China Satellite Navigation Conference (CSNC 2024) Proceedings: Volume I (Lecture Notes in Electrical Engineering, 1092) 9819969271, 9789819969272

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Lecture Notes in Electrical Engineering 1092

Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC 2024) Proceedings Volume I

Lecture Notes in Electrical Engineering

1092

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

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Changfeng Yang · Jun Xie Editors

China Satellite Navigation Conference (CSNC 2024) Proceedings Volume I

Editors Changfeng Yang China Satellite Navigation Engineering Centre Beijing, China

Jun Xie China Academy of Space Technology Beijing, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-6927-2 ISBN 978-981-99-6928-9 (eBook) https://doi.org/10.1007/978-981-99-6928-9 © Aerospace Information Research Institute 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Editorial Board

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

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

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

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Editorial Board

Topic: S04: Time Frequencies and Precision Timing Chairman Aimin Zhang, National Institute of Metrology, Beijing, China Vice-Chairman Liang Wang, The 203th Research Institute of China Aerospace Science and Industry Corporation, Beijing, China Lijun Du, Xi’an Branch of China Academy of Space Technology, Shaanxi, China Ya Liu, National Time Service Center, Chinese Academy of Sciences, Shaanxi, China

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

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

Editorial Board

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

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

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Editorial Board

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

Editorial Board

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

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

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

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

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Editorial Board

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

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

Editorial Board

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

Preface

BeiDou Navigation Satellite System (BDS) is China’s global navigation satellite system which has been developed independently. BDS is similar in principle to global positioning system (GPS) and compatible with other global satellite navigation systems (GNSS) worldwide. The BDS will provide highly reliable and precise positioning, navigation and timing (PNT) services as well as short-message communication for all users under all-weather, all-time and worldwide conditions. China Satellite Navigation Conference (CSNC) is an open platform for academic exchanges in the field of satellite navigation. It aims to encourage technological innovation, accelerate GNSS engineering and boost the development of the satellite navigation industry in China and in the world. The 14th China Satellite Navigation Conference (CSNC 2024) is held during 2024, Jinan, China. Including technical seminars, academic exchanges, forums, exhibitions and lectures. The main topics are as followed:

Conference Topics S01 S02 S03 S04 S05 S06 S07 S08

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

The proceedings (Lecture Notes in Electrical Engineering) have 151 papers in eight topics of the conference, which were selected through a strict peer-review process from 345 papers presented at CSNC2024. In addition, another 170 papers were selected as the electronic proceedings of CSNC2024, which are also indexed by “China Proceedings of Conferences Full-text Database (CPCD)” of CNKI and Wan Fang Data. We thank the contribution of each author and extend our gratitude to 299 referees and 53 session chairmen who are listed as members of editorial board. The assistance of CNSC2024’s organizing committees and the Springer editorial office is highly appreciated. Beijing, China

Changfeng Yang Jun Xie

Contents

GNSS Applications UAV Dam Crack Detection System Based on Beidou and LIDAR . . . . . . . . . . . . Junjie Wang, Chengyao Tan, Tong Hu, Yu Xie, Yang Zhang, and Linlin Cui Beidou+5G-Based Plug-In Data Platform to Enhance the Accuracy of Smart Terminal App Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kai Wang, Kezhao Li, Shuaikang Lv, Yingxiang Jiao, Yunyan Shen, Zhe Yue, and Keke Xu Analysis on Effects of L-Band Solar Radio Bursts on GNSS . . . . . . . . . . . . . . . . . Yibo Si and Bin Wang GNSS-IR Retrieval of Soil Moisture in Sugarcane Plantation Based on Cross-Correlation Satellite Selection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . Beiwen Xu, Qin Ding, Caiyun Jiang, Siming Li, Guangyan Chen, Qianru Wei, and Yueji Liang Extraction of Soil Moisture Based GNSS-R Considering Vegetation Factors . . . Qinyu Guo, Shuangcheng Zhang, Qi Liu, Zhongmin Ma, Ning Liu, Shengwei Hu, Lin Bao, Xin Zhou, Hebin Zhao, Lifu Wang, and Tianhe Wan A Non-contact Tilt Compensation Method Based on Monocular Camera/GNSS/INS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cong Wu, Yuanjun Chen, Chunhua Li, and Guofu Pan CYGNSS High Spatiotemporal Resolution Flood Monitoring Based on POBI Interpolation: A Case Study of 2022 Pakistan Catastrophic Floods . . . . Zhongmin Ma, Shuangcheng Zhang, Ning Liu, Qi Liu, Shengwei Hu, Yuxuan Feng, Hebin Zhao, Qinyu Guo, and Chen Wei Modeling and Performance Evaluation of TomoSAR System Based on Reflected Signal of Beidou Navigation Satellite . . . . . . . . . . . . . . . . . . . . . . . . . Chenghao Wang, Feifeng Liu, Cheng Hu, Zhanze Wang, and Zhixiang Xu Soil Moisture Inversion Based on Dual-Frequency Signal of QZSS GEO Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yahui Kong, Lili Jing, Fan Gao, Nazi Wang, Tianhe Xu, Xinyue Meng, Yunqiao He, and Baojiao Ning

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Comparison and Analysis of Tidal Level Monitoring Accuracy Between GNSS-IR and Satellite Altimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Naiquan Zheng, Hongzhou Chai, Zhiyuan An, Peng Chen, Lingqiu Chen, and Lixia Liu Performance Assess of BDS-3 PPP-B2b Signal Service and Its Application in Precipitable Water Vapor Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Ying Xu, Panpan Zhao, Jin Wang, and Xiangdan Meng Deformation Monitoring Experiment and Data Analysis of Beidou Surface Deformation Measuring Radar and GBSAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Zhixiang Xu, Feifeng Liu, Zhanze Wang, Shuyao Zhang, and Jiahe Bi Research on Zenith Tropospheric Delay Model Based on TCN Improving HGPT2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Dengao Li, Danyang Shi, Jumin Zhao, Fanming Wu, Liangquan Yan, Ran Feng, Xinfang Zhang, and Jinhua Zhao Prediction of Ionospheric TEC Based on BLS-LSTM-GRU Hybrid Model . . . . . 155 Dengao Li, Xinfang Zhang, Jumin Zhao, Fanming Wu, Ran Feng, Jinhua Zhao, and Danyang Shi Heavy Rainfall Prediction Model Using Sample Entropy Derived from GNSS-PWV and PSO-SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Fanming Wu, Dengao Li, Jinhua Zhao, Ran Feng, Danyang Shi, Xinfang Zhang, and Jumin Zhao High Precision ZTD Model for the Chinese Southeast Region Using ERA5 Reanalysis Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Fangxin Hu, Pengfei Xia, Shirong Ye, and Jia Luo Research on the Construction of “BeiDou Navigation Satellite System Application Industry Development Index” System . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Jianhua Wei and Bin Li Design and Implementation of Integrated Navigation and Positioning System for Towed Streamer Marine Seismic Exploration . . . . . . . . . . . . . . . . . . . . 201 Haonan Zhang, Kaiwei Sang, Cuilin Kuang, Chufeng Duan, and Baocai Yang Analysis of GNSS Coordinate Time Series in North China by Independent Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Guanghong Lan and Kaihua Ding

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A Machine-Learning-Based Missing Data Interpolation Method for GNSS Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Wenzong Gao, Charles Wang, and Yanming Feng Construction of Beidou Space Time Technology Application Micromajor and Practice of Characteristic New Engineering Education . . . . . . . . . . . . . . . . . . 242 Jianping Xing, Xingmei Yang, Chong Cao, Lingguo Meng, Yafei Ning, Hairui Liu, and Shengli Wang BDS Multi-frequency Soil Moisture Retrieval Considering the Amplitude Stability of Reflected Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Huiyi Xian, Zhongpei Guan, Fei Shen, Xinyun Cao, and Yulong Ge The Evaluation Analysis of RDSS Timing Service for Beidou-3 . . . . . . . . . . . . . . 264 Xianglei Wang, Teng Han, and Chao Xie Identification of Tropopause Height Using COSMIC-2 Occultation Atmospheric Refractivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Ting Ni, Hang Guo, Jian Xiong, Longfei Lv, and Zihan Wan Research on the Application Service System of BeiDou Navigation Satellite System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Mudan Su, Jun Lu, Yeye Sui, and Xiangyi Zhang PNT Architectures and New Technologies NLOS Positioning Optimization Method Based on Unknown Location IRS . . . . 295 Yuchen Jiang, Lu Yin, and Zhongliang Deng UWB/INS Integrated Positioning Method Considering Time Latency and NLOS Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Xiaoji Dai, Tianhe Xu, Min Li, Tianyou Jiang, and Linghan Yao A Gaussian Process Surrogate Model Assisted Multi-optimization Algorithm for Pulsar Period Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Yusong Wang, Yidi Wang, and Wei Zheng GNSS-5G-SINS Resilient Integrated Navigation Algorithm for Indoor and Outdoor Seamless Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Tianyou Jiang, Tianhe Xu, Wenfeng Nie, Xiaoji Dai, Linghan Yao, and Fan Gao Three-Dimensional Station Distribution Design for TDOA Positioning System of Sea Launch Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Maolin Chen, Xianglu Li, Changjiang Liu, Zhengyu Ji, and Yimao Sun

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An Improved DOA Estimation Method Based on Sparse Reconstruction . . . . . . . 358 Jiahao Yang, Zhongliang Deng, Zhichao Zang, and Biao Lei A Joint Adjustment Method for Precise GNSS/Acoustic Underwater Positioning Based on Single-Differenced Observations . . . . . . . . . . . . . . . . . . . . . . 368 Zhen Sun, Zhenjie Wang, and Zhixi Nie A Doppler Frequency Shift Abrupt Processing Method for High-Speed Train Localization in Long Tunnel Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Chengyang Huang, Lu Yin, Zhongliang Deng, and Shinan Li An Innovation Sequence Variance Interference Detection Algorithm Based on Reference Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Yichen Wang, Xiaohui Liu, Chao Wen, and Zichen Xu Research on Shadow Matching Algorithm Based on Consistency Probability Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Xiang Lv, Zhongliang Deng, and Nijun Ye Ubiquitous Localization and Trajectory Tracking Approach for GNSS Jammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Jiaxing Liu, Jun Xie, and Linshan Xue Research on 3D Positioning Technology of UWB Single Base Station . . . . . . . . . 427 Jingjing Zhang, Lu Huang, Jia Su, Zihan Yang, and Qingwu Yi Towards Cis-Lunar Navigation: Design and Analysis of a SmallSat System with Time-Transfer from BDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Xiao Chen, Zhongkai Zhang, Yong Zheng, Zhanglei Chen, and Conghai Ruan Research on Heterogeneous Model Exchange and Hierarchical Integration for Civil Aircraft Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 Xiangzheng Tu, Jiaxue Li, Xiaoxiao Lv, and Wenrui Jin Link Planning Algorithm of Communication and Navigation Constellation Based on Earth-Moon Libration Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 Linshan Xue, Ziyu Wang, and Ping Li Celestial Navigation and Positioning Method Based on Super-Large Field of View Star Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 He Zhang, Chao Zhang, Shuai Tong, Ruopu Wang, Chonghui Li, Yingguo Tian, Donghan He, Dongfang Jiang, and Junyu Pu

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A 5G-Assisted GNSS Spoofing Detection Method in a GNSS-5G Hybrid Positioning System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 Lu Bai, Chao Sun, Andrew G. Dempster, and Wenquan Feng Thoughts on Key Technologies of Underwater PNT System . . . . . . . . . . . . . . . . . 497 Xia Guo, Xing Li, Jun Lu, Kun Jiang, Jiangning Xu, Min Jiang, M. A. Yueyuan, and Jian Shi Design and Practice of Digital Test and Verification of BeiDou Navigation Satellite System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 Wei Wang, Shuren Guo, Jun Lu, Weiguang Gao, Qiang Chai, Gong Zhang, Kai Xu, and Wenxiang Liu A Multi-source Data Fusion Navigation Method of Spacecraft with Limited GNSS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Leyao Li, Jiansong Chang, and Jianxin Guo A PSO-Based Power Allocation Strategy for D2D and MS-NOMA Signals in Positioning-Timing-Communication Integration System . . . . . . . . . . . . . . . . . . 530 Shisheng Dai, Lu Yin, Wenxiao Ge, and Nikola Djuric Space Observation Data Processing of XPNAV-01 . . . . . . . . . . . . . . . . . . . . . . . . . . 541 Linli Yan, Qingyong Zhou, Shaojuan Fan, Xiaolong Hao, Kun Jiang, and Xiwei Chong Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

GNSS Applications

UAV Dam Crack Detection System Based on Beidou and LIDAR Junjie Wang, Chengyao Tan, Tong Hu, Yu Xie, Yang Zhang, and Linlin Cui(B) College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610225, China [email protected]

Abstract. With the rapid development of dam construction, the demand for dam management and maintenance is rapidly expanding. Dam cracks are the core of dam management and maintenance, and rapid and effective detection of cracks and their spatial location and geometric parameters are the basis for dam maintenance. However, dam safety supervision mainly relies on manual work, which is very labor-intensive and time-consuming, and the detection is not fine enough. Therefore, we propose a new and efficient low-cost dam inspection system - UAV dam crack detection system based on Beidou and LIDAR. The UAV is equipped with LIDAR to obtain a high-precision three-dimensional point cloud of the dam surface, use the filtering algorithm to obtain the height difference and intensity contrast of the same dam surface, and then obtain the candidate point cloud of cracks according to the height difference and intensity contrast, use the maximum entropy threshold segmentation method to extract the candidate point cloud, and then filter and denoise the candidate point cloud based on the trough effect, and extract the cracks and their geometric parameters according to the morphological filtering. The texture information obtained from the conventional optical camera is used to construct a 3D model of the dam, and the cracks are displayed on the 3D model to statistically evaluate the severity of the cracks. The system aims to get more and more accurate information about the location and geometry of dam cracks through the combination of Beidou system and LIDAR, so as to better detect the hidden danger of dam safety, save human and material resources for dam safety management, and make the management more convenient and efficient. Keywords: Beidou · UAV · LIDAR · Crack detection

1 Introduction In recent years, with the rapid development of China’s economy and the need for infrastructure construction, water conservancy projects have been developed on a large scale. However, with the growth of dam operation time, the dam body due to water erosion and structural aging and other factors and cracks, and eventually lead to dam safety risks, and cracks will gradually extend to the inside of the dam body, from the quantitative change caused by qualitative change, and eventually lead to breakage. In addition, dam leakage may lead to salinization, marshification and other phenomena, which will cause huge economic losses, and even serious casualties. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 3–13, 2024. https://doi.org/10.1007/978-981-99-6928-9_1

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In the crack field survey of 68 dam sections of Taipingwan Dam in 2019, 8 cracks were found in only 2 dam sections [1]. More than 50 cracks were found in a crack inspection of Zhu Zhuang Reservoir in 2020 [2], and a large number of cracks of different sizes were also found in a crack inspection of the Zhuchang River Reservoir in 2021 [3]. The statistics released by the Chinese Society of Dam Engineering at the end of 2020 show that dam crack detection is extremely important, but, relying on manual inspection, the workload is large, the work cycle is long, which can waste huge energy as well as financial resources, and may be dangerous [4]. In addition, due to the staff being suspended high in the air, the observation field of view is limited, which may also produce problems such as incomplete and meticulous exclusion. Therefore, there is an urgent need to carry out intelligent detection of cracks in dams in China. This paper presents a technology scheme of UAV combined with Beidou positioning and LIDAR to achieve intelligent detection of cracks in dams, solving all the inconveniences of manual ranking, improving work efficiency and ensuring staff safety. At the same time, the cracks can be displayed in three dimensions to improve the maintainability of the dam, which has practical application and economic value and is of great significance for the scientific prevention and control of dam disasters.

2 Current Status of Research Reservoir dams are the key targets of low-altitude protection in China, and are the key research projects in water conservancy engineering. In order to prevent dangerous accidents and guarantee the safe use of dams for a long time, it is very important to study fast and efficient dam crack detection technology to guarantee the safety and stability of dams and reservoirs. The traditional crack monitoring method is the manual detection method, which finds the area where cracks may exist by manual visual inspection, and then manually measures its length, width and other main characteristics. Manual contact with the surface of the dam detection is very prone to safety accidents, there are large risks and large workload; subjective, low reliability, the results are not intuitive, poor standardization; due to the impact of errors, accuracy and other issues, the results only have reference value, can not establish the full cycle of the dam crack operation system, poor expandability. In order to improve the efficiency, accuracy and safety of detection, many scholars have conducted research in recent years. On the one hand, Ouyang proposed to establish an intelligent dam distributed fiber-optic intelligent sensing system for prediction and detection of cracks in dams based on the advantages of high sensitivity and easy installation of fiber-optic sensors [5]. With the distributed fiber optic sensor to capture random cracks and use the distributed fiber optic strain detection system to forecast and detect cracks, this system can achieve real-time detection and feedback of cracks in the dam to ensure the long-term safety and stability of the dam. On the other hand, due to the wide application of nondestructive testing method in engineering inspection, Zhang proposed a geological radar detection technology for dam crack detection [6], by emitting highfrequency electromagnetic pulses to detect the location and geometric parameters of the dam cracks, so as to carry out rapid and accurate detection of the large and complex structure of the dam. In addition, due to the rapid development of computer technology,

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machine vision detection of cracks has also become one of the widely used technologies nowadays. Among them, Xu et al. proposes to detect the leakage of dam surface based on UAV platform combined with tilt photography technology, which collects data by UAV and constructs a model by tilt photography to detect cracks, surface breakage and leakage of dams [7]. Deng et al. further proposes to use UAV tilt photography measurement technology combined with machine vision crack recognition to detect cracks on the surface of the dam, and to rank the cracks existing in the dam through UAV data collection, tilt photography 3D modeling and improved full convolutional neural network (I-CFN) [8]. The above-mentioned methods are more convenient, flexible and targeted than traditional manual inspection, which to a certain extent improves the efficiency of dam crack detection and reduces the risk of personnel and equipment safety, and is a new means of dam safety inspection. However, the quality of dam crack images is affected by the environment and often suffers from low contrast, uneven illumination, and blurred underwater dam images, and the effect of crack extraction using digital image processing techniques is very unsatisfactory, with problems such as texture noise and incomplete extraction of complex cracks. Based on the above problems, this project proposes an unmanned aerial vehicle (UAV) dam crack detection system based on Beidou and LIDAR, using UAVs equipped with various sensors such as LIDAR, combined with Beidou navigation and positioning system for crack detection and its location and attribute information extraction. The UAV operation is efficient and convenient, and LIDAR can accurately obtain the geometric features of cracks and other features such as surface deformation and structural damage of the dam. Based on this system, it can better detect the hidden danger of dam safety, save manpower and material resources for dam safety management, and make the management more convenient and efficient. In the future, a crack database can be established in combination with artificial intelligence, big data analysis, Internet of Things and other technologies to establish a whole life cycle operation system for dam inspection and maintenance.

3 System Introduction The system is mainly divided into five parts: data acquisition, data management, data processing, accuracy verification, and control center (Fig. 1). Data acquisition part: Based on the DJI M300 UAV with Beidou system, it carries optical camera and LIDAR to photograph and scan the surface of the dam to get the laser point cloud data and image data of the dam surface. Data management part: find the historical information of the dam and store it and the obtained point cloud and image in the database for easy organization and management. Data processing part: Use the laser point cloud data to detect cracks in the dam, and count the geometric parameters of the cracks and classify and grade the cracks. Accuracy verification part: The preliminary crack results are synchronized to the maintenance personnel, and the specific images of cracks are uploaded through handheld terminal devices to compare with the algorithm results for accuracy verification. Control center part: firstly, the obtained cracks are presented in the 3D model of the dam, and a crack distribution map is displayed to evaluate and classify the severity of cracks; secondly, as the interaction place of the three processes of data

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acquisition, data processing and accuracy verification, the function of data transmission is executed to guarantee the synchronization of information between decision makers and implementers.

Fig. 1. System composition

4 System Implementation 4.1 Data Acquisition The data acquisition system uses UAVs equipped with LiDAR, Beidou chips, inertial measurement units (IMUs), and optical cameras to conduct aerial flights of the dam to obtain information about its location and attributes. The optical camera collects the dam texture information, and the Beidou satellite navigation and positioning system (BDS) [9] and LiDAR provide real-time scanning data for secondary decoding of the coordinates of the 3D point cloud. The UAV provides full coverage of the dam through route setting; LIDAR detects the distance and angle between it and the target dam; Beidou satellite navigation and positioning system (BDS) to obtain the position information of the UAV in real time; Inertial Measurement Unit (IMU) outputs the instantaneous attitude information of the sensor such as angle elements including heading angle, roll angle and pitch angle in real time; optical camera collects the texture information of the dam for subsequent 3D display. Figure 2 shows the data and relative position relationships collected by the three main sensors: LiDAR, Beidou satellite navigation and positioning system (BDS), and inertial measurement unit (IMU), and serves to solve the coordinates of the 3D point cloud. The meanings of the parameters in Fig. 2 are as follows: (XP , YP , ZP ) represents the 3D coordinates of the target point of the dam; (XBDS , YBDS , ZBDS ) is the BDS antenna

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Fig. 2. Schematic diagram of the calculation principle of 3D point cloud coordinates [10]

center coordinates; (ω, ϕ, κ), RM IMU (ω, ϕ, κ) represent the sensor transverse rocking, pitch and yaw angles provided by the IMU and the rotation matrix of the IMU to the measurement coordinate system, respectively. rP S (αd) is the coordinate vector of the target point P with respect to the scanner coordinate system, α and d denote the scanning angle and measurement distance, respectively; RIMU S (ω, ϕ, κ) represents the rotation matrix from the laser scanner coordinate system to the IMU coordinate system, and (ω, ϕ, κ) is the deflection angle between the scanner and the IMU coordinate system, respectively, which is determined by the system check calibration; (lX , lY , lZ ), (LX , LY , LZ ) represent the rotation matrix from the IMU origin to the LIDAR origin and the BDS origin, respectively. Offset from IMU origin to LIDAR origin and BDS origin, respectively. Based on the above data, the relationship between the coordinates of each target point in the 3D point cloud of the dam is solved by the following Eq. (1): ⎡

⎤M ⎤M ⎡ XP XBDS ⎢ ⎥ ⎥ ⎢ ⎣ YP ⎦ = ⎣ YBDS ⎦ ZP ZBDS

⎛

⎤IMU ⎡ ⎤IMU ⎞ l L X X ⎜ INU ⎟ ⎢ ⎥ ⎥ ⎢ s ⎟ + R N (ω,ϕ,κ) .⎜ − ⎣ LY ⎦ ⎝ RS (ω, ϕ, κ) · rρ (ad ) + ⎣ lY ⎦ ⎠ MUU lZ S Lz GNSS ⎡

(1)

Based on this, the high-precision 3D point cloud acquisition and analysis of the dam surface can be realized, and the real-time monitoring of the UAV flight path and the real-time acquisition and analysis of the location of the acquisition point can also be realized. If abnormalities are detected in the flight path of the UAV or in the location of the acquisition point, the data acquisition device can provide timely feedback so that the data acquisition plan can be adjusted in a timely manner.

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4.2 Data Management The dam data management part is three modules: 3D point cloud data management module, optical image data management module, and historical crack detection data management module. The 3D point cloud data management module mainly stores the data acquired by three sensors, namely LiDAR, BDS and IMU, as well as the later 3D point cloud coordinate solution results. The optical image data management module mainly stores the texture data of the dam captured by the optical camera and the subsequent processing results, including real-time image data, pre-processed data and historical image data. The historical crack detection data management module mainly includes the aggregation of historical crack detection results to form the ROI area (crack risk area) of the dam. 4.3 Data Processing Dam crack detection requires not only detecting the presence of cracks and distinguishing the types of cracks, but also counting the physical characteristics of the cracks, such as their location, width, length, area, and orientation. Among them, crack width is an important basis for classifying crack types [11]. There are many methods for crack extraction, such as threshold segmentation, finite element method and Fully Convolutional Networks. This paper focuses on the recognition method based on laser point cloud data. After a crack appears in the dam, the height value and laser reflection intensity value at the crack are lower than those at the surface of the dam. Therefore, the height difference and intensity contrast between the crack and the surface of the dam body are first obtained using the filtering algorithm, and then the candidate point cloud of the crack is obtained based on the height difference and intensity contrast. When detecting the candidate point cloud, the candidate point cloud is extracted using the maximum entropy threshold segmentation method, and then the candidate point cloud is filtered and denoised based on the trough effect. Finally, the cracks and their geometric parameters are extracted based on morphological filtering [10, 12]. Height difference and strength contrast relative to the surface of the dam. With any point as the center, the median of its eight neighborhoods is used as the intensity value of the local dam, and the point cloud in the height difference neighborhood is leastsquares fitted to obtain the local dam surface. The height difference and intensity contrast between the center point cloud and the local dam surface are calculated and stored in PH and PI , respectively, as shown in the following Eq. (2). PH = Pm − Pz ; PI = Im − Iz

(2)

Pm and Im are the m-th point cloud, respectively, and IZ and PZ are the local dam strength and elevation values obtained by median filtering and least squares fitting, respectively.

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Extraction of Crack Candidate Points. Select point clouds that meet the height difference condition and slope condition as low valley candidates in PH :  h(i, j) < −hd (3) slopef (i, j) > vh hd denotes the maximum depth the crack may reach, slopef (i,j) denotes the average slope centered at (i, j), calculated by 8-neighborhood coordinates, and vh denotes the minimum gradient variation requirement of the candidate point cloud, which needs to be set by itself. The extracted trough candidate point cloud is stored in the dataset Gy , see above Eq. (3).   k  1    slopef (i, j) =  (slopet(i, j, m));  k 1

Z(i, j, k) − Z(i, j) slopet(i, j, m) =  (X (i, j, k) − X (i, j))2 + (Y (i, j, k) − Y (i, j))2

(4)

k denotes the number of valid point clouds in the 8-neighborhood centered at (i, j), and slopet(i,j) is the slope of the m-th point cloud to the center point. x(i,j,k), y(i,j,k), and z(i,j,k) denote the 3D coordinates of the k-th point cloud, and x(i,j), y(i,j), and z(i,j) denote the 3D coordinates of the center point cloud, respectively, see the above Eq. (4). The point cloud with lower reflection intensity than the dam surface is extracted according to the maximum entropy threshold segmentation method in PI , and a maximum intensity difference value F is set for the crack point cloud. This value can be selected according to the histogram to account for 5% of the corresponding intensity value. The point clouds that satisfy the intensity difference are selected and stored in Gc . The same point clouds may be found in Gc and Gv , and the concatenated set of the two data sets is taken as G. Morphological Filtering and Accuracy Verification. Morphological filtering is performed for the obtained candidate point clouds, using closed-operator processing with expansion followed by erosion. Eight-neighborhood is used for joint zone selection, and the minimum number of point clouds contained in the joint zone is set as C. The independent patches with the number of point clouds less than C are deleted. Extract the shape parameters of the joint zone: maximum length (along the x-axis direction) and maximum width (along the y-axis direction). The larger value of the crack length and width is compared with the set crack length threshold L. If it is larger than the threshold L, this area is a crack. To ensure the accuracy of crack detection, manual field visits are used for verification, and handheld terminals are equipped for technicians. Based on the laser point cloud detection results, the decision maker indexes the spatial location information of the crack in the data management system and transmits its spatial location information and geometric parameters to the operator’s handheld terminal. According to the information obtained, the handheld terminal provides the operator with precise navigation

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positioning of the area, which facilitates the operator to find the crack quickly and accurately. After the operator takes the actual measurement of the detection result area, the actual measurement results and images are transmitted to the data management system through the terminal. The decision maker verifies the accuracy of the laser point cloud extraction results with the field inspection results, and on this basis guarantees the credibility and validity of the algorithm results. The crack detection results after the accuracy verification are fed back to the technicians as the final detection results to execute relevant remedial measures, and the location information of each crack is matched with the relevant repair records for perfection to facilitate the construction of a perfect crack database at a later stage. 4.4 Control Center The control center includes two main parts: data transmission and data display. Data transmission includes: transferring the results of 3D point cloud coordinate solution and preliminary crack detection results to the data management system; transferring the crack detection results to the operator’s handheld terminal as well as receiving the operator’s fieldwork results; releasing the manager’s decision scheme and receiving the operator’s actual feedback to realize the efficiency of the crack detection process and improve the reliability of the crack detection results, data transmission process. The data display mainly completes the visualization of crack detection results, point cloud 3D models, and the fitting results of tilt photography images and point cloud 3D models, such as crack distribution maps, zoning and grading detection statistics, and crack detection result analysis. Based on such dam information, the decision management personnel realize digital management of dam cracks, which makes dam crack detection more convenient and provides data basis for dam crack remediation plan with more scientificity.

5 Crack Detection Simulation Experiment Because of the expensive equipment required and the difficulty in obtaining rel-evant data, this study uses simulated data (DEM images based on laser point cloud generation), to verify the feasibility of this scheme and to demonstrate the crack detection results, as well as to evaluate the accuracy of the results. The simulation experiment uses DEM images based on laser point cloud generation and field images to simulate real dam cracks. First, based on the DEM image, the crack detection was performed by using the threshold segmentation method; second, based on the field image, the real crack results were obtained by visual interpretation; finally, the real cracks were compared and analyzed with the experimental results to verify the crack detection accuracy. It is verified that the crack detection accuracy of this experiment is 82%, which can detect large cracks, but fails to detect fine cracks. The experimental results are shown in Fig. 3.

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Fig. 3. Crack detection results of simulation experiment (Note: Figure (a) is DEM image generated based on laser point cloud; Figure (b) is the crack detection results based on the threshold segmentation method. Figure (c) is the result of visual interpretation of the fracture. Figure (d) is the superposition result of crack detection based on threshold segmentation method and original image)

6 Innovation and Application Prospects 6.1 Innovation Points With the precise positioning function of Beidou positioning and navigation system, combined with a variety of sensors such as LiDAR, we obtain high-precision dam crack location and attribute data, and then use the dam crack detection algorithm to realize the accurate detection of dam cracks. Build a three-dimensional model of the dam for digital management, not only to facilitate intuitive display and efficient management, but also the future combined with artificial intelligence, Internet of Things and other technologies to establish the dam crack monitoring, detection, maintenance of the whole life cycle of the operation system to provide a solid data base. 6.2 Application Prospects Can to a certain extent to solve the current dam crack detection is not accurate enough, high cost, long detection time, can effectively reduce the cost of dam maintenance, reduce the national maintenance of water conservancy projects on part of the pressure. With the gradual application of a new generation of LIDAR scanning technology in engineering inspection projects, the use of UAVs combined with LIDAR to detect cracks in dams can be used to the maximum extent to achieve the application value of

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the emerging technology, and can be extended to the safety inspection of aircraft take-off runways, ship hulls, etc. With the continuous improvement of Beidou positioning accuracy and LIDAR scanning accuracy, the detection accuracy of dam cracks will also be improved, and in the future, it will be organically combined with more types of sensors to make its use more valuable. 6.3 Uncertainties and Shortcomings Due to the lack of actual measurement data of UAV-mounted LIDAR detection of dam cracks, the above study is limited to reasonable estimation within the theoretical range, i.e., it adopts the current theory of relevant algorithms as the basis. Although simulation experiments have been conducted, it is still necessary to verify the accuracy through actual data to support the above theory. The current program mainly focuses on the part of the dam above the water surface for crack detection, the lack of underwater dam crack detection, and the actual shooting is affected by bad weather and the depth of the water after the bad weather, with certain limitations. Due to the limitations of the current Beidou positioning accuracy and LIDAR scanning accuracy, the detection of dam cracks based on the existing laser 3D point cloud algorithm may make some of the dam cracks can not be accurately identified and located, which still needs to be continuously improved and enhanced in the future. Acknowledgments. Funded by Sichuan Science and Technology Program (2023NSFSC0250). Ministry of Education industry-university cooperative education project (202102245026). College Students’ Innovative Entrepreneurial Training Plan Program (202210621045, S202210621118).

References 1. Wu, W.Y., Fang, G.Z., Wei, Y.: Analysis on causes and harmness of cracks on dam crest using numerical simulation. Yangtze River 51(S2), 270–274 (2020) 2. Tian, X.W.: Concrete crack repair of Zhuzhuang reservoir dam. Water Sci. Eng. Technol. 2, 46–49 (2020) 3. Deng, L.N.: Causes analysis treatment technology of concrete cracks in Zhuchanghe Reservoir Dam. Water Conserv. Constr. Manage. 41(7), 44–48 (2021) 4. China Dam Engineering Society: China Dam Engineering Society 2020 Annual Report. http://www.chincold.org.cn/chincold/rootfiles/2023/01/17/1671019479025604-167 1019479089257.pdf. Last accessed 20 Sept 2022 5. Ouyang, B.Y.: Application research of distributed optical fiber sensing technology in intelligent dam safety monitoring. Technol. Innov. Appl 6, 6–7 (2016) 6. Zhang, C.: Application of geological radar technology to detect cracks in a dam body. Shanxi Hydrotechn. 1, 25–27+31 (2018) 7. Xu, C.Y., Yang, Y., Zhong, L.: Research on slope safety monitoring technology based on UAV proximity photogrammetry. Henan Water Resour. South-to-North Water Divers. 50(7), 82–84 (2021)

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8. Deng, Y.X., Luo XJ, S, Li HL, T.: Research on crack detection of hydropower station dam surface based on tilt photogrammetry technology of UAV. Technol. Innov. Appl. 5, 158– 161+166 (2021) 9. Zhu, E.H., Guo, H.R., Li, J.L.: Performance analysis of real-time PPP based on BDS-3 PPP-B2b service. J. Geodesy Geodyn. 42(6), 616–621 (2022) 10. Zhong, M.Q.: Research on methods of pavement condition survey using mobile laser scanning data (Dissertation). Changan University, Xian (2020) 11. Guan, H., Li, J., Cao, S., Yu, Y.: Use of mobile LiDAR in road information inventory: a review. Int. J. Image Data Fusion 7(3), 219–242 (2016) 12. Xiao, W.T.: Research on detection and management of surface cracks in tunnel lining based on 3D laser scanning (Dissertation). Xiamen University, Xiamen (2019)

Beidou+5G-Based Plug-In Data Platform to Enhance the Accuracy of Smart Terminal App Applications Kai Wang1(B) , Kezhao Li1,2(B) , Shuaikang Lv1 , Yingxiang Jiao1 , Yunyan Shen1 , Zhe Yue1 , and Keke Xu1 1 School of Surveying and Land Information Engineering, Henan Polytechnic University,

Jiaozuo 454000, China [email protected], [email protected] 2 Collaborative Innovation Center of BDS Research Application, Zhengzhou 450052, China

Abstract. Real-time high-precision positioning and navigation of smart terminals has a huge potential demand in the field of positioning, but for reasons of cost and power consumption, its low-cost global navigation satellite system (GNSS) positioning chips and antennas carrying received satellite observation data are of poor quality, prone to circumferential jumping, and seriously affected by multi-path effects, making it difficult to meet the requirements of high-precision positioning. There is a huge potential demand for real-time high-precision positioning and navigation for smart terminals in the field of positioning. However, for reasons of cost and power consumption, the low-cost global navigation satellite system (GNSS) positioning chips and antennas on which they are mounted receive poor quality satellite observation data, which are prone to circumferential jumping and are seriously affected by multi-path effects, making it difficult to achieve the requirements of high-precision positioning. Meanwhile, with the arrival of 5th Generation Mobile Communication Technology (5G) communication technology, its characteristics of low latency, large bandwidth and large number of connections make it easier to transmit a large amount of GNSS observation data in real time. In order to modify certain smart terminals to meet the demand of high accuracy, combined with 5G high-speed network, A method was proposed to build an plug-in data platform using BeiDou high-precision board + 5G and Bluetooth technology to enhance the accuracy of smart terminal Application (APP) applications. The plugin data platform is divided into a server module and a user terminal module. The server module continuously receives real-time satellite observation data from the base station. The user terminal module mainly receives the satellite observation data by using the Unicorecomm UB4B0M board, outputs the data from the serial port through the board backplane, then transmits the data to the Arduino microcontroller via the serial to Transistor-Transistor Logic (TLL) module, and finally sends the data to the intelligent terminal APP by the HC-05 Bluetooth module; after the terminal receives the data, the terminal APP submits the time stamp to the server, which matches the satellite observation data of the base station and sends it back to the terminal APP via 5G high-speed network in real time for real-time carrier phase difference calculation. The experimental verification shows that the intelligent terminal plug-in data platform operates stably and correctly, and can © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 14–24, 2024. https://doi.org/10.1007/978-981-99-6928-9_2

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achieve centimeter-level navigation and positioning accuracy, which can provide technical reference for the transformation of existing low-precision intelligent terminals and the development of future high-precision intelligent terminals. Keywords: BeiDou · 5G · Intelligent terminal navigation application · Location service

1 Introduction At present, smart terminals have become the most widely used terminals for GNSS positioning and used in various mobile services. However, it is difficult to improve its navigation and positioning accuracy because of various problems such as poor quality of GNSS observation data of smart terminals, are easy to be affected by multi-path effect in complicated environment and special anomaly error. Take the popular smartphone in the general smart terminal GNSS as an example. In May 2016 Google announced at the "Google I/O" conference that raw GNSS survey observations can be accessed through the Application Programming Interface (API) of the Android Nougat operating system [1–3]. After that many scholars have studied and analyzed the raw GNSS observation data and positioning accuracy of popular consumer-grade GNSS chipsets equipped with smartphones. Pesyna et al. [4] evaluated the positioning accuracy of mass consumer chipsets and concluded that mass consumer chipsets can only achieve a positioning accuracy of 2 to 3m, which drops to 10m or even hundreds of meters under unfavorable multipath effect conditions. Li et al. [5] analyzed the measurement error characteristics of observed data from smartphones and geodetic receivers, resulting that GNSS signals received by smartphones have uneven signal strength, rapid carrier-to-noise ratio variations, and pseudo-range noise about 10 times higher than that from geodetic receivers. Zhang [6] et al. evaluated the quality and positioning accuracy of raw GNSS measurement observations from smartphones equipped with Android Nougat, and concluded that the average carrier-to-noise ratio of smartphone GNSS observations was about 10 dB-Hz lower than that of geodetic receivers, with single-difference pseudorange residuals between −20 m and 20 m. From the above literature it is concluded that the quality of GNSS observations received by ordinary smart terminals is poor and much lower than that of geodetic receivers, for the following reasons. 1. Hardware limitations due to cost considerations. Most manufacturers of production intelligent terminals use Global Positioning System (GPS) single-frequency chips and low-cost passive linear polarization antennas to track GPS L1 C/A code measurements for cost reasons, which are highly susceptible to multipath effects in complex environments such as cities [7]. Although smartphones with multi-frequency GNSS chips are now in production from large handset manufacturers, there are problems with not being able to access multi-frequency signals from the application programming interface due to other hardware limitations on the device [8].

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2. Duty cycle technology for device power consumption considerations. Some smartphones use duty cycle technology in order to reduce power consumption. The default GNSS sampling rate for smartphones is 1 Hz, and when the duty cycle is on, the GNSS chip only tracks the carrier phase for part of the milliseconds per second, and does not record the phase change for the remaining milliseconds [9]. This results in the obtained carrier phase per second being discontinuous, i.e., there are circumferential hops per second. 3. Other anomalous errors due to manufacturability limitations. Li [9] found an unaligned random initial phase bias in the carrier phase observations of smartphones. Humphreys [10] et al. found a time-dependent linear bias in the carrier phase of the Samsung Galaxy S5 cell phone. All these errors affect the whole-period ambiguity fixation and make the carrier phase data unavailable in the observed data. Due to the rapid development of the 5th Generation Mobile Communication Technology (5G), its upload and download speed can reach 10 times faster than that of the 4th Generation Mobile Communication Technology (4G), and the information transmission delay can be reduced to 5-10ms. The information transmission delay can be reduced to 5-10ms, which makes it easier to transmit a large amount of GNSS observation data in real time [11]. In this paper, to address the problem that the poor quality of data received by antennas and chips used in smart terminals cannot meet the requirements of highprecision navigation, we propose a method to build a plug-in data platform with Beidou high-precision board +5G and Bluetooth technology to enhance the application accuracy of smart terminal applications (APP) by combining 5G technology (Note: BeiDou high-precision board receives data from all GNSS systems [12]). The platform achieves the purpose of enhancing the navigation and positioning accuracy of smart terminals by replacing the original satellite observation data of the smart terminal APP with the base station for carrier phase difference decomposition calculation. Although the platform does not overlap with the smart terminal antenna position, in the future the lightweight platform can be used as a terminal plug-in to replace ordinary smart terminals (such as mobile phones) for navigation and positioning.

2 Plug-In Data Platform Design The plug-in data platform design consists of a server module and a user terminal module. The hardware part of the server module contains the server and the base station, both of which are in the same LAN and use TCP/IP protocol for network communication through socket technology. The server is a DELL EMC PowerEdge R740 rackmount server and the base station is a CHCNAV P5 star-based differential receiver, as shown in Fig. 1. After receiving the data, the base station establishes a Socket server to continuously send binary data to the client. The server software is partially written based on the open source WEB application framework Django and runs on a server. The software implements a socket client on the HTTP server for continuously receiving the base station data, decoding and storing it.

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At the same time, the software HTTP server receives the network request sent by the intelligent terminal APP carrying the observation time, matches the stored base station data, and sends the matched data back to the intelligent terminal APP via the 5G network.

Fig. 1. Server module hardware part

The user terminal module part includes the Android phone and the plug-in data platform. The Android phone of this design adopts Xiaomi 8, and the board of plug-in data platform adopts Unicorecomm UB4B0M board, using Arduino MEGA microcontroller and HC-05 Bluetooth module to receive and send the data of the board, as shown in Fig. 2.

Fig. 2. User terminal module hardware part

The plug-in data platform can realize sending the data from BeiDou high-precision board to the intelligent terminal APP to replace the original satellite observation data of the intelligent terminal APP for high-precision positioning and navigation, the overall architecture of the platform is shown in Fig. 3, and the main processes are:

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1. The BeiDou high-precision board tracks the BeiDou satellite signals and later sends the satellite observation data through the board backplane. 2. The board backplane sends data to the Arduino microcontroller through the serial port. As the Arduino microcontroller does not support direct serial communication, a serial to TLL module needs to be connected at the serial port in order to transfer the data [13, 14]. 3. The Arduino microcontroller uses hard serial communication to send data to the HC-05 Bluetooth module. The user’s smart terminal APP connects to the HC-05 Bluetooth module, receives the board data and decodes it to replace the original satellite observation data of the smart terminal. 4. The user intelligent terminal APP sends a network request with observation time to the server side. The server responds to the request, matches the data from the base station and sends it back to the user’s smart terminal APP via the 5G high-speed network. The user’s smart terminal APP receives the data and solves the coordinates.

Fig. 3. Plug-in data platform overall architecture diagram

3 Experimental Results and Analysis In order to analyse the quality and positioning accuracy of GNSS observations from the platform. The Xiaomi 8, a dual-band smartphone, is used as a general smart terminal, and the I90, a geodesic receiver, is used to compare the quality of observation data with the plug-in data platform. 3.1 Quality Comparison of GNSS Observations As shown in Fig. 4, the experimental equipment was placed in sequence and the observation data were collected for 2 h. By comparing the number of visible stars and the

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signal-to-noise ratio of the plug-in data platform, the normal smart terminal and the geodetic receiver, the quality of the GNSS observations from the plug-in data platform and the advantages of the plug-in data platform over the normal smart terminal are assessed.

Fig. 4. Static data acquisition experiments

Number of Visible Satellites Figure 5 shows the number of visible satellites for the plug-in data platform, the general intelligent terminal and the geodesic receiver, respectively. As can be seen from the figure, the total number of visible satellites of all three devices is above 20, among which the total number of visible satellites of the plug-in data platform and geodesic receiver is in the range of 45–55, and the total number of visible satellites of the general intelligent terminal is in the range of 20–30. For each GNSS system, the difference in the number of visible stars is less than 5 for all three devices except in the BeiDou Satellite Navigation System (BDS). In the BDS system, the number of visible stars of ordinary intelligent terminal is in the range of 0–10, which is much smaller than the range of 20–30 for plug-in data platform and geodesic receiver. From the aforesaid analysis, it is concluded that the satellite signal tracking capability of the plug-in data platform, especially for BDS satellites, is better than that of ordinary intelligent terminals and is similar to that of geodesic receivers. Signal-to-Noise Ratio The signal-to-noise ratio (SNR) is the ratio of the carrier signal power to the noise power and is expressed as SNR =

PR N

(1)

The signal-to-noise ratio is mainly affected by antenna gain, satellite elevation angle, multipath, and other factors, and can directly reflect the quality of the measured GNSS

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observations [12]. Figure 6 shows the frequency distribution histograms of the carrier-tonoise ratio of the plug-in data platform, geodetic receivers and general smart terminals at GPS (L1/L5), BDS (B1I/B2I), GLONASS (L1/L2) and Galileo (E1/E5a) frequencies.

