a fast convergence speed. In a conclusion, the proposed method is simpler and faster when compared with the nonlinear modeling methods. In this paper, GNSS-R observations, DDMA and LES, are used to establish two models, respectively, based on the EOF analysis method. The resulted two kinds of wind speed retrieval are linearly combined as the final wind speed result by using the MV method. The ERA5 and ASCAT wind speed data are used for sea surface truth data in the modeling and validation data for accuracy evaluation.

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2 Wind Speed Inversion Method by EOF Analysis The flow chart of the sea surface wind speed modeling based on EOF is shown in Fig. 1. As illustrated in the flowchart, firstly, GNSS-R observations, DDMA and LES, are gridded to construct matrix X, and matrix C is calculated by C ¼ XX T . Then eigenvalue decomposition was used to derive the eigenvalue matrix K, and the eigenvector matrix E. The coefficient matrix P is calculated by P ¼ ET X. The EOF analysis is to decompose the observation matrix X into the wind speed function and the incident angle function: X ¼ EP. Each column of the square matrix E is the wind speed eigenvector, which describes the characteristics of GNSS-R observation at a specific wind speed. They are called empirical orthogonal functions (EOF). Each row in P is the incident angle coefficient corresponding to the wind speed eigenvector, which describes the amplitude of the GNSS-R observation changing with the angle of incidence at a specific wind speed. They are called principal components. Each wind speed eigenvector and its corresponding incident angle coefficient together are called a mode. A series of modes can be used to describe GNSS-R observations, and the remaining modes are used to represent noise.

Fig. 1. The flow chart of sea surface wind speed modeling based on EOF

Finally, the eigenvalues are sorted from largest to smallest. The modes with the largest eigenvalues are selected to construct Enew and Pnew . The matrix Xnew , Xnew ¼ Enew Pnew ;

ð1Þ

is the wind speed retrieval model.

3 GNSS-R Wind Speed Retrieval 3.1

Data

The data consist of two parts: (1) Spaceborne GNSS-R data and related indices, such as range corrected gain (RCG) and signal incident angle; (2) reference wind speed data for the modeling training and the accuracy evaluation. The reference wind speed data are linearly interpolated to match the time and location of GNSS-R observations.

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3.1.1 Spaceborne GNSS-R Observation Data GNSS-R observations data used in this paper are measured by CYGNSS in 2019, downloaded from the physical oceanography distributed active archive center (PO. DAAC). Two GNSS-R observations, DDMA and LES, are used for wind speed retrieval. The DDMA is the average value of DDMs within a delay-Doppler window near the specular reflection point. The LES is the slope of the leading edge of the integrated delay waveform (IDW), which is obtained as incoherent integration of DDMs along the Doppler dimension, and over a range of Doppler frequencies [12, 18]. These two GNSS-R observations are sensitive to sea surface wind speed, and they have been successfully used for wind speed retrieval in both TDS-1 and CYGNSS. In addition, in order to reduce the error of the retrieval model, it is necessary to consider the signal incident angle and RCG in the retrieval model. The RCG specifies the influence of antenna gain and the signal propagation distance on received signal energy, the higher the RCG, the better the data quality. 3.1.2 Reference Wind Speed Data The reference wind speed data are used for the model training and the accuracy evaluation. Apart from sea surface buoy data, which can be used as the reference, there are several publicly available wind speed datasets, including reanalysis data like ERA5, ERA-interim, MERRA2 (The Modern-Era Retrospective Analysis for Research and Applications, Version 2), etc., and scatterometer data like ASCAT. This paper uses the ERA5 and the ASCAT data. (1) ERA5 wind speed data. ERA5 data is from the European Centre for medium-range weather forecasts (ECMWF). The time resolution of the data is 1 h and the spatial resolution is about 30 km. The ERA5 wind speed is wind speed at the height of 10 m above the sea surface. (2) ASCAT wind speed data. The data is sea surface wind vector data acquired by Advanced Scatterometer mounted on MetOp-A and MetOp-B satellites. The ASCAT observation ranges from 90° S to 90° N with a spatial resolution of 25 km and a temporal resolution 2 s. The data is provided by KNMI (Koninklijk Nederlands Meteorologisch Instituut) and can be downloaded from https://podaac. jpl.nasa.gov/datasetlist?search=ascat. 3.2

Data Quality Control

Data quality control is necessary before the retrieval of the sea surface wind speed. If no quality control was carried out before the modeling, GNSS-R observations with low quality would affect the accuracy of the retrieval. The quality control is primary carried out for removing outliers, which is realized in three steps: (1) The DDMA and LES observations with RCG < 10 are excluded; (2) The ERA5 and ASCAT data are removed if their difference exceeds 3 m/s; (3) After the previous two steps, pairs of GNSS-R observations and reference wind speeds are obtained. Before the modeling, we segmented these pairs of data with a wind speed interval of 0.3 m/s, and applied the “3r” criterion to eliminate the outliers of the pairs in each wind speed section.

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Fig. 2. The density profile of the DDMA with regards to the ERA5 wind speed: (a) before and (b) after data quality control

After (2), 11.90% of the total data is eliminated, and 3.08% after (3). The data remained after the outliers removal is used in the following modeling. This dataset is separated to be 80% and 20% for training and test sets, respectively. The training data volume is 4115972, and the test data volume is 1028993. Figure 2 is the density profile of the DDMA data with regards to the corresponding ERA5 wind speeds (a) before and (b) after the data quality control. The data eliminated in Fig. 2(a) have a low data density distribution and do not conform to the monotone decreasing non-linear relationship between the GNSS-R observations and wind speed. 3.3

Data Gridding

Figure 2(b) shows that with the decrease of the DDMA, the wind speed shows an exponential increase. This phenomenon explains why the accuracy of wind speed retrieving deteriorates when the wind speed increases, as reported in previous research [10]. In order to model this nonlinear relationship between GNSS-R observations and wind speed, the natural logarithms of the GNSS-R observations are taken. The

Fig. 3. Gridded values of logarithmic DDMA. It should be noted that there is still a small amount of data with a reference wind speed higher than 20 m/s in Fig. 2(b). The grid of these data lost many points. Therefore, the wind speed range in grid used for EOF analysis is 0–20 m/s

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logarithmic DDMAs are grided according to the incident angle and the wind speed, as shown in Fig. 3. The grid resolution is 0.1°  0.1 m/s. The incident angle range is 0– 70°, and the wind speed range is 0–20 m/s. It can be seen that the grids below 10 m/s wind speed are smooth, and the higher wind speed grids are not homogeneous. It should be noted that at the higher wind speed end, there are data missing because rare data for wind speeds above 10 m/s. The nearest neighbor interpolation is utilized to fill the grid of missing data. The interpolated grid is used for the subsequent eigenvalue decomposition. The data with the wind speed higher than 20 m/s are not used, although there are few after the data quality control as shown in Fig. 2(b). This study focuses on the modeling for wind speeds below 20 m/s. The high wind speed model is different from the low wind speed model, and it is not the in the scope of this study. 3.4

EOF Decomposition

In this study, the gridded logarithmic DDMA is decomposed into the wind speed eigenvector matrix E, and then the principal component matrix P is calculated. E and P are as shown in Fig. 4. Both matrices are reordered according to the eigenvalues from the largest to the smallest. There are bands close to 0 in the right columns of the E matrix and the bottom rows of the P matrix. These bands result from the matrix reordering.

Fig. 4.

(a) The empirical orthogonal function matrix; (b) the principal component matrix

Figure 5 shows the first 5 rows of the incident angle coefficient matrix, corresponding to the first 5 principal components: (a) shows the first incident angle coefficient, and (b) shows the rows from the second to the fifth. It can be seen that the absolute value of the first principal component is significantly larger than the second to the fifth. The EOF analysis shows the eigenvalue of the first principal component accounts for more than 99% of the sum of all others. It indicates that the first principal component makes a major contribution to the GNSS-R observations, and it can represent the variation characteristics of the GNSS-R observations.

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Fig. 5. The first five rows of the principal component matrix: (a) the first principal component; (b) the second to the fifth principal components

3.5

GNSS-R Wind Speed Modeling

We get the model Xnew by reconstructing the eigenvector matrix and the coefficient matrix with the first principal component and its corresponding wind speed eigenvector. Figure 6 is the DDMA retrieval model. It can be seen that the model is smoother than Fig. 3. The noise is eliminated when the wind speed is greater than 15 m/s. Figure 7 shows the DDMA and LES models by EOF analysis.

Fig. 6. DDMA wind speed retrieval model

(a)

(b)

Fig. 7. Retrieval models with an incident angle interval of ten-degree: (a) the DDMA wind speed retrieval model and (b) the LES wind speed retrieval model

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269

Algorithm Performance Analysis

3.6.1 Assessment Method In order to assess the performance of the algorithm, we used three indicators: the mean bias
d, the standard deviation r, and the RMSE, which are demonstrated as N  N X X 
d ¼ 1 ^ i  WSi ¼ 1 WS di ; N i¼1 N i¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u 1 X 2 di 
d ; r¼t N i¼1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t r2 ; N i¼1 i

ð1Þ

ð2Þ

ð3Þ

^ i is defined as the retrieval wind speed, and WSi is the reference wind speed. where WS 3.6.2 Results and Validations of the Wind Speed Retrieval The sea surface wind speed retrieval is based on the retrieval models in Sect. 3.5. Results of the DDMA model and the LES model are shown in the Fig. 8. The horizontal axis is the ERA5 reference wind speed, and the vertical axis is the retrieval wind speed. The Fig. 8 shows that the retrieved results of the two models are almost the same as the reference wind speed, but the retrieval results are larger than the reference in the wind speed range of 8–15 m/s. The mean bias of retrieved wind speed by the DDMA model is –0.36 m/s, and the RMSE is 2.36 m/s. The mean bias of retrieved wind speed by the LES model is –0.15 m/s, and the RMSE is 2.40 m/s. We use the MV [12] method to linearly combine the two kinds of retrieval of the DDMA and LES models to improve the accuracy. The MV method exploits the degree of decorrelation between the errors in the two kinds of retrieval to minimize the RMSE

Fig. 8. Retrieval wind speed by DDMA model (a) and LES model (b)

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in the combined wind speed. The RMSE of results by the MV method will always be less than or equal to the smallest from the individual models. The formula is as follows: ~
! WSMV ¼ m ws ;

ð4Þ

~ is the coefficient vector of linear combination: where ! ws ¼ ðWSDDMA ; WSLES Þ, m ~¼ m

N X N X

!1 s1 ij

S1~ e;

ð5Þ

i¼1 i¼1

~ e is the unit vector. S1 is the inverse of the covariance matrix between the individual 1 retrieval errors,and s1 ij are the elements of S . The RCG will affect the retrieval. As the RCG decreases, the retrieval will become worse. This phenomenon is prominent when RCG < 100. The MV method uses different coefficients to linearly combine both models’ retrieval results according to the RCG. The ranges of the segments and the linear combination coefficients are shown in the Table 1 below. Table 1. The ranges of the RCG and the coefficients m ~ used for the linear combination ~ The ranges of the RCG m [0, 20) (0.31, 0.69) [20, 50) (0.41, 0.59) [50, 100) (0.49, 0.50) [100, 250) (0.58, 0.41)

The final retrieval obtained by the MV method is illustrated in the Fig. 9. The final retrieval is slightly improved in the wind speed range of 8–15 m/s.

Fig. 9. The comparison of the MV retrieval wind speed with ERA5 wind speed (left) and the ASCAT wind speed (right)

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When the reference wind speeds are lower than 20 m/s, compared with the ERA5 reference wind speed, the mean bias and RMSE of the final results are 0.026 m/s and 1.77 m/s. Compared with the ASCAT reference wind speed, the mean bias and RMSE are 0.23 m/s and 1.67 m/s, respectively. The accuracy of the final retrieval is significantly improved. The difference between the two mean biases is probably caused by the systematic bias between the two reference winds. The Fig. 10 illustrates the variation of the mean bias and RMSE between the final retrieval and reference wind speeds. In Fig. 10, retrieved wind speeds within 0.5 m/s before and after the integer reference wind speed are used for segmented statistics. The amount of retrieved wind speeds within the range of 19.5–20 m/s reference wind speed are few, account for 0.0069% of the total retrieval when taking ERA5 as the reference, and 0.011% for ASCAT. So, there is no statistic at 20 m/s reference wind speed in Fig. 10. Almost all the mean biases are less than 2 m/s, except for 19 m/s point in Fig. 10(c). Below 5 m/s reference wind speed, the mean bias is from –0.039 to – 0.15 m/s for ERA5 reference wind and between –0.062 and 0.30 for ASCAT. For RMSEs, when the reference wind speeds are lower than 8 m/s, the RMSEs are lower than 2 m/s, and when the reference wind speeds are from 10 m/s to 20 m/s, the maximum value of RMSEs is 4.50 m/s.

(a)

(b)

(c)

(d)

Fig. 10. The mean bias and the RMSE of the MV retrieved wind speed: (a), (b) ERA5 wind speed is used as the reference; (c), (d) ASCAT wind speed is used as the reference

4 Conclusion This paper proposes a new method to for GNSS-R sea surface wind speed retrieval based on EOF analysis. This method establishes a relationship between the GNSS-R observations and sea surface wind speed. The GYGNSS observations and reference

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windspeeds, including ERA5 and ASCAT wind speeds are used to test the retrieval algorithm and evaluate accuracy. The result demonstrates that the accuracy of EOFbased modeling method is comparable to the statistical regression modelling and the CDF modeling method. The method has great potential in GNSS-R sea surface wind speed retrieval because of its advantages of simple modeling process and small amount of calculation. Moreover, this method is not only suitable for retrieval of wind speed below 20 m/s, but also for retrieval of high wind speed, as well as the retrieval of other geophysical parameters such as significant wave height and mean square slope. BeiDou-3 Navigation Satellite System (BDS-3) has been completed in 2020, and more GNSS-R satellite platforms carry BeiDou signal processing payloads. Future work will focus on further exploiting the EOF- based modeling method for GNSS-R, which includes: (1) BDS-R (BeiDou Navigation Satellite System Reflectometry) sea surface wind speed modeling; (2) typhoon wind speed retrieval; (3) the utilization of other GNSS-R observations, such as DDM signal-to-noise ratio. Acknowledgment. The research is jointly financially supported by the National Key Research and Development Program of China (No. 2016YFB0501405) and General Program of National Natural Science Foundation of China (No. 11973073). Thanks to the Jet Propulsion Laboratory (JPL) and the European Centre for Medium-Range Weather Forecasts (ECMWF) for the data.

References 1. Martín-Neira, M.: A passive reflectometry and interferometry system (PARIS): application to ocean altimetry. ESA J. 17, 331–55 (1993) 2. Yang, D., Li, X., Wang, F.: Analysis of application status of GNSS reflected signal in ocean remote sensing. Radio Eng. 49(10), 843–848 (2019). (Ch) 3. Gao, F., Xu, T., Wang, N., et al.: A shipborne experiment using a dual-antenna reflectometry system for GPS/BDS code delay measurements. J. Geodesy 94(9), 88 (2020) 4. Wu, X., Jin, S., Chang, L.: Monitoring bare soil freeze–thaw process using GPSinterferometric reflectometry: simulation and validation. Remote Sens. 10(2), 14 (2017) 5. Yan, Q., Huang, W.: Sea ice remote sensing using GNSS-R: a review. Remote Sens. 11(21), 2565 (2019) 6. Jin, S., Zhang, Q., Qian, X.: New progress and application prospects of global navigation satelite system reflectometry (GNSS + R). Acta Geodaet. et Cartographica Sin. 46(10), 1389–1398 (2017). (Ch) 7. Pan, Y., Ren, C., Liang, Y., Zhang, Z., Shi, Y.: Inversion of surface vegetation water content based on GNSS-IR and MODIS data fusion. Satell. Navig. 1(1), 21 (2020) 8. Zavorotny, V.U., Voronovich, A.G.: Scattering of GPS signals from the ocean with wind remote sensing application. IEEE Trans. Geosci. Remote Sens. 38, 951–64 (2000) 9. Clarizia, M.P., Gommenginger, C.P., Gleason, S.T., Srokosz, M.A., Galdi, C., Di, B.M.: Analysis of GNSS-R delay-Doppler maps from the UK-DMC satellite over the ocean. Geophys. Res. Lett. 36, L02608 (2009) 10. Foti, G., Gommenginger, C., Jales, P., et al.: Spaceborne GNSS reflectometry for ocean winds: first results from the UK TechDemoSat-1 mission. Geophys. Res. Lett. 42(13), 5435– 41 (2015)

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11. Ruf, C.S., Atlas, R., Chang, P.S., Clarizia, M.P., Garrison, J.L., Gleason, S., et al.: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Am. Meteorol. Soc. 97(3), 385–95 (2016) 12. Jing, C., Niu, X., Duan, C., Lu, F., Di, G., Yang, X.: Sea surface wind speed retrieval from the first chinese GNSS-R mission: technique and preliminary results. Remote Sens. 11(24), 3013 (2019) 13. Clarizia, M.P., Ruf, C.S., Jales, P., Gommenginger, C.: Spaceborne GNSS-R minimum variance wind speed estimator. IEEE Trans. Geosci. Remote Sen. 52(11), 6829–43 (2014) 14. Dong, Z., Jin, S.: Evaluation of spaceborne GNSS-R retrieved ocean surface wind speed with multiple datasets. Remote Sens. 11(23), 2747 (2019) 15. Bu, J., Yu, K., Zhu, Y., Qian, N., Chang, J.: Developing and testing models for sea surface wind speed estimation with GNSS-R delay doppler maps and delay waveforms. Remote Sens. 12(22), 3760 (2020) 16. Clarizia, M.P., Ruf, C.S.: Statistical derivation of wind speeds from CYGNSS data. IEEE Trans. Geosci. Remote Sens. 58(6), 3955–64 (2020) 17. Liu, Y., Collett, I., Morton, Y.J.: Application of neural network to GNSS-R wind speed retrieval. IEEE Trans. Geosci. Remote Sens. 57(12), 9756–66 (2019) 18. Sparnocchia, S., Pinardi, N., Demirov, E.: Multivariate Empirical Orthogonal Function analysis of the upper thermocline structure of the Mediterranean Sea from observations and model simulations. Ann. Geophys. 21(1), 167–87 (2003) 19. Clarizia, M.P., Ruf, C.S.: Wind speed retrieval algorithm for the cyclone global navigation satellite system (CYGNSS) mission. IEEE Trans. Geosci. Remote Sens. 54(8), 4419–32 (2016)

Commercial Vehicle Road Collaborative System Based on 5G-V2X and Satellite Navigation Technologies Bo Wang1(&), Chunqiang Chen2(&), and Tianchen Zhang3(&) 1

Fujian Key Laboratory of Intelligent and Connected Commercial Vehicle (Information Science), Fuzhou, China [email protected] 2 Satellite Positioning Technology Research Center of Wuhan University, Wuhan, China 3 Fuzhou Internet of Things Open Lab, Fuzhou, China

Abstract. With the rapid social economic development and the acceleration of industrialization, traffic jams, road safety, energy consumption and environmental pollution, caused by automobile usage, are becoming more challenging than ever before. The fifth-generation mobile communication technology (5G) with ten times higher peak bit rate than 4G, millisecond-level transmission delay and 100 billion-level connection capability, meets the requirements of low latency and high reliability 4.1

Analysis on the Time Delay Accuracy

In 1, September, the difference of the systematic error of the time delay between 1, 4 and 6 beams was calculated by adopting the beam 6 as the reference beam, the differences between the different out-station beams in Hainan station on that day were shown in Table 1.

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Table 1. The systematic error of the time delay in different out-station beams in Hainan station (Unit: m) Out-station beam

In-station beam

Channel

OMC

1 4 6

3 3 3

4 4 4

32.56 −12.88 21.62

The systematic error of the time delay 10.94 −34.5 –

The difference of the systematic error of the time delay in Hainan station for seven consecutive days was calculated, and its multi-day consistency was analyzed. The 7day consistency accuracy of the time delay of the out-station beams in Hainan station can be obtained, as shown in Table 2. Table 2. The consistency of time delay’s systematic error of different RDSS out-station beams in different days in Hainan station (Unit: m) Date Out-station beam OMC 1

2

3

4

5

6

7

1 4 6 1 4 6 1 4 6 1 4 6 1 4 6 1 4 6 1 4 6

32.56 −12.88 21.62 32.79 −12.56 22.15 34.22 −12.06 22.55 33.03 −13.37 21.50 34.42 −12.13 22.82 34.64 −12.15 22.90 34.77 −12.20 22.97

Consistency Before calibration 10.94 −34.5 – 10.64 −34.71 – 11.67 −34.61 – 11.53 −34.87 – 11.60 −34.95 – 11.74 −35.05 – 11.80 −35.17 –

After calibration 0 0 – −0.30 −0.21 – 0.73 −0.11 – −0.59 −0.37 – 0.66 −0.45 – −0.80 −0.55 – 0.86 −0.67 –

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From the Table 2, it can be seen that the residual error of the systematic error within different out-station beams was less than 0.9 m and the maximum was 0.86 m after deducting the reference value of one day, that is to say, the calibration accuracy of the time delay of different out-station beams in BDS was better than 2.87 ns. 4.2

Positioning Experiment

In 1, September, the Hainan station responded to the out-station beams 1,4 and 6, while on 4, September, the Hainan station responded to the out-station beams 1,4, only the time delay of the beam 6 was calibrated. The systematic error of the time delay in the out-station beam 1 and 4 was not calibrated. The positioning accuracy on the 4th day was shown in Fig. 1.

Fig. 1. The original positioning result in Hainan Station

From the Fig. 1, for 4, September, the horizontal positioning accuracy was 19m with the time delay configuration value of the out-station beam 6 in 1st day. Due to the out-station beam 1 and 4 in the 4th day, the systematic error of the time delay between the out-station beam 1 and the out-station beam 6 in the 1st day was adopted to correct the time delay of the out-station beam 1. The positioning accuracy by the adjusted time delay was shown in Fig. 2. From the Fig. 2, it can be seen that the positioning accuracy of the first half-day was obviously improved, but the location error of the second half-day was large. The reason was that the second half-day part is the observation period of the out-station beam 4, and the systematic error of the time delay between the out-station beam 4 and the out-station beam 6 was not adopted.

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Fig. 2. The positioning result after correcting the time delay of out-station beam 1

Fig. 3. The positioning result after correcting the time delay of out-station beam 1 and 4

The systematic error of the time delay between the out-station beam 1, 4 and 6 was adopted to correct the time delay of the out-station beam 1, 4 in 4th day respectively. The positioning accuracy by the adjusted time delay was shown in Fig. 3. As can be seen from the Fig. 3, the positioning accuracy was stable all day, and the horizontal positioning accuracy was 2.555 m.

5 Conclusion Aiming at the problem that the positioning accuracy of the RDSS user has jump in different degree when changing the response beam, this paper adopts the differential method to calibrate the time delay of different out-station beams, which solve the problem of the systematic error in different RDSS equipments, to improve the service performance of RDSS. The results are as follows:

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(1) By multi-day consistency evaluation method, the calibration accuracy of the time delay of different out-station beams is better than 2.87 ns. At present, the observation accuracy of RDSS is 1 to 2 m, so the accuracy of RDSS’s time delay can meet the accuracy requirement of time delay calibration. (2) By the time delay before and after the calibration, the horizontal accuracy of RDSS receiver in Hainan station is improved from 19 m to 2.555 m, and the percentage is raised to 87%. The positioning accuracy is much better than the 20 m of the horizontal positioning accuracy in the current Beidou calibration area. The method proposed in this paper solves the problem of positioning accuracy’s jump when the RDSS user switches the response beam, which makes the user not aware of the switch beam, and improves the service performance of RDSS system greatly. (3) Compared with the existing calibration method of sending off on-line equipment to equipment calibration field for re-calibration, the advantages of the method proposed in this paper are as follows: firstly, the method does not require off-line RDSS equipment, and the on-line system can run continuously and stably. Secondly, the method can automatically calculate the delay time of RDSS by software, and the calibration is simple and time-consuming without manual intervention and maintenance. From the data processing, this method solves the difficult of time-delay calibration of RDSS equipment and improves the service performance of RDSS system. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos.: 41874043, 41704037, 41804030).

References 1. Son, P.W., Park, S.H., Seo, K., Han, Y., Seo, J.: Development of the Korean eLoran testbed and analysis of its expected positioning accuracy. In: IALA 2018 KOREA, 19th Conference INCHEON, 30th May 2018, pp. 1–10 (2018) 2. Offermans, G., et al.: eLoran initial operational capability in the United Kingdom–first results. In: Proceedings of the ION ITM, Dana Point, CA, USA, 2015, pp. 27–39 (2015) 3. Li, X., et al.: Orbit and positioning accuracy for the new generation beidou satellites during the earth eclipsing period. J. Navig. 71(5), 1–19 (2018) 4. Li, X., et al.: Construction of a BDSPHERE solar radiation pressure model for BeiDou GEOs at vernal and autumn equinox periods. Adv. Space Res. 62(7), 1717–1727 (2018) 5. Yang, Y.: Progress, contribution and challenges of compass/beidou satellite navigation system. Acta Geodaetica et Cartographica Sinica 39(1), 16 (2010) 6. Tan, S.: The Engineering of Satellite Navigation and Positioning, vol. 1, pp. 12–27. National Defense Industry Press (2011) 7. Tan, S.: The Comprehensive RDSS Global Position and Report System, vol. 7, pp. 26–32. National Defense Industry Press (2010) 8. Tan, S.: Theory and application of comprehensive RDSS position and report. Acta Geodaetica et Cartographica Sinica 38(1), 1–5 (2009) 9. Zheng, J.: Design of general aviation emergency communication, surveillance and rescue service system based on RDSS. Modern Navig. 1, 1–5 (2016)

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10. Xing, N., Su, R., Zhou, J., et al.: Analysis of RDSS positioning accuracy based on RNSS wide area differential technique. Sci. China Phys. Mech. Astron. 56(10), 1995–2001 (2013) 11. Zhan, J., Pang, J., Zhang, G., Ou, G.: Modeling and simulation testing of RDSS timing. Sci. Sin. Phys. Mech. Astron. 41(5), 620–628 (2011) 12. Zheng, C., Li, D., Wang, X., Zhang, J.: A motion based method and emulation of RDSS integer ambiguity. J. Geom. Sci. Technol. 27(3), 169–175 (2010) 13. Yuan, Y., Huang, J., Wu, P.: A Beidou RDSS positioning model and its error analysis without elevation. J. Navig. Posit. 2(3), 15 (2014) 14. Liu, Y., Liu, G., Chen, X., Hao, X., Shi, B., Hu, X.: Discussion on adding RDSS to IGSO satellite in 2nd generation Beidou navigation satellite system. J. Geodesy Geodyn. 32(3), 72–75 (2012) 15. Jiao, C., Dou, C., Fan, J., Liu, F.: Tri-satellite quick positioning algorithm based on generalized RNSS/RDSS system. J. Ordnance Equip. Eng. 2016(8), 105–108 (2016) 16. Yuan, Y., Huang, J., Tao, J.: A Beidou RDSS positioning model and its error analysis without elevation. Comput. Appl. Softw. 34(3), 114–118 (2017) 17. Zhao, J., Qu, J., Yuan, H.: A new ambiguity resolution method using combined RNSSRDSS of Beidou. Acta Geodaetica et Cartographica Sinica 45(4), 404–410 (2016) 18. Scott, J., Hoy, M.: Group delay measurement of frequency converting devices using a comb generator. IEEE Trans. Instrum. Measur. 59(11), 3012–3017 (2010) 19. Rashidzadeh, R.: An all-digital self-calibration method for a venire-based time-to-digital converter. IEEE Trans. Instrum. Measur. 59(2), 463–469 (2010) 20. Cui, X., Bi, S., Zhong, Z., Liu, T., Wang, J.: Delay measurement of RDSS channel based on digital receiver. J. Test Measur. Technol. 28(1), 1–6 (2014) 21. Pang, J., Zhang, Y., Zhan, J., Ou, G.: Research on key techniques of the Beidou RDSS receiver test system. J. Astronaut. Metrol. Measur. 36(4), 95–100 (2016) 22. Chen, X., Tan, Z.: Testing and evaluation of the testing system for compass user terminals. J. Inf. Eng. Univ. 16(3), 318–320 (2015) 23. Cui, X., Li, Y., Cong, F., Si, D., Wang, Q.: Delay measurement of RDSS channel using correlation between input and output signal. J. China Univ. Metrol. 25(1), 22–27 (2014) 24. Liang, G.: Research on EIRP calibration method of RDSS closed-loop test system. Fore. Electron. Measur. Technol. 36(5), 18–20 (2017)

Research on the Influence of Pseudo-range Biases on Precise Orbit Determination and Clock Error Calculation for Beidou Navigation Satellites Chengeng Su1, Gong Zhang2(&), and Jun Lu1 1

Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China 2 Institute of Telecommunication and Navigation, CAST, Beijing 100094, China

Abstract. Pseudo-range bias refers to the constant measurement deviation caused by the non-ideal characteristics of satellite navigation signals in different technical states receivers. Pseudo-range bias is not expressed by the existing navigation parameters, so it becomes a new error source affecting navigation service and GNSS precision data processing. In this paper, the calibration method of pseudo-range bias is given, and pseudo-range biases of Beidou and GPS signals are measured. The measurement of navigation signal shows that the pseudo-range biases of Beidou B1 and GPS L1 are about 0.4–0.8 m, while those of Beidou B2/B3 and GPS L2/L5 are about 0.16–0.4 m. On this base, this paper analyzes the influence of pseudo-range error on precise orbit determination and clock bias calculation of Beidou navigation satellite. The results show that the orbit calculation of Beidou IGSO and MEO satellites is not sensitive to the pseudo-range bias, and the existence of pseudo-range bias only causes the change of orbits in centimeter level for Beidou IGSO and MEO satellite. The influence of pseudo-range bias on the three directions of Beidou GEO satellite is quite different. The pseudo-range bias results in centimeter error in radial and normal direction, and several meters deviation in tangential direction in satelliteto-earth orbit determination mode. Satellite clock error is sensitive to pseudorange bias. Pseudo-range error does not lead to the variation of satellite clock error with time, but it will lead to constant deviation of satellite clock error. In view of the above results, it is suggested that pseudo-range bias can be used as a new error source for GNSS precision data processing, and its effects on precise orbit determination and clock bias calculation could be fully considered. Keywords: BDS calculation


Pseudo-range biases
Orbit determination
Clock error

1 Overviews High precision orbit and clock error parameters are the important premise of positioning, navigation and timing services [1]. The orbit and clock error determination of navigation satellite is generally based on statistical methods, and the measurement © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 492–501, 2021. https://doi.org/10.1007/978-981-16-3138-2_46

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model error is the key factor affecting the precision of orbit and clock error determination [2]. The measurement models for precise orbit determination and clock error calculation of navigation satellites generally include satellite antenna phase center deviation, variation and phase winding, ionospheric delay, tropospheric delay, receiver phase center deviation and variation, pseudo-range carrier measurement multipath noise [3–6]. Among them, the satellite antenna phase center deviation, variation and phase winding, ionospheric delay, tropospheric delay, receiver phase center deviation and variation can be accurately modeled or calibrated in advance, and the impact of the error on satellite precise orbit determination and clock error solution can be controlled in a negligible range. This paper focuses on a widely ignored measurement model error, which is called pseudo-range bias, and analyzes and evaluates its influence on precision orbit determination and clock error calculation. Pseudo-range bias is the constant deviation of pseudo-range measurement caused by the non-ideal characteristics of satellite navigation signals. The pseudo-range bias was first found in 1993. The downlink signal of svn19 in GPS blockII satellite is abnormal, and different types of receiver pseudo-range measurement have different deviations, resulting in a significant decline in the accuracy of user differential positioning [7]. References [8–10] show that even if the GPS satellites are in a healthy state, there are pseudo-range biases in the measurement of the satellite navigation signals, which are important errors affecting the service performance of SBAS. In the references [11, 12], different types of receivers are set as zero baselines to study the phenomenon of satellite pseudo-range biases. The results show that the downlink navigation signals of GPS, GLONASS, Galileo and Beidou satellites all have pseudo-range deviation. Stanford University has made an analysis on the pseudo-range deviation of GPS satellite caused by non-ideal characteristics of navigation signals. The results show that the pseudo-range deviations are related to the correlation interval of the receivers. The larger the correlation intervals are, the greater the pseudo-range deviations caused by signal distortion are. The average pseudo-range deviations caused by the receiver correlation interval of 0.1–1.0 code slice are 0.3 m, and the average pseudo-range deviations caused by the receiver correlation interval of 0.1–0.2 code slice are 0.15 m. Reference [13] studies the influence of pseudo-range biases on the positioning error of WAAS users. For single frequency users, the ionosphere is the main error, and the influence of pseudo-range deviation is relatively small; for dual frequency or multi frequency users, the ionospheric combination scale factor can amplify the pseudo-range bias, and the pseudo-range bias becomes an important error of dual frequency combination observation, and it is proposed to limit the correlation distance of user receiver, which avoid the significant degradation of dual frequency user positioning performance. The German DLR team has also done researches on the pseudo-range biases of GPS and Galileo navigation satellites. The magnitude of the pseudo-range biases are closely related to the correlator interval of the receiver and the anti-multipath algorithm. The pseudo range bias of GPS L1C/A signal is greater than P(Y) code, and the pseudo-range biases of all Galileo signals are significantly less than GPS. Reference [14] analysed the mechanism of pseudo-range bias of Beidou satellite, gave the relationship between the pseudo-range bias of B1I and B3I signals and the parameters of receiver correlator, and put forward the setting suggestions of correlator spacing and front-end bandwidth in Beidou user receiver.