(a). The number of observable satellites of plug-in data platform

(b). The number of observable satellites of general intelligent terminal

(c). The number of observable satellites of geodetic receivers

Fig. 5. The number of observable satellites of device

As can be seen from Fig. 6, the signal-to-noise ratios of the plug-in data platform and the geodetic receiver are mostly distributed in the interval of 30–50 dB-Hz at each frequency, and in the interval of 50–60 dB-Hz at all frequencies except GPS L1 and

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Galileo E1. The signal-to-noise ratios of general intelligent terminals at each frequency are mostly distributed in the 20–40 dB-Hz range. Only on BDS B1I and GLONASS L1, there are a small number of distributions in the 40–50 dB-Hz range. From the above analysis, it can be concluded that the quality of satellite observation data received by the plug-in data platform on all frequencies is better than that of the general intelligent terminal, equal to or even partially better than that of the geodesic receiver.

Fig. 6. Signal-to-noise ratio distribution frequency histogram

3.2 Navigation and Positioning Results and Analysis To evaluate the positioning accuracy of the plug-in data platform to enhance the navigation of smart terminal APP. Carrier phase difference decomposition was performed on the observations from the above experimentally collected plug-in data platform to compare their positioning accuracy. Carrier Phase Differential Positioning Results and Analysis Carrier phase differential positioning is solved for the data and Fig. 7 shows the carrier phase differential positioning error for the plug-in data platform. As can be seen from the graph, the positioning accuracy is centimeter level and the standard deviation of the positioning error in the ENU direction is 0.004m, 0.007m and 0.012m respectively. This

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Fig. 7. Plug-in data platform carrier phase differential positioning error

proves that the plug-in data platform can enhance the smart terminal APP navigation to achieve centimeter-level carrier phase differential positioning accuracy and has good navigation and positioning effects. Carrier Phase Differential Positioning Kinetic Track Analysis On the lawn behind the School of Surveying, Mapping and Land Information Engineering at Henan University of Technology, holding a plug-in data platform, walking at a constant speed and analysing the positioning trajectory. The kinematic track of the experimental data after the carrier phase differential localization solution is shown in Fig. 8. The red dot in the diagram indicates the carrier phase differential positioning solution and the yellow line indicates the RTK solution output from the board. As can be seen from the graph, the motion trajectory is stable and similar to the board RTK solution.

Fig. 8. Plug-in data platform carrier phase differential positioning route

4 Conclusions This paper firstly introduces the reasons why the poor quality of raw observation data of general intelligent terminals cannot be used for high-precision positioning. And then a method to improve the navigation accuracy of APP of general intelligent terminals based

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on the plug-in data platform of BeiDou + G is proposed. The quality of satellite observation data and positioning performance of the plug-in data platform, the Xiaomi 8 smartphone and the geodetic receiver CHCNAV I90 were compared through experimental data analysis. Based on the experimental results, we can obtain the following conclusions. The quality of satellite observation data from the plug-in data platform is better than that of general intelligent terminals across the board, and is prior the mean value of the geodesic receiver. The plug-in data platform can enhance the carrier phase differential positioning accuracy of smart terminal APP navigation to centimeter level. In the future, the data platform can be lightened to make it a portable terminal plug-in to improve the positioning performance of ordinary smart terminals. Acknowledgments. This work is funded by the National Natural Science Foundation of China (No. 41774039, 42204040), the State Key Lab Project of China (No. 6142210200104) and the Key Project of Science and Technology of Henan (No. 212102210085). The authors would like to thank C.K, who is a professor at The Ohio State University, for providing the valuable advice.

References 1. Robustelli, U., Baiocchi, V., Pugliano, G.: Assessment of dual frequency GNSS observations from a Xiaomi Mi 8 android smartphone and positioning performance analysis. Electronics 8(1), 91 (2019) 2. Shuo, Z., Jinzhong, B., Yantian, X., Zhonghai, Z..: Analysis of GNSS data quality and positioning accuracy of dual frequency smartphone. Sci. Surv. Mapp. 45(02), 22–28 (2020) 3. Geng, J., Jiang, E., Li, G.: An improved hatch filter algorithm towards sub-meter positioning using only Android raw GNSS measurements without external augmentation corrections. Remote Sens. 11(14), 1679 (2019) 4. Pesyna, K.M., Humphreys, T.E., Heath, R.W., Novlan, T.D., Zhang, J.C.: Exploiting antenna motion for faster initialization of centimeter-accurate GNSS positioning with low-cost antennas. IEEE Trans. Aerosp. Electr. Syst. 53(4), (2017) 5. Li, G., Geng, J.: Characteristics of raw multi-GNSS measurement error from Google Android smart devices. GPS Solutions 23(3) (2019) 6. Zhang, X., Tao, X., Zhu, F., Shi, X., Wang, F.: Quality assessment of GNSS observations from an Android N smartphone and positioning performance analysis using time-differenced filtering approach. GPS Solutions 22(3) (2018) 7. Shinghal, G., Bisnath, S.: Conditioning and PPP processing of smartphone GNSS measurements in realistic environments. Satell. Navig. 2(1) (2021) 8. Barbeau, S.: Crowdsourcing GNSS capabilities of android devices. https://barbeau.medium. com/crowdsourcing-gnss-capabilities-of-android-devices-d4228645cf25. Last accessed 05 Apr 2021 9. Li, G.: Theory and Method of GNSS Ambiguity Resolution for Smartphones. Wuhan University (2021) 10. Humphreys, T.E., Murrian, M., van Diggelen, F., Podshivalov, S., Pesyna, K.M.: On the feasibility of cm-accurate positioning via a smartphone’s antenna and GNSS chip. In: Proceeding of IEEE/ION PLANS 2016 on Proceeding, pp. 232–242. Savannah, GA (2016)

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11. Ji, W.: Multi-dimensional Information Fusion Localization Algorithm based on 5G Technology. East China Normal University (2022) 12. Unicorecomm.UB4B0M board product introduction. https://www.unicorecomm.com/pro ducts/detail/1. Last accessed 22 Mar 2023 13. Ruxiao, Y., Wenling, H.: Design of control system for manipulator based on bluetooth module. Ind. Control Comput. 30(12), 66–68 (2017) 14. Wang, R.: Research on Monitoring Devices of Hanging Ground Lead in Catenary Maintenance on the Basis of 4G Network Communication. Xian University of Technology (2018) 15. Zhu, Y.: Soil Moisture Retrieval Using BDS Signal-to-Noise Ratio. Nanjing Normal University (2021)

Analysis on Effects of L-Band Solar Radio Bursts on GNSS Yibo Si1(B) and Bin Wang2 1 Beijing Satellite Navigation Center, Beijing, China

[email protected]

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

[email protected]

Abstract. The strong L-band solar radio bursts will affect the navigation signals captured and tracked by the Global Navigation Satellite System (GNSS) receivers located in the sunlit hemisphere (sunny side), thus affecting the stability and accuracy of GNSS services. In this paper, an L-band solar radio burst erupted on August 28, 2022 was detected and analyzed based on GNSS Monitor System. Similar to December 13, 2006, the incident affected the GNSS tracking stations in the sunny side to varying degrees. Based on IGS data and low orbit satellite data, the characteristics and influence of the two events are compared. The analysis results show that: (1) solar L-band radio bursts will have different degrees of impact on the sun side navigation users; (2) the influence degree is positively correlated with the solar altitude angle; (3) the influence mode is similar to space-based suppression interference. Keywords: L-band solar radio burst · GNSS · SNR · Position error · Space-based interference

1 Introduction Solar activity often affects satellite navigation system services. During the active periods of the solar system, it often causes severe disturbances in the ionosphere and changes in the gradients of electron density. In some severe cases, it may cause the decrease of the carrier-to-noise ratio of the signal, the increase of measurement error, even the decrease of the accuracy of ionospheric correction, etc. Solar radio bursts are direct interference from the sun. When its frequency band covers the frequency of navigation signals, it will cause varying degrees of interference to GNSS receivers in the form of strong noise. The eruption mechanism of solar radio bursts is very complicated, generally accompanied by solar flares, with a wide burst frequency band and a variety of burst types. However, the occurrences of L-band strong solar radio bursts are rare. Since the wide use of GNSS services, the most representative ones are the four consecutive solar

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 25–38, 2024. https://doi.org/10.1007/978-981-99-6928-9_3

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flare events in December 2006, all of which were accompanied by L-band solar radio bursts. The radio burst on December 13, 2006 happened to be on the sunny side of China [1]. On August 28, 2022, based on the GNSS monitoring system, this type of event was detected again. Through the analysis of IGS tracking station and low-orbit satellite data, the characteristics, principles and impacts of the two events were compared.

2 Background 2.1 Surveillance Background From 17:45 to 18:40 on August 28, 2022 (UTC time), Beidou, GPS, GLONASS, Galileo and other satellite navigation systems have an abnormal drop in carrier-to-noise ratio at all frequency points in nearly a hundred of IGS tracking stations located in Americas, western Europe, Atlantic Ocean, and the eastern Pacific Ocean [2]. After a joint analysis with the space environment monitoring departments, it was concluded that the solar activity interfered with the GNSS service signal on the sun-facing side of the earth during this period. According to the data analysis of IGS tracking stations, the tracking stations with abnormal carrier-to-noise ratio basically cover half of the earth, and they are all within the twilight line (i.e. the sun irradiated surface, at 18:00 on August 28, 2022); during the abnormal period (around 18:00), the subsolar point is near 9.7°N, 97.2°W, located in Central America. Similar to the radio burst during 2:00–4:30 on December 13, 2006, the parts of Asia and Oceania was just on the sunny side, and the subsolar point was near 23°S, 126°E, which was located in Australia. 2.2 Fundamentals of Data Through the observation files and ephemeris files output by the IGS tracking station receivers distributed around the world, the downlink signal situation and service performance of the satellite navigation system can be calculated and analyzed. In addition, in the past 10 years, low-orbit satellites with an orbital altitude below 1000 km have developed rapidly, and GPS satellites can be tracked by on-board GPS receivers for orbit determination. Among them, the Swarm satellite is a type of low-orbit satellites launched by the European Space Agency (ESA) in 2013 for geomagnetic observation. It consists of 3 small satellites A, B, and C, with an orbital height of about 680km and a period of 2.2 h. On the same orbital plane, there are more than 6 satellites tracking GPS throughout the day [3]. The GPS receiver on the Swarm satellites can receive GPS satellite signals and generate observation files. The following analysis is based on the IGS station data of the two events in 2022 and 2006 and the Swarm low-orbit satellite data in 2022. Since in 2006, only the GPS system was officially providing services among the four major satellite navigation systems, and the Swarm satellite receiver only supports GPS, so we will take the L1 and L2 frequency of the GPS system as an example, from the carrier-to-noise ratio of signal, positioning accuracy, etc. to analyze its impact.

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3 Effects on Receiving Signals The carrier-to-noise ratio is used to measure the quality of the signal and indirectly reflect the measurement accuracy of the carrier phase. Carrier-to-noise ratio can also be used as a measure of the magnitude of interference a signal endures. 3.1 Analysis of Carrier-To-Noise Ratio Interference of GPS Signal in IGS Tracking Stations As illustrated in Fig. 1, the twilight line of 18:00 on August 28, 2022 is drawn, and we select the data of four IGS tracking stations located on the sunny side for analysis. Figures 2, 3, 4 and 5 are the time sequence diagrams of the GPS signal carrier-to-noise ratio of the four selected stations. Among them, the upper picture is the L1 frequency point, the lower picture is the L2 frequency point, the left side of the vertical axis is the CNR value, the horizontal axis is the time axis, and the colored curves are the CNR timing curves of different satellites. It can be seen from the figures that the carrier-tonoise ratios of the four tracking stations all decreased in varying degrees between 17:45 and 18:40, with a magnitude of 5-17dB.

Fig. 1. Subsolar point, twilight line and site distribution map (2022.08.28 18:00)

In addition, the G05 satellite enforced a power boost operation during this period, which has a certain compensation effect on the decrease of the carrier-to-noise ratio caused by the L radio burst. Taking the TLSE station in France as an example (shown in Fig. 6), the right side of the vertical axis is the value of the solar altitude angle, and the black curve is the solar altitude angle curve. At 17:47, the sun elevation angle at TLSE station was about 5 degrees, and at the L2 frequency point, while the signal carrier-tonoise ratio of other GPS satellites decreased by about 5dB, after the power enhancement operation of G05 satellite, the carrier-to-noise ratio still has an increase about 7dB.

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Fig. 2. Time sequence diagram of carrier-to-noise ratio of GLPS station

Fig. 3. Time sequence diagram of carrier-to-noise ratio of SGPO station

For the BOAV station in Brazil (Fig. 7), the solar altitude angle is about 60 degrees, and the power enhancement operation of the G05 satellite does not significantly improve the signal carrier-to-noise ratio of the station. The IGS tracking station ALIC data on December 13, 2006, which was located in the sun side, was selected for analysi. The timing sequence diagram of its GPS signal carrier-to-noise ratio was shown in Fig. 8. It can be concluded from the figure that the carrier-to-noise ratio of the ALIC station drops more or less between 2:00 and 4:30, and the carrier-to-noise ratio drops by about 20dB from 3:31 to 3:36.

Analysis on Effects of L-Band Solar Radio Bursts on GNSS

Fig. 4. Time sequence diagram of carrier-to-noise ratio of POVE station

Fig. 5. Time sequence diagram of carrier-to-noise ratio of ASCG station

Fig. 6. Time sequence diagram of carrier-to-noise ratio and solar altitude of TLSE station

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Fig. 7. Time sequence diagram of carrier-to-noise ratio and solar altitude of BOAV station

Fig. 8. Time sequence diagram of signal-noise-ratio and solar altitude of ALIC station

3.2 Interference Analysis of Carrier-To-Noise Ratio of Swarm Satellites GPS Signal By analyzing the onboard GPS observation files and ephemeris files of the three Swarm satellites [4], the sub-satellite point trajectories of the three satellites from 17:45 to 18:40 are given, as shown in Fig. 9, where the trajectory of Swarm A and C satellites are almost the same. From the timing sequence chart of carrier-to-noise ratio of receiving GPS signals (from Figs. 10, 11 and 12), it can be seen that at about 17:50 on August 28, the altitude angle of the sun at the sub-satellite point of Swarm A and C satellites was about 60 degrees, and the carrier-to-noise ratio decreased about 5-15dB; the altitude angle of the sun at the sub-satellite point of B is about 28 degrees, so the carrier-to-noise ratio decreased slightly.

Analysis on Effects of L-Band Solar Radio Bursts on GNSS

Fig. 9. Sub-satellite point trajectory of Swarm (17:45–18:40) and twilight line (18:00)

Fig. 10. Time sequence diagram of GPS carrier-to-noise ratio of Swarm-A

Fig. 11. Time sequence diagram of GPS carrier-to-noise ratio of Swarm-B

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Fig. 12. Time sequence diagram of GPS carrier-to-noise ratio of Swarm-C

3.3 The Relationship Between Altitude Angle of the Receiver to the Sun and the Change of Its Carrier-To-Noise Ratio By drawing the twilight lines and the position of the subsolar point at the time of radio bursts, we illustrate the distribution of IGS tracking stations (Fig. 1) and the position of the sub-satellite point of the Swarm satellites at the same time (Fig. 10). Except for a few tracking stations, the GNSS service signals received by almost all the tracking stations located on the sunny side of the earth are affected. We select and calculate the sun altitude angle and GPS carrier-to-noise ratio decrease of four tracking stations and three Swarm satellites at 18:00. The result is shown in Table 1. Similarly, we analyze the sun altitude angle and GPS carrier-to-noise ratio decrease at 3:30 of the three tracking stations on December 13, 2006, and the result is shown in Table 2. As it shows, except for a few tracking stations/receivers far away from the subsolar point, almost all other tracking stations/receivers on the sunny side are affected, and the degree of the influence is proportional to the altitude angle of the sun, i.e. the receivers near the subsolar point are greatly affected, while those far away from the subsolar point are less affected. 3.4 Characteristic of Interference The decrease of the carrier-to-noise ratio of the GNSS receiver is caused by the increase of the background noise. Observing the time sequence diagram of the carrier-to-noise ratio at the time when each receiver is interfered by two solar radio burst events, it can be found that the curve trend is basically the same, only the amplitude is different, and the disturbed pattern is similar to suppressive interference. It can be concluded that they come from the same interference source according to the distribution of total electron content (TEC) of the global fast ionospheric product released by the European Orbit Determination Center (CODE) in Fig. 13, it can be found that there is no abnormality in the ionosphere. Therefore, the GNSS cycle slip and loss of signal caused by radio bursts are essentially different from those caused by changes in the ionosphere. Such phenomena can be regarded as space-based suppressive interference initiated by the sun.

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Table 1. Corresponding table of position, solar altitude, carrier-to-noise ratio decreasing at the peak time of SRB event (2022.08.28) Station name

Latitude

Longitude

Solar altitude

Carrier-to-noise ratio decreasing

GLPS

−0.743

−90.304

62.02

GPS: 8-17dB BDS:8-10dB GLO: 8-12db GAL:8-10dB

SGPO

38.803

−104.525

40.26

GPS: 5-15dB BDS:7-10dB GLO: 8-12db GAL:7-10dB

POVE

−8.709

−63.896

23.00

GPS: 5-8dB GLO: 5-7db GAL:5-8dB

ASGC

−7.916

−14.333

10.66

GPS: 3-7dB GLO: 3-5db GAL:3dB

SWARM-A

−15.410

−45.439

60.99

GPS: 5-15dB

SWARM-B

41.508

158.218

28.08

GPS: 5dB

SWARM-C

−14.879

−46.091

61.34

GPS: 5-15dB

Table 2. Corresponding table of position, solar altitude, carrier-to-noise ratio decreasing at the peak time of SRB event (2006.12.13) Station name

Latitude

Longitude

Solar altitude

Carrier-to-noise ratio decreasing

ALIC

−22.321

133.884

83.55

GPS: 10-20dB

KUMN

25.02

102.79

41.66

GPS: 5-15dB

LHAZ

29.65

91.10

27.62

GPS: 5-10dB

L-band solar radio bursts and ionospheric scintillations have similar effects, both of which can give rise to a variation of GNSS signals in C/N0. The difference between scintillations and SRBs is that SRB events cause an increase in the spectral noise density of the GNSS receiver, whereas scintillations cause variations in the GNSS signal power [5].

4 Effects on Positioning The strong electromagnetic interference environment will affect the strength of the received signal, causing the satellite signal to be too weak or even loss the signal, or the increase of the positioning error, even the interruption of the service. On August 28,

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Fig. 13. TEC Map of CODG (2008.08.28 18:00)

2022, taking the GLPS station which experienced the most affected signal carrier-tonoise ratio as an example (Fig. 2), it can be seen from the DOP value and single-point positioning accuracy that the positioning service is not affected (Fig. 14).

Fig. 14. Time sequence diagram of number of visible GPS satellites, DOP and positional accuracy of GLPS station (2022.08.28)

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The influence of the solar radio bursts on precision positioning was analysed with the observation-minus-computation (OMC) residuals and ambiguities variation of carrier phase. As can be seen from Fig. 15, although the phase ambiguity has changed during solar radio bursts of 28 August 2022, it does not have an impact on precise positioning results which can be seen from the subplot of phase OMC residuals.

Fig. 15. Time sequence diagram of GPS phase OMC residuals, and phase ambiguities for GLPS station (2022.08.28)

On December 13, 2006, taking the ALIC station which experienced the most affected signal carrier-to-noise ratio as an example (Fig. 8), the number of visible satellites dropped significantly (less than 4) from 3:31, and the positioning was interrupted for 6 min, and it occurred several times that the DOP value was unstable between 2:00 and 4:30 (Fig. 16). The influence of the solar radio bursts on precision positioning was analysed with the observation-minus-computation (OMC) residuals and ambiguities variation of carrier phase. As can be seen from Fig. 17, unlike the solar radio burst on August 28, 2022, the solar radio burst on December 13, 2006 has a significant impact on the carrier phase observations. During this solar radio burst, the large variations of phase observations can be seen, and the continuity of the phase ambiguities is destroyed, and this have a significant impact on precise positioning results which can be seen from the subplot of phase OMC residuals.

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Fig. 16. Time sequence diagram of GPS carrier-to-noise, Number of visible GPS satellites, DOP and Positional accuracy of ALIC station (2006.12.13)

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Fig. 17. Time sequence diagram of GPS phase OMC residuals, and phase ambiguities for ALIC station (2006.12.13)

5 Conclusion In this paper, an L-band solar radio burst erupted on August 28, 2022 was detected and analyzed based on GNSS Monitor System. Similar to December 13, 2006, the incident affected the GNSS tracking stations in the sunny side to varying degrees. Based on IGS data and low orbit satellite data, the characteristics and influence of the two events are compared. The analysis results show that: (1) Solar L radio bursts will have varying degrees of impact on the signal carrier-to-noise ratio and positioning services of GNSS on the sunny side; (2) The impact on the carrier-to-noise ratio is due to the increase of the noise, which is irrelevant to the ionosphere; (3) The disturbed pattern is similar to suppressive interference, and the source of the interference is the sun, i.e. we can regard the sun as a space-based interference source; (4) Regardless of whether it is a ground tracking station or a low-orbit satellite onboard GPS receiver, the degree of the impact is positively correlated with the sun altitude angle, and the tracking stations near the subsolar point is most affected; (5) The current GPS II-RM/IIF satellite can adjust its power ranges from 5 to 7dB, but this capability has limited compensation for receivers that are closer to the subsolar point, and only for receivers that are farther away from the subsolar point this technology has obvious advantage; (6) The impact on the positioning accuracy depends on whether it causes the satellite to lose signal and the number of lost locks. On August 28, 2022, the positioning was not affected, but on December 13, 2006, signal interruption and carrier phase

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cycle slip has been found, resulting in severe impacts such as decreased positioning accuracy and even the interruption of the positioning service; (7) It can be found from the carrier-to-noise ratio time sequence diagram of each monitoring station that the carrier-to-noise ratio of the GPS L2 frequency point has a significantly higher variation than the L1 frequency point, and the detailed reasons of this phenomenon are under our investigation; (8) Based on the data analysis of globally distributed tracking stations such as IGS, it can provide timely and accurate surveillance information for space environment, and mitigate the issues such as insufficient overseas monitoring capabilities and the lack of real-time information.

References 1. Huang, W.G., Ercha, A., Shen, H., et al.: Impact of intense L-band solar radio burst on GNSS performance and positioning accuracy. Chin. J. Radio Sci. 33(1), 1–7 (Ch) (2018) 2. Wuhan University IGS Data Center. www.igs.gnsswhu.cn 3. Tian, Y.G., Hao, J.M., et al.: Analysis on swarm satellite satellite-borne GPS data quality. J. Geodesy Geodyn. 1(1), 72–76 (Ch) (2018) 4. https://swarm-diss.eo.esa.int/ 5. Huang, W., Aa, E., Shen, H., Liu, S.: Satistical study of GNSS L-band solar radio bursts. GPS Solutions 22(114) (2018)

GNSS-IR Retrieval of Soil Moisture in Sugarcane Plantation Based on Cross-Correlation Satellite Selection Method Beiwen Xu, Qin Ding, Caiyun Jiang, Siming Li, Guangyan Chen, Qianru Wei, and Yueji Liang(B) College of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, China [email protected]

Abstract. Timely and accurate monitoring of soil moisture in farmland is of great significance to the evaluation of crop growth and drought. Global Navigation Satellite System interferometric reflectometry (GNSS-IR), as a new remote sensing technology, can invert soil moisture based on the signal-to-noise ratio recorded by the measuring receiver. At present, existing studies tend to invert soil moisture in bare soil or low vegetation cover environments, and satellite selection depends on empirical values or prior information. Accordingly, a multisatellite combination method based on cross-correlation satellite selection for soil moisture inversion is proposed. Firstly, the trend and modulation terms in the signal-to-noise ratio of each satellite are effectively extracted by wavelet analysis. The characteristic of the wave term is analyzed, and the arc segment with an obvious and stable periodic oscillation is selected. Then, based on the interference phase of each satellite obtained by nonlinear least squares fitting, a cross-correlation satellite selection method (CCSSM) is established. The available satellites are selected by setting a reasonable threshold. Finally, three multi-satellite combination models for soil moisture inversion are constructed, and the inversion effects of each model are compared and analyzed. Taking the sugarcane planting area as an example, the results indicate that satellites can be screened quickly and effectively by CCSSM, and the selected satellites have strong cross-correlation. For short-term Global Navigation Satellite System (GNSS) observation data, it is more advantageous to use multiple linear regression model to invert soil moisture than machine learning. Keywords: Soil moisture · GNSS-IR · Wavelet analysis · Cross-correlation satellite selection method · Multisatellite combination

1 Introduction Soil moisture (SM) is an important parameter in agricultural environmental research. Scientific and accurate monitoring of SM is of great significance for agricultural drought monitoring, rational irrigation and drainage of agricultural water, and crop growth assessment. Although traditional in-situ observation methods, such as current sensor, time © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 39–50, 2024. https://doi.org/10.1007/978-981-99-6928-9_4

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domain reflectometer, optical fiber sensor and direct sampling, can provide SM information, they require a lot of field operations and complicated post-processing. Moreover, their adaptability is limited, and full remote automatic monitoring is not easy to realize. In recent years, using remote sensing technology to invert regional SM has become a hot spot for domestic and international research, but the resolution of local SM by remote sensing is limited, and it is also difficult to achieve real-time. With the development of the Global Navigation Satellite System (GNSS), the use of GNSS satellite reflection signals to monitor SM has become a new tool for remote sensing monitoring. It has the advantages of all-day, all-weather wide coverage and high spatial and temporal resolution. Currently, GNSS satellite reflection signals have been applied to monitor environmental parameters such as snow depth, sea surface wind speed, SM, and vegetation moisture and their changes [1–4]. For SM monitoring, many scholars have achieved rich results in satellite signal reflection point projection, effective monitoring area calculation, SM depth detection, signal separation, and SM model construction [5–9]. However, the existing studies have tended more towards SM inversion in bare soil or low vegetation-cover environments. Considering that each satellite maintains a fixed orbit and appears at different times, the surface information it responds to tends to be different as well. Some scholars have shown that the combination of multiple satellites facilitates the acquisition of more accurate SM [10, 11]. However, for the satellite selection problem, it currently relies mainly on a priori information or human experience to determine. In the future, GNSS satellites will reach more than a hundred, which can provide a free and long-term stable L-band signal source, and the reasonable construction of the satellite selection method will be more conducive to carrying out real-time, high-precision SM monitoring. Therefore, in order to solve the satellite selection problem, a Cross-correlation Satellite Selection Method (CCSSM) is proposed, and the multisatellite combination method for SM inversion is constructed in this paper. Using the sugarcane plantation area SM as the research object, we firstly study the separation of the trend and modulation terms of each satellite using wavelet analysis and then establish a correlation selection method to select the available satellites. Finally, multiple linear regression, Back-Propagation (BP) neural network, and least squares support vector machine (LS-SVM) are used to establish SM inversion models to verify the feasibility and effectiveness of multi-satellite selection, respectively.

2 Principles and Methods Satellite Signal Reflection Principle. Signal-to-noise ratio (SNR) is a measure of receiver signal quality, affected by antenna gain parameters, multi-path effect and receiver noise. When the satellite altitude angle is low, the SNR is more significantly affected by the multi-path effect. The signal received by GNSS antenna is often a mixture of direct and reflected signals superimposed, as shown in Fig. 1.

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Assuming the primary reflection hypothesis, when ε is small, θ = β + ε ≈ β, SNRm can be expressed as: SNRm = Am cos(

4π H sin θ + ϕm ) λ

(1)

where, θ is the satellite incidence height, H is the vertical height of the antenna from the bottom; ε is the inclination angle of the slope, β is the angle between the satellite signal and the slope; SNRm is the reflected signal, Am is the reflected signal component amplitude; λ is the carrier wavelength, ϕm is the relative delayed phase of the reflected signal. According to existing research, wavelet analysis can effectively separate the modulation terms of each satellite and improve the data quality [10, 12]. Therefore, in this paper, the Coif5 wavelet is selected to carry out multiscale decomposition of SNR to obtain the reflection signal of each satellite. Further, the interference phase of each satellite is obtained by nonlinear least squares fitting of the reflected signal. Cross-Correlation Satellite Selection Method. For SNR data of the same satellite, its ascending part (S) and descending part (J) can be considered as two independent satellite orbits, this paper treats them separately. In addition, not all satellite orbits can be applied for SM monitoring [5]. For sugarcane planting area, the interference phase of different satellites makes different responses to SM due to a combination of factors such as satellite orbit, topographic relief around the area, and inconsistency in the top of the sugarcane canopy. Choosing the interference phase that is more relevant to the SM is directly related to the results of the SM inversion. If there is a good correlation between the interference phase of certain satellites and the SM, then there is also a strong correlation between the interference phase of these satellites is also strong. Based on this principle, A CCSSM is proposed in this paper. The specific process of the method is as follows: (1) Initially, Satellites with complete data (more than 95% of the overall complete data) are screened. (2) The number of interrelationships r between a certain i satellite and other j satellites is found. The equation is as follows: r(ϕi , ϕj ) = √

Cov(ϕi , ϕj )  , (i, j = 1, 2, 3, ..., 32, i = j) D(ϕi ) D(ϕj )

(2)

where i, j are the PRN number of the satellite; ϕi , ϕj A, B represent the interference phase sets of satellites i, j, respectively; Cov(ϕi , ϕj ) is the covariance of satellites i, j; D(ϕi ), D(ϕj ) represent the variance of satellites i, j, respecvely. (3) The threshold value r1 for the number of interrelationships is set, The number ni of satellites i with r less than or equal to r1 is counted, and its proportion P1 (i) is found.In turn, the threshold w1 of P1 (i) is set reasonably, and satellites with P1 (i) greater than or equal to w1 were eliminated, i.e., satellites with a poor number of

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interrelationships are eliminated. The specific equation is as follows: ⎧ r = k1 , (k1 = 0.1, 0.2, 0.3, ..., 1) ⎪ ⎪ 1 ⎨ ni P1 (i) = m−1 ⎪ ⎪ ⎩ w1 = k2 , (k2 = 0.1, 0.2, 0.3, ..., 1)

(3)

where m is the total number of satellites. (4) Based on the satellites initially screened in step (3), According to step (2), the number of interrelationships r between each satellite and the other satellites continues to be calculated. In turn, the threshold is set to r2 and the number of satellites t with r greater than or equal to r2 in each satellite is counted and their proportion P2 (t) is found. Further, the threshold w2 of P2 (t) is reasonably set, and satellites with P2 (t) greater than or equal to w2 are filtered, i.e., strongly correlated satellites. The specific equation is as follows: ⎧ r2 = k3 , k3 ≥ k1 (k2 = 0.1, 0.2, 0.3, ..., 1) ⎪ ⎪ ⎨ nt P2 (t) = (4) s − 1 ⎪ ⎪ ⎩ w2 = k4 , (k2 = 0.1, 0.2, 0.3, ..., 1) where s, t are the number of satellites and satellite numbers filtered by step (3), respectively. (5) Based on the number of satellites filtered in step (4) is set to h. The number of interrelationships between satellites is calculated and the mean value ri1 of the sum of absolute values of interrelationships for each satellite is found. Further, the threshold of the mean value is set to r3 , and if the mean value of each satellite is greater than or equal to, the optimal satellite is output. Otherwise, go back to step (4) and continue to optimize the filtering until the conditions are met. The formula for calculating the mean value is as follows: e 

  r ϕi1 , ϕj1 

ri1 =

h=1

h

(5)

where ri1 is the mean  value of satellite i1; e is the number of satellites screened in step (4); eh=1 r ϕi1 , ϕj1  is the sum of the absolute values of the number of interrelationships between satellite i1 and the other h satellites. SM Inversion. Based on the results of CCSSM, in this paper, the SM multi- satellite combination model was developed by multiple linear regression, BP neural network and LS-SVM, respectively. The process is shown in Fig. 2. 1. Satellite reflection signal separation. The RTKLIB software was used to solve the GNSS observation data to obtain: SNR (L2 carrier) and altitude angle files, and the trend and modulation terms of each satellite were separated by Coif5 wavelets;

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2. Modulation terms resampling. The environment of the sugarcane plantation area and the reflection trajectory of each satellite were combined, and the satellite altitude angle was selected The modulation terms that varies with the ephemeris was resampled and was transformed into a relationship with the sine of the satellite incidence altitude angle sin θ ; 3. Interference phase estimation. a nonlinear least squares fitting algorithm was used to perform a sinusoidal fit to the resampled modulation terms, and the interference phase of each satellite was obtained; 4. Available satellite selection. The satellites were selected to satisfy that there should be a continuous interference phase throughout the observation time. According to the CCSSM principle, different correlation number thresholds were set, and the available satellites were selected; 5. SM inversion. Based on the selected interference phase of each satellite, the model input and output sets are set reasonably. Three SM inversion models were developed separately. The results of each model are evaluated and the best model is selected to invert the SM.

Fig. 1 Multipath error geometry model

Fig. 2 Inversion flow of SM

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3 Experiment Analysis Considering that the sugarcane in Chongzuo, Guangxi, is an important sugarcane production base in China, a certain sugarcane plantation in Chongzuo, Guangxi, was selected as an experiment in this paper. GNSS receivers were used for observation. The longitude and latitude of the site are: 107°25 35.15 E, 22°13 2.107 N. The surrounding environment of the site is shown in Figs. 3 and 4. Combined with the fieldwork, it can be seen that the sugarcane planting site is located on a basin between hills, and the surrounding environment is more complex, with large undulations in the direction of the road. Therefore, the satellite altitude cutoff angle of the receiver was set to 10°, and the sampling rate was 5 Hz in the experiment. The observation time is from July 20 to August 4, 2021, with 11 h of observation per day for a total of 15 days. Among them, there was no observation data on July 25. For the effective monitoring area of SM, the Fresnel principle was used for the calculation [6]. The Fresnel reflection region for satellite altitude angles in the range of 10° to 30° is given in Fig. 4. At the same time, multiple wireless probe devices were used to collect the SM around the site, with a sampling interval of 5 s and a detection depth of 6.6cm. The accuracy of the device for SM measurement is ± 3% in the range of 0 ~ 53% and ± 5% in the range of 53 ~ 100%. In the experiment, the mean value of SM corresponding to the time of GNSS observation was taken as the reference value, and the rainfall and SM Mean Value are shown in Fig. 5.

Fig. 3 Site Environment

Fig. 4 Sugarcane plantation and effective monitoring area

As can be seen in Figs. 3 and 4, the site is in a mountainous environment, and the experimental area was dominated by mid-growth sugarcane crops. When the satellite

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Fig. 5 Soil moisture and precipitation

altitude angle is 10°, the reflection trajectory of some satellites are basically out of the measurement area. During the observation period, through several sampling measurements of sugarcane growth height, it was found that: the overall growth of sugarcane in the experimental area was not uniform, and the range of sugarcane height variation was basically between 1.60 and 2.75m. Further combined with Fig. 5, it can be seen that during this observation time period, several rainfall events occurred with a large variation in SM, which is favorable to carry out SM monitoring. According to existing studies, it is favorable to carry out SM inversion when the satellite altitude cutoff angle is 5° to 30° [5]. Therefore, the initial satellite altitude cutoff angle range in this paper was set to 10° to 30°. After several trials, the number of decomposition layers for wavelet analysis was determined to be six layers to eliminate the SNR trend terms. For this site, PRN 15 and PRN 18 were randomly selected, and their reflection signal variation curves are shown in Fig. 6. The reflected signal variation of these two satellites does not show consistency, and the multipath cycle oscillation amplitude is large. Obviously, the mountainous environment is more complex, and the direct determination of a uniform range of satellite altitude cutoff angles is not conducive to the accurate estimation of the interference phase of each satellite. Therefore, in this paper, based on the fluctuation amplitude of each satellite reflection signal after resampling, the arc segment with more obvious and stable characteristics of periodic oscillation was selected to be fitted by combining the topographic environment around the station and the satellite reflection trajectory. For example, the red curves in Fig. 6 are the reflected signal arcs selected by the two satellites. The range of altitude cutoff angles selected for each satellite is shown in Table 1.

Fig. 6 SNR change curve after removing the trend term

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B. Xu et al. Table 1. Selected satellite altitude angle range for each satellite

Number

Height angle range

Number

Height angle range

PRN 02 (J)

13° ~ 30°

PRN 17 (J)

13° ~ 27°

PRN 03 (J)

21° ~ 24°

PRN 18 (S)

18° ~ 28°

PRN 05 (S)

25° ~ 30°

PRN 19 (J)

14° ~ 19°

PRN 06 (J)

11° ~ 17°

PRN 20 (J)

21° ~ 27°

PRN 10 (S)

21° ~ 26°

PRN 22 (J)

12° ~ 17°

PRN 12 (J)

13° ~ 20°

PRN 25 (S)

11° ~ 16°

PRN 13 (J)

21° ~ 26°

PRN 29 (S)

12° ~ 22°

PRN 14 (J)

11° ~ 23°

PRN 30 (J)

11° ~ 19°

PRN 15 (J)

21° ~ 30°

–

–

Based on the cutoff angle range selected for each satellite, the corresponding arc segments were fitted with nonlinear least squares fitting to obtain the interference phase of each satellite. In the experiment, 17 satellites with continuous phases were selected. According to the CCSSM, r1 was set to 0.30, and the weight of each satellite was obtained as shown in Table 2. Eight satellites have P1 is greater than 0.60, indicating that these satellites have poor interrelationships or essentially no correlation. Therefore, in this paper, w1 was set to 0.60, and 10 satellites were screened for the first time, as shown in Table 3. It can be seen that r3 was set to 0.30, and seven satellites were found to have the same weight, all greater than 0.70. Therefore, we set w2 to 0.70 and screened seven satellites: PRN 03, 05, 10, 12, 13, 20, and 25. Meanwhile, the sum of the absolute values of the number of interrelationships among the satellites was taken as the mean value to obtain: 0.47, 0.69, 0.48, 0.54, 0.54, 0.52, and 0.56. The mean values of the sum of the absolute values of the interrelationship numbers of these seven satellites are all good, indicating a strong correlation between the satellites. To further verify the accuracy of the selected satellites, the correlation between the interference phase and SM of 17 satellites was counted in Fig. 7. It is not difficult to find that the thresholds set by the method in this paper are reasonable, and the correlation between the selected satellites and soil moisture is good. Therefore, in this paper, 0.45 was set and the above 7 satellites were selected to build the multi-satellite combination inversion model. To further verify the effectiveness of the selected satellite inversion SM, three experimental schemes were set up for comparative analysis in this paper: scheme 1-multiple linear regression; scheme 2-BP neural network; and scheme 3-LS-SVM. In order to reduce the modeling errors of schemes 2 and 3, the interference phases needed to be preprocessed, and all the interference phases were normalized to the interval [−1, 1], which was restored to the original interval after model testing. For model training and testing, the first 11 days were used as the training set and the last 4 days as the test sample. The inversion results and inversion errors of each scenario are shown in Figs. 8 and 9.

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Table 2. The proportion of each satellite at the threshold r1 Number

P1

Number

P1

PRN 02

0.69

PRN 17

0.69

PRN 03

0.38

PRN 18

0.56

PRN 05

0.56

PRN 19

0.75

PRN 06

0.63

PRN 20

0.50

PRN 10

0.56

PRN 22

0.75

PRN 12

0.56

PRN 25

0.50

PRN 13

0.50

PRN 29

0.38

PRN 14

0.63

PRN 30

0.88

PRN 15

0.75

–

–

Table 3. The proportion of each satellite at the threshold r2 Number

P2

Number

P2

PRN 03

0.75

PRN 18

0.38

PRN 05

0.75

PRN 20

0.88

PRN 10

0.75

PRN 25

0.88

PRN 12

0.75

PRN 29

0.50

PRN 13

0.88

–

–

Fig. 7 The correlation coefficient between each satellite interference phase and SM

As seen in Figs. 8 and 9, for the modeling stage, the fitting process of Scheme 1 is more stable, and the inversion error is smoother compared to Schemes 2 and 3. All three schemes fluctuated to different degrees during the testing phase, while the inversion effect of scheme 2 is poorer. This is mainly due to the short observation period of this experiment, while neural network modeling training often requires longer observation data. In order to further evaluate the performance of each scheme comprehensively, the correlation coefficient (R), root mean square error (RMSE), and mean absolute error

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Fig. 8 Inversion results of SM

Fig. 9 Inversion errors of SM

(MAE) between the test results and the SM reference value were used in this paper (Table 4). It can be seen that, for the modeling phase, both schemes 1 and 2 have correlation coefficients greater than 0.89 with SM. For RMSE and MAE, all three schemes are less than 0.040, and scheme 1 is the best. For the test phase, the R of scheme 1 reaches 0.92, both better than the other two schemes. As for RMSE and MAE, scenarios 1 and 3 are basically around 0.060, and scenario 2 is basically less than 0.030. Table 4. Accuracy statistics of each scheme Scheme

Modeling

Testing

R

RMSE

MAE

R

RMSE

MAE

1

0.95

0.018

0.016

0.92

0.062

0.060

2

0.89

0.030

0.026

0.81

0.028

0.024

3

0.83

0.033

0.018

0.74

0.061

0.057

4 Conclusion In this paper, based on the sugarcane planting environment, a new satellite selection method has been established. At the same time, the multi-satellite combination inversion model has also been constructed for SM inversion. Theoretical analysis and experiments show that: (1) In a mountain environment, the fluctuation amplitude of reflected signals from different satellites is quite different, and there is no obvious pattern. It is difficult

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to extract the effective arc segment by unifying the satellite altitude angle. (2) Multiple satellites can be effectively selected by the cross-correlation satellite selection method. When the threshold of the cross-correlation coefficient is set to 0.30 and the weight threshold is set to more than 0.70, the correlation between the selected satellite and SM is high. (3) For SM inversion of sugarcane plantations, both the multiple linear regression model and the least squares support vector machine have achieved good results. The multiple regression model is more suitable for short-term SM inversion. No matter in which stage of the modeling or testing process, the correlation coefficient between its inversion results and SM is greater than 0.900. This further verifies the rationality of satellite selection. Therefore, this method has high flexibility in satellite selection, which is helpful to the application and popularization of GNSS-IR technology. For the setting of satellite altitude angle in a complex environment, this paper mainly focuses on artificial determination. In the future, an adaptive and effective arc segment cutting method based on the fluctuation characteristics of satellite-reflected signals will be discussed. Funding. This work was supported by Guangxi Natural Science Foundation (Grant No. 2021GXNSFBA220046) and the National Natural Science Foundation of China (Grant No. 41901409).