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2 Definition and Calibration Results of Pseudo-range Bias 2.1

Pseudo-range Bias Definition

The non-ideal characteristics of the entire transmission channel will cause signal distortion, due to the factors such as satellite frequency resources, device technology, atmosphere and user reception environment. When the user receives the satellite navigation signal for correlation operation, the correlation function will undergo nonlinear distortion, which will cause the asymmetry of the correlation curve, resulting in the deviation of the lock point of the phase discrimination curve of the code tracking loop, and eventually lead to the ranging error. Due to the non-ideal characteristics of the downlink navigation signal, different types of receivers produce constant deviations of different sizes and signs for downlink navigation signal from the same satellite, which is called pseudo-range bias. The pseudo-range bias is related to the front-end filter bandwidth, correlator interval and anti-multipath algorithm of the receiver. Due to the different non-ideal characteristics of different satellite downlink navigation signals and the different states of monitoring receivers and user receivers, pseudo-range bias can not be completely eliminated, nor can it be expressed by existing navigation message parameters. It is a new error source that affects the accuracy of ground processing and user positioning and timing service of navigation system, so it is necessary to evaluate its impact on navigation system. 2.2

Pseudo-range Bias Calibration Algorithm

The analysis and calibration of pseudo-range bias can be adopted by using two different types of receivers deployed with short baseline or zero baseline to calculate the pseudorange bias. The specific method is as follows. If the two receivers R1 and R2 are externally connected with the same frequency signal, and the distance between them is not more than 20 m. the downlink navigation signal at a certain frequency point to be measured is DGNSS, the pseudo range observation equation of satellite I by the two receivers is shown in Eq. (1). Taking the receiver R1 as an example, Pir1 is the pseudo-range observation value, i qr1 is the satellite ground distance calculated by the prediction ephemeris, orbeir1 is the projection of the prediction ephemeris error in the satellite ground direction, dtr1 is the GNSS receiver clock error, dti is the satellite clock error, c is the speed of light, DCBD is r1 DGNSS is the satellite code the receiver code deviation parameter of DGNSS signal, DCBi i is the total electron content of oblique deviation parameter of DGNSS signal, TECr1 i i path, f1 is the frequency point frequency of DGNSS signal, TECr1 =f12 and Tr1 are ionospheric delay and tropospheric delay, relir1 is relativistic period term, air1 is pseudorange measurement error of receiver R1, eir1 is pseudo-range multipath error and noise. Receiver R2 is similar. Since the distance between the two receivers is less than 20 m and the same frequency signal is externally connected, the influence of satellite ephemeris error, satellite clock error, ionospheric delay, tropospheric delay and receiver clock error on pseudo-range measurement for the receiver R1 and R2 is the same. When R1 and R2

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are used for differential processing of pseudo-range observation of satellite I, the mathematical expectation only includes the difference between pseudo-range bias and code bias parameters of R1 and R2 for satellite I (code bias is constant in several days), as shown in Eq. (2). GNSS GNSS Pir1 ðDGNSS Þ ¼ qir1 þ c  ðdtr1  dti Þ þ c  ðDCBD þ DCBD Þ i r1

þ

i TECr1 i þ Tr1 þ relir1 þ orbeir1 þ air1 ðDGNSS Þ þ eir1 f12

GNSS GNSS Pir2 ðDGNSS Þ ¼ qir2 þ c  ðdtr2  dti Þ þ c  ðDCBD þ DCBD Þ i r2

þ

i TECr2 i þ Tr2 þ relir2 þ orbeir2 þ air2 ðDGNSS Þ þ eir2 f12

i i GNSS E[rOCr1r2 ðDGNSS Þ ¼ c  dDCBD r1r2 þ dar1r2 ðDGNSS Þ DGNSS GNSS GNSS dDCBD  DCBD ; dair1r2 ðDGNSS Þ ¼ air1 ðDGNSS Þ  air2 ðDGNSS Þ r1r2 ¼DCBr1 r2

2.3

ð1Þ

ð2Þ

Pseudo-range Bias Measurement Results

BeiDou Navigation Satellite System (BDS) broadcasts four kinds of civil navigation signals in B1, B2 and B3 frequency bands, including B1I, B3I, B1C and B2A. Among them, B1I and B3I are the original signals of BDS, and B1C and B2A are the new signals of beidou-3. The pseudo-range biases measurement results of some Beidou satellites obtained by the double difference method of collocated receivers are shown in Fig. 1. It can be seen from the figure that the pseudo-range bias of new signal B2A of Beidou-3 is the smallest, about 10 cm. At frequency B1, the pseudo-range biases of new signal B1C of Beidou-3 is obviously better than that of original signal B1I. The pseudo-range observation data of GPS L1 C/A, L2C and L5 navigation signals are processed by the same method, and the pseudo-range biases are calculated. Taking the navigation signals of BDS-3 B1I, B3I, B1C, B2a. and GPS L1 C/A, L2C, L5 as the objects, the maximum and minimum pseudo-range deviations of each signal are compared, and the results are shown in Fig. 2. It can be seen from the figure that the pseudo range biases of B1 (L1) band at 1575.42 MHz center frequency point is larger than that of other bands, among which the pseudo-range bias of BDS-3 B1I and GPS L1 C/A signal are at the same level, about 0.8 m. The pseudo-range bias of beidou-3 new signal B1C is the smallest, about 0.4 m, which is also much better than that of GPS L1 C/A. In other frequency bands, the B2a pseudo-range bias of Beidou-3 new signal is the smallest, which is better than that of GPS L5 signal. With the development of BDS, the quality of new signals is improved, and the pseudo-range biases are greatly reduced.

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Fig. 1. Pseudo-range biases comparison of Beidou satellite signals at different frequency points

Fig. 2. Pseudo-range biases comparison of Beidou satellite and GPS Satellite signals at different frequency points

3 Influence of Pseudo-range Bias on the Calculation of Beidou Satellite Orbit and Clock Error 3.1

Calculation Strategies of Orbit and Clock Error

The orbit determination of Beidou satellites includes two methods: satellite-to-ground link orbit determination and the joint orbit determination with satellite-to-ground and inter-satellite data. The satellite-to-ground link orbit determination uses the pseudorange phase data of regional monitoring stations, while the joint orbit determination adds high precision inter-satellite link measurement data. The calculation strategies of the two methods are shown in Table 1. It can be seen from the table that the influence of pseudo-range deviation is not fully considered in the current Beidou satellite orbit and clock error calculation, and it is not taken as the error source of data processing.

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Table 1. Beidou satellites orbit determination strategies Satellite-to-ground link orbit determination Orbit determination arc Measurement data

Dynamical models Solar radiation pressure model parameters Tropospheric parameters Satellite antenna phase deviation Clock error processing Pseudo-range and phase weights

3.2

Satellite-to-ground and intersatellite link joint orbit determination

3Days Non difference ionospheric combined pseudo-range phase data from regional monitoring station and inter-satellite bidirectional ranging data Two-body motion, Earth's non-spherical gravity, Sun-Moon gravity, Solar radiation pressure, Solid tides and tidal uptake Five parameters

Non difference ionospheric combined pseudo-range phase data from regional monitoring station

2 h to solve one group PCO Differential solving Helmert variance component estimation

Influence of Pseudo-range Bias on Orbit Determination of SatelliteTo-Earth Orbit Determination

In order to analysed the influence of pseudo-range bias on navigation system, two groups of monitoring receivers R1 and R2 with different technical status were used to carry out special experiments. The influence of pseudo-range biases on orbit and clock error calculation results of three types of satellites in BDS was obtained. The influence of pseudo-range biases on orbit deviation of satellite-to-earth orbit determination for Beidou satellites are shown in Fig. 3. It can be seen from the figure that the pseudo-range biases cause obvious constant deviation for all satellite clock error solutions. The fluctuation of the deviation is not more than 0.3 ns, and the maximum mean deviation is −7.43 ns. The overlapping arc method is used for statistics. The influence of pseudo-range biases on orbit deviation of satellite-to-earth orbit determination for Beidou satellites are shown in Fig. 4. It can be seen from the figure that the radial and normal deviation caused by pseudo-range biases for three kinds of satellite orbit determination is small, but the tangential deviation caused by pseudo-range biases for GEO satellite orbit determination is large. The influence of pseudo-range biases on orbit and clock error calculation for Beidou satellites using satellite-to-earth orbit determination are shown in Table 2.

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Fig. 3. Influence of Pseudo-range biases on clock error of satellite-to-earth orbit determination for Beidou satellites

(a) MEO

(b) IGSO

(c) GEO

Fig. 4. Influence of Pseudo-range biases on orbit deviation of satellite-to-earth orbit determination for Beidou satellites

Table 2. Influence of pseudo-range biases on orbit and clock error calculation for Beidou satellites using satellite-to-earth orbit determination Beidou satellites Orbit error (m) R T N MEO 0.012 0.194 0.032 IGSO 0.022 0.138 0.114 GEO 0.011 5.635 0.107

3.3

Clock error (ns) 3D 0.203 3.82 0.182 4.74 5.636 4.79

Influence of Pseudo-range Bias on Orbit Determination of SatelliteTo-Satellite Orbit Determination

The same method is used to evaluate the influence of pseudo-range biases on orbit and clock error calculation results of three types of satellites in BDS. The orbit and clock error calculation of three types of satellites adopts the joint orbit determination with satellite-to-ground and inter-satellite link data. Beidou-3 satellites are equipped with inter satellite link, the influence of pseudo-range biases on the results of joint orbit determination is discussed only for beidou-3 satellites.

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Fig. 5. Influence of Pseudo-range biases on clock error of satellite-to-satellite orbit determination for Beidou satellites

The influence of Pseudo-range biases on clock error of satellite-to-satellite orbit determination for Beidou satellites is shown in Fig. 5. It can be seen that the pseudorange biases cause obvious constant deviation for all satellite. The fluctuation of the deviation is not more than 0.3 ns, and the maximum mean deviation is −7.47 ns. The influence of pseudo-range biases on orbit deviation of satellite-to-satellite orbit determination for Beidou satellites is shown in Fig. 6. The influence of pseudo-range biases on the orbit determination of MEO satellite can reach 0.203 m only in the satellite-toground link orbit determination mode, while it can be reduced to 0.01 m in the joint orbit determination mode. In addition, in satellite-to-earth orbit determination mode, the tangential error of pseudo-range bias to GEO satellite orbit can reach about 5.6 m, while in the joint orbit determination mode, the tangential error can be reduced to about 0.02 m.

(a) MEO

(b) IGSO

(c) GEO

Fig. 6. Influence of Pseudo-range biases on orbit deviation of satellite-to-satellite orbit determination for Beidou satellites

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Table 3. Influence of pseudo-range biases on orbit and clock error calculation for Beidou satellites using satellite-to-satellite orbit determination Beidou satellites Orbit error (m) R T N BDS-3 MEO 0.001 0.007 0.007 BDS-3 IGSO 0.015 0.076 0.065 BDS-3 GEO 0.001 0.018 0.003

Clock error (ns) 3D 0.010 4.00 0.101 4.76 0.018 3.94

It can be seen that the inter-satellite link data can greatly reduce the impact of pseudo-range biases on precise orbit determination of MEO and GEO satellites. Table 3 shows the influence of pseudo-range biases on orbit and clock error calculation for Beidou satellites using satellite-to-satellite orbit determination. In the operation of BDS, the ground segment unifies the technical status of the monitoring receivers participating in orbit determination and clock error calculation, so that the influence of pseudo range biases is avoided and the accuracy of the orbit and clock error is significantly improved.

4 Conclusions and Suggestions This paper systematically analyzes the calibration algorithm of pseudo-range bias and completes quantitative calibration for Beidou and GPS satellites. The pseudo-range bias is used as a new error source to evaluate its impact on precise orbit determination and clock error calculation of Beidou satellites. The results are as follows. The orbit calculation of Beidou IGSO and MEO satellite is less affected by the pseudo-range bias, while the GEO satellite has a meter level or even ten meter level deviation in the tangential direction in satellite-to-earth orbit determination mode. The orbit calculation of Beidou three types satellite is less affected by the pseudo-range bias in joint orbit determination mode. Satellite clock error is sensitive to pseudo-range bias, which will lead to constant error in satellite clock error solution. For the high-precision data processing of navigation satellite, it is suggested that the technical status of the receivers involved in the calculation should be consistent, so as to avoid the pseudo-range biases among receivers as far as possible, and avoid the influence of the pseudo-range biases on the precise orbit determination and clock error calculation.

References 1. Teunissen, P.J.G., Montenbruck, O. (eds.): Springer Handbook of Global Navigation Satellite Systems. SH, Springer, Cham (2017). https://doi.org/10.1007/978-3-319-42928-1 2. Montenbruck, O., Steigenberger, P., Hauschild, A.: Broadcast versus precise ephemerides: a multi-GNSS perspective. GPS Solut. 19(2), 321–333 (2015) 3. Chen, J., Hu, X., Tang, C., et al.: SIS accuracy and service performance of the BDS-3 basic system[J]. Sci. China-Phys. Mech. Astron. 63(6), 1–12 (2020)

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4. Li, R., Cao, Y., Hu, X., et al.: Analysis of the wide area differential correction for BeiDou global satellite navigation system. Res. Astron. Astrophys. 18(11) (2018) 5. Steigenberger, P., Montenbruck, O.: Galileo status: orbits, clocks, and positioning. GPS Solut. 21(2), 319–331 (2017) 6. Binghao, W., Jianhua, Z., et al.: Influence of the GEO satellite orbit error fluctuation correction on the BDS WADS zone correction. Satell. Navig. 1(1), 18 (2020) 7. Phelts, R.E., Akos, D.M., Enge, P.: Robust signal quality monitoring and detection of evil waveforms. In: Proceedings of the ION NTM 2000, Institute of Navigation, Anaheim, CA, 26–28 January 2000, pp. 1180–1190 (2000) 8. Wong, G., Phelts, R.E., Walter, T., Enge, P.: Characterization of signal deformations for GPS and WAAS satellites. In: Proceedings of the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2010), Portland, OR, September 2010, pp. 3143–3151 (2010) 9. Wong, G., Chen, Y.-H., Phelts, R.E., Walter, T., Enge, P.: Measuring code-phase differences due to inter-satellite hardware differences. In: Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 2150–2158 (2012) 10. Wong, G., Phelts, R.E., Walter, T., Enge, P.: Bounding errors caused by nominal GNSS signal deformations. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 2657–2664 11. Hauschild, A., Montenbruck, O.: The effect of correlator and front-end design on GNSS pseudorange biases for geodetic receivers. Navigation 63(4), 443–453 (2016) 12. Hauschild, A., Montenbruck, O.: A study on the dependency of GNSS pseudorange biases on correlator spacing. GPS Solut. 20(2), 159–171 (2016) 13. Wong, G., Chen, Y.-H., Phelts, R.E., Walter, T., Enge, P.: Mitigation of nominal signal deformations on dual-frequency WAAS position errors. In: Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation, Tampa, Florida, September 2014, pp. 3129–3147 (2014) 14. He, C., Lu, X., et al.: Initial analysis for characterizing and mitigating the pseudorange biases of BeiDou navigation satellite system. Satell. Navig. 1(1), 3 (2020)

Satellite Laser Links Pointing Accuracy Analysis Methods Zheng Song(&), Ping Wang, Chengbin Kang, Jianxin Guo, and Huichao Zhou China Academy of Space Technology, 100094 Beijing, China

Abstract. Due to the small scattering angle of the laser beam at the transmitting end and the small captured field of view at the receiving end of the laser intersatellite equipment, the pointing accuracy of the laser inter-satellite is the key to the successful laser link building. The uncertain area of the laser capture field of view is closely related to the laser pointing error. It is necessary to analyze the various factors that cause the laser pointing error in the satellite system and their effects on the acquisition and tracking. In this paper, the error sources affecting the laser pointing accuracy are analyzed firstly, including the error of laser terminal equipment itself, the error of satellite attitude control, the error of satellite structure installation, the error of time and the error of orbit ephemeris. Then, the satellite three-axis error comprehensive calculation method is used to model all kinds of errors, and the comprehensive evaluation of the influence of errors on pointing accuracy is given, which solves the problem of accurate evaluation of uncertain area of field of view captured by inter-satellite laser link. Finally, based on the simulation study, the adaptability analysis of the satellitebased realization of the laser inter-satellite link is carried out, which provides the design basis for the engineering realizability. Keywords: Satellite laser links


Pointing accuracy
Error analysis

1 Introduction Due to the small scattering angle of the laser beam at the transmitting end and the small captured field of view at the receiving end of the laser inter-satellite equipment, the pointing accuracy of the laser inter-satellite is the key to the successful laser chain building. The angle range of the laser pointing error is called the capture field-of-view uncertainty region. The uncertain area of the laser capture field of view is closely related to the laser pointing error. It is necessary to analyze the various factors that cause the laser pointing error in the satellite system and their effects on the acquisition and tracking. It is difficult to determine the uncertain region of laser link capture field of view (FOV) in the design of satellite-borne laser link, and it is also a key index that affects the design state of inter-satellite laser link. Although the laser terminal pointing error was analyzed in literature [1] and [2], only the errors of pitching axis and azimuth axis were analyzed respectively, and the triaxial synthesis error was not considered. The accuracy analysis method mentioned in Literature [3] simply calculated pointing errors by statistical square tolerance method (RSS), and the error classification was not © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 502–510, 2021. https://doi.org/10.1007/978-981-16-3138-2_47

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refined enough. Although references [4] and [5] considered the factors of satellite triaxial synthesis, the paper discussed the antenna error and did not analyze the error according to the characteristics of the laser terminal. Therefore, it is necessary to analyze the pointing error of laser inter-satellite link based on the influence of the attitude error of satellite three-axis. This paper presents a method for analyzing and calculating the pointing error model of inter-satellite laser link, which solves the problem of capturing uncertain area of field of view by laser link. This method from the Angle of view of the satellite system, analysis of various error sources affecting the precision of laser alignment, include laser terminal itself, satellite attitude errors, satellite structure and installation error and so on three types of inherent error sources, control calculation of laser alignment also introduced the ephemeris error, rounding error, software calculation information transmission time delay error and other factors. The errors were classified according to the constant error, the error related to the orbital period change and the short-term random error, and the error modeling was carried out based on the satellite three-axis attitude error synthesis algorithm, and the error model data were matched with the engineering results. The simulation analysis of the attitude disturbance caused by the satellite platform provides a powerful design and analysis basis for the high precision pointing control of the very narrow beam laser link between satellites.

2 Definitions 2.1

Laser Target Pointing Angle

As shown in Fig. 1, the satellite coordinate system is defined as O-XYZ. According to the convention, the origin of the coordinate system is the center of mass of the satellite; +Z axis is the yaw axis of the satellite, pointing to the center of the earth; +X axis is the rolling axis of the satellite, perpendicular to +Z axis, pointing to the motion direction of the satellite; Y axis is perpendicular to X axis and Z axis, forming a right-handed system. In the satellite coordinate system, the target pointing vector OP of the laser can be expressed by the target pointing angles h and /, where, h: Target pointing elevation angle, the angle between laser target pointing vector OP and satellite coordinate system +Z axis. The theoretical range is [0°, 90°]. /: Target pointing azimuth angle, the projection of the laser target pointing vector OP in the XOY plane of the satellite coordinate system and the included angle of the satellite coordinate system +X axis. Direction is specified by the right hand screw rule. The theoretical range is [−180°, 180°). The coordinate of the laser target pointing vector in the satellite coordinate system is: rOP

0 1 0 1 x sin h cos / ¼ @ y A ¼ @ sin h sin / A z cos h

ð1Þ

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Laser Pointing Error Angle

Laser pointing error angle: The angle De between the actual pointing direction of the laser beam OP’ and the pointing direction OP, as shown in Fig. 1.

Z P P’

θ

Δε

O

Y

φ X

Fig. 1. Laser target pointing angle and error angle

2.3

Laser Pointing Accuracy

For the emitting end, the maximum laser pointing error Angle is defined as the laser pointing accuracy. For the receiver, the maximum of the laser pointing error Angle is defined as the capturing uncertain area of the field of view. Therefore, pointing accuracy of laser and capturing uncertain area of field of view are different expressions of the influence of laser pointing error on both ends of laser transceiver and receiver.

3 Laser Pointing Error Source Analysis Laser pointing error sources include three kinds of inherent error sources: the error of laser terminal itself, the error of satellite attitude control, and the error of satellite structure and installation. In addition, factors such as orbit error, rounding error, and time error caused by the delay of information transmission by software will be introduced into the inter-satellite laser pointing calculation process. These error sources will affect the pointing accuracy and the size of the captured uncertain area of the field of view. According to the variation law of laser pointing error, it can be divided into constant error, periodic error related to orbital period and short-term random error. For accurate analysis, the errors need to be factored into the satellite’s roll, pitch, and yaw attitudes.

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Laser Terminal Error Sources

The error source of laser terminal itself mainly considers the thermal deformation of optical antenna, assembly error, structural deformation, installation accuracy, as well as the control accuracy of coarse pointing assembly (CPA) and fine pointing assembly (FPA). The errors of the laser terminal itself are shown in Table 1 below. Table 1. Laser terminal device error Items Optical antenna thermal deformation accuracy Optical antenna assembly accuracy Optical antenna structure deformation accuracy Optical antenna installation accuracy

FPA control accuracy CPA control accuracy

Specific items Transceiver channel main structure Main structure of optical antenna CPA nonorthogonality Optical assembly Structural stress release deformation Ground gravity deformation X axis Y axis Z axis Azimuth axis Elevation axis Azimuth axis Elevation axis

Errors

@LIF j j > > ¼ ¼ ððU T
! H eA ÞT13 013 1 0 015 I1m Þ < A @XA > @L j > j > : HRj ¼ AB ¼ ððU T
! eB ÞT13 013 1 0 015 I1n Þ @XR

ð5Þ

Where, U T is transfer matrix from inertial system to conventional terrestrial system; j and ! eB are unit sight vector quantity from satellite A and B to satellite j, respectively; I1m and I1n are 1  m and 1  n dimension vector, respectively; Among I1m and I1n ,the channel of satellite j is 1,while the others are 0.

j ! eA

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The EKF model of RTPOD can be expressed as following: 

Xk ¼ Uk;k1 Xk1 þ Wk1 Zk ¼ Hk Xk1 þ Vk

ð6Þ

Where, Xk and Zk are state vector and observation vector in EKF model, respectively; Uk;k1 is state transition matrix and its associated derivation formula refer to [12] and [13] for PAOD and PROD, respectively; Hk is design matrix; Wk1 and Vk are system noise and observation noise, respectively.

3 Simulation Scenarios and RTPOD Strategy 3.1

Simulation Scenarios

Due to the lack of space-borne BDS-3 measurements, the GNSS Hardware-In-the-Loop simulation system of differential InSAR formation satellites, composed of a Spirent GSS9000 Multi-GNSS, two GNSS receivers and a ground test equipment, is built on the ground to test the RTPOD algorithm. The schematic diagram of the system is shown in Fig. 1. The GNSS receivers, which can work in GPS or BDS-3 mode with 12 tracking channels, are independently developed by Beijing Research Institute of Telemetry. The GPS/BDS-3 pseudo range and carrier phase measurement errors are better than 30 cm and 2 mm, respectively.

Fig. 1. Schematic diagram of differential InSAR GNSS HIL simulation system

In the GNSS HIL simulation system, the GNSS simulate signals can be tracked by the GNSS receivers, In order to simulate the inter satellite link to interact with the GNSS raw data in real-time, a straight-through cable is used on the ground. Then the RTPOD is completed in the embedded system of the GNSS receiver, and RTPOD results are received and stored by ground test equipment. According to the baseline length, this paper designs three simulation scenarios of A-B1, A-B2 and A-B3 with inter satellite distances of 1 km, 50 km and 200 km, respectively. The satellite A and satellite B1, B2, B3 are as the master and slave

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satellite, respectively. The average orbit heights of differential InSAR satellites are about 515 km. The initial orbit parameters of each satellite are listed in Table 1. Table 1. Initial orbit parameters of differential InSAR satellites Parameter Semi-major axis (km) Inclination (deg) Right ascension (deg) Eccentricity Mean anomaly (deg) Argument of perigee (deg)

A 6893.134 97.44 0.00 0.001 0.00 0.00

B1 6893.134 97.44 0.00 0.001 0.0083 0.00

B2 6893.134 97.44 0.00 0.001 0.4156 0.00

B3 6893.134 97.44 0.00 0.001 1.662 0.00

In order to ensure the simulation scenarios as close as possible to the real situation, the real BDS-3/GPS ephemeris are downloaded from websites. The BDS-3 constellation has a total of 30 satellites including 3 GEO, 3 IGSO and 24 MEO satellites, while the GPS constellation has a total of 32 MEO satellites. The tests are repeated every simulation scenario according to the GPS or BDS-3 mode. 3.2

RTPOD Strategy

The processing scheme for the RTPOD (including PAOD and PROD) is shown in Fig. 2. All the strategies and settings of RTPOD are listed in Table 2. Firstly, the GPS/BDS-3 observations are pre-processed at the beginning, then the PAOD and PROD filters are started by using the results of Single Point Positioning (SPP) and Real-Time Differential (RTD) pseudo range, respectively. Then the time update and measurement update processes of PAOD and PROD are completed in turn. Finally, the RTPOD results are output through orbit prediction and interpolation. The updating process is completed by time-sharing and multi-step and the computation time of each step is less than 100 ms in the receiver. Before the measurement update of PROD, when the baseline is larger than 5 km, the SD float solution mode is adopted, otherwise, using the Double Difference (DD) fixed solution. In order to reduce the calculation time, the LAMBDA method is used to solve only the DD Integer ambiguity of GPS/BDS-3 single-frequency data, and then the DD Integer Ambiguity Resolution(IAR) is used as “observed” to update the SD ambiguity and its covariance [5, 13].

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Fig. 2. The processing scheme for the RTPOD of differential InSAR satellites Table 2. Strategies and settings of RTPOD Model/Parameter GNSS observation data Cycle slip detection EOP parameters Earth Gravity Field Luni-solar gravitation Earth tides Atmosphere Drag Solar radiation pressure Empirical acceleration Ambiguity estimation Estimator Update interval

Relevant setting PAOD: GPS/BDS-3 UD observations, PROD: GPS/BDS-3 SD/UD observations MW and GF combination Rapid predicted EOP in IERS Bulletin A EGM2008 70  70 Moon and Sun’s position are computed via analytic method [12] Low precision model, solid only Modified Harris-Priester model, fixed effective area, estimates Cd and dCd [13] Cannonball model, fixed effective area, estimates Cr and dCr Dynamic Model Compensation (DMC) with a first-order Gauss Markov model PAOD: UD Pseudo-Ambiguity, with separation and absorption of broadcast ephemeris error [14], PROD:SD float ambiguities, DD-IAR (baseline 0 0.013 > 0 0.006 > 0

Finally, the second-order Volterra adaptive prediction algorithm was used to predict the ERP residuals respectively, and the final prediction results were obtained by adding the residuals and LS extrapolation values. At the same time, the effects of zonal Earth tides should be removed to get the LODR series. MAE was used to evaluate the accuracy of the results of each period, and then the average value was taken as the final prediction accuracy. Some results are shown in Table 2. Table 2. MAE statistical table of this method Forecast span/d LOD/ms 1 0.033 3 0.055 5 0.072 7 0.089 9 0.101 12 0.113 15 0.126 18 0.136 21 0.146 25 0.154 30 0.162

Xp/mas 0.482 0.940 1.349 1.678 1.987 2.464 2.904 3.336 3.770 4.322 4.995

Yp/mas 0.299 0.579 0.799 0.988 1.162 1.436 1.614 1.957 2.219 2.566 3.005

In order to further verify the experimental results, Contrast the results drawn in this paper with EOP PCC. Literature [4] provided the specific information and results of each participating group in this comparison activity. Since the result of EOP PCC is given in the form of graph, this paper only compares it with MAE statistical graph of forecast results. As shown in the figure below, Figs. 2, 3 and 4 show the comparison effect between the method in this paper and the EOP PCC results. The left figure represents the EOP PCC results, and the right figure is the forecast results in this paper. Compared with the forecast results of EOP PCC, it shows that the prediction accuracy of the two components of LOD and PM of this method is improved. As shown in Fig. 2, for LOD, the highest accuracy of EOP PCC within 30 days is the result of Gross’s group, and the MAE within 30 days is between 0.2 ms and 0.25 ms, while the method in this paper is only 0.162 ms, indicating a significant improvement inaccuracy. For the PM, the optimal results of EOP PCC are all the combined prediction results represented by Cp, and its value represents the weighted combination of

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each group. As shown in Fig. 3, the prediction accuracy of Xp component by the proposed method is the most obvious. At the 30th day, the prediction accuracy of the proposed method is 4.995 mas, which is more than 35% higher than that of EOP PCC at about 8 mas. For the prediction of Yp component in Fig. 4, the result of the method in this paper is 3.005 mas on the 30th day, and the prediction error is also greatly reduced. Through the analysis of the example, it can be proved that the method proposed in this paper is quite feasible. And compared with the short-term prediction results of 30d in EOP PCC, the prediction accuracy of the method proposed in this paper is higher. The method proposed in this paper can be used as a reference for future ERP forecast work.

Fig. 2. Comparison of the forecast results of LOD

Fig. 3. Comparison of the forecast results of Xp

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Fig. 4. Comparison of the forecast results of Yp

4 Conclusion Considering the chaotic characteristics of ERP time series, we combined LS fitting extrapolation, phase space reconstruction and second order Volterra adaptive prediction algorithm to forecast ERP time series by making full use of Volterra series’ fitting and approximation ability to nonlinear time series. Experimental results show that this method has higher prediction accuracy than EOP PCC short-term prediction results. And this method can provide a new idea and scheme for future ERP prediction.

References 1. Modiri, S., Belda, S., Hoseini, M., et al.: A new hybrid method to improve the ultra-shortterm prediction of LOD. J. Geodesy 94(23), 1–14 (2020) 2. Yao, Y., Yang, Y., Sun, H., et al.: Geodesy discipline: progress and perspective. Acta Geodaetica et Cartographica Sin. 49(10), 1243–1251 (2020) 3. Xu, X., Zotov, L., Zhou, Y.: Combined prediction of earth orientation parameters. In: China satellite Navigation Conference (CSNC) 2012 Proceedings, [Part 2]: 3rd China Satellite Navigation Conference (CSNC 2012), 15–19 May 2012, pp. 361–369, Guangzhou, China (2012). http://doi.org/10.1007/978-3-642-29175-3-32 4. Kalarus, M., Schuh, R., Kosek, R., et al.: Achievements of the earth orientation parameters prediction comparison campaign. J. Geodesy 84(10), 587–596 (2010) 5. Schuh, H., Ulrich, M., Egger, D., et al.: Prediction of earth orientation parameters by artificial neural networks. J. Geodesy 76(5), 247–258 (2002) 6. Xu, X., Zhou, Y: High precision prediction method of earth orientation parameters. J. Spacecraft TT&C Technol. 02, 74–80 (2010) 7. Jia, S., Xu, T., et al.: Middle and long-term prediction of UT1-UTC based on combination of gray model and autoregressive integrated moving average. Adv. Space Res. 59, 888–894 (2017)

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8. Sun, Z., Xu, T.: Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model. Geodesy Geodyn. 3(03), 57–64 (2012) 9. Yibin, Y., Shunqiang, Y., Peng, C.: A new LS + AR model for additional error correction for polar motion prediction. Sci. Sin. Terrae 43(04), 665–676 (2013) 10. Sun, J., Guo, J., Shuyan, G.: Chaotic properties and prediction of ionospheric total electron content based on cosine and cluster analysis. Geomatics Inf. Sci. Wuhan Univ. 39(04), 441– 444 + 456 (2014) 11. Mao, Y., Tianfeng, L., Benming, J.: A review of chaos theory in power system load prediction. J. Northeast Dianli Univ. 35(03), 18–21 (2015) 12. Song, L., Lijun, L., Yongle, X.: Chaotic prediction for short-term traffic flow of optimized BP neural network based on genetic algorithm. Control Decis. 26(10), 144–148 (2011) 13. Jinhu, L., Lu, J.,Chen, S.: Chaotic Time Series Analysis and Its Application, pp. 28–33. Wuhan University Press, Wuhan (2002) 14. Kugiumtzis, D.: State space reconstruction parameters in analysis of chaotic time series—the role of the time window length. Phys. Atom. Nonlinear Phenom. 95(1), 13–28 (1996) 15. Kim, H.S., Eykholt, R., Salas, J.D.: Nonlinear dynamics, delay Times, and embedding window. Phys. Nonlinear Phenom. 127(1), 48–60 (1999) 16. Rosenstein, M.T., Collins, J.J., Luca, C.J.D.: A practical method for calculating largest lyapunov exponents from small data sets. Phys. 65, 117–134 (1993) 17. Jiashu, Z., Xianci, X.: Predicting low-dimensional chaotic time series using Volterra adaptive filers. Acta Phys. Sin. 49(03), 18–23 (2000)

Performances Analysis of Tightly-Combined Multi-system RTK Positioning with BDS-3/GPS/Galileo Song Zhu and Wei Li(&) School of Geography and Information Engineering, China University of Geosciences, Wuhan, China [email protected]

Abstract. As the new generation of BeiDou satellite navigation system (BDS3) achieved its global networking, the users around the world can obtain the positioning, navigation and timing (PNT) service from the complete constellation of BDS-3. The new signals in BDS-3 satellites, B1C and B2a, have overlapping frequencies with GPS, QZSS (L1 and L5) and Galileo (E1 and E5a), which enhanced the compatibility and interoperability between BDS-3 and the other Global Navigation Satellite Systems (GNSS). In this article, we summarized the global visibility and Positioning Dilution Of Precision (PDOP) of BDS-3. Then, with the overlapping frequencies, we analyzed the performance of multi-system real-time kinematic (RTK) positioning. The results show that BDS-3 satellite has good global visibility, which possess the ability of independent positioning. And BDS-3 has good compatibility with other systems. While the multi-system tightly-combined model is applied, the positioning accuracy and the success rate of integer ambiguity resolution will be significantly improved. As the cutoff angle rising, the improvement of success rate may be up to 83.7%. Multi-system tightly-combined RTK (TCRTK) can achieve high (more than 95%) instantaneous ambiguity fixed rate even under a high cut off angle. Keywords: BDS-3 model


Multipath
Real-time kinematic
Tightly-combined

1 Introduction The third generation of BeiDou navigation satellite system (BDS-3) is one of the Global Navigation Satellite System (GNSS) constructed by China, which is on base of the first generation of BeiDou experimental satellite (BDS-1) and the second generation of BeiDou regional navigation satellite system (BDS-2)(CSNO 2019a, CSNO 2019b). From March 30th, 2015 when the first BDS-3 satellite was launched, to December 27th, 2018 when China officially announced the achievement of the fundamental construction of BDS-3 and its service towards the global, BDS is contributing to the GNSS. On June 23th, 2020, BDS-3 has achieved its global networking, and the full constellation of BDS-3 includes 3 Geostationary Orbit (GEO) satellites, 3 Inclined Geo-Synchronous Orbit (IGSO) satellites and 24 Medium Earth Orbit (MEO) satellites, providing © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 609–618, 2021. https://doi.org/10.1007/978-981-16-3138-2_56

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Positioning, Navigation and Timing (PNT) service to the global(Ning et al. 2013, Yang 2010, Yang et al. 2011). Figure 1 shows the average number of visible BDS-3 satellites and the corresponding mean Position Dilution of Precision (PDOP) on October 26th, 2020 around the global with a cut off angle of 10°. The whole day’s average number of the visible BDS-3 satellite is more than 6.68 while the mean PDOP is lower than 2.6. The results reflect the favourable service performance of BDS-3. Due to the existence of IGSO and GEO satellites, the visibility and PDOP of BDS-3 perform better around the Asia-Pacific region.

Fig. 1. Distribution of number of BDS-3 satellites (a) and its mean PDOP (b) around the global on October 26th, 2020.

Inherited the B1I and B3I signals transmitted by BDS-2 satellites, BDS-3 satellites open new signals B1C and B2a and modify the modulation of B2I to B2b which will provide regional Precise Point Positioning (PPP) service (Yang et al. 2019, Guo et al. 2019). The new signals B1C and B2a is compatible and interoperable with some other GNSS. Table 1 show some information of different GNSS signals. Table 1. Frequency and wavelength of different GNSS Signal B1I B2I/B2b B3I B1C B2a L1 L5 E1 E5a

Frequency/MHz 1561.098 1207.140 1268.520 1575.420 1176.450 1575.420 1176.450 1575.420 1176.450

Wavelength/cm 19.20 24.83 23.63 19.03 25.48 19.03 25.48 19.03 25.48

System BDS-2/3 BDS-2/3 BDS-2/3 BDS-3 BDS-3 GPS GPS Galileo Galileo

Since its construction, BDS-3 has been widely concerned by the researchers around the world. Yang (Yang et al. 2019, Yang 2010) makes a comprehensive introduction of the development of BDS and the characteristics of BDS-3 signals were further

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demonstrated. The advantage of BDS-3 quad-frequency signals and its application in extra-wide-lane (EWL) or wide-lane (WL) for ambiguity resolution (AR) are analyzed by Li (Li et al. 2020). In aspects of carrier-to-noise density ratio, pseudo range multipath (MP), double-differenced observation residuals, Precise Orbit Determination (POD), Differential Code Biases (DCB) and so on, plenty of research about the quality of BDS-3 signals has been carried out with respect to other GNSS (Li et al. 2019a, 2019b, Yin et al. 2020, Zhang et al. 2019a, 2019b). The common result is that the quality of BDS-3 signals is comparable to the other GNSS in all the aspects. As the GNSSs develop, multi-system positioning become more available (Hou et al. 2021, He et al. 2014, Odolinski and Teunissen 2017). Liu (Liu et al. 2020) finds the glass of the high speed train have a negative impact on the GNSS observations. Odijk (Odijk and Teunissen 2013) introduces the inter-system double-difference (DD) between GPS and Galileo satellites at the overlapping frequency L1-E1 and found the differential inter-system bias (ISB) between the GNSSs so stability that it can be regard as a constant. The ISBs between the identical type of receivers are close to zero while the ISBs between different type of receivers are quite stable in a short time. Then lost of experiments has been carried out to verify the characteristics of ISB (Zhang et al. 2016, Gao et al. 2018, Wu et al. 2019). Once ISB is determined, we can make inter-system double-difference and regard the multi-system as one single system. That is to say, one pivot satellite is enough and there are more redundant observations. And this kind of relative positioning is also named tightly-combined RTK. Though some research focus on the TCRTK between BDS-3 and other GNSS, but the experiments lack of the full constellation of BDS-3. Now, with the complete BDS-3 networking, we can make a comprehensive analysis of its positioning performance. In this article, we extract the ISBs and evaluate their stability between the identical and different type of receivers. Then, the performance of TCRTK of BDS-3, GPS and Galileo is assessed by comparing with that of loosely-combined RTK (LCRTK).

2 Function Model The RTK positioning require two or more GNSS receivers to track the same satellites at the meanwhile. Assume the receiver r (rover station) and b (base station) are tracking the satellites s in the system  (BDS, GPS and Galileo), then the observation of the signals at rover station can be described as: psr ¼ qsr þ cðdtr  dts Þ þ drs þ T þ I þ mpp þ esr /sr ¼ qsr þ cðdtr  dts Þ þ kðusr þ dsr þ Nrs Þ þ T  I þ mp/ þ esr

ð2:1Þ

where psrB and /srB denote the code and phase observation in meters between sB and r, respectively; dtr and dtsB are the clock bias at receiver and satellite while the c denotes the speed of light; drsB and dsrB are the hardware delays between receiver and satellite of code and phase observation, respectively; usrB is the initial phase bias between receiver and satellite; NrsB denotes the ambiguity; T and I denote the troposphere and ionosphere delays; mpp and mp/ are the MP of code and phase observation; esr and esr are the unmodelled errors such as noise.

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In the stochastic model, the elevation dependent weighting method is applied, with the random noise of 0.3 m and 0.003 m for code and phase observation, respectively. 2.1

Function Model of LCRTK

With the satellite 1G being the pivot satellite, we can give the double-differenced observation within the system as: p1br s ¼ q1br s þ e1br s 1 s /1br s ¼ q1br s þ kNbr þ e1br s

ð2:2Þ

where ½:1br s ¼ ð½:1b  ½sb Þ  ð½1r   ½sr Þ denotes the intra-system DD operation. In the DD observation equation, the atmosphere delays are ignored in the short baseline scenario, so that the unknown parameters include three-dimension coordinate and DD ambiguities of ðn  1Þ dimension at each frequency. If only the intra-system DD is formed, the multi-system LCRTK model can be written as: p1brG sG ¼ q1brG sG þ e1brG sG p1br s ¼ q1br s þ e1br s 1G sG /1brG sG ¼ q1brG sG þ kNbr þ e1brG sG 1 s 1 s 1 s /br ¼ qbr þ kNbr þ e1br s

ð2:3Þ

where  denote different GNSSs such as BDS-3 and Galileo. In the LCRTK model, each GNSS system corresponds to a pivot satellite within the system. 2.2

Function Model of Inter-system Bias

If the truth coordinates of both rover and base station are known, then the inter-system DD observation equations with GPS as the pivot system can be conducted as: G P1brG s ¼ q1brG s þ dbr þ 1brG s 1G s 1G s 1G s 1G s /br ¼ qbr þ kðNbr þ dG br Þ þ ebr

ð2:4Þ

G where the dG br and dbr are the differential ISBs for phase in unit of cycles and code in unit of meters, respectively. In Eq. (2.4), there is a rank deficiency between the phase ISB and the ambiguities. To eliminate the rank deficiency, we need to choose another pivot satellite 1B and make a transformation as: 1G s 1G 1 1 s 1 s eG Nbr þ dG þ dG br ¼ Nbr þ Nbr br ¼ Nbr þ d br

ð2:5Þ

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Then the ISB function model can be described as: G þ e1brG s P1brG s ¼ q1brG s þ dbr 1G s 1G s 1G s 1 s /br ¼ qbr þ kðNbr þe d G br Þ þ ebr

ð2:6Þ

In the parameter e d G rb;fB , the DD ambiguity of two pivot satellites is taken into account. Considering the integer nature of ambiguity, the phase ISB correction can be extracted by subtract the DD integer ambiguity: G 1G 1 1G 1 dbr ¼ e d G ¼ dG  z1brG 1 Þ br  zbr br þ ðNbr

ð2:7Þ

G

where drb denotes the phase ISB correction between the two system and z1rbG 1 denotes the integer ambiguity between the two pivot satellites. 2.3

Function Model of TCRTK

If the differential ISBs are estimated successfully, then we can correct the corresponding errors in the process of inter-system DD with the ISBs. Then the inter-system DD equation with the pivot satellite 1G is written as: P1brG sG ¼ q1rbG sG þ e1brG sG G P1brG s ¼ q1brG s  dbr þ e1brG s 1G sG 1G sG 1G sG /br ¼ qbr þ kNbr þ e1brG sG G 1G s /1brG s ¼ q1rbG s þ kðNbr  dbr Þ þ e1brG s

ð2:8Þ

where the  denotes the different GNSSs (BDS-3 and Galileo). In Eq. (2.8), the ISBs are corrected while inter-system DD is conducted. Compared with the LCRTK in Eq. (2.3), the TCRTK regards the mixed systems as one system after the ISB corrected so only one pivot satellite is enough between different systems. Through decreasing the number of the pivot satellites, TCRTK can enhance the strength of the model by increasing the number of redundancy.

3 Datasets and Experiments As shown in Fig. 2, the distribution of the IGS stations that can track B1C and B2a signals in BDS-3 are displayed. The baselines named MET3-METG and GODNGODS is chosen for the experiments. More information about the chosen stations is shown in Table 2. It should be noted that MET3-METG denotes the baselined of different receiver types (JAVAD and SEPTENTRIO) and GODN-GODS denotes the baseline of identical receiver type (JAVAD and JAVAD). All the datasets are observed on October 26th, 2020.

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Fig. 2. Distribution of IGS stations that track BDS satellites. Table 2. Information about the experimental receivers. Station MET3 METG GODN GODS

3.1

Receiver JAVAD TRE_3 DELTA SEPT POLARX5 JAVAD TRE_3 DELTA JAVAD TRE_3 DELTA

Antenna JAVRINGANT_DM TRM59800.00 TPSCR.G3 JAVRINGANT_DM

Location America America Finland Finland

Length − 2.79 km − 76 m

ISB Time-Series

Before the TCRTK is conducted, it’s necessary to extract the ISB between different systems. In the experiments, we chose BDS-3 as the pivot system. That means only one BDS-3 satellite participate in the estimation of ISB. The time-series of ISB between BDS-3 and GPS/Galileo is shown in Fig. 3. The subplot (a) and (b) represent the results of the baseline GODN-GODS while (c) and (d) denote the results of the baseline MET3-METG. The related signal is given in the subplots. In the baseline GODN-GODS, the phase and code ISB are both near zero and stable in the one day’s observation. In the baseline MET3-METG, though the ISBs don’t have the mean value of zero, but the distribution is stable. That means, we can regard the ISBs as a constant while we make inter-system DD. 3.2

RTK Positioning Performance

Having got the ISB between different systems, the inter-system DD can be conducted smoothly. In this part, the positioning results of the two baselines are assessed. We use the double-frequency B1C/L1/E1 and B2a/L5/E5a for the experiments. The evaluation index includes positioning accuracy and the success rate (SR) of fixed solution which is defined as(Odolinski et al. 2014):

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Fig. 3. The time-series of ISBs between BDS-3 and GPS/Galileo. (a) and (b) denote the identical receivers while (c) and (d) denote the different receivers.

SR ¼

# of correctly fixed epochs total # of epochs

ð3:1Þ

Figure 4 shows the positioning errors of the baseline GODN-GODS and MET3METG. The scatterplot and vertical error series are plotted. (a)/(c) and (b)/(d) denote the results of LCRTK and TCRTK, respectively. Due to the relatively short distance of the baselines and the adequate number of satellites, we set a high cut off angle of 40° in this experiment. From Fig. 4, we achieved centimetre-level accuracy in fixed solutions in both LCRTK and TCRTK. And the SRs are all higher than 90% even with a high cut off angle of 40°. An important result is that the positioning accuracy of TCRTK is obviously higher than LCRTK and the higher SR can be achieved by TCRTK. With the longer distance, the baseline MET3-METG has achieved more improvement from LCRTK to TCRTK. The accuracies of fixed solution and float solution are improved by 14.2%–15.5% and 6.7%–23.3% and the promotion of SR is 1.2%–8.4% from LCRTK to TCRTK. The promotion rate is defined as:

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Fig. 4. Positioning errors of the baseline GODN-GODS (the top panel) MET3-METG (the bottom panel). (a) and (c) denote the results of LCRTK while (b) and (d) denote the results of TCRTK respectively. The correctly fixed, float and wrongly fixed solution are denoted by green, red and blue dot. The 95% confidence interval is denoted by blue line. All the results are with a cut off angle of 40°.

Fig. 5. Positioning accuracy and SR under different cut off angle from 10° to 50° of the baselines GODN-GODS (a), MET3-METG (b).

Performances Analysis of Tightly-Combined Multi-system RTK

promotion ¼

value of LCRTK  value of TCRTK  100% value of LCRTK

617

ð3:2Þ

In Fig. 5, the positioning accuracy and SR under different cut off angle from 10° to 50° are displayed. In all the results, TCRTK can achieve higher accuracy and SR. As the cut off angle increasing, the more promotion can be found in the SR from LCRTK to TCRTK. The accuracy of float solution and fixed solution can be improved by 25.2% and 28.3% at most, respectively. As for the SR, the most improvement of 83.7% can be achieved. In the TCRTK, the SR is higher than 95% with a high cut off angle of 50°.

4 Conclusion In this article, we summarized the visibility of BDS-3 satellites and its average PDOP around the world. The average visible number of BDS-3 satellites is higher than 6.68 while its average PDOP is lower than 2.6, which reflect the good visibility of BDS-3. Then, we extracted the ISB between BDS-3 and GPS/Galileo with the overlapping frequency B1C/L1/E1 and B2a/L5/E5a. The stable distribution of the ISB series means that we can regard the ISB as a constant while we make inter-system DD equation. Finally, the positioning performance of LCRTK and TCRTK with combined BDS3/GPS/Galileo observations is evaluated from positioning accuracy and SR. All the results reflect the advantage of TCRTK. From LCRTK to TCRTK, the improvement of 25.2% and 28.3% in the accuracy of fixed solution and float solution is found, respectively. As for the SR, with the cut off angle increasing, the 83.7% improvement can be found at most. And the SR is higher than 95% even with a high cut off angle of 50° in TCRTK. Acknowledgements. This study is funded by the National Science Foundation of China (Grant No. 41804033), Open Research Fund Program of State Key Laboratory of Geodesy and Earth’s Dynamics (SKLGED2019-3-2-E), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant No. CUGL180831), the teaching Laboratory of China University of Geosciences (Wuhan) (SKJ2020209).

References CSNO The Application Service Architecture of BeiDou Navigation Satellite System (Version 1.0)., China satellite navigation office Technical Report (2019a) CSNO Development of the BeiDou Navigation Satellite System (Version 4.0)., China satellite navigation office Technical Report (2019b) Gao, W., et al.: Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases. GPS Solutions 22(1), 1–13 (2018) Guo, S., et al.: BDS-3 RNSS technical characteristics and service performance. Acta Geodaet. Cartographica Sin. 48(07), 810–821 (2019) He, H., et al.: Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning. GPS Solutions 18(3), 393–403 (2014)

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Hou, P., Zhang, B., Yuan, Y.: Combined GPS + BDS instantaneous single- and dual-frequency RTK positioning: stochastic modelling and performance assessment. J. Spat. Sci. 66(1), 3–26 (2021) Li, B., Zhang, Z., Miao, W., Chen, G.E.: Improved precise positioning with BDS-3 quadfrequency signals. Satell. Navig. 1(1), 30 (2020) Li, X., et al.: Estimation and analysis of differential code biases for BDS3/BDS2 using iGMAS and MGEX observations. J. Geodesy 93(3), 419–435 (2019a) Li, X., et al.: Precise orbit determination for BDS3 experimental satellites using iGMAS and MGEX tracking networks. J. Geodesy 93(1), 103–117 (2019b) Liu, Z., Gong, Y., Zhou, L.: Impact of China’s high speed train window glass on GNSS signals and positioning performance. Satell. Navig. 1(1), 14 (2020) Ning, J., Yao, Y., Zhang, X.: Review of the development of global satellite navigation system. J. Navig. Positioning 1(01), 3–8 (2013) Odijk, D., Teunissen, P.J.G.: Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution. GPS Solutions 17(4), 521–533 (2013) Odolinski, R., Teunissen, P.J.G.: Low-cost, high-precision, single-frequency GPS–BDS RTK positioning. GPS Solutions 21(3), 1315–1330 (2017) Odolinski, R., Odijk, D., Teunissen, P.J.G.: Combined GPS and BeiDou instantaneous RTK positioning. Navig. (Washington) 61(2), 135–148 (2014) Wu, M., Liu, W., Wang, W., Zhang, X.: Differential inter-system biases estimation and initial assessment of instantaneous tightly combined RTK with BDS-3, GPS, and Galileo. Remote Sens. 11(12), 1430 (2019) Yang, Y.: Progress, contribution and challenges of compass/BeiDou satellite navigation system. Acta Geodaet. Cartographica Sin. 39(01), 1–6 (2010) Yang, Y., Gao, W., Guo, S., Mao, Y., Yang, Y.: Introduction to BeiDou-3 navigation satellite system. Navigation 66(1), 7–18 (2019) Yang, Y., Li, J., Xu, J., Tang, J., Guo, H., He, H.: Contribution of China’s Beidou satellite navigation system to global PNT users. Bull. Surveying Mapp. 56(21), 1734–1740 (2011) Yin, Z., Wang, G., Hu, Z., Bo, Y.: Quality analysis of BDS-3 observations. Sci. Surveying Mapp. 45(06), 37–45 (2020) Zhang, X., Wu, M., Liu, W.: Model and performance analysis of tightly combined BeiDou B2 and Galileo E5b relative positioningfor short baseline. Acta Geodaet. Cartographica Sin. 45 (S2), 1–11 (2016) Zhang, Y., Kubo, N., Chen, J., Wang, J., Wang, H.: Initial positioning assessment of BDS new satellites and new signals. Remote Sens. 11(11), 1320 (2019) Zhang, Z., Li, B., Nie, L., Wei, C., Jia, S., Jiang, S.: “Initial assessment of BeiDou-3 global navigation satellite system: signal quality, RTK and PPP. GPS Solutions, 23(4), 1–12 (2019)

A Super-Long-Term Prediction Method of Earth Polar Motion Based on Spectrum Analysis Weitao Lu(&), Lue Chen, Zhijin Zhou, Songtao Han, and Tianpeng Ren National Key Laboratory of Science and Technology on Aerospace Flight Dynamics, Beijing Aerospace Control Center, No. 120, Box 5130, Haidian District Beijing, China

Abstract. The super-long-term prediction technology of Earth Orientation Parameter (EOP) is a key foundation in autonomous orbit determination for earth-orbit spacecraft. Currently the classical prediction method of EOP is LS + AR, while the accuracy of periodic components and the corresponding frequency of EOP in the LS model is to affect the prediction performance. This paper focuses on the super-long-term prediction method of the polar motion. Firstly, the spectrum analysis of the 14C04 data series released by IERS is done to confirm the periodic components. Secondly, the periods of Chandler motion and annual motion are estimated by using spectral centroid method, which are about 433.75 days and 365 days respectively. Furthermore, the fence effect of FFT and prediction error are used to testify the correctness of the periods. Finally, the 180-day, 365-day and 730-day prediction of polar motion are conducted and compared with the observed value released by IERS, showing that the corresponding prediction error are 12 mas, 20 mas, and 55 mas. The results of the paper can be used as a good reference for long-term prediction of EOP. Keywords: Earth Orientation Parameter (EOP)
Polar Motion (PM) long-term prediction
Spectrum analysis
LS + AR


Super-

1 Introduction The Earth’s rotation reflects the coupling process between the solid Earth and atmosphere, oceans, mantle, core of the earth on multiple spatial and temporal scales, which can be described by the Earth’s orientation parameters (EOP). EOP mainly includes precession, nutation, polar motion and length of day (LOD), all of which are the transformation parameters between the terrestrial and celestial reference systems, playing a key role in many areas such as deep space exploration, satellite precise orbit determination and astrogeodynamics [1]. Because of complex data process, EOP is usually released with several days to two weeks delay. In order to meet the demand of real-time orbit-determination in autonomous navigation, it is to very meaningful to make super-long-term prediction of EOP [2]. Considering the pression and nutation already have accurate model, and yield little error in satellite navigation, however the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 619–628, 2021. https://doi.org/10.1007/978-981-16-3138-2_57

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prediction of PM and LOD has a significant influence on navigation satellite orbitdetermination [3], so this paper will mainly focus on researching the Poly Motion (PM) prediction method. The principal model of PM is founded by an American scientist, Chandler, who finds that the PM motion is mainly composed by annual and Chandler component, and also points out that the Chandler motion with a 434-day period is the main component in PM [4]. Based on this, Zhu firstly proposed a LS prediction method, and solved the LS parameters by least squares fitting with a certain length of PM observed data [5, 6]. Kosek first applicates the AR method to EOP prediction, improving the prediction performance remarkably [7]. The result of the Earth Orientation Parameters Prediction Comparison Campaign (EOP PCC) also shows that LS + AR method has a better performance in PM short-term prediction [8]. To predict the EOP, the LS + AR method firstly founds a LS model, and solves the model parameters by least squares fitting, and then obtains the difference sequence between the original and LS modeled data to found AR model, finally predict the EOP data by LS + AR model. Obviously, there are two hypothesizes in the abovementioned process, 1) the period components of PM are already known, 2) the frequency of each components is already known. While there is not a unified understanding of the two problems. Claus Oesterwinter pointed out the period of Chandler motion is about 432.0-day by processing ILS, BIH, DMA and IPMS data [9]. Dennis gave a result of 435-day by processing Circular D data [10] while Zhu modeled Chandler motion as a 433.5-day periodic signal [5]. Moreover, Zhang and Chen think there are also semi-annual and 1/3-annual component besides annual and Chandler motion [11, 12]. The different opinions on PM model are inevitable to degrade the prediction performance. This paper makes a research on periodic components of PM and the corresponding frequency by making spectrum analysis on the latest IERS released EOP data, and found a PM model for super-long-term prediction, which provides a technical support for the spacecraft autonomous navigation.

2 Spectrum Analysis on PM Data 2.1

Period Components Analysis and Frequency Estimation

The EOP 14C04 data is obtained from IERS website (ftp://ftp.iers.org/products/ eop/long-term/c04_14/), with a time-span from 1962.01.01 to 2020.12.27, and the time interval of the data is one day. Figure 1(a) shows the original Poly Motion X Component (PMX), indicating an obvious linear trend and period oscillation. The linear trend is removed firstly by LMS fitting and differencing to emilite its influence on spectrum. As shown in Fig. 1(b), the differenced data has a character of near-periodicity and symmetry. The spectrum of the above differenced data is shown in Fig. 2, and the spectrum resolution is about 0.01725 circle per year (cpy). As depicted in Fig. 2(a), there are two main components in PM motion, and the frequencies at the peak position are 0.8454

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cpy and 1.0007 cpy. The corresponding periods are 423-day and 365-day, which are obviously the Chandler motion and annual motion. Also, it is easy to find that there are no spectrum peaks around 2 cpy (standing for semi-annual motion) and 3 cpy (standing for 1/3-annual motion). So, we can assume that the PM motion are mainly composed by Chandler motion and annual motion.

Fig. 1. The PMX series released by IERS (a) the original PMX (b) PMX after removing linear component

Fig. 2. The PM = PMX−1j * PMY spectrum (a) the total spectrum (b) the detail of annual component (c) the detail of Chandler component

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Subsequently, the detail spectrums of Chandler and annual motion in Fig. 2(b) and (c) show that the amplitudes of two spectrum around annual peak are comparatively small, which are one-order of magnitude lower relative to peak spectrum. While the two adjacent spectrums around Chandler peak have lower amplitude but are different from each other. As we all know that the FFT has fence effect, as shown in formula (2.1). XðkÞ ¼

sinðpðk þ dÞÞ ; k 2 ½0; 1; 1 sinðNp ðk þ dÞÞ

ð2:1Þ

In which, d 2 ½0:5; 0:5Þ stands for the bias between signal frequency and spectrum resolution, and k stands for the peak spectrum and its two neighbors. From formula (2.1), we can find that when d = 0, that is the signal frequency is integral multiples of spectrum resolution, the spectrum amplitude is almost to 1, and its neighbors’ amplitude are nearly to zeros. In other side, when d = ±0.5, there are two peak spectrums with approximately equal amplitude. So it is assured to say that there is no spectrum leakage when d = 0, and there are definitely several spectrums when is close to ± 0.5. So, in view of the total data length being 58-year and the detail spectrum of annual component, we can say that there is no spectrum leakage in Fig. 2(b), that is to say the frequency of annual component is equal to the frequency of peak spectrum. And the annual period is 365-day (1.0007 cpy). while there is spectrum leakage in Fig. 2(c). The peak spectrum and its two neighbors occupy more than 85% power in sinusoid signal [13]. Here we use spectral centroid method [14, 15] to estimate the frequency of Chandler motion, as shown in formula (2.2), where S and f represent the amplitude and frequency of the spectral lines, and the subscript P, L and R stands for the peak spectral line and its two neighbors. The result is about 433.75 days (0.842 1cpy,1.1875 yr per cycle). fC ¼

2.2

jSP j  fP þ jSL j  fL þ jSR j  fR jSP j þ jSL j þ jSR j

ð2:2Þ

The Testification of Period Component Frequency

The FFT fence effect is used to testify the frequency correctness here. When there is no spectrum leakage, the data sample length should be integral multiples of signal period, otherwise not. Based on the above estimated result, setting the data length to be 17350 days, corresponding to 40 Chandler periods, and the spectrum resolution is about 0.02105 cpy. The spectrum is shown in Fig. 3. Firstly, there are two pairs symmetrical peaks located around 1 cpy in Fig. 3(b). Suppose the frequency of annual component is 1.0007 cpy, being same as the result in Fig. 2, this frequency is approximately integral multiples of spectrum resolution with a 0.5 times bias, that is to say the true frequency is located at the middle position. So, the assumption is true, and the frequency of annual component is 365 days. On the other hand, the second and third peaks in Fig. 3(c) have comparatively equal amplitude, which indicates that there is no spectrum leakage for Chandler component. So, the Chandler component period is about 433.75 days.

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Fig. 3. The PM spectrum with different sample length (a) the total spectrum (b) the detail of annual component (c) the detail of Chandler component

Furtherly, setting the period of annual component to be 365-day and Chandler period taking several different values, including 435-day [10], 433.5-day [5], 432-day [9], the fitting residuals are shown in Fig. 4. The 433.75-day situation obtained the smallest residual, which proves the correctness of Chandler frequency estimation.

Fig. 4. The LMS fitting residual with various Chandler period

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3 PM Prediction Scheme 3.1

PM Data Model

The poly motion is mainly composed by annual and Chandler component. Though the period of Chandler has been estimated as 433.75-day, Ref. [5] points that the circle model is also suitable for Chandler motion, and it doesn’t make little difference compared with ellipse model. Considering that the less parameters of the LS model are, the less fitting error can be obtained, this paper conducts two PM data models, as depicted in formular (3.1), where the periods of annual and Chandler motion are 365day and 433.75-day respectively. It is easy to find that the number of circle model is one fewer than that of ellipse model. ( 2pt 2pt X ¼ X0 þ X1 t þ A1 sinð Þ þ A2 cosð Þ þ PA PA


2pt
C1 sinð2pt Pc Þ þ C2 cosð Pc Þ Ellipse
pffiffiffi p
2C sinð2pt Pc þ 4Þ Circle

ð3:1Þ

The parameters of the two models are estimated by using 58-yr length of 14C04 data, and the residuals of the two Chandler models are shown in Fig. 5, from which we can find that the residual for ellipse model is a little less, so it is reasonable to say that the ellipse model is more suitable for Chandler motion.

Fig. 5. The LMS fitting residual with Chandler motion modeled as circle and ellipse

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Based on the above analysis, the PM model is constructed and shown in formula (3.2), where X0 is the constant term, X1 the coefficient of linear term, PA the period of the annual component (365-day), A1, A2 the coefficients of the annual component, and PC the period of the Chandler component (433.75-day), C1, C2 the coefficients of the Chandler component. X ¼ X0 þ X1 t þ A1 sinð

3.2

2pt 2pt 2pt 2pt Þ þ A2 cosð Þ þ C1 sinð Þ þ C2 cosð Þ PA PA Pc Pc

ð3:2Þ

Prediction Flow

The iterative prediction strategy is adopted to fully use the original data information, that is the predicted value is appended to the original data and the LS + AR model is founded iteratively in each step. The detail flow is described as following. 1) make difference process to the original PM data and get the differential data series; 2) establish the LS model and obtain the residual sequence between the original EOP data and the LS model; 3) establish AR model; 4) make one-step prediction of the differential date; 5) renew the differential data series, and jump to step 2) until the predication is done; 6) make inverse difference processing to realize the prediction of PM

4 PM Prediction Experiment The data used here is also the latest 14C04 series released on 2020-01-26 by IERS. The AR model order is confirmed by using FPE criteria, and the Mean Absolute Error (MAE) is adopted to evaluate prediction performance [16, 17]. In formular (4.1), pij stands for the jth predicted value when prediction time-span is i days, and oij is the corresponding observed value. MAEi ¼


n
1X
i

pj  oij
n j¼1

ð4:1Þ

The final prediction error, MAEPM, is calculated by formular (4.2), containing the prediction error of PMX and PMX. MAEPM

4.1

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 MAEPMX þ MAEPMY ¼ 2

ð4:2Þ

Mid-Long-Term Prediction

The prediction starts from 2019-01-01 to 2020-5-15, 500 days in total, and forecasts 180 days each time. The results are shown in Fig. 6. It is easy to find that the prediction trend is highly consistent with the IERS results. Figure 6(b) gives the prediction errors

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when period of Chandler Wobble is set to different values. we can find that when the prediction day is no longer than about 100 days, the prediction errors with different Pc are almost same, while when prediction day becomes longer, the prediction error is little smaller when Pc = 433.75day. Moreover, the prediction errors for 30-day, 90-day and 180-day are about 7 mas, 9.9 mas, and 12 mas respectively.

Fig. 6. The mid-long-term prediction performance of PM (a) the compare of predicted and released PM in a single prediction (b) the mid-long-term prediction performance of PM with different Pc

4.2

Super-Long-Term Prediction and Discuss

Further-on, the super-long-term prediction are conducted here. The prediction starts from 2017-01-01 to 2017-7-20, 200 days in total, and forecasts one year and two year each time. The results are shown in Fig. 7, from which we can find 1) for LS + AR method, the prediction error of 365-day (one year long) and 730-day (two-years long) are 20 mas and 55 mas, respectively, and also 2) the prediction error is jittering along with the prediction time, and moreover 3) the prediction errors of LS + AR method and LS method are strongly correlative. These phenomena show that the super-long-term prediction performance is dominated by LS model accuracy, which is up to the correctness of the period components of poly motion. In order to find the reason for the prediction error jitter in Fig. 7, we give one example of the predicting process in Fig. 8. It can be found that the trends of predicted value and IERS released value for both PMX and PMY are very close, while the difference increased significantly with the prediction time becoming longer, which is the embodiment of time accumulation of LS model error. On the other hand, it can be seen intuitively that the prediction error jitter is caused together by the periodic character of poly motion and the LS model error. The results in Fig. 7 and Fig. 8 show that it is essential to take the time-varying character of polar motion into account in super-long-term predication, though the period components are comparatively stable. The time-frequency technology may be applicated to the EOP prediction in the following work.

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Fig. 7. The PM super-long-term prediction performance

Fig. 8. The compare of predicted and IERS released value of PM (a) PMX (b) PMY

5 Conclusion In refer to the EOP long-term prediction need of Earth Orientation Parameter (EOP) in autonomous orbit determination, this paper applicates the spectral centroid method to estimate Chandler motion period and testify its correctness by using FFT fence effect. Furthermore, the LMS fitting test proves that Chandler motion is better to be modeled as ellipse. Finally, the mid-long-term and super-long-term prediction of polar motion are conducted and compared with the IERS released value. The results show that the prediction performance is improved when the period of Chandler Wobble is set 433.75 day, and the 180-day, 365-day and 730-day prediction errors are 1 2 mas, 20 mas, and 5 5 mas respectively. When prediction term becomes longer, the prediction error is significantly large, so it is worthy trying to adopt time-frequency technology to EOP

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prediction. The results of the paper can be used as a good reference for long-term prediction of EOP.