References 1. Li, Y., Chang, X., Yu, K., et al.: Estimation of snow depth using pseudorange and carrier phase observations of GNSS single-frequency signal. GPS Solutions 23(4), 1–13 (2019) 2. Zhang, S., Liu, K., Liu, Q., et al.: Tide variation monitoring based improved GNSS-MR by empirical mode decomposition. Adv. Space Res. 63(10), 3333–3345 (2019) 3. Wang, X., He, X., Chen, S., et al.: Preliminary study on theory and ground-based GNSS-IR wind speed. Acta Geodaetica et Cartographica Sinica 50(10), 1298–1307 (2021) 4. Wan, W., Zhang, J., Dai, L., et al.: A new snow depth data set over northern China derived using GNSS interferometric reflectometry from a continuously operating network (GSnow-CHINA v1. 0, 2013–2022). Earth Syst. Sci. Data 14(8), 3549–3571 (2022) 5. Chew, C., Small, E., Larson, K.: An algorithm for soil moisture estimation using GPSinterferometric reflectometry for bare and vegetated soil. GPS solutions 20(3), 525–537 (2016) 6. Ao, M., Zhu, J., Hu, Y., et al.: Retrieval soil moisture with GPS SNR interferogram in time window. Geomatics Inf. Sci. Wuhan Univ. 43(09), 1328–1332 (2018) 7. Wu, X., Jin, S., Chang, L.: Monitoring bare soil freeze–thaw process using gps-interferometric reflectometry: simulation and validation. Remote Sens. 10(1), 14 (2017) 8. Zhang, S., Wang, T., Wang, L., et al.: Evaluation of GNSS-IR for retrieving soil moisture and vegetation growth characteristics in wheat farmland. J. Surv. Eng. 147(3), 04021009 (2021) 9. Li, Y., Yu, K., Jin, T., et al.: Soil moisture estimation using amplitude attenuation factor of low-cost GNSS receiver based SNR observations. In: 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, pp. 7654–7657 IEEE (2021)

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10. Liang, Y., Lai, J., Ren, C., et al.: GNSS-IR multisatellite combination for soil moisture retrieval based on wavelet analysis considering detection and repair of abnormal phases. Measurement 203, 111881 (2022) 11. Zhou, X., Zhang, S., Zhang, Q., et al.: Research of deformation and soil moisture in loess landslide simultaneous retrieved with ground-based GNSS. Remote Sensing 14(22), 5687 (2022) 12. 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)

Extraction of Soil Moisture Based GNSS-R Considering Vegetation Factors Qinyu Guo1,2 , Shuangcheng Zhang1,2(B) , Qi Liu1 , Zhongmin Ma1 , Ning Liu1 , Shengwei Hu1 , Lin Bao1 , Xin Zhou1 , Hebin Zhao1 , Lifu Wang3 , and Tianhe Wan3 1 College of Geology Engineering, Chang’an University, Xi’an 710054, China

[email protected]

2 State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China 3 Altay National Reference Meteorological Station, China Meteorological Administration,

Altay 836500, China

Abstract. One of the keys to retrieve soil moisture (SM) using the Spaceborne Global Navigation Satellite System-Reflectometry (GNSS-R) technique is to correct for the influence of vegetation. In this paper, the surface reflectivity is calculated using the Cyclone Global Navigation Satellite System (CYGNSS) data, and combine the Vegetation Water Content (VWC) provided by Soil Moisture Active Passive (SMAP) data to establish linear regression model to retrieve SM products with a temporal resolution of 3 days and a spatial resolution of 36 km on a pantropical scale, and each of the models is parameterized pixel-by-pixel to allow for tuning in accordance with regional variations. According to the experimental findings, CYGNSS may offer useful SM estimations across regions with moderate vegetation, and the correlation coefficient (R) with SMAP reference data is up to 0.7. However, in the arid and densely vegetated regions, the retrieval performance is degraded, and the R is 0.4 and 0.3 in the forest and bare soil areas, respectively. The overall root mean square error (RMSE) is 0.042 cm3 /cm3 . In addition, a timeseries comparison of in-situ data from the International Soil Moisture Network (ISMN) and the CYGNSS SM revealed a good correlation. The study proves the necessity of considering vegetation effect in SM retrieval, which is of positive significance for the promotion of the operational application of Spaceborne GNSS-R SM retrieval. Keywords: Spaceborne GNSS-R · CYGNSS · Soil moisture · Vegetation water content · Linear regression model

1 Introduction Soil moisture (SM) is an important parameter in the energy exchange process between land and atmosphere, plays a very important role in the climate system [1]. Traditional SM monitoring techniques, such as drying and time-domain reflectometry, have great accuracy but are difficult to use for large-scale monitoring because of the high time consumption and equipment cost [2]. The growth of satellite-based remote sensing technology provides a new opportunity for continuous acquisition of large-scale SM data [3, © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 51–59, 2024. https://doi.org/10.1007/978-981-99-6928-9_5

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4]. In recent years, Spaceborne GNSS-R technology has gradually become a research hotspot to obtain large-scale and continuous SM data. By processing GNSS(Global Navigation Satellite System) satellite signals reflected from the earth surface, this technology can be used to retrieve geophysical parameters of ocean and land. GNSS-R SM detection has many advantages, such as low cost, wide coverage and a large number of signal sources, which can realize all-day and all-weather monitoring [5–8]. At present, a large number of literatures have studied the feasibility and effectiveness of SM retrieval using satellite-borne GNSS-R. Chew et al. used TDS-1 (TechDemoSat1) data to prove that space-borne GNSS-R can be used to retrieve SM [9]. However, due to the long revist time of the TDS-1 satellite and the limited space coverage, the amount of data collected cannot achieve daily estimates of SM. By contrast,the CYGNSS (Cyclone Global Navigation Satellite System) satellite constellation launched by NASA in 2016 has short revisit time and large data volume. Previous studies have shown that the correlation between time fluctuation of CYGNSS signal and SM is better than that of TDS-1 data [10], which brings a new opportunity for obtaining SM with high spatial and temporal resolution. Chew et al. found a strong positive correlation between the change amount of CYGNSS reflectivity and SMAP SM, proving that CYGNSS can be used to develop global SM products with high temporal resolution (maybe every 6 h) [10]. Clarizia et al. proposed a triple linear regression algorithm of “Reflectivity— Vegetation—Roughness” to retrieve SM [11]. Yan Qingyun et al. improved Clarizia et al. ‘s algorithm and used CYGNSS DDM statistical moment to characterize the surface roughness information, reducing the dependence on external auxiliary data [12]. Guo Fei et al. considered the influence of surface temperature on space-borne GNSS-R SM retrieval, and used a linear regression model to retrieve the quasi-global SM based on CYGNSS data, proving the necessity of surface temperature in SM retrieval [13]. In addition, with the rapid development of machine learning, artificial neural network, random forest and support vector regression are also widely used in SM retrieval [14–16]. The retrieval of SM by machine learning method can flexibly select the input parameters and deal with the nonlinear relationship between the parameters. However, it is often faced with problems such as high dependence on auxiliary data, large amount of training data required by the model and poor generalization ability of the training model. In contrast, the method of SM retrieval based on empirical model is less dependent on auxiliary data, and can show a clearer relationship between CYGNSS observation data and SM. Moreover, it is more convenient to establish the retrieval model grid by grid for local parameterization. In addition, existing studies have shown that there is a significant correlation difference between different vegetation parameters and the attenuation effect of microwave signals. For example, the Vegetation Optical Depth (VOD) data of vegetation provided by SMAP L3 products has a poor correlation with the attenuation of vegetation at microwave frequencies [11]. Based on this, this paper attempted to use the data of Vegetation Water Content (VWC) in SMAP and CYGNSS observations to establish a linear regression model for SM retrieval. Finally, the retrieval results were compared with the reference data.

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2 Observation Data 2.1 CYGNSS GNSS-R Data CYGNSS is an Earth observation mission of NASA, which was launched on December 15, 2016. A total of eight small satellites are equipped with four-channel GNSS-R dualbase radar receivers that collect GPS (Global Position System) signals reflected from the ground and ocean [17]. These small satellites operate over the pan tropics with an orbital inclination of 35 degrees, covering about 38° N to 38° N, and the average revisit period is only 7 h [18]. The study uses CYGNSS Level 1 v3.1 scientific data products. In order to improve the retrieval accuracy, this paper carried out quality control on the CYGNSS data set. In addition to using the quality flag, the following data were also filtering: (1) the incidence angle greater than 65°; (2) SNR less than 0dB; (3) Receiver antenna gain less than 0dB; (4) Peak DDM values outside of delay bins 4 and 15 were filtered out. 2.2 SMAP Data This paper uses the SMAP L3 SM products, which has a spatial resolution of 36km. The daily data consists of two parts: descending (AM) and ascending (PM) [4]. In this paper, “SM” and “VWC” data are used as auxiliary parameters for model training and prediction. In order to fully cover the research area, the data of three consecutive days are averaged [12]. Also, CYGNSS data are gridded to the same EASE-Grid as SMAP data for later comparison and verification [11]. Figure 1 shows the 2020 mean data of SMAP SM and VWC and CYGNSS reflectivity.

Fig. 1. Annual means of: (a) SMAP SM and (b) SMAP VWC, and (c) CYGNSS reflectivity

2.3 ISMN Data In this paper, the International Soil Moisture Network (ISMN) dataset was used to independently verify the CYGNSS SM. Due to the limited penetration depth of L-band

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in soil, the observation value of 5cm SM was adopted, and only the data labeled “good” of hourly SM was retained, which was processed as three-day average and compared with CYGNSS retrieval results [19].

3 Methodology By receiving and processing L-band electromagnetic signals transmitted by GPS satellites, CYGNSS can retrieve the relevant parameters of the scattered surface. The GNSS signal power reflected by the surface consists of two parts: coherent and incoherent scattering component. Based on the assumption that CYGNSS land surveys are primarily specular point reflections, that is, the coherent scattering component is the dominant component in the reflected signal, then the power expression of the coherent component is as follows [20]: Prlcoh =

G r λ2 rl 4π (Rt + Rr )2 4π Prt G t

(1)

where, Prlcoh is the coherent component; Prt is the transmitting power of the signal; G t and G r are the gain of transmitting antenna and receiving antenna respectively; Rt and Rr are respectively the distance between the transmitter and the receiver and the specular point; λ is the wavelength. Then the surface reflectivity rl can be calculated by CYGNSS BRCS (bistatic radar cross section) σ [14]: rl =

σ (Rt + Rr )2 4π (Rt Rr )2

(2)

By correcting the signal frequency attenuation effect caused by surface roughness and vegetation cover, Fresnel reflection coefficient is calculated as follows:   (3) rl (θ ) = Rrl (θ )2 γ 2 exp −4k 2 s2 cos2 (θ ) where, θ is the incident angle; Rrl is the Fresnel reflection coefficient; Transmissivity γ indicates the attenuation caused by vegetation on signal transmission. The exponential term, where k is the signal wave number and s is the surface root mean square height, represents the impact of surface roughness. Then, the relationship between reflection coefficient and dielectric constant was established by Fresnel reflection equation. Finally, the dielectric model was used to retrieve the SM. Although Eq. (3) establishes an retrieval model of surface reflectivity considering the influence of roughness and vegetation, it is still difficult to use specific coefficient equations for SM retrieval on a global scale due to the absence of auxiliary data with high enough spatial and temporal resolution and precision. Therefore, the linear regression model was used in this paper to estimate SM by grid. In order to improve the spatial coverage of the retrieval results, the CYGNSS observations were grid based on a threeday period. This paper ignores the variation of roughness within the study time range,

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but considers the influence of vegetation through the variation of VWC. The retrieval model is as follows: CYGNSS SM = a · rl + b · VWC + c

(4)

where, a, b, and c are the to-be-determined coefficients.

4 Results and Analysis 4.1 Evaluation at Quasi-global Scale Figure 2 shows the calculation results of the R and RMSE of the CYGNSS SM and SMAP SM for each grid, where the values are 0.55 and 0.04 cm3 /cm3 , respectively. The temporal correlation between CYGNSS SM and SMAP SM varies by region, with generally higher correlations and lower RMSE in medium vegetation coverage and semiarid regions. For highly vegetated areas the R is significantly reduced, mostly around 0.4, and the root mean square error can even reach 0.07 cm3 /cm3 . This may be because dense vegetation will cause more attenuation of the microwave signal frequencies, making the urface reflectivity less sensitive to soil moisture. Moreover, the data quality of SMAP is also a factor leading to the poor correlation between CYGNSS SM and SMAP SM in these regions.

Fig. 2. (a) Temporal correlation and (b) RMSE between CYGNSS SM and SMAP SM

Figure 3 shows the data of land types in the pan-global area. To further demonstrate how vegetation coverage affects the accuracy of CYGNSS SM data, the R between CYGNSS SM and SMAP SM of different land types were aggregated to obtain the mean value, as shown in Fig. 4. For the regions such as savanna, grassland and farmland, the R is relatively high, generally above 0.65. However, due to the influence of vegetation and roughness, the coherent scattering component in the reflected signal decreases, while

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the incoherent scattering component increases. Therefore, for the regions with dense or low vegetation coverage, the R decreased significantly, generally below 0.5, further indicates that the retrieval performance of CYGNSS SM is improved when the vegetation coverage changes from low/high to medium.

Fig. 3. Land type data

Fig. 4. (a) Means of R based on different land types. Each lans type’s number of grids is indicated by a gray bar. (b) Means of R and RMSE based on different vegetation coverage.

Several grids were randomly selected for time series analysis. As shown in Fig. 5, CYGNSS SM can well reflect the dynamic variation trend of SMAP SM over time, but the measurement accuracy needs to be improved.During certain periods, CYGNSS SM was unable to capture detailed change information. In general, CYGNSS SM and SMAP SM have good consistency. In the selected grids, the mean R is 0.8, and the mean RMSE is 0.049 cm3 /cm3 .

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Fig. 5. SM time series between CYGNSS and SMAP in random grids

4.2 Validation at In-situ Sites Comparison is made between the CYGNSS retrieval results and the in-situ measurements carried out at ISMN sites. Figure 6 shows the time series analysis data of SM at six representative sites. In the stable SM period, the fitting degree between CYGNSS SM and ISMN SM was better. However, when SM changes greatly, CYGNSS SM will give higher or lower estimates. In contrast, the correlation between SMAP SM and ISMN SM is better, but in general, CYGNSS SM and ISMN SM have a good consistency. At all sites, the mean R between the two was 0.68, and the mean RMSE was 0.073 cm3 /cm3 .

Fig. 6. SM time series between CYGNSS, SMAP, and ISMN at six sites

5 Conclusion and Discussion In this paper, based on the surface reflectivity of CYGNSS and the VWC data provided by SMAP, the linear regression modele were established to retrieve the pan-global SM products in 2020. The correlation between the retrieval results and the SMAP reference

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data is closely related to the vegetation density in the region, and the retrieval performance is the best in the region with the medium vegetation coverage. In addition, a time series analysis was conducted between the retrieval results and SM from ISMN measured sites, which showed a good consistency between them in the selected sites. CYGNSS has an average revisit period of only 7.2 h. In this paper, in order to improve the spatial coverage of data, three consecutive days of CYGNSS observation values were grid, which resulted in the waste of high time resolution of CYGNSS data to a certain extent. However, high temporal resolution and high spatial resolution are often incompatible. Therefore, it is necessary to balance the temporal resolution and spatial resolution of data according to the demand in practical application. There is a correlation difference between different vegetation parameters and the attenuation effect of microwave signal frequency. Previous studies mostly focused on the correction of the retrieval effect by the VOD. This paper attempts to establish a model using theVWC parameter for the first time, although good results have been achieved in the area of moderate vegetation coverage, the retrieval accuracy in other areas needs to be improved. In the follow-up study, more vegetation parameters such as leaf area index (LAI) and aboveground biomass can be considered to analyze the influence of vegetation on the retrieval process. Acknowledgments. The author would like to thank NASA for providing the CYGNSS and SMAP data. Thank you to the Global Energy and Water Exchanges Project (GEWEX), the Committee on Earth Observation Satellites (CEOS) et al. for providing the ISMN data. All anonymous reviewers and editors are thanked for their constructive review of this manuscript.

Funding. This research was funded by the National Natural Science Foundation of China Projects (Grant No.42074041); The National Key Research and Development Program of China (Grant No.2019YFC1509802); State Key Laboratory of Geo-Information Engineering (Grant No. SKLGIE2022-ZZ2-07). This research was also supported in part by the Fundamental Research Funds for the Central Universities, Chang’an University, (Grant No. 300102260301, 300102262401), in part by the Shaanxi Province Science and Technology Innovation Team (Grant No. 2021 TD-51), and in part by the Shaanxi Province Geoscience Big Data and Geohazard Prevention Innovation Team (2022).

References 1. Dobriyal, P., Qureshi, A., Badola, R., et al.: A review of the methods available for estimating soil moisture and its implications for water resource management. J. Hydrol. 458, 110–117 (2012) 2. Western, A.W., Blöschl, G., Grayson, R.B.: Geostatistical characterisation of soil moisture patterns in the Tarrawarra catchment. J. Hydrol. 205(1–2), 20–37 (1998) 3. Kerr, Y.H., Waldteufel, P., Wigneron, J.-P., et al.: Soil moisture retrieval from space: the soil moisture and ocean salinity (SMOS) mission. IEEE Trans. Geosci. Remote Sens. 39(8), 1729–1735 (2001) 4. Entekhabi, D., Njoku, E.G., O’Neill, P.E., et al.: The soil moisture active passive (SMAP) mission. Proc. IEEE 98(5), 704–716 (2010) 5. Tao, T., Li, J., Zhu, Y., et al.: Spaceborne GNSS-R for retrieving soil moisture based on the correction of stage model. Acta Geodaetica et Cartographica Sinica 51(9), 1942–1950 (2022)

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6. Carreno-Luengo, H., Ruf, C.S.: Retrieving freeze/thaw surface state from CYGNSS measurements. IEEE Trans. Geosci. Remote Sens. 60, 1–13 (2022) 7. Liu, Q., Zhang, S., Nan, Y., et al.: Flood detection of south asia using spaceborne GNSS-R coherent signals. Geomatics Inf. Sci. Wuhan Univ. 46(11), 1641–1648 (2021) 8. Bu, J., Yu, K., Han, S.: Construction of spaceborne GNSS-R ocean waves significant wave height retrieval model. Acta Geodaetica et Cartographica Sinica 51(9), 1920–1930 (2022) 9. Chew, C., Rashmi, S., Cinzia, Z.: Demonstrating soil moisture remote sensing with observations from the UK TechDemoSat-1 satellite mission. Geophys. Res. Lett. 43(7), 3317–3324 (2016) 10. Chew, C.C., Small, E.E.: Soil moisture sensing using spaceborne GNSS reflections: comparison of CYGNSS reflectivity to SMAP soil moisture. Geophys. Res. Lett. 45(9), 4049–4057 (2018) 11. Clarizia, M.P., Pierdicca, N., Costantini, F., et al.: Analysis of CYGNSS data for soil moisture retrieval. IEEE J. Sel. Topics Appl. Earth Obs. Remote Sens. 12(7), 2227–2235 (2019) 12. Yan, Q., Huang, W., Jin, S., et al.: Pan-tropical soil moisture mapping based on a three-layer model from CYGNSS GNSS-R data. Remote Sens. Environ. 247, 111944 (2020) 13. Zhu, Y., Guo, F., Zhang, X.: Effect of surface temperature on soil moisture retrieval using CYGNSS. Int. J. Appl. Earth Obs. Geoinf. 112, 102929 (2022) 14. Eroglu, O., Kurum, M., Boyd, D., et al.: High spatio-temporal resolution CYGNSS soil moisture estimates using artificial neural networks. Remote Sens. 11(19), 2272 (2019) 15. Hu, Y., Wang, J., Li, Z., et al.: Land surface soil moisture along sichuan-tibet traffic corridor retrieved by spaceborne global navigation satellite system reflectometry. Earth Sci. 47(6), 2058–2068 (2022) 16. Lei, F., Senyurek, V., Kurum, M., et al.: Quasi-global machine learning-based soil moisture estimates at high spatio-temporal scales using CYGNSS and SMAP observations. Remote Sens. Environ. 276, 113041 (2022) 17. Ruf, C.S., Chew, C., Lang, T., et al.: A new paradigm in earth environmental monitoring with the CYGNSS small satellite constellation. Sci. Rep. 8(1), 8782 (2018) 18. Ruf, C.S., Atlas, R., Chang, P.S., et al.: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Am. Meteor. Soc. 97(3), 385–395 (2016) 19. Vreugdenhil, M., Gruber, A., Hegyiová, A., et al.: Global automated quality control of in situ soil moisture data from the international soil moisture network. Vadose Zone J. 12(3) (2013) 20. De Roo, R.D., Ulaby, F.T.: Bistatic specular scattering from rough dielectric surfaces. IEEE Trans. Antennas Propag. 42(2), 220–231 (1994)

A Non-contact Tilt Compensation Method Based on Monocular Camera/GNSS/INS Cong Wu(B) , Yuanjun Chen, Chunhua Li, and Guofu Pan Guangzhou Hi-Target Navigation Tech Co.Ltd., Guangzhou 511400, China [email protected]

Abstract. RTK with tilt compensation can achieve centimeter-level highprecision measurement. It belongs to contact measurement technology. However, in the case of signal limitation scenarios, the precision of contact measurement will be greatly reduced, or even unable to measure. This paper aims to analyze the potential and performance of a monocular camera combined with tilt compensation technology for non-contact measurement. According to the 3D model based on image reconstruction and the prior position and attitude of the GNSS receiver, the overall bundle adjustment is carried out to improve the attitude accuracy of the camera, thereby improving the accuracy of non-contact measurement. The error model of non-contact measurement is also derived in this paper, which has a very important guiding significance in practical engineering applications. The non-contact measurement method proposed in this paper does not need control points and can measure the absolute coordinates of target points in near real-time. The experimental results show that the method proposed in this paper can achieve centimeter-level high-precision measurement within the measurement range of 10m, and the mean values of horizontal, vertical, and 3D errors are 0.027 m, 0.018 m, and 0.032 m respectively. Keywords: Tilt compensation · Non-contact measurement · Bundle adjustment

1 Introduction In recent years, in the field of surveying and mapping, RTK with tilt compensation technology has become more and more mature. RTK with tilt compensation technology maintains the attitude estimation of the GNSS receiver in real-time through the combination of GNSS, IMU, magnetic compass, and other sensors, and can measure the position of the target point when the measuring pole is tilted [1]. However, RTK with tilt compensation technology has the following problems: 1. the bending deformation of the measuring pole will affect the accuracy of the measurement; 2. requires physical contact, greatly reducing usability in inaccessible areas; 3. In the scene where the GNSS signal is blocked, the accuracy of the measurement will decrease, or even not be measurable; © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 60–74, 2024. https://doi.org/10.1007/978-981-99-6928-9_6

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With the rapid development of robotics and autonomous driving, the direction of multi-sensor fusion such as GNSS, IMU, vision, and laser has received more and more attention, and non-contact measurement technology is also constantly developing. For example, the V10 imaging rover launched by Trimble is equipped with 12 cameras, inclinometers, and a magnetic compass. After collecting data at multiple stations, import the data from the rover into the post-processing software for modeling and calculation. Not only can it cope with the scene where RTK with tilt compensation cannot work, but it also greatly improves the working efficiency. However, to ensure measurement with centimeter-level accuracy, the V10 imaging rover still needs to appropriately add artificial connection points and control points in the post-processing process, which cannot be fully automated [2]. According to the error analysis of non-contact measurement in this paper, the attitude accuracy of the GNSS receiver estimated by the GNSS/INS combined algorithm cannot meet the accuracy of the non-contact measurement task requirements, see Sect. 4 for details.

Fig. 1. Schematic illustration of non-contact measurement

The non-contact measurement method proposed in this paper is based on the GNSS/INS combination algorithm to provide the prior pose of the GNSS receiver to improve the accuracy of the 3D model based on image reconstruction. Then, according to the 3D model, combined with the prior pose of the GNSS receiver, the overall bundle adjustment is performed to improve the attitude accuracy of the camera and the relative attitude accuracy between images. As shown in Fig. 1, assuming that the position and attitude of the camera at the time of shooting are known, and the target point to be measured can be observed on multiple images, then the three-dimensional coordinates of the target point can be solved without physical contact. Experimental results show that within the measurement range of 10m, the measurement accuracy of the centimeter level can be achieved. Compared with other non-contact measurement methods, it only needs to be equipped with a monocular camera, no control points and manual participation are required during the measurement operation, and can be measured in close to real-time.

2 Coordinate System, Symbol Definition In this paper, the navigation coordinate is denoted as n, the camera coordinate is denoted as c, the reference coordinate selected based on any camera coordinate is denoted as w, and the IMU coordinate of GNSS receiver is denoted as b. The three-dimensional n , the upper right n indicating that the vector is generally recorded in the form of Pnf three-dimensional vector is expressed in the n coordinate, and the lower right n is the

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starting point of the vector and f is the endpoint of the vector. The rotation matrix is generally recorded in the form of Rnb , which represents the transformation relationship from the n coordinate to the b coordinate.

3 Basic Model of Non-contact Measurement n n c Pnf = Pnc + Rnc Pcf

(1)

n is the position of Equation (1) shows the basic model of non-contact measurement, Pnf n , Rn ) is the pose of camera, P c is the vector from the camera to the target point, (Pnc c cf the target point. The hardware structure relationship between the camera and the GNSS receiver is shown in Fig. 2. n n b = Pnb + Rnb Pbc Pnc

(2)

Rnc = Rnb Rbc

(3)

Fig. 2. The diagram of the camera and IMU hardware structure n , Rn ) can be calculated according to (P n , Rn ) which is the pose of IMU, P b which (Pnc c nb b bc is the lever arm between the camera and the IMU and Rbc which is the transformation matrix from the b coordinate to the c coordinate. c c Assuming that in a certain coordinate, the pose of images is known, Rcji , Pcjjci which is the pose transformation relationship between two images can be obtained. As shown in Fig. 3, xi ↔ xj is the corresponding projection point of the target point in the image pair, and the optical centers of the two frames of cameras pass through the rays of their respective projection points to converge to the X in three-dimensional space.   c c c = τ xi xj Rcji Pcjjci with i = j Pcf (4) c

c

c can τ (·) is the forward intersection operator [3]. Based on xi ↔ xj , Rcji and Pcjjci , Pcf be calculated by different forward intersection operators.

4 Error Analysis of Non-contact Measurement In this section, we focus on the problem of the camera attitude accuracy required when non-contact measurement needs to meet the accuracy of 5 cm horizontally and vertically. b is a small number of centimeters, it can be considered that the position error Since Pbc of the camera is equivalent to the GNSS receiver. Based on (1), according to the law of error propagation, we can get:      n n c = δ Pnc (5) + δ Rnc Pcf δ Pnf

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X

xi Oi

xj Oj

Fig. 3. The diagram of the forward intersection

The error of the target point is composed of two items, the first is the error of the c . camera, and the second is the error of the joint action of the camera attitude and the Pcf To analyze the relationship between the error of the camera attitude and the error of the c is no error to simplify the error model of non-contact target point, it is assumed that Pcf measurement. Based on the left multiplication perturbation model, there are:     c c c c ≈ I + δ × Rnc Pcf δ Rnc Pcf − Rnc Pcf =δ × Rnc Pcf (6)  T The error of camera attitude is denoted as δ= δ(θ ) δ(γ ) δ(φ) , corresponding to the errors of pitch, roll, and yaw, respectively. The symbol × is the conversion symbol from vector to anti-symmetric matrix [4]. Following the definition of Euler angles in reference [4], there is a transformation from Euler angles to a cosine matrix, where s represents sine and c represents cosine: ⎡

⎤ cφ cγ − sφ sθ sγ −sφ cθ cφ sγ + sφ sθ cγ Rnc = ⎣ sφ cγ + cφ sθ sγ cφ cθ sφ sγ − cφ sθ cγ ⎦ cθ sγ sθ cθ cγ

(7)

Since the camera will face the target point to be measured, the error model is simpli T c = fied again, assuming Pcf 0 0 d , d is the distance from the target point to the optical center of the camera. Therefore, combining with Eq. (7), we have: ⎤ ⎡  d cφ sγ + sφ sθ cγ  n c Pcf = Rnc Pcf = ⎣ d sφ sγ − cφ sθ cγ ⎦ (8) dcθ cγ Substituting (8) into (6), we get: 

c δ Rnc Pcf



  ⎤ −d δ(φ) sφ sγ − cφ sθ cγ + d δ(γ )cθ cγ ⎦. =⎣ dδ(φ) cφ sγ + sφsθ cγ − dδ(θ )cθ cγ  −d δ(γ ) cφ sγ + sφ sθ cγ + d δ(θ ) sφ sγ − cφ sθ cγ ⎡

(9)

As shown in Fig. 4, O − xc yc zc is the coordinate axis of the c system, O − ENU is the coordinate axis of the n system, and the angle between the zc axis and the U axis is τ which is the inclination angle of the camera sensor. After the c coordinate is leveled, the angle between the yc axis and the N axis is ψ which is the heading deviation angle of the two coordinate systems.

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d O

U

U

zc

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N

xc

zc

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yc

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yc

Fig. 4. Diagram of camera coordinate and navigation coordinate n from τ and ψ. According to paper [5], we can calculate Pcf

⎡

⎤ dsτ sψ = ⎣ dsτ cψ ⎦ dcτ

n Pcf

(10)

Comparing the third item of (8) and (10), there are: cτ = cθ cγ

(11)

During normal operation, the inclination angle of the camera is usually very close to 90°. Therefore, it can be considered that: cτ = cθ cγ ≈ 0 Substituting (12) into the first two items of (9), we get: ⎧     ⎨ δE Rn P c ≈ −d δ(φ) sφ sγ − cφ sθ cγ c cf     ⎩ δN Rn P c ≈ d δ(φ) cφ sγ + sφ sθ cγ c cf

(12)

(13)

    c c δE Rnc Pcf and δN Rnc Pcf are the errors in the east and north directions of the horizontal component due to the yaw error, respectively.    The error of the horizontal c c : n component can be obtained based on δE Rc Pcf and δN Rnc Pcf   c δH Rnc Pcf =



 2  2 c c δE Rnc Pcf + δN Rnc Pcf

Substituting (11) and (13) into (14), we get:    2  c δH Rnc Pcf = d δ(φ) 1 − cθ cγ = dsτ δ(φ)

(14)

(15)

Based on the third item of (10), according to the law of error propagation, the error in the vertical component due to the error of the inclination angle can be deduced:   c δV Rnc Pcf = −dsτ δ(τ ) (16) Referring to the accuracy indicators of GNSS receivers, the general horizontal accuracy is 8 mm + 1 ppm, and the vertical accuracy is 15 mm + 1 ppm. Combined with

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n is much smaller than the error subsequent analysis, it can be found that the error of Pnc c n n of Rc Pcf . Therefore, ignoring the error of Pnc , simplifying the error model again, we have: ⎧   ⎨ δH P n = dsτ δ(φ)  nf (17) ⎩ δV P n = −dsτ δ(τ ) nf

So far, we have deduced the relationship between the error of camera attitude and the error of horizontal-vertical. Equation (17) shows that the error of horizontal is mainly caused by the error of yaw, and the error of vertical is mainly caused by the error of inclination angle. The error of horizontal and vertical is positively correlated with the measurement distance and the inclination angle. Figure 5 shows the relationship between the upper limit threshold of the camera attitude error and the measurement distance when meets the accuracy of 5 cm horizontally and vertically, assuming that the inclination angle is 90°. When the measurement distance is 10m, the accuracy of pitch, roll and yaw of the camera needs to be within 0.28°.

Fig. 5. The relationship between the upper limit threshold of camera attitude error and measurement distance(accuracy within 5 cm)

In a static state, even with a low-cost MEMS IMU, the accuracy of the pitch and roll can be within 0.06° [5]. It is mentioned in the paper [1] that under sufficient motion excitation, the initialization of the attitude can generally be completed within 10s, and the initial accuracy is about 2°. As mentioned in the experimental part, the attitude accuracy after the convergence of the GNSS/INS combination is generally within 1.5°. It can be known from (3) that the error of the camera attitude is composed of two parts: the error of Rnb and the error of Rbc . After calibration [6], the error of Rbc is significantly smaller than the error of Rnb . Therefore, it can be considered that the error of the camera attitude is comparable to the error of Rnb . As shown in Fig. 5, when the attitude accuracy of the camera is 1.5°, it can only be measured at a distance of less than 2m, which greatly limits the practicability of non-contact measurement technology. If the noncontact measurement is to be able to work at longer distances, the attitude accuracy of the camera must be improved. Therefore, the focus of non-contact measurement technology is the high-precision pose estimation of the camera.

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IMU

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Fig. 6. The flow chart of camera attitude optimization

5 Camera Attitude Optimization Image-based 3D reconstruction is to reconstruct the 3D model of the environment and estimate the pose of the image from a series of images taken from different angles according to the projection relationship [7]. But the reconstructed model is defined under the w coordinate and lacks real scale information. Therefore, it is impossible to directly measure the absolute position on the system based on the reconstructed model. The prior pose of the GNSS receiver based on RTK with tilt compensation can not only improve the accuracy of the reconstruction model, and restore the real scale, but also orient the reconstruction model to the n coordinate. Finally, based on the constraint relationship of the features between the images and the prior pose of the GNSS receiver, the overall bundle adjustment is performed to jointly improve the pose accuracy of the camera and the relative pose accuracy between the images. As shown in Fig. 6, the posterior pose estimation of the camera under n coordinate can be completed in three steps. The first step is to obtain the prior pose of the GNSS receiver at the moment of taking the photo, which is provided by the RTK with tilt compensation. The second step is to build a 3D model based on the images and restore the true scale of the 3D model through the prior position information. The third step is to perform overall bundle adjustment based on the 3D model and the prior pose of the GNSS receiver to obtain the posterior pose estimation of the camera. 5.1 Get Camera Prior Pose From the analysis in Sect. 4, it can be seen that the GNSS/INS combined system can n provide the P nc which is the priori position of the camera with horizontal accuracy of 8

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n

mm + 1 ppm and vertical accuracy of 15 mm + 1 ppm, as well as Rc which is the prior attitude of the camera with yaw accuracy of 1.5°. 5.2 Reconstruction of 3D Model First, feature extraction and feature matching are performed on the images, and the matched feature pairs are considered as connection between images, as shown in Fig. 7. Features should remain unchanged under motion changes so that they can be uniquely identified across multiple images. Feature

Image 1

Image 2

Image 3

Fig. 7. Feature pairs between images

It is very important to select an appropriate initialization image pair. If the initialization is based on an image pair with poor geometric constraints or poor correlation with other images, subsequent reconstruction failures are likely to occur. Through the c c c intersection operator (4), we can get Pcjjf , Pcjjci , Pcjjcj , and the geometric relationship among them is shown in Fig. 3. According to the law of cosines, there are: ⎛ 2  c 2  c 2 ⎞ c c c c Pcjjci − Pcjjf + Pcjjcj − Pcjjf − Pcjjci − Pcjjcj ⎜ ⎟   c   c (18) αf = arccos⎝ ⎠ cj cj j j 2 Pcj ci − Pcj f · Pcj cj − Pcj f We calculate the average value α  of the intersection angles αf of feature point pairs in two frames of images, when α  is less than a certain threshold, we consider the geometric constraints of the image pair are not strong enough to initialize the model.  n   αf n (19) α= f =1

Select the appropriate image pair from all the images to initialize the model, select any c frame from the initialization image pair as the w frame, and then continuously select the optimal image from the candidate images and perform rear intersection with the current model [8], until all available images are done with the rear intersection. Count the number of feature points that have completed the front intersection on each frame of the image in the candidate image. We think that if the number of features that have completed the front intersection in the image is more, and the distribution on the image is more scattered, the uncertainty of the image pose obtained by the backward intersection is lower.

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5.3 Optimizing Camera Pose In the model reconstruction process, the front intersection and the rear intersection are independent, but the two are strongly correlated. In the forward intersection, the uncertainty of the camera pose is transferred to the position of the feature. In the rear intersection, the uncertainty of the position of the feature will also be transferred to the pose of the camera. The overall bundle adjustment can combine the forward and the rear intersection to construct a nonlinear optimization model about the camera pose and the position of features [9]. By minimizing the reprojection error of features, the accuracy of the camera pose and relative pose between images is improved. After forward and rear intersections, a global bundle adjustment is performed:   m n      Rw P w P w x 2 (20) ρ rc ci wci wfj ij  E= 2

i=1 j=1

Among them, ρ is a robust kernel function, which is used to reduce the weight of mismatched feature pairs to reduce the impact of gross errors. xij is the pixel of feature j in image i. rc is the feature reprojection residual function and the optimization variables w , Rw ) and the position of the feature P w under the include the pose of the camera (Pwc c wf w coordinate. In order to measure the absolute position of the target point directly on the image, we expect to be able to perform global bundle adjustment in the n coordinate. However, the above-mentioned reconstructed 3D model is defined in the w coordinate, so absolute orientation is required to determine the transformation relationship between the w coordinate and the n coordinate. Thanks to the prior pose of the GNSS receiver n provided by the GNSS/INS integrated system, the prior transformation matrix Rw of the two coordinate systems can be obtained. If the GNSS receiver does not support tilt compensation, it can only provide a prior n position information, and cannot directly obtain Rw . Paper [10] allows the camera and IMU to observe the physical vector in the vertical direction in multiple postures to determine the transformation between the c coordinate and the b coordinate. Using this idea for reference, the absolute orientation can be performed based on the geometric structure relationship between the shooting positions to determine the transformation matrix of the w coordinate and the n coordinate. It should be noted that if the shooting positions are collinear or close to collinear, due to the degradation of the geometric structure, the orientation accuracy will decrease or even absolute orientation cannot be performed. Finally, combined with the prior pose of the GNSS receiver, the overall bundle adjustment is performed in the n coordinate: ⎛ ⎞    n m    2     ⎠  n Pn x n 2 + ⎝rp Rnc Pnc ρ rc Rnci Pnc (21) E= nfj ij  i i i 2 i=1

j=1

2

Among them, rp is the residual function of the camera prior pose constraint, and the n , and P n under the n coordinate. If the GNSS receiver optimization variables are Rnc , Pnc nf does not support tilt compensation, then rp corresponds to the residual function of the camera prior position constraints.

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6 Experiment and Results In order to evaluate the accuracy of the algorithm proposed in this paper, a total of 100 sets of data were collected, and a total of 450 target points were measured in the collected data. The measurement results of the total station are used as reference values, compared with the results of non-contact measurement, and the horizontal-vertical, and 3D measurement errors of the target point are counted. 6.1 Experimental Design The impact of factors such as shooting method, number of photos, measurement distance, and lighting conditions on the accuracy of algorithm is considered. Shooting methods include cross-track shooting, large arc shooting, small arc shooting, and straight-line shooting. Among the 100 sets of data collected, the least number of images is 3, and the largest number is 25. According to the measurement distance, it is divided into three groups, which are less than 3 m, 3 m to 7 m, greater than 7 m, and the farthest is no more than 15 m. The collected data covers scenes with different lighting conditions such as sunny days, cloudy days, after rain, noon, and evening.   n It can be known from (5) that the error of the target point is composed of δ Pnf   c . The error of P c is related to the relative pose error between the image and δ Rnc Pcf cf pairs, the pixel extraction error of the target point, and the size of the intersection angle. Use the following four methods to process 100 sets of experimental data, compare the measurement results of the four methods and analyze the influence of different error terms. The first method is the direct projection method, denoted as prior. Based on the n n pose of GNSS receiver from the tilt compensation, (P nc , Rc ) which is the camera’s prior pose is directly transformed. As in (22), the relative pose between images is calculated n n c n n c through (P nc , Rc ) and then P cf is calculated based on (4). Substitute (P nc , Rc ), and P cf into (1), and finally measure the position of the target point.   T  T  c c n n n n n Rcji = Rcj Rci Pcjjci = Rcj P nci − P ncj

(22)

The second method is the projection method based on the 3D model, denoted as the n n prior + 3D model. The second method also uses (P nc , Rc ) to measure the position of the target point. The difference from the first method is that, as in (23), based on the camera pose obtained after the overall bundle adjustment of the 3D model, the relative c is calculated based on formula (4). pose between images is calculated, and then Pcf   T  T  c cj w w − Pw Pwc Rcji = Rw Rw cj ci Pcj ci = Rcj wc i j

(23)

The third method is a GNSS-Assisted non-contact measurement method (GNSS c is consistent with Assist Visual Tilt Measure, GAVTM). The calculation method of Pcf n

the second method. In the third method, only P nc is available, so the absolute orientation must be carried out through the geometric structure formed by the shooting position. In

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n , Rn ) after global bundle adjustment is the position measurement of the target point, (Pnc c used. The fourth method is a non-contact measurement method based on GNSS/INS Assisc tance(GNSS/INS Assist Visual Tilt Measure, GIAVTM). The calculation method of Pcf is consistent with the second method, and the position measurement of the target point n , Rn ) which is the camera posterior pose after the overall is carried out by using (Pnc c n bundle adjustment. However, compared to the third method, the fourth method has Rc available.

6.2 Experimental Results

Fig. 8. Statistical distribution of 3D errors in four non-contact measurement methods

We count the 3D errors of 450 target points. Figure 8 shows the statistical distribution of 3D errors corresponding to the four methods. Among them, the left side of Fig. 8 is the cumulative distribution function (CDF), and the right side is the boxplot. Only 25.6% and 41.5% of the samples in the prior and prior + 3D model have 3D errors within 5 cm. In contrast, 84.1% and 84.6% of the samples of GAVTM and GIAVTM have 3D errors of less than 5 cm, respectively. The median of the 3D errors of GAVTM and GIAVTM is both 0.029 m, and the upper and lower quartiles are 0.020 ~ 0.041 m and 0.021 ~ 0.043 m respectively, which shows that in the measurement of 450 target points, the middle 50% of the 3D error is within the above error range. Compared with prior, the prior + 3D model uses a higher-precision image relative c , which significantly pose from the global bundle adjustment in the calculation of Pcf improves the measurement accuracy. Compared with the prior + 3D model, GAVTM and GIAVTM have a higher precision camera pose after using the global bundle adjustment when measuring the position of the target point, which has a very significant improvement in the accuracy of the position measurement of the target point. The above statistics do not distinguish between different measurement distances. According to the error analysis in Sect. 4, the impact of the error of camera’s attitude on the error of measurement will amplify as the measurement distance increases. We divide 100 sets of data into three distance segments according to the measurement distance, which are less than 3m, 3m to 7m, greater than 7m, and the farthest is no more than 15m.

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The purpose of subdividing the measurement distance is to study the performance of noncontact measurements at different measurement distances more deeply. The histogram on the left side of Fig. 9 is the mean value of the coordinate errors corresponding to the four methods on horizontal, vertical and 3D. The histogram on the right side is the proportion of the 3D errors of the four methods that are less than or exceed 5 cm. The mean 3D errors of prior in the three distance segments are 0.043 m, 0.098 m and 0.2409 m respectively. The prior + 3D model corresponds to 0.033 m, 0.063 m and 0.119 m. The mean 3D errors of GAVTM and GIAVTM are all within 5 cm, which are 0.025 m, 0.031 m, 0.046 m, and 0.025 m, 0.032 m, 0.042 m respectively. It can be found that the measurement error of prior and prior + 3D model will increase significantly as the measurement distance increases. Although the measurement error of GAVTM and GIAVTM will increase slightly, the mean measurement error can still be within 5cm. c is not considered and According to the error analysis in Sect. 4, when the error of Pcf the measurement accuracy meets 5cm, if the pose of the tilt compensation is directly used for calculation, according to the actual accuracy of the attitude from tilt compensation, it can only use within 2 m. From Fig. 9, we can find that the proportions of samples that meet the measurement accuracy of 5 cm in the prior and prior + 3D model are 82.9%, 25.7%, 0.0%, and 90.2%, 46.0%, 10% respectively in the three distance segments. The error model derived in Sect. 4 can well reflect the real measurement performance and has very important guiding significance in practical engineering applications. GAVTM and GIAVTM improve the pose accuracy of the camera and the relative pose accuracy between images, within a measurement distance of less than 7m, more than 94% of the samples have a measurement accuracy within 5 cm, and within a measurement distance of 7 to 15 m, there are still more than 75% of the samples whose measurement accuracy meets 5 cm. We can find that the performance of GAVTM and GIAVTM is very close both in each distance segment and overall performance. But it is worth noting that, as we discussed in Sect. 5.3, GAVTM cannot handle samples with weak geometry such as small arc shots, straight shots, etc. Figure 10 shows the success and failure ratios of GAVTM in the three distance segments. This ratio is the same as the ratio of strong and weak geometry samples in the three distance segments. However, GIAVTM can solve both samples with strong geometric structures and weak geometric structures. We also analyzed samples with a measurement accuracy exceeding 5 cm. Samples with a measurement distance of more than 10m, and poor lighting conditions (in the evening, after rain) accounted for a higher proportion. We will mark the target point in the real scene, but in the samples over 10m, it can be found that the mark of the target point is already very blurred in the image, and it is difficult to accurately obtain the corresponding pixel in the image. Moreover, the farther the measurement distance is, the higher the attitude accuracy of the camera is required. If the environment with poor lighting is encountered, the accuracy of measurement will be greatly affected.

7 Conclusion This paper deduces the error model of non-contact measurement and proposes a noncontact measurement method based on monocular camera/GNSS/INS. Experiments were conducted to evaluate the accuracy and reliability of the method by considering

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Fig. 9. Statistical distribution of 3D errors in four non-contact measurement methods at different distances

the shooting method, number of shots, measurement distance, and lighting conditions. The main research conclusions of this paper are as follows: c can be improved by improving the (1) Based on the 3D model, the accuracy of Pcf accuracy of the relative pose between images, thereby improving the measurement accuracy of measurement; (2) The overall bundle adjustment combined with the 3D model and the prior information from tilt compensation can effectively improve the attitude accuracy of the camera and the accuracy of the relative pose between images, further improving the accuracy of measurement; (3) Integrating more available prior information not only improve the accuracy of measurement but also broaden the usage scenarios of non-contact measurement;

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Fig. 10. Proportions of successes and failures at the three distances (GAVTM)

(4) The non-contact measurement method proposed in this paper does not require control points and can measure the position of the target point close to real-time. The non-contact measurement error model derived in this paper can well reflect the real measurement performance, and has very important guiding significance in practical engineering applications. And the non-contact measurement method based on monocular camera/GNSS/INS proposed in this paper can perform centimeter-level position measurement and can be applied to various high-precision measurement tasks.