References 1. Xu, X.: Research on High Accuracy Prediction Methods of Earth Orientation Parameters. University of Chinese Academy of Sciences (2012) 2. Liu, W., Li, Z., Liu, W., et al.: Influence of EOP Prediction Errors on Orbit Prediction of Navigation Satellites. GNSS World China, 34(6), 17–22 (2009) 3. Weixing, Z., Wanke, L., Xiaoying, G.: Analysis of influence of EOP prediction error on autonomous orbit determination. J. Geodesy Geodyn. (5), 106–110 (2011) 4. Ye, S., Huang, C.: Astrogeodynamics. Jinan: Shandong Science and Technology Press, pp. 226–229 (2000) 5. Zhu, S.Y.: Prediction of polar motion and polar motion. Columbus: Department of Geodetic Science and Surveying, The Ohio State University (1981) 6. Zhu, S.Y.: Prediction of earth rotation and polar motion. Bull. Geod. 56, 258–273 (1982) 7. Kosek, W., McCarthy, D.D., Johnson, T.J., et al.: Comparison of polar motion prediction results supplied by the IERS Sub-bureau for Rapid Service and Predictions and results of other prediction methods [EB/OL]. https://www.researchgate.net/publication/228413477_ Comparison_of_polar_motion_prediction_results_supplied_by_the_IERS_Sub-bureau_for_ Rapid_Service_and_Predictions_and_results_of_other_prediction_methods 8. Kalarus, M., Schuh, H., Kosek, W., et al.: Achievements of the earth orientation parameters prediction comparison campaign. J. Geodesy 84(10), 587–596 (2010) 9. Oesterwinter, C.: Polar motion through 1977 from doppler satellite observations. In: Symposium - International Astronomical Union, Volume 82: Time and the Earth’s Rotation, pp. 263–278 (1979) 10. Mac Carthy, D.D., Luzum, B.J.: Prediction of earth orientation. Bull. Geodesique, 65, 18–21 (1991) 11. Zhang, H.: Research on the Prediction Theories and Algorithms of Polar Motion of Earth Orientation Parameters. Central South University (2012) 12. Chen, L., Tang, G., Xu, X., et al.: Research on high accuracy dual differential LS + AR method in earth polar motion parameters prediction. J. Geodesy Geodyn. 35(5), 1–5 (2015) 13. Macleod, M.D.: Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones. IEEE Trans. Sign. Process. 46(1), 141–148 (1998) 14. Lin, H., Ding, K.: Anti-noise performance of energy centrobaric correction method using four points for discrete spectrum. J. Vib. Eng. 22(6), 659–664 (2009) 15. Chen, H., Sun, J., Han, J., et al.: Correction method for discrete spectrum based on energy centrobaric method and extremum method. J. Vib. Measure. Diagn. 32(A1), 141–145,156 (2012) 16. Lue, C., Geshi, T., Songjie, H., et al.: High accuracy differential prediction of UT1-UTC. J. Deep Space Explor. 1(3), 230–235 (2014) 17. Wu, F.: Several Improved Methods for Prediction of Earth Rotation Parameters. China University of Mining and Technology (2019)

Availability and Prediction Performance Evaluation of BDS-3 Satellite Clock Error Products Guo Chen2, Yaping Gao2, Wenju Fu1(&), Xi Chen2, and Jiali Yang2 1

State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan, China [email protected] 2 Colloge of Earth Sciences, Chengdu University of Technology, Chengdu, China

Abstract. With the completion of BDS-3 constellation deployment in China, various analysis centers have begun to provide BDS-3 precise satellite clock products. Satellite clock error is a key product of GNSS Navigation Positioning and Timing (PNT) technology. Therefore, evaluating the availability and prediction performance of BDS-3 satellite clock error products is of great significance to the application of BDS-3 PNT technology. This paper describes the current BDS-3 constellation status, evaluates the availability of the clock error products of three analysis centers, gives the detailed implementation method and specific steps of the prediction model, uses the model to predict BDS-3 clock error, and finally evaluates the performance of BDS-3 satellite clock error products. One-month BDS-3 precise clock products provided by GFZ, CHD, and WHU analysis centers are used for product availability analysis and prediction experiments. The results show that: (1) The availability of the C38-C46 satellites clock error is much worse than other BDS-3 satellites according to the difference between analysis center products. The clock STD precision is about 0.19 ns for C19-C37 satellites while it is about 0.53 ns for C38-C46 satellites. The clock phase jump occurs in the day boundary; (2) The precise clock error provided by WHU analysis center is used to predict the BDS-3 satellite clock error. The prediction accuracy of BDS-3 within 30 min is between 0.025 ns and 0.074 ns. When the prediction arc increases to 1 h, the accuracy is between 0.056 ns and 0.103 ns. The prediction accuracy of some rubidium clocks is 0.015 ns worse than that of hydrogen clocks. The precision statistics of BDS-3 and BDS-2 satellite clock prediction during the same time show that the prediction accuracy of BDS-3 clock error is 0.059 ns, which is significantly better than the accuracy of 0.295 ns for BDS-2 satellite. Keywords: BDS-3
Precise satellite clock error Linear polynomial model


Clock error prediction


© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 629–642, 2021. https://doi.org/10.1007/978-981-16-3138-2_58

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1 Introduction At present, the accuracy of real-time precise single-point positioning largely depends on the accuracy of satellite clock error [1, 2], and the accuracy of clock error correction is generally required to be better than 0.1 ns. The International GNSS Service (IGS) and the International GNSS Monitoring & Assessment System (IGMAS) can broadcast precise clock products to users, which cannot meet the timeliness requirements of the public users. However, clock error prediction can effectively make up for this defect [3–5]. Therefore, this paper focuses on the analysis of the third generation of BeiDou Navigation System (BDS-3) prediction performance and data availability provided by several analysis centers. In recent years, many scholars have done a lot of research and analysis on the data produced by analysis centers. By using the multi-system track and clock products provided by IGMAS for comprehensive analysis, it is concluded that the accuracy of the final precise clock error is about 0.1–0.5 ns [6, 7], Guo et al. [8] compared and analyzed the orbit and clock errors and the accuracy of Signal-In-Space Range Error (SISRE) broadcast by Galileo satellite navigation system (Galileo) and Block IIF of Global Positioning System (GPS) during 2015–2018. Some scholars also did research and analysis on the prediction performance of BDS. Huang et al. [9] analyzed the performance of BDS atomic clocks, revealed the BDS of China running in good condition. Fu [10] analyzes the BDS, GPS, and Global Navigation Satellite System (GLONASS) on-orbit satellite clock performance. There are also many researches on the established prediction model and about how to improve the accuracy of prediction. Yu et al. [11] combined the grey model with the modified exponential curve model, greatly weakened the residual error and improved accuracy by nearly 50% relative to the traditional model. Wang et al. [12] proposed a satellite clock error prediction method based on the clock error rate fitting model, which fits the clock error rate sequence with the additional periodic term and quadratic polynomial as the basic model. Yan et al. [13] proposed a semi-parametric adjustment model that takes into account the model for the BDS clock error prediction and effectively overcomes the influence of the inaccuracy of the clock error period correction term. The above research on the performance of the BDS atomic clock and the evaluation and analysis of the precise clock error products of the analysis centers is mainly focused on BDS-2, but the BDS-3 has not been involved. To evaluate the availability and prediction performance of BDS-3 clock error products, this paper firstly make the statistics of the BDS-3 satellite constellation and collects clock products provide for a total of 31 days during November 29, to December 29, 2020 from CHD (Chang’an University), GFZ (Deutsches GeoForschungsZentrum Potsdam), and WHU (Wuhan University). This paper evaluates product availability information, calculates data difference among analysis centers, and makes the statistics of the standard deviation of the data difference. Then, we use the first-order polynomial model to carry out the BDS-3 satellite clock short-term prediction, and finally analyze the prediction performance in terms of the prediction accuracy.

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2 Usability Analysis of Satellite Clock Error Products 2.1

Availability of BDS-3 Satellite

At present, the constellation status of BDS-3 is widely concerned by the public. This paper collects the information of the constellation status of BDS-3, which provides by the test and evaluation research center of the China satellite navigation system management office, as shown in Table 1. As you can see, up to January 21, 2021, there are 29 BDS-3 satellites in orbit working normally, and 5 satellites, such as C31, C56, C57, C58, and C61 in orbit experiment and test. In BDS-3, there are 24 medium earth orbit (MEO) satellites, 3 inclined geosynchronous orbits (IGSO) satellites, and 3 geosynchronous orbits (GEO) satellites. The atomic clocks of BDS-3 are divided into two types, rubidium atomic clocks and hydrogen clocks, of which 14 satellites are equipped with rubidium atomic clock and 20 satellites are equipped with hydrogen atomic clock. Among all BDS-3, the earliest satellites C57 and C58 were launched on July 25, 2015, and the recently launched BDS-3 satellite was C61, which was launched on June 23, 2020. It is still in-orbit testing stage. Table 1. BDS-3 satellite constellation information Item Healthy MEO GEO IGSO On-orbit experiment On-orbit test Rubidium clock Hydrogen clock

2.2

IGS-SVN 19–30, 32–46, 59, 60 19–23, 25–30, 32–37, 41–46, 57, 58 59, 60, 61 31, 38, 39, 40, 56 31, 57, 58 61 19–24, 32, 33, 36, 37, 45, 46, 57, 58 25–31, 34, 35, 38–44, 56, 59, 60, 61

Availability Analysis of Clock Error Products

To analyze the availability of BDS-3 precise products provided by three analysis centers. This chapter collects the data missing information, calculate data difference, and make the statistic of standard deviation among the analysis centers [14]. Figure 1 shows the epoch continuity and the availability information of clock error data provided by the GFZ, CHD, and WHU analysis centers. The abscission of a), b), c) in Fig. 1 is the number of epochs while d) is the percentage of available data. The ordinate of a), b), c) and d) in Fig. 1 is the satellite list. Perhaps due to the fault of the data uploading server network and other reasons, this paper doesn’t consider the missing data of the whole day. For the cases of less than 15 consecutive missing epochs, few missing data can be obtained by interpolation of adjacent data and thus it doesn’t affect the accuracy of subsequent experiments. It can be seen that the satellite clock data have little difference provided by the three analysis centers. The GFZ analysis center misses C59 satellite, while C41-C46

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satellites miss 3–4 h clock data on each day. The WHU analysis center misses the data of C59 and C60 satellites, and there was no missing clock error for other satellites except C43. The CHD analysis center also lost data of C59 and C60 satellites. C41-C46 satellites appear data missing for several hours after December 19. The missing rate of clock data of C41-C46 and C60 satellites provided by GFZ analysis center is about 14.1%. The missing rate of C43 satellite data provided by WHU analysis center is 6.5%, while other satellite clock data are not significantly missing. The missing rate of C38 and C39 satellite data provided by CHD analysis center is about 1.1%, the missing rate of C41, C42, C43, and C44 satellite data is about 5.1%, while the C45 and C46 satellite data is 7.2% and 20.3% respectively.

Fig. 1. Epoch continuity and availability of BDS-3 satellites

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Since the subsequent prediction experiments are based on the clock error provided by the analysis centers, and the prediction accuracy is largely affected by the accuracy of the clock error itself in the fitting period. It is necessary to calculate data differences among the analysis centers and accurate information of the clock products. The calculation process of data difference among analysis centers and the standard deviation is given below. The detailed statistical information is shown in Fig. 2 and Fig. 3. Since the reference satellites of the GFZ, WHU, and CHD analysis centers are different, it is necessary to eliminate the respective reference satellite clock error before calculating the differences among analysis centers. X Kac1 ðiÞ ¼ xK ðiÞ  xL ðiÞ

ð1Þ

where X Kac1 ðiÞ represents the clock error value of the K satellite minus the clock error reference at the time of i epoch at the analysis center ac1, and xK ðiÞ represents the original clock error observation value of the K satellite, and xL ðiÞ is the clock error reference of the reference L satellite. Y K ðiÞ ¼ X Kac1 ðiÞ  X Kac2 ðiÞ

ð2Þ

where Y K ðiÞ is the data difference between two analysis centers, X Kac1 ðiÞ, X Kac2 ðiÞ are the clock error value of two analysis centers at the time of i epoch minus the clock reference; ac1 and ac2 represent two different analysis centers. Y ðiÞ ¼

X

Y K ðiÞ=N

ð3Þ

where Y ðiÞ is the mean value of Y K ðiÞ and N is the total number of epochs of one day’s clock error data, and the value is 2880 in this paper. STD ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X 2 ðY K ðiÞ  Y ðiÞÞ =N

ð4Þ

where STD represents the value after calculating the standard deviation of one day’s data. To reflect the differences in the data of different analysis centers in one month, it is also necessary to average the STD during this month. Figure 2 shows the statistics of the BDS-3 differences among analysis centers. The abscissa is the BDS-3 satellite list, and the ordinate is the STD value. Figure 3 shows the clock data difference between analysis centers of C38-C46 satellites using 66240 epochs. Because of the data provided by each analysis center misses 2–4 days, which in these periods cannot be counted, these epochs are eliminated. The ordinate is the STD value of data difference among the analysis centers. Combining Fig. 2 and Fig. 3, it can be seen that most of the satellite clock error data of three analysis centers have small differences, and STD remains about 0.19 ns. However, for C38-C46 satellites there are more data miss than other satellites for all analysis centers. The data differences are obviously large and the STD is about 0.53 ns. This may be due to the short continuous data resulting in low ambiguity parameter estimation accuracy, which affects the clock error parameter estimation accuracy. It is

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found in Fig. 3 that the clock error phase will jump in the day boundary. As the time increases, the difference between two analysis centers’ clock data gradually becomes small. This may be due to the clock error phase jump taken by the orbit error in the day boundary, especially for C38-C46 considering that their tracking data are less and has a bad global distribution at present.

Fig. 2. STD of BDS-3 satellite clock differences among three analysis centers

Fig. 3. Difference between satellite clock products from analysis center

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3 Data Preprocessing Before the clock error prediction, we need to remove gross data. Because the precise products may contain rough error points, which will have a serious impact on the accuracy of the prediction, we need to preprocess the original clock error sequence. The median method (MAD) was used to detect the rough error points. The median MAD can be expressed as [15]: MAD ¼ Meadiafjyi  mj=0:6745g

ð5Þ

where m is the median of the clock error sequence; when this equation jyi  mj [ ( n  MAD) is satisfied, the observed value yi is defined as one gross. The integer n is determined according to experience in this paper and is set as 10.

4 Polynomial Model with Additional Periodic Term Correction 4.1

Introduction to the First Order Polynomial Model

At present, the models widely used for clock error prediction include polynomial model, grey model and Auto-Regressive Moving Average (ARMA) models [1616]. This article chooses polynomial model with a periodic term to predict the satellite clock errors, which can be expressed as: li ¼ x0 þ x1  ti þ eðti Þ

ð6Þ

where x0 and x1 are the phase deviation and frequency deviation of the atomic clock, respectively, ti is the prediction time, and eðti Þ is random noise. To solve the parameters x0 and x1 , this paper chooses to use the sequential leastsquares method. The clock error sequence is first divided into two groups, namely l0 and l1 , and the error observation equation is as follows: V 0 ¼ A0 X 0  L0

ð7Þ

where V 0 represents the residual,  X  0 represents the algebraic parameter, L0 reprel0 sents clock error sequence, L0 ¼ l1 , and A0 represents coefficient matrix, A0 ¼   1 t0 . According to the least square criterion, it can be obtained: 1 t1  ^0 ¼ AT0 X

A0

1

AT0 L0

ð8Þ

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where Q0 is introduced and satisfies the following equation: Q0 ¼ N 1 0

ð9Þ

where N 0 ¼ AT0 PA0 , P represents the weight matrix. An initial estimated parameters can be obtained from Eq. (8), and then introduce a new clock error data l2 . A1 ¼ ð 1 t2 Þ, where t2 is the epoch moment of the next data, then Eq. (8) becomes: b1 ¼ X

T !1 T A0 A0 A0 L0 A1 A1 A 1 l2

ð10Þ

Then we can obtain:  N1 ¼

A0 A1

T

 P1

A0 A1

 ð11Þ

Simplify the Eq. (11): N 1 ¼ N 0 þ AT1 P1 A

ð12Þ

Then Q1 ¼ N 1 1 , and it can be obtained from Eq. (10) and Eq. (12):   b 0 þ Q1 AT1 l2  A1 X b1 ¼ X b0 X

ð13Þ

This is an update of the last parameter estimation. The solution is sequentially estimated when introducing more new observations one by one. 4.2

Additional Periodic Term Correction Model

Since the model obtained by Eq. (13) does not eliminate the influence of periodic term, the periodic term correction should be added in the forecast method, and its calculation formula is as follows [17, 18]: 0

L ¼ Asinð

2p t i þ u0 Þ T

ð14Þ

where A represents the amplitude, T is the period of the sinusoid which equals to 0 the orbital period, u0 represents the phase shift of the sinusoid, L represents the value of periodic term correction. It can be written as:    2p 2p ti þ a1 cos t_ L ¼ a0 sin T T l 0



ð15Þ

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where a0 and a1 are the parameters, which can be obtained by the least-square method:  1 0 Y ¼ BT B BT R

ð16Þ

where R is used for the fitting residuals after fitting to form a one-dimensional matrix. And matrix B can be written as:   cos 2p T t0_ B B ¼ @ ...   cos 2p T t_i 0

 1 sin 2p T t0 C .. .  A sin 2p T ti

ð17Þ

According to the parameter solved by Eq. (16) and (17), the value of the periodic 0 term L can be computed and added to the original prediction results.

5 Experimental Analysis and Results 5.1

Prediction Accuracy and Strategy

The prediction experiment in this paper uses the data provided by the WHU analysis center for reducing the length of this paper. To count the accuracy of the first-order polynomial model under different fitting arc and prediction arc, a simple prediction strategy is adopted in this paper. The fitting time length varies from 1 h to 24 h with 30 min increase while the prediction arc length is from 5 min to 1 h. The sliding window here is set as 5 min, namely, the fitting and predicting window slide forward in units of 5 min and the predicting process is conducted in every single slide. Taking the precise clock error as the true value, the precision of the sliding period is expressed as: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 XN RMS ¼ ½Dei ðtÞ2 i¼1 N

ð18Þ

where Dei ðtÞ is the residual of i th epoch. The Root Mean Square (RMS) represents the prediction accuracy of this period and N is the number of prediction epochs. We obtain the accuracy of the sliding predicted clock error for n groups (the value is 12 in this paper), and the accuracy of the prediction arc length t (t  1 h) is the average value of the n times of prediction accuracy. 5.2

Analysis of Experimental Results

Based on the above prediction strategy, the clock error prediction experiment was carried out on December 24–25, 2020. The RMS accuracy of different fitting and prediction arc is computed. The prediction performance of BDS-3 clock error products is analyzed in detail and the comparison with BDS-2 is also made.

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Figure 4 shows the one-hour prediction residual error of the BDS-3 satellite with 0.5 h fit data. The horizontal coordinate indicates 120 epochs in one hour and the vertical coordinate indicates the prediction residual error value. It can be seen from the figure that the satellite prediction residuals gradually increase with the fitting time. When the fitting time increases from 0 to 0.5 h, the most residual value changes smoothly within the range of ±0.05 ns. More than 30 min, the prediction residual value of C39, C40, C43, C45, and C46 satellites has a more obvious increasing trend. At the end of the fitting epoch, the prediction residual value is within ±0.2 ns. There are also some satellites with relatively good prediction accuracy, such as C23, C25, C28, C29, and C34, etc., and the residual value at the last epoch is about ±0.03 ns. Overall BDS3 prediction residual value is about ±0.059 ns.

Fig. 4. BDS-3 prediction residual chart

Figure 5 shows the prediction accuracy of the fitting duration from 0.5 h to 23 h. The abscissa represents the fitting time, and the ordinate represents the residual Root Mean Square (RMS) of the prediction arc. It can be seen from the figure that for most BDS-3 satellites the prediction accuracy decreases with the increase of the fitting time. When the fitting time is after 3 h, the accuracy variation trend is gradually flat. When the prediction arc is within 30 min, most BDS-3 prediction precision is between 0.025–0.074 ns. The highest accuracy is achieved when the fitting time is 0.5 h. When the prediction arc increases to 1 h, most satellites can reach an accuracy of 0.06 ns, and a few satellites, such as C22, C24, C32, C39, C40 and C45, etc. prediction accuracy is within 0.25 ns. The overall prediction accuracy is between 0.056–0.103 ns. It can be seen from this that all working BDS-3 satellites are in a stable and healthy state.

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Fig. 5. Prediction accuracy of BDS-3 satellite clock with different fitting arc and prediction arc

Figure 6 shows the accuracy of clock error prediction with 0.5 h fit arc for predicting 5 min, 15 min, 30 min, and 60 min, respectively. It can be seen from Table. 1 and Fig. 5–7 that the average predicted RMS value of the hydrogen atomic clock carried by C34, C35, C38, C42, and C44, etc. satellites is about 0.052 ns, which is significantly greater than the rubidium atomic clock carried by C19, C21, C22, and C46, etc. satellites is about 0.067 ns. This is because the stability of the hydrogen atomic clock is better than that of the rubidium atomic clock. The average accuracy of BDS-3 satellite clock error prediction is about 0.059 ns. When the prediction arc is reduced to 30 min, the prediction accuracy of all satellites is better than 0.065 ns.

Fig. 6. Prediction accuracy of different prediction length with 0.5 h fit data

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At present, BDS-2 is still in use and its working performance has attracted public attention. To understand the difference in the performance of the clock error prediction between BDS-2 and BDS-3 satellites, it is necessary to compare and analyze their prediction accuracy during the same period. Figure 7 shows the RMS accuracy of BDS-2 and BDS-3 satellites clock error prediction for 1 h with 0.5 h fit data. It can be seen from the figure that the clock error prediction accuracy of most BDS-2 satellites is about 0.295 ns. Some satellites are relatively poorer than 0.5 ns, such as C02, C10, and C11. The clock error prediction accuracy of BDS-2 satellites such as C01, C03, and C05, etc is comparable to BDS-3. Most BDS-3 satellites achieve the RMS accuracy of below 0.1 ns and only a few satellites is between 0.1 ns and 0.13 ns. Overall, the clock error prediction accuracy of BDS-3 satellite is 0.236 ns higher than that of BDS-2 satellite, which shows that the prediction performance of BDS-3 satellite is significantly better than BDS-2 satellite.

Fig. 7. Prediciton comparison between BDS-2 and BDS-3 satellites

6 Conclusion This paper collects the BDS-3 satellite information in detail and computes the availability of the precise clock products provided by WHU, GFZ, and CHD analysis centers. The data difference of different clock products among analysis centers is carried out and the standard deviation of the differenced data is computed. The detailed modeling process of the polynomial forecast model is given and used to make shortterm forecasts. Then we evaluate the accuracy and analyze its prediction performance. Finally, the prediction performance of BDS-2 and BDS-3 atomic clocks is analyzed through prediction experiments. The clock precision is computed according to the difference between different clock products from WHU, CHD, and GFZ analysis center and some conclusions can be drawn. For C39-C46 satellites, there are varying degrees of data loss for precise clock product provided by each analysis center and results demonstrate that these satellites can’t achieve a good estimation precision as other BDS-3 satellites. The standard

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deviation of the clock difference among analysis centers calculated in this paper is around 0.19 ns for C19-C38 satellites while that of C39, C41-C46, and C60 satellites is around 0.53 ns. The data of each analysis center differs in series and there is clock phase jump phenomenon in the day boundary. Data from the WHU analysis center are used to do the clock forecasting experiment for a specific period and draw the following conclusions: 1. The prediction accuracy of the BDS-3 clock error decreases with the increase of the fitting arc and prediction arc. When the prediction arc is within 30 min, the prediction accuracy is between 0.025 ns and 0.074 ns. When the prediction arc increases to 1 h, the prediction accuracy is between 0.056 ns and 0.103 ns. 2. In the one-hour prediction arc with 0.5 h fit arc experiment, overall satellites’ prediction residual value changes smoothly when the prediction time increases from 0 to 0.5 h, while some satellites change obviously with the fitting time is more than 0.5 h. The overall BDS-3 satellite prediction residual value is about 0.059 ns. The prediction accuracy of some rubidium clocks equipped with BDS-3 satellite is around 0.067 ns, which is worse than the accuracy of about 0.052 ns for hydrogen clocks. 3. The prediction accuracy of few BDS-2 satellites is comparable to BDS-3, which is at about 0.1ns. The overall BDS-3 and BDS-2 satellite prediction accuracy is 0.059 ns and 0.295 ns, respectively. The prediction performance of BDS-3 is much better than BDS-2. Acknowledgments. Thanks to WHU and CHD Analysis Center of IGMAS and GFZ Analysis Center of IGS for providing precise clock products. This work was supported by the Program of the National Natural Science Foundation of China (No. 41904038) and the China Postdoctoral Science Foundation (No. 2019M662713).

References 1. Jin, S., Su, K.: PPP models and performances from single- to quad-frequency BDS observations. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-020-00014-y 2. Huang, G., Zhang, Q., Li, H., Fu, W.: Quality variation of GPS satellite clocks on-orbit using IGS clock products. Adv. Space Res. 51(6), 978-987 (2013) 3. WenJu, F., Qin, Z., GuanWen, H.: Analysis of combined real-time prediction model of BDS/ GPS system time difference. Geodesy Geodyn. 35(04), 653–6576 (2015) 4. Montenbruck, O., Steigenberger, P., Prange, L., et al.: The multi-GNSS experiment (MGEX) of the international GNSS Service (IGS)–achievements, prospects and challenges. Adv. Space Res. 59(7), 1671–1697 (2017) 5. Wang, J., Li, T, Xie, D., Lu, N.: Research on the short-term prediction of Beidou precision satellite clock error. Surveying Mapp. Sci. 45(01), 33–41 (2020) 6. Guo J, Xu, L., Zhao, Q.L., et al.: Precise orbit determination for quad-constellation satellites at Wuhan University: strategy, result validation, and comparison. J. Geodesy, 90(2), I−17 (2016) 7. Guofeng, J., Zhiqiang, Y., Xiaolin, J.: Precise orbit and clock products for multi—GNSS system from MGEX and iGMAS. J. Geodesy Geodyn. 39(1), 13–19 (2019). (in Chinese) 8. Wu, W., Guo, F., Zheng, J.: Analysis of Galileo signal-in-space range error and positioning performance during 2015–2018. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/ s43020-019-0005-1

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9. Huang GuanWen, Y., Hang, G.H., Zhang JuQing, F., WenJu, T.J.: Analysis on medium and long term clock error characteristics of Beidou in orbit satellite clock. J. Wuhan Univ. (Inf Sci. Ed.) 42(07), 982–988 (2017) 10. WenJu, F.: Clock characteristics analysis and clock error prediction of GNSS satellite in orbit. Chang’an University (2014) 11. Ye, Y., Zhang H.J., XiaoHui, L., Xiao, B., Chen, Q.Y.: Medium and short term prediction of GPS satellite clock error based on GM (1,1) and combination model. Acta Astron. Sin. 59(03), 19−30 (2018) 12. Fuhong, W., Boyang, X., Xuewen, G.: Clock error prediction method of GPS satellite considering clock error change rate. Acta Surveying Mapp. 45(12), 1387–1395 (2016) 13. Yan, X., Li, W., Yang, Y., Pan, X.: BDS satellite clock offset prediction based on a semiparametric adjustment model considering model errors. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-019-0007-z 14. Qianqian, Y., Yidong, L., Wenting, Y.: Comparison and analysis of IGS real-time products. Geodesy Geodyn 32(06), 123–128 (2012) 15. Huang, B., Yang, B., Minggu, L., et al.: An improved method for MAD gross error detection of clock error. Geomatics Inf. Sci. Wuhan University (2020). https://doi.org/10.13203/j. whugis20190430 16. ShiQi, J., BoFeng, L.: Application of ARIMA model in short term prediction of satellite clock error. J. Navig. Positioning 7(04), 118–124 (2019) 17. Ma Zhuo Xi: Yang Li, Jia Xiao Lin, Study on the characteristics and prediction of the period term of BDS satellite atomic clock. Geodesy Geodyn. 37(03), 292–296 (2017) 18. GuanWen, H., et al.: Real-time clock error prediction model with additional period and neural network compensation. Acta Astronautica Sin. 39(01), 83–88 (2018)

Comparative Analysis of Beidou Single and Dual Frequency Positioning Accuracy Evaluation Lei Chen(&), Hongliang Cai, Ling Pei, Yinan Meng, Wei Zhou, and Tianlin Zhu Beijing Institute of Tracking and Telecommunication Technology, Beijing, China

Abstract. Aiming at the situation that the BeiDou Navigation Satellite System’s (BDS) single-frequency positioning accuracy is better than dual-frequency positioning found in the daily monitoring and evaluation of the International GNSS Monitoring and Assessment System iGMAS, the observation data of iGMAS overseas stations and domestic station receivers in the same time period are selected for comprehensive analysis. The sequence analysis of different satellite B1I/B3I dual-frequency UERE by different types of monitoring receivers shows that the fluctuation of dual-frequency UERE sequence is larger than that of single-frequency UERE sequence, which is caused by the ionospheric combination amplifying the pseudo-range multipath error; However, dual-frequency UERE of different types of receivers has different mean values, which are caused by group delay parameter errors,this error is indirectly caused by the deviation of the pseudorange measurement constant caused by the nonideal characteristics of the downlink navigation signal. The pseudorange multipath error can be eliminated by phase smoothing pseudorange, but the analysis shows that the group delay parameter error is mainly caused by the satellite downlink navigation signal distortion, that is, the downlink signal quality is the key to restricting Beidou dual-frequency positioning accuracy. This paper proposes the following research directions for the optimization and improvement of dual-frequency positioning accuracy during the smooth transition period and the Beidou-3 separate service period, and the user receiver configuration parameter design, which lays the foundation for better use of dual-frequency to achieve higher-precision positioning. Keywords: GNSS
BeiDou
Single frequency
Dual frequency
Positioning accuracy

1 Introduction Ionospheric delay error is an important source of error in GNSS user positioning, and the distance error it causes is in the range of several meters to tens of meters [1]. According to different strategies for dealing with ionospheric delay errors, satellite navigation system services include single-frequency positioning mode and dual-frequency positioning mode. Single-frequency users use the model parameters broadcast by the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 643–652, 2021. https://doi.org/10.1007/978-981-16-3138-2_59

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satellite navigation system to correct the ionospheric delay, and the correction ratio is about 50% to 75% [2–4]. With the aid of the dispersion effect of ionospheric delay with satellite frequency, dual-frequency users can form a dual-frequency non-ionospheric combined observation, which completely eliminates the influence of the ionospheric first-order terms. The distance error caused by the higher-order terms of the ionosphere is about centimeter level, which is a negligible error for real-time pseudorange positioning users [5]. Although dual-frequency users are not affected by the ionospheric delay correction error, the dual-frequency combination will amplify the multipath effect of pseudo-range measurement, noise, and satellite group delay parameter errors [6–10]. Literature [11] analyzes and compares the difference of Beidou-2’s single-frequency and dualfrequency positioning accuracy, and points out that the pseudorange multipath effect of the user receiver, especially the long-period fluctuation with the altitude angle, is an important factor that causes the positioning error of dual-frequency users to be greater than that of single-frequency users [12]. Clarifying the difference between dualfrequency and single-frequency positioning accuracy is of great significance for guiding users to use and further improve the satellite navigation system. There is still a lack of comparative research on the positioning accuracy of single-frequency and dualfrequency users of GNSS, especially Beidou-3. This paper compares and analyzes the single-frequency and dual-frequency positioning accuracy of the Beidou-3 satellite navigation system, and studies the methods for improving the dual-frequency positioning accuracy. The author first the single- and dual-frequency positioning principle of Beidou-3 system, derives the factors affecting the single- and dual-frequency positioning accuracy, uses the measured data to evaluate the influencing factors of the dual-frequency positioning accuracy, and gives suggestions for improving the dual-frequency positioning accuracy.

2 GNSS Single and Dual Frequency Positioning Principle Beidou-3 satellite broadcasts smooth transition signals B1I and B3I to achieve a smooth transition with Beidou-2 services and broadcasts better performance B1C and B2a to provide users with single and dual-frequency positioning services. The location service mode provided by Beidou-3 system to users is summarized as follows. Table 1. Service plan of Beidou-3 Single frequency Dual frequency Dual-frequency smooth transition signal service B1I B1I + B3I New system signal service B1C B1C + B2a

This section takes the smooth transition signal as an example to analyze the factors affecting the accuracy of single and dual frequency positioning. The single-frequency service frequency of the smooth transition signal is B1I, and the dual-frequency service

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frequency is the dual-frequency ionospheric combination of B1I and B3I. The observation equations of B1I pseudorange and B3I pseudorange are as follows: P1 ¼ q þ c  Dtsta  c  Dtsat þ

TEC þ DErr þ c  TGD1 þ f1 f12

ð1Þ

TEC þ DErr þ f3 f32

ð2Þ

P3 ¼ q þ c  Dtsta  c  Dtsat þ

Among them, P1 and P3 are the pseudo range observations of frequency B1 and frequency B3, f1 and f3 are the frequencies of frequency B1 and frequency B3, q is the distance between satellite and ground, Dtsta is the unknown receiver clock error parameter, which needs to be used as the parameter to be estimated for the positioning solution; Dtsat is the satellite clock error, which is calculated from the satellite clock error parameters issued by the satellite; TEC is the total electronic content of the satellite oblique path, which causes the distance error to be inversely proportional to the frequency square; TGD1 is the group delay parameter to be corrected for B1 pseudo range; f1 and f3 are the multipath effect and noise of the pseudorange at frequency B1 and B3; DErr is the frequency independent error, including tropospheric delay error, relativistic periodic term and tidal displacement correction, which can be corrected by modeling, and its residual error is negligible for pseudo range positioning. The dual-frequency positioning user uses the pseudo range of B1 and B3 frequency points to perform an ionospheric-free observation combination, and derives its dualfrequency ionospheric-free observation combination as follows: PC ¼ q þ c  Dtsta  c  Dtsat þ DErr þ

f12  c  TGD1 þ fPC ðf12  f32 Þ

ð3Þ

Among them, PC is the pseudorange observation of the dual-frequency ionospheric-free combination of B1I and B3I, and fPC is the measurement multipath effect and noise of the dual-frequency ionospheric-free combination pseudorange. fPC is the combination of B1I multipath noise f1 and B3I multipath noise f3 . Since f1 and f3 are independent random variables, according to the law of error propagation, there are: f2PC ¼

f12 f12 f32 f32 2 þ   f   f23 1 ðf12  f32 Þ ðf12  f32 Þ ðf12  f32 Þ ðf12  f32 Þ

ð4Þ

Bring in the B1I and B3I frequencies, the following results are obtained: PC ¼ q þ c  Dtsta  c  Dtsat þ DErr þ 2:943  c  TGD1 þ fPC

ð5Þ

f2PC ¼ 2:943  2:943  f21 þ 1:943  1:943  f23

ð6Þ

Single-frequency users cannot completely eliminate the ionospheric delay error, and the model is used for correction, and the residual ionospheric error is about 25%. It

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is found by comparison that although dual-frequency users completely eliminate the ionospheric delay error, they amplify the pseudorange measurement multipath effect and noise by 2 to 3 times, and the satellite group delay parameter error by 2 to 3 times. If the amplified error is greater than the residual ionospheric error, the positioning accuracy of dual frequency users may be worse than that of single frequency users. This article focuses on comparing the single and dual frequency positioning accuracy of the Beidou-3 satellite. As mentioned above, the dual-frequency service mode will amplify the multipath effects of pseudoranges, noise, and constellation delay parameter calculation errors. In the second part of this article, the discussion focuses on the impact of the above-mentioned errors on the accuracy of Beidou-3 dual-frequency positioning and the error reduction algorithm.