References 1. Luo, X., et al.: High-precision RTK positioning with calibration-free tilt compensation. In: FIG Congress (2018) 2. Cera, V., Campi, M.: Evaluating the potential of imaging rover for automatic point cloud generation. In: ISPRS—International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. XLII-2/W3, pp. 147–154 (2017) 3. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2003) 4. Yan, G., Weng, J.: Strapdown Inertial Navigation Algorithm and Integrated Navigation Principle. Northwest University of Technology Press, Xi’an (2019) 5. Chen, Q., Lin, H., Guo, R., Niu, X.: Rapid and accurate initial alignment of the low-cost mems IMU chip dedicated for tilted RTK receiver. GPS Solutions, 24(119) (2020) 6. Furgale, P., Rehder, J., Siegwart, R.: Unified temporal and spatial calibration for multi-sensor systems. In: IEEE/RSJ International Conference on Intelligent Robots & Systems. IEEE (2013) 7. Schonberger, J.L., Frahm, J.M.: Structure-from-motion revisited. In: IEEE Conference on Computer Vision & Pattern Recognition, pp. 4104–4113. IEEE (2016) 8. Lepetit, V., Moreno-Noguer, F., Fua, P.: EPnP: an accurate O(n) solution to the PnP problem. Int. J. Comput. Vision 81(2), 155–166 (2009)

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9. Triggs, B., Mclauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle Adjustment—A Modern Synthesis. Springer, Berlin, Heidelberg (2000) 10. Lobo, J., Dias, J.: Relative pose calibration between visual and inertial sensors. Int. J. Robot. Res. (2007)

CYGNSS High Spatiotemporal Resolution Flood Monitoring Based on POBI Interpolation: A Case Study of 2022 Pakistan Catastrophic Floods Zhongmin Ma1 , Shuangcheng Zhang1,2(B) , Ning Liu1 , Qi Liu1 , Shengwei Hu1 , Yuxuan Feng1 , Hebin Zhao1 , Qinyu Guo1 , and Chen Wei1 1 College of Geology Engineering, Chang’an University, Xi’an 710054, China

[email protected] 2 State Key Laboratory of Geo-Information Engineering, Xi’an 710054, China

Abstract. Global Navigation Satellite System Reflectometry (GNSS-R) technology is gaining more and more attention from the scientific community due to its advantages of being all-weather, unaffected by clouds and rainfall, and low cost. The Cyclone Global Navigation Satellite System (CYGNSS), NASA’s first constellation of small satellites with space borne GNSS-R, was launched in late 2016, and CYGNSS data has now been shown to be useful for flood detection, in addition to the designed mission of inversion of sea surface wind fields. However, the quasi-random sampling of the surface by the CYGNSS constellation limits its potential for flood detection. Spatial interpolation techniques can bridge this gap and provide a complete coverage of high-resolution daily flood monitoring. In this paper we first introduce the CYGNSS surface reflectivity (SR) calculation method, secondly introduce a new spatial interpolation method (POBI) based on the interpolation of previously observed behavior and finally analyses the performance of CYGNSS high-resolution flood monitoring based on POBI using the 2022 Pakistan catastrophic floods as an example. The results show that compared with the common spatial interpolation methods, the CYGNSS observations based on the POBI method can not only obtain high-resolution flood monitoring results (daily, 3km), but also preserve the surface heterogeneity and discontinuity much better. The comparison with flood monitoring results obtained using microwave remote sensing data also demonstrates the feasibility of CYGNSS high spatial and temporal resolution flood monitoring based on POBI interpolation. Keywords: CYGNSS · Spatial interpolation · Flood monitoring · GNSS-R · SMAP

1 Introduction When flooding occurs, high spatial and temporal resolution flood detection can not only inform government rescue decisions, but also help in post-disaster reconstruction planning [1–3]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 75–84, 2024. https://doi.org/10.1007/978-981-99-6928-9_7

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Currently, satellite remote sensing is considered to be the most effective method of monitoring floods [4]. However, optical remote sensing is limited by the fact that the surface is usually obscured by clouds at the time of flooding [5]; microwave remote sensing is considered to be the best method for monitoring flooding because it can penetrate clouds and, to a certain extent, vegetation [6, 7]. However, existing microwave remote sensing satellites provide data with limited spatial or temporal resolution [8]. CYGNSS is a constellation of eight LEO spacecraft launched by NASA in late 2016, each carrying a specially designed GNSS-R receiver, each capable of tracking and processing four GPS signals reflected from the Earth’s surface simultaneously. Compared to radiometers, CYGNSS is less sensitive to surface roughness as it measures forward scattered signals [9–11]. Although CYGNSS is designed to acquire ocean surface wind speeds in the tropical range, previous studies have shown that CYGNSS data can also be used to monitor land surface hydrological components such as soil moisture [12–15], vegetation biomass [16], water bodies [17–19], and wetlands [20]. Although existing research has initially demonstrated the feasibility of using CYGNSS data to detect flood distribution [21–23], and the results have a higher spatial and temporal resolution compared to conventional microwave remote sensing satellites and optical remote sensing satellites. However, the current research still suffers from the following deficiencies. (1) High temporal resolution and high spatial resolution cannot be achieved at the same time. (2) Incapacity to reflect the spatial heterogeneity and discontinuity of the study area. To address the above two issues, this paper proposes to introduce spatial interpolation into CYGNSS data processing with reference to discrete meteorological data processing methods. The feasibility of CYGNSS high spatial and temporal resolution flood monitoring is explored using Chew’s proposed spatial interpolation method based on previous observations (POBI) [24]. The second part of the article presents the data and methods, while the third part presents the flood monitoring results. Conclusions are given in the last part.

2 Data and Methods 2.1 Study Area Since June 2022, Pakistan has experienced heavy monsoon rains in many parts of the country and flooding in three quarters of the country. A large number of buildings, roads and bridges were washed away, causing severe casualties and economic damage, and the floods are considered the world’s deadliest floods since the South Asian floods of 2017. This paper will analyses the high-resolution flood monitoring capability of CYGNSS data based on the POBI method, using the 2022 mega-floods in Pakistan as an example. Because of the long duration of this flood, and due to limitations of length, this paper has chosen to study the surface inundation conditions for every fifteen days during the flood. Namely, the study dates are: 1 June 2022; 15 June 2022; 1 July 2022; 15 July 2022; 1 August 2022; 15 August 2022; 1 September 2022; 15 September 2022; 1 October 2022; 15 October 2022; 1 November 2022.

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2.2 CYGNSS Data The CYGNSS constellation consists of eight small satellites in near-Earth orbit at an altitude of about 510 km, with an orbital inclination of about 35° and a detection range of about 38° between north and south latitudes. The DDM is the fundamental observable of GNSS-R and contains the physical information of the reflecting surface. CYGNSS can measure 32 reflections from the surface per second, with a revisit time of about 3–7 h and a spatial resolution of about 3.5 × 0.5 km [25]. This paper uses the CYGNSS L1 level 3.0 product for the period 1 January 2019 to 1 November 2022. CYGNSS data can be downloaded for free via https://podaac.jpl.nasa.gov/ (Accessed Nov 30 2022). 2.3 SMAP Data and SMOS Data The SMAP satellite was launched by NASA in 2015 to observe global surface soil moisture and freeze-thaw conditions. SMAP uses L-band radiometers for detection, with revisit intervals of approximately 1–3 days, and two types of observations, ascending (6:00am) and descending (6:00pm), with data and processed products available for free download via NASA National Snow and Ice Data Center website. This paper uses SMAP L3 Level daily soil moisture products with a spatial resolution of 9 × 9 km. The time frame is from 1 June 2022 to 1 November 2022. Due to the failure of the SMAP satellite between 7 August 2022 and 22 September 2022, soil moisture data was not available, so we chose to use SMOS soil moisture data to fill this gap. The SMOS satellite was launched by ESA at the end of 2009 and operates in the same L-band frequency. The main mission is to observe global soil moisture and ocean salinity. The SMOS L3 level daily soil moisture product is used in this paper, with a spatial resolution of 25k × 25km. Studies have demonstrated that the upper limit of soil moisture is about 0.4cm3 /cm3 for unflooded areas and about 0.4 to 0.45cm3 /cm3 for flooded areas [26]. 2.4 CYGNSS SR CYGNSS L1 level products need to be further calculated to generate surface reflectivity before they can be used for flood detection. Quality control of the DDM is required prior to the calculation. In addition to the quality labels included in the CYGNSS data, the following data filtering is done in this study to ensure the quality of the results: (1) DDM SNR (Signal-to-noise ratio) greater than 1.5dB; (2) receiver antenna gain greater than 0dB; and (3) mirror reflection point height angle greater than 30°. According to the method proposed by Chew [21], assuming that the reflected signal is dominated by coherent reflections, the coherent reflected power is Prlc =

G r λ2 τrl 4π (Rts + Rsr )2 4π Prt G t

(1)

where Prlc is the coherent reflected power, Prt is the GPS satellite transmit power, G t is the GPS satellite antenna gain, G r is the CYGNSS antenna gain, Rts and Rsr are the distances from the GPS satellite to the specular point and from the specular point to the CYGNSS receiver respectively, λ is the GPS L1 signal wavelength (19cm), τrl is the

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ground reflectivity, and all other parameters are provided by the CYGNSS L1 product. Converting the surface reflectivity in Eq. (1) to dB gives: SR[dB] = 10logPrlc − 10logPrt − 10logG t − 10logG r − 20logλ + 20log(Rts + Rsr ) + 20log(4π )

(2)

The surface reflectivity is affected by the incidence angle and can be corrected using the following equation: SR = SR − 10logcosn θ

(3)

In the above equation, n is a constant between 0 and 2, and here we take n = 1 [13]. To further obtain the distribution of flooding from the SR, we used the threshold method commonly used in CYGNSS inversion flooding. Briefly, the SR values corresponding to permanent water bodies in the study area are first collected and their average value is calculated as the threshold value. When flooding occurs, an area is considered to be inundated when its SR exceeds the threshold value and vice versa. The detailed process for selecting the thresholds is given in the next section. 2.5 POBI Spatial Interpolation Method Chew offers a new solution to the problem that CYGNSS gridded data cannot achieve both high temporal and high spatial resolution at the same time, and that they do not represent the heterogeneity and discontinuity of the ground surface well. It is based on the assumption that CYGNSS SR data can be interpolated at unsampled locations by quantifying the change in SR at unsampled locations in the past versus SR at nearby locations in the past, i.e., the method is a combination of autoregressive spatial interpolation and time series analysis. Specifically, the SR is first gridded, then using a large number of historical CYGNSS observations, the SR of each gridded grid with its nearby grids sampled at the same time in the past is extracted, and a linear regression of these observations is performed to calculate the slope and intercept. In this way, later, when a grid has no SR, a search can be made for grids with SR in the nearby areas of that grid, and finally a weighted average is used to find the SR of that grid. For reasons of length, the details of the POBI method are not described in detail in this paper. We chose to use CYGNSS data from the calibration period (1 January 2019 to 31 December 2021) to calculate the linear regressions, coherence coefficients and standard deviations of residuals required for the POBI method. Afterwards, we will use the 2022 Pakistan mega-flood to validate the feasibility of the POBI method for high-resolution flood detection. A detailed description of the POBI method can be found in the corresponding paper [24].

3 Results 3.1 SR Threshold To distinguish between inundated and non-inundated areas, we use the threshold method, i.e., an area is considered to be inundated when the CYGNSS SR exceeds a predetermined threshold and vice versa. This method has also been widely used in previous

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studies using CYGNSS data to invert the state of surface inundation. However, the threshold is not a constant value due to the different topography, roughness, vegetation and other parameters of the study area. Therefore, in order to make the inversion results more reliable, an appropriate threshold should first be selected according to the actual conditions of the study area.

Fig. 1. (a) Land use and land cover of Pakistan, which can be downloaded from the GlobeLand30: Global Geographic Information Public Product website, at a spatial resolution of 30m, version 2020. (b) CYGNSS SR observations (scattered form) from June 1, 2022 to June 5, 2022.

Figure 1 illustrates the land use and land cover in Pakistan and the distribution of CYGNSS SR in Pakistan (in scatter form) between 1 June 2022 and 5 June 2022. As can be seen from the figure, SR is sensitive to surface dielectric constant and water bodies, and is greater in water bodies and wetland areas in southern Pakistan. To investigate the differences in SR corresponding to different ground features in Pakistan, we processed all CYGNSS L1 data (662,934 DDMs) from Pakistan for the period 1 April 2022 to 30 June 2022. Spatial analysis was then used to count the number of CYGNSS observation points in the different land use and land cover categories and to calculate their corresponding SR values. Table 1 shows the results of the statistical analysis (glaciers are not included in the final count due to their under-representation). Table 1. Surface reflectivity (SR) statistics for different land types in Pakistan (1 April 2022 to 30 June 2022). Land use and cover

SR number

Proportion (%)

SR (dB)

Cropland

346,491

52.26

−15.24

Barren land

226,431

34.16

−20.46

Woodland

10,328

1.56

−21.85

Grassland

57,320

8.65

−20.86

Water

10,496

1.58

−10.68

Artificial land

11,868

1.79

−15.79

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As shown in Table 1, the SR values corresponding to different land use and land cover types vary considerably. Although we did not consider the effects of topography and surface roughness in our statistical analysis, the statistical results still show well the different sensitivity of CYGNSS SR to different surface features. Water bodies correspond to the highest SR value of about −11 dB. Based on the above statistical results, we chose −11dB as the threshold value for this paper. 3.2 SMAP Flood Monitoring Results Due to the lack of real comparative data on temporal and spatial scales, we chose both SMAP data to invert the inundated areas. This method has also been widely used in previous studies. Specifically, an area is considered inundated when soil moisture exceeds 0.4 cm3 /0.4 cm3 and vice versa. As the SMAP re-entry cycle is approximately 3 days, we processed the SMAP data on a 3-day cycle.

Fig. 2. Soil moisture variation in Pakistan between 1 June 2022 and 1 November 2022. Figures 2f to 2h were obtained from SMOS satellite and the rest were obtained from SMAP satellite.

As shown in Fig. 2, between June 2022 and November 2022, Pakistan experienced large changes in soil moisture due to continued heavy rainfall. To further obtain the specific distribution of flooding, we used the threshold method mentioned in the methods section to analyses the extent of inundation obtained from the SMAP soil moisture inversion. The variation in the inundated areas obtained from SMAP soil moisture using the threshold method is given in Fig. 3. As can be seen from the figure, there were no extensive flooded areas in Pakistan until mid-July (Figs. 3a–c). After mid-July, extensive flooded areas began to appear on the surface due to the effects of continued heavy rainfall. A comparison of the inundated areas in the black boxes in Fig. 3 shows that the effects of flooding were most severe in August and gradually diminished thereafter, although some areas were still inundated in southern Pakistan until early November (black boxes below Fig. 3(k)).

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Fig. 3. Changes in inundated areas in Pakistan between 1 June 2022 and 1 November 2022 (obtained from SMAP, inundated areas in blue, non-inundated areas in grey, as below).

3.3 CYGNSS Flood Monitoring Results After POBI Interpolation As mentioned earlier, since the common spatial interpolation methods do not perform very well for the application of CYGNSS data to detect flooding, in this section we will try to use the newly proposed POBI spatial interpolation method for CYGNSS SR observations.

Fig. 4. POBI interpolation results for daily CYGNSS SR observations (from June 1, 2022 to November 1, 2022).

The interpolation results of the POBI interpolation method for the daily CYGNSS SR observations are given in Fig. 4. As can be seen from the figure, compared to common interpolation methods, the results after POBI interpolation not only obtained complete coverage of the daily observations, but also retained the heterogeneity and discontinuity of the ground surface better. The changes in surface inundation in Pakistan obtained using CYGNSS SR after POBI interpolation are given in Fig. 5. It can be seen from the figure that there were

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Fig. 5. Change in surface inundation in Pakistan obtained using CYGNSS SR after POBI interpolation (from 1 June 2022 to 1 November 2022, the red curves in the figure are the primary and secondary rivers in Pakistan).

no extensive inundated areas in Pakistan before mid-July (Fig. 5a–c). After mid-July, extensive inundated areas began to appear on the surface due to the effects of continued heavy rainfall. A comparison of the inundated areas in the black boxes in Fig. 5 shows that flooding was most severe in August, with extensive inundated areas in both north-eastern and southern Pakistan. The distribution of flooding decreases thereafter, but some areas were still inundated until early November in southern Pakistan (black box below Fig. 5k). The change in surface inundation in Pakistan obtained using the POBI interpolated SR is highly consistent with the change in surface inundation obtained using SMAP and SMOS, and the former has a higher spatial and temporal resolution. The results in Fig. 5 provide preliminary evidence of the feasibility of CYGNSS high spatial and temporal resolution flood monitoring based on the POBI interpolation method.

4 Conclusion Based on CYGNSS L1 data, this paper first calculates the basic observation SR of CYGNSS, and then investigates the feasibility of using CYGNSS for high-resolution flood mapping by combining the water-sensitive property of SR with the POBI spatial interpolation method. Using the 2022 Pakistan mega-flood as an example, the inundated area distribution is successfully inverted while better preserving the surface heterogeneity and discontinuity. Compared to the SMAP data flood monitoring results, the two are in good agreement, and the flood distribution obtained from the SMAP results and CYGNSS results are basically similar, but the CYGNSS results have better temporal and spatial resolution, and at the same time, a finer mapping and quantification of the inundated area and flood duration can be achieved. The results are of great relevance for emergency management and planning. With the successful launch of more GNSS-R LEO satellites in the future, it is believed that more and higher quality satellite-based GNSS-R data will be available in the near future (e.g. CYGNSS-FOLLOW-ON, EAS’ HydroGNSS), which will undoubtedly further promote the development of satellite-based GNSS-R terrestrial applications.

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Acknowledgments. Thanks to NASA for the CYGNSS and SMAP data and to ESA for the SMOS data. All anonymous reviewers and editors are thanked for their constructive review of this manuscript.

Funding. This research was funded by the National Natural Science Foundation of China Projects (Grant No.42074041); The Scientific Innovation Practice Project of Postgraduates of Chang’an University (300103722043).

References 1. Jonkman, S.N.: Global perspectives on loss of human life caused by floods. Nat. Hazards 34, 151–175 (2005) 2. Hirabayashi, Y., et al.: Global flood risk under climate change. Nat. Clim. Chang. 3, 816–821 (2013) 3. Klemas, V.: Remote sensing of floods and flood-prone areas: an overview. J. Coast. Res. 31, 1005–1013 (2015) 4. Bates, P.D.: Remote sensing and flood inundation modelling. Hydrol. Process. 18, 2593–2597 (2004) 5. Asner, G.P.: Cloud cover in landsat observations of the Brazilian Amazon. Int. J. Remote Sens. 22, 3855–3862 (2001) 6. Rundquist, D.C., Narumalani, S., Narayanan, R.M.: A review of wetlands remote sensing and defining new considerations. Remote Sens. Rev. 20, 207–226 (2001) 7. Klemas, V., Pieterse, A.: Advances in watershed science and assessment. In: The Handbook of Environmental Chemistry, vol. 33. Springer, Berlin/Heidelberg, Germany (2015) 8. Kuenzer, C., Guo, H., Huth, J., Leinenkugel, P., Li, X., Dech, S.: Flood mapping and flood dynamics of the Mekong Delta: ENVISAT-ASAR-WSM based time series analyses. Remote Sens. 5, 687–715 (2013) 9. Ruf, C., et al.: CYGNSS: enabling the future of hurricane prediction [remote sensing satellites]. IEEE Geosci. Remote Sens. Mag. 1, 52–67 (2013) 10. Ruf, C., et al.: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Am. Meteorol. Soc. 97, 385–395 (2015) 11. Ruf, C., et al.: CYGNSS Handbook Cyclone Global Navigation Satellite System. Michigan Publishing, Ann Arbor, MI, USA (2016) 12. Camps, A., Park, H., Pablos, M., Foti, G., Gommenginger, C.P., Liu, P.W., Judge, J.: Sensitivity of GNSS-R spaceborne observations to soil moisture and vegetation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9, 4730–4742 (2016) 13. Chew, C.C., Small, E.E.: Soil moisture sensing using spaceborne GNSS reflections: comparison of CYGNSS reflectivity to SMAP soil moisture. Geophys. Res. Lett. 45, 4049–4057 (2018) 14. Kim, H., Lakshmi, V.: Use of cyclone global navigation satellite system (CyGNSS) observations for estimation of soil moisture. Geophys. Res. Lett. 45, 8272–8282 (2018) 15. Yan, Q., Huang, W., Jin, S., Jia, Y.: Pan-tropical soil moisture mapping based on a three-layer model from CYGNSS GNSS-R data. Remote Sens. Environ. 247, 111944 (2020) 16. Santi, E., Paloscia, S., Pettinato, S., Fontanelli, G., Clarizia, M.P., Comite, D., Dente, L., Guerriero, L., Pierdicca, N., Floury, N.: Remote sensing of forest biomass using GNSS reflectometry. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 13, 2351–2368 (2020) 17. Li, W., Cardellach, E., Fabra, F., Ribó, S., Rius, A.: Lake level and surface topography measured with spaceborne GNSS reflectometry from CYGNSS mission: example for the Lake Qinghai. Geophys. Res. Lett. 45, 13–332 (2018)

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18. Gerlein-Safdi, C., Ruf, C.S.: A CYGNSS-based algorithm for the detection of inland waterbodies. Geophys. Res. Lett. 46, 12065–12072 (2019) 19. Ruf, C., Chew, C., Gerlein-Safdi, C., Warnock, A.: resolving inland waterways with CYGNSS. In: Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium, pp. 954–957 (2021) 20. Morris, M., Chew, C., Reager, J.T., Shah, R., Zuffada, C.: A novel approach to monitoring wetland dynamics using CYGNSS: everglades case study. Remote Sens. Environ. 233, 111417 (2019) 21. Chew, C., Reager, J.T., Small, E.: CYGNSS data map flood inundation during the 2017 Atlantic hurricane season. Sci. Rep. 8, 9336 (2018) 22. Wan, W., et al.: Using CYGNSS data to monitor China’s flood inundation during typhoon and extreme precipitation events in 2017. Remote Sens. 11, 854 (2019) 23. Zhang, S., et al.: Using CYGNSS data to map flood inundation during the 2021 extreme precipitation in Henan Province, China. Remote Sens. 13(24), 5181 (2021) 24. Chew, C.: Spatial interpolation based on previously-observed behavior: a framework for interpolating spaceborne GNSS-R data from CYGNSS. J. Spat. Sci. 1–14 (2021) 25. Al-Khaldi, M.M., Johnson, J.T., Gleason, S., Loria, E., O’Brien, A.J., Yi, Y.: An algorithm for detecting coherence in cyclone global navigation satellite system mission level-1 delaydoppler maps. IEEE Trans. Geosci. Remote Sens. 59, 4454–4463 (2020) 26. Rahman, M.S., Di, L., Shrestha, R., et al.: Agriculture flood mapping with soil moisture active passive (SMAP) data: a case of 2016 Louisiana flood[C]. In: 2017 6th International Conference on Agro-Geoinformatics (2017)

Modeling and Performance Evaluation of TomoSAR System Based on Reflected Signal of Beidou Navigation Satellite Chenghao Wang1,2 , Feifeng Liu1,2(B) , Cheng Hu1,2 , Zhanze Wang1,2 , and Zhixiang Xu1,2 1 Radar Research Laboratory, School of Information and Electronics, Beijing Institute of

Technology, Beijing 100081, China [email protected] 2 Key Laboratory of Electronic and Information Technology in Satellite Navigation (Beijing Institute of Technology), Ministry of Education, Beijing 100081, China

Abstract. TomoSAR improves the information dimension of radar image from 2D to 3D, and is widely used in elevation modeling, deformation inversion of infrastructure such as high-rise buildings, dams and mining areas, and forest vegetation biomass estimation. However, the revisiting time of traditional spaceborne TomoSAR is more than 10 days, it is difficult to monitor and forecast the sudden deformation in real time. Furthermore, most of the low-orbit satellites are deployed in the north-south direction, so the deformation measurement accuracy in the north-south direction is relatively poor. The orbit baselines in height direction of low orbit satellites are small, so the image quantity and cost of high resolution tomography processing are huge. Therefore, low orbit TomoSAR is difficult to achieve high frequency, high precision and low-cost three-dimensional deformation measurement. Although GEO SAR and MEO SAR systems have the advantages of shorter revisit period, longer observation time and larger beam coverage area theoretically, there are no satellites in orbit at present. GNSS-TomoSAR, based on the reflected signals of navigation satellites, uses the in-orbit navigation satellite as the irradiation source, and a stationary receiver is placed on the ground to receive the echo signal reflected from the scene for synthetic aperture radar tomographic processing, which can achieve high frequency, high precision and low-cost three-dimensional deformation monitoring of the scene. GNSSTomoSAR is a relatively novel signal processing concept, which is rarely studied at home and abroad. In this paper, the signal processing model of GNSS-TomoSAR is established, the performance boundary of GNSS-TomoSAR is discussed, and the actual track of Beidou IGSO satellite is used to conduct the simulation of height inversion of point target in GNSS-TomoSAR configuration. In above, the application prospect of GNSS-TomoSAR technology is preliminarily explored, lying a foundation for GNSS-TomoSAR real data processing. Keywords: Beidou navigation satellite · Synthetic aperture radar · SAR Tomography

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1 Introduction With the continuous economic development of our country, the number of large infrastructure such as high-rise buildings, open-pit mines and dams is increasing continuously, and is widely distributed in most areas of our country. The health degree analysis and high frequency and high precision monitoring of large-scale infrastructure are of great significance for ensuring the safety of people’s life and property [1]. Spaceborne SAR has advantages such as large beam coverage area, stable motion trajectory and long platform life, etc., and has been widely studied by countries all over the world [2, 3]. Spaceborne TomoSAR, developed on the basis of traditional spaceborne SAR, retains the advantages of traditional spaceborne SAR, such as high monitoring accuracy and large range, and at the same time has the ability of highly dimensional positioning. For highly malleable strong scattering targets, it can retrieve electromagnetic scattering and deformation characteristics at different heights [4–6]. However, the current orbital altitude of spaceborne SAR in orbit is under 1000 km, and the revisit time is more than 10 days, so it is difficult to monitor and forecast sudden deformation in near real time. Most low-orbit satellites are deployed in the northsouth direction, so the deformation measurement accuracy in the north-south direction is relatively poor. Therefore, low orbit TomoSAR is difficult to achieve high frequency and high precision three-dimensional deformation information measurement. Although GEO SAR and MEO SAR systems have the advantages of shorter revisit period, longer observation time and larger beam coverage area theoretically, there are no satellites in orbit at present. Bistatic TomoSAR based on global navigation satellites (GNSS-TomoSAR), uses the in-orbit navigation satellites as the illuminators, places a stationary receiver on the ground to receive the direct signal from satellites and echo signal reflected by scene for processing, carries out capture and tracking, synchronization, imaging, tomographic, differential interferometry processing, measures the three-dimensional scattering intensity and deformation information of the target. Since only a passive receiving system needs to be deployed on ground, the cost of GNSS-BSAR system is much lower than that of traditional spaceborne SAR systems which require active transmitters. At present, mature global navigation systems include Beidou, GPS, Galileo and GLONASS, with more than 100 satellites in orbit and abundant space resources. Among them, the Beidou Navigation System has both IGSO and MEO satellites. The re-visit cycle of Beidou IGSO satellite is about 1 day, and that of MEO satellite is about 7 days, which is much shorter than that of low-orbit SAR. At the same time, abundant navigation satellites can also provide multi-angle observation resources to realize three-dimensional deformation inversion. Moreover, in addition to the B3I/B2a/B2b multi-frequency joint processing and the B3I/ GPS/Galileo/GLONASS cross-system joint processing, the Beidou third-generation navigation satellites can further improve the frequency and accuracy of deformation monitoring. Although some research work has been carried out at home and abroad for GNSSbased bistatic SAR system (GNSS-BSAR) and its differential interferometry application [7–13], the relevant research progress of GNSS-TomoSAR is limited at present. System modeling and performance evaluation targeted to the special geometric configuration of

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GNSS-TomoSAR were needed to be carried out to lay the foundation for the practical application of GNSS-TomoSAR.

2 Signal Model of GNSS-TomoSAR The system configuration of GNSS-TomoSAR is shown in Fig. 1. Direct signal antenna and echo antenna are placed on the ground, the distance between them is about tens of centimeters, therefore they can be considered in the same position. The direct signal antenna receives the signal transmitted directly from the navigation satellites, and the echo antenna receives the navigation signal reflected back from the target scene. The direct signal antenna and echo antenna transmit the signal to the receiver for down conversion processing. The direct wave signal is used to solve the position of ground equipment and satellite, conduct time and frequency synchronous processing, eliminate part of the phase error of signal propagation path; The echo signal is used for subsequent two-dimensional imaging and tomographic processing. For a single satellite, it is assumed that the data of the N repeated orbits are collected, and the coordinate system is established with the center of the N/ 2nd repeated orbits as the origin. In the coordinate system, r is the direction of slant range, s is the direction of cross-range, i.e., the direction of elevation, a is orthogonal to both r and s.

Fig. 1. System configuration of GNSS-TomoSAR.

According to the bistatic configuration of ground-based receiver, suppose that the coordinate of center of scene is (r, s, a), the coordinate is (rE , sE , aE ),   of echo antenna the coordinate of center of number n repeated orbits is Brn , Ben , Ban , intensity of elevation scatterers to be estimated is r n (s), the echo obtained in number n repeated orbits can be presented as:    −j · 2π n (1) Sn = γ (s) · exp [Rn (s) − Rn (0)] ds λ Among Above, Rn (s) is the bistatic slant range between the satellite and target, Rn (0) is the slant range between the satellite and (r, 0, a) point. Rn (s) = Rs−Q (s) + RQ−E (s) − Rs−E

(2)

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Rs−Q (s) is the distance between the center of the nth repeat track and the center of the scene, RQ−E (s) is the distance from the echo antenna in the center of the scene, Rs−E is the distance from the center of the nth repeat track to the echo antenna.   Rs−Q (s) = Psn − PQ    2  2  2 = r − Brn + s − Ben + a − Ban 2    2  2 s − Ben r − Brn + a − Ban +  ≈ (3) 2  2 2 r − Brn + a − Ban 2    n 2    Ba s − Ben · r − Brn n ≈ r − Br +  2 +  2  2

2 r − Brn 2 r − Brn + a − Ban   RQ−E (s) = PQ − PE   = (r − rE )2 + (s − sE )2 + (a − aE )2  (s − sE )2 (4) ≈ (r − rE )2 + (a − aE )2 +  2 (r − rE )2 + (a − aE )2   (s − sE )2 · r − Brn (a − aE )2

≈ (r − rE ) + + 2(r − rE )2 2 (r − rE )2 + (a − aE )2   Rs−E (s) = Psn − PE    2  2  2 = rE − Brn + sE − Ben + aE − Ban 2    2  2 sE − Ben n n ≈ rE − Br + aE − Ba +  2  2 2 rE − Brn + aE − Ban (5) 2    aE − Ban n ≈ rE − Br +  2 2 r − Brn  2  2  2 sE − Ben · rE − Brn + aE − Ban  + 2  2

2 rE − Ban + aE − Ban Substitute (2), (3), (4), (5) into (1),we can get:    2 s − 2Ben s · r − Brn [Rn (s) − Rn (0)] ≈  2  2

2 r − Brn + a − Ban   2 s − 2sE s · (r − rE )2 + (a − aE )2

+ 2 (r − rE )2 + (a − aE )2 ≈

s2

− 2Ben s

+

s2

2r s2 − Ben s − sE s = r

− 2sE s 2r

(6)

Modeling and Performance Evaluation of TomoSAR System Based on

Substitute (7) into (1), we can get:    −j · 2π n Sn = γ (s) · exp [Rn (s) − Rn (0)] ds λ   2   −j · 2π s − Ben s − sE s n = γ (s) · exp ds λ r     n  2 s + s j · 2π B −j · 2π s E e + ds = γ n (s) · exp λr λr

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(7)

In the equation above, the index s2 and sE s are fixed, so they can be compensated.    j2π Ben s n Sn = = γ (s) · exp (8) λr If the target scattering coefficient is the same, i.e. γ 1 (s) = γ 2 (s) = ... = γ n (s) 



j2π Ben s γ (s) · exp λr

Sn =  = γ (s)· exp(−j2π εn s)

(9)

 (10)

= FT{γ (s)} Bn

In (10), εn = − λre , γ (s) is the Fourier transform of the received signal in elevation in the case of uniform sampling. The observation equation can be rewritten in discrete form: g = Rγ + ε

(11)

g represents the n-dimensional observation vector; γ represents the discrete scattering rate vector of L dimension (L represents the number of highly upward scattering points), the atoms γl = γ (sl ), sl (l = 1, 2, . . . , L) represent the altitude position of L scattering points; R is the mapping matrix of N × L dimension, the atoms are: Rnl = exp(−j2π ξn · sl )

(12)

  ξn = − Ben + sE /λr

(13)

In (12):

ε represents the n-dimensional noise vector. It can be seen that TomoSAR is essentially to recover the height-scattering rate γ from the received signal g. According to the definition of beamforming (BF): γ (s)=r(s)∗ g(s) In above, r (s)* is conjugate to r(s).

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3 GNSS-TomoSAR Performance Indicators The main performance indexes of GNSS-TomoSAR include range resolution, azimuth resolution, resolution in elevation, maximum unfuzzy height and Cramero lower bound of height estimation error. Among them, the range and azimuth resolution of GNSSBSAR has been introduced and analyzed in detail in literature [9]. Therefore, the concepts of GNSS-TomoSAR height dimension resolution, maximum unfuzzy height and Cramero lower bound of height estimation error are mainly introduced below. According to radar resolution theory, the greater the length of the altitude to baseline, the greater the altitude to synthetic aperture angle. And the higher the resolution in elevation. The expression of height-oriented resolution is: ρs =

λ θsyn

· sin θ =

λr λ · sin θ = · sin θ B/r B

(14)

λ is the wavelength, B is total baseline length in elevation during navigation satellite observation period, r is the slant distance between the center position of the N/ 2nd repeated track and the target point, θ is the incident angle at the target point. The calculation method of maximum unfuzzy height is: hmax =

λr · sin θ b

(15)

In (15), b is the mean baseline interval in the direction of altitude during the observation period of navigation satellite. It can be seen that the relationship between the height resolution and the maximum unblurred height is inversely proportional. In other words, the increase of baseline length is beneficial to the improvement of the height resolution, but will lead to the decrease of the maximum unblurred height. According to literature [14], the CRLB of position estimation error in the case of a single scatterer can be written as: σsq ,0 =

λr0  4π 2 · N · SNRq · σb √

(16)

In above, λ is the wavelength, r0 represents the slant distance between radar and target scatterer, N is the total amount of data obtained, SNRq represents the signal-tonoise ratio of scatterers in the image, σb stands for the standard deviation of the elevation baseline Ben , which can be expressed as:    n  2    2 σb = std Be = E Ben − E Ben (17)

4 Verification by Simulation Since December 2021, our research group has deployed GNSS-BSAR ground receiving system in Zhujiawan, Yubei District, Chongqing, to monitor the deformation of slope scene, as shown in Fig. 2.

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Fig. 2. Receiver system of GNSS-BSAR

A total of 59 days of the Beidou PRN6, PRN9, PRN39 and PRN40 IGSO satellites have been acquired from December 2021 to March 2022. The parameters and typical image of the GNSS-BSAR system based on Beidou IGSO satellite are as follows (Table 1 and Fig. 3) Table 1. GNSS-BSAR system parameters based on Beidou IGSO satellite Frequency band

Bandwidth(MHz)

Accumulate time (s)

Range resolution (m)

Azimuth resolution (m)

B3I

10.23

600

8–15

5–8

Fig. 3. GNSS-BSAR image of target scene

The GNSS-BSAR measured image is analyzed, and the average SNR of the target point is about 10dB. Calculate the elevation baseline length, resolution in elevation, maximum unfuzzy height and target CRLB of four IGSO satellites in the total observation time, as shown in the following Table 2. Taking the receiver position as the origin and setting the target position of the point at (100 m,100 m,10 m), TomoSAR height dimension reconstruction simulation is carried out by using 59-day repeated orbit tracks of four IGSO satellites, Beidou PRN6, PRN9, PRN39 and PRN40, respectively. The results are shown in Fig. 4. It can be seen that the elevation dimension tomography positioning simulation results of the Beidou PRN6, PRN9, PRN39 and PRN40 are consistent with the target setting

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PRN

Total elevation baseline (km)

Mean elevation baseline (km)

Resolution in elevation (m)

Maximum unfuzzy height (m)

CRLB (m)

6

693.02

9.63

4.56

373.73

1.51

9

1103.90

15.33

3.36

289.97

1.08

39

665.50

9.24

5.51

474.95

0.92

40

308.43

4.28

11.65

994.47

0.44

Fig. 4. Point target positioning result in height of PRN6,9,39,40

position. The 3dB resolution of elevation dimension positioning is 5.2 m, 2.6 m, 2.0 m and 2.6 m, respectively, and the order of magnitude is similar to the theoretical calculation results of height dimension resolution.

5 Conclusion GNSS-TomoSAR based on Beidou reflection signal is a new application direction of navigation satellite system. It has the outstanding advantages of high dimensional resolution, high monitoring frequency, abundant satellites and frequency resources, and low cost. It has important research value in the measurement of three-dimensional scattering characteristics of artificial infrastructure and high-precision deformation inversion. In this paper, the signal model of GNSS-TomoSAR was established, the performance indicators of GNSS-TomoSAR based on Beidou were evaluated, and the actual tracks of four Beidou IGSO satellites were used to conduct the GNSS-TomoSAR elevation

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reconstruction simulation. The results show that GNSS-TomoSAR can invert the target height more accurately and has a theoretical basis for the processing of measured echo data.

References 1. Zhang, L.: Research on non-ideal errors and fast processing of GNSS-InBSAR deformation. Beijing Institute of Technology, Beijing (2020) 2. Way, J., Smith, E.A.: The evolution of synthetic aperture radar systems and their progression to the EOS SAR. .IEEE Trans. Geosci. Remote Sens. 29(6), 962–985 (1991) 3. Elachi, C., Bicknell, T., Jordan, R.L., et al.: Spaceborne synthetic-aperture imaging radars: applications, techniques, and technology. Proc. IEEE 70(10), 1174–1209 (1982) 4. Lombardini, F., Montanari, M., Gini, F.: Reflectivity estimation for multibaseline interferometric radar imaging of layover extended sources. IEEE Trans. Signal Process. 51(6), 1508–1519 (2003) 5. Fornaro, G., Serafino, F., Soldovieri, F.: Three-dimensional focusing with multipass SAR data. IEEE Trans. Geosci. Remote Sens. 51(3), 507–517 (2003) 6. Fornaro, G., Lombardini, F., Serafino, F.: Three-dimensional multipass SAR focusing: experiments with long-term spaceborne data. IEEE Trans. Geosci. Remote Sens. 43(4), 702–714 (2005) 7. Tzagkas, D.M., Antoniou, M., Cherniakov, M.:Coherent change detection experiments with GNSS-based passive SAR[C]. In: Radar Conference IEEE (2017) 8. Liu, F., Fan, X., Zhang, T., Liu, Q.: GNSS-based SAR interferometry for 3-D deformation retrieval: algorithms and feasibility study. IEEE Trans. Geosci. Remote Sens. 56(10), 5736– 5748 (2018) 9. Fan, X.: Research on GNSS-based InSAR artificial features imaging and deformation monitoring technology. Beijing Institute of Technology, Beijing (2018) 10. Zhang, T.: Change detection using global navigation satellite system based bistatic differential interferometric synthetic aperture radar. Beijing Institute of Technology, Beijing (2018) 11. Wang, C., Wang, Z., Liu, F., et al.: Geometry optimization of bistatic SAR with GNSS transmitters and sloping fields imaging. Signal Proc. 37(7):1171–1179 12. Wang, Z., Liu, F., Lv, R., et al.: Data acquisition of GNSS-based InSAR: joint accuracyefficiency optimization of 3-D deformation retrieval. IEEE J. Select. Top. Appl. Earth Observ. Remote Sens. 15, 7886–7898 (2022) 13. Wang, Z., Liu, F., Zeng, T., et al.: Interferometric phase error analysis and compensation in GNSS-InSAR: a case study of structural monitoring. Remote Sens. 13(15), 3041 (2021) 14. Zhu, X.X., Bamler, R.: Tomographic SAR inversion by L1-norm regularization—the compressive sensing approach. IEEE Trans. Geosci. Remote Sens. 48(10):3839–3847 (2010)

Soil Moisture Inversion Based on Dual-Frequency Signal of QZSS GEO Satellite Yahui Kong1 , Lili Jing1 , Fan Gao1,2(B) , Nazi Wang1 , Tianhe Xu1 , Xinyue Meng1 , Yunqiao He1 , and Baojiao Ning1 1 School of Space Science and Physics, Shandong University, Weihai 264209, China

[email protected] 2 Shandong Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment,

Weihai 264209, China

Abstract. In recent years, soil moisture retrieval using GNSS reflection signals has become a topic of great concern to scholars. However, most researchers adopt GPS and BDS signals to carry out the related research. There are insufficient studies on soil moisture inversion using QZSS (Quasi-Zenith Satellite System), and the performance of soil moisture inversion with different QZSS signals has not been evaluated yet. This study aims to provide new results by conducting a soil moisture monitoring experiment of QZSS-Reflectometry (QZSS-R) using the QZSS GEO satellite signal in the experimental field of Weihai Academy of Agricultural Sciences, Shandong Province. The original Intermediate Frequency (IF) data were collected, and the experimental data on October 21, 2022 (during bare soil period) were processed by using the self-developed GNSS-R software receiver. The results of different soil moisture inversion models were evaluated for L1 C/A and L5 signals, and it is found that the signal quality of L5 is better than that of L1 C/A in QZSS-R soil moisture inversion. For the Topp model, the RMSE (Root Mean Square Error) of L5 and L1 C/A inversion results are 0.0240 cm3 /cm3 and 0.1725 cm3 /cm3 . For the Wang model, the RMSE of L5 and L1 C/A inversion results are 0.0317 cm3 /cm3 and 0.1856 cm3 /cm3 respectively. These results demonstrate that the soil moisture estimations accuracy of QZSS L5 signal are superior to that of L1 C/A. Keywords: QZSS-R · Soil moisture · L5 · L1 C/A · GEO

1 Introduction Soil moisture is a crucial parameter for studying crop drought and plays a significant role in agriculture. In remote sensing, soil volumetric water content is a common indicator of soil moisture. There are various detection methods, including the weighting method after dried, ray method, dielectric property method, nuclear magnetic resonance method, separation tracer method, remote sensing, GNSS-R, and more [1]. Among these, GNSSR technology has unique advantages for soil moisture monitoring, such as all-weather applicability, strong penetration, real-time continuity, cloud and weather independence, and high sensitivity to soil moisture [2]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 94–106, 2024. https://doi.org/10.1007/978-981-99-6928-9_9

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The Global Navigation Satellite System (GNSS) is an all-day space-based radio navigation and positioning system that provides users with three-dimensional coordinates, velocity, and time information at any location on or near the Earth’s surface [3]. With the development of GNSS, researchers such as Auber [4] and Kavak [5] have discovered that the reflected signals from GNSS can also be used to retrieve information about the Earth’s surface features, leading to the development of a new field of research called GNSS-R technology. With the continuous development and improvement of GNSS, GNSS-R technology has also matured. As a result, regions such as the United States and Europe have invested a significant amount of manpower, material resources, and financial resources to carry out ground-based, airborne, and space-borne GNSS-R observation experiments [6–8]. There are relatively mature GNSS-R theories, methods, and technologies for estimations of various aspects such as sea surface height [9, 10], soil moisture [11], sea surface wind fields [12], snow thickness [13], and so on. The QZSS system is a regional satellite system with high-precision characteristics in eastern Asia [14], making it suitable for soil moisture monitoring in eastern China. QZSS-R technology estimates soil moisture using soil surface information carried by the reflected signal of the Quasi-Zenith Satellite of Japan. Currently, few studies have been conducted on this. To improve the accuracy of the inversion results, this paper selects the GEO signals of QZSS for processing since the elevation angle of geosynchronous orbit (GEO) satellites keeps almost the same relative to the same location. However, there is a lack of research on the performance evaluation of the inversion results using different signals. Therefore, this paper also evaluates the inversion results of L5 and L1 C/A signals. This article is based on the QZSS GEO satellite and conducted a ground-based GNSSR soil moisture experiment in the experimental field of Weihai Academy of Agricultural Sciences, Shandong Province. The GNSS-R equipment was used to receive direct and reflected signals in the L1 C/A and L5 bands, and the signals were processed using a self-developed GNSS-R Software-Defined Receiver (SDR). Compared with traditional hardware receivers, the SDR has higher flexibility [15, 16] and can support multiple systems and frequencies. Unlike previous software receivers used for sea surface height measurement [17], this receiver can be specifically used for signal processing in GNSSR soil moisture inversion and can process multiple frequency satellite signals such as L1 C/A and L5 signals. After rough and fine capturing of direct and reflected signals, 1ms coherent integration and 200ms incoherent accumulation were performed to obtain the power ratio between direct and reflected signals, which was used for soil moisture inversion. The Topp empirical model [18] and Wang empirical model [19] were then used to calculate the soil moisture from power ratios. The data was collected on October 21, 2022, which was the bare soil period and was not affected by vegetation or other coverings.

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2 Experiment Theory 2.1 Principle of GNSS-R Soil Moisture Inversion When an electromagnetic wave reflects off the ground, its power density changes relative to the direct signal, providing information about soil moisture. To capture both signals, a right-hand circularly polarized antenna and a left-hand circularly polarized antenna are used to receive the direct signal and the reflected signal, respectively. Many studies have confirmed that reflected signal power is correlated with soil volumetric water content [20]. By considering the relationship between reflectivity and dielectric constant, and the relationship between dielectric constant and soil moisture, it is possible to establish a model that relates correlation power to soil moisture [21]. According to the previous work [22], the relationship between relative power and dielectric constant is shown in Eq. 1:   (ε − 1)2 ·sin2 θ · ε − cos2 θ PR −4k 2 ·σh 2 ·sin2 θ = R(ε, θ ) = 2  2 · e √ √ PD ε · sinθ + ε − cos2 θ sinθ + ε − cos2 θ (1) where R(ε, θ ) represents the reflectivity, PD and PR represent the received power of the direct and reflected signals, respectively, with units of dBW; ε represents the dielectric constant, with units of F/m; θ represents the satellite elevation angle, with units of degrees; k = 2πc f represents the wave number, with units of m−1 ; and σh represents the standard deviation of the surface height, with units of meters. The soil dielectric constant model describes the relationship between soil dielectric constant and soil volumetric water content. Several models are commonly used, such as the Dobson semi-empirical model [23], Topp empirical model [18], Hallikainen semi-empirical model [24], and Wang empirical model [19]. The Topp model and the Wang model have applicable frequency bands of 1 MHz–1 GHz and 1.4 GHz–5 GHz, respectively, which align with the frequencies of L1 and L5 signals. It can be concluded that the Topp model is more suitable for the QZSS L5-band signal, while the Wang model is more appropriate for the L1-band signal. These two models are presented in Eqs. 2 and 3. The simplified Topp’s empirical model is: ε = 3.03 + 9.3mv + 146.0m2v − 76.7m3v

(2)

The simplified Wang’s empirical model is: ε = 3.1 + 17.36mv + 63.12m2v

(3)

where mv represents the volumetric water content of the soil, with a unit of cm3 /cm3 . Thus, by adopting the mathematical process from power ratio between reflected and direct signal to soil dielectric then to calculate soil volumetric water content, GNSS-R soil moisture inversion can be achieved.