3 BDS/GPS Positioning Accuracy Analysis of iGMAS Station We selected 7 iGMAS overseas stations and 3 IGMAS domestic stations from January 1 to January 7, 2020. The distribution of the stations is shown in Fig. 1. Calculate the positioning results under the 12 modes of GPS, BDS dual system and BDS-3 only. The positioning modes are shown in Table 1. Among them, the height angle is set to 15°, and the sampling interval is 30 s. The precise coordinates of 10 iGMAS stations are calculated by PPP, and the accuracy of the calculated station coordinates is better than 2 cm [13, 14] (Table 2).

Fig. 1. Distribution of iGMAS sites

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Table 2. Positioning mode of iGMAS station System Frequency point selection Ionospheric model Pseudorange selection

GPS L1 GPSK8

L1L2

Dual frequency cancellation Phase smoothing pseudorange Original pseudorange

BDS-3 B1I BDSK8

B1IB3I Dual frequency cancellation

Based on iGMAS stations, the original pseudorange data of BDS and GPS and the phase smoothing pseudorange data are used for single-frequency and dual-frequency standard positioning. The method of carrier phase smoothing pseudorange is shown in literature [15]. The detailed results are shown in Tables 3 and 4. As can be seen: 1) When GPS uses original pseudorange positioning, the single-frequency accuracy of iGMAS station is better than dual-frequency. When phase smoothing pseudo-range positioning is used, the dual-frequency positioning accuracy of the station is basically equivalent to that of single-frequency, with certain fluctuations; 2) In the original pseudorange positioning results of BDS3, the single-frequency positioning accuracy of iGMAS station is better than that of dual-frequency; when using phase smoothing pseudorange positioning, the dual-frequency positioning accuracy of IGMAS station is better than that of single-frequency.

Table 3. Standard positioning accuracy of iGMAS using GPS observation data (PDOP < 8, 1 r) unit: m Mode

L1 H V 3D Use phase to smooth pseudorange observation data 0.89 2.15 2.37 Use raw observation data 0.97 2.38 2.60

L1/L2 H V 3D 1.18 1.96 2.33 1.55 2.53 2.99

Table 4. Standard positioning accuracy of iGMAS using BD3 observation data (PDOP < 8, 1r) Unit: m Mode

B1I H V 3D Use phase to smooth pseudorange observation data 0.81 2.06 2.26 Use raw observation data 0.96 2.29 2.53

B1I/B3I H V 3D 1.01 1.40 1.76 1.55 2.23 2.75

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4 Influence of Pseudo Range Multipath Error on Dual Frequency Positioning Accuracy The influence of multipath effect is determined by the relative amplitude, phase, phase rate and delay of indirect signal. The magnitude of multipath error can reach centimeter level in carrier phase measurement [16], but the pseudo range error caused by multipath effect and observation noise can reach several meters [17]. Aiming at the phenomenon that the positioning accuracy of single frequency is better than that of double frequency in the original pseudo range positioning results of igmas station based on BDS-3, The positioning residuals of the original pseudo range and the phase smoothed pseudo range of Brch station on one day are plotted, as shown in Fig. 2 to Fig. 3. The left picture is the single-frequency positioning residual, and the right picture is the dualfrequency positioning residual. In the figure, the abscissa is time in hours, and the ordinate is residuals in meters. In Fig. 2, the standard deviation of single frequency positioning of Brch station of iGMAS is about 0.4 m, and the standard deviation of dual frequency positioning is about 1.1 m; in Fig. 3, the residual of dual frequency positioning of Brch station is less than that of single frequency positioning. Because the K8 ionospheric model parameters broadcast by BDS have high accuracy, And 2020 is the low peak year of ionospheric activity, The residual ionospheric delay of the Beidou single-frequency user after the model correction is smaller than the multipath effect and noise amplified by the original pseudo-range dual-frequency ionospheric-free combination. The single-frequency positioning accuracy using the original pseudorange is better than that of dual-frequency. The phase smoothing pseudorange can eliminate most of the multipath noise, Its residual pseudo-range multipath noise is smaller than the residual ionospheric delay of single-frequency users, As a result, the dual-frequency positioning accuracy after phase smoothing pseudorange processing is improved to slightly better than single-frequency positioning.

Fig. 2. The original pseudorange positioning residual sequence diagram at branch station

Fig. 3. Phase smoothing pseudorange positioning residual sequence diagram at branch station

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Because the parameters of K8 ionospheric model broadcast by BDS have high accuracy, and 2020 is a low peak year of ionospheric activity, the residual ionospheric delay of the Beidou single-frequency user after the model correction is smaller than the multipath effect and noise amplified by the original pseudo range dual frequency non ionospheric combination, which makes the positioning accuracy of the original pseudo range single frequency better than that of the dual frequency. The phase smoothing pseudorange can eliminate most of the multipath noise. The residual pseudorange multipath noise is smaller than the residual ionospheric delay of the single-frequency user, which leads to the improvement of dual frequency positioning accuracy slightly better than single frequency positioning.

5 Analysis of the Influence of Group Delay Parameter Error on Dual Frequency Positioning Accuracy Satellite group delay is the transmission delay difference of different signal components on the satellite or different signal components on the same frequency. Beidou broadcast ephemeris clock difference parameters are calculated based on B3 frequency point, so when using other single frequency signals or using dual frequency ionospheric free combination, TGD or DCB parameters need to be introduced for correction [18]. Therefore, b1i single frequency users and b1i/b3i dual frequency users need to modify the TGD parameters broadcast by navigation messages to correct the transmission delay difference at different frequencies. It can be seen from the analysis in Sect. 2 that the B1I/B3I dual-frequency user positioning mode amplifies the satellite group delay parameter error. Unlike other error terms, the satellite group delay parameter error causes a constant deviation for the UERE sequence, and will not cause fluctuation of uere sequence. In order to analyze the delay parameter error of Beidou satellite navigation message group, the B1I/B3I dual-frequency ionospheric-free combination UERE of all satellites of different types of iGMAS monitoring receivers is calculated. The three igmas stations and corresponding receivers participating in the calculation and evaluation are shown in the Table 5 below. Table 5. iGMAS station receiver configuration information participating in the evaluation of group delay parameter error Station name Site bjf1 Beijing xia1 Xian sha1 Shanghai

Type CETC-54-GMR-4016 gnss_ggr UB4B0-13478

The statistics of the average values of B1I/B3I dual-frequency UERE of all satellites of the different types of iGMAS mentioned above are shown in the table below. It can be seen that different types of igmas receivers have different mean deviations in size and symbol for all Beidou satellites. The UERE mean deviation is a manifestation

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of the delay parameter error of navigation message group. However, it should be noted that for the same satellite, the average values of dual-frequency UERE seen by different types of iGMAS receivers are not completely the same. Among them, the difference in the average value of the satellite B1I/B3I dual-frequency UERE observed by different types of receivers is not the same. The difference in the average B1I/B3I dualfrequency UERE of the C46 satellite observed by gnss_ggr and UB4B0-13478 is the largest, about 2.26 m; the difference in the average B1I/B3I dual-frequency UERE of the C35 satellite observed by CETC-54-GMR-4016 and UB4B0-13478 is relatively large Small, about 0.06 m (Table 6). Table 6. UERE average value of B1I/B3I dual frequency combination of different types of iGMAS receivers (unit m) Sat no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 19 20 21 22 23

CETC-54GMR-4016 0.71 0.88 0.72 1.17 0.25 0.17 0.08 0.70 −0.10 0.08 1.25 0.61 −0.89 0.62 −0.32 −0.95 −0.57 −0.74 −1.16 −1.33

gnss_ggr UB4B013478 0.69 1.11 1.35 −0.43 0.15 0.24 0.05 0.96 −1.11 −0.07 0.15 0.97 0.63 0.16 1.04 1.30 0.17 1.05 0.30 1.74 1.57 0.59 1.07 1.08 −0.73 0.91 1.54 0.73 −0.14 0.84 −0.78 −0.06 −0.42 0.52 −0.86 −0.05 −0.78 1.21 −1.54 −1.13

Sat no. 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 41 42 44 45

CETC-54GMR-4016 −0.63 −0.26 −0.05 −0.82 −0.21 −0.37 −1.22 −0.19 −0.63 −0.38 −0.39 −1.09 −0.78 −0.16 −0.01 0.12 −0.81 −0.70 −0.65 −0.54

gnss_ggr UB4B013478 −0.88 −1.59 −0.02 −1.34 −0.19 0.81 −0.69 −1.02 −0.03 −1.42 −0.70 −0.30 −0.58 0.25 −0.52 0.58 −0.66 0.87 −0.74 0.29 −0.51 −0.45 −0.80 1.08 −1.01 −0.21 −0.32 −0.60 0.12 −0.25 −0.02 −0.78 −0.75 −1.15 −0.91 −0.08 −0.59 1.13 −0.38 1.03

The above-mentioned B1I/B3I dual-frequency UERE average difference reflects the difference of pseudorange measurement constant deviation generated by different types of receivers for different satellite downlink navigation signals. Literature [19] and [20] reported this phenomenon in detail. Due to the non-ideal characteristics of the satellite downlink navigation signal, different types of receivers produce different pseudorange measurement deviations when measuring the satellite downlink signal. This deviation is highly coupled with the satellite group delay parameter. If there is a difference between the technical status of the user receiver and the Beidou ground transportation control

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system monitoring receiver, the pseudorange deviation will lead to the error of the Beidou satellite navigation message group delay parameters observed by the user receiver. In addition, the pseudo range deviation of different types of receivers is different, and the delay parameter error of the observed navigation message group is not the same, which leads to their dual-frequency UERE with different signs and sizes. It can be seen from Sect. 1 that the group delay parameter error has a more significant impact on dual-frequency users than on single-frequency users. The pseudorange measurement deviation caused by the distortion of the satellite downlink navigation signal indirectly leads to a large error when the navigation message group delay parameter is applied to the user receiver. This error is also the key factor that restricts the improvement of dual frequency positioning accuracy.

6 Conclusion This paper uses the observation data of iGMAS station in the same time period for positioning calculation. By comparing and analyzing the single-frequency and dualfrequency positioning results of GPS and BDS, and analyzing the positioning residuals, it is considered that the single frequency positioning accuracy is better than that of dual frequency positioning. The main reason is that when the ionospheric model can better correct the ionospheric error, the dual frequency positioning will amplify the multipath noise, and the amplified noise is greater than the corrected ionospheric error, resulting in the dual frequency positioning accuracy worse than that of single frequency positioning. However, most of the multipath and noise can be eliminated by using phase smoothed pseudo range. When using phase smoothed pseudo range for positioning, the accuracy of dual frequency positioning is greatly improved. By analysing the mean values of B1I/B3I dual-frequency UERE of different satellites by different types of receivers at iGMAS station, it is shown that there are mean deviations of different sizes and symbols of different satellite B1I/B3I dualfrequency UERE observed by different types of receivers. In the follow-up, the influence factors such as multipath noise, pseudo range deviation and residual stratification will be deeply analyzed. Through the comparison of more comprehensive positioning data (such as the regions with poor ionospheric model correction, such as the north and south poles), the conclusion of this paper will be further verified. It also studies and proposes to reduce the impact of multipath noise during dual-frequency positioning, laying a foundation for fully satisfying Beidou system service performance specifications and making better use of dual-frequency to achieve higher-precision positioning services.

References 1. 袁运斌. 基于 GPS的电离层监测及延迟改正理论与方法的研究. 中国科学院研究生院 博士论文 (2002) 2. Klobuchar, J.A.: Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans. Aerosp. Electron. Syst. 3, 325–331 (1987)

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Augmenting GNSS PPP Accuracy in South China Using Water Vapor Correction Data from WRF Assimilation Results Yangzhao Gong1,2, Zhizhao Liu1,2(&), Pak Wai Chan3, and Kai Kwong Hon3 1 Department of Land Surveying and Geo-Informatics (LSGI), The Hong Kong Polytechnic University (PolyU), Kowloon, Hong Kong, People’s Republic of China [email protected] 2 Research Institute for Sustainable Urban Development, The Hong Kong Polytechnic University (PolyU), Kowloon, Hong Kong, People’s Republic of China 3 The Hong Kong Observatory, Kowloon, Hong Kong, People’s Republic of China

Abstract. Wet delay in Global Navigation Satellite System (GNSS), mainly caused by water vapor in the atmosphere, is difficult to be accurately modeled using empirical wet delay models as water vapor is highly variable in both space and time. In this paper we propose correcting the GNSS wet delay using water vapor data from Weather Research and Forecasting (WRF) model’s assimilation results. We conduct six consecutive 24-h WRF forecasts to model the threedimension (3D) distribution of water vapor in the South China region 20° N– 33° N and 108° E–123° E from 0 h UTC April 06, 2020 to 0 h UTC April 11, 2020. GNSS Precipitable Water Vapor (PWV) from 27 stations of the Crustal Movement Observation Network of China (CMONOC) and meteorological profiles from 22 radiosonde stations are assimilated into WRF model to improve the water vapor modeling performance of WRF. Totally, four WRF schemes are adopted, i.e. WRF scheme 0: WRF without water vapor data assimilation; WRF scheme 1: WRF with GNSS PWV assimilation only; WRF scheme 2: WRF with radiosonde profiles assimilation only; WRF scheme 3: WRF with both GNSS PWV and radiosonde profiles assimilation. The water vapor data from the four WRF schemes are used to augment Precise Point Positioning (PPP) by correcting GNSS wet delay at seven International GNSS Service (IGS) stations distributed in South China. The static PPP results show that using the water vapor correction data from different WRF schemes can improve PPP positioning accuracy by 29.5% to 42.3% in the vertical component of GNSS stations. In addition, the WRF-augmented PPP can shorten convergence time by 43.3% to 57.3% in the GNSS station vertical component, if using 10 cm positioning error as the convergence criterion. The kinematic PPP results show that WRF-augmented PPP can improve positioning accuracy in the vertical component by 20.0% to 33.6%.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 653–670, 2021. https://doi.org/10.1007/978-981-16-3138-2_60

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Y. Gong et al. Keywords: Global Navigation Satellite System (GNSS)
Weather Research and Forecasting (WRF) model
Data assimilation
Precipitable Water Vapor (PWV)
Precise Point Positioning (PPP)

1 Introduction GNSS Precise Point Positioning (PPP) is a capable positioning technique that can use a single GNSS receiver to determine receiver’s coordinates with a accuracy level of centimetre even sub-centimetre [1–3]. Different from differential GNSS positioning method, PPP cannot utilize GNSS observations from neighbouring receivers to mitigate errors, such as tropospheric wet delay. Therefore, how to mitigate the impacts of wet delay in PPP has long been a research topic in the GNSS community. One widely used method is to treat wet delay as an unknown parameter and estimate wet delay in parallel with receiver coordinates, receiver clock offset and other parameters [1]. This method normally needs at least 30 min to achieve centimetre level of coordinate solutions [4–6]. Another method is to correct wet delay directly using external water vapor information [7–9]. For this method, the positioning accuracy highly depends on the accuracy of external water vapor information used. Normally, the external water vapor can be from empirical tropospheric delay models, regional GNSS network, collocated water vapor observation systems, Numerical Weather Prediction (NWP) models and others. Using empirical tropospheric delay models to correct wet delay is a simple and convenient way to mitigate the wet delay in PPP. This method has been widely adopted in many studies [10–12]. However, due to the low accuracy of wet delay derived from the empirical tropospheric delay models, the PPP positioning accuracy in vertical component is normally over 10 cm while the horizontal component normally is less affected by atmospheric wet delay [12, 13]. Several studies obtained wet delay corrections from regional GNSS network [14–16]. These studies proved that convergence speed and positioning accuracy can be improved by using tropospheric delay information from regional tropospheric delay models. However, in order to obtain accurate regional tropospheric delay corrections, a dense GNSS network is needed. Using water vapor information from other collocated observation systems can also improve GNSS positioning performance [9, 17]. However, normally no collocated water vapor observation system is available at most GNSS stations. In the recent years, the accuracy and spatial resolution of NWP model has undergone a significant improvement [18, 19]. NWP model has been used to correct wet delay for GNSS positioning [7, 20–22]. For example, Lu et al. [7] used ZWD from a global NWP model, i.e., the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP), to improve BDS real-time positioning performance. In their study, the ZWD from NCEP was treated as a priori ZWD value and the ZWD residual was treated as the unknow parameter to be estimated. The PPP results at more than 30 globally distributed International GNSS Service (IGS) stations showed that NCEP-augmented PPP can shorten convergence time up to 60.0% and 66.7% in east and up components, respectively, compared with standard PPP results.

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Additionally, NCEP-augmented PPP improved positioning accuracy in east, north, and up components by around 40%, 50%, and 30%–40%, respectively. Wilgan et al. [22] conducted an experiment using high spatial resolution (4 km) Weather Research and Forecasting (WRF) model to augment GNSS real time PPP. Their experiment results showed that WRF-augmented real time kinematic PPP reduced the convergence time from 67 min to 58 min to achieve an accuracy of 10 cm level in horizontal component and from 79 min to 63 min in vertical component. These studies demonstrated that PPP performance can be improved using the water vapor augmentation information from NWP models. However, Global NWP products have a low spatial resolution. For example, the spatial resolution of advanced global NWP reanalysis product, ECMWF Reanalysis v5 (ERA5), can only reach 31 km [23]. For WRF model, its modeling results can have a high spatial resolution. In addition, WRF has a data assimilation system that can assimilate external meteorological observations to improve WRF weather modeling performance [24, 25]. However, very few studies have investigated the benefits of WRF data assimilation for PPP augmentation. In this study, the state-of-the-art NWP model, WRF model, was used to provide wet delay corrections to improve PPP performance in South China region. To further improve the accuracy of water vapor from WRF model, we assimilated two sets of water vapor data into the WRF model. One is the water vapor data from 27 GNSS stations of the Crustal Movement Observation Network of China (CMONOC) and the other is the meteorological profiles from 22 radiosonde stations in the South China region. The data were assimilated into WRF model in four different assimilation schemes, as shown in Table 1, i.e. WRF scheme 0: WRF without data assimilation; WRF scheme 1: WRF with assimilation of GNSS PWV only; WRF scheme 2: WRF with assimilation of radiosonde profiles only; WRF scheme 3: WRF with assimilation of both GNSS PWV and radiosonde profiles. Table 1. WRF schemes and the data to be assimilated WRF WRF WRF WRF WRF

scheme no. Data assimilated 0 – 1 GNSS PWV 2 Radiosonde profiles 3 GNSS PWV + radiosonde profiles

In order to assess the accuracy of the water vapor results from the four different WRF schemes, the WRF water vapor modeling results are first validated by PWV data from GNSS stations. Then, the WRF water vapor data are utilized to augment PPP performance at seven IGS stations distributed in South China by correcting wet delay in GNSS signals. This also allows the assessment of the performance of WRF modeling via the examination of the PPP accuracy [17]. The remaining paper is organized as follows. In Sect. 2, the WRF configuration and the methods used to retrieve WRF PWV are described. In Sect. 3, the data assimilated, namely CMONOC GNSS PWV and radiosonde profiles, and the IGS GNSS

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observations used in PPP validation are introduced. In Sect. 4, the WRF PWV are evaluated by PWV from 27 CMONOC GNSS stations. In Sect. 5, WRF wet delay are used to augment GNSS PPP at seven IGS stations and the WRF-augmented PPP results are analyzed. In Sect. 6, the conclusions are summarized.

2 Description of WRF Experiment 2.1

WRF Configuration

WRF model is an advanced NWP model and has been widely used in various research fields, such as weather simulation [26], climate change forecasting [27], as well as geodetic surveying [22]. Based on the initial weather conditions, WRF can model or forecast the variation of meteorological parameters including water vapor field, for the following multiple days or even longer. In this study, WRF with Advanced Research WRF (ARW) core version 4.2 was used. Two two-way nested domains were adopted to cover the South China area around 20° N–33° N and 108° E–123° E. The locations of two WRF domains are shown in Fig. 1. Six consecutive 24-h WRF forecasts, i.e. WRF forecasts 1 to 6, were initialized at 0 h UTC on April 06 to April 11, 2020, respectively. The ECMWF ERA5 reanalysis products were used as the initial conditions and boundary conditions for the WRF model in this experiment. The spatial structure of WRF model set and microphysics options adopted in this WRF model are shown in Table 2.

Fig. 1. The locations of two WRF modeling domains used in this study. d01 (red) and d02 (blue) denote the WRF domain 01 and domain 02, respectively. The WRF grid spacings of domain 01 and domain 02 are 9 km and 3 km, respectively

To improve WRF water vapor modeling performance, GNSS PWV and radiosonde meteorological profiles were assimilated into WRF model domain 01 and domain 02 at the WRF initial time (0 h UTC, April 06 to April 11, 2020). WRF 3DVAR data

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Table 2. Design and configuration of WRF model

Number of grid point (NorthSouth  East-West) Grid spacing Number of WRF layers Model top pressure Cumulus parameterization Longwave radiation Shortwave radiation Planetary boundary layer Surface layer Land surface

Domains Domain 01 154  157

Domain 02 148  151

9 km

3 km 33

50 hPa Kain-Fritsch [28] RRTMG longwave scheme [29] RRTMG shortwave scheme [29] Yonsei university scheme [30] Revised MM5 scheme [31] 5–layer thermal diffusion scheme [32]

33 50 hPa – RRTMG longwave scheme [29] RRTMG shortwave scheme [29] Yonsei university scheme [30] Revised MM5 scheme [31] 5–layer thermal diffusion scheme [32]

assimilation method was used since 3DVAR can assimilate external data effectively with less computational burden compared to WRF 4DVAR [24]. To investigate the impacts resulting from different WRF data assimilation schemes, four WRF schemes were studied in this paper, as shown in Table 1. 2.2

Retrieval of ZWD and PWV Based on WRF Outputs

WRF model can provide modeling results of various meteorological variables including mixing ratio of vapor, air potential temperature, air base state pressure, air perturbation pressure. These output variables can be used to calculate ZWD using the following formulas. First, the water vapor mixing ratio (Q, unit: kg
kg−1) can be converted to water vapor partial pressure (e, unit: hPa) [33]: e¼

P
Q 0:622 þ Q

ð1Þ

where P is the air total pressure in unit of hPa, which is the sum of air base state pressure and perturbation pressure: P ¼ Pbase þ Pper

ð2Þ

where Pbase and Pper are the air base state pressure and perturbation pressure, respectively, both in unit of hPa. Then the atmosphere wet refractivity Nw can be calculated as follows [34]:

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Nw ¼

 Rd e e þ k3 2 k2  k1 T Rw T

ð3Þ

where Rd= 287.053 J
K−1
kg−1 and Rw = 461.495 J
K−1
kg−1 are the gas constants for dry air and water vapor, respectively. T is the air temperature in unit of Kelvin. k1 = 77.6890 K/hPa, k2 = 71.2952 K/hPa, k3 = 375463 K2/hPa are refractivity constants [35]. The formula used to convert air total potential temperature to air temperature can be expressed as [33]:


P T ¼ ðTh þ 300Þ 1000

Rc d p

ð4Þ

where Th denotes the potential temperature in unit of Kelvin. P refers to the air pressure in unit of hPa. Rd has been defined in formula (3). cp is the specific heat capacity at a constant pressure. The ratio of Rd and cp, i.e. Rd/cp = 2/7, is the Poisson constant. Finally, the WRF ZWD can be derived using [34]: ZWD ¼ 106

1 Z

Nw ðhÞdh

ð5Þ

hs

where h is the height of layer in unit of meter. WRF ZWD can be converted to PWV using a PWV conversion factor (PWVfactor) [36]: ð6Þ

PWV ¼ ZWD  PWVfactor PWVfactor ¼

105  w 461:495 k2  k1 M Md þ

k3 Tm



ð7Þ

where k1, k2, k3 have been defined in formula (3). Mw = 0.018016 kg/mol and Md = 0.028964 kg/mol are the molar mass of water vapor and dry air, respectively. Tm represents the weighted temperature in unit of Kelvin. Tm can be calculated using an empirical model [37]: Tm ¼ 70:2 þ 0:72Ts

ð8Þ

where Ts is the temperature near the Earth surface in unit of Kelvin. In this study, Ts is retrieved from ERA-5 single pressure reanalysis product.

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3 Description of Data 3.1

Data Assimilated

3.1.1 CMONOC GNSS PWV A total of 27 China CMONOC GNSS stations, as shown in Fig. 2, are used to generate PWV for this study. The PWV are then assimilated into WRF model according to the designed WRF schemes. The CMONOC GNSS PWV data are extracted directly from the troposphere products of China Earthquake Administration [38]. GAMIT/GLOBK positioning software is adopted to generate this troposphere product using differential positioning method [39]. For this troposphere product, tropospheric delay is estimated as an unknown parameter in hourly intervals. The PWV from 27 CMONOC GNSS stations are assimilated into WRF model at WRF initial time. After the WRF model forecasts water vapor data for the next 1 h to 24 h, the CMONOC GNSS PWV are also used to validate these results, as shown in Sect. 4. It should be noted that, PWV data at the GNSS station (27.9° N, 109.8° E) are missing at data assimilation time point (0 h UTC) from April 06 to April 09, 2020. The number of GNSS PWV assimilated for each day from April 06 to April 11, 2020 has been listed in Table 3.

Fig. 2. The distribution of 27 CMONOC GNSS stations (red dots), 17 radiosonde stations (green dots), and 7 IGS GNSS stations (blue dots) used in this study. PWV from CMONOC GNSS stations were first assimilated into WRF model and then used to validate WRF PWV forecasting results. Radiosonde profiles were assimilated into WRF model. IGS GNSS observations were used in PPP validation

3.1.2 Radiosonde Profiles Radiosonde meteorological profiles used in this study are obtained from the Integrated Global Radiosonde Archive (IGRA). Currently, IGRA provides radiosonde profile records at more than 1000 globally distributed radiosonde stations. Normally two profiles are observed at each station at 0 h and 12 h UTC per day. In this study,

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Table 3. Number of GNSS PWV observations and radiosonde profiles assimilated for each day from April 06 to April 11, 2020. Date 06 07 08 09 10 11 (April 2020) GNSS 26 26 26 26 27 27 Radiosonde 21 17 18 10 15 17

meteorological profiles, i.e. relative humidity, temperature, and pressure profiles from 22 IGRA radiosonde stations, are assimilated into WRF model. The distribution of 22 radiosonde stations is also shown in Fig. 2. Also, data from several radiosonde are missing at 0 h UTC from April 06 to April 11, 2020. The detailed number of radiosonde profiles assimilated on each day from April 06 to April 11, 2020 is shown in Table 3. 3.2

IGS GNSS Observations in PPP Experiment

GNSS observations with sampling rate of 30 s from seven IGS stations were used to conduct PPP experiment to evaluate the WRF-generated PWV data. The locations of seven IGS stations are displayed in Fig. 2 and the type of GNSS receivers for seven IGS stations are listed in Table 4. Only GPS observations were used in PPP in this study.

Table 4. The type of GNSS receivers at seven IGS stations used in PPP validation IGS station CKSV HKSL HKWS JFNG KMNM SHAO TWTF

Type of GNSS receiver TRIMBLE ALLOY LEICA GR50 LEICA GR50 TRIMBLE NETR9 TRIMBLE ALLOY ASHTECH UZ-12 SEPT POLARX4

4 Validation of WRF PWV With the four designed WRF schemes, we can output the PWV from the WRF forecasting model. We forecast the WRF PWV every hour with lead time from 1 h to 24 h (lead time of 1 h to 24 h for WRF forecasts 1 to 6: 1 h UTC to 24 h UTC, April 06 to 11, 2020). The WRF forecasting PWV from different WRF schemes are evaluated by China CMONOC GNSS PWV. Figure 3 shows the hourly PWV RMSE of different WRF schemes at different WRF lead time. We can find that the PWV RMSE of those WRF schemes with

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assimilation of GNSS PWV (WRF schemes 1 and 3) within the first 5–7 h are evidently smaller than that of WRF without data assimilation (WRF scheme 0). This implies that assimilating GNSS PWV improves the initial water vapor information in WRF model, leading to better forecasting output. It also shows that assimilating radiosonde profiles (WRF scheme 2) has a limited impact in PWV RMSE in com-

Fig. 3. The hourly PWV RMSE of four WRF schemes evaluated by 27 China CMONOC GNSS PWV at WRF lead time of 1 h to 24 h for WRF forecasts 1–6. WRF forecasts 1–6 are six consecutive 24-h WRF forecasts initialized at 0 h UTC from April 06 to 11, 2020, respectively. Lead time of 1 h to 24 h for WRF forecast 1 to 6: 1 h UTC–24 h UTC, April 06 to 11, 2020.

parison with GNSS PWV. When WRF forecasting lead time is more than 7 h, we can see that all the four WRF schemes have very similar performances. The PWV RMSE of different WRF schemes within the first 7 h forecasting are summarized in Table 5. As we can see, within the first 7 h, the average PWV RMSE of WRF scheme 0 for three WRF forecasts is 2.3 kg/m2. Assimilation of GNSS PWV improves the WRF water vapor forecasting results. The average PWV RMSE for WRF schemes 1, 2, 3 are 1.9 kg/m2, 2.3 kg/m2 and 2.0 kg/m2, respectively. This means an improvement of up to 17.4% in accuracy of water vapor forecasting performance due to data assimilation.

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Table 5. The PWV RMSE of four WRF schemes (WRF schemes 0–3) evaluated by 27 China CMONOC GNSS PWV within the first 7 h for WRF forecasts 1–6. WRF forecasts 1–6 are six consecutive 24-h WRF forecasts initialized at 0 h UTC, from April 06 to 11, 2020, respectively. The percentage denotes the RMSE reduction of WRF with data assimilation (WRF schemes 1–3) compared with WRF without data assimilation (WRF scheme 0). Negative/positive percentage means an RMSE decrease/increase in PWV forecasting accuracy. Unit of PWV RMSE: Unit: kg/m2 WRF scheme 0 WRF scheme 1 WRF scheme 2 WRF scheme 3 WRF forecast 1 2.6 WRF forecast 2 1.8 WRF forecast 3 1.9 WRF forecast 4 1.9 WRF forecast 5 2.3 WRF forecast 6 3.1 Average

2.3

2.1 (−19.2%) 1.5 (−16.7%) 1.6 (−15.8%) 1.5 (−21.1%) 2.0 (−13.0%) 2.6 (−16.1%) 1.9 (−17.4%)

2.8 (7.7%) 1.8 (0%) 2.0 (5.3%) 1.9 (0%) 2.4 (4.3%) 3.1 (0%) 2.3 (0%)

2.3 (−11.5%) 1.5 (−16.7%) 1.8 (−5.3%) 1.5 (−21.1%) 2.0 (−13.0%) 2.7 (−12.9%) 2.0 (−13.0%)

5 Augmenting PPP with PWV Data from WRF Forecasting 5.1

PPP Strategies

In this study, we aim to augment PPP performance through the use of PWV data from each WRF data assimilation scheme. At the same time, we can evaluate the PPP accuracy of each WRF assimilation scheme. Two PPP processing strategies are adopted. For the first PPP strategy, a prior tropospheric wet delay is calculated using Saastamoinen model [40] based on the standard meteorological parameters (relative humidity: 50%, air temperature: 15 °C, air pressure: 1013.25 hPa) [41]. The tropospheric wet delay residual is then estimated as an unknown parameter with a spectral density of 3  10−8. This PPP method is the traditional PPP method and is denoted as “Estimated” PPP in this study. Another PPP strategy is using wet delay corrections derived from WRF model to correct PPP wet delay directly. In these two strategies, the tropospheric dry delay is corrected using the same method, which are calculated using Saastamoinen dry delay model [40] based on the pressure data from ECMWF ERA5 single pressure reanalysis product. The ratio between pseudorange observation standard deviation and carrier phase observation standard deviation is set to 100:1. In addition, an elevation-dependent weighting strategy is used to determine weight for pseudorange and carrier phase observations. As shown in Fig. 3, the assimilation of GNSS PWV and radiosonde profiles mainly improves the WRF water vapor forecasting within the first 5–7 h. Therefore we conduct PPP test within the first 7 h of WRF lead time only. The cutoff angle of GNSS observations used in PPP is set to 10°. The daily static PPP coordinate solutions using Bernese positioning software version 5.2 are treated as the benchmark coordinates [41].