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2.2 QZSS System and L1 C/A, L5 Signal Characteristics The QZSS system consists of one GEO satellite and three IGSO satellites. During the experiment, the elevation angle of the GEO satellite changes very little and can be considered almost constant, while the elevation angle of the IGSO satellites changes significantly over time. The coverage area of the GEO satellite is wide, and usually three GEO satellites can achieve signal coverage for most areas of the world except for the polar regions. In addition, the GEO satellite always moves with the rotation of the Earth, making it always be visible to users in the coverage area. Furthermore, due to the high orbit altitude, the GEO satellite has good anti-shielding capability, which gives it significant advantages in applications in cities, canyons, mountains and other areas. The trajectory of the GEO satellite subsatellite point of the QZSS system is shown in Fig. 1.

Fig. 1. Subsatellite point trajectory of QZSS system J07 satellite.

Currently, the main service area of QZSS covers Japan and the surrounding Pacific region. The L1 C/A, L1C, L2C, and L5 signals broadcast by QZSS are compatible and interoperable with GPS. The design goal of these signals is to make minimal changes to customer’s receivers so that they can receive signals from both GPS and QZSS simultaneously. Therefore, the modulation scheme and navigation message format of QZSS are consistent with those of GPS [25]. The carrier frequency of the L1 signal is 1575.42 MHz, while the carrier frequency of the L5 signal is 1176.45 MHz. Because the wavelength of the L5 signal is longer and the free space attenuation is smaller, the power of the L5 signal reaching the ground is higher than that of the L1 signal under the same conditions. In fact, the power of the L5 signal is about 4 times higher than that of the L1 signal, or 6dB higher under the same conditions. The signal structure characteristics of L1 C/A and L5 are shown in Table 1. Based on the signal structure parameters shown in Table 1 and the basic principles of signal modulation, it can be concluded that: 1. Compared to the L1 C/A signal, the code period and code rate of the L5 signal have been increased by 10 times, making it more resistant to frequency-selective fading caused by multipath effects. From the perspective of single-satellite ranging error,

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Parameter

L1 C/A

L5 I

Q

Modulation method

BPSK(1)

BPSK(10)

BPSK(10)

Code length (chips)

1023

10230

10230

Bit rate (Mcps)

1.023

10.23

10.23

Mainlobe bandwidth (MHz)

2.046

20.46

20.46

Information rate (bps)

50

50

–

Symbol rate (sps)

50

100

–

Error correction coding

–

convolutional coding R = 1/2 K=7

–

Code type

L1 C/A

L5I

L5Q

the ranging accuracy of L5 can reach 30m, while that of L1 C/A is only 300m [26]. Therefore, the L5 signal can improve the accuracy of position calculation. 2. In terms of navigation message transmission, L5 maintains the same subframe structure as L1 C/A, but adopts 1/2 rate forward error correction convolutional coding (FEC), thus having the ability of navigation message error correction. This coding method can improve the receiver’s ability to resist narrowband interference, and uses Newman-Hoffman (N-H) code to make the signal’s autocorrelation characteristics stronger. It improves data bit synchronization and improves positioning speed in low-power environments. 3. The L5 signal uses dual channels for data and pilot signals, and its pilot channel has no 180° ambiguity, thus improving carrier recovery capability and achieving instantaneous carrier ambiguity resolution. 4. The L1 Enhanced Signal includes two carrier signals, L1C D and L1C P, which have orthogonal phase relationships with each other. When the Q branch accommodates L1C P, the I branch accommodates L1C D. L1C D and L1C P are modulated by BPSK with their respective signal sequences. The L5 signal has two mutually orthogonal carriers, each of which is modulated by two sequences, CL5I5 and CL5Q5 [27]. Taking all of the above into consideration, the quality of the L5 signal should theoretically be superior to that of the L1 C/A signal. 2.3 Signal Power Acquisition Before the GNSS-R soil moisture inversion, it is necessary to process the direct and reflected signals to obtain the parameters needed for the inversion. The corresponding process is shown in Fig. 2. In this paper, the power ratio between the reflected signal and the direct signal is used to calculate the soil moisture information, and the signal power ratio data is extracted

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Fig. 2. GNSS-R digital IF signal processing route.

from the original Intermediate Frequency data using a software receiver developed by our team. Among them, the Intermediate Frequency data sampling rate is 62 MHz, the SDR processing L5 code processing flow is shown in Fig. 3 [22].

Fig. 3. Basic principle of L5 SDR.

The replica of the direct and reflected signals are correlated with L5 pilot signal and data signal, respectively, and then the results are added to generate a 1 ms DelayDoppler Map (DDM). Due to the relatively weak reflected signals from the soil surface, the results are then be non-coherently accumulated for 200ms to obtain an effective DDM. The peak of the DDM obtained from the direct and reflected signals is used to calculate the power ratio. The scattering amplitude of the direct signal at time t 0 of the satellite and the superimposed signal of the reflected signal at t 0 + τ (τ is the time delay of the reflected signal relative to the direct signal) [28] can be expressed as:  Ti Yd ,q (0, fd ) = Ad (t0 + t)D(t0 + t)dt (4)  Yr,q (0, fd ) =

0

Ti

Ar (t0 + t)D(t0 + t)dt

(5)

0

where Ti is the integral time in milliseconds. Ad (·) represents the amplitude of the direct signal, and D(·) represents the signal data bits. Yd ,q and Yr,q represent the amplitudes of

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the received direct and reflected signals, respectively, in units of decibels (dB). Therefore, the surface reflectivity, that is, the power ratio of the reflected signal to the direct signal after incoherent correlation [29], can be expressed as:    Yr,q 2 R =   Yd , q

2  T   i  Ad (t0 + t + τ )D(t0 + t + τ )dt       0  =  T i      Ad (t0 + t)D(t0 + t)dt   

(6)

0

    2  Yr (τ fr ) 2  Ar Ti 2  ≈  = Ar = Pr R =     2 Yd (0fd ) Ad Ti Pd Ad

(7)

where |·| denotes the average operator in a fixed time. Using the Eqs. 4–7, the reflectivity can be extracted from the signal, that is, the power ratio between the reflected signal and the direct signal.

3 Experiment and Results In order to study the performance of the QZSS L1 C/A and L5 in retrieving soil moisture, a ground-based GNSS-R experiment was conducted on October 21, 2022 at the experimental field of Weihai Academy of Agricultural Sciences, Shandong Province, China (located at 37.34° N, 122.00° E). 3.1 Area of Study The environment of the experimental site is shown in Fig. 4, and the GNSS-R equipment is located in the northwest corner of the experimental area. There are no tall buildings or plants obstructing the area near the test field. In addition, the Fresnel reflection zone of the GNSS-R antenna is bare soil, so it is not necessary to consider the vegetation impacts. During the experiment period, the weather was stable and there was no rainfall.

Fig. 4. Satellite image of the experimental site.

A column of approximately 15 m in height was erected in the experimental field to carry the GNSS-R equipment. The direct signal was received by the upward-looking

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antenna, while the reflected signal was received by the downward-looking antenna. The signal reached the Intermediate Frequency signal collector via the GNSS-R antenna, and was then connected to a laptop in real-time storage through a USB3.0 connection. In the experiment, the setup of the direct and reflected antennas and the signals transmission diagram is shown in Fig. 5. The height of the direct antenna is 13.646 m, and the height of the reflected antenna is 13.446 m. Two antennas with the same gain are fixed on two sides of an equilateral triangle to reduce the influence of the difference in antenna gain on the reception of direct and reflected signals. The upward and downward antennas are at a 30° angle to the horizontal, which is conducive to receiving signals from the south and ensures that the incident angles of the direct and reflected signals are equal.

Fig. 5. Straight and reflection antennas construction and signals transmission diagram.

3.2 Soil Moisture Detection Results The observation data of the power ratios between reflected and direct signals were obtained using the GNSS-R software receiver shown in Fig. 3. The coherent integration and non-coherent integration accumulation times were set to 1ms and 200 ms, respectively. Due to the large storage space required for storing Intermediate Frequency data, the data was collected every 2 min per hour and continuously collected for 24 h to reduce the storage space requirements. At the same time, in order to obtain in-suit soil moisture data, a MicroLog CS655 soil moisture sensor with a measurement accuracy of 3% and a depth of 5cm was deployed within the coverage area of the reflected signal. The soil moisture sensor measures the water content of the soil using time-domain reflectometry (TDR) based on the propagation characteristics of electromagnetic waves in the soil.

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L5 Signal Results The soil moisture estimation results of QZSS L5 signal obtained by the correlation power and different models are compared with the reference values obtained by the TDR, as shown in Figs. 6 and 7:

Fig. 6. L5 signal inversion results using Wang model.

Fig. 7. L5 signal inversion results using Topp model.

Figure 6 shows the inversion results of L5 signal using Wang model, and Fig. 7 shows the inversion results of L5 signal using Topp model. Both are shown from 00:00 to 24:00 on 21 October 2022. In the two figures, the trend of soil moisture estimated from the L5 signal is basically consistent with the true value, and the results obtained using two different models have the following characteristics:

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The soil moisture estimated from L5 signal and the true values began to rise slowly from 0:00, and reached the maximum at about 10:00 a.m.. Then it began to decline, and droped to the minimum at about 6:00 p.m.. Finally, it rose slowly until 24:00. On the whole, the inversion results of L5 signal within 24 h are consistent with the actual situation. The RMSE between L5 signal inversion results of Wang model and true values is 0.0317 cm3 /cm3 . The RMSE between the L5 signal inversion results of Topp model and the true values is 0.0240 cm3 /cm3 , in addition, the accuracy of the inversion results is consistent with the theoretical results analyzed in Sect. 2.1. L1 C/A Signal Results The soil moisture estimation results of the QZSS L1 C/A signal obtained from the correlation power and different models are compared with the reference values obtained by the TDR, as shown in Figs. 8 and 9:

Fig. 8. L1 C/A signal inversion results using Wang model.

Figure 8 shows the inversion results of L1 C/A signal using Wang model. Figure 9 shows the inversion results of L1 C/A signal using Topp model. The time period shown in the figure is from 0:00 to 24:00 on October 21, 2022. In the two figures, the soil moisture estimated by L1 C/A signal is significantly different from the true value, and the results obtained by using two different models have the following characteristics: The change in the actual soil moisture started at 0:00 and slowly increased until it reached its maximum at about 10 a.m., then began to decrease until it droped to its minimum at about 6 p.m., and then continued to increase slowly until 24:00 on the day. The soil moisture estimated from the L1 C/A signal was not valid from 0:00 to 2:00, and then began to decrease rapidly, reaching a minimum at about 12:00, and then rose more rapidly until 24:00. This is not consistent with the change of actual soil moisture. On the whole, the true values of soil moisture show a downward trend in a day. For this phenomenon, L5 and L1 C/A signals have the same characteristics.

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Fig. 9. L1 C/A signal inversion results using Topp model.

The RMSE between the inversion results of L1 C/A signal using Wang model and the true values is 0.1856 cm3 /cm3 . The RMSE between the inversion results of L1 C/A signal using Topp model and the true values is 0.1725 cm3 /cm3 . It can be seen from the above analysis that the inversion results of different models using L1 C/A signal have low accuracy, and the trend of soil moisture within 24 h estimated by L1 C/A signal is inconsistent with the trend of the true values of soil moisture. Analysis of Inversion Results of Different Signals Using the Same Model In the case of Wang model or Topp model, the soil moisture values estimated by L5 and L1 C/A signals are compared with each other respectively. By comparing Figs. 6 with 8, it can be found that: The inversion results of the L5 signal in the Topp model are more accurate. The estimated soil moisture values are very close to the true values, and the trend is also consistent with the actual one. The estimation accuracy of L1 C/A signal in the two models is poor, and the soil moisture values are far from the true values. In addition, the fluctuation trend of L1 C/A estimation results is inconsistent with the true values. Therefore, the L5 signal soil moisture inversion results are better than the L1 C/A signal. Combining the feature analysis and estimation results between the two signals mentioned above, it is enough to prove that the accuracy of soil moisture inversion using L5 signal is higher than that of soil moisture inversion using L1 C/A signal. Analysis of Inversion Results of the Same Signal Using Different Models For the estimation of soil moisture from L5 signal, Wang empirical model and Topp empirical model are used for inversion. The results are shown in Figs. 6 and 7. It can be concluded that the overall trend of inversion results using Wang and Topp models is relatively gentle within 24 h.

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Comparing the above two models, it is found that the inversion results using the two models are not much different, but it can also be found that the Topp model has higher statistical accuracy and its change is more gentle, which is more consistent with the actual change. Therefore, it can be proved that the Topp model is more suitable for inversion of soil moisture from L5 signal. This is mainly due to the different applicable frequency bands of the two models, which may have different effects on the results of different signals.

4 Generalize In this paper, the characteristics and models of L1 C/A signal and L5 signal in soil moisture inversion are analyzed theoretically, and verified by field experiments. The following conclusions are drawn: 1. For the Topp model, the RMSE of L5 and L1 C/A inversion results are: 0.0240 cm3 /cm3 , 0.1725 cm3 /cm3 , while for Wang model, the RMSE of estimations are 0.0317 cm3 /cm3 and 0.1856 cm3 /cm3 , respectively. 2. The effect of soil moisture inversion using QZSS GEO satellite L5 signal is better than that of L1 C/A signal, and its accuracy is higher. This provides a reference for improving the inversion accuracy of GNSS-R. 3. Topp model is more suitable for soil moisture estimation from L5 signal. Acknowledgement. Thanks to Weihai Academy of Agricultural Sciences, Shandong Province for providing the experimental site. This paper was supported by the Key Research and Development Program of Shandong Province (Major Scientific and Technological Innovation Project) (2021ZDSYS01), the National Natural Science Foundation of China (41604003 and 41704017) and the Natural Science Foundation of Shandong Province (ZR2022MD046).

References 1. Zhang, X., Hu, Z., Chu, S.: Methods for measuring soil water content: a review. Chinese J. Soil Sci. 2005(01), 118–123 (2005) 2. Mao, K., Wang, J., Zhang, M., et al.: Research on soil moisture inversion by GNSS-R signal. Remote Sens. Inform. 2009(03), 92–97 (2009) 3. Hofmann-Wellenhof, B., Lichtenegger, H., Wasle, E.: GNSS-Global Navigation Satellite Systems: GPS, GLONASS, Galileo and More, vol. 43(11). Springer (2008) 4. Auber, J.C., Bilbaut, A., Rigal, J.M.: Characterization of multipath on land and sea at GPS frequencies. In: ION-GPS-94 Conference. Paris, France (1994) 5. Kavak, A., Vogel, W.J., Xu, G.: Using GPS to measure ground complex permittivity. Electron. Lett. 34(3) (1998) 6. Katzberg, S.J., Torres, O., Grant, M.S., et al.: Utilizing calibrated GPS reflected signals to estimate soil reflectivity and dielectric constant: results from SMEX02. Remote Sens. Environ. 100(1), 17–28 (2005) 7. Pierdicca, N., Pulvirenti, L., Ticconi, F., et al.: Radar bistatic configurations for soil moisture retrieval: a simulation study. IEEE Trans. Geosci. Remote Sens. 46(10), 3252–3264 (2008)

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8. Grant, J.P., Wigneron, J.P., Van de Griend, A.A., et al.: A field experiment on microwave forest radiometry: L-band signal behaviour for varying conditions of surface wetness. Remote Sens. Environ. 109(1), 10–19 (2007) 9. Shao, L., Zhang, X., Liu, J., et al.: GNSS-R sea surface altimetry algorithm. Hydrophobic Surv. Chart. 30(02), 1–3+10 (2010) 10. He, Y.: Research on Baseband Signal Processing of High Precision GNSS-R Sea Surface Altimetry. Shandong University (2022) 11. Zhang, X., Yan, S.: Soil moisture estimation using GPS reflected signals. Glob. Position. Syst. 34(03), 1–6 (2009) 12. Zhou, X., Ye, X., Yu, Y., et al.: Sea surface wind speed measurement using GNSS reflection signal. J. Electron. Inf. Technol. 35(07), 1575–1580 (2013) 13. Li, Y.: Research on theory and method of snow thickness measurement based on GNSS-R. Wuhan University (2019) 14. Xia, Y., Wang, Q., Song, Z., et al.: Japan QZSS satellite navigation system. Satellite Appl. 2015(04), 40–43 (2015) 15. Kai, B., Dennis, M.A., Nicolaj, B., et al.: A software-defined GPS and Galileo receiver. Birkhäuser Boston (2007) 16. Xie, G.: GPS principle and receiver design. Electronic Industry Press (2009) 17. Meng, X.: Design of GNSS-R real-time software defined receiver and its applications. Shandong University (2022) 18. Topp, G.C., Davis, J.L., Annan, A.P.: Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16(3), 574–582 (1980) 19. Wang, J.R., Schmugge, T.J.: An empirical model for the complex dielectric permittivity of soils as a function of water content. IEEE Trans. Geosci. Remote Sens. GE 18(4), 288–295 (1980) 20. Yan, S., Gong, J., Zhang, X., et al.: Ground based GNSS-R observations for soil moisture. Chin. J. Geophys. 54(11), 2735–2744 (2011) 21. Zavorotny, V.U., Voronovich, A.G.: Scattering of GPS signals from t he ocean with wind remote sensing application. IEEE Trans. Geosci. Remote Sens. 38(2), 951–964 (2000) 22. Wang, N., Gao, F., Kong, Y., et al.: Soil moisture estimation based on GNSS-R using L5 signals from a Quasi-Zenith Satellite System. IEEE Geosci. Remote Sens. Lett. (2022) 23. Dobson, M.C., Ulaby, F.T., Hallikainen, M.T., et al.: Microwave dielectric behavior of wet soil-Part II: dielectric mixing models. IEEE Trans. Geosci. Remote Sens. 1985(1), 35–46 (1985) 24. Hallikainen, M.T., Ulaby, F.T., Dobson, M.C., et al.: Microwave dielectric behavior of wet soil-part 1: empirical models and experimental observations. IEEE Trans. Geosci. Remote Sens. 1985(1), 25–34 (1985) 25. Japan Cabinet Office: Performance Standard and Interface Specification: IS-QZSS-PNT-003 (2018) 26. He, C.: GNSS Space Signal Quality Assessment Method Research and Ranging Performance Impact Analysis. Chinese Academy of Sciences Graduate School (National Time Service Center) (2013) 27. Shao, J., Feng, W., Shen, J.: QZSS and signal design. Sci. Surv. Map. 34(S2), 225–227 (2009) 28. 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) 29. Egido, A.: GNSS Reflectometry for Land Remote Sensing Applications. Starlab, Barcelona (2013)

Comparison and Analysis of Tidal Level Monitoring Accuracy Between GNSS-IR and Satellite Altimetry Naiquan Zheng1

, Hongzhou Chai1(B) , Zhiyuan An2 , Peng Chen2 Lingqiu Chen1 , and Lixia Liu3

,

1 Institute of Geospatial Information, PLA Information Engineering University,

Zhengzhou 450001, China [email protected] 2 College of Geomatics, Xi’an University of Science and Technology, Xi’an 710054, China 3 The First Geographic Information Mapping Institute, Ministry of Natural Resources, Xi’an 710054, China

Abstract. The coexistence of multiple methods has become a general trend in tidal level monitoring, especially the Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology and satellite altimetry technology provide a richer database for sea level monitoring. Few studies have carried out the comparison of tidal level accuracy obtained by the two methods. Based on this, this study takes BUR2 station as an example to carry out the research on tidal level monitoring of GNSS-IR and satellite altimetry (HY-2B and Jason-3), and compares them with the measured tidal level data provided by the tidal gauge station (BURTG). First, unify the respective time bases to Coordinated Universal Time (UTC) and the elevation base to Tide Gauge Zero (TGZ). Then, the characteristics of the two methods to monitor the tidal level are compared and analyzed. GNSS-IR technology has higher temporal resolution (R: 0.957, RMSE: 0.257 m, ME: −0.008 m, Number: 73936), while HY-2B (R: 0.994, RMSE: 0.105 m, ME: 0.025 m, Number: 178) and Jason-3 (R: 0.995, RMSE: 0.113 m, ME: −0.040 m, Number: 461) have higher inversion accuracy. This study explored the respective characteristics of GNSS-IR technology and satellite altimetry technology for tidal level monitoring, laying a foundation for the subsequent integration of tidal level monitoring. Keywords: Tide level monitoring · GNSS-IR · Satellite altimetry · SNR

1 Introduction As data is closely related to human production and life, accurately detecting the sea level is vital. Water gauges, tide gauge stations, radar monitors and pressure sensors are the more widely used methods for determining sea level. With the continuous enrichment of detection methods, technologies such as GNSS-IR and satellite altimetry have emerged, gradually developing sea level monitoring from traditional measurement to © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 107–117, 2024. https://doi.org/10.1007/978-981-99-6928-9_10

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remote sensing. GNSS-IR technology has increasingly matured in sea level monitoring [1, 2]. The continuous expansion of the global shore-based Continuously Operating Reference Stations (CORS) provides a rich data source for GNSS-IR technology to monitor sea levels. Over the years, satellite altimetry has become an essential method of sea level independent of infrastructure. Especially in deep sea areas where it is not easy to build tide gauge stations, satellite altimetry is of great significance for evaluating sea level changes. At present, the widely used altimetry satellites mainly include HY-2B of the National Satellite Ocean Application Service (NSOAS) in China, Jason-1/2/3 and ICESat-2 of National Aeronautics and Space Administration (NASA), ENVISAT, CryoSat-2 and Sentinel-3A/B of European Space Agency (ESA) and SARAL satellite in cooperation by India and France. The development of GNSS-IR technology has been relatively long. In 1993, MartinNeira applied the combination of direct and reflected signals to ocean altimetry for the first time and proposed the concept of PARIS (Passive Reflectometry and Interferometry System) [3]. After years of development, Löfgren et al. proved that the signals received by GNSS receivers contain partially reflected signals, which can be used to monitor sea level changes in 2011 [4]. In the same year, Jin et al. also gave the concept of GNSS-IR and its development status [5]. In 2019, Wang et al. proposed to use wavelet decomposition to remove the influence of noise in SNR and concluded that wavelet decomposition could improve the time resolution of inversion while ensuring accuracy [6]. In 2021, Zheng et al. conducted a multi-frequency and multi-GNSS sea level fusion study underlying the observation data of the MAYG station, which significantly improved the spatial and temporal resolution [7]. In 2022, Hu et al. proposed a new GNSS-IR sea level estimation model combined with Variational Mode Decomposition (VMD). The experimental results reveal that the VMD method has achieved good accuracy and stability [8]. Satellite altimetry monitoring of sea levels has also developed rapidly. Previous studies on inland water levels have been conducted [9–11], and the monitoring of sea levels has also attracted the interest of many researchers. In 2019, Kao et al. evaluated the high performance of the LRM data of the Cryosat-2 satellite and the Ka-band data of the SARAL/AltiKa satellite in Taiwan. The experimental results illustrated that the measurement accuracy of SARAL/AltiKa is better than that of Cryosat-2 [12]. In 2021, Chen et al. used the HY-2B altimeter (Pass No. 362 and Pass No. 375) to measure the Sea Surface Height (SSH) of the Wanshan calibration station and used the geoid model data to improve the calibration accuracy. It is concluded that the altimetry deviation of the HY-2B satellite is about 2.12 cm [13]. Currently, relying on the coexistence of multiple observation methods, it is urgent to carry out the research on the comparison of tidal level monitoring accuracy. Two altimetry satellites, HY-2B and Jason-3, are selected near the GNSS BUR2 station. The advantages and disadvantages of the tidal level monitored by the two methods in terms of temporal resolution and accuracy were explored. The data and methods are introduced in Sect. 2, which mainly introduces the geographical location of the station and its original data, the unification of time datum, the conversion of elevation datum, the principle of GNSS-IR technology and satellite altimetry technology. Section 3 conducts precision comparison experiment based on the data of 2021. The conclusions are drawn in Sect. 4.

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2 Datasets Description 2.1 Datasets The BUR2 station is set up by Geoscience Australia (GA), located in BURNIE (Latitude: −41.0501°, Longitude: 145.9148°) in the southeast corner of Australia, with a receiver type SEPT POLARX5 and a receiver antenna type LEIAT504 SCIS. This station’s observation file sampling interval is 30 s, and GA provides the data (ftp://ftp.data.gnss.ga.gov. au/daily/2021/). In addition, a tide gauge station named BURNIE (BURTG) is located 2 m away from the GNSS station. The Australian Government Bureau of Meteorology (BOM) provides the measured sea level data (http://www.bom.gov.au/oceanography/) with a sampling interval of 1 h. The HY-2B satellite, launched on October 25, 2018, successfully continued the mission of the HY-2A satellite. The raw data used in this study are the data of the secondlevel products after inversion through the first-level product data and after sea and land identification and quality control. Level 2 product data is divided into three products: Interim Geophysical Data Records (IGDR), Sensor Geophysical Data Records (SGDR) and Geophysical Data Records (GDR). The nominal satellite altitude is approximately 971 km. The repeat cycle for the HY-2B satellite is 14 days of the earth’s surface (ocean and land) from 80.70°N to 80.70°S with a theoretical 386 tracks per cycle [14]. HY-2B altimeter data used in this study were level 2 1-Hz SGDR data in 2021 (from Cycle 0058, Pass 0043 to Cycle 0083, Pass 0043) distributed by the NSOAS, Ministry of Natural Resources of the People’s Republic of China (https://osdds.nsoas.org.cn/maps_SeaActi onLink). In addition, the Ku-band (13.58 GHz) data, considered more accurate than the C-band (5.25 GHz), were also utilized in this study. The Jason-3 satellite is an international cooperative satellite altimetry mission satellite that was cooperatively launched by the NASA, National Oceanic and Atmospheric Administration (NOAA), European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) and Center National d’Etudes Spatiales (CNES), which was launched on 17 January 2016. The Jason-3 missions are primarily equipped with dual-frequency radar altimeters (Ku-band and C-band, 13.575 GHz and 5.3 GHz, respectively) that operate in the conventional Low-Resolution Mode (LRM) [15]. Jason-3 is on a 10-day repeat cycle orbit at an altitude of 1336 km and a 66° inclination [16]. Therefore, Jason-3 altimeter data used in this study were the same as HY-2B altimeter data (SGDR data of level 2 with 1-Hz Ku-bands in 2021, from Cycle 181, Pass 088 to Cycle 216, Pass 088) (https://tds.aviso.altimetry.fr/thredds/catalog/dataset-l2-geophy sical-data-record-jason-3-sgdr-f/catalog.html). The geographical location of the BUR2 station in this study is shown in Fig. 1(a). It is located directly on the coast, which is very suitable for studying GNSS-IR sea level inversion. In Fig. 1(b and c), the BUR2 stations is represented by red triangles. The research interval of HY-2B and Jason-3 for the satellite altimetry experiment in 2021 is the oceanic range of longitude 145.3°−146.2°, latitude −41.1°−40.4°, which is framed by the solid black line in Fig. 1(c).

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Fig. 1. Location of BUR2 station

2.2 Unification of Time Bases This study unified the time base as UTC to unify the time bases of GNSS-IR, satellite altimetry, and tide gauge stations. The time reference corresponding to GNSS-IR is given by the header file of the station observation file. The time base specified in the header file of the BUR2 station is GPS time. GPS time was aligned with UTC at 0:00 on January 6, 1980. Today, the GPS and UTC time scales are off by 18 s. In the sea area where the sea level fluctuates wildly, a time delay of 18 s will cause a cm-level error, which can not be ignored in the BUR2 station. The time of satellite altimetry is UTC, and the time base in the NC file of the NetCDF format data set is in seconds, referring to 00:00:00.00 on January 1, 2000, so it needs to be converted to the time in date format. The time base corresponding to the tide gauge station is indicated as UTC in the data description (http://www.bom.gov.au/oceanography/projects/abslmp/data/data. shtml), so no time base conversion is required. 2.3 Elevation Datum Conversion The essence of GNSS-IR technology is to use the change of SNR caused by the multipath effect to calculate the vertical reflection distance hR from the antenna phase center to the reflecting surface. Then, the vertical reflection distance hR is subtracted from the height of the station h (h = a + b−c), and the height of the sea level relative to the measured sea level reference TGZ (Tide Gauge Zero) of the tide gauge station can be obtained. Among them, a = 3.9 m represents the height from the BUR2 station to the reference ellipsoid, which is given by the bur2_20210721.log file (https://www.sonel.org/spip. php?page=gps&idStation=2056) provided by Systeme d’ Observation du Niveau des Eaux Littorales (SONEL). b = 8.573 m, representing the height from the reference

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ellipsoid to Revised Local Reference (RLR), obtained from the Ellipsoidal information provided by Permanent Service for Mean Sea Level (PSMSL) (https://www.psmsl.org/ data/obtaining/rlr.diagrams/683.php). c = 5.100 m, indicating the distance from TGZ to RLR, also supplied by SONEL (https://www.sonel.org/spip.php?page=nivellement& idStation=2178). The principle of satellite altimetry is to use the height of the satellite altimeter relative to the reference ellipsoid (Altitude) to subtract the distance from the satellite altimeter to the sea level (Range) to obtain the distance from the sea level to the reference ellipsoid (Halt ). To evaluate the tidal level monitoring accuracy of GNSS-IR and satellite altimetry technology, the tidal height Halt obtained by satellite altimetry is converted to the height with the Mean Sea Level (MSL) as the reference datum by correcting the parameter HMSS of the Mean Sea Surface (MSS) model. By adding a constant HMT , it is converted to the height relative to the measured sea level reference TGZ of the tide station. Among them, HMT =1.977 m, representing the absolute height from MSL to TGZ, provided by the RLR Diagram for BURNIE of PSMSL (https://www.psmsl.org/data/obtaining/rlr. diagrams/683.php). Figure 2 displays the schematic diagram of the BUR2 station using GNSS-IR technology and satellite altimetry to retrieve sea level height and its reference conversion diagram.

Fig. 2. Diagram of shore-based GNSS-IR tide level monitoring technology, satellite altimetry technology and datum conversion

2.4 Principle of GNSS-IR Technology In Fig. 2, D1 is the distance from the reflection point to the receiver, D2 is the distance less traveled by the incident signal to the ground than the direct signal received by

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the receiver, and D is the path delay caused by multi-path effect during satellite signal propagation. Taking GLONASS-S2P-11 satellite on April 28, 2021 (DOY118) as an example, Fig. 3 shows the change of δSNR with time and elevation angle. The left ordinate is the value range of SNR and δSNR respectively, and the right ordinate is the value range of corresponding elevation angle. At the same time, it shows the complete lifting process of GLONASS. The part enclosed by a black rectangle at both ends is SNR and δSNR trend of 5°–15°. Lomb-Scargle spectral Periodogram (LSP) analysis was performed on the δSNR, and the frequency f of the δSNR was obtained as: 2π f =

4π hR d ϕ = d sin(e) λ

(1)

where, λ is the wavelength of different frequencies and e is the satellite elevation angle. From this, the vertical reflection distance hR can be obtained as: hR =

λf 2

(2)

Fig. 3. δSNR variation with time and elevation angle

2.5 Principle of Satellite Altimetry Technology At first, Table 1 gives the satellite correction parameters and their sources of HY-2B and Jason-3. All geophysical corrections used in this study are taken from the altimetrik data sets. The main formula of satellite altimetry can be expressed as: Halt = Altitude − Range − Correction

(3)

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where, Halt represents the height from the instantaneous sea level to the reference ellipsoid, Altitude represents the height of the satellite altimeter relative to the reference ellipsoid, Range represents the height from the satellite altimeter to the instantaneous sea level, Correction means all correction values that need to be corrected. Its formula can be expressed as: Correction = Hdry + Hwet + Hion + Hpole_tide + Hearth_solid _tide + Hload _tide_sol1 + HSSB

(4)

where, Hdry represents dry tropospheric correction, Hwet represents wet tropospheric correction, Hion represents ionospheric correction, and Hpole_ tide represents polar tide correction, Hearth_ solid_ tide represents earth solid tide correction, Hload_ tide_ sol1 represents load tide correction, HSSB represents the correction effected by the Sea State Bias (SSB). The SSB is one of the main errors that tend to result in the deterioration of SSHs in altimetric measurements, which is aroused due to the waves. Before the satellite altimetry results are compared to the GNSS-IR results, the altimetry results need to be converted to the elevation reference datum of the tide gauge station. The longitude and latitude of the sub-satellite point at different times of different satellites are slightly different. For this reason, this study introduces the MSL elevation reference datum and converts the Halt with the reference ellipsoid as the elevation reference datum to the height with the MSL as the elevation reference datum through the MSS correction parameter HMSS . The MSL reference datum and the TGZ reference datum have a constant HMT , from which the specific conversion formula can be obtained as follows: Halt_TGZ = Halt − HMSS + HMT

(5)

where, Halt_TGZ represents the sea level height obtained by satellite altimetry relative to the TGZ reference datum.

3 Comparison and Characterization of Tide Level Monitoring Between GNSS-IR and Satellite Altimetry In this section, the data of the BUR2 station in 2021 is used to investigate sea level height retrieval by GNSS-IR technology and satellite altimetry, respectively. Simultaneously, three evaluation parameters, Correlation Coefficient (R), Root Mean Square Error (RMSE) and Mean Error (ME), are used to evaluate the inversion accuracy of sea level height. GNSS-IR and satellite altimetry are two different sea level monitoring technologies. Therefore, the monitoring accuracy is bound to be different. To evaluate the monitoring effect, this section uses the data in 2021 to carry out the GNSS-IR experiment of the BUR2 station and the satellite altimetry experiment of the nearby sea area. Figure 4(a) expresses the satellite sky plots of the BUR2 station. It can be found that there is no satellite trajectory in the south of the station because the station is located in the southern hemisphere of the earth. The plots represent not only the azimuth range and elevation angle but also the coverage area [17]. Sky plots showing the satellite tracks for GPS (G), GLONASS (R), Galileo (E) and BDS (C) on DOY118, 2021. The curve formed by

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N. Zheng et al. Table 1. Sources of the main parameters for satellite altimetry

Parameter

HY-2B

Jason-3

Institution

National centers for environmental prediction (NCEP)

Centre National d’Etudes Spatiales (CNES)

File data type

SIDR

GDR-expertise dataset

Altimeter sensor Name

HY2_RA1

Poseidon-3B

Radiometer sensor name

CMR

AMR

Cycle number

0058–0083

181–216

Pass number

0043

088

Tidal loading

GOT4.10c

GOT4.10c

Dry tropospheric

NCEP

European center for medium range weather forecasting (ECMWF)

Wet tropospheric

NCEP

ECMWF

Ionospheric correction

HY-2B RA-NSOAS

GIM-NASA/JPL

Pole tide

Wahr (1985) Deformation of the earth induced by polar motion

Desai, S., Wahr, J. & Beckley, B. J Geod (2015) 89: 1233

Solid earth tide

Cartwright and Edden (1973) Corrected tables of tidal harmonics. J. Geophys. J. R. Astr. Soc., 33, 253–264

Cartwright and Edden (1973) Corrected tables of tidal harmonics. J. Geophys. J. R. Astr. Soc., 33, 253–264

Sea state bias

Empirical solution fitted on HY-2A data

Tran 2020 empirical solution fitted on one year of Jason-3 GDR_F data from MLE4 retracking

Mean sea surface

MSS_CNES_CLS-2015

MSS_CNES_CLS-2015

all the sub-satellite points during the satellite’s movement around the earth is called the sub-satellite point trajectory. The point where the line connecting the satellite’s centroid and the earth’s center intersects the Earth’s surface is called the sub-satellite point. The sub-satellite point trajectories of all cycles of HY-2B and Jason-3 in 2021 are shown in Fig. 4(b) and (c). The satellite sub-satellite points of each cycle are relatively concentrated and only produce a slight offset. To compare the monitoring effects of sea level height retrieved by GNSS-IR, HY-2B and Jason-3, Fig. 5 demonstrates the comparison diagram between the inversion sea level height and the sea level measured by the tide gauge station and its correlation analysis diagram. Figure 5(a) and (d) denote the effect of sea level height retrieved by GNSS-IR technology after removing the triple mean square error. It can be seen from the figure

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Fig. 4. The sky map of BUR2 station and sub-satellite point trajectories of all cycles of HY-2B and Jason-3 satellites in 2021

that the rose-gray scatter points are in good agreement with the measured sea level and have good inversion accuracy, with R of 0.957, RMSE of 0.257 m and ME of −0.008 m. The number of sea levels retrieved reaches 73,936, which has a high time resolution and is very suitable for sea level fitting. In recent years, the sea level measured by GNSS-IR can reach centimeter level, but the measured results in this study are worse. It is speculated that there may be two reasons as follows: On the one hand, the inversion difference is caused by different stations and different surrounding environments. On the other hand, part of the research only shows the stations with high data accuracy, which easily makes the public misunderstand the accuracy of the method. Figure 5(b) and (e) reveal the sea level inversion results obtained by the HY-2B satellite altimetry. The pink-green scatter points represent the sea level height at a particular instant obtained by satellite altimetry. The R retrieved from HY-2B 1-year data is 0.994, the RMSE is 0.105 m, and the ME is 0.025 m. Although the inversion accuracy is significantly better than the GNSS-IR technology, the number is only 178. Moreover, it can also be seen from the schematic diagram of the correlation analysis that the scattered points are concentrated on both sides of y = x, indicating that the satellite altimetry has a high tidal level monitoring accuracy. Figure 5(c) and (f) manifest the sea level inversion effect obtained by the Jason-3 satellite altimetry. Likewise, the wheat-seedlings-green scatter points represent sea level heights from the Jason-3 satellite altimetry. Its one-year data inversion has an R of 0.995, an RMSE of 0.113 m, an ME of -0.040 m and a number of 461. The inversion accuracy is roughly equivalent to HY-2B, maintaining a high sea level monitoring accuracy.

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It can be seen from the above analysis that the sea level retrieved by GNSS-IR technology has a higher temporal resolution. In contrast, the sea level retrieved by satellite altimetry (HY-2B and Jason-3) has higher accuracy. Therefore, the two can form a straightforward compliment, which is very suitable for research of sea level inversion.

Fig. 5. Diagram of sea level height retrieved by GNSS-IR technology and obtained by satellite altimetry (HY-2B and Jason-3)

4 Conclusions This study mainly investigates the accuracy of tidal inversion and its characteristics of GNSS-IR and satellite altimetry (HY-2B and Jason-3) at the BUR2 station in 2021, and its specific experimental findings are as follows. (1) The GNSS-IR technique has better inversion accuracy, with R of 0.957, RMSE of 0.257 m, ME of −0.008 m, and the number of 73,936. (2) HY-2B satellite altimetry obtained R of 0.994, RMSE of 0.105 m, ME of 0.025 m, and the number of 178. (3) Jason-3 satellite altimetry obtained R of 0.995, RMSE of 0.113 m, ME of −0.040 m, and the number of 461. It is concluded that the tide level inversion by GNSS-IR technique has a high temporal resolution, while the tide level inversion by satellite altimetry (HY-2B and Jason-3) has a high accuracy. However, the conclusion of this study is only for the BUR2 station experiment, the conclusions of different stations may be slightly different, still need to be specific station specific analysis.

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Acknowledgments. This study was supported by the National Natural Science Foundation of China (42074014).

References 1. Jin, S., Qian, X., Wu, X.: Sea level change from BeiDou navigation satellite systemreflectometry (BDS-R): first results and evaluation. Global Planet. Change 149, 20–25 (2017) 2. Larson, K.M., Ray, R.D., Nievinski, F.G., et al.: Levelling co-located GNSS and tide gauge stations using GNSS reflectometry. IEEE Geosci. Remote Sens. Lett. 10(5), 1200–1204 (2013) 3. Martin-Neira, M.: A passive reflectometry and interferometry system (PARIS): application to ocean altimetry. ESA J. 17(4), 331–355 (1993) 4. Löfgren, J.S., Haas, R., Scherneck, H.-G., et al.: Three months of local sea level derived from reflected GNSS signals. Radio Sci. 46(6) (2011) 5. Jin, S., Feng, G.P., Gleason, S.: Remote sensing using GNSS signals: current status and future directions. Adv. Space Res. 47(10), 1645–1653 (2011) 6. Wang, X., Zhang, Q., Zhang, S.: Sea level estimation from SNR data of geodetic receivers using wavelet analysis. GPS Solut. 23(1), 6 (2019) 7. Zheng, N., Chen, P., Li, Z.: Accuracy analysis of ground-based GNSS-R sea level monitoring based on multi GNSS and multi SNR. Adv. Space Res. 68(4), 1789–1801 (2021) 8. Hu, Y., Yuan, X., Liu, W., et al.: GNSS-IR model of sea level height estimation combining variational mode decomposition. IEEE J. Select. Top. Appl. Earth Observ. Remote Sens. 11 (2011) 9. Dubey, A.K., Gupta, P., Dutta, S., et al.: Water level retrieval using SARAL/AltiKa observations in the Braided Brahmaputra River, Eastern India. Mar. Geodesy 38(sup1), 549–567 (2015) 10. Schwatke, C., Dettmering, D., Börgens, E., et al.: Potential of SARAL/AltiKa for inland water applications. Mar. Geodesy 38(sup1), 626–643 (2015) 11. Verron, J., Sengenes, P., Lambin, J., et al.: The SARAL/AltiKa altimetry satellite mission. Mar. Geodesy 38(sup1), 2–21 (2015) 12. Kao, H.-C., Kuo, C.-Y., Tseng, K.-H., et al.: Assessment of cryosat-2 and SARAL/AltiKa altimetry for measuring inland water and coastal sea level variations: a case study on Tibetan Plateau lake and Taiwan Coast. Mar. Geodesy 42(4), 327–343 (2019) 13. Chen, C., Zhu, J., Ma, C., et al.: Preliminary calibration results of the HY-2B altimeter’s SSH at China’s Wanshan calibration site. Acta Oceanol. Sin. 40(5), 129–140 (2021) 14. Wang, J., Xu, H., Yang, L., et al.: Cross-calibrations of the HY-2B altimeter using Jason-3 satellite during the period of april 2019–september 2020. Front. Earth Sci. 9, 647583 (2021) 15. Yang, L., Xu, Y., Lin, M., et al.: Monitoring the performance of HY-2B and Jason-2/3 sea surface height via the China altimetry calibration cooperation plan. IEEE Trans. Geosci. Remote Sens. 60, 1–13 (2022) 16. Biancamaria, S., Schaedele, T., Blumstein, D., et al.: Validation of Jason-3 tracking modes over French rivers. Remote Sens. Environ. 209, 77–89 (2018) 17. Altuntas, C., Tunalioglu, N.: Feasibility of retrieving effective reflector height using GNSSIR from a single-frequency android smartphone SNR data. Digital Signal Proc. 112, 103011 (2021)

Performance Assess of BDS-3 PPP-B2b Signal Service and Its Application in Precipitable Water Vapor Retrieval Ying Xu1 , Panpan Zhao1 , Jin Wang1,2(B) , and Xiangdan Meng1 1 College of Geodesy and Geomatics, Shandong University of Science and Technology,

Qingdao 299590, China [email protected] 2 State Key Laboratory of Geo-Information Engineering, Xi’an 710000, China

Abstract. The BDS-3 PPP-B2b signal provides the high-precision real-time precise point positioning (RTPPP) service for China and its surrounding areas, without relying on the internet communication to data reception. This technology can provide precise positioning services and Precipitable Water Vapor (PWV) retrieval services for open seas in eastern China, remote areas in Asian countries, as well as regions where communication system destroyed by disasters. For the limited studies exploring the BDS-3 PPP-B2b performance of signal service and application in PWV retrieval, this paper used one-month observation data from 8 IGS MGEX stations in China and neighboring countries to analyze the service capability of the PPP-B2b signal. The results show that the B2b orbit product’s precision in radial (R), along (A), and cross (C) directions are better than 0.08, 0.25, and 0.30 m, respectively. The standard deviation (STD) of clock offsets is better than 0.23 ns. The accuracy of static PPP solutions is at the centimeter level, while it is at the decimeter level for the dynamic PPP solutions. The central stations have better results than those at the boundary of the service areas. For exploring the application of the PPP-B2b signal in the retrieval application service of PWV, the zenith tropospheric delay (ZTD) is estimated based on the PPP-B2b signal, which is highly consistent with the results from the WUM analysis center products. The accuracy of the root mean square (RMS) is 3.41mm and the STD is 2.84 mm for PWV retrieval products based on PPP-B2b, which compared with the post-production. The RMS for the boundary station is less than 4 mm, meeting the accuracy requirements. The experiments indicate that the PPP-B2b signal can provide precise positioning services for the service areas, where lack of communication, and provide more reliable data for applications such as real-time numerical weather prediction. Keywords: BDS-3 · PPP-B2b · Service performance · ZTD · PWV

1 Introduction On December 27, 2019, the China Satellite Navigation System Management Office (CSNSMO) released the B2b signal for Radio Navigation Satellite System (RNSS) service and the PPP-B2b signal for precise point positioning service. The PPP-B2b signal © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 118–131, 2024. https://doi.org/10.1007/978-981-99-6928-9_11

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is broadcasted by GEO satellites, which support the real-time precise point positioning (RTPPP) services for users in China and its surrounding areas [1]. The PPP-B2b signal has the capability to broadcast precise correction messages for 26 BDS-3 satellites, which can greatly enhance the research, development, and application of the RTPPP [2]. However, due to its short opening time, research on the PPP-B2b service is still in the early stages. In a recent study, He et al. analyzed the message broadcasted by the PPP-B2b signals [3]. Nie et al. conducted an evaluation of the PPP-B2b service. In their study, the accuracy of satellite orbit and clock errors was analyzed using 3 days PPP-B2b signals. Their analysis revealed that the accuracy of BDS-3 satellite orbit in radial, along, and cross directions was 0.138, 0.131, and 0.145 m, respectively. Similarly, the corresponding accuracy of GPS satellite orbit was 0.104, 0.160, and 0.134 m in the radial, along and cross directions, respectively [4]. Tang et al. processed the PPP-B2b signal of four stations in China and found that the PPP horizontal accuracy (95%) of the BDS system is better than 30 cm, the vertical direction is better than 60 cm, and the average convergence time is less than 30 min [5]. Similarly, Ren et al. evaluated the positioning performance of the real-time PPP using 10 iGMAS stations in China and neighboring countries, while no in-depth research was conducted on the service range of PPP-B2b signals [6]. At present, research on PPP-B2b service is mainly focused on evaluating iGMAS stations in China in terms of correction and positioning accuracy, with few evaluations conducted at sea or in other countries. In this paper, the service performance of PPP-B2b signals is evaluated using eight IGS MGEX stations distributed in China and neighboring countries. Specifically, we focus on evaluating the correction accuracy, correction availability, and positioning accuracy of the PPP-B2b service. This study seeks to contribute to a deeper understanding of the performance of PPP-B2b signals, particularly in areas beyond the scope of previous research. Currently, global climate change is causing irregular weather patterns, leading to an increase in rainstorm disasters, which seriously affect human production and life. Therefore, accurate and systematic monitoring of atmospheric water vapor is crucial for early warning of natural disasters [7]. The precipitable water vapor (PWV) is a significant indicator for measuring atmospheric water vapor. The accurately monitoring its changes can help improve the predictions accuracy for rainstorm disasters to reduce the losses of personnel and property. Traditional methods for observing water vapor primarily include radiosondes, microwave radiometers, and satellite remote sensing. Radiosonde (RS) is one of the most accurate methods for detecting water vapor; However, it unsuitable for small and medium-scale meteorological research because of the low temporal resolution, sparse site distribution, and high cost [8, 9]. As the development of the Global Navigation Satellite System (GNSS), the concept of GNSS meteorology was initially introduced in the 1990s [10]. The GNSS water vapor detection technology offers high resolution, low cost, continuous observation, high precision, and is immune to adverse environmental conditions. Consequently, monitoring atmospheric water vapor using GNSS technology has been extensively applied. Rocken et al. demonstrated that the PWV calculated based on GPS is equivalent to the PWV obtained by radiosonde and microwave radiometer [11]. Zhang et al. confirmed that GPS real-time data can be used to obtain PWV with an accuracy better than 3 mm [12]. Gao et al. used BDS to obtain PWV, which the accuracy

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is comparable to GPS [13]. With the launch of the BDS-3 PPP-B2b signal service, the advantage of not dependent on the internet provides a new means for the retrieval of precipitable water vapor. Xu et al. conducted an experiment at Shanghai, using GPS observation data, BDS-3 observation data, broadcast ephemeris, and PPP-B2b correction data. They employed GPS/BDS-3 combined static PPP to estimate zenith tropospheric delay (ZTD) and invert PWV. The results showed that the ZTD and GAMIT results obtained from BDS-3 PPP-B2b products have the same overall trend. The mean absolute error (MAE) for the PWV estimation is 3.23 mm and the root mean square error (RMSE) is 4.03 mm [14], when compared to radiosonde data. Currently, there are limited studies on the feasibility of using BDS-3 PPP-B2b signal service for atmospheric precipitable water. The existing research is based on domestic stations, and in-depth analysis of it is necessary within the service scope. This paper aims to conduct atmospheric water vapor retrieval based on PPP-B2b signals, using 8 IGS MGEX stations which China and the edge of the service scope. Firstly, this paper introduces the recovery method of BDS-3 PPP-B2b signals and the principle of PWV retrieval based on signal service. Then, 8 IGS MGEX stations in China and neighboring countries are used to analyze the scope of the service and capability of PPP-B2b signals. Finally, the accuracy of PWV retrieval based on PPP-B2b service using BDS-3 observation data is analyzed and the conclusions are discussed.

2 Methodology This paper evaluates the service range and service capability of BDS-3 PPP-B2b signal, and analyzes the application of atmospheric water vapor retrieval based on PPP-B2b signal. In this section, the PPP model and the PPP-B2b signal correction method are introduced, and the atmospheric water vapor retrieval model is presented. 2.1 The Theoretical Methods of PPP (1) PPP model In dual-frequency PPP data processing, the ionosphere-free combination is usually used to eliminate the influence of the first-order term of the ionospheric delay. The pseudorange and phase ionosphere-free combination observation equations can be expressed as [15]. s PIF,r =

=

ρrs

LsIF,r = =

ρrs

s − f 2 Ps f12 P1,r 2 2,r

f12 − f22

+ c(dtr − dt ) + Mwet · ZWD s

f12 Ls1,r f12

− f22 Ls2,r − f22 s

+ c(dtr − dt ) + Mwet · ZWD

(1) + λbsr,IF

+ εP,IF (2)

s + λBr,IF

+ εL,IF

s, where r is the receiver, s is the satellite, i is the frequency (i = 1, 2), PIF,r and LsIF,r are the pseudo-range, phase ionosphere-free combination observations, respectively;

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c denotes the speed of light in vacuum; fi , Pi and Li are frequency, ionosphere-free combined pseudorange and phase observations, respectively; ρrs is the geometrical range between the satellite and the receiver; dt r and dt s are clock offsets for receiver and satellite, respectively; Mwet is the ZWD mapping function; ZWD is the zenith wet delay at the station, and the Zenith Hydrostatic Delay (ZHD) is corrected by model; pseudorange hardware biases; λ is the wavelength of the ionosphere-free combination; bsr,IF is phase hardware bias and ambiguity, εP,IF and εL,IF are the pseudorange and carrier phase multipath effects and other unmodeled errors, respectively. bsr,IF is the pseudorange hardware biases; λ is the wavelength of the ionosphere-free combination; bsr,IF is phase hardware bias and ambiguity, εP,IF and εL,IF are the pseudorange and carrier phase multipath effects and other unmodeled errors, respectively. (2) Orbit correction There are three orbital correction parameters of PPP-B2b signal, which are the components of orbital correction vector in along, radial and cross directions. The implementation process of orbit correction with the orbital parameters of PPP-B2b signal is as follows: (1) Using Beidou broadcast ephemeris to calculate the position of Beidou satellite. (2) The IODE of the navigation message is matched with the IODN in the orbit correction message. (3) Calculate the satellite position correction vector δX , which is denoted as [2]: ⎧ r ⎪ ⎨ eradial = |r| r×˙r (3) ecross = |r×˙r | ⎪ ⎩ ealong = ecross × eradial δX = [ealong ecross eradial ] · δO

(4)

where r is the position vector calculated by the broadcast ephemeris, r˙ is the velocity vector calculated by the broadcast ephemeris, eradial is the unit vector in the radial direction, ecross is the unit vector in the cross direction, and ealong is the unit vector in the along direction. (4) Calculate the corrected satellite position, the formula is as follows: Xorbit = Xbrdc − δX

(5)

(3) Clock correction For satellite clock offset corrections, its IOD Corr firstly is matched to that in orbit corrections. Then, the matched satellite clock correction is used to recover the precise clock offsets with the coarse value calculated by the broadcast ephemeris. The calculation formula is as follows: C0 (6) ts−c = tbrdc − C where ts−c represents the corrected satellite clock offsets correction, tbrdc represents the satellite clock offsets correction calculated by the broadcast ephemeris, C0 represents the clock offsets correction parameter provided by PPP-B2b, and C is the speed of light. After successfully matching the orbit correction information and clock correction information of the PPP-B2b signal with the navigation message, the corrections can be used in RTPPP.

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2.2 The Atmospheric Water Vapor Retrieval Method Based on PPP-B2b Signal In data processing, the tropospheric delay of GNSS observations in the zenith direction satisfies the following relationship [16]. ZTD = ZWD + ZHD

(7)

where ZHD is Zenith Hydrostatic Delay, which is calculated and corrected by Saastamoinen model in this paper. ZWD is Zenith Wet Delay, which is calculated as an unknown parameter in Eq. (2). After calculating ZWD, PWV can be further calculated from the following conversion equation [17]: PWV =  · ZWD

(8)

where  is the conversion coefficient between ZWD and PWV, which is denoted as:    −1 k3 6  = 10 Rv ρw _ + k2 × 100(Pa/hPa) (9) Tm where Rv is the water vapor gas constant, the specific value is 461.495 (J ·Kg −3 ·K −3 ), ρW is the liquid water density, the value usually is 461.495 (Kg/K −3 ), K2 , K3 are constants, Tm is the atmospheric weighted average temperature, which can be obtained by Bevis formula Tm = 70.2 + 0.72T, T is the site atmospheric temperature, the unit is K, and the root mean square error of Tm calculated by Bevis formula in the mid-latitude region is 4.74K [10].

3 Evaluation of the PPP-B2b Signal Service Range In order to study the service range of PPP-B2b signal, this section selects the data from July 6 to August 4, 2021. The PPP-B2b correction, CNAV broadcast ephemeris, postprecision ephemeris and BDS-3 observation data are adopted in this experiment. The PPP-B2b correction comes from the FeiNa receiver. In this section, the accuracy of satellite orbit and satellite clock offset corrected by PPP-B2b signals is firstly evaluated. Secondly, the number of the effective satellite which can receive the corrections for the selected station, the availability ratio of PPP-B2b signal and the positioning accuracy under static and pseudo-dynamic conditions are analyzed. 3.1 Accuracy Evaluation of Satellite Orbit Corrected by PPP-B2b Signal To evaluate the satellite orbit accuracy after PPP-B2b signal correction, this paper used the final precision product of WUM as the reference. Figure 1 shows the radial, along and cross components of the difference between the satellite orbit corrected by PPPB2b signal and the reference true value of DOY187 in 2021. It can be seen that the orbit accuracy in the radial direction is always higher than that in the along and cross directions. To obtain the statistical results, 30-day data, including the PPP-B2b correction and CNAV1 navigation message, from DOY187 to DOY216 in 2021 is used to calculate

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Fig. 1. PPP-B2b real-time precise satellite orbit errors series.

Fig. 2. The RMS of PPP-B2b real-time precision satellite orbit errors.

the orbit accuracy of MEO satellite and IGSO satellite of BDS-3 with PPP-B2b signal correction. Figure 2 shows the RMS values of the orbital errors. To intuitively analyze the accuracy of the two orbits, the corresponding average RMS and STD statistics of the BDS-3 MEO satellite and BDS-3 IGSO satellite are listed in Table 1. The average RMS of MEO satellite orbit error in radial, along and cross directions are 7.16 cm, 21.45 cm and 18.09 cm, respectively. In contrast, the accuracy of IGSO satellite is poor. The average RMS of orbit error in radial, along and cross directions are 15.56 cm, 33.25 cm and 27.09 cm, respectively. Table 1. Table captions should be placed above the tables. Type

MEO satellite (cm)

IGSO satellite (cm)

R

A

C

R

A

C

RMS

7.16

21.45

18.09

15.56

33.25

27.09

STD

2.88

6.90

8.48

10.34

12.63

15.34

3.2 Accuracy Evaluation of Satellite Clock Offset Corrected by PPP-B2b Signal To evaluate the satellite clock offset accuracy after PPP-B2b signal correction, this paper used the final precision product of WUM as the reference. Figure 3 shows the satellite clock offset corrected by PPP-B2b signals on DOY187 in 2021.

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Fig. 3. PPP-B2b real-time precise satellite clock offset series.

To obtain the statistical results, 30-day data, including the PPP-B2b correction and CNAV1 navigation message, from DOY187 to DOY216 in 2021 is used to calculate the STD of each satellite clock offsets of the BDS-3. The STD of PPP-B2b real-time precision satellite clock offset of almost all satellites is within 0.3 ns, and its average clock offset STD is 0.189 ns, which is comparable to the accuracy of the current post-precision products. 3.3 Evaluation of PPP-B2b Service Performance BeiDou Navigation Satellite System Open Service Performance Standard (Version 3.0) points out that the BDS can provide the PPP service to users in China and its surrounding areas in the scope of 10° N ~ 55° N, 75° E ~ 135° E, on the surface of the Earth and its near-earth areas extending within 1,000 km above the Earth surface. The paper selected eight IGS MGEX stations distributed in China and neighboring countries. The specific distribution of each station is shown in Fig. 4. JFNG (Wuhan) and URUM (Urumqi) located in China, and GAMG (South Korea), USUD (Japan), ULAB (Mongolia), LCK4 (Uttar Pradesh), PTGG (Philippines) and IISC (India) located in China’s neighboring countries. After that, the dual-frequency ionosphere-free combination of B1I frequency and B3I frequency is used to perform PPP positioning experiments in static mode and dynamic mode respectively.

Fig. 4. Station location.

As shown in Fig. 5, the number of PPP-B2b signal effective correction satellites at JFNG station, PTGG station and IISC station of DOY187 in 2021. The number of available satellites for JFNG, PTGG and IISC stations decreased in turn. The reason is that the three stations are distributed from the center of the service range to the boundary.

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Fig. 5. The number of PPP-B2b effective correction satellites at JFNG, PTGG and IISC stations.

To further analyze the PPP-B2b signal service range, 30-day data, from DOY187 to DOY216 in 2021 is used to calculate the average number of visible satellites, the average number of available PPP-B2b correction satellites, and the average PPP-B2b correction availability rate of the selected 8 stations. As shown in Table 2, the BDS-3 can provide more than 11 visible satellites for users in China and surrounding areas, and the average number of available PPP-B2b correction satellites vary from 7 to 9. The average PPP-B2b correction availability rate of each station decreases with the increase of the distance from the center of the PPP-B2b service area. The JFNG station had the highest availability, which is 74%, while the IISC station had the lowest availability, which is 51.44%. Table 2. The average number of visible satellites, the average number of available PPP-B2b correction satellites, and the average PPP-B2b correction availability rate of the selected 8 stations Stations

The average number of visible satellites

The average number of available PPP-B2b correction satellites

The average PPP-B2b correction availability rate%

jfng

11.62

8.60

74.01

gamg

13.90

9.06

65.18

urum

14.82

8.20

55.33

ptgg

14.15

8.41

59.48

iisc

13.93

7.16

51.44

lck4

12.28

7.68

62.60

ulab

14.15

8.28

58.55

usud

12.09

7.80

64.51

In this paper, the positioning accuracy of PPP-B2b signal is evaluated by using the known coordinates of IGS weekly solution file stations as reference. In Figs. 6 and 7, the positioning errors of B2b PPP at the JFNG, PTGG and IICS on E, N, and U components are showed for the static positioning mode and the kinematic positioning mode. Similar results can be obtained by other stations in the study time interval. It can be seen from Figs. 6 and 7 that the positioning error and convergence speed of JFNG station are slightly better than those of PTGG station and IISC station. The

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Fig. 6. Positioning error series of static positioning mode PPP.

Fig. 7. Positioning error series of kinematic positioning mode PPP.

possible reason is that the JFNG station has more available satellites. As shown in Figs. 6 and 7, JFNG station has better positioning accuracy and convergence speed than PTGG and IISC. The possible reason is that the JFNG had more available satellites. The updirection error of JFNG station is basically consistent with the east direction and north direction error. While, for PTGG station and IISC station, the error in the up direction is obviously larger than that in the east and north directions. To further analyze the PPPB2b signal service capability, 30-day data, from DOY187 to DOY216 in 2021 is used to calculate the positioning results using the selected 8 stations. The RMS of E, N, and U components, horizontal (H), and 3-dimensions (3D) for 8 stations on static positioning mode and kinematic positioning mode regarding B2b PPP are calculated and listed in Table 3. In the static positioning mode, the error RMS of the E, N, and U components of all stations are similar, and can reach centimeter-level accuracy. In all stations, the error RMS in the north direction is smaller than that in the east and up directions. The error RMS in the 3D of all stations varies from 3 to 8 cm, and the RMS of the JFNG station is the best. In the kinematic positioning mode, even at the edge of the PPP-B2b service area, the 3D error is kept within 31 cm, which indicates that the PPP-B2b service can provide decimeter-level kinematic PPP positioning services for all users in the service area.

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Table 3. Positioning results of PPP-B2b service. Stations

Static (cm)

Kinematic (cm)

E

N

U

H

3D

gamg

3.8

0.5

1.6

3.8

4.1

iisc

1.9

2.3

4.2

3.0

5.2

jfng

1.7

0.7

2.3

1.9

lck4

1.0

1.4

7.5

1.7

ptgg

2.0

0.3

2.9

ulab

1.5

0.5

urum

1.7

1.5

usud

4.1

0.9

E

N

U

H

3D

8.2

5.7

16.0

9.9

18.8

18.3

5.4

23.9

19.1

30.5

3.0

7.9

5.3

9.7

9.5

13.5

7.7

18.1

5.3

18.5

18.8

26.4

2.0

3.5

15.2

4.3

18.2

15.7

24.1

5.7

1.6

6.0

9.0

9.2

17.8

12.8

21.9

7.6

2.3

8.0

17.6

4.9

11.6

18.2

21.6

2.7

4.2

5.0

12.7

5.7

15.1

13.9

20.5

4 Application of PPP-B2b Signal in Water Vapor Retrieval The above experiments prove that the static PPP accuracy of the PPP-B2b signal service scope center and scope boundary station is centimeter level, and the kinematic PPP accuracy is decimeter level, which meets the positioning requirements. This section will analyze the application performance of PPP-B2b signal in atmospheric water vapor. This section selects the data from July 6 to July 10, 2021, the PPP-B2b correction, CNAV broadcast ephemeris, post-precision ephemeris, post-ZTD products and ERA5 pressure stratification data are adopted in this experiment. The ERA5 pressure stratification data is derived from the ERA5 reanalysis data set provided by the European Centre for MediumRange Weather Forecasts (ECMWF). The horizontal resolution of ERA5 reanalysis data is 0.25°* 0.25°, the temporal resolution is 1 h, and the vertical stratification is divided into 37 layers. 4.1 Accuracy Evaluation of ZTD To further verify the accuracy of PPP-B2b retrieval of atmospheric precipitable water vapor, this paper compares the ZTD product (IGS-ZTD) provided by IGS as reference. Since the resolution of IGS-ZTD product is 5 min and the resolution of ZTD obtained by PPP-B2b retrieval is 30s, the resolution of both ZTD data is set to be the same for comparison accuracy. The ZTD error results of PPP-B2b retrieval are shown in Fig. 8 using the data from DOY187 to DOY191 in 2021. As shown in Fig. 8, the ZTD error calculated by PPP-B2b real-time PPP is basically distributed within ±50 mm, and the error series is relatively stable. The corresponding error statistical results are listed in Table 4. It can be seen that the three error indexes of the center station of the service scope are within 20 mm, and the three error indexes of the edge station of the service scope are within 37 mm.

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Fig. 8. ZTD error of 8stations.

Table 4. Statistical results of ZTD error Stations

MAE/mm

RMS/mm

STD/mm

gamg

13.5

16.8

15.7

iisc

31.5

36.8

25.5

jfng

15.1

19.0

16.7

lck4

11.1

13.9

12.5

ptgg

23.8

30.0

26.9

ulab

9.4

11.9

10.8

urum

10.32

12.4

11.9

usud

15.9

18.1

13.9

4.2 Accuracy Evaluation of PWV According to the PWV retrieval equation, about every 7-mm ZTD error will give rise to 1-mm PWV error. It can be seen that the ZTD calculated by PPP-B2b can be used for water vapor retrieval. In order to analyze the application performance of PPP-B2b signal in atmospheric water vapor, the PWV retrieved from ZTD product of IGS analysis center (IGS-ZTD) and the PWV retrieved from PPP product of WHU analysis center (PPP-WHU) were used as reference to evaluate the accuracy of PWV retrieved from PPP-B2b signal. Figure 9 is the PWV comparison chart based on three products calculated by eight stations of DOY187-DOY191 in 2021. The results indicate that the three groups of sequence trends are relatively consistent. The accuracy of PWV is calculated in Table 5. The RMS of PWV error retrieved by PPP-B2b in the middle station of service scope is 2–3.5 mm, and the RMS of stations at the edge of service scope is 3–5 mm, which meets the accuracy requirements.

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Fig. 9. PWV of 8stations.

Table 5. Statistical results of PWV error Stations

IGS-ZTD

PPP-WHU

(MAE)/mm

(RMS)/mm

(STD)/mm

(MAE)/mm

(RMS)/mm

(STD)/mm

gamg

2.15

2.67

2.50

1.91

2.52

2.38

iisc

4.04

4.70

3.27

4.29

4.89

3.17

jfng

2.61

3.28

2.88

2.34

2.93

2.37

lck4

1.66

2.07

1.87

1.79

2.18

1.8

ptgg

3.82

4.82

4.32

3.71

4.97

4.47

ulab

2.02

2.57

2.34

1.35

1.83

1.61

urum

2.33

3.20

2.72

1.61

2.15

2.01

usud

3.30

4.01

2.88

3.94

4.52

3.17

5 Conclusion In order to evaluate the service range of PPP-B2b signals and analyze the application performance of PPP-B2b signals in Precipitable Water Vapor Retrieval, eight IGS MGEX stations located in China and neighboring countries are selected in this study. The accuracy of satellite orbit and clock offset following PPP-B2b signal correction, as well as the number of satellites that effectively correct the signal at the selected stations are analyzed. Additionally, the availability of the PPP-B2b signal correction and the accuracy of positioning under static and pseudo-dynamic conditions are also discussed. Finally, the accuracy of PWV retrieval products based on PPP-B2b was evaluated in experiments. In terms of service performance, the results of the study indicate that the accuracy of B2b orbit products in R, A, and C directions is superior to 0.08 m, 0.25 m, and 0.30 m, respectively. The STD of the clock offsets is better than 0.23 ns. The static PPP accuracy of all stations is at the centimeter level, while the kinematic PPP accuracy is at the decimeter level. Specially, the station located in the center of the service scope provides better results than that at the boundary of the service scope.

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In terms of atmospheric water vapor retrieval, The RMS of PWV retrieval error based on PPP-B2b is 3.41mm, and the STD is 2.84 mm. Specially, the RMS of the boundary station of the service scope is less than 4 mm, meeting the accuracy requirement for the atmospheric water vapor retrieval. Based on these findings, it can be concluded that the PPP-B2b signal can provide precise positioning services in areas within the service scope. Additionally, this technology can provide more reliable data to support the real-time numerical weather prediction and other related applications. Acknowledgements. This work was supported by grants from the National Natural Science Foundation of China (No. 42174035, No. 42204032), the National Key Research and Development Program (No.2022YFB3903800), the Shandong Province Science Foundation for Youths (No. ZR2022QD015), the State Key Laboratory of Geo-Information Engineering (No. SKLGIE2020M-2–1) and Talent introduction plan for Youth Innovation Team in universities of Shandong Province (innovation team of satellite position and navigation).

References 1. Yang, Y., Gao, W., Guo, S., et al.: Introduction to BeiDou-3 navigation satellite system. Navigation 66(1), 7–18 (2019) 2. Song, W., Zhao, X., Lou, Y., et al.: BDS-3 PPP-B2b service performance assessment. Geomat. Inform. Sci. Wuhan University 48(3), 408–415 (2021) 3. He, X., Liu, C., Chen, Y., et al.: Analysis of B2b signal of BDS III satellite. Appl. Electron. Techn. 46(3), 1–4 (2020) 4. Nie, Z., Xu, X., Wang, Z., et al.: Initial assessment of BDS PPP-B2b service: precision of orbit and clock corrections, and PPP performance. Remote Sens. 13(11), 2050 (2021) 5. Tang, B., Li, J., Jia, X., et al.: Analysis and application of precise point positioning service for BDS-3. Naviga. Position. Timing 8(03), 103–108 (2021) 6. Ren, Z., Gong, H., Peng, J., et al.: Performance assessment of real-time precise point positioning using BDS PPP-B2b service signal. Adv. Space Res. 68(8), 3242–3254 (2021) 7. Mo, Z., Huang, L., Guo, X., et al.: GNSS atmospheric water vapor retrieving accuracy analysis in Guilin based on ERA5. J. Nanjing Univ. Inform. Sci. Technol. (Natural Science) 13(02), 131–137 (2021) 8. Dalu, G.: Satellite remote sensing of atmospheric water vapour. Int. J. Remote Sens. 7(9), 1089–1097 (1986) 9. Liu, B., Wang, Y., Lou, Z., et al.: The MODIS PWV correction based on CMONOC in Chinese mainland. J. Surv. Map. 48(10), 9 (2019) 10. Bevis, M., Businger, S., Hering, T.A., et al.: GPS meteorology: remote sensing of atmospheric water vapor using the global positioning system. J. Geophys. Res. Atmos. 97(D14), 15787– 15801 (1992) 11. Rocken, C., Anthes, R., Exner, M., et al.: Analysis and validation of GPS/MET data in the neutral atmosphere. J. Geophys. Res. Atmos. 1022(D25), 29849–29866 (1997) 12. Yuan, Y., Zhang, K., Witold, R., et al.: Real-time retrieval of precipitable water vapor from GPS precise point positioning. J. Geophys. Res. D. Atmos.: JGR 119(16):10043–10057 (2014) 13. Gao, Z., Li, J., Liu, Y.: Research on the accuracy of atmospheric precipitable water vapor with BDS. Bull. Surv. Map. 47(5), 35–38 (2019) 14. Tu, M., Su, H., Lei, Y., et al.: Study and implementation of single station atmospheric water vapor retrieving algorithm based on BDS PPP-B2b. In: China Satellite Navigation Conference (CSNC) pp. 82–87 (2022)

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15. Kouba, J., Héroux, P.: Precise point positioning using IGS orbit and clock products. 5(2), 12–28 (2021) 16. Boehm, J., Heinkelmann, R., Schuh, H.: Short note: a global model of pressure and temperature for geodetic applications. J. Geodesy 81(10), 679–683 (2007) 17. Bevis, M., Businge, R.S., Chiswell, S., et al.: GPS meteorology: mapping zenith wet delays onto precipitable water. J. Appl. Meteorol. 33(3), 379–386 (1994)

Deformation Monitoring Experiment and Data Analysis of Beidou Surface Deformation Measuring Radar and GBSAR Zhixiang Xu, Feifeng Liu(B) , Zhanze Wang, Shuyao Zhang, and Jiahe Bi Beijing Institute of Technology, 5 Zhongguancun South Street, Haidian District, Beijing, China [email protected]

Abstract. The Beidou surface deformation measuring radar can realize the threedimensional deformation measurement of the whole scene by using a single receiver. Since the system uses an in-orbit satellite as a transmitter, its long-term measurement costs are much lower than GBSAR and space-borne InSAR systems. However, due to the small power of navigation star to earth, the signal to noise ratio of scene echo is low. Based on the comparison between the high precision GBSAR one-dimensional deformation measurement data and the deformation measurement results of the Beidou surface deformation measurement radar repeater, this paper initially verifies the deformation measurement capability of the Beidou surface deformation measurement radar. This paper first introduces the Beidou surface deformation measuring radar, and then lists the PS processing flow of the Beidou surface deformation measuring radar according to the characteristics of the system. Finally, a multi-system joint verification experiment is carried out in Zhujiawan area of Chongqing, and a cross-system measurement accuracy verification method is proposed. Based on the three days’ measurement results, it is proved that GBSAR and Beidou surface deformation measurement radar have the same measurement results, and the three-dimensional deformation measurement results of the strong scattering point are consistent with the actual situation. The experiment proves that the Beidou surface deformation measuring radar has the ability to measure the three-dimensional deformation of the whole scene and can be widely used in disaster prediction. Keywords: Beidou surface deformation measurement radar · GBSAR · Deformation monitoring experiment

1 Introduction In the early 21st century, synthetic aperture radar (SAR) based on the Global Navigation Satellite System (GNSS) was first proposed as a bistatic SAR [1]. In 2003, Cherniakov et al. used the concept of GNSS-InBSAR for the first time to realize avalanche measurement [2]. In recent years, the research on GNSS-InBSAR has developed from one-dimensional deformation measurement (radar line of sight direction deformation measurement) to three-dimensional deformation measurement. When natural disasters © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 132–143, 2024. https://doi.org/10.1007/978-981-99-6928-9_12

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occur, deformation usually occurs in multiple directions [3]. The Beidou deformationmeasuring radar is a kind of GNSS-InBSAR. Therefore, the Beidou deformationmeasuring radar is very important for landslide warning measurement and infrastructure safety measurement. The Beidou surface deformation measuring radar uses the Beidou navigation satellite as the signal transmitter, and the signal receiver is fixed on the ground to receive the signal directly transmitted by the satellite and the signal reflected by the measurement scene. Compared with traditional InSAR systems, for example, TerraSAR-X has a heavy orbit period of more than 10 days, while Beidou navigation satellite has a shortest heavy orbit period of 1 day, so the Beidou surface deformation measurement radar has the advantage of a short measurement period [4]. Currently, Beidou satellites in orbit that can be used for interference processing include 10 IGSO satellites and 27 MEO satellites. For the same measurement scene, signals from 4 to 8 satellites can be received at the same time, so the Beidou surface deformation measurement radar can realize multi-angle deformation measurement. At the same time, since the Beidou surface deformation measurement radar uses the signal of the Beidou navigation satellite as the external radiation source, only the receiver is needed to complete the deformation measurement work, so the Beidou surface deformation measurement radar has the characteristics of low cost. Liu et al. used navigation satellite signals for three-dimensional deformation measurement. However, the deformation measurement accuracy of Beidou surface deformation measurement radar for the scene needs to be verified [5]. Therefore, this paper conducted an experimental study to verify the deformation measurement accuracy of Beidou surface deformation measurement radar by using GBSAR data and repeater data. In this paper, a cross-system deformation measurement experiment is carried out. By comparing the results of artificial strong scattering morphometry, it is verified that the Beidou surface deformation measurement radar can achieve high precision deformation measurement. The arrangement of this paper is as follows: the second chapter mainly introduces the basic situation of the whole experiment, the third chapter describes how to determine the experiment time and the data processing method, the fourth chapter shows the comparison results of the deformation measurement, and the fifth chapter gives the conclusion.

2 Introduction to Beidou Surface Deformation Measurement Radar In order to realize the three-dimensional deformation monitoring of the monitoring point, this section mainly introduces the basic situation of the whole experimental equipment. In this experiment, the Beidou-2 IGSO satellite is selected as the transmitter, and the receiving equipment is fixed on the ground. The following table lists the system parameters (Table 1). The radar configuration of Beidou surface deformation measurement is shown in the figure below. The transmitter is Beidou IGSO satellite and the receiver is stationary. The receiver has two antennas, respectively receiving echo signal and direct wave signal (Fig. 1).

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Parameter

Value

Period of heavy orbit of satellite

1 day

Wavelength

0.2365 m

Bandwidth

10.23 MHz

Orbital altitude of satellite

About 36000 km

Signal receiver gain

30~80 dB

Fig. 1. System configuration

3 Data Acquisition and Deformation Inversion In this section, the processing method of three-dimensional deformation from the selection of experimental sites to the acquisition of measurement points is proposed: The experimental time is obtained by using the experimental design, the radar echo data is reversely projected to each pixel in the imaging region by using the BP imaging algorithm, and then the echo at each pixel is coherentially superimposed to obtain the SAR image, after which the permanent scatterer (PS) is extracted and the systematic error is compensated, and the single Angle and multi-angle deformation are obtained. Finally, cross-system measurement results are compared. The overall signal processing flow is shown in the Fig. 2. 3.1 Experimental Design and Data Acquisition In order to realize three-dimensional deformation measurement, it is necessary to carry out experimental design according to the position of the Beidou satellite in orbit, and carry out the design of resolution and PDOP before data collection.

Deformation Monitoring Experiment and Data Analysis of Beidou Surface

Design of experiment

Compensaon of error

Data acquision

Single Angle deformaon acquision

BP imaging

Three-dimensional deformaon acquision

PS point extracon

Cross-system deformaon comparison

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Fig. 2. Signal processing flow

Analysis of resolution The system adopts bistatic configuration and the resolution is different from that of single–base SAR system. Compared with traditional chirp signals, the transmitting signal of GNSS system is CA code, and the distance pulse compression results in triangular wave, while the azimuth pulse compression results are still sinc signals. According to the expression of resolution element, the fuzzy function between the target vector A and its adjacent target vector B can be expressed as   [TA + RA ]T (B − A) χ (A, B) ≈ exp j2π λ   T 2 cos(β/2) (B − A) ×p c   2[ωTA TA + ωRA RA ]T (B − A) × mA λ   [TA + RA ]T (B − A) = exp j2π λ     T 2ωE T (B − A) 2 cos(β/2) (B − A) × mA (1) ×p c λ where, TA and RA respectively represent the unit vector from the transmitter and receiver to the target A; β is double base Angle,  represents the unit vector along the bisector of double base Angle; ωTA and ωRA are the line of sight unit vector of transmitter and receiver in aperture center relative to target A; T and R are unit vectors in the effective direction of motion of the transmitter and receiver respectively; ωE represents the equivalent angular velocity, and represents the unit vector in the direction of motion of the equivalent angular velocity. p is the result after the compression of the range pulse,

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and mA is the result after the compression of the azimuth pulse. λ is the wavelength and c is the speed of light. In addition, considering the spatial variability of the resolution in the scene, under the condition that the receiver is stationary, the projection of the system range and azimuth resolution on the projector plane is 0.586c 2B cos(β/2)T ( TA × Z) 0.886λ ρa = T ( × Z) 2Tint ωTA TA

ρr =

(2)

where, B is the signal bandwidth of CA code, Tint is the synthetic aperture time, β is the double base Angle,  is the component of the direction of β bisector, ωTA is the angular velocity of the transmitter relative to point target A, TA is the unit vector of the effective direction of motion of the transmitter, and c is the speed of light. r , a are r = × Z a =  × Z

(3)

where, × represents the cross product, is the equivalent direction of motion, and Z is the unit normal vector of the projection plane. PDOP analysis The configuration of the system will directly affect the theoretical accuracy of threeˆ of the form variable D dimensional deformation inversion. The optimal estimation D is  −1 ˆ = HTH ˜ D (4) HT ˜ is the observed quantity of , H is the deformation observation matrix. The where,  estimated error of the state quantity is defined as ˆ δD = D − D

(5)

Then the variance of the estimation error can be expressed as    −1  −1 D(δD) = H T H H T E nnT H H T H

(6)

For Beidou deformation-measuring radar, only the interference phase of heavy orbit time should be considered. The interference phase error is related to the coherence coefficient, which can be expressed as γ = γtem · γnoi · γspa

(7)

where, γtem represents the temporal coherence coefficient, γnoi represents the noise coherence coefficient, and γspa represents the spatial coherence coefficient.

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In the processing, the time coherence coefficient γtem is approximately 1, and when the SNR is 25 dB, the noise coherence coefficient is 0.9968. Therefore, it can be approximated that noise has no effect on the coherence coefficient, namely γ ≈ γspa The spatial coherence coefficient can be expressed as   ¨ 2π 2 ˜ |W (x, y)| exp −j (r(x, y; tk ) − r(x, y; tn )) dxdy γspa = λ

(8)

(9)

˜ (x, y) is the point spread function after normalization. r(x, y; t) represents the where, W distance from the satellite to the target point at time t. Furthermore, the deformation detection accuracy can be expressed as  2 λ λ 1 − γspa σϕ ≈ σw = (10) 2 2π 2π 2γspa where, σϕ is the standard deviation of the interference phase. The error accuracy of multiple satellites is   −1  −1  2 2 2 H HTH H T diag σw1 , σw2 · · · σwM D(δD) = H T H ⎞ ⎛ D12 D13 D11 ⎟ ⎜ D22 D23 ⎠ = ⎝ D21 D31 D32 D33 Further, define the extension PDOP as  PDOP = D11 + D22 + D33 The deformation sensitivity in each direction is  PDOPX = D11  PDOPY = D22  PDOPZ = D33

(11)

(12)

(13)

The experiment time can be obtained through the resolution and PDOP simulation analysis of the navigation satellite trajectory obtained in advance. 3.2 PS Point Selection and Error Compensation According to the concept of permanent scatterers, the coherence of PS points is high, and the corresponding phase noise is also high. The target of PS points can be screened through the interference phase noise of pixels. However, due to the interference of atmospheric delay, terrain error and other factors, it is difficult to obtain reliable phase

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noise. Therefore, the amplitude value of the pixel is used instead of the phase noise level to identify the pre-selected PS points. In order to perform single Angle deformation inversion, the pre-selected PS points need to be registered. The analysis cost function is established as follows.  2      2 ∗ I1 (m, n) · I2 (m + i, n + j) (14) max|C(i, j)| = max  i,j i,j  m n where, I1 (·) and I2 (·) correspond to the SAR image values of two adjacent time series, and i and j are the offsets. SAR image values and position information of all budget PS points are traversed. Through the combination of pre-selected PS points of different adjacent time series, the combination with the largest cost function value is selected as the registered PS point sequence [6]. The following formula is used to calculate the amplitude deviation index of each pixel, and PS points whose calculated index is greater than the set threshold are eliminated. σnl ∼ σA = DA (15) σv ∼ = = g mA After obtaining the PS points, the phase extraction difference of each image’s PS points can be used to obtain the difference phase containing the deformation information. Differential phase includes atmospheric phase, deformation phase and white noise phase, and its expression is shown as follows. ϕinfer = ϕdefor + ϕatm + ϕnoise

(16)

According to electromagnetic wave propagation theory, echo phase can be expressed as ϕ(t) =

2π f c

 n(r, t)dr

(17)

where, n is the atmospheric refractive index, r is the position, f is the carrier frequency, c is the velocity light and t is the time of signal transmission [6]. Since the direct wave phase is used as a reference for error elimination in the process of synchronization, the part of the interference phase affected by atmosphere can be modeled as 2π f [n(tm ) − n(ts )]  r (18) c where,  r is the distance between each PS point and the Beidou surface deformation measurement radar signal receiver.  ϕatm =

3.3 Three-Dimensional Deformation Inversion After the differential phase error compensation of PS point is completed, the single Angle PS point deformation of single star observation is obtained, and the differential phase is converted into a single Angle shape variable, as shown in the following equation. c ϕ (19) defor = 2π f

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where,  ϕ is the compensated differential phase. For M observation satellites, the relation between three-dimensional shape variable and single Angle PS point deformation is M ×1 = HM ×3 · D3×1 + nM ×1 T  M ×1 = ϕdefo1 ϕdefo2 · · · ϕdefoM

HM ×3

 T T ⎤ ⎡ PS1 (tn ) − PQ (tn ) PE − PQ (tn )  −   ⎢  PE − PQ (tn ) ⎥ ⎢ PS1 (tn ) − PQ (tn ) ⎥ ⎢ T T ⎥  ⎢ ⎥ PE − PQ (tn ) ⎥ ⎢ PS2 (tn ) − PQ (tn ) ⎢ ⎥     − 2π ⎢ P (t ) − P (t ) PE − PQ (tn ) ⎥ S2 n Q n = ⎢ ⎥ ⎥ λ ⎢. ⎢. ⎥ ⎢. ⎥ ⎢ ⎥  T T ⎥ ⎢ ⎣ PSM (tn ) − PQ (tn ) PE − PQ (tn ) ⎦   −   PSM (tn ) − PQ (tn ) PE − PQ (tn )  T D3×1 = Dx Dy Dz nM ×1 = [n1

(20)

n2 · · · nM ]T

where, M ×1 is the observation result of M satellites, HM ×3 is the deformation observation matrix, and D3×1 is the actual displacement of the target. 3.4 Comparison of Deformation with Monitoring Points The L band repeater is suitable for Beidou deformation-measuring radar. It is mainly composed of omnidirectional antenna, gain module and horn antenna. The omnidirectional antenna receives the signal sent by the Beidou satellite. After the signal is amplified by the gain module, the signal is transmitted by the horn antenna and received by the Beidou surface deformation measurement radar signal receiver. Compared with other scatters in the natural scene, the scatterer is arranged as a strong scattering point in the measurement scene, and its position can be clearly found in the radar image. The angular reflector is suitable for GBSAR. It is also a strong scattering point relative to GBSAR, and its position can be clearly found from radar images. When the L-band repeater and angular reflector are not deployed, the deformation point obtained by the Beidou surface deformation measuring radar is the origin of the Beidou surface deformation measuring radar signal receiver and the coordinate in the northeast coordinate system, while the deformation point obtained by GBSAR is the origin of the GBSAR equipment and the signal transmission direction (distance direction) is the longitudinal axis. The direction of radar movement (azimuth direction) is the coordinate in the horizontal coordinate system. To compare the deformation points across the system, the transformation of the coordinates of the two system deformation points must be completed.

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The coordinate of a deformation point P monitored by GBSAR system is (x0 , y0 ), then the deformation point takes GBSAR system as the origin, and the coordinate in the northeast coordinate system should be P(x1 , y1 ) = (x0 cos θ + y0 sin β, x0 sin θ + y0 cos β)

(21)

where, θ is the Angle between azimuth and due east, and β is the Angle between distance and due north. The deformation direction of the deformation point monitored by GBSAR system is the line of sight direction of the radar, and the three-dimensional deformation detected by the Beidou surface deformation measurement radar should be projected onto the line of sight direction of GBSAR system. It is assumed that deforeast , defornorth and deforsky are the deformation values of the three directions of the northeast day monitored by the Beidou surface deformation measurement radar at the Q point. Then the deformation of this point in the line of sight direction of GBSAR system is deforvision = deforeast sin α + defornorth sin β + deforsky sin γ

(22)

where, α, β and γ are the Angle between GBSAR system and the line of sight and the northeast sky.

4 Experimental Results In this chapter, an experiment with low resolution and excellent PDOP value is designed for Zhujiawan experiment. After obtaining satellite signals, BP imaging is carried out to obtain radar images. After PS point extraction and error compensation is carried out on radar images, a single Angle PS point deformation is obtained. Finally, the threedimensional Beidou deformation at the same monitoring point is projected to the line of sight direction of GBSAR system, and the deformation is compared with that monitored by GBSAR system. In this experiment, a hillside in Zhujiawan, Chongqing is selected. The layout of Beidou surface deformation measurement radar receiver and L-band transponder is shown in the Fig. 3.

Fig. 3. A mountain gully in Zhujiawan, Chongqing

According to the experimental terrain of Zhujiawan, Beidou surface deformation measurement radar experiment is designed. The relationship between the area of resolution unit, PDOP and experiment time is shown in the Fig. 4.

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Fig. 4. Time-varying simulation of area of resolution unit

Through the experimental design, the optimal area of resolution unit is 53 m2 , and the best PDOP value is 11.28 mm. The experiment lasts from May 16, 2022 to May 19, 2022. The L-band transponder arrangement of Beidou surface deformation measurement radar is shown in the following figure in the deformation monitoring scenario (Fig. 5).

Fig. 5. Field deployment diagram of L-band transponder

Imaging result of the L-band transponder in Beidou surface deformation measurement radar is shown in the figure below. Compared with other natural scatters in the scene, the transponder has stronger scattering characteristics, so it has the largest amplitude value in the image (Fig. 6).

Fig. 6. Beidou surface deformation measurement radar imaging result

The phase value of the position is selected for differential processing to obtain the differential phase. After the completion of error compensation, the single Angle deformation of the position can be obtained. After the single Angle deformation is put into the observation matrix, the three-dimensional deformation monitored by Beidou surface deformation measurement radar at the position can be obtained, as shown in the Fig. 7.

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Fig. 7. L-band transponder position deformation detected by Beidou surface deformation measurement radar

By placing an angular reflector at the L-band repeater position, the strong scattering point measured at this position in the GBSAR radar image can be accurately obtained, and its phase is selected for interference to obtain the deformation value. The GBSAR imaging result and the deformation measured at this point during the period from May 16, 2022 to May 19, 2022 are shown in the Fig. 8.

Fig. 8. L-band transponder position deformation detected by GBSAR

The frequency of deformation data acquired by GBSAR system is once every 5 to 6 min, while the frequency of deformation data acquired by Beidou surface deformation measurement radar is once a day. Therefore, sampling of data acquired by GBSAR system is needed to reduce the frequency of data acquired by GBSAR system to once a day. After comparison of experimental time, the track numbers of GBSAR system corresponding to the data acquisition time of Beidou surface deformation measurement radar in these three days are respectively the 56th, 288th and 521th track, so the deformation values monitored by GBSAR are respectively 0.88 and −6.16 mm. The Angle between GBSAR view Angle and the three directions of the northeast sky is calculated. The comparison of the three-dimensional deformation results measured by Beidou surface deformation measurement radar at the L-band transponder position and projected on GBSAR line of sight direction is shown in the following Table 2. Table 2. Comparison of GBSAR and Beidou surface deformation measuring radar The first day

The second day

GBSAR (mm)

0.88

−6.16

Beidou surface deformation measuring radar (mm)

−7

−14

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In the comparison of deformation monitoring results of L-band transponder locations, the projection of the Beidou surface deformation measuring radar deformation monitoring values on GBSAR is somewhat different from that on GBSAR, but the deformation monitoring results of the two systems are consistent.