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PPP Results with Wet Delay Corrections from WRF Domain 01

5.2.1 Static and Kinematic PPP Positioning Accuracy In this section, the wet delay corrections from WRF forecasting in geographic domain 01 are used to augment the performance of static and kinematic PPP. We did the RMSE statistics with the PPP positioning errors. The PPP usually needs to take approximately half an hour to get GNSS carrier phase ambiguities resolved [42]. In this study we thus only analyze the positioning results after GNSS carrier phase ambiguities have converged. Given that the first portion of PPP results have large positioning errors, we selected PPP results only in the period from 2 h to 7 h UTC over April 06 to 11, 2020. The 6-day average RMS of static PPP positioning errors in east, north, and up components and overall three-dimension (3D) for each IGS station are shown in Fig. 4. As we can see, compared with “Estimated” static PPP results, the RMS of positioning errors of all WRF-augmented static PPP in the up component are smaller at most IGS stations. In contrast, no improvement or even slight degradation is found in horizontal positioning accuracy of WRF-augmented PPP. We can also notice that the WRFaugmented PPP positioning results at station SHAO are much worse than that of “Estimated” PPP. One potential reason could be that station SHAO is geographically located near the edge of WRF domain 01, where WRF may have a poor forecasting performance.

Fig. 4. 6-day average RMS of positioning errors in east, north, and up components and overall 3D for traditional “Estimated” static PPP scheme and four WRF-augmented static PPP schemes at seven IGS stations during April 06 to 11, 2020. Only the positioning results from 2 h to 7 h UTC for each day are used in RMS statistics

The average RMS of positioning errors for seven IGS stations for April 06–11, 2020 are summarized in Table 6. To avoid the significant statistical errors introduced by the special case, the positioning results at IGS station SHAO are excluded in

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statistics. Table 6 indicates that WRF-augmented static PPP improves the PPP 3D positioning accuracy significantly. The WRF schemes 0 to 3 improve the PPP 3D positioning accuracy by 35.4%, 24.8%, 34.0%, and 25.5%, respectively, in comparison with traditional static PPP method where the water vapor error is “Estimated” as one unknown parameter. The WRF schemes augment the up component more prominently than the horizontal one. In the up component, the traditional “Estimated” PPP has an RMSE error of 28.1 mm. This RMSE reduces to 16.2 mm, 19.8 mm, 16.7 mm, and 19.7 mm, respectively, after applying the water vapor data from WRF schemes 0 to 3. This suggests an improvement of 42.3%, 29.5%, 40.6%, and 29.9% in up component for the WRF schemes 0–3, respectively. Nevertheless, the WRF-augmented PPP’s positioning results have a degradation in the horizontal component, particularly in east component. Despite the degradation in horizontal component, the overall 3D positioning accuracy after the WRF augmentation still show an improvement of 24.8% to 35.4%, as shown in Table 6. Table 6. Average RMS of static PPP positioning errors in east, north, and up components and overall 3D based on the positioning results at seven IGS stations during April 06 to 11, 2020. Only the positioning results during 2 h to 7 h UTC for each day are used in statistics. The percentage denotes the error reduction of each WRF-augmented PPP (WRF schemes 0–3) compared with traditional “Estimated” PPP. Negative/positive percentage means an RMS decrease/increase in positioning errors. Unit of positioning error: mm Estimated WRF scheme 0 WRF scheme 1 WRF scheme 2 WRF scheme 3 static PPP East 5.4 7.2 6.5 7.2 6.5 (33.3%) (20.4%) (33.3%) (20.4%) North 4.1 3.9 4.1 3.9 4.1 (−4.9%) (0%) (−4.9%) (0%) Up 28.1 16.2 19.8 16.7 19.7 (−42.3%) (−29.5%) (−40.6%) (−29.9%) 3D 29.4 19.0 22.1 19.4 21.9 (−35.4%) (−24.8%) (−34.0%) (−25.5%)

The 6-day average kinematic PPP positioning errors in east, north, and up components and overall 3D for each IGS station are shown in Fig. 5. Similar to static PPP results, all WRF-augmented kinematic PPP schemes show a smaller positioning error in the up component compared with the traditional kinematic PPP (“Estimated” PPP). The average kinematic PPP positioning errors for seven IGS stations using different PPP schemes are shown in Table 7. The kinematic positioning results for IGS station SHAO are also excluded in kinematic PPP accuracy statistics for the same reason stated above. We can see that, compared with “Estimated” kinematic PPP, WRF-augmented PPP schemes 0 to 3 improve the positioning accuracy in up component by 33.3%, 21.5%, 33.6%, and 20.0%, respectively. For 3D positioning accuracy, the corresponding improvements for WRF-augmented PPP schemes 0 to 3 are 25.5%, 14.8%, 26.3%, and 14.8%, respectively.

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Fig. 5. 6-day average RMS of positioning errors in east, north, and up components and overall 3D for traditional “Estimated” kinematic PPP scheme and four WRF-augmented kinematic PPP schemes at seven IGS stations for April 06-11, 2020. Only the positioning results from 2 h to 7 h UTC for each day are used in RMS statistics Table 7. Average RMS of kinematic PPP positioning errors in east, north, and up components and overall 3D based on the positioning results at seven IGS stations from April 06 to 11, 2020. Only the positioning results during 2 h to 7 h UTC for each day are used in statistics. The percentage denotes the error reduction of each WRF-augmented PPP (WRF schemes 0–3) compared with the traditional “Estimated” PPP. Negative/positive percentage means an RMS decrease/increase in positioning errors. Unit of positioning error: mm

East North

Estimated kinematic PPP 8.1 8.2

Up

33.0

3D

35.7

WRF scheme 0 9.2 (13.6%) 8.9 (8.5%) 22.0 (−33.3%) 26.6 (−25.5%)

WRF scheme 1 10.0 (23.5%) 8.3 (1.2%) 25.9 (−21.5%) 30.4 (−14.8%)

WRF scheme 2 9.1 (12.3%) 8.7 (6.1%) 21.9 (−33.6%) 26.3 (−26.3%)

WRF scheme 3 9.8 (21.0%) 8.0 (−2.4%) 26.4 (−20.0%) 30.4 (−14.8%)

We notice that WRF-augmented PPP scheme 0 (without data assimilation) even has a positioning accuracy better than WRF-augmented PPP with data assimilation (WRF schemes 1–3). However, we find PWV from WRF with data assimilation have a smaller RMSE when evaluated by GNSS PWV as shown in Sect. 4. This could be explained as follows. Assimilating external water vapor data into WRF model at WRF initial time improves the WRF water vapor initial structures, which improves the water

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vapor forecast performance primarily within the beginning a few hours. We however use the results from 2 h UTC to 7 h UTC (WRF forecasting lead time of 2 h to 7 h) to analyze positioning results after carrier phase ambiguities have converged. When the lead time extends, assimilation of external water vapor data may lead to insignificant positive impacts or even negative impacts. As said, the assimilation of water vapor data into WRF model can help improve the WRF performance in the very beginning hours. The PPP carrier phase ambiguity resolution takes place in the beginning hours too. Therefore, we expect the WRF-augmented PPP with data assimilation should has a faster ambiguity convergence speed in the PPP early stage. The static PPP convergence time, analyzed in the next Sect. 5.2.2, confirms our analysis. 5.2.2 Static PPP Convergence Time The time used for GNSS carrier phase ambiguity resolution, leading to static PPP solution convergence in the east, north, and up components, is an important factor in performance assessment. The convergence time is defined as the period from the first epoch of static PPP to the last epoch with a positioning error in a given component larger than the convergence criterion. The convergence criterion defined in this study is that positioning error is less than 10 cm in a given component. The average convergence time for different WRF-augmented PPP schemes are summarized in Table 8. We can find that WRF-augmented PPP improves convergence speed in both north and up components. WRF-augmented PPP schemes 0–3 shorten the convergence time in up component by 47.1%, 57.3%, 43.3%, and 54.8%, respectively. The convergence time in the north component is reduced by up to 3.4% using different schemes. It is worth mentioning that WRF-augmented PPP scheme 1 (with GNSS PWV assimilation) and scheme 3 (with both GNSS PWV and radiosonde profiles assimilation) has a faster convergence speed than WRF-augmented PPP scheme 0 (without data assimilation). It implies that WRF schemes 1 and 3 provide more accurate wet delay corrections at the early stage of PPP calculation. This is expected and consistent with our analysis in the last paragraph of Sect. 5.2.1. Table 8. Average convergence time in east, north, and up components in static PPP for seven IGS stations during April 06 to 11, 2020. Unit of convergence time: minutes. The convergence time in one component is defined as the last epoch in that component with a positioning error exceeding the defined convergence criterion. The convergence criterion is defined as 10 cm in this study Estimated static PPP East 8.6 North 2.9 Up 15.7

WRF scheme 0 WRF scheme 1 WRF scheme 2 WRF scheme 3 9.4 (9.3%) 2.8 (−3.4%) 8.3 (−47.1%)

9.4 (9.3%) 2.8 (−3.4%) 6.7 (−57.3%)

9.7 (12.8%) 2.8 (−3.4%) 8.9 (−43.3%)

9.3 (8.1%) 2.9 (0%) 7.1 (−54.8%)

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6 Conclusions We have conducted six consecutive 24-h WRF modeling by assimilating water vapor at 0 h UTC of each day from April 06, 2020 to April 11, 2020 in the South China region 20° N–33° N and 108° E–123° E. The WRF water vapor forecasting results are evaluated by GNSS-derived PWV. We then adopted the WRF forecast water vapor to augment the performance of GNSS static and kinematic PPP. To obtain more accurate WRF water vapor forecasting results, we assimilate PWV from 27 China CMONOC GNSS stations and meteorological profiles from 22 radiosonde stations into WRF model with four data assimilation schemes, i.e. WRF scheme 0: WRF without data assimilation; WRF scheme 1: WRF with assimilation of GNSS PWV only; WRF scheme 2: WRF with assimilation of radiosonde profiles only; WRF scheme 3: WRF with assimilation of both GNSS PWV and radiosonde profiles. The comparison of WRF forecast PWV with CMONOC GNSS PWV shows that assimilating GNSS PWV and radiosonde PWV can improve the accuracy of WRF PWV results with a forecasting lead time of 5–7 h. Without data assimilation into WRF, the RMSE of WRF PWV forecasting results within the first 7 h is 2.3 kg/m2. With data assimilation into WRF, the RMSE of WRF schemes 1 to 3 are 1.9 kg/m2, 2.3 kg/m2 and 2.0 kg/m2, respectively. The largest PWV accuracy improvement is 17.4% with WRF scheme 1. Our results indicate that PPP-augmented by WRF forecast PWV improves the overall 3D positioning accuracy and convergence time, particularly in up component. The static PPP results show that the up component positioning errors are reduced by 42.3%, 29.5%, 40.6%, and 29.9% using WRF-augmented PPP schemes 0 to 3 respectively. The corresponding 3D positioning errors with WRF-augmented PPP schemes 0 to 3 are also reduced by 35.4%, 24.8%, 34.0%, and 25.5%. With the PWV augmentation from WRF forecasting schemes 0 to 3, the static PPP ambiguity convergence time is shortened by 47.1%, 57.3%, 43.3%, and 54.8%, respectively, using 10 cm as the convergence criterion. The kinematic PPP results show that the up component positioning errors are reduced by 33.3%, 21.5%, 33.6%, and 20.0% using WRF-augmented PPP schemes 0 to 3, respectively. The 3D positioning errors for WRF-augmented PPP schemes 0 to 3 are reduced by 25.5%, 14.8%, 26.3%, and 14.8%, respectively. The accuracy of WRF water vapor forecasting results is expected to be further improved if PWV data from more GNSS stations are assimilated into the WRF model. Consequently, the WRF-augmented static and kinematic PPP performances are expected to be further improved. Acknowledgments. The support from the Key Program of the National Natural Science Foundation of China (No. 41730109) is acknowledged. The work described in this paper was also supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 15211919 Q73B). The Emerging Frontier Area (EFA) Scheme of Research Institute for Sustainable Urban Development (RISUD) of the Hong Kong Polytechnic University (No. 1-BBWJ) is also acknowledged. The authors thank GNSS data product service platform of China Earthquake Administration for providing GNSS PWV data of the Crustal Movement Observation Network Of China (CMONOC) (http://

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www.cgps.ac.cn). The National Oceanic and Atmospheric Administration (NOAA) is thanked for providing the Integrated Global Radiosonde Archive (IGRA) radiosonde data (ftp://ftp.ncdc. noaa.gov/pub/data/igra/). We thank online archives of the Crustal Dynamics Data Information System (CDDIS), NASA Goddard Space Flight Center, Greenbelt, MD, USA, for providing IGS GNSS data (https://cddis.nasa.gov/archive/gnss/data/daily/). The European Centre for Medium-Range Weather Forecasts (ECMWF) (https://cds.climate.copernicus.eu/#!/search?text= ERA5&type=dataset) is appreciated for providing the ECMWF ERA5 reanalysis data.

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17. Liu, Z., Li, M., Zhong, W., Wong, M.S.: An approach to evaluate the absolute accuracy of WVR water vapor measurements inferred from multiple water vapor techniques. J. Geodyn. 72, 86–94 (2013) 18. Powers, J.G., Klemp, J.B., Skamarock, W.C., et al.: The weather research and forecasting model: overview, system efforts, and future directions. Bull. Am. Meteor. Soc. 98, 1717– 1737 (2017) 19. Dullaart, J.C., Muis, S., Bloemendaal, N., Aerts, J.C.: Advancing global storm surge modelling using the new ERA5 climate reanalysis. Clim. Dyn. 54, 1007–1021 (2020) 20. Hobiger, T., Shimada, S., Shimizu, S., Ichikawa, R., Koyama, Y., Kondo, T.: Improving GPS positioning estimates during extreme weather situations by the help of fine-mesh numerical weather models. J. Atmos. Solar Terr. Phys. 72, 262–270 (2010) 21. Ibrahim, H.E., El-Rabbany, A.: Performance analysis of NOAA tropospheric signal delay model. Meas. Sci. Technol. 22, 115107 (2011) 22. Wilgan, K., Hadas, T., Hordyniec, P., Bosy, J.: Real-time precise point positioning augmented with high-resolution numerical weather prediction model. GPS Solutions 21, 1341–1353 (2017) 23. Hersbach, H., Bell, B., Berrisford, P., et al.: The ERA5 global reanalysis. Q. J. Roy. Meteorol. Soc. 146(730), 1999–2049 (2020) 24. Barker, D.M., Huang, W., Guo, Y.-R., Bourgeois, A., Xiao, Q.: A three-dimensional variational data assimilation system for MM5: implementation and initial results. Mon. Weather Rev. 132, 897–914 (2004) 25. Huang, X.-Y., Xiao, Q., Barker, D.M., et al.: Four-dimensional variational data assimilation for WRF: formulation and preliminary results. Mon. Weather Rev. 137, 299–314 (2009) 26. Leung, L.R., Qian, Y.: Atmospheric rivers induced heavy precipitation and flooding in the western US simulated by the WRF regional climate model. Geophysical Research Letters, vol. 36 (2009) 27. Gao, Y., Xu, J., Chen, D.: Evaluation of WRF mesoscale climate simulations over the Tibetan Plateau during 1979–2011. J. Clim. 28, 2823–2841 (2015) 28. Kain, J.S.: The Kain-Fritsch convective parameterization: an update. J. Appl. Meteorol. 43, 170–181 (2004) 29. Iacono, M.J., Delamere, J.S., Mlawer, E.J., Shephard, M.W., Clough, S.A., Collins, W.D.: Radiative forcing by long-lived greenhouse gases: calculations with the AER radiative transfer models. Journal of Geophysical Research: Atmospheres, vol. 113 (2008) 30. Hong, S.-Y., Noh, Y., Dudhia, J.: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Weather Rev. 134, 2318–2341 (2006) 31. Jiménez, P.A., Dudhia, J., González-Rouco, J.F., Navarro, J., Montávez, J.P., GarcíaBustamante, E.: A revised scheme for the WRF surface layer formulation. Mon. Weather Rev. 140, 898–918 (2012) 32. Dudhia, J.: A multi-layer soil temperature model for MM5. In: Preprints, The Sixth PSU/NCAR Mesoscale Model Users’ Workshop, pp. 22–24 (1996) 33. Mateus, P., Nico, G., Catalão, J.: Uncertainty assessment of the estimated atmospheric delay obtained by a numerical weather model (NMW). IEEE Trans. Geosci. Remote Sens. 53, 6710–6717 (2015) 34. Askne, J., Nordius, H.: Estimation of tropospheric delay for microwaves from surface weather data. Radio Sci. 22, 379–386 (1987) 35. Rüeger, J.M.: Refractive index formulae for radio waves. Integration of Techniques and Corrections to Achieve Accurate Engineering, pp. 19–26 (2002) 36. Bevis, M., et al.: GPS meteorology: mapping zenith wet delays onto precipitable water. J. Appl. Meteor 33, 379–386 (1994)

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The Precise Point Positioning Algorithm and Its Performance Evaluation Using Combined BDS-3 and BDS-2 Lun Ai1,2, Jie Wu1(&), Binbin Wang2, Ruwei Zhang2, and Wei Li3 1

2

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China [email protected] Zhang Beijing Research Institute of Telemetry, Beijing 100076, China 3 Air Force Equipment Department, Shijiazhuang 050081, China

Abstract. The BDS-3 system has been fully constructed and formally opened in 2020. Precise Point Positioning (PPP) is of high value in research and application regions. In order to analyze the PPP result using BDS-3 and BDS-2, this article first introduces the information of BDS-3 and its differences with BDS-2. Then, the PPP algorithm based on BDS-2 and BDS-3 is discussed in detail. Besides, the differences between BDS-2 and BDS-3 in satellite attitude models, as well as the processing method of inter system bias are compared and analyzed. In the static PPP experiment based on BDS-3 and BDS-2, the position RMS are 0.31 cm, 0.47 cm, 1.11 cm in east, north and up directions respectively, and the convergence time is about 24.80 min. In the kinematic PPP experiment, the three-dimensional position RMS are 2.67 cm, 4.05 cm, 8.04 cm, and the convergence time is up to 36.84 min. Compared to using BDS2 only, the PPP result based on BDS-3 and BDS-2 has been significantly improved. Keywords: BDS-3
PPP Performance evaluation


System bias
Satellite attitude models


1 Introduction The construction of the Chinese BeiDou Navigation Satellite System (BDS) is divided into three steps: (1) BDS-1, which provides active positioning and short message communication services only for the Chinese users by 2000; (2) BDS-2, which provides passive positioning and short message communication services for the AsianPacific region by 2012; (3) BDS-3, which provides high-quality services such as combination of navigation and positioning, communication and data transmission to global users by 2020 [1, 2]. Precise Point Positioning is a high-precision satellite positioning algorithm, which has important research value in the fields of crustal deformation monitoring, low-orbit satellite orbit determination, space atmosphere monitoring, time synchronization and intelligent transportation [3–6]. The current research hotspots of PPP algorithms are concentrated on multi-system multi-frequency combination PPP, real-time PPP, PPP © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 671–680, 2021. https://doi.org/10.1007/978-981-16-3138-2_61

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with fixed ambiguity, and PPP-RTK [7–13]. Shi et al. proved that the effect of BDS-3 on improving PPP static positioning accuracy is limited using Multi-GNSS Experiment (MGEX) data [14]. Zhang et al. firstly determine the precise orbit of BDS satellites based on 116 ground stations and then test the kinematic PPP. When using only BDS2, the horizontal positioning accuracy is 1.4–2.0 cm, the vertical positioning accuracy is 4.2–4.8 cm and the convergence time is 64 min. When using combined BDS-2 and BDS-3, the horizontal positioning accuracy is 0.9–1.9 cm, the vertical positioning accuracy is 2.2–3.9 cm and the convergence time is 25 min [15]. Jiao et al. model the system bias between BDS-2 and BDS-3, the positioning error in three dimensional are improved by 2.38%, 9.71%, 6.74% respectively and the convergence time are shortened by 2.39%, 10.21%, 6.28% [16]. The above research results mainly introduce the improvement of BDS-3 on PPP, of which results are quite different, and the implementation method is not discussed in detail. Therefore, this paper elaborates the combined BDS-3/BDS-2 PPP algorithm and its implementation process. The BDS-3 and BDS-2 is briefly introduced, focusing on the analysis of the PPP algorithm of BDS-3 and BDS-2, including system bias processing method and the difference in satellite attitude model. The data from the international GNSS Monitoring and Assessment System (iGMAS) stations is processed to evaluate the performance of the BDS-3/BDS-2 PPP algorithm.

2 BDS-3 and BDS-2 At present, the BDS service is jointly provided by the BDS-2 and the BDS-3. BDS-2 is composed of four Medium Earth Orbit (MEO) satellites, five Inclined Geostationary Satellite Orbit (IGSO) satellites and five Geostationary Earth Orbit (GEO) satellites. The BDS-3 is composed of twenty-four MEO satellites, three IGSO satellites and three GEO satellites. BDS-3 adopts BeiDou Coordinate System (BDCS), which belongs to the Earth-Centered Earth-Fixed (ECEF) coordinate system, and has the same parameters as the China Geodetic Coordinate System 2000 (CGCS2000) used by BDS-2. The time system of BDS-3 and BDS-2 is BeiDou Time (BDT), which is the atomic time with the same starting time. The signals broadcasted by BDS-2 include B1I, B2I, and B3I. The signals broadcasted by BDS-3 include B1I, B3I, and the new system signals B1C, B2a, and B2b. There are differences and similarities between BDS-2 and BDS-3 in constellation, signal frequency and basic service types. At present, BDS-3 can significantly increase the number of observed satellites and improve the Position Dilution of Precision (PDOP) value. Therefore, it is of great significance to fuse data of BDS-2 and BDS-3, and to study its improvement on the PPP algorithm.

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3 Precise Point Positioning Algorithm 3.1

PPP Mathematical Model

The combined BDS-3/BDS-2 PPP algorithm discussed in this paper using the ionospheric-free combination observation equation is as follows: 8 C2 P ¼ q þ cDtr  cDts þ Trop þ dP þ eP > > > < LC2 ¼ q þ cDt  cDts þ Trop þ Amb þ d þ e r L L C3 s > P ¼ q þ cDt þ Bias  cDt þ Trop þ d þ e > r P P > : C3 L ¼ q þ cDtr þ Bias  cDts þ Trop þ Amb þ dL þ eL

ð1Þ

where P and L are the ionosphere-free combination of pseudorange and carrier phase. The superscript C2 represents the BDS-2 observation and C3 represents the BDS-3 observation. Bias is the inter-system bias parameter between BDS-3 and BDS-2. Depending on the type of receiver, it can be set as non-parameter model, constant model, random walk model and white noise model. The definition of other symbols is same to reference. After linear expansion of geometric distance, tropospheric delay modeling and systematic error correction, observation equation can be expressed in matrix form. As shown in formula (1), X is the parameter vector, A is the design matrix, L is the observation vector, V is the error vector, D is the covariance matrix of observations, P is the weight matrix of observations, d20 is the prior variance of unit weight. V ¼ A
X  L; D = d20 P1

ð2Þ

The left of the formula (2) is the function model of PPP, while the right is the random model, the two are collectively referred to the PPP mathematical model. The PPP random model is a diagonal matrix, whose elements are the prior variance of the ionospheric-free pseudorange combination and carrier phase combination. 3.2

PPP Data Processing Flow

The PPP algorithm uses final ephemeris and observation data in the form of files. All observation data is preprocessed, including cycle slip detection and error source modeling. Parameter estimation is carried on with Kalman filter. The PPP data processing flow is shown in Fig. 1. In the PPP data processing flow, data preparation is to convert final ephemeris files and observation files into standard Standard Product# 3 (SP3) and Receiver Independent Exchange Format (RINEX). Data preprocessing mainly includes cycle slip detection and error source modeling. The TurboEdit method is used to detect cycle slips. The phase center offset of satellite antennas and receiver antennas, relativistic effects, carrier phase wind-up, earth rotation, solid tides, ocean tides, pole tides and other systematic error are corrected. The parameter estimation part includes the construction of the PPP mathematical model, and the Kalman filter is used to estimate the

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parameters of each epoch. The weight of the observations is adjusted according to the post-fit residual, the Kalman filter and the weight adjustment iteratively run until all the outliers are processed.

Observation Files

Ephemeris Files

Convert the File Format

Detect cycle slip Using TurboEdit method

Model and Correct the systematic error

Construct the PPP Mathematical Model

Adjust the Weight of Observations

Estimate the PPP Parameter using Kalman Filter

Outliers

Yes

No End

Fig. 1. The data processing flow of PPP

3.3

Satellite Attitude Models

Because of the phase center offset of the satellite antenna and phase wind-up are related to the satellite attitude model, different satellite attitude models can lead to decimeterlevel errors on the observations [17]. According to the different types of navigation satellites and sun elevation to the orbital plane, there are three attitude modes for BDS satellites: nominal attitude mode, orbit-normal attitude mode, and maneuver attitude mode. 1. Nominal attitude mode When the sun elevation is greater than or equal to 3°, the IGSO and MEO satellites of BDS-2 and BDS-3 will adopt nominal attitude mode. This attitude mode is defined as the Z axis pointing from the satellite to the center of the earth, the Y axis is always perpendicular to the plane composed of the sun, the earth and the satellite and parallel to the solar panel, and the X axis is determined by the right-hand rule. ! ! r sat r sat  ! r sat ! e z ¼  !  ; ! e y ¼  ! ! r sat r sat  r sat

sun sun

! ! ; !  ex¼ ey ez

ð3Þ

e y, ! e z are the unit vector of the axis of the satellite body in the ECEF where ! e x, ! * coordinate system. ! r sat is the vector of satellite position, r sat sun is the vector from the

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satellite to the sun. The nominal attitude mode can also be expressed by the yaw attitude angle: w¼ tan1 ðSoy =Sox Þ

ð4Þ

where w is the yaw angle, which is the angle between the satellite body X axis and the velocity direction, Sox is the X-axis component of the unit solar vector in the orbit plane, Soy is the Y-axis component of the unit solar vector in the orbit plane. 2. Orbit-normal attitude mode When the sun elevation is less than 3°, the GEO satellites of BDS-3 and all satellites of BDS-2 will adopt the orbit-normal attitude mode. The X axis is consistent with the velocity direction of the satellite, the Z axis points to the earth, and the Y axis is determined by the right-hand rule. ! ! r sat v sat ! e z ¼  !  ; ! ey¼! ex¼! e z  !  ; ! ey! ez r sat v sat

ð5Þ

In the formula (5), ! v sat is the velocity direction of the satellite, and the definition of other symbols is consistent with formula (3). When the yaw attitude angle is used to express the satellite attitude mode, the yaw angle in the orbit-normal attitude mode is zero. 3. Maneuver attitude mode When the sun elevation is less than 3°, the IGSO and MEO satellites of BDS-3 will adopt maneuver attitude mode. This attitude mode is defined as the Z axis pointing to the earth, the X axis facing the sun and the Y axis approximately perpendicular to the satellite-sun vector. The yaw attitude angle is: 

w = tan1 ð0:05236=Sox Þ w = tan1 ð0:05236=Sox Þ

b[0 b\0

ð6Þ

4 PPP Experiment We select seven receivers from iGMAS stations in this PPP experiment, during day of year 201 to 207, 2020. The distribution of the stations is shown in Fig. 2.

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Fig. 2. The distribution of iGMAS stations

In the static PPP experiment, Fig. 3 shows the time series of the static PPP coordinate bias of KUN1 station in the day of year 201. The upper part of the figure shows the static positioning results using only BDS-2, and the lower part shows the static positioning results using combined BDS-3 and BDS-2. Figure 4 shows the static PPP results root mean square (RMS) of the seven iGMAS stations in 2020, from the day of year 201 to 207. The upper part of the figure shows the static positioning results using only BDS-2, and the lower part shows the static positioning results using combined BDS-3 and BDS-2. As shown in Fig. 3 and Fig. 4, the combination of BDS-3 and BDS-2 can significantly improve the positioning accuracy of static PPP using only BDS-2.

Fig. 3. The static PPP result of KUN1

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Fig. 4. The static PPP RMS of seven iGMAS stations

Similar to the static positioning experiment, Fig. 5 and Fig. 6 shows the time series of the kinematic positioning coordinate bias of KUN1 station and the kinematic PPP results rms of the seven iGMAS stations. It can be seen that the combination of the BDS-3 and BDS-2 can effectively improve the positioning accuracy of kinematic PPP using only BDS-2.

Fig. 5. The kinematic PPP result of KUN1

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Fig. 6. The kinematic PPP RMS of seven iGMAS stations

As shown in the Table 1, we summarize the position performance including positioning accuracy and convergence time (CT) in the static and kinematic PPP experiment. The unit of positioning accuracy in the directions of N, E, and U is centimeters, and the unit of convergence time is minutes. Table 1. The statistical information of PPP results Positioning mode Static PPP (N, E, U:cm;CT:min) N E U CT BDS2 0.84 1.38 3.48 81.27 BDS-3/BDS-2 0.31 0.47 1.11 24.80

Kinematic PPP N E U CT 6.95 8.04 22.31 \ 2.67 4.05 8.04 36.84

According to the Table 1, the static PPP RMS of BDS-2 in the N, E, and U directions are 0.84 cm, 1.38 cm, and 3.48 cm, while the static PPP RMS of the combined BDS-3 and BDS-2 is 0.31 cm, 0.47 cm, 1.11 cm. Compared with using only BDS-2, the combination of BDS-3 and BDS-2 improves the positioning accuracy by 63%–68%, and the convergence time is also shortened from 81.27 min to 24.80 min. In terms of kinematic experiment, the positioning RMS of using only BDS-2 is 6.95 cm, 8.04 cm, 22.31 cm, and the positioning accuracy is 2.67 cm, 4.05 cm, and 8.04 cm using combined BDS-3 and BDS-2, which is 50%–64% better than BDS-2, and the convergence time is 36.84 min. Due to the poor positioning performance of BDS-2 kinematic PPP, the convergence time is not counted.

5 Conclusion This paper first introduces the BDS-3 and BDS-2 system in constellation, signal frequency, time system, coordinate system, and basic services. The precise point positioning algorithm based on BDS-3 and BDS-2 is described in detail, including

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mathematical models and data processing procedures. The paper focuses on the difference between BDS-2 and BDS-3 in satellite attitude and the method of processing inter-system bias, which must be correctly modeled in PPP. Data from seven stations of iGMAS for a week has been processed in static PPP mode and kinematic PPP mode respectively, and the conclusions as follow: (1) In the static PPP mode, the positioning RMS of combined BDS-3 and BDS-2 in N, E and U directions are 0.31 cm, 0.47 cm and 1.11 cm, which is 63%–68% better than that of using only BDS-2, and the convergence time is shortened from 81.27 min to 24.80 min; (2) In the kinematic mode, the positioning RMS of combined BDS-3 and BDS-2 in N, E and U directions are 2.67 cm, 4.05 cm and 8.04 cm, which is 50%–64% better than that of using only BDS2, and the convergence time is 36.84 min. In conclusion, the construction and use of BDS-3 has a significant improvement effect on the PPP accuracy and convergence time of the current BDS. It is worth noting that the final ephemeris products used in this paper only include the BDS satellite, of which PRN is smaller than 38, and the number of BDS-3 satellites used in the PPP experiment is 18. With the continuous improvement of final ephemeris products, more BDS-3 satellites will be available, thus further improve the positioning performance of PPP. Acknowledgements. This work was supported in part by the National Key Research and Development Program of China (No. 2019YFC1511504, No.2017YFB0503402) and National Natural Science Foundation of China (No. 41774017).