5 Conclusion Beidou surface deformation measurement radar can realize the deformation monitoring of surface scene. Compared with the traditional InSAR system, Beidou surface deformation measurement radar has the advantage of short monitoring cycle. At the same time, it can use multiple satellites in orbit of the Beidou navigation System as transmitters, which has the advantages of low cost and three-dimensional. Therefore, Beidou surface deformation measurement radar has high research value. In this paper, a comparison experiment of deformation monitoring results between Beidou surface deformation measurement radar and GBSAR system is completed. Aiming at the monitoring scene of GBSAR system, the method of resolution and PDOP combined estimation is used to complete the experimental design. After PS point extraction and error compensation, the single Angle deformation of the point of concern is obtained, and then the three-dimensional deformation is obtained by the observation matrix. Compared with the deformation detected by GBSAR system, it is proved that Beidou surface deformation measurement radar has the capability of three-dimensional deformation monitoring of the opposite scene. Acknowledgments. This project is supported by the National Key Research and Development Program (No. 2021YFB3901400) and the National Natural Science Foundation of China (No. 62071045).

References 1. Cherniakov, M.: Space-surface bistatic synthetic aperture radar— Prospective and problems, pp. 22–25. RADAR, Edinburgh, U.K. (2002) 2. M. Cherniakov, T. Zeng, and E. Plakidis: Galileo signal-based bistatic system for avalanche prediction. IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), pp. 784–786 (2003) 3. Huang, R., Fan, X.: The landslide story. Nature Geosci. 6, 325–326 (2013) 4. Wang, Zhanze, Feifeng Liu, Tao Zeng, and Chenghao Wang: Interferometric Phase Error Analysis and Compensation in Beidou surface deformation measurement radar: A Case Study of Structural Monitoring. Remote Sensing 13, no. 15: 3041 (2021) 5. Liu, F., Fan, X., Zhang, T., Liu, Q.: GNSS-Based SAR Interferometry for 3-D Deformation Retrieval: Algorithms and Feasibility Study. IEEE Trans. Geosci. Remote Sens. 56(10), 5736– 5748 (2018) 6. Liu, B.-Q., Feng, D.-Z., Shui, P.-L., Wu, N.: Analytic Search Method for Interferometric SAR Image Registration. IEEE Geosci. Remote Sens. Lett. 5(2), 294–298 (2008) 7. Mateus, P., Nico, G.; Tome, R., Catalao, J. and Miranda: P.M.A. Experimental Study on the Atmospheric Delay Based on GPS, SAR Interferometry, and Numerical Weather Model Data. IEEE Transactions on Geoscience and Remote Sensing, 51, 6–11 (2013)

Research on Zenith Tropospheric Delay Model Based on TCN Improving HGPT2 Model Dengao Li1,3,4,5(B) , Danyang Shi1,3 , Jumin Zhao2,3,4,5 , Fanming Wu1,3 , Liangquan Yan1,3 , Ran Feng1,3 , Xinfang Zhang1,3 , and Jinhua Zhao2,3 1 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China

[email protected]

2 College of Information and Computer, Taiyuan University of Technology, Taiyuan 030024,

China 3 Key Laboratory of Big Data Fusion Analysis and Application of Shanxi Province,

Taiyuan 030024, China 4 Intelligent Perception Engineering Technology Center of Shanxi, Taiyuan 030024, China 5 Shanxi Province Engineering Technology Research Center of Spatial Information Network,

Taiyuan 030024, China

Abstract. The zenith tropospheric delay (ZTD) obtained by global navigation satellite system (GNSS) atmospheric sounding is a pivotal data source for water vapor monitoring. Meteorological changes in Antarctica play an important role in analysis of the global climate, but factors such as complex climatic conditions can limit the collection of meteorological data needed for ZTD retrieval. Therefore, it is necessary to establish high-precision ZTD models that do not rely on measured meteorological data. The existing global pressure and temperature 3 (GPT3) model has limited ability to capture complex weather variations and cannot obtain high-precision GPT3_ZTD. To address the above issues, this research proposes a high-precision ZTD model through using temporal convolutional network (TCN) for improving the hourly global pressure and temperature 2 (HGPT2) model. The HGTP2 model based on Fourier analysis and the time-segmentation concept can consider the linear trend of climate variations, simultaneously the TCN is introduced to simulate the long-term temporal dependence of HGPT2_ZTD, so as to achieve the goal of obtaining high-precision ZTD without relying on measured meteorological data. The experimental results show that the precision of TCN_ZTD obtained from the proposed model is higher than GPT3_ZTD and HGPT2_ZTD when using the GNSS_ZTD observations obtained from 35 stations in Antarctica as a reference, and the improvement of the model is obvious. Keywords: GNSS · ZTD · GPT3 · HGPT2 · TCN

1 Introduction Antarctica is the southernmost part of the Earth, it plays an important role in the global climate system. Water vapor in the atmosphere is an important factor for the study of climate change. Ground-based GNSS water vapor detection technology develops rapidly © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 144–154, 2024. https://doi.org/10.1007/978-981-99-6928-9_13

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and can be used as an effective supplement to traditional water vapor monitoring [1]. The zenith tropospheric delay (ZTD) caused by satellite signals passing through the troposphere is a key information for meteorological research. The separated zenith wet delay (ZWD), combined with surface meteorological parameters, can be used to retrieve the water vapor in the atmosphere near the measurement stations. Thus, it can serve the research on climate change and the monitoring of extreme weather [2, 3]. Therefore, how to obtain high-precision ZTD is a key issue to be studied. At present, the main method to obtain ZTD is still to construct high-precision ZTD models for global or regional applications by analyzing the spatiotemporal characteristics of specific parameters. The parametric ZTD models accurately reflect the meteorological characteristics and changes near the measurement station by inputting the measured meteorological parameters at the target location, such as the Hopfield model, Saastamoinen model and Black model. Among them, Saastamoinen model is still commonly used to calculate the static part [4]. However, the collection of surface meteorological data is not so smooth. Firstly, the climate conditions in Antarctica are complex. Extremely low temperature and heavy snow can cause equipment failure and affect the maintenance of automatic weather stations and the work progress. Secondly, there are few meteorological sensors near GNSS stations, so it is difficult to obtain meteorological observation values in practical application. Finally, in recent years, the plans for scientific expedition of countries have been forced to change due to the impact of the pandemic, so researchers cannot conduct field visits. Due to the difficulties in obtaining meteorological data, researchers have developed empirical ZTD models based on local standard atmosphere or global meteorological reanalysis data, which can achieve estimation of ZTD without measured meteorological parameters. Boehm et al. established the global pressure and temperature (GPT) model based on the ERA-40 reanalysis data provided by ECMWF. The pressure and temperature can be obtained by inputting the Doy and location information, and then the delay can be obtained [5]. Subsequently, the GPT2, GPT2w and GPT3 models were also proposed. GPT2w added humidity decay rate and atmospheric weighted average temperature parameters [6]. GPT3 model added the estimation of hydrostatic gradients in different directions. It can provide global surface temperature and pressure information without measured meteorological data when estimating ZTD. However, it only considers the annual variation of parameters, and cannot obtain different parameters at any time, so its ability to capture complex weather changes is limited. Moreover, the best horizontal resolution of this model is 1° × 1°, and the highest time resolution is 6h. Meteorological parameters are prone to significant changes due to topography and extreme weather [7]. Pedro Mateus et al. proposed an hourly global pressure and temperature (HGPT) model based on the data of 0.25° × 0.25°spatial resolution and 1h temporal resolution. This model follows the concept of time segmentation and can explain the linear trend of global climate change scenarios. The model can calculate surface meteorological parameters at any location and time [8]. Subsequently, an improved version HGPT2 model was proposed, with the main difference being that it could not only calculate the previous parameters, but also provide information about relative humidity and ZWD [9]. In recent years, neural networks and machine learning algorithms have been introduced into the field of GNSS and applied to the correction of tropospheric delay model,

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the inversion of tropospheric delay, and the prediction of precipitable water. A regional NWP tropospheric delay inversion method based on GRNN can improve the accuracy of tropospheric delay [10]. The regional ZTD models based on GPT3 and ANN have higher accuracy than Saastamoinen and GPT3 models [11]. Later, LSTM and RBF neural networks were introduced to modify the GPT3 model to calculate ZTD [12] and the blind source separation method combined with neural networks to establish the ZTD model in West Antarctica [13], both of which have achieved good results. The HGPT2 model has not been widely used to estimate the accuracy of ZTD since it was established. In this study, the tropospheric products from 35 stations in Antarctica released by Nevada Geodetic Laboratory (NGL) were used as reference for related experiments [14]. Through experimental comparison, we found that the accuracy of ZTD calculated by HGPT2 model was higher than that calculated by GPT3 model, so we decided to conduct further research on the basis of HGPT2. At the same time, temporal convolutional network (TCN) is introduced to simulate the long-term temporal dependence of HGPT2_ZTD, and HGPT2 is optimized by using its advantage of time series prediction. It should be noted that models of GPT series and HGPT series mainly provide meteorological parameters required by the first type of model, and ZTD needs to be further obtained by the Saastamoinen model.

2 Data The experimental data used in this study were obtained from 35 GNSS stations in Antarctica in the tropospheric products of NGL, and the observation time span was from January 1, 2018 to July 16, 2022. The observation values were named GNSS_ZTD. The distribution of observation sites is shown in Fig. 1. Most of them are located in west Antarctica, and a few are located in east Antarctica. The geographical area involves inland, peninsula, east and west coasts.

Fig. 1. Distribution of observation stations in Antarctica.

The establishment of the model in this study is based on the extraction of more than 300000 data of each measuring station every day at an interval of 4 h. For the stations with serious data missing, we adopt a separate modeling method to prevent the accuracy from decreasing due to the lack of time. The accuracy of the ZTD value of the NGL

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official website has been shown to be close to the official accuracy of the international GNSS service [15], and has been applied to the study of the troposphere.

3 Models and Methods 3.1 GPT3 Model The GPT3 model uses the ERA-Interim monthly average atmospheric pressure level data to calculate various meteorological parameters that can be used for geodesy and climate analysis, including Pressure (P) in hPa, Temperature (T) in K, water vapor pressure (e) in hPa, etc., mainly through the following Eq. (1). These parameters can then be used to calculate the GPT3_ZTD.     doy doy 2π + Y2 sin 2π M(t) = Y0 + Y1 cos 365.25 365.25     doy doy 4π + Y4 sin 4π (1) + Y3 cos 365.25 365.25 where M(t) represents the meteorological parameters to be estimated, doy represents the day of the year, Y0 represents its mean value, Y1 , Y2 are the annual amplitudes (annual cycle parameter), and Y3 , Y4 are the semiannual amplitudes (semiannual cycle parameter) [7]. 3.2 HGPT2 Model The HGPT2 model is the first global model to use the full level and temporal resolution of ERA5. The model follows the concept of time segmentation, extracting simulations from time series of 1-h temporal resolution every hour of the day, and calculating meteorological parameters using three periodic coefficients of Fourier analysis of ERA5 dew point temperature data from 20 years, namely annual, semi-annual and quarterly [8, 9]. The following Eqs. (2)~(6) were used to calculate the meteorological parameters such as temperature (T), pressure (P), relative humidity (RH), and water vapor pressure (e) to calculate the HGPT2_ZTD.   2π (t − t0 ) + yh1 Th (t) = ah + bh · (t − t0 ) + xh1 · cos 365.25     2π (t − t0 ) 2π (t − t0 ) + yh2 + xh3 · cos + yh3 . (2) + xh2 · cos 182.63 91.31   2π (t − t0 ) Ph (t) = ah + bh · (t − t0 ) + xh1 · cos + yh1 365.25   2π (t − t0 ) (3) + yh2 + xh2 · cos 182.63   2π (t − t0 ) h h h h RH (t) = x0 + x1 · cos + y1 365.25

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 + xh2 · cos

   2π (t − t0 ) 2π (t − t0 ) + yh2 + xh3 · cos + yh3 182.63 91.31

(4)

where t is the MJD format of the date, h is the hour derived from t, t0 represents the first observation date. a and b are linear regression coefficients. x0 , x1 , x2 and x3 are mean, annual, semiannual and quarterly amplitudes respectively, y1 , y2 and y3 are annual, semiannual and quarterly initial stages respectively. Wexler formula was used to calculate the saturated water vapor pressure, and the data of relative humidity (RH) was used to further calculate the water vapor pressure for the estimation of ZTD [16]. es = es _Wexler(T, P)  e = eS ·

RH 100

(5)

 (6)

The classical Saastamoinen model was used to calculate ZTD in this study, as shown in Eqs. (7)~(9). ϕ is latitude, H is height, Pispressure, T is temperature, e is water vapor pressure [2, 17]. 0.0022768 × P 1 − 0.00266 × cos(2ϕ) − 0.00028 × H    1255 ZWD = 0.002277 · + 0.05 · e T

ZHD =

ZTD = ZHD + ZWD

(7) (8) (9)

3.3 Temporal Convolutional Network There is still a certain gap between the ZTD obtained by the HGPT2 model and the reference value GNSS_ZTD. In this study, we decided to use temporal convolutional network (TCN) to bridge this gap. The ZTD estimated by using TCN to improve the HGPT2 model is named TCN_ZTD. The TCN mainly uses the powerful features of convolutions to extract features across time steps and consists of causal, expanded convolutional layers with the same lengths of input and output. There are two reasons for choosing TCN. Firstly, the causal convolution in the network structure of TCN makes the network suitable for processing data with time series relationship. Its characteristics are that the former part of the data can only be known before the latter part of the data, which is a strict time constraint model. The existing ZTD data has a strong correlation with time, and TCN is suitable for mining and fitting the change trend of HGPT2_ZTD in the time line, so that TCN_ZTD with higher accuracy can be obtained on the basis of HGPT2 model. Secondly, the expanded convolution in the TCN network structure has a larger receptive field, so that the network can remember more historical information, obtain more data rules affecting ZTD in the prediction of ZTD, and improve the accuracy of the final ZTD [18].

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The structure of the TCN-HGPT2 model constructed in this paper is shown in Fig. 2. The location information and time series data of the station were used as the input of the HGPT2 model, and the meteorological parameters obtained could be used to output HGPT2_ZTD. The location and time information were used as the new input, and the ZTD was predicted by TCN. The number of hidden layers was set to 3, which increased the visual field and ensured the speed of network calculation. Finally, a higher accuracy ZTD is obtained.

Fig. 2. Diagram of the TCN-HGPT2 model structure.

4 Experiment and Discussion This section introducts and discusses the accuracy of ZTD estimated using the models mentioned above. The data from January 1, 2018 to December 31, 2021 were used as training data, and the data from January 1, 2022 to July 16, 2022 were used as testing data. The mean absolute error (MAE) and root mean square error (RMSE) of each measurement station were used to evaluate the accuracy of ZTD under each model. The calculation methods are shown in Eqs. (10)~(11). Here A_ZTDi represents the ZTD value under various models, GNSS_ZTDi refers to the reference value, and N is the number of data calculated. MAE =

N 1  |A_ZTDi − GNSS_ZTDi | N i=1

(10)

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  N 1  RMSE = (A_ZTDi − GNSS_ZTDi )2 N

(11)

i=1

4.1 Comparison Between HGPT2_ZTD and GPT3_ ZTD In order to discuss the GPT3 model and HGPT2 model, the data of 35 measurement stations in 5 years were used to calculate and analyze, and the HGPT2_ZTD sequence of 83% of the stations had higher consistency with the GNSS_ZTD sequence. Figure 3(a) and (b) show that the HGPT2_MAE and HGPT2_RMSE values of most of the stations are smaller, indicating that they are closer to the GNSS_ZTD as reference values. Even if the HGPT2_MAE and HGPT2_RMSE values of six stations (as shown in group2) are relatively higher, the average differences are only 0.002505m and 0.003465m, mainly because these six stations are located in the Antarctic Peninsula, which is the warmest and has the greatest amount of precipitation in the Antarctic continent. The Antarctic Peninsula is bordered by sea to the east and west, the coast is tortuous, and there are many offshore islands with high average altitudes. The complex topography and abundant water vapor will lead to large changes in ZTD. This is proved by the higher MAE and RMSE values of the six measurement stations in this area. Since GPT3 and HGPT2 models are based on global meteorological reanalysis data, the ability to estimate parameters is fixed, and the accuracy of ZTD is higher in regions with small climate change and lower in regions with complex and diverse climate. However, the seasonal periodicity of temperature introduced by HGPT2 model can better explain the seasonal signal fluctuations and the change rate introduced by HGPT2 model can better explain the climate change. At the same time, the improvement of time resolution can more accurately reflect the change trend. It is of practical significance to optimize and improve the HGPT2 model.

Fig. 3. (a) Histogram of MAE at 35 stations for GPT3_ZTD and HGPT2_ZTD. (b) Histogram of RMSE at 35 stations for GPT3_ZTD and HGPT2_ZTD.

4.2 Accuracy of TCN_ZTD Firstly the statistical results of MAE and RMSE about 35 stations in this study under the three models (GPT3, HGPT2, HGPT2 + TCN) were analyzed from the overall

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perspective. Figure 4 and Fig. 5 respectively show the MAE and RMSE of the three models at each measurement station, and the performance of the models is shown using the multi-level color intervals. As can be seen from (a) of Fig. 4, when using the GPT3 model, the overall GPT3_MAE of each measuring station are high and the errors are relatively large, most of which belong to the first two interval levels. Moreover, the color levels are related to the geographical areas, and the deviation trend in the same area is similar. Compared with (a), using the HGPT2 model in (b) the average HGPT2_MAE values decrease, the deviations of inland Antarctica decrease directly by a gradient and the HGPT2_MAE of east and west coasts also improve, but several stations with poor performance on the Antarctic Peninsula can still be observed. Only (c) showed significantly better TCN_MAE results than other models in all stations, with significantly improved accuracy. As can be seen from (a) of Fig. 5, when using the GPT3 model, the overall GPT3_RMSE of each station are higher. Compared with (a), when using the HGPT2 model in (b) the accuracy is improved, and the HGPT2_RMSE of inland Antarctica directly decrease by one gradient. The statistical results of TCN_RMSE were better than those of other methods at all sites, and the accuracy was significantly improved, especially for the stations in the Antarctic Peninsula region.

(a)GPT3_MAE

(b)HGPT2_MAE

(c)TCN_MAE

Fig. 4. Distribution of MAE at 35 stations for the three models.

(a)GPT3_RMSE

(b)HGPT2_RMSE

(c)TCN_RMSE

Fig. 5. Distribution of RMSE at 35 stations for the three models.

Table 1 summarizes the average MAE and RMSE of the differences between the ZTD derived from the three models and the reference GNSS_ZTD for all stations, the values in square brackets are the minimum and maximum values. In terms of means, the HGPT2 model outperformed the GPT3 model, but the worst values for each statistic appeared in the HGPT2 model approach. From the statistical results, it can be found

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that TCN is superior to the other two models in the minimum value, maximum value and average value after improving the HGPT2 model (the model in this paper), and the accuracy is improved to a certain extent. Table 1. Summary of performance evaluation of different model methods. MAE (m)

RMSE (m)

GPT3_ZTD

0.023 [0.018,0.028]

0.029 [0.022,0.035]

HGPT2_ZTD

0.021 [0.015,0.030]

0.026 [0.019,0.038]

TCN_ZTD

0.017 [0.012,0.025]

0.019 [0.014,0.028]

Then, the accuracy of TCN_ZTD after optimizing the HGPT2 model using temporal convolutional network in this study was analyzed detailedly, also using the two evaluation indicators of MAE and RMSE. Figure 6 (a) and (b) show the histograms of MAE and RMSE of HGPT2_ZTD and TCN_ZTD at 35 stations respectively. From the data in Figure (a), we can observe that the TCN_MAE of all the stations decrease to a certain extent, and the accuracy of this model is 15.3% higher than that of the single HGPT2 model. The average TCN_MAE of the six stations located on the Antarctic Peninsula was 16.5% higher than that of the HGPT2 model. Figure (b) shows that the TCN_RMSE of all stations also significantly decrease, the accuracy is 25.5% higher than that of the HGPT2 model. The average TCN_RMSE of the six stations located in the Antarctic Peninsula is 38.1% higher than that of the HGPT2 model. Therefore, TCN_ZTD has a higher agreement with GNSS_ZTD during the prediction period, and the prediction accuracy of millimeters can be achieved at all GNSS stations.

Fig. 6. (a) Histogram of MAE at 35 stations for HGPT2_ZTD and TCN_ZTD. (b) Histogram of RMSE at 35 stations for HGPT2_ZTD and TCN_ZTD.

5 Conclusion Using the TCN to improve the HGPT2 model can well combine the characteristics of periodic variation of HGPT2 model and well simulate the temporal dependence of HGPT2_ZTD, so to estimate the ZTD according to the temporal series. The experimental

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and the statistical results of MAE and RMSE show that the minimum value of the proposed model can reach 0.012m, and the mean value is 0.017m. When calculating the RMSE of a single station, the minimum value can reach 0.014m, and the mean value is 0.019m. Compared with the single GPT3 model, TCN_ZTD has improved MAE and RMSE by 21.1% and 32.3%. And compared with the single HGPT2 model, TCN_ZTD has improved MAE and RMSE by 16.5% and 38.1%, respectively. The overall accuracy of TCN_ZTD is better than GPT3_ZTD and HGPT2_ZTD. The TCN has a certain effect on improving the HGPT2 model. Different climates and geographical locations can lead to some variations in ZTD at different stations, and further modeling and improvement based on the spatial distribution of multiple stations are needed if ZTD is to be estimated more efficiently in space. Acknowledgment. We sincerely thank NGL for providing relevant data.

References 1. Yao, Y., Zhao, Z.: Research progress and prospect of GNSS tropospheric water vapor monitoring. Acta geodaetica et cartographica sinica 51(06), 935–952 (2022) 2. Davis, J., Herring, T.A., Shapiro, I.I., Rogers, A.E.E., Elgered, G.: Geodesy by radio interferometry. Effects of atmospheric modeling errors on estimates of baseline length. Radio Sci. 20, 1593–1607 (1985) 3. Bevis, M., Businger, S., Herring, T.A., Rocken, C., Anthes, R.A., Ware, R.H.: GPS meteorology: remote sensing of atmospheric water vapor using the Global Positioning System. J. Geophys. Res. Atmos. 97, 15787–15801 (1992) 4. Saastamoinen, J.: Contributions to the theory of atmospheric refraction. Bull. Géod. 46, 279– 298 (1972) 5. Böehm, J., Heinkelmann, R., Schuh, H.: Short note: a global model of pressure and temperature for geodetic applications. J. Geodesy 81(10), 679–683 (2007) 6. Böhm, J., Möller, G., Schindelegger, M., Pain, G., Weber, R.: Development of an improved empirical model for slant delays in the troposphere (GPT2w). GPS Solut. 19, 433–441 (2015) 7. Landskron, D., Böhm, J.: VMF3/GPT3: refined discrete and empirical troposphere mapping functions. J. Geod. 92, 349–360 (2018) 8. Mateus, P., Catalão, J., Mendes, V.B., Nico, G.: An ERA5-based hourly global pressure and temperature (HGPT) model. Remote Sens. 12, 1098 (2020) 9. Mateus, P., Mendes, V.B., Plecha, S.M.: HGPT2: an ERA5-based global model to estimate relative humidity. Remote Sens. 13(11), 2179 (2021) 10. Li, L., Xu, Y., Yan, L., et al.: A regional NWP tropospheric delay inversion method based on a general regression neural network model. Sensors (Basel, Switzerland), 20(11) (2020) 11. Yang, F., Guo, J., Zhang, C., et al.: A regional zenith tropospheric delay (ZTD) model based on GPT3 and ANN. Remote Sens. 13(5), 838 (2021) 12. Li, S., Xu, T., Xu, Y., et al.: Forecasting GNSS zenith troposphere delay by improving GPT3 model with machine learning in Antarctica. Atmosphere 13 (2022) 13. 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, Switzerland), 20(8) (2020) 14. Blewitt, G., Hammond, W.C., Kreemer, C.: Harnessing the GPS data explosion for interdisciplinary science. EOS 99 (2018). https://doi.org/10.1029/2018EO104623

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15. Ding, J., Chen, J.: Assessment of empirical troposphere model GPT3 based on NGL’s global troposphere products. Sensors 20, 3631 (2020) 16. Wexler, A.: Vapor pressure formulation for water in range 0–100 °C. A revision. J. Res. Natl. Bur. Stand. 80A, 775–785 (1976) 17. Saastamoinen, J.: Contributions to the theory of atmospheric refraction—Part II. Refraction corrections in satellite geodesy. Bull. Géod. 47, 13–34 (1973) 18. Bai, S., Zico, J„ Koltun, K.V.: An empirical evaluation of generic convolutional and recurrent networks for sequence modeling, arXiv e-prints, (2018). https://arxiv.org/abs/1803.01271

Prediction of Ionospheric TEC Based on BLS-LSTM-GRU Hybrid Model Dengao Li1,3,4,5(B) , Xinfang Zhang1,3 , Jumin Zhao2,3,4,5 , Fanming Wu1,3 , Ran Feng1,3 , Jinhua Zhao2,3 , and Danyang Shi1,3 1 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China

[email protected]

2 College of Information and Computer, Taiyuan University of Technology, Taiyuan 030024,

China 3 Key Laboratory of Big Data Fusion Analysis and Application of Shanxi Province,

Taiyuan 030024, China 4 Intelligent Perception Engineering Technology Center of Shanxi, Taiyuan 030024, China 5 Shanxi Province Engineering Technology Research Center of Spatial Information Network,

Taiyuan 030024, China Abstract. In satellite communications, global navigation satellite systems(GNSS) and other important space activities, the value of total electron content (TEC) in the ionosphere directly affects the size of ionospheric delay. Achieving accurate prediction of ionospheric total electron content through modeling can effectively improve the reliability and accuracy of GNSS positioning. Considering the high prediction accuracy of long short-term memory neural network (LSTM) and the fast training speed of gated recurrent unit network (GRU), but it is easy to fall into the local optimum, while the width learning system(BLS) can effectively avoid this drawback. Therefore, this paper proposes a model for predicting the total electron content of the ionosphere, which consists of a broad learning system, an LSTM network and a GRU networks. Six parameters of TEC, geomagnetic index Dst, Kp, Ap, solar activity index F10.7, and hour (HD) are selected as input features from the observed data to predict the variation of the total ionospheric electron content. The results generate prediction maps of the total ionospheric electron content and are compared with empirical models and conventional neural network models at different times and solar activity conditions. The experimental results show that the root mean square error (RMSE) of the prediction results of this BLS-LSTM-GRU model is decreased by 23.07%, 17.48% and 9.46% compared with the IRI-2016, NeQuick and CNN-LSTM prediction models, respectively, with higher prediction accuracy. Keywords: Total electron content · Broad learning system · Long short-term memory · Gated recurrent unit

1 Introduce In satellite communications, global satellite navigation systems (GNSS), and other important space activities, satellite signals and ground signals can pass through the atmosphere. In the atmosphere, the ionosphere is an atmospheric space 60 km to 2000 km © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 155–164, 2024. https://doi.org/10.1007/978-981-99-6928-9_14

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above the ground. In them, the ionosphere produces a large number of electrons and ions due to the activity of photoionization, which will have various degrees of influence on radio signals. The total electron content of the ionosphere (TEC) is the value of the physical characteristics of the ionosphere. Its value will directly affect the size of the ionosphere delay, thus having a certain effect on the whole navigation and positioning effect [1, 2]. The researchers found that the prediction results of the total electron content of the ionosphere through modeling are more accurate, which can effectively improve the reliability and accuracy of GNSS positioning [3, 4]. In the past studies, the calculation method of the total electron content of the ionosphere adopts empirical models, based on the previous observation data, such as the Klobuchar model, the NeQuick model, the international reference ionosphere IRI, etc. The parameters of the Klobuchar model are broadcast together via the GPS Radio Star Calendar. The model assumes an ideally smooth ionosphere change, simple structure and easy to implement, and computationally very fast. The model considers the period and amplitude changes at the Sunday scale and is able to reflect the changing properties of the ionosphere. However, because the model does not consider the influence of the ionosphere daily fluctuation, the correction effect of the model is not ideal in the case of low height angle or the ionosphere disturbance [5]. NeQuick The model was jointly proposed by the Italian International Center for Theoretical Physics, Wave Propagation and High Altitude Physics Laboratory (ARPL-ICTP) and the Institute of Geophysics and Astrophysics at the University of Graz, Austria, and was adopted by the Galileo system to serve its single-frequency users. The model can quickly calculate the total electron content in the vertical and oblique directions, and can describe the electron density at the specified geographical location and time point based on the parameters hmF2 and NmF2, so as to obtain the vertical profile of the ionosphere electron density. However, the solar activity factor in this model adopts the monthly average, which cannot change the daily ionosphere error to the positive value [6]. The International Reference Iosphere is an international project sponsored by the Space Research Council (COSPAR) and the International Radio Science Union (URSI) to generate an empirical standard model of the ionosphere based on all available data sources. Several steadily improved versions of the model have been released. For a given location, time, and date, IRI provides a lunar level of the electron density, electron temperature, ionic temperature, and ionic composition in the range of the ionosphere height [7–9]. As for the empirical model mentioned above, because the model is based on previous observation data, in the calculation of the total electron content of the ionosphere, the researchers have been looking for a more efficient and accurate calculation model. Many researchers have studied the changes in the ionosphere using regional models. Linear or nonlinear filters were used to simulate the TEC values at the regional level. For linear modeling, autoregressive (AR) or AR moving average (ARMA) filters derived from the time-series signal processing research community were used [10–14]. These filters are linear regressions of the time domain and, therefore, they do not capture the complex and highly nonlinear phenomena that occur in the ionosphere. In current research, deep learning is using deep learning to predict the total electron content of the ionosphere. In paper [15], the authors propose a deep learning model, including a one-dimensional convolutional layer for optimal feature extraction and a

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superimposed recurrent layer for time-series modeling. To effectively predict the TEC values, and to replace the data derived from the global ionosphere graphs (GIMs)with data with global characteristics, with the same or better accuracy than the regional data. The model is suitable for the prediction of ionosphere delays at different receiver locations. The model was tested at stations at different times, under different solar and geomagnetic conditions, and at different latitudes, providing reliable estimates of ionosphere activity in the regional order. However, the use of deep learning method to predict the total electron content of the ionosphere is easy to fall into the local optimal situation, so that the predicted results gradually deviate from the observed value. Therefore, the researchers consider the use of feature extraction method combined with deep learning to solve the problems mentioned above. The methods for feature extraction are easy to implement and the common methods for feature extraction include, Variable sorting, Feature Subset Selection, Punishment of least squares, Random feature extraction method, Including non-adaptive random projection and random forest, convolution-based input mapping, and so on. In the paper [16], a ioniographic TEC prediction model based on deep learning is proposed, which consists of convolutional neural network (CNN), long and short-term memory neural network and attention mechanism. Attention mechanisms are added in the pooling and fully connected layers, and weights are assigned to improve the model, and compared with empirical and traditional neural network models. The accuracy and correlation of the prediction results remained stable under different months and different geomagnetic conditions. Considering the high prediction accuracy of long-and short-term memory neural network and the fast training speed of gated recurrent unit network (GRU), but easy to fall into the local optimal situation, the width learning system (BLS) can effectively avoid this defect. Therefore, we propose a model to predict the total electronic content of the ionosphere, which consists of a width-learning system, an LSTM network, and a GRU network fusion. From the observed data, six parameters of TEC, geomagnetic index Dst, Kp, Ap, solar activity index F10.7, hour (HD) were selected as input features to predict the change of the total electron content in the ionosphere. In the following content, the second section introduces the source and processing of the data and the allocation of the test and verification sets in the data set; the third section explains the principle, structure and the integrated overall model framework; the fourth section is the experiment and analysis of the proposed method; and the fifth section summarizes the conclusion of the research results.

2 Data and Preprocessing 2.1 Data From the observed data, six parameters of TEC, geomagnetic index Dst, Kp, Ap, solar activity index F10.7, and hour were selected as input features to predict the change of the total electron content in the ionosphere.The ionosphere total electron content data was downloaded from the Crustal Dynamics Data Information System (CDDIS) (https://cddis.nasa.gov/) to select the total electron content from the period from 2007 to 2017 years. The Ionospheric TEC dataset is the global ionosphere TEC data generated

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in the standard IONEX (Ionospheric Map-switching Format) file format provided by IGS. The format in the file is: the temporal resolution is 1 h, the spatial longitude range of west longitude 180° to east longitude 180°, the resolution of 5°. The latitude ranges from north latitude 87.5° to south latitude 87.5° with a resolution of 2.5°. The global TEC map grid point scale is 71 × 73. The geomagnetic index has an influence on the total electron content at different latitudes. The index Dst will be downloaded from the International Geomagnetic Reference Field (IGRF) (https://www.ngdc.noaa.gov/IAGA/vmod/igrf). Geomagnetic index Kp, Ap were available at the Helmholtz Potsdam Center, Helmholtz Centre PotsdamGerman Research Centre for Geosciences (GFZ) download (https://www.gfz-potsdam). Solar activity Index F10.7 is the determination of the solar radio emission intensity in a 100 MHz bandwidth of 1800 MHz (wavelength of 10.7 cm) centered on 1 h, downloaded from the celestrak Organization (https://celestrak.org/SpaceData/SpaceWx-for mat.php). 2.2 Pretreatment Furthermore, we can combine the data of 24 TEC maps from the previous two days as input for a sample whose output is 24 TEC maps from the third day, based on the periodic daily variation of TEC. We can derive a five-dimensional tensor from this structure with dimensions of (number, 24,71,73,1), where the numbers represent the total number of samples in the dataset, 24 represent that each sample contains 24 TEC maps, 71 and 73 are the dimensions of the TEC map in each hour, and 1 represents the number of color channels in the map, because the TEC per latitude and longitude is a one-dimensional value. The dataset division is shown in Table 1. Table 1. The size of the dataset

Sample size

Training set

Validation set

Test set

(365 × 6 + 366 × 2) × 0.9

(365 × 6 + 366 × 2) × 0.1

365 × 2

The full data set contains data from 11 years from 2007 to 2017, where data from 2014 (high solar activity year) and 2017 were selected as the test set, and the remaining 9 years (2007–2013 and 2015–2016), 90% into the training set and 10% into the validation set.

3 Methods In this paper, we propose a model to predict the total electronic content of the ionosphere, which consists of the width learning system BLS, LSTM network and GRU network fusion. The following introduces the principle and structure of BLS network, LSTM network and GRU network respectively.

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3.1 Width Learning Network Principle and Structure On the basis of the random vector function link neural network (RVFLNN), C.L. Philip Chen proposed a width learning system (BLS) designed to provide an alternative method for deep structure [17]. For feature extraction, “mapping feature” can be used as input for RVFLNN. The width learning system is designed based on the idea of mapping features as RVFLNN inputs. The design idea of BLS is as follows: First, use the features of the input data mapping as the “feature nodes” of the network. Second, the mapped features are enhanced to be the’enhanced nodes “with randomly generated weights. Finally, all the mapped features and enhancement nodes are directly connected to the output, and the corresponding output coefficients can be derived by Pseudo pseudoinverse. In addition, the BLS can update the system (the input incremental learning, in an efficient and efficient manner) in the newly added data, as shown in Fig. 1.

Fig. 1. LSTM Broad Learning System structure diagram

The calculation process of the BLS width learning system is as follows, assuming the input data: Zi = ϕ(XWei + βei ), i = 1, 2, ..., n

(1)

Em = ξ(Zn Whm + βhm )

(2)

Y = HW n = [Z n |Em ]W n

(3)

3.2 Principles and Structure of the LSTM Neural Network The LSTM neural network introduces a state value and “gate” control structure based on the recurrent neural network [18]. To selectively filter information selectively, the transmission of data information between different units in the hidden layer is controlled by three thresholds: input gate, forgetting gate, and output gate. The internal structure of the LSTM and the form of the data flow are shown in Fig. 2.

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Fig. 2. LSTM neural network structure diagram

The role of the forgetting gate is to decide whether to retain the previous information or not, and to multiply it with the memory information of the previous hidden state, to determine whether the information is retained. The input gate controls the input of the current information. When the information passes through the input unit, it multiplies the input door to determine whether the current information is written. The cell state is equivalent to the path that transfers the information through the sequence. The output gate controls the output of the current memory information, multiplying it by the current memory information to determine whether to output the information. In the process of LSTM information flow, the calculation formula of forgetting gate is as follows: ft = σ (Wf · [ht−1 , xt ] + bf )

(4)

it = σ (Wi · [ht−1 , xt ] + bi )

(5)

 Ct = tanh(WC · [ht−1, xt ] + bC )

(6)

Ct = ft ∗ Ct−1 + it ∗  Ct

(7)

ot = σ (Wo [ht−1 , xt ] + bo )

(8)

ht = ot ∗ tanh(Ct )

(9)

3.3 Principles and Structure of GRU Gated Cycle Unit Network The GRU is a simple form of the LSTM network, and it works very well, so it is currently a very manifold network [19]. The structural diagram of the GRU network is shown in Fig. 3. The two gates in the GRU model are the reset gate and the update gates. The reset gate is similar to the forgetting gate in the LSTM neural network. The forgetting gate in the LSTM is the information of the memory unit at the moment before forgetting, while the reset gate of the GRU model is calculated as follows: rt = σ (Wr · [ht−1 , xt ] + br )

(10)

Zt = σ (WZ · [ht−1 , xt ] + bZ )

(11)

 ht = tanh(Wh · [rt · ht−1 , xt ] + bh )

(12)

ht ht = (1 − zt ) · ht−1 + zt · 

(13)

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Fig. 3. GRU network structure diagram

3.4 A Hybrid Model Based on the BLS-LSTM-GRU Figure 4 shows the architecture of the BLS-LSTM-GRU network. Network configuration settings include: data preprocessing; input layer; The BLS Width learning system; LSTM network; GRU network;output layer.

Fig. 4. BLS-LSTM-GRU Network structure diagram

4 Experiment 4.1 Data Collation and Experimental Setup In this study, the experimental data were divided into two parts: the training set and the test set. The models were trained using data from 2007 - 2013,2015 -2016 as the training set, and data from 2014 and 2017 were used as the test set. First, the outlier and missing values of TEC data are solved; eliminate the outliers and fill up the gaps by bilinear interpolation Loss of value. Changes in TEC are associated with both HD and solar geomagnetic activity. Solar and geomagnetic activity can be characterized by the Ap, Kp, Dst, and F10.7 indicators. Then, the six features were considered as the training set. A total of 3 days were used for a set of data as sample sliding segmentation. Each sample predicted the TEC values 1 day after that using the data from the first two days, and the training set samples were fed into the network to train the prediction model. The geomagnetic activity was irregular, and two extremely large magnetic storms occurred in 2015. Solar activity peaked in 2014, consistent with the maximum of TEC values. 4.2 Evaluation Indicators To verify the advantages of BLS-LSTM-GRU model in ionosphere TEC prediction, IRI-2016 model, NeQuick model, and CNN-LSTM neural network were selected for

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comparative analysis. NeQuick The model is based on the NeQuick-2 version published by the Abdus Salam International Center for Theoretical Physics (ICTP), using the daily solar radio flux as the input data. The input data for the CNN-LSTM model are the same as in the model presented here. The prediction performance of each model was evaluated based on test set predictions of station location, temporal variation, and geomagnetic activity. We also used root mean square error (RMSE) to evaluate model performance. The RMSE is the sample standard deviation of the difference between the predicted values and the observed values (called the residuals). Root mean square error to illustrate the degree of dispersion of the samples. When doing a nonlinear fit, the smaller the RMSE, the better. The calculation formula is as follows:  N 2 i=1 (TECpi − TECri ) (14) RMSE = N

4.3 Accuracy Assessment of Different Test Sites Table 2 shows the overall evaluation indicators for the four models. Statistical results were obtained from the 24 GNSS stations in the 22 test sets, 24 h per day, and 365 days per year. The IRI-2016 model has the largest RMSE and minimal correlation. The RMSE for NeQuick, CNN-LSTM, and BLS-LSTM-GRU models were 3.51 TECU, 2.13 TECU, and 1.17 TECU, and the MAEs were 1.54 TECU, 1.41 TECU, and 1.21 TECU, respectively. This indicates that the BLS-LSTM-GRU model has a good prediction performance, and the improved model has the best prediction performance. Table 2. Comprehensive evaluation index of the four models in each test site Model

RMSE (TECU)

MAE (TECU)

IRI-2016

4.36

2.34

NeQuick

3.51

1.54

CNN-LSTM

2.13

1.41

BLS-LSTM-GRU

1.57

1.21

4.4 Assessment of Accuracy Under Different Geomagnetic Conditions To investigate the predictive power of the present model under different geomagnetic activities, we divided the data into magnetic static days and magnetic burst days for comparative analysis. The Kp index was used as an indicator of the geomagnetic activity. Table 3 shows the evaluation metrics of 4 models under different geomagnetic conditions. The RMSE of the four models were 4.13 TECU, 3.51 TECU, 3.25 TECU and 2.13 TECU, and MAEs were 3.61 TECU, 3.32 TECU, 2.74 TECU and 2.52 TECU, respectively.

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Table 3. Evaluation metrics of 4 models under different geomagnetic conditions Model

RMSE (TECU)

MAE (TECU)

IRI-2016

4.13

3.61

NeQuick

3.51

3.32

CNN-LSTM

3.25

2.74

BLS-LSTM-GRU

2.13

2.52

5 Conclusion In the evaluation of the accuracy of the different experimental sites, the statistical results were obtained from 24 GNSS stations in the 22 test sets per day for 24 h and 365 days per year. The empirical model IRI-2016 model has the largest RMSE and minimal correlation. The RMSE for NeQuick, CNN-LSTM, and BLS-LSTM-GRU models were 3.51 TECU, 2.13 TECU, and 1.17 TECU, and MAEs were 1.54 TECU, 1.41 TECU, and 1.21 TECU, respectively. This indicates that the BLS-LSTM-GRU neural network model has a good prediction performance, and the improved model has the best prediction performance. For the evaluation metrics of 4 models under different geomagnetic conditions, the RMSE of the four models were 4.13 TECU, 3.51 TECU, 3.25 TECU and 2.13 TECU, and MAEs were 3.61 TECU, 3.32 TECU, 2.74 TECU and 2.52 TECU, respectively. The results generate a prediction map of the total electronic content of the ionosphere and compared with empirical models and traditional neural network models under different time and solar activity conditions. The experimental results show that the root mean square error of the BLS-LSTM-GRU model decreased by 23.07%, 17.48% and 9.46% with higher prediction accuracy compared with IRI-2016, NeQuick and CNN-LSTM, respectively. Acknowledgment. We sincerely thank CDDIS for providing relevant data.