References 1. Yang, Y.X., Mao, Y., Sun, B.J.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1, 1 (2020) 2. Lu, J., Guo, X., Su, C.G.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1, 27 (2020) 3. Li, X.X., Zhang, X.H., Li, P.: PPP for rapid precise positioning and orbit determination with zero-difference integer ambiguity fixing. Chin. J. Geophys. 55(3), 833–840 (2012) 4. Xiao, G.W., Ou, J.K., Liu, G.L., et al.: Construction of a regional precise tropospheric delay model based on improved BP neural network. Chin. J. Geophys. 61(8), 3139–3148 (2018) 5. Shi, C., Zhang, D., Song, W., et al.: BeiDou wide-area precise timing prototype system. Acta Geod. Cartogr. Sin. 49(3), 269–277 (2020) 6. Du, Y.J., Wang, J.L., Rizos, C., et al.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2, 3 (2021) 7. Zhang, B.C., Chen, Y.C., Yuan, Y.B.: PPP-RTK based on undifferenced and uncombined observations: theoretical and practical aspects. J. Geodesy 93(7), 1011–1024 (2018) 8. Xiao, G.W., Liu, G.Y., Ou, J.K., et al.: MG-APP: an open-source software for multi-GNSS precise point positioning and application analysis. GPS Solutions 24(B3), 113–178 (2020) 9. Zhang, X.H., Hu, J.H., Ren, X.D.: New progress of PPP/PPP-RTK and positioning performance comparison of BDS/GNSS PPP. Acta Geod. Cartogr. Sin. 49(9), 1084–1100 (2020) 10. Chen, X.Y.: An alternative integer recovery clock method for precise point positioning with ambiguity resolution. Satell. Navig. 1, 28 (2020)

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11. An, X.D., Meng, X.L., Jiang, W.P.: Multi-constellation GNSS precise point positioning with multi-frequency raw observations and dual-frequency observations of ionospheric-free linear combination. Satell. Navig. 1, 7 (2020) 12. Jin, S.G., Su, K.: PPP models and performances from single- to quad-frequency BDS observations. Satell. Navig. 1, 16 (2020) 13. Li, B.F., Zhang, Z.T., Miao, W.K., et al.: Improved precise positioning with BDS-3 quadfrequency signals. Satell. Navig. 1, 30 (2020) 14. Shi, J.B., Ouyang, C.H., Huang, Y.S., et al.: Assessment of BDS-3 global positioning service: ephemeris, SPP, PPP, RTK, and new signal. GPS Solutions 24(3), 24–81 (2020) 15. Zhang, Z.T., Li, B.F., Nie, L.W., et al.: Initial assessment of BeiDou-3 global navigation satellite system: signal quality, RTK and PPP. GPS Solutions 23(4), 1–12 (2019) 16. Jiao, G.Q., Song, S.L., Jiao, W.H.: Improving BDS-2 and BDS-3 joint precise point positioning with time delay bias estimation. Meas. Sci. Technol. 31(2), (2020) 17. Ye, S.R., Xia, F.Y., Zhao, L.W., et al.: Impact analysis of yaw attitude on BDS precise point positioning. Acta Geod. Cartogr. Sin. 46(8), 971–977 (2017)

Research on Orbital Position Adjustment Control Strategy of Beidou IGSO Satellite Based on Differential Evolution Algorithm Ying Zhang(&), Dingwei Wang, Quanjun Li, Lei Shi, and Yingying Zhang Key Laboratory for Spacecraft In-Orbit Fault Diagnosis and Maintenance and Xi’an Satellite Control Center, Xi’an 710043, China

Abstract. In order to realize the smooth transition from Beidou-2 system to Beidou-3 system, the orbital positions of IGSO-2 and IGSO-3 satellites will be adjusted. Multiple constraints such as control time, geographic longitude of ascending node, semi major axis, eccentricity and argument of perigee need to be considered in IGSO satellite orbital position adjustment. It takes a long time to make the strategy by trial and error method in the project, and the strategy can not achieve the minimum fuel consumption. In order to solve this problem, the IGSO satellite orbital position adjustment is decomposed into drift control and brake control. The control quantity of drift control is obtained by analytical method, and the brake control is transformed into control optimization problem with multiple constraints. A in-plane two-body motion model is established, and the constraint conditions are analyzed. The calculation method of IGSO satellite braking control strategy based on differential evolution algorithm is proposed. The objective function is established by integrating fuel consumption and constraint conditions, and the control time and speed increment of multi batch control are solved. The simulation results show that the algorithm improves the formulation time of IGSO satellite orbital position adjustment control strategy from the original hour level to the minute level, at the same time, the fuel consumption is minimized, which is conducive to extending the life of the satellite. Keywords: Beidou IGSO satellite evolution


Orbital position adjustment
Differential

1 Introduction The orbit control of IGSO satellites has perfect basic theoretical support, but in practice, the orbital position adjustments of IGSO satellites need to take into account multiple constraints, such as drift time, geographic longitude of rising intersection point, semi-major axis of orbit, eccentricity rate, perigee amplitude and so on. At present, in practical operation, manual trial calculation is still used to determine the strategy of orbit control, which takes a long time, and the strategy can not achieve the minimum fuel consumption. In order to solve this problem, the process of IGSO satellite orbital position adjustments can be decomposed into start-drift control and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 681–689, 2021. https://doi.org/10.1007/978-981-16-3138-2_62

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braking control. The control quantity of start-drift control is obtained by using analytical method, and the braking control is transformed into a control optimization problem under multiple constraints. Establishing the in-plane two-body motion model, and analyzing the constraint conditions, the braking control strategy calculation method of IGSO satellites based on differential evolution algorithm was proposed. The objective function was established by integrating fuel consumption and constraint conditions to solve the control time and speed increment of multi-batch control. The algorithm in this paper only needs the input of start-drift time, total drift time, target longitude, eccentricity and perigee amplitude, then the multi-batch control time and speed increment under the condition of minimum fuel consumption can be solved. Through simulation verification, the algorithm will increase the time of IGSO satellites orbital position adjustment control strategy determination from the original hour level to the minute level, and at the same time the algorithm control the fuel consumption required minimum, which is beneficial to prolonging the working life of the satellite.

2 Orbit Adjustment and Control of IGSO Satellite During the long-term management of geosynchronous satellites, orbital position adjustment, which means orbital position transfer and recapture, is often carried out. Usually, the task of orbital position transfer is to start from the specified date and change the satellite from the current longitude to target longitude within the time interval. The eccentricity is limited in the drift process. Generally, the longitude difference of orbit transfer task is much larger than the dead zone of the two longitudes, and the average drift rate and daily oscillation in the orbital position transfer process are much larger than those in the position holding period. There are two methods of orbital position transfer, The first is to realize elliptical drift orbit by single batch control, and the second is to realize circular drift orbit by two batch control [1]. In order to maintain the navigation constellation configuration and provide continuous and reliable services, Beidou IGSO satellite has certain orbit constraints and control constraints [2], so the satellite can only be controlled in a limited period of time; after the last batch of control, the satellite needs time for orbit measurement, orbit determination and evaluation, and the control strategy modification. After that, the next batch control can be implemented. To sum up, the orbital position adjustment control problem of Beidou IGSO satellite is an optimization problem to minimize the speed increment under multiple constraints. For the complex nonlinear and multi constraint characteristics of practical engineering problems, traditional optimization methods such as Newton method and simplicity method need to traverse the whole search space, which is time-consuming and easy to produce “combination explosion” [3]. At present, there are many intelligent optimization algorithms to solve complex multi constraint optimization problems, and differential evolution algorithm is suitable for solving complex optimization problems. The orbital position adjustment control of Beidou IGSO satellite is divided into two parts: drift control and braking control. Because the orbit constraint is weak for drift control and strong for braking control. Therefore, the optimization algorithm is not considered in the calculation of drift strategy, otherwise the dimension of variables will

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be increased and the calculation time will be prolonged. In general, the control time is given by the satellite operational control unit according to the requirements of the drift mission and the control constraints, and the circular drift orbit is controlled by two batches of double pulses. The first batch of control time and the second batch of control time are separated by half a day. According to the target geographic longitude of ascending node and the current geographic longitude of ascending node, the drift direction is determined, and the drift height is determined according to the drift time. The average longitude drift rate and relative synchronous orbit height of the drift orbit are calculated by formula (1) and formula (2). k2  k1 n  0:5

ð1Þ

hf ¼ 78vk

ð2Þ

vk ¼

Where, vk is the horizontal longitude drift rate and hf is the drift height. In order to ensure the space security of the satellite and keep the relative distance between the satellite and other space targets, the satellite is designed to maintain a circular orbit during the drift period. Taking westward drift as an example, the apogee and perigee altitudes of the original orbit of the satellite are set as ha ; hp . If the satellite eccentricity is small and the apogee height ha is lower than the drift height hf , the first batch will raise the orbit
 height 12 hf  hp at the apogee and the second batch will raise the orbit height
 1 height 2 hf  ha at the new apogee. If the satellite eccentricity is large and the apogee
 ha is higher than the drift height hf , the first batch will raise the orbit height 12 hf  hp
 at the apogee and the second batch will lower the orbit height 12 ha  hf at the new perigee.

3 Application of Differential Evolution Algorithm The operation steps of differential evolution algorithm are as follows: (1) Initialization For the brake control problem of Beidou IGSO satellite orbital position adjustment, a parameter vector x with dimension D = 4 is established as an individual. The choice of the number of parameter vectors must ensure that the constraint function can be satisfied. Under this condition, the number of parameter vectors should be as small as possible to constrain the size of the solution space. x ¼ ½dt1 ; Dvx1 ; dt2 ; Dvx2 

ð3Þ

NP individuals are regarded as the population of each generation, and each individual is represented as a population.

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xi;G ði ¼ 1; 2;


; NPÞ

ð4Þ

Where i is the sequence number of individuals in the population, G is the evolutionary algebra, and NP is the population size. In this problem, NP is set to 40. The initial population is randomly selected from the values within a given boundary constraint. It is assumed that the random initial population conforms to the uniform probability distribution. If the boundary of parameter variable is xLj \xj \xU j , then   L L xji;0 ¼ rand ½0; 1
xU j  xj þ xj ði ¼ 1; 2;


; NP; j ¼ 1; 2;


; DÞ

ð5Þ

Where rand ½0; 1 is the random number generated between [0,1]. (2) Variation For each target vector xi;G ði ¼ 1; 2;


; NPÞ, the mutation vector of the basic differential evolution algorithm is generated by the following formula [4]:
 si;G þ 1 ¼ xr1 ;G þ F
xr2 ;G  xr3 ;G

ð6Þ

In the formula, the randomly selected sequence numbers r1 ; r2 ; r3 are different from each other, and r1 ; r2 ; r3 should also be different with the sequence number i of target vector. For the brake control problem of Beidou IGSO satellite orbital position adjustment, the mutation operator F takes 0.8 to control the amplification effect of deviation variable. (3) Cross In order to increase the diversity of the interference parameter vector, the crossover operation is introduced, and the test vector becomes:
 ui;G þ 1 ¼ u1i;G þ 1 ; u2i;G þ 1 ;


; uDi;G þ 1 ( uji;G þ 1 ¼

sji;G þ 1 ; randbð jÞ  CR [ j ¼ rnbrðiÞ

xji;G þ 1 ; randbð jÞ [ CR \ j 6¼ rnbrðiÞ ði ¼ 1; 2;


; NP; j ¼ 1; 2;


; DÞ

ð7Þ

ð8Þ

Which randbð jÞ represents the jth estimated value of the random number generator between [0,1]; rnbrðiÞ 2 ð1; 2;


; DÞ represents a randomly selected sequence, which is used to ensure that at least one parameter ui;G þ 1 is obtained from si;G þ 1 [5]; For the brake control problem of the Beidou IGSO satellite orbit track position adjustment, the crossover operator CR takes the value 0.95. (4) Select For the brake control problem of the Beidou IGSO satellite orbit track position adjustment, Constraints can be divided into track constraints and control constraints. Orbital constraints include semi-major axis, eccentricity, argument of perigee, and

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geographic longitude of ascending node. In order to enhance the stability of the constraint, the eccentricity and argument of perigee are converted into eccentricity vectors.   e ¼ ex ; ey ¼ ½e cos x; e cos x

ð9Þ

The above constraints can be expressed by the corresponding error function da; dex ; dey ; dk. 

ja  aT j; ja  aT j  ea 0 ; ja  aT j\ea

ð10Þ

jex  exT j; jex  exT j  eex 0 ; jex  exT j\eex

ð11Þ

( ey  eyT ; ey  eyT  eey dey ¼ 0 ; ey  eyT \eey

ð12Þ

da ¼  dex ¼

 dk ¼

jk  kT j; jk  kT j  ek 0 ; jk  kT j\ek

ð13Þ

Which, aT ; exT ; eyT ; kT is the target value of each constraint parameter, and ea ; eex ; eey ; ek is the allowable error threshold of each constraint parameter. Control constraints include orbital control time and orbital control interval. For orbital control time constraints, the orbital control time t must be within the orbitable time period ½tL ; tU . The error function of the orbital control time t is expressed as ( dt ¼

tU tL 2

 t  tL þ2 tU ; t 62 ½tL ; tU  0 ; t 2 ½tL ; tU 

ð14Þ

The orbit control times t corresponding to the two orbit changes are t1 ¼ t0 þ Dt1 , t2 ¼ t0 þ Dt1 þ Dt2 . For the orbit control interval constraint, it is required that the two orbit control intervals Dt2 must be greater than the minimum control interval Dtmin , and the error function of the orbit control interval Dt2 is expressed as  dDt ¼

Dtmin  Dt2 ; Dt2 \Dtmin 0

; Dt2  Dtmin

ð15Þ

The optimization goal of the braking control problem of the Beidou IGSO satellite orbit track position adjustment is the least fuel, that is, the minimum speed increase. Considering that the constraint conditions must be met, in order to speed up the

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convergence speed of the constraint conditions, the orbit constraint is added to the objective function with a certain coefficient, and the objective function is obtained as:

o ¼ jDvx1 j þ jDvx2 j þ g


da dex dey dk þ þ þ ea ek eex eey

 ð16Þ

Which, g is the weight coefficient of the constraint condition, which is 0.5 according to experience. ea , eex , eey , ek are the allowable error thresholds of the orbital semi-major axis, the component of the eccentricity vector on the x-axis, the component of the eccentricity vector on the y-axis, and the geographic longitude of the ascending node. (5) Termination condition Aiming at the braking control problem of Beidou IGSO satellite orbit track position adjustment, the judgment criterion is set as follows: the constraint function value is 0 and the objective function keeps the current value in the next 500 iterations, then the algorithm operation is terminated and the current population’s best is output. The individual is the optimal solution.

4 Simulation and Result Analysis 4.1

Simulation Example

Assume that an Beidou IGSO satellite needs to drift from 107.5° east longitude on January 25, 2021, and drift to 95° east longitude before February 4, 2021. The initial orbit is shown in Table 1. The geographic longitude of the ascending node after the fixed point is required to be 95° east longitude, the semi-major axis is 42165.7 km, the eccentricity is 0.0025, and the argument of perigee is 180°.

Table 1. The initial orbit of an IGSO satellite Epoch time Semi-major axis/km Eccentricity Inclination/Degree Ascending node right ascension/Degree Argument of Perigee/Degree Flat anomaly/Degree Ascending node geographic longitude/Degree

2021-01-25 08:00:00 42163.56 0.001703 55.067 175.925 181.128 235.008 107.5

According to the above requirements, the relative GEO orbital height during the satellite drift is 139 km. Comparing the altitude of the satellite’s perigee and apogee with the height of the drifting star, the drift strategy is determined as follows: The first

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batch raised the orbital height by 89 km at apogee, the second batch raised an orbital height of 18 km at the new apogee. The specific strategy is shown in Table 2.

Table 2. The drift control strategy of an IGSO satellite Time Tangential speed increment (m/s) Semi-major axis change (KM) 2021-1-26 04:18 +4.23 +116.1 2021-1-26 16:18 +1.63 +44.8

Extrapolate the drift-off track to before braking control, and use differential evolution algorithm to optimize the braking control strategy. After the optimization, the satellite braking control strategy is shown in Table 3.

Table 3. An IGSO satellite brake control strategy Time Tangential speed increment(m/s) Semi-major axis change(KM) 2021-2-1 5:43 −4.31 −118.2 2021-2-2 21:53 −1.49 −40.9

Use STK software to extrapolate the control strategy and obtain the orbit parameters after satellite control as shown in Table 4. Table 4. Orbit parameters of an IGSO satellite after control Track parameters after real control Semi-major axis/km Eccentricity Argument of Perigee/Degree Ascending node right ascension/Degree

4.2

42165.28 0.00253 178.837

Nominal orbital parameters 42165.7 0.0025 180

Difference from nominal orbital parameters −0.42 0.000032 −1.163

94.655

95

−0.345

Result Analysis

Set different fixed-point longitudes and different floating stars as shown in Table 5.

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For each group of different orbit position adjustment problem settings listed in Table 5, the calculation is carried out according to the above simulation calculation process, and the orbit parameter error after control is shown in Fig. 1.

Fig. 1. The orbit parameter error after contror

As can be seen from Fig. 1, (1) The orbit parameter errors of the above strategies are all within the required range of Beidou IGSO satellite orbit keeping accuracy. Because the objective function is the minimum speed increment, the optimization objective is the minimum

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objective function, thus achieving the best fuel for the Beidou IGSO satellite orbit adjustment Optimal control strategy. (2) According to the algorithm optimization strategy of this paper, the controlled track and the nominal track have a certain error. After analysis, the reason is that the used track motion model is based on two-body motion and the extrapolation accuracy is insufficient. A high-precision orbit-like perturbation extrapolation model for calculation.

5 Summary Aiming at the problem of IGSO satellite orbit position adjustment under multiple constraints in current engineering, this paper decomposes IGSO satellite orbit position adjustment into drift control and brake control. The control quantity of drift control is obtained by analytical method, and brake control is transformed into multiple constraints. Control optimization problem under conditions. The two-body motion model in the orbital plane is established, and the IGSO satellite brake control strategy calculation method based on the differential evolution algorithm is proposed. The objective function is established by integrating fuel consumption and constraint conditions, and the control time and speed increment of multi-batch control are solved. The simulation shows that the algorithm improves the formulation time of the IGSO satellite orbital position adjustment control strategy from the original hour level to the minute level, and at the same time minimizes the fuel consumption, which is beneficial to prolong the satellite life. It can be applied to the adjustment of the orbital position of other geostationary satellites, and has reference significance for optimization problems under multiple constraints.

References 1. Soop, E.M.: Handbook Of Geostationary Orbits (1990) 2. Li, X.J., Liu, X.P., Xin, J., et al.: Attitude control modes and characteristic analysis for BeiDou satellites. J. Geomatics 44(5), 69–72 (2019). (in Chinese) 3. Xuegang, Z.: Global optimization algorithm for non-convex optimization problems. Changsha: Doctoral Dissertation of Central South University, pp. 1–12 (2010) 4. Zhang, S., Zhang, Y.S., Dai, H.Y., et al.: Orbit reconstruction configuration of navigation constellation based on differential evolution algorithm. Chin. Space Sci. Technol. 38(4), 27– 35 (2018). (in Chinese) 5. Canales-Bustos, L., Santibanez-Gonzalez, E., Candia-Vejar, A.: A multi-objective optimization model for the design of an effective decarbonized supply chain in mining. Int. J. Prod. Econ. 193, 434–454 (2017)

Performance Analysis of Real-Time PPP-RTK with Multi-scale Enhancement Network Lihua Wan(&), Xiaomeng Wu, Peng Zhang, Qi Zeng, Huijun Guo, Renpan Wu, and Yue Xu Shanghai Huce Navigation Co., Ltd., Gaojing Road 599, Shanghai 201702, China [email protected]

Abstract. Due to the presence of satellite orbit/clock errors, tropospheric delay and ionospheric delay, both convergence time (CT) and time to first fix (TTFF) of real-time precise point position (PPP) range from 15 min to 30 min, which strictly limits the applications of real-time PPP. However, with the precise corrections of satellite orbit/clock and atmospheric delays from regional or local network applied, the real-time PPP-RTK can achieve centimeter-accuracy solution in a few seconds with ambiguity resolved. In this study, firstly the realtime precise orbit determination (POD) is conducted with global distributed stations base on a self-developed PPP-RTK software service. Then 5-s sampling satellite clock and uncalibrated phase delay (UPD) are determined and broadcast to users. As shown by the results, the accuracy of real-time predicted orbit of GPS/GLONASS/Galileo/BDS2/BDS3 in radial direction is 2.2 cm, 3.8 cm, 3.3 cm, 6.8 cm and 5.9 cm, respectively, w.r.t the final products; the accuracy of satellite clock is 0.101 ns, 0.153 ns, 0.163 ns, 0.247 ns and 0.227 ns, respectively; the SISRE of real-time products is 0.082 ns, 0.121 ns, 0.125 ns, 0.121 ns and 0.141 ns, respectively, for each system. The availability of realtime corrections is 99.8%, 97.0%, 86.1%, 99.5% and 93.5%, respectively, for above each satellite system. Secondly, the tropospheric and ionospheric delays are retrieved from regional station based on undifferentiated and uncombined PPP solution with ambiguity resolved (PPPAR) by using the real-time orbit, satellite clock and UPD products. Then the atmospheric model parameters are broadcast to user end after modeled with different methods at server end. Finally, the comprehensive performances of the PPP-RTK service are tested in field. As the statistic results show, the latency of the real-time products ranges form 7 s to 15 s with a mean value 8.4 s, which means a high timeliness. Besides, the mean TTFF of PPPAR is about 14.76 min when no atmospheric corrections applied, the position accuracy can reach 2.59 cm and 3.97 cm, respectively, in horizontal and the vertical. However, the TTFF of PPP-RTK is evidently reduced to 9.92 min when corrections from a regional network with 300 km station spacing applied, which is about 32.8% improvement. The position accuracy of PPP-RTK is equivalent to PPPAR after both solutions converged. What’s more, as the results shown, centimeter-accuracy solution can be achieved directly within few seconds when atmospheric corrections from a small scale network with 60 km station spacing applied. The relevant position accuracy is better than 1.5 cm and 3.0 cm in horizontal and the vertical,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 690–704, 2021. https://doi.org/10.1007/978-981-16-3138-2_63

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respectively. In addition, both fix rate and success rate of PPP-RTK can reach 99.9% in a open scene when using a small scale network. Keywords: Precise orbit determination
Undifferenced and uncombined PPP
Ambiguity resolution
PPP-RTK
Regional enhancement network

1 Introduction Precise Point Positioning (PPP) was firstly proposed at the end of the last century [1]. Since then, PPP technology has been widely used in many engineering and geophysical researches, such as low earth orbit (LEO) satellite orbit determination [2], high-rate satellite clock estimation [3], atmospheric environment monitoring [4, 5], earthquake early warning [6] and so on. However, the long convergence time and the highly dependence on orbit and clock products has severely limited the application of PPP technology in many real-time positioning scenarios. In 2005, Wübbena firstly proposed the PPP real-time kinematic technology based on RTK network [7], which makes it possible for PPP to achieve centimeter-accuracy within few seconds. The main idea of this technology is to pre-calculate the satellite orbit/clock and regional atmospheric corrections in advance. The user end then can easily perform PPP with ambiguity resolved(PPPAR) by using above corrections, which means centimeter-level or even millimeter-level positioning accuracy. Based on this conception, considerable efforts have been devoted to fast ambiguity resolution [8–10], regional atmospheric modelling [11–13], and reducing PPP convergence time [14, 15]. At present, many scholars have conducted detailed analysis on the performance of PPP-RTK. For example, Ma [16] and Nadarajah [17] computes the atmospheric corrections based on different regional networks and then broadcasts the corrections to PPP user. As the results shown, the convergence time is evidently reduced when multiGNSS system and multi-frequency used or when the number of satellites increased [18, 19]. However, the effect of the newly built BDS3 system was not analyzed on the performance of PPP-RTK. Then many efforts are devoted to analyzed the contribution of BDS2/BDS3 on the PPP-RTK [20] in detail. However, these studies are basically carried out based on final orbit and clock products, which ignoring the influence of the accuracy and delay of real-time products. In recent years, although there are many studies concentrated on the performance of the International GNSS Service (IGS) realtime service (RTS) [21, 22] base on on real-time PPP. There are only few researches to analyze the performance of real-time PPP-RTK such as Literature [23] what’s more, due to the low availability of multi-GNSS products from IGS-RTS, these articles have not yet analyzed the comprehensive performance of PPP-RTK with five satellite systems, namely, GPS, GLONASS, Galileo, BDS2 and BDS3. In this paper, firstly Precise Orbit Determination (POD) is carried out in real-time based on a self-developed software with global stations, followed by Satellite Clock Estimation (SCE) and satellite uncalibrated phase delay (UPD) estimation. Specifically, the real-time orbit actually is the forecast part of ultra-rapid orbit, which is updated every 3 h. Besides, the satellite clock and UPD are estimated by real-time Kalman filter and update every 5 s. Secondly, undifference and uncombined PPP are implemented

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for all regional stations in order to retrieve the atmospheric delays including tropospheric delay and ionospheric delay. Then these atmospheric delays from PPPAR solution are modeled by different methods and further broadcast to user end together with above satellite orbit, satellite clock and UPD products. Finally, these products and the performance of real-time PPP-RTK system are analyzed based on field test. In addition, this paper also focuses on the performance differences of real-time PPP-RTK with multi-scale enhancement network.

2 Description of Data Used in This Study In this paper, globally distributed stations are used for POD, Satellite Clock Estimation and UPD estimation. Since ultra-rapid orbits are used for this paper, there is no need for strictly real-time data streams. However, satellite clock estimation usually requires data delay within 3 s. This finally leads to a different selection criteria for POD and SCE, which makes the stations used for POD and SCE are not exactly the same. Figure 1 shows the distribution of the stations used for POD (blue dots) and satellite clock estimation (red dots). The station used for UPD estimation are aligned with that of satellite clock estimation. As shown by the figure, stations for satellite clock/UPD estimation are densified in China. This is to make the real-time products more reliable for Asia-Pacific region, thereby improving the performance of the PPP-RTK around that region.

Fig. 1. Distribution of stations for POD/ Clock/UPD estimation (left) and for atmospheric corrections (right)

As for the estimation of atmospheric corrections including troposphere and ionosphere, two different enhancement networks are used, namely, 300 km station spacing network (following referred as regional network) and 60 km station spacing network (following referred as local network). The distribution of the two networks are also displayed in Fig. 1. As shown by the right figure, the stations in the regional network are basically evenly distributed in southeastern China. The shortest distance between adjacent stations is 119.9 km and the longest distance between stations exceeds 1000 km with an average distance of 300 km. The stations in the local network are distributed in Shanghai and its surrounding areas. The shortest distance between adjacent stations is 19.3 km, the longest distance between stations exceeds 100 km with an average distance of 60 km.

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3 Data Processing Strategies and Methods 3.1

Strategies of POD

Since the release of BDS3, there are currently more than 100 GNSS satellites operating stably in orbit. Among all the IGS Analysis Centers (ACs), most of them only provides GPS and GLONASS real-time products; few of them provides Galileo and BDS2 realtime products such as GFZ, CNES, WHU and so on, even less of ACs provides BDS3 real-time products. In this paper, ultra-rapid satellite orbits for the five satellite system, namely, GPS, GLONASS, Galileo, BD2 and BDS3 are computed and updated every 3 h based on self-develop software. These ultra-rapid orbits have been continuously and stably released on ftp://gnssproduct.huacenav.com/ since the mid of 2019, which is now free to access for the public. In particular, products of BDS3 C38 and above satellites are not provided due to the lack of enough BDS3 observations. As for the earth albedo radiation, the model described in literature [24] has been adopted. The antenna power of each satellite is taken from literature [25] in order to calculate the antenna thrust. As for the solar radiation pressure, the ECOM and ECOM2 model [26, 27] proposed by CODE (Center for Orbit Determination in Europe) are deployed. Table 1 shows the detail information of basic strategies and force model used for generation of ultra-rapid orbits in this paper. Table 1. General Strategies and models used for POD Item Basic strategy Satellite system Frequency Troposphere Mapping function Terrestrial frame Priori orbit/EOP PCO/PCV Force model Third-body force Geopotential Tidal displacements Air drag Earth albedo radiation Antenna thrust Solar radiation pressure

3.2

Strategy/model GPS, GLONASS, Galileo, BDS2(non-GEO), BDS3(*C37) GPS/GLONASS:L1 L2, Galileo: E1 E5a, BDS2/BDS3: B1 B3 Zenith wet delay + gradient parameter GMF IGS14 from SINEX Broadcast ephemeris/IERS Bullet_A igs14_2132.atx DE405: Sun, Moon, Venus, Mars, Jupiter EGM2008 Solid Earth tides: IERS 2010, Ocean tides: FES2004 model Not Applied GPS/GLONASS Applied GPS/GLONASS/Galileo/BDS2 Applied Galileo/BDS3 ECOM2, Others ECOM

Satellite Clock Estimation and UPD Estimation

There are two main ideas for satellite clock estimation. The first one is estimate the satellite clock directly based on PPP with both code and phase observation [28], which is time consuming and is suitable for post-processing. The other one is much more effective due to the avoiding of dealing with the ambiguity parameter [3]. In the second

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method, the code observations are used to only estimate the initial satellite clock, while the phase observations are only used to estimate the relative satellite clock between adjacent epoch. Taking into account the requirement of real-time efficiency, this paper adopts the second method. Omitting the derivation, formula (1) and (2) gives the ionosphere-free (IF) combination of phase and code measurements:  
 j j j L3;r ¼ qrj þ c dtr  dt j þ mrj Trj þ k3 B3;r þ e L3;r

ð1Þ

 
 j j P3;r ¼ qrj þ c dtr  dt j þ mrj Trj þ e P3;r

ð2Þ

where c is the speed of light, the superscript j represents the satellite, the subscript r j j represents the receiver; L3;r is IF phase combination; P3;r is IF code combination; qrj is the geometric distance from the satellite to the receiver; dtr is the receiver clock error, dt j is the satellite clock error; mrj is the troposphere mapping function, Trj is the zenith j is the float ambiguity of wet delay; k3 is the wavelength of IF phase combination; B3;r j j IF combination; eðL3;r Þ is the residual of phase equation; eðP3;r Þ is the residual of code equation. After forming difference between adjacent epoch, formula (2) can be rewritten as: j j DL3;r ¼ Ddtr ðiÞ  Ddt j ðiÞ þ Dmrj ðiÞ
Tr ðiÞ þ DeðL3;r Þ

ð3Þ

where Ddtr ðiÞ is the difference of receiver clock between two epoch, Ddt j ðiÞ is the difference of satellite clock between two epoch. Similarly, the epoch difference equation for code can be constructed as follow: j DP3;r ¼ dtr ð0Þ  dt j ð0Þ þ

i1 X p¼1

Ddtr ðpÞ 

i1 X

j Ddt j ðpÞ þ Dmrj ðiÞ
Tr ðiÞ þ DeðP3;r Þ ð4Þ

p¼1

where dtr ð0Þ and dt j ð0Þ are the initial clock errors of receiver and satellite, respectively. In formula (3) and (4), the unknown parameters are dtr ð0Þ, dt j ð0Þ, Ddtr ðiÞ, Ddt j ðiÞ, Ddtr ðiÞ and Trj . After introducing a time benchmark (usually use a station clock as time reference), the above unknown parameters can be solved by using observations from dozens of stations. Finally, the satellite clock at epoch p can be expressed as the following formula (5). For more detail information please refer to reference [3]. dt j ðpÞ ¼ dt j ð0Þ þ

i1 X p¼1

Ddt j ðpÞ

ð5Þ

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As for the estimation of UPD, the principle is much more clearly. The main idea is to separate the integer part and the fractional part of the float ambiguity. Ignore the j derivation, the float ambiguity of B3;r can be reformulated as: j k3 B3;r ¼

k1 f12 k2 f 2 f2 j j j j B1;r  2 2 2 B2;r ¼ kw Bw;r þ kn B1;r 2 f1 þ f2  f2 f1  f2

ð6Þ

f12

with j j ~ w;r Bw;r ¼N þ fw;r  fwj

ð7Þ

j j ~ 1;r ¼N þ fn;r  fnj B1;r

ð8Þ

j j where fi is the carrier frequency; Bw;r and B1;r is the wide lane and narrow lane floating j ~ w;r ambiguity, which both absorbs the receiver and satellite hardware delay; N ,which j j ~ is the can be obtained by rounding MW combination, is the integer part of Bw;r ; N 1;r

j integer part of B1;r ; fw;r and fwj is the wide lane UPD of receiver and satellite, respectively; fn;r and fnj is the narrow lane UPD of receiver and satellite, respectively. Due to the strong correlation between satellite and receiver UPD in formula (7) and (8), it is necessary to introduce a UPD benchmark to solve the rank deficiency equation. j j ~ w;r , the narrow lane float ambiguity B1;r can After obtaining the wide lane UPD and N j ~ be extract by substituting wide lane UPD and Nw;r into the formula (6). Similarly, the narrow lane UPD can be estimated in the same way as wide lane UPD. The details derivation can be referred to [8, 27, 28]. In addition, due to the existence of inter frequency biases, the UPD of GLONASS satellite are not calculated in this paper.

3.3

Undifferenced and Uncombined PPP

Unlike the estimation of satellite clock and UPD, the extraction of troposphere delay and ionosphere delay is based on undifference and uncombined PPP. Omitting the derivation, the undifference and uncombined PPP equation are given as [14, 31]:  
 j j ~ i;rj þ e Li;r Li;r ¼ qrj þ c d~tr  d~t j  ci~I j þ mrj Trj þ ki N

ð9Þ

 
 j j ¼ qrj þ c d~tr  d~t j þ ci~I j þ mrj Trj þ e Pi;r Pi;r

ð10Þ

with  8 d~tr ¼ dtr þ dIF;r c > >  > < d~t j ¼ dt j þ d j c IF ~I j ¼I j þ bðDCBr  DCB j Þ >  
>  > j :k N j s ~j þ dIF;r  dIF þ Ci
bðDCBr  DCB j Þ i i;r ¼ ki Ni;r þ bi;r  b

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where dIF;r is the receiver hardware delay of IF combination, dIFj is the satellite hardware delay of IF combination; DCBr and DCB j is the differential code bias of receiver and satellite,  respectively,between
the two used frequency; ci and b are known coefficient, ci ¼ f12 fi2 , b ¼ f22 f12  f22 . The other parameters are the same as mentioned above. Because the hardware delay of the satellite is relatively stable and its values are provided by IGS AC, thus the dIFj and DCB j can be directly corrected by using the public products in advance. As for dIF;r , it can be absorbed by the receiver clock error so no consideration needs. Besides, DCBr cannot be separated with I j , thus the sum of DCBr and I j is regarded as one parameter ~I j . In addition, because the precise orbit, satellite clock and UPD products are provided by the server end, the ambiguity can be solved based on formula (9) and (10), which will guarantee a much more precise results of ionosphere and troposphere delay. 3.4

Atmosphere Modeling and PPP-RTK Positioning Model

For the small scale enhancement network (such as the local network in this paper), a lower-order surface model is used to fit the slant ionosphere delay as:

 ~I j ¼ I j þ bDCBr ¼ a0 þ a1 lat j  lat0j þ a2 lon j  lat0j

ð11Þ

where lat j and lon j is the longitude and latitude of the satellite ionospheric Pierce Point (IPP), respectively; lat0j and lat0j is the longitude and latitude of the reference point, respectively; ai is the coefficient which needs to be solved. As mentioned in Sect. 3.3, the DCBr is absorbed in ~I j and can not be separated with a0 . For the convenience of use, usually the single difference of ionospheric delays are modeled instead of undifference delays. Thus the formula (11) can be rewritten as follows:

 ~I j  ~I ref ¼ a0j þ a1j lat j  lat0j þ a2j lon j  lat0j    

ref  aref latref  lat0ref þ aref lonref  lat0ref 0 þ a1 2



ð12Þ

When the number of equations exceeds 4 for each satellite j, the coefficients aij can be solved. As for the modeling of tropospheric delay correction, a distance-based interpolation method is adopted. The lower-order surface model is not suitable to describe slant ionosphere when the enhancement network getting larger (such as the regional network in this paper). Thus a different method is deployed as explained by following equations: 8 j j 40:28106 >
mf j
VTEC þ bDCBr < ~I ¼I þ bDCBr ¼ f12 n m PP > Cij ðu  u0 Þi ðS  S0 Þ j : VTEC ¼

ð13Þ

i¼0 j¼0

where VTEC is the vertical total electron content (VTEC); mf j is the ionospheric mapping function; m and n are the order of the model; Cij is the coefficient parameters

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which is to be estimated; u is the geodetic latitude of the satellite IPP, u0 is the geodetic latitude of the reference center; S is the solar time angle at the observation time, S0 is the solar time angle at the reference center. In formula (13), only Cij and DCBr are the parameter need to be solved, other parameters are known with m ¼ n ¼ 4 in this paper. In addition, due to the huge difference between different station, the tropospheric delay is no longer modeled. After obtaining the atmospheric corrections, these extra information can be introduced into the observation equations in order to accelerate the convergence of PPP. Generally, the obtained atmospheric corrections can be imposed as a constraint on the ionospheric or tropospheric parameter of the associated observations. The constraint can be expressed in form of an additional pseudo observation equation as follows [32]:
 v ¼ ~I j  Imj þ DCBr ;

r2Im

ð14Þ

where Imj is the ionospheric delay calculated according to the model, r2Im is the accuracy of the model, ~I j is the parameter of the PPP equations as described above. Because the DCBr is unknown and usually can not be estimated separately, formula (14) needs to reformulated in the form of single difference in order to eliminate the receiver DCB. Similarly, the tropospheric delay from the model can also be imposed as a constraint as shown in formula (15) vT ¼ T  Tm ;

r2Tm

ð15Þ

where Tm is the tropospheric delay calculated from the model and r2Tm is the corresponding accuracy. Combined Formula (14) and (15) with formula (9) and (10), PPPRTK positioning can be realized with fast convergence.

4 Real-Time Products and Performance Analysis of PPPRTK 4.1

Real-Time Products Analysis

The precise orbit used in real-time positioning is the prediction part of ultra-rapid orbit. Thus the positioning result is only affected by the accuracy of prediction part from 3 h to 6 h part since the ultra fast orbit is updated every 3 h. In addition, due to degrade of satellite clock, the real-time performance of PPP-RTK will be badly affected even for few seconds delay. In order to ensure that the evaluation results are close to the real situation, the real-time correction of RTCM stream are used for the evaluation instead of ultra-rapid products. Even thought the RTCM stream includes only the orbit and clock corrections, they can be recover to orbits and clock products by using the broadcast ephemeris. The specific conversion method can be referred to reference [21, 22].

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Specially, since different clock products refers to a different benchmarks, it is impossible to directly perform the evaluation for clock. Thus the double difference clock between products and satellites is formed firstly and is used for the evaluation in stead. The principle of the evaluation is described in detail in [33]. Table 2 shows the accuracy statistics of real-time products for each satellite system from January 1, 2021 to January 15, 2021 with respect to GBM final products. As comparison, the accuracy of ultra-rapid orbit is also listed in Table 2. As we can see, the accuracy of real-time orbits degrades slightly in radial direction w.r.t ultra-rapid observation part orbits. The overall radial accuracy of GPS/GLONASS/Galileo/BDS3 system is 2.2 cm, 3.8 cm, 3.3 cm and 5.9 cm, respectively, which is very close to that of observation part with a difference less than 5 mm. However, the accuracy of realtime orbit for BDS2 is 0.068 m, which is remarkable degraded when compared to observation part (0.049 m). The reasonable explain is that BDS2 is still regional satellite navigation system and the prediction accuracy can not be as good as global satellite navigation system, especially for those IGSO satellites. Besides, the accuracy of GPS satellite clock is the best and the average RMS is about 0.030 m (0.101 ns); the RMS of Galileo and GLONASS satellite clock are 0.046 m (0.153 ns) and 0.049 m (0.163 ns), respectively; BDS2 and BDS3 shows a very close result and the RMS of BDS2and BDS3 clock is about 0.074 m (0.247 ns) and 0.068 m (0.227 ns), respectively. It should be pointed out that due to the lack of BDS3 tracking stations, which will cause BDS3 satellite to have insufficient observations when passing over some areas, thus affecting the continuity and accuracy of statistical results for BDS3. Table 2. Statistical results of ultra-rapid orbits and real-time products System

Ultra-rapid orbit Radial/m Cross/m GPS 0.019 0.019 GLONASS 0.037 0.049 Galileo 0.032 0.041 BDS2 0.049 0.055 BDS3 0.057 0.086

Real-time products Along/m Orbit in Radial/m Clock/ns 0.022 0.022 0.101 0.068 0.038 0.163 0.045 0.033 0.153 0.067 0.068 0.247 0.126 0.059 0.227

Because the satellite clock product will absorb the radial error of orbits, the precise orbit and clock products usually need to be used together by user end. Besides, the overall accuracy of orbit/clock also is an important consideration when analyzing the product accuracy. The signal in space range error (SISRE) is usually used to assess the overall accuracy, which can be described as following [34]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi 2 2 2 2 SISRE ¼ ½RMSðRradial þ clk Þ þ wa;c Ralong þ Rcross

ð16Þ

where wa;c is the scale factor and set to 1/7 in this study. The statistical results of SISRE for several consecutive days are shown in Fig. 2 (left). In addition, the accuracy of

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real-time orbit in radial direction is also shown separately in Fig. 2 (left) as a comparison. Furthermore, because the continuity of real-time products directly affects the overall positioning results, thus the availability of each satellite is also analyzed and shown in Fig. 2 (right).

Fig. 2. SISRE (left) and availability (right) of real-time products for each satellite system.

As shown by Fig. 2, the SISRE of GPS satellite is basically within 0.07 m, and that of other satellite systems is basically within 0.10 m. The mean value of SISRE for GPS, GLONASS, Galileo, BDS2 and BDS3 satellite systems is 0.082 ns (2.46 cm), 0.121 ns (3.63 cm), 0.125 ns (3.75 cm), 0.121 ns (3.63 cm), and 0.141 ns (4.23 cm), respectively. As for the product availability, GPS and GLONASS systems perform the best due to the adequate and and evenly distributed stations around the world. The average availability the whole GPS system and GLONASS system is 99.4% and 97.0%, respectively. Galileo and BDS systems started relatively late and the construction of tracking stations is still imperfect and inadequate, which leads to the incapable of computation of real-time products for some periods. Thus the availability of products is slightly lower than that of GPS and GLONASS. In addition, because the broadcast ephemeris of Galileo E14 and E18 satellites often set to unhealthy, thus the two satellites are not included in the statistics. As the results show, the overall availability of Galileo, BDS2 and BDS3 products is 91.9%, 97.7% and 92.5%, respectively. All in all, the integrity of real-time products is better than 90% for all system among which GPS is the highest and more than 99%, which can fully meet the requirements of realtime positioning. As for the UPD products, which is related to the orbit/clock products, it may absorb the orbit and clock error. Thus it is hard to compare the two UPD products between different agencies, especially for narrow-lane UPD. In this paper, the UPD products are analyzed together with the positioning performance. 4.2

PPPAR/PPP-RTK Positioning Analysis

In order to analyze the improvement of convergence time and accuracy at terminal side by using enhanced atmospheric corrections from different scale networks, this paper

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concentrates on the analysis of the performance difference between float PPP, PPPAR and PPP-RTK based on several filed tests. As mentioned before, float PPP tests only use the real-time orbit and clock products acquired from the RTCM data stream; PPPAR tests use both the orbit/clock products and UPD products; while PPP-RTK tests make use of all the corrections from RTCM stream, including atmospheric corrections, orbit/clock and UPD products. Figures 3 and 4 shows all the positioning results of float PPP, PPPAR and PPP-RTK from open scene tests. The PPP-RTK results in Fig. 3 apply the atmospheric corrections from a regional enhancement network, while the PPP-RTK results in Fig. 4 apply atmospheric corrections from a local enhancement network. As viewed from the Fig. 3 (left), when no atmospheric corrections applied, both float PPP and PPPAR need at least 1000 epochs (about 17 min) to converge, and the accuracy after convergence shows a really small difference between float PPP and PPPAR. However, when atmospheric corrections from a regional enhancement network with 300 km station spacing, PPP-RTK basically completes the convergence process within 5 min and the accuracy reaches several centimeters immediately after ambiguity resolved. Figure 3 (right) shows another test at different site, as illustrated by the figure, even though the ambiguity of PPPAR is resolved at the first 15 min without atmospheric information, the deviation in the north is larger than 10 cm at about 11 min. After applying the atmospheric information, PPP-RTK achieves the fastest convergence with ambiguity fixed. Beside, the positioning result shows no deviation in the north direction, but shows a deviation of about 8cm in the east direction when it is first fixed at about 6 min.

Fig. 3. Real-time positioning results of PPP/PPPAR/PPP-RTK from test case 1 (left) and case 2 (right) with regional atmospheric corrections.

The test results in Fig. 4 show that the PPP-RTK performances are further improved after reducing the station spacing to 60 km. As shown, PPP-RTK can be converged and ambiguity can be fixed within 10 epochs after applying the corrections from a local enhancement network with 60 km station spacing. After convergence, the accuracy is better than 3 cm and 5 cm in horizontal direction and vertical direction, respectively. Besides, no deviation can be found through the whole positioning session. In another words, the local atmospheric information can not only accelerate the convergence of the

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positioning, but also greatly improve the accuracy as well as reducing the ambiguity false fixed rate. What’s more, the age of the real-time products provided by the selfdeveloped PPP-RTK system is also shown in Figs. 3 and 4 (right-bottom). As shown, the latency basically ranges from 7 s to 15 s with a average latency 8.4 s.

Fig. 4. Real-time positioning results of PPP/PPPAR/PPP-RTK from test case 3(left) and case 4 (right) with local atmospheric corrections.

The statistics results of all the hundreds of tests are given in Table 3. The statistical accuracy of positioning performance only involved the results after convergence, which is defined as following: if the horizontal and vertical deviations are less than 10cm and last for more than 10 min, it is considered as convergence. PPP-RTK_Regional in the table represents the PPP-RTK result with atmospheric corrections from network with 300 km station spacing, PPP-RTK_Local represents the PPP-RTK result with atmospheric corrections from network with 60 km station spacing. It can be seen from Table 3 that the accuracy of float PPP results is the lowest, and the positioning deviation reaches 10.22 cm with 99.7% confidence interval (i.e. 3d). The accuracy of PPPAR and PPP-RTK_Regional shows only a little bit difference, however, the TTFF is reduced from 14.76 min to 9.92 min, which means a improvement of 32.8%. After applying the local atmospheric enhancement information, PPP-RTK_Local performs the best. As shown by the results, both the positioning accuracy, convergence time and fix rate are greatly improved. The horizontal accuracy is within 2 cm and the vertical accuracy is within 3 cm. In addition, the TTFF of can be shortened to less than 10 s. Last but not least, the probability of ambiguity false fixed is significantly reduced by using the tropospheric and ionospheric information from local enhancement network, which in return improves the statistical accuracy of positioning after convergence.

Table 3. Statistical results of kinematic results from open scene Float PPP PPPAR PPP-RTK_Regional PPP-RTK_Local

Horizontal/cm 3.56 2.59 2.36 1.03

Vertical/cm TTFF/min Fix rate/% 3d/cm 4.08 – – 10.22 3.97 14.76 90.08 7.99 4.06 9.92 92.74 8.12 2.16 0.10 99.99 2.62

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5 Conclusion In this study, the comprehensive performance of the PPP-RTK service system are analyzed in detail as well as the relevant real-time products including the real-time precise orbit determination, satellite clock estimation and satellite UPD estimation, which are conducted based on the self-developed software. Besides, the overall delay and the availability of the real-time products are also discussed. Firstly, the satellite precision orbit, satellite clock and UPD products are estimated in real time by using the globally distributed stations. As the results show, the accuracy in radial direction degrades less than 5mm for MEO satellite when compared to ultrarapid orbits. However, the accuracy of BDS2 IGSO satellite degrades nearly 2cm in radial direction. In addition, as shown by the filed test, the availability of the real-time products of the PPP-RTK system is more than 90%, and the average delay of the products is 8.4 s, which totally meets the requirements of real-time positioning. Furthermore, the performance of the whole PPP-RTK system with different scale enhancement network is verified in real time. As shown by the field test, PPP-RTK can achieve ambiguity fixed solution within 10 s with local atmospheric corrections generated from 60 km station spacing network. What’s more, the accuracy and the success fix rate of PPP-RTK with atmospheric corrections are both greatly improved when compared with that without using atmospheric corrections. Acknowledgments. This work is supported by the Science and Technology Commission of Shanghai Municipality (19511100200, 18DZ1100201).

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The Median Method of Gross Error Elimination in Multi-satellite Precise Orbit Determination Yufei Yang(&), Chong Li, Maolei Wang, Zhixue Zhang, Shuxin Jin, Liwei Zhang, and Linze Li Beijing Satellite Navigation Center, Beijing 100094, China

Abstract. The Multi-satellite Precise Orbit Determination (MPOD) is the most commonly used method in orbit determination of Global Satellite Navigation System (GNSS). In daily operation, malfunctions occur sometimes and gross errors appear in the observation of some monitoring station receivers. Too many gross errors during the orbit determination arc may cause the increasing number of orbit determination iterations or even the crash of MPOD program. In this study, the influence of receiver gross errors is studied, and the median method of gross error elimination is proposed, which makes use of the insensitivity of the median to gross error. The results show that in extreme cases when gross errors exist both in the observation of multiple receivers and satellites, they can also be eliminated very well, which ensures the normal operation of MPOD program and greatly improves the reliability and robustness of orbit determination operation. After a lot of tests, the median method has been successfully applied to online MPOD operation. Keywords: Satellite navigation Gross error
Median
Stability


Multi-satellite precise orbit determination


1 Introduction The Multi-satellite Precise Orbit Determination (MPOD) is the most commonly used method in orbit determination of Global Satellite Navigation System (GNSS) (Beutler et al. 1994, Teunissen and Montenbruck 2017). In the beginning, there are six global distributed monitoring stations of Global Positioning System (GPS) ground segment. In 2008, ten (National Geospatial Intelligence Agency) NGA stations were added through the L-AII program. The average Signal in Space Error (SISRE) of GPS is better than 0.6 m. It is reported that the real-time precise orbit determination and clock error measurement technology of Jet Propulsion Laboratory (JPL) was applied on the Next Generation Operational Control System (OCX), in which the satellite orbit and clock error was estimated by filter method epoch by epoch, and the accuracy of 1-h prediction SISRE better than 0.25 m, 24-h prediction SISRE better than 1.50 m can be achieved (Bertiger et al. 2010, Bauer et al. 1998). The monitoring stations of GLONASS system are all distributed in mainland of Russia, which has a large east-west span. Special designs of satellite orbit ensure that the control and maintenance of the whole arc of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 705–713, 2021. https://doi.org/10.1007/978-981-16-3138-2_64

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GLONASS satellites can be realized based only on the regional distributed stations (Revnivych 2002, 2012). In March 2015, Galileo ground control segment was upgraded by adding 4 monitoring stations and 51 uplinger station, thus the ground segment has 15 monitoring stations and 5 uplinger stations. The accuracy of Galileo satellite broadcast ephemeris and broadcast clock error parameters was further improved, and the SISRE-orb was reduced from the original 0.75 m to 0.22 m (Dow et al. 2009). Usually, the MPOD is performed every hour by GNSSs, the predicted orbits are obtained by orbit integrating using the estimated orbital parameters, and the broadcast ephemeris parameters are fitted based on predicted orbits (Tapley et al. 2004, Tang et al. 2016, Yang et al. 2018). The reliability and robustness of MPOD operation is critical to ensure the continuous and stable operation of GNSSs for providing service (Yang et al. 2019, Zhou et al. 2011). In daily operation, malfunctions occur sometimes and gross errors appear in the observation of some monitoring station receivers. The impact of phase observation gross errors can be eliminated by cycle slip detection and repair (GE Maorong 1995, GUO Jing 2014). When the amount of pseudorange gross errors is small, they can also be eliminated through several times of gross error detection after least square (LSQ) estimation (YANG Yufei et al. 2018, 2019). However, when there are too many pseudorange gross errors during the orbit determination arc, it may cause large the postestimation Root Mean Square (RMS) of the residuals and the malfunction of the gross error detection based on RMS, which will further leading to the increasing number of iterations or even the crash of MPOD program.

2 Influence of Gross Error on MPOD In the MPOD, the clock of one receiver or satellite is usually selected as the time reference, of which the clock error is fixed to zero. The clock errors of all other satellites and receivers are regarded as the epoch-independent parameters to be solved. Because of the cycle ambiguity of the phase observation, the clock error actually depends on the pseudorange observation, which means, in the case of no gross error, the receiver clock error of the specific epoch is equal to the average deviation of all pseudorange observation between all satellites and the receiver at the specific epoch. When pseudorange gross error exist between one receiver and satellite, the observation deviates from the real value, which leads to the deviation between estimated receiver clock error and its real value and further pollute the pseudorange residuals between the receiver and all the other satellites. Under normal circumstances, when the amount of pseudorange gross errors is small, they can be eliminated through several times of gross error detection after least square (LSQ) estimation. However, large numbers of gross errors during the MPOD arc may cause the increasing number of orbit determination iterations. The normal observations may also be eliminated wrongly by the gross error detection based on the RMS of residuals. Too many eliminated normal observations may cause the rank defection of the LSQ normal equation and the crash of orbit determination program.

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Fig. 1. The influence of gross error on the pseudorange residuals of the S5 in first MPOD iteration

For example, the receiver of the Station NO.5 (S5) malfunctioned and its locks of pseudorange observation of satellites C02, C04, and C06 were lost, resulting in gross error of the pseudorange observation at many epochs. Figure 1 shows the first iteration pseudorange residuals between all satellites and S5. Points of different colors and shapes represent pseudorange residuals between different satellites and S5. The RMS of S5 in this orbit determination arc is bigger than 10,000 m.

Fig. 2. The influence of gross errors on the pseudorange residuals of C04in first MPOD iteration

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Figure 2 shows the pseudorange residuals of the first MPOD iteration between all stations and C04 in the abnormal period. Points of different colors and shapes represent the pseudorange between all stations and C04. It can also be found that the RMS of pseudorange residuals of C04 reaches larger than 30,000 m, and the RMS of residuals with S5 is the largest.

Fig. 3. The influence of gross error on the pseudorange residuals in first iteration of the normal receiver

In addition, it can be seen from Fig. 3 that the pseudorange gross errors also pollute the pseudorange residuals of the other receivers and satellites through the receiver and satellite clock errors, resulting in the collapse of the MPOD program.

3 The Median Method of Gross Error Elimination When the collapse of the MPOD software happens, the reason of MPOD failure can be found by analyzing the pseudorange residuals by professionals, and the MPOD program can be recovered by remove the abnormal receiver or satellite. However, the malfunction analysis requires high professional accomplishment of operators and a lot of time. Meanwhile, the gross errors of the abnormal receiver or satellite only exist in a small number of epochs compared to the whole MPOD arc. Directly eliminating all the observation of the abnormal receiver or satellite, will reduce the accuracy of the MPOD results.

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Fig. 4. Calculation flow of median method of gross error elimination

Based on reasons mentioned above, a median method for gross error elimination based on first iteration residuals is proposed, which makes use of the insensitivity of the median to gross error. The calculation flow is shown in Fig. 4: 1. Calculate the residual values (Observation minus Calculation, O-C) of all pseudorange observations of epoch i using initial satellite orbits, satellite clock errors, station coordinates, station clock errors and other information; 2. Calculate the median value between all satellites and Sj at epoch i, and whether there is any difference between O-C and the median value larger than the threshold is detected. If no difference exceeds the threshold, it is considered that the pseudorange observation of Sj for all satellites in epoch i are normal. If there are satellites that exceed the threshold, the observation of the satellite with the largest difference with median is removed.

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3. Calculate the median value between all stations and Ck at epoch i, and whether there is any differences between O-C and the median value larger than the threshold is detected. If no difference exceeds the threshold, it is considered that the pseudorange observation of Sj for all station in epoch i are normal. If there are stations that exceed the threshold, the observation of the station with the largest difference with median is removed. 4. And then, the observation of the next epoch is processed until the last epoch. The choosing of the threshold value should take into account the effect of gross error elimination and the risk of wrong processing. If the threshold is set too large, the gross error cannot be eliminated completely. If the threshold is set too small, too much normal data will be eliminated. According to repeated analysis and testing, the threshold can be set to 1000 m.

4 Verification of Elimination Effect The abnormal observation values were preprocessed by using the median method, and the results are shown in Figs. 5, 6 and 7.

Fig. 5. Pseudorange residuals of first MPOD iteration of S5 after the gross error elimination preprocess

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Fig. 6. Pseudorange residuals of first MPOD iteration of C04 after the gross error elimination preprocess

Fig. 7. Pseudorange residuals of first MPOD iteration of normal receiver after the gross error elimination preprocess

As can be seen from the figures, after the gross error elimination preprocess, all of the gross errors between C02, C04, C06 and S5 were eliminated, and the RMS of pseudorange residuals of the S5 in this orbit determination arc decreased from bigger than 10000 m to 13 m. The RMS of pseudorange residuals of the normal satellites and

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stations also return to normal value. The obvious variety still in the pseudorange residuals of first iteration is caused by the low precision of the initial satellite orbits. With the improvement of orbit precision and the further elimination of gross error, the residuals will become smaller and smaller until the end of orbit determination iteration.

5 Conclusions The median method of gross error elimination proposed in this paper can eliminate gross error of pseudorange observation automatically, and the process of fault alarm, manual analysis and judgment, and the software restarting are avoided, which lower the requirements of professional accomplishment of operators and improve the timeconsuming performance. In addition, the median method avoids simply eliminating all the observation of the abnormal satellite or station, which improve the accuracy of the MPOD results. After a lot of tests, the median method has been successfully applied to the online operation.

References Beutler, G., Brockmann, E., Gurtner, W., et al.: Extended orbit modeling techniques at the CODE processing Center of the International GPS Service for Geodynamics (IGS): theory and initial results. Manuscr Geodaet 19, 367–386 (1994) Teunissen, P.J.G., Montenbruck, O. (eds.): Springer Handbook of Global Navigation Satellite Systems. SH, Springer, Cham (2017). https://doi.org/10.1007/978-3-319-42928-1 Bertiger W., Bar-Sever, Y., Harvey, N., Miller, K., et al.: Next generation GPS ground control segment (OCX) navigation design. In: Institute of Navigation GNSS Meeting, Portland, OR, September 2010 Bauer, F.H., Hartman, K., Lightsey, E.G.: Spaceborne GPS current status and future visions. In: ION GPS-98, Nashville (1998) Revnivych, S.: Developments and plans of the GLONASS system. In: UN/USA International Meeting of Experts the Use and Application of Global Navigation Satellite Systems, Vienna, Austria (2002) Revnivykh, S.: GLONASS status and modernization. In: Proceedings of ION GNSS 2012, Nashville, TN, pp. 3931–3949 (2012) Dow, J.M., Neilan, R.E., Rizos, C.: The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J. Geod. 83(7), 191–198 (2009) Tapley, B.D., Schutz, B.E., Born, G.H.: Statistical Orbit Determination. Elsevier Academic Press, Cambridge (2004) Tang, C.P., Hu, X.G., Zhou, S.S., et al.: Improvement of orbit determination accuracy for BeiDou navigation satellite system with two-way satellite time frequency transfer. Adv. Space Res. 2016, S0273117716303052 (2016) Yang, Y., Xu, Y., Li, J., Yang, C.: Progress and performance evaluation of BeiDou global navigation satellite system: data analysis based on BDS-3 demonstration system. Sci. China Earth Sci. 61(5), 614–624 (2018). https://doi.org/10.1007/s11430-017-9186-9 Yang, Y., Gao, W., Guo, S., et al.: Introduction to BeiDou-3 navigation satellite system. J. Inst. Navig. 66(1), 7–18 (2019)

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Zhou, S.S., Hu, X.G., Wu, B., et al.: Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network. Sci. China Ser. G (Phys. Mech. Astron.) 54(6), 1089–1097 (2011). https://doi.org/10.1007/s11433-011-43429 Maorong, G.E. Study on theory and software of precise orbit determination for GPS satellite. Wuhan University (1995) Guo, J.: The impacts of attitude, solar radiation and function model on precise orbit determination for GNSS satellites. Wuhan University (2014) Yufei, Y., Junyi, X., Yangyi, X.: Processing strategy comparison and accuracy analysis of zerodifference/double-difference GNSS precise orbit determination. J. Geomat. Sci. Technol. 35 (03), 4–13 (2018) Yufei, Y., Yuanxi, Y., Xiaogong, H., et al.: Comparison and analysis of two prbit determination methods for BDS-3 satellites. Acta Geodaetica et Catographica Sinica 48(7), 831–839 (2019). https://doi.org/10.11947/j.AGCS.2019.20180560

Author Index

A Ai, Lun, 570, 671 B Bai, Lu, 285 Bi, Jingxue, 403 C Cai, Baigen, 12, 182 Cai, Hongliang, 643 Cao, Hongji, 403 Cao, Jianfeng, 511 Cao, Jingchun, 403 Chai, Bin, 3 Chai, Hongzhou, 353, 413 Chan, Pak Wai, 653 Chen, Chunqiang, 274 Chen, Guang’e, 320 Chen, Guo, 629 Chen, Hanlin, 521 Chen, Jiawei, 333 Chen, Lei, 643 Chen, Ling, 243 Chen, Lingling, 123 Chen, Lue, 619 Chen, Wen, 33 Chen, Xi, 629 Chen, Xingtong, 192 Chen, Yanling, 262 Chen, Yaozhong, 3 Chen, Zhe, 403 Cheong, Joon Wayn, 285 Ci, Ying, 453

D Dai, Wujiao, 80 Dai, Zhendong, 296 Dempster, Andrew G., 285 Dong, Danan, 33 Dou, Xinyu, 192 Du, Zhenqiang, 353, 413 F Fang, Yanan, 453 Fang, Zhaobao, 235 Feng, Wenquan, 285 Fu, Bolin, 60 Fu, Erjiang, 173 Fu, Wenju, 629 G Gao, Chengfa, 343 Gao, Fan, 22, 43 Gao, Yaping, 629 Gao, Zhouzheng, 333 Geng, Tao, 521 Gong, Xuewen, 570 Gong, Yangzhao, 653 Gong, Yisong, 584 Gu, Xinru, 403 Guo, Huijun, 690 Guo, Jianxin, 502 Guo, Jie, 584 Guo, Jinglei, 483 Guo, Kai, 453 Guo, Peng, 262 Guo, Rui, 483 Guo, Xiangxin, 427

© Aerospace Information Research Institute 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 772, pp. 715–718, 2021. https://doi.org/10.1007/978-981-16-3138-2

716 H Han, Songhui, 584 Han, Songtao, 619 He, Hongchang, 60 He, Weixin, 213 He, Yuli, 560 He, Yunqiao, 22 Hon, Kai Kwong, 653 Hou, Wei, 253 Hu, Shan, 560 Hu, Xiaogong, 262 Hu, Yuxin, 243 Huang, Liangke, 60 Huang, Lu, 439 Huang, Qiang, 3 J Ji, Bin, 389 Jia, Chun, 389 Jia, Haonan, 439 Jiang, Nan, 145 Jiang, Wei, 182 Jin, Shuxin, 705 Jing, Lili, 133 Ju, Bing, 511 K Kan, Junyao, 333 Kang, Chengbin, 502 L Lei, Han, 453 Lei, Mengfei, 101 Li, Bing, 243 Li, Bofeng, 320 Li, Chong, 705 Li, Guozhong, 584 Li, Huizi, 253 Li, Jialei, 182 Li, Jiangyang, 54 Li, Jianwen, 584 Li, Jie, 453 Li, Jiyang, 159 Li, Jun, 439 Li, Junyu, 60 Li, Kun, 511 Li, Liang, 367, 389, 531, 547 Li, Linze, 705 Li, Qiang, 367, 521 Li, Quanjun, 681 Li, Shuang, 439 Li, Shuyan, 111 Li, Song, 43, 145

Author Index Li, Wei, 609, 671 Li, Xiaojie, 483 Li, Xinna, 584 Li, Yan, 90 Li, Yang, 389 Li, Yineng, 70 Li, Zengke, 463 Li, Zhaozhe, 80 Li, Zhong, 320 Li, Zuohu, 379 Liang, Xiaodong, 101 Liang, Yueji, 159 Lin, Jiale, 599 Liu, Chunhe, 353, 413 Liu, Han, 123 Liu, Hui, 213 Liu, Huicui, 511 Liu, Jian, 427 Liu, Jianye, 70 Liu, Lilong, 60 Liu, Peilin, 296 Liu, Qi, 192, 204, 343 Liu, Qiang, 296 Liu, Shuai, 483 Liu, Xiaosong, 367 Liu, Yanbai, 427 Liu, Yongqiang, 182 Liu, Yongsheng, 343 Liu, Zan, 463 Liu, Zhimin, 521 Liu, Zhizhao, 224, 653 Lu, Debiao, 12 Lu, Jun, 492 Lu, Weitao, 619 Lyu, Sijie, 473 M Ma, Boyuan, 192 Ma, Jiajia, 159 Ma, Qinsheng, 90 Ma, Zhongmin, 192 Mao, Jun, 379 Meng, Yinan, 643 Miao, Weikai, 320 P Pan, Changchun, 3 Pei, Ling, 643 Peng, Jilun, 192, 204 Peng, Yu, 33 Q Qian, Jiuchao, 296 Qiao, Shubo, 599

Author Index R Rao, Jinbo, 235 Ren, Hui, 483 Ren, Tianpeng, 619 Ren, Zhao, 80 Ruan, Hongliang, 133 S Shao, Bo, 204 Shao, Huichao, 427 Shi, Jiaqi, 173 Shi, Lei, 681 Shi, Mingchen, 353, 413 Shi, Tao, 243 Song, Zheng, 502 Su, Chengeng, 492 Su, Xing, 521 Sun, Bo, 133 Sun, Chao, 285 Sun, Xiaojuan, 243 T Tang, Chengpan, 483 Tang, Jinyi, 101 Tang, Qinghui, 483 Tao, Tingye, 54 Tian, Yijun, 483 Tian, Zhiyu, 70 Tong, Laga, 173 Tu, Zhen, 427 W Wan, Lihua, 690 Wang, Aisheng, 310 Wang, Binbin, 671 Wang, Bo, 274 Wang, Chengcheng, 463 Wang, Chong, 453 Wang, Dingwei, 681 Wang, Fuhong, 570 Wang, Jian, 12, 182 Wang, Juntao, 54 Wang, Liduan, 379 Wang, Lixia, 204 Wang, Maolei, 705 Wang, Nazi, 22 Wang, Ping, 502 Wang, Qianxin, 511 Wang, Shuaimin, 43 Wang, Wei, 473 Wang, Xiaoya, 262 Wang, Xijiang, 379 Wang, Yangming, 111 Wen, Zhe, 159 Wu, Haiyan, 243

717 Wu, Jianming, 262 Wu, Jie, 671 Wu, Mengjie, 262 Wu, Renpan, 690 Wu, Xianyu, 235 Wu, Xiaomeng, 690 Wu, Yukuan, 483 X Xiang, Minzhi, 353, 413 Xiang, Yan, 473 Xiao, Yu, 12 Xie, Sidan, 159 Xie, Xin, 521 Xin, Jie, 483 Xing, Lei, 111 Xiong, Si, 60 Xu, Hailong, 599 Xu, Qibing, 123 Xu, Rui, 70 Xu, Tianhe, 22, 43, 145 Xu, Xiaojing, 33 Xu, Xintong, 213 Xu, Yue, 690 Xue, Yiming, 192 Y Yan, Songhua, 90 Yan, Wenlin, 310 Yang, Fuxin, 367, 531, 547 Yang, Jiali, 629 Yang, Lei, 133 Yang, Runxi, 547 Yang, Wentao, 22 Yang, Xiangsheng, 463 Yang, Yufei, 705 Yang, Zhehua, 463 Yang, Zhimei, 123 Yao, Guobiao, 403 Ying, Rendong, 296 Yu, Baoguo, 439 Yu, Shiwei, 224 Yu, Wenkun, 80 Yu, Wenxian, 473 Yu, Xiao, 243 Z Zeng, Qi, 690 Zeng, Qinghua, 70 Zhan, Shanshan, 3 Zhang, Chenglong, 33 Zhang, Fan, 353 Zhang, Gong, 492 Zhang, Heng, 439 Zhang, Jie, 531, 547

718 Zhang, Junli, 521 Zhang, Kefei, 173 Zhang, Lili, 253 Zhang, Liwei, 705 Zhang, Lixin, 123 Zhang, Minghao, 173 Zhang, Peng, 690 Zhang, Pengyong, 253 Zhang, Qiuzhao, 310 Zhang, Ruwei, 570, 671 Zhang, Shuangcheng, 192, 204 Zhang, Tao, 12 Zhang, Tianchen, 274 Zhang, Wanwei, 570 Zhang, Ying, 681 Zhang, Yingying, 681 Zhang, Yizhou, 70 Zhang, Yudong, 310 Zhang, Yuhua, 133 Zhang, Zhen, 43 Zhang, Zhixue, 705 Zhao, Changsheng, 310

Author Index Zhao, Hongbo, 285, 560 Zhao, Lin, 367, 389, 531, 547 Zhao, Qingbo, 531 Zhao, Wu, 343 Zhao, Yanmin, 133 Zhong, Bin, 570 Zhou, Bin, 213 Zhou, Hanxiao, 253 Zhou, Huichao, 502 Zhou, Junhua, 101 Zhou, Junming, 3 Zhou, Wei, 60, 643 Zhou, Xin, 204 Zhou, Zhijin, 619 Zhu, Ge, 60 Zhu, Jun, 453 Zhu, Song, 609 Zhu, Tianlin, 643 Zhu, Yongchao, 54 Zhuang, Chen, 560 Zou, Hua, 343