References 1. Yuan, Y.: Models and methods for precise determination of ionospheric delay using GPS. 017(002), 187–196 (2007) 2. Meyer, F., Bamler, R., Jakowski, N., et al.: The potential of low-frequency SAR systems for mapping ionospheric TEC distributions. IEEE Geosci. Remote Sens. Lett. 3(4), 560–564 (2006) 3. Forbes, J.M., Palo, S.E., Zhang, X.: Variability of the ionosphere. J. Atmos. Solar Terr. Phys. 62(8), 685–693 (2000) 4. Jiang, H., Liu, J., Wang, Z., et al.: Assessment of spatial and temporal TEC variations derived from ionospheric models over the polar regions. J. Geodesy 93(4), 455–471 (2018) 5. Klobuchar, J.A.: Ionospheric time-delay algorithm for single-frequency GPS users (1987) 6. Nava, B., CoSson, P., Radicella, S.M.: A new version of the NeQuick ionosphere electron density model. J. Atmos. Solar Terr. Phys. 70(15), 1856–1862 (2008)

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7. Rawer, K., Bilitza, D., Ramakrishnan, S.: Goals and status of the international reference ionosphere. Rev. Geophys. 16 (1978) 8. Bilitza, D.: Progress report on IRI status. Adv. Space Res. 10(11), 3–5 (1990) 9. Bilitza, D., Bhardwaj, S., Koblinsky, C.: Improved IRI predictions for the GEOSAT time period. Adv. Space Res. 20(9), 1755–1760 (1997) 10. Kong, Y., Chai, H., Li, J.Y., et al.: A modified forecast method of ionosphere VTEC series based on ARMA model. In: 2017 Forum on Cooperative Positioning and Service (CPGPS). IEEE (2017) 11. Acharya, R., Roy, B., Sivaraman, M.R., et al.: Prediction of ionospheric total electron content using adaptive neural network with in-situ learning algorithm. Adv. Space Res. 47(1), 115–123 (2011) 12. Sparks, L., Blanch, J., Pandya, N.: Estimating ionospheric delay using kriging:1. Methodology, Radio Sci. 46(RS0D21), 1–13 (2011) 13. Wang, C., Xin, S., Liu, X., et al.: Prediction of global ionospheric VTEC maps using an adaptive autoregressive model. Earth, Planets and Space 70(1), 18 (2018) 14. Xia, G., Liu, M., Zhang, F., Zhou, C.: CAiTST: conv-attentional image time sequence transformer for ionospheric TEC maps forecast. Remote Sens. 14, 4223 (2022). https://doi.org/10. 3390/rs14174223 15. Kaselimi, M., Voulodimos, A., Doulamis, N., Doulamis, A., Delikaraoglou, D.: Deep recurrent neural networks for ionospheric variations estimation using GNSS measurements. IEEE Trans. Geosci. Remote Sens. 60, 1–15 (2022), Art no. 5800715. https://doi.org/10.1109/ TGRS.2021.3090856 16. Tang, J., Li, Y., Ding, M., Liu, H., Yang, D., Wu, X.: An ionospheric TEC forecasting model based on a CNN-LSTM-attention mechanism neural network. Remote Sens. 14, 2433 (2022). https://doi.org/10.3390/rs14102433 17. Chen, C., Liu, Z.: Broad learning system: an effective and efficient incremental learning system without the need for deep architecture. IEEE Trans. Neural Netw. Learn. Syst. 29(99), 10–24 (2018) 18. Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997).https://doi.org/10.1162/neco.1997.9.8.1735 19. Chung, J., Gulcehre, C., Cho, K.H., et al.: Empirical evaluation of gated recurrent neural networks on sequence modeling. Eprint Arxiv (2014)

Heavy Rainfall Prediction Model Using Sample Entropy Derived from GNSS-PWV and PSO-SVM Fanming Wu1 , Dengao Li1,3,4,5(B) , Jinhua Zhao2 , Ran Feng1 , Danyang Shi1 , Xinfang Zhang1 , and Jumin Zhao2,3,4,5 1 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China

[email protected]

2 College of Information and Computer, Taiyuan University of Technology, Taiyuan 030024,

China 3 Key Laboratory of Big Data Fusion Analysis and Application of Shanxi Province,

Taiyuan 030024, China 4 Intelligent Perception Engineering Technology Center of Shanxi, Taiyuan 030024, China 5 Shanxi Province Engineering Technology Research Center of Spatial Information Network,

Taiyuan 030024, China

Abstract. There is a growing interest to use Global Navigation Satellite System (GNSS) inversed PWV for heavy rainfall prediction. When heavy rainfall occurs, it requires the atmosphere to contain sufficient water vapour and undergo strong upward motion. However, existing models using GNSS-PWV for heavy rainfall prediction have not accounted for the effect of the complex motion of water vapour. In this paper, an hourly heavy rainfall prediction model using sample entropy derived from GNSS-PWV and PSO-SVM is proposed. The sample entropy of GNSS-PWV is used to measure the complexity of the water vapour movement process before heavy rainfall occurs. Meanwhile, combining GNSSPWV time domain features and co-located meteorological data, the occurrence of hourly heavy rainfall events is predicted by support vector machine optimized with particle swarm. To verify the validity and feasibility of the proposed algorithm, Hong Kong’s HKSC station in Sham Shui Po is used for the model to train and test. The result shows that probability of detection, false alarm rate and critical success index of the proposed algorithm in this paper have significantly improved over other heavy rainfall prediction models. Keywords: GNSS-PWV · Sample entropy · Time domain feature · Particle swarm optimization algorithm · Support vector machine

1 Introduction Heavy rainfall seriously endangers human life and property. In July 2021, a continuous heavy rainfall event in Zhengzhou, Henan Province, killed more than 300 people and caused serious damage to the city’s infrastructure [1]. Therefore, effective monitoring © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 165–175, 2024. https://doi.org/10.1007/978-981-99-6928-9_15

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and forecasting of heavy rainfall is necessary. There is a strong correlation between the variation of water vapour content in the atmosphere and the occurrence of heavy rainfall [2]. Precipitable water vapour (PWV) is an important indicator of water vapour and enables the measurement of water vapour content [3]. Traditional PWV detection methods such as radio sounders and ground-based water vapour radiometers have disadvantages such as low spatial and temporal resolution or high cost [4]. Due to its high temporal resolution, high accuracy, all-weather capability, and 24-h observation capability, the Global Navigation Satellite System (GNSS) is widely used to detect PWV [5]. It has been shown that GNSS-PWV can be used for rainfall prediction. A rainfall prediction method is proposed by Yao et al. by combining three PWV correlation factors. The proposed model produces a true detection rate (TDR) of 82%, but the false alarm rate (FAR) reaches 60–70% for Zhejiang Province [6]. Li et al. added PWV reduction and PWV reduction rate to the three-factor approach, which effectively reduced the FAR by 32.9% [7]. The above methods all consider the change of PWV in the time domain, but heavy rainfall will cause water vapour to move upward as well as accumulate in large quantities, and it is important to consider the movement state of water vapour before heavy rainfall occurs. Sample entropy (SampEn), as a method of describing the regularity and complexity of the system, can be used to quantify the movement of water vapor [8]. Meanwhile, other meteorological elements also influence the occurrence of rainfall, therefore, this paper also considers meteorological elements such as temperature, pressure and humidity. Support vector machine (SVM), as a supervised machine learning method, can effectively predict rainfall [9]. However, the performance of SVM depends on the penalty factor and kernel parameters. Particle swarm optimization (PSO) is an iteration-based optimization algorithm with the advantages of less reliance on empirical parameters and fast convergence [10]. In this paper, the SVM parameters are optimised by PSO and improve the prediction accuracy. In this paper, we combines the SampEn of GNSS-PWV with time-domain features, while considering meteorological data to forecast hourly heavy rainfall events using PSO-SVM.

2 Study Area and PWV Sample Entropy Extraction 2.1 Study Area In the World Meteorological Organization, heavy rainfall is defined as a unit hour of rainfall between 10 mm and 50 mm, or a daily rainfall of more than 50 mm. Hong Kong’s summers are hot and humid, with most of the heavy rainfall occurring in summer. Therefore, this study uses the summer months (June to August) of each year during 2015– 2020 in Hong Kong to train and test the heavy rainfall prediction model. Sham Shui Po (SSP), Stonecutters Island (K10A) and So Uk (K06A) are the three weather stations in Sham Shui Po, which meet the requirement of co-located stations with HKSC of Hong Kong Continuous Operational Reference Station (CORS) network, the distances are all less than 3 km, the geographical distribution is shown in Fig. 1, and the coordinates

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Fig. 1. Location of stations (HKSC, weather stations, radiosonde)

and distances are shown in Table 1. Assume the maximum hourly rainfall of the three weather stations is the hourly rainfall of the HKSC station (www.weather.org.hk). Table 1. HKSC and co-located weather stations’ location and distance (km) Station

K10A 22.327 (Lat./z)

HKSC

22.322 (Lat./ z)

K06A 114.139 (Lon./z)

0.590

22.340 (Lat./ z)

SSP 114.160 (Lon./z)

2.803

22.336 (Lat./ z)

114.137 (Lon./ z)

1.581

114.141 (Lon./z)

2.2 The Method of GNSS Inversion PWV When GNSS signals are transmitted, tropospheric delay affects their transmission. The zenith tropospheric delay (ZTD) product is considered to be representative of atmospheric tropospheric delay, and the ZTD estimate in this study is calculated utilizing the GAMIT/GLOBK, which uses double-difference phase observations, with the cuttingoff angle of 10° is set and the mapping function of VMF1 is used. ZTD is subdivided into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). Then, the ZHD is obtained using the Saastamoinen model, subtract ZHD from ZTD to obtain ZWD above the GNSS station and use Eq. (1) to convert ZWD to GNSS-PWV. PWV =

106 × ZWD   w ρwater mRw Tkm3 + k2 − m md × k1

(1)

where, ρwater is the density of liquid water, R is the universal gas constant, 3 R = 8314  Pa · m (K · kmol), mw is the molar mass of water vapour, mw = 18.02 kg kmol, k 1 , k 2 , k 3 are constants, k1 = 77.604 ± 0.014 K hPa, k 2 = 70.4  K/hPa, k3 = (3.776 ± 0.014) × 105 K2 hPa. Tm is the weighted average temperature in the vertical direction of the observatory. In this study, the linear model established by chen for 8 years of meteorological data in Hong Kong is used to obtain the station’s Tm [11]: Tm = 106.7 + 0.605 · (Ts + 273.15)

(2)

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where T s represents the temperature at the station’s surface (°C).

Fig. 2. Temperature, humidity, pressure, rainfall, and GNSS-PWV for each summer between 2015 and 2020

GNSS-PWV data with 30s intervals are calculated from the HKSC observation files. Meteorological data are taken into consideration because heavy rainfall is influenced by meteorological conditions. The meteorological data obtained from the meteorological observation files of HKSC. The hourly RH, P, T, rainfall (obtained from weather stations) and GNSS-PWV are shown in Fig. 2 for Summer (June–August) in each of the years 2015–2020. 2.3 GNSS-PWV Time Domain Feature Extraction Due to the collision and merging of clouds and raindrops before precipitation occurs, the corresponding water vapor falls after reaching its peak. Based on Li et al.’s five-factor threshold model for predicting heavy rainfall, this study extracted five time-domain features of GNSS-PWV before the prediction time point [7]. The extraction methods of the five time-domain features are given in Table 2. For the purpose of demonstrating the validity of GNSS-PWV time-domain features, hourly precipitation and PWV data from three different time periods are analyzed: July 11 to July 21, 2015, July 29 to August 8, 2016, and July 1 to July 11, 2018, as shown in Fig. 3. A significant increase in PWV occurs during the hours before heavy rains begin, followed by a sharp drop after peaking. 2.4 GNSS-PWV Sample Entropy Extraction SampEn is a time series complexity measure proposed by Richman et al. [12]. It has been found that larger values of SampEn correspond to more irregularities of PWV. In this study, the embedding dimension m is set to 2 and r is set to 0.1 times sequence S’s standard deviation. The steps of the calculation follow: (1) Construct an m-dimensional vector by reconstructing the phase space of S: Si = {s(i), s(i + 1), . . . , s(i + m − 1)}, 1 ≤ i ≤ N − m + 1

(3)

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Table 2. Time-domain features extraction method of GNSS-PWV Time-domain feature

Method

1

PWV

The hourly PWV

2

PWV increment

The maximum PWV - the minimum PWV prior peak

3

PWV decrement

The maximum PWV - the minimum PWV after peak

4

Rate of increment

(The maximum PWV - the minimum PWV prior peak)/Value of the corresponding time difference

5

Rate of decrement

(The maximum PWV - the minimum PWV after peak)/Value of the corresponding time difference

Fig. 3. GNSS-PWV obtained from HKSC stations with corresponding hourly precipitation at three different time periods

Fig. 4. Three time periods of GNSS-PWV SampEn with corresponding hourly precipitation

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(2) Calculate any two vectors S i and Sj (1 ≤ j ≤ N − m + 1, j = i) at maximum distance dij to each other:   (4) dij = max |s(i + k) − s(j + k)| , k = 0, 1, . . . , m − 1 (3) Count the number Num of dij ≤ r and calculate its ratio to N-m: Num N −m

(5)

N −m+1  1 Bim (r) N −m+1

(6)

Bim (r) = (4) Take the average for Bim (r): Bm (r) =

i=1

(5) Increase the m to m + 1 and repeat steps (2)–(4) to calculate Bim+1 (r). Finally, the SampEn of the S is:  Bim+1 (r) SampEn(m, r, N ) = − ln (7) Bim (r) Figure 4 shows the correlation between SampEn of GNSS-PWV and hourly rainfall for the selected time period (Fig. 3). When heavy rainfall occurs (except for case (1) in 2016), the GNSS-PWV SampEn is in the extreme (maximum or minimum) range in most cases, indicating that the water vapour required for heavy rainfall to occur has completed its vertical movement or is in its most intense movement, the heavy rainfall is most likely to occur in these two states. A significant correlation between heavy rainfall and PWV was not observed in case (1) in 2016, suggesting that heavy rainfall may also be influenced by other factors. In other words, the SampEn can be used as one feature to describe water vapor movement before heavy rainfall occurs.

3 PSO-SVM-Based Heavy Rainfall Prediction Model 3.1 PSO-SVM Algorithm SVM uses kernel function can effectively solve the classification problem of small sample, non-linear and high-dimensional data. Based on the results of previous studies, the radial basis function (RBF) is used in this study. The RBF kernel parameters g and penalty factor c can greatly affect the accuracy of the score. In this study, g and c are optimised using PSO with the following steps: (1) initialise the parameters of the particle swarm algorithm, such as the number of iterations, population size, inertia factor, learning factor, position and velocity of each particle. (2) calculating the fitness of each particle, which is assessed using K-fold crossvalidation. (3) updating the velocity and position of the particles by iteration. (4) determine whether the termination condition is satisfied, if so, stop the optimization search process and obtain the optimal parameters (g, c), if not, return to step (2) and proceed to the next iteration.

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3.2 Model for Predicting Heavy Rainfall

Fig. 5. Hourly heavy rainfall prediction algorithm flow chart

To reduce the effect of scale differences between features, the features are normalised [13]. After normalisation of the raw data, all features mapped to between 0 and 1, and are calculated as follows: x =

x − min(x) max(x) + min(x)

(8)

After normalisation, the PSO-SVM intense rainfall prediction model is built, training using 2015–2018 data and testing using 2019 and 2020 data. Figure 5 displays the overall model diagram for the hourly heavy rainfall prediction developed in this paper. 3.3 Evaluation Indicators TDR, FAR, and critical success index (CSI) are used in this study for forecast evaluation. TDR indicates the probability of accurately predicting rainfall when it occurs; An FAR indicates how likely it is that a prediction will be incorrect without rainfall; In meteorological applications, CSI is an indicator most closely related to the target meteorological event, and the equations are: TDR =

TP TP + FN

(9)

FAR =

FP FP + TP

(10)

TP TP + FN + FP

(11)

CSI =

where The TP is when heavy rainfall is forecast and occurs; FN is an “omission” case, when heavy rainfall actually occurs but is not forecast; and FP is a “misdiagnosis” case, when heavy rainfall is forecast but does not actually occur.

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4 Results and Discussion 4.1 Feature Correlation Analysis The correlation analysis of the 11 features for 2015–2020 is shown in Fig. 6. It can be seen from the figure that PWV values are positively correlated with PWV increment and negatively correlated with PWV decrement. Meanwhile, the correlation coefficient between the HOD and T is −0.78, and the correlation between the DOY and RH is 0.53. The correlation coefficients between RH, T, DOY and HOD with PWV are all greater than 0.2, and the correlation coefficient between HOD and SampEn is 0.21. Correlation analysis reveals the characteristics of the two types of data and therefore needs to be further validated with different combinations of features to determine the best set of features.

Fig. 6. Feature-by-feature correlation analysis

4.2 Effect of Different Features on Model Prediction Results Using five different combinations of features to build PSO-SVM heavy rainfall prediction models and to compare performance. The results of the comparisons are shown in Table 3. It can be seen that the worst performance in predicting heavy rainfall is achieved when only using PWV values. When PWV increment and PWV increment rate are added, the prediction performance is significantly improved, with 13.16% improvement in TDR. The FAR of the model was reduced significantly when five time-domain features are used. With the addition of SampEn, TDR and FAR improved further to 93.42% and 24.47% respectively, and CSI increased by 41.83% compared to using PWV value only. The best performance is achieved when weather data is added, with TDR, FAR and CSI reaching 96.05%, 18.89% and 78.49% respectively. 4.3 Impact of Different Machine Learning Algorithms on Model Prediction Results Compared to other classical machine learning algorithms including back propagation neural network (BPNN), decision tree (DT), SVM with unoptimised parameters. Features using all 11 features, Table 4 displays the results.

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Table 3. Performance of prediction models built with different features Features

TP

FN

FP

TDR(%)

FAR(%)

CSI(%)

PWV

52

24

98

68.42

65.33

29.89

PWV + increment + increment rate

62

14

87

81.58

58.39

38.04

Five PWV time-domain features

66

10

38

86.84

36.54

57.89

Five PWV time-domain features + SampEn

71

5

23

93.42

24.47

71.72

All features

73

3

17

96.05

18.89

78.49

Table 4. Different machine learning algorithms’ performance on prediction models Different algorithms

TP

FN

FP

TDR(%)

FAR(%)

CSI(%)

BPNN

69

7

68

90.79

49.64

47.92

DT

67

9

76

88.16

53.15

44.08

SVM

70

6

29

92.11

29.29

66.67

PSO-SVM

73

3

17

96.05

18.89

78.49

The results show that when using BPNN, the TDR for heavy rainfall prediction is 90.79% and the performance is higher DT. When using SVM, the model FAR is reduced by about 20% compared to BPNN, and CSI is increased by about 20% compared to BPNN and DT. After PSO optimization of SVM, the heavy rainfall prediction model performed best. 4.4 Forecasting Model Comparison Also, comparisons were made with other existing models for predicting heavy rainfall in Fig. 7. With a TDR of 72% and FAR of 21%, Benevides et al. proposed a non-linear autoregressive neural network prediction model using PWV and meteorological data [14]. Using PWV and meteorological data, Li et al. developed a BPNN-based heavy rainfall prediction model with a TDR of 94.5% and a FAR of 20.8% [15]. The algorithm in this paper also improves on it. This paper presents an algorithm that outperforms existing models for predicting heavy rainfall.

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Fig. 7. Forecasting model comparison

5 Conclusion This paper uses GNSS-PWV SampEn to measure airflow upwards and proposes a model for predicting heavy rainfall using GNSS-PWV SampEn and PSO-SVM. To accurately predict heavy rainfall, five time-domain features and SampEn of PWV are used, along with meteorological factors, and the PSO-SVM algorithm. Acknowledgments. The paper is supported by the Research and Development Project of Key Core and Common Technology of Shanxi Province (2020XXX007), and Key Research and Development Projects of Shanxi Province (202102020101001).

References 1. Yin, J., et al.: A possible dynamic mechanism for rapid production of the extreme hourly rainfall in Zhengzhou City on 20 July 2021. J. Meteorol. Res. 36, 6–25 (2022) 2. Ye, H., Fetzer, E.J., Wong, S., Behrangi, A., Yang, D., Lambrigtson, B.H.: Increasing atmospheric water vapor and higher daily precipitation intensity over northern Eurasia. Geophys. Res. Lett. 42, 9404–9410 (2015) 3. Manandhar, S., Lee, Y.H., Yu, S.M.: GPS-PWV based improved long-term rainfall prediction algorithm for tropical regions. Remote Sens. 11(22), 2643 (2019) 4. Dembelov, M.G., Bashkuev, Y.B.: Estimation of the tropospheric moisture content derived from GPS observations, radio sounding data, and measurements with a water vapor radiometer. Atmos. Oceanic Optics 35(4), 359–365 (2022) 5. Bevis, M., Businger, S., Chiswell, S., Herring, T.A., Ware, R.H.J.J.O.A.M.: GPS meteorology: mapping zenith wet delays onto precipitable water 33, 379–386 (1994) 6. Yao, Y., Shan, L., Zhao, Q.: Establishing a method of short-term rainfall forecasting based on GNSS-derived PWV and its application. Rep 7(1), 12465 (2017) 7. Li, H., Wang, X., Wu, S., et al.: Development of an improved model for prediction of short-term heavy precipitation based on GNSS-derived PWV. Remote Sens. 12(24), 4101 (2020) 8. Zhang, Y., Ma, J., Zhang, C., et al.: Electroencephalography sample entropy of driver passive fatigue threshold in automated driving (2021) 9. Zhao, Q., Liu, Y., Yao, W., et al.: Hourly rainfall forecast model using supervised learning algorithm. IEEE Trans. Geosci. Remote Sens. (99), 1–9 (2021) 10. Yun, F., Dong, H., Liang, C., et al.: Feature selection of XLPE cable condition diagnosis based on PSO-SVM. Arab. J. Sci. Eng. 1–11 (2022) 11. Chen, Y.: Inversing the content of vapor in atmosphere by GPS observations=. Modern Surveying and Mapping (2005)

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12. Richman, J.S., Moorman, J.R., et al.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. (2000) 13. Palaniappan, R., Ravi, K.: Improving visual evoked potential feature classification for person recognition using PCA and normalization. Pattern Recogn. Lett. 27(7), 726–733 (2006) 14. Benevides, P., Catalao, J., et al.: Neural network approach to forecast hourly intense rainfall using GNSS precipitable water vapor and meteorological sensors. Remote Sens. (2019) 15. Li, H., Wang, X., Zhang, K., et al.: A neural network-based approach for the detection of heavy precipitation using GNSS observations and surface meteorological data[J]. J. Atmos. Solar Terr. Phys. 225(1), 105763 (2021)

High Precision ZTD Model for the Chinese Southeast Region Using ERA5 Reanalysis Data Fangxin Hu1,2(B) , Pengfei Xia2 , Shirong Ye2 , and Jia Luo1 1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

[email protected] 2 GNSS Research Center, Wuhan University, Wuhan 430079, China

Abstract. Improving the accuracy of troposphere Zenith Total Delay (ZTD) is essential in Global Navigation Satellite System (GNSS). In this study, a high precision ZTD model for Chinese Southeast region is constructed by the ERA5 reanalysis data, considering the relationship between ZTD and elevation mainly shows a negative exponential form and the ZTD at a certain elevation has a significant periodicity. Therefore, combining the periodicity of ZTD at the Mean Sea Level (MSL) with the elevation normalization factor, the ZTD of test stations can be acquired by restoring the grid ZTD to the same elevation with test stations. The ZTD derived from the static PPP (Precise Point Positioning) solutions in 2022 of CMONOC (Crustal Movement Observation Network of China) was used as the reference value to measure the accuracy of the model, and the error RMS (Root Mean Square) of the test stations was in the range of 1.73 cm ~ 5.12 cm, and the MAE (Mean Absolute Error) was in the range of 1.40 cm ~ 4.33 cm. The total error RMS is 3.39 cm and the MAE is 2.53 cm. This model fully takes the variability of ZTD with elevation in different latitude and longitude regions into account, and can meet the troposphere delay correction needs of regional GNSS navigation and positioning. Keywords: ERA5 reanalysis data · Troposphere zenith total delay · Negative exponential form · Elevation normalization factor

1 Introduction Troposphere delay is one of the major errors in GNSS, which is caused by the change of propagation speed and propagation path of electromagnetic wave signals through the neutral troposphere. A high accuracy troposphere delay model can provide a more accurate priori troposphere delay error for satellite navigation positioning and reduce the positioning convergence time. There are several ways to model the troposphere delay: the first one is relying on measured meteorological parameters, commonly used are Hopfiled model [1] and Saastamonien model [2], the accuracy of the model can reach the decimetre or centimetre level, but the model relying on measured meteorological parameters needs to be equipped with meteorological observation equipment which cost is high, such as sounding stations, and the product provided has a lag and is not suitable for real-time applications. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 176–186, 2024. https://doi.org/10.1007/978-981-99-6928-9_16

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The second way is to estimate the troposphere delay as a parameter while the dry delay of ZTD is corrected using a model in Precise Point Positioning using ionospheric-free combination, specifically, the zenith wet delay combined with a mapping function as the estimated parameter obtained by solving uniformly with other errors, ZTD obtained by this way usually regarded as a reference for model evaluation. The third way is modelling based on atmospheric products obtained by meteorological interpolation, such as the models UNB model [3] and UNB3 [4] model promoted by the WAAS (wide area augmentation system).The UNB3 model has low accuracy in the high altitude region [5], and the improved UNB3m model was subsequently obtained by using relative humidity instead of water vapor pressure, but the model has a large bias in wet delay above 2 km elevation [6]. The EGNOS model used by the European Geostationary Navigation Overlay Service [7] has an accuracy comparable to that of models rely on measured meteorological parameters [8]. The model obtained by meteorological interpolation cannot accurately describe the variation characteristics of meteorological parameters in time space, so some scholars construct a global temperature and pressure grid model at the global temperature and pressure grid. Landskron (2018) proposed the GPT3 (Global Pressure and Temperature3) model based on the VMF3 (Vienna Mapping Function3) mapping function [9]. The model is constructed with a grid point containing the spatial and temporal characteristics of the meteorological parameters required for the troposphere zenith delay, such as air pressure, temperature, specific humidity, water vapor pressure decay factor and water vapor average temperature at the elevation of the grid point, etc. The ZTD is then obtained by calculating the dry delay from the Saastamonien model and the wet delay model proposed by Askne and Nordius [10]. The troposphere ZTD is closely related to the elevation, and the ZTD of a radio signal received at a certain altitude can be obtained by integrating the atmospheric refractive index over its propagation path. Yao et al. [11] proposed a troposphere delay correction model based on the spherical harmonic function with RMS of 4.24 cm by analyzing the time variation characteristics of the global troposphere zenith delay grid, and used an exponential model when considering the effect of elevation while the ZTD variation coefficient with elevation in the model is a global average coefficient. Chen et al. [12] proposed a ZTD model for mainland China based on GNSS data from CMONOC, which also used an exponential form to represent the relationship between ZTD and station elevation. The elevation normalization coefficients were given in different five latitude ranges to normalize the ZTD of base stations to the ellipsoidal plane, and the period characteristics of the normalized ZTD were analyzed to construct an ellipsoidal grid with an RMS value of 3.4 cm. Song et al. [13] used the SHAO-C model for the Chinese region with ECMWF pressure-level data, in which the ZTD at the reference height of each grid point is fitted with a cosine function, while the variation of ZTD along the height is expressed as a second-order polynomial. The model is more accurate than the EGNOS model in the Chinese region with large elevation fluctuations. Xia et al. [14] proposed a real-time troposphere grid model for the Chinese region based on ERA5 reanalysis data and real-time GNSS station data sources, which fully considers the timeseries of long-term ZTD variation with elevation for different grid points and is applied to precision single-point localization to reduce the localization convergence time.

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This paper presents a regional troposphere ZTD model based on the fifth generation reanalysis meteorological data ERA5 of the European Center for Medium-Range Weather forecasts (ECMWF), which makes full use of the stratification characteristics of the ERA5 reanalysis data and provides the grid elevation normalization factor describing the variation of ZTD with elevation according to the 0.5°*0.5° grid points. The temporal characteristics of the ZTD at MSL of the grid network are analyzed for providing the real-time troposphere ZTD. Compared with the troposphere delay modeling based on real-time solutions, the troposphere ZTD grid model obtained by ERA5 reanalysis data can compensate the shortcomings of the grid network that cannot obtain ZTD due to the small distribution of real-time stations. Therefore, the area of southeast China with less distribution of land-based networks is adopted as the modeling area and its accuracy is verified. The main processes are as follows: 1) The southeastern region of China (15◦ N ∼ ◦ 35 N , 100◦ E ∼ 125◦ E) is selected as the modeling area, and the mean value of elevation normalization factor describing the variation of ZTD with elevation h on the 0.5°*0.5° grid point for the whole year of 2021 is calculated based on the ERA5 reanalysis data. 2) The ZTD at the MSL are obtained by fitting the ZTD of levels with elevation through the negative exponential form. We analyze the spatial and temporal characteristics of the ZTD at MSL of each grid point, and then obtain the period coefficients by fitting the Fourier series taking the annual mean, annual amplitude, semi-annual amplitude and daily amplitude into account. 3) Construct a regional troposphere ZTD grid model and provide the product for users: firstly, find the four closest grid points of the user’s location in the grid, get the period coefficients at the four grid points and calculate the ZTD at the MSL of grids. Using the elevation normalization factor in step 1 to restore the ZTD at the MSL of grids to the same elevation as the test stations. Through interpolation, users can get the ZTD of test stations.

2 Elevation Normalization Factor Grid 2.1 Calculate ZTD by ERA5 Reanalysis Data The European Center for Medium-Range Weather Forecasts (ECMWF) is an institution composed of 34 countries. Currently, the ECMWF Center can provide decades-long reanalysis products, and ERA5 is its fifth generation of reanalysis data. The grid products have a maximum horizontal resolution of 0.25°*0.25°, a time resolution of 1 h, a vertical resolution of 37 pressure levels, and a data release delay of about 5 days. Firstly, the atmospheric refractive index is calculated based on the meteorological parameters pressure p (hpa), water vapor pressure e (hpa), and temperature T (K) in the ERA5 product, and then the ZTD can be obtained by integrating the refractive index at each layer level: N = k1

e e (p − e) + k2 + k3 2 T T T

htop ZTD = Ndh + ZTDsaas h1

(1)

(2)

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where k1 = 77.6890, k2 = 71.2952, and k3 = 3.75463e5. ZTDsaas represents the total delay to the process above the highest level of ERA5 reanalysis data. When the elevation reaches 50km, the water vapor content is close to zero and the wet delay can be ignored. Therefore, the traditional Saastamonien model can be used to calculate the zenith dry delay ZHD as the total delay more accurately, and the model calculation formula is as follows: P (3) ZTDsaas = 0.002277 ∗ 1 − 0.00266cos(2ϕ) − 0.00028h ϕ represents the latitude, and h represents the elevation (km). The ZTD of different layers are shown as follows:

Fig. 1. ZTD of ERA5 level and fitting curve

2.2 Elevation Normalization Factor Fit The relationship between ZTD and elevation h normally satisfies the negative exponential form, and the coefficient b in Eq. (4) describing the variation of ZTD with elevation h is called the elevation normalization factor. ZTD = a · exp(b · h)

(4)

The blue curve in Fig. 1 is a negative exponential form fitting curve. The above equation was used to calculate the mean elevation normalization factor b over the 0.5°*0.5° grid point in the southeast region of China (15◦ N ∼ 35◦ N, 100◦ E ∼ 125◦ E) in 2021, plotted as Fig. 2. The elevation normalization factor describes the variation of ZTD with elevation on the vertical profile. It can be seen from Fig. 2 that the elevation normalization factor is latitude-dependent. The average elevation normalization factor is larger at low latitudes where the ocean area and the water vapor is concentrated in the bottom atmosphere, and the water vapor content varies more with increasing altitude. In contrast, the water vapor content is smaller in the inland plateau region, and the change is not obvious with the increase of height, so the average elevation normalization factor is smaller than that of the coastal region. The mean elevation normalization factor is used to restore the ZTD at the MSL to a certain elevation for users.

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Fig. 2. Mean elevation normalization factor of grid

3 ZTD Spatial and Temporal Characteristics Analysis The ERA5 reanalysis data has roughly a 5-day delay, so building a real-time troposphere delay grid requires an analysis of historical ZTD variation characteristics. The ZTD at the MSL was obtained by normalizing the ERA5 grid point ZTD data to MSL by formula (4) where the coefficient h equals 0. The red points in the following figure represents the ZTD at the MSL of grid points for the grid points from 2019 to 2021.

Fig. 3. ZTD time series of MSL from 2019 to 2021

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It can be seen from Fig. 3 that ZTD at the MSL have a strong periodic variation, and the period coefficients of ZTD at the MSL of grid points are solved using a unified least squares fit of the grid point data from 2019 to 2021. The fitting formula is a Fourier series that takes the annual, semi-annual and daily periodic variations into account for the subsequent extraction of prediction. The fitting formula is as follows.     doy doy + a2 sin 2π · b = a0 + a1 cos 2π · 365.25 365.25     doy doy + a4 sin 4π · + a3 cos 4π · 365.25 365.25     hod hod + a6 sin 2π · (5) + a5 cos 2π · 24 24 The annual mean, annual amplitude, semi-annual amplitude, and daily amplitude of the entire regional grid points are plotted as follows.

Fig. 4. Annual mean, annual amplitude, semi-annual amplitude and daily amplitude of ZTD at the MSL

It can be seen from Fig. 4 that the annual mean term is mainly strongly correlated with latitude, specifically, the annual mean of ZTD at the MSL is larger at low latitudes than that at high latitude range. The annual amplitude is related to the elevation, and the annual amplitude is larger in the plateau area. The daily amplitude is influenced by the coast, and the daily cycle amplitude is larger in the coastal part.

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4 Regional Troposphere Zenith Total Delay Grid Model According to the periodicity analysis of ZTD at the MSL of grids, we can overcome the shortcoming of the time delay by ERA5 meteorology products. Only the doy in a year and hod in a day are acquired for the prediction. Therefore, the overall steps to obtain the regional real-time ZTD are as follows: (1) Firstly, the seven periodic coefficients describing the ZTD at the MSL and the mean elevation normalization factors at the four grid points adjacent to the station are obtained. (2) Through the period coefficients a0 ~a6 of four grids, the ZTD at the MSL can be calculated with the time information the users required. (3) Finally, with the average elevation factors of four grid points, the ZTD at the MSL of grid points can be restored to the users’ elevation. Through the interpolation, we can get the ZTD for users. Stations of the CMONOC GNSS stations in the southeast region of China are selected, and the ZTD solved by the PPP for the first three months of 2022 is used as the reference value to measure the accuracy (sampling rate 30s) for this model, and the distribution of the stations is as follows (Fig. 5).

Fig. 5. GNSS stations of CMONOC location

The elevation range of the selected stations varies significantly, which can well reflect the model accuracy of different elevations and locations. The parameters estimated from PPP are set as follows, where the GMF projection function is used for the mapping function [15] (Table 1). The model was used to calculate the ZTD for each station and compared with the static PPP solution. Calculate the Root Mean Square (RMS) and Mean Absolute Error (MAE) for each station, and the results are as follows (Fig. 6). The RMS of the test stations ranged from 1.73 cm to 5.12 cm, and the MAE ranged from 1.40 cm to 4.33 cm. Statistics of the overall test stations accuracy, the total error RMS is 3.39 cm and MAE is 2.53 cm.

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Table 1. Parameters setting of calculating ZTD by PPP. Errors

Strategy

Satellite orbits and clock error

Using WUM center orbital clock products

Satellite attitude correction

Using WUM center satellite attitude products

Relativistic effects

Empirical model correction

Satellite cut-off elevation

7°

Pseudorange and phase observation noise Pseudorange: 0.3m; phase observation: 0.003m Ionosphere delay

Dual frequency IF combination is used to eliminate the influence of ionosphere

Troposphere delay

Model corrected zenith dry delay Parameter estimation of zenith wet delay and horizontal gradient

Phase ambiguity

Fixed solution based on WUM center bias product

Antenna phase correction

igs14.atx

Phase winding

Empirical model correction

Solid tide correction

Empirical model correction

Receiver clock bias

White noise estimation

Code bias correction

Correction with IGS center DCB products

Fig. 6. RMS and MAE of stations from Jan. to Mar. in 2022 ERA5 model

Compared with the Hgpt model published in 2020, an empirical model for meteorology parameters include pressure and temperature. For the same test stations above, the error RMS and MAE in 95% confidence interval can be shown in Fig. 7 and Table 2.

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Fig. 7. Error RMS and MAE of stations from Jan. to Mar. in 2022 in 95% confidence interval of Hgpt model and ERA5 model Table 2. Statistic of total error RMS and MAE of Hgpt model and ERA5 model. RMS (cm)

MAE (cm)

Hgpt model

2.68

2.05

Model based on ERA5

2.37

1.89

In 95% confidence interval, the results show that the total error RMS and MAE for the model in this study are 2.37 cm and 1.89 cm while the total error RMS and MAE for the Hgpt model are 2.68 cm and 2.05 cm. The ZTD grid model based on the ZTD at the MSL has a significant improvement than the normal empirical ZTD model.

5 Conclusion In this paper, the ERA5 reanalysis data provided by The European Center for MediumRange Weather forecasts (ECMWF) are used to model the regional troposphere ZTD grid. In order to describe the relationship between ZTD and elevation h, the ZTD for each layer is firstly calculated from the 2021 ERA5 reanalysis meteorological data, and then the elevation normalization factor is obtained by curve fitting in a negative exponential form, meanwhile, the ZTD at the MSL can be also calculated through the fitting form. The average elevation normalization factor of each grid point in 2021 is used for restoring the ZTD at the MSL to the same elevation as users’ test stations. The observed data provided by the ERA5 reanalysis data has a delay of about 5 days, and in order to meet the needs of real-time model, the spatial and temporal characteristics

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of the ZTD at the MSL of each grid point are analyzed. Finally, with the ZTD at the MSL and the mean elevation normalization factor, high precision troposphere ZTD grid model is established. Compared with the ZTD derived from PPP, with statistic of all test solutions, the error RMS of the test stations ranges from 1.73 cm to 5.12 cm and MAE ranges from 1.40cm to 4.33cm, and the total error RMS is 3.39cm and MAE is 2.53cm which has a great accuracy.Compared with the empirical numerical Hgpt model, in the 95% confidence interval, model promoted by this study has a total error RMS 2.37 cm and MAE 1.89 cm while the Hgpt Model has a total error RMS 2.68 cm and MAE 2.05 cm. The troposphere model based on the ERA5 reanalysis data is effective and fully takes the variability of ZTD with elevation in different latitude and longitude regions into account, which can meet the troposphere delay correction needs of regional GNSS navigation and positioning for users.

References 1. Hopfield, H.S.: Two-quartic tropospheric refractivity profile for correcting satellite data. J. Geophys. Res.Geophys. Res. 74(18), 4487–4499 (1969) 2. Saastamoinen, J.: Atmospheric correction for the troposphere and stratosphere in radio ranging of satellites. Use of Artificial Satellites for Geodesy Geophysics Monograph Service 15, 247–251 (1972) 3. Collins, J.P., Langley, R.B.: A tropospheric delay model for the user of the wide area augmentation system. vol. 20. Fredericton, NB, Canada: Department of Geodesy and Geomatics Engineering, University of New Brunswick (1997) 4. Collins, J.P., Langley, R.B.: The residual tropospheric propagation delay: how bad can it get?. In: Proceedings of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 729–738 (1998) 5. Collins, J.P., Langley, R.B., LaMance, J.: Limiting factors in tropospheric propagation delay error modelling for GPS airborne navigation. In: Proceedings of the Institute Navigation on 52nd Annual Meet, vol. 3 (1996) 6. Leandro, R.F., Santos, M.C., Langley, R.B.: UNB neutral atmosphere models: development and performance. In: Proceedings of the 2006 National Technical Meeting of the Institute of Navigation, pp. 564–573 (2006) 7. Penna, N., Dodson, A., Chen, W.: Assessment of EGNOS tropospheric correction model. J. Navig. 54(1), 37–55 (2000) 8. Qu, W., Zhu, W., Song, S., Ping, J.S.: The evaluation of precision about Hopfield, saastamoinen and EGNOS tropospheric delay correction model. Acta Astronom, 49(1), 113–122 (2008) 9. Daniel, L., Johannes, B.: VMF3/GPT3: refined discrete and empirical troposphere mapping functions. J. Geodesy 92(4), 349–360 (2018) 10. Askne, J., Nordius, H.: Estimation of tropospheric delay for microwaves from surface weather data. Radio Sci. 22(03), 379–386 (1987) 11. Yao, Y., He, C., Zhang, B.: A new global zenith tropospheric delay model GZTD, Chin. J. Geophys. 56(7), 2218–2227 (2013) 12. Chen, J., Wang, J., Wang, J., Tan, W.: SHAtrop: empirical ZTD model based on CMONOC GNSS network. Geomatics and Information Science of Wuhan University 44(11), 1588–1595 (2019) 13. Song, S., Zhu, W., Chen, Q., Liou, Y.: Establishment of a new tropospheric delay correction model over China Area. Sci. China (Phys., Mech. Astronomy), 54(12), 2271–2283 (2011)

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14. Xia, P., Tong, M., Ye, S., Qian, J., Fangxin, H.: Establishing a high-precision real-time ZTD model of China with GPS and ERA5 historical data and its application in PPP. GPS Solutions 27(1), 1–16 (2023) 15. Boehm, J., Niell, A., Tregoning, P., et al.: Global Mapping Function (GMF): a new empirical mapping function based on numerical weather model data. Geophys. Res. Lett. 33(7) (2006)

Research on the Construction of “BeiDou Navigation Satellite System Application Industry Development Index” System Jianhua Wei(B) and Bin Li Beidou Application Development Research Institute, Beijing 100089, China [email protected]

Abstract. The “BeiDou Navigation Satellite System Application Industry Development Index” system (abbreviation: “BDS Index”, BDI) constructs with 3 level and more than 70 indicators from four dimensions: Education/scientific research and development, Technical performance, Economy, Social benefit. The indicators could monitor and identify the health problems of BeiDou Navigation Satellite System Application Industry (abbreviation: BDS Industry). The experts of “BDS Industry Development Think Tank” (abbreviation: “BDTT”) hold meeting to analyze the health problems and make suggestions, try to find out the bottleneck and obstacles of the BDS industry, and then leverage the companies to work out the solutions fixing the problems. BDI system would track the results and evaluate the solutions. So that through such kind of methodology to form the BDI positive feedback closed-loop ecosystem to achieve the purpose of promoting the high-quality development of the BDS industry. Keywords: BDS Index · BDI · BDS think tank · BDTT

1 Background As BeiDou Navigation Satellite System 3 (BDS-3) has completed the construction and provided open global service, China has built the BDS into a top-class system with cutting-edge technologies, pioneering design and powerful functions. BDS technology has been accelerated applying to the national economy and society. The BDS industrialization gradually formed. In order to ensure steady development of the BDS industry, BeiDou Application Development Institute initiated BDI system construction researching. 1.1 Present Situation Analysis GNSS and LBS Association of China published “China Satellite Navigation and Location Service Industry Development White Paper” [1] annually. China Securities Index Co., Ltd released “China Securities Satellite Navigation Industry Index”. They are good references for constructing BDI system. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 187–200, 2024. https://doi.org/10.1007/978-981-99-6928-9_17

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The “White Paper” could report the status of BDS industry with a variety of statistical data, which is similar to the disease statistical report of National Health Commission. The “China Securities Satellite Navigation Industry Index” can accurately reflect the stock market value of listed companies in the BDS industry, similar to the production and operation statements of pharmaceutical factories. At present, there is no systems just like hospital /physical examination center, which can monitor the health status of BDS industry through multiple inspection indicators to provide diagnostic report and treatment plan. In order to promote the healthy development of BDS industry, we need to establish an index system similar to hospital system to track the BDS industry development health. 1.2 Necessity The BDS industry is developing in the direction of scale, complexity, lead to the monitoring and analysis the BDS industry becoming more difficult and beyond the decision makers personal ability. So establish BDI system, can be timely, accurate and comprehensive for observing the trend of BDS industry development and health problems, auxiliary leaders scientific decision-making and formulate macro-control policies. In addition, The State Council Information Office of the People’s Republic of China published the white paper titled “China’s BDS Navigation Satellite System in the New Era” [2] on November 4, 2022. In the Chap. 4: “Promoting Sustainable Development of the BDS Applications Industry”, Sect. 3: “Fostering a Sound Ecosystem for Industrial Development”, announced that China would “Establishing an industrial assessment system. To ensure the healthy and sustainable development of the BDS applications industry, China has worked to improve the feedback mechanism for BDS applications and established an assessment system for key industries and fields, major regions, mass applications, and international applications.” This white paper are the guidance for BDI system construction.

2 System Design 2.1 Construction Purpose The purpose of building the BDI system is to make health monitoring and prediction of the development trend of the BDS industry, so as to comprehensively and systematically provide scientific decision-making reference basis for governments, scientific research institutions, enterprises and investment companies in the ecological chain of the BDS industry. 2.2 Modeling Method Since there is no satellite navigation industry index that could be studied as reference. So that the BDI research team has independently developed and designed “index bionic modeling method” (hospital ecosystem as bionic object): constructing BDI indicator database simulating the physical examination center of hospital; constructing BDTT

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simulating hospital outpatient doctors; experts of BDTT analyzing BDI data and advising simulates the doctor diagnosing and prescribing; collection and monitoring the data of BDI simulates the hospital laboratory to collect and investigate the sample data of patients; constructing the BDI system business model simulating the supply chain system between the hospital and pharmaceutical factory. The research team constructed the whole BDI system as hospital-like ecosystem with this method finally. 2.3 Algorithm The construction process of BDI system mainly includes five steps: BDS industry research, monitoring indicator database construction, sample data collection and association, index weight determination and index model system construction. The research team developed BDI algorithms mainly reference the index indicator database construction method, index modeling method, data collection method, key technology selection evaluation method, evaluation index system construction method, sustainable development value evaluation method, expert brainstorming method, hierarchical analysis method, Delphi method from the publications of “Artificial Intelligence Index Report 2022” [3], “Global Financial Centers Index” [4], “A-share Listed Company sustainable Development Value Assessment Report” [5], “Intelligent Operation, Maintenance and Practice of the BDS Navigation Satellite System” [6] “BDS Navigation Satellite System Open Service Performance Standard” [7], “DIIS Theory and Methodology in Think Tanks” [8], “Research on Basic Theory and Application Method of Defense Critical Technology Selection” [9], “Evaluation Index System for Think Tank Experts” [10]. Finally built BDS industry monitor system with 4 level-1 indicators, 19 level-2 indicators, 48 level-3 indicators. The classification of indicators refers to the method of international and domestic cases, divides to 3 level with tree structure. Consulting “Artificial Intelligence Index Report 2022” [3] indicator classification methodology and considering the BDS industry features, BDTT drew the profile of BDI with more than 100 attributes at three levels, and then the experts study and select the final attributes as indicators loading into index database based on the principles of independence (each index represents one dimension, and the dimensions conform to the concept of orthogonality of linear algebra), representativeness, quantifiable, measurable, data accessibility, and comprehensiveness. For instance, The first-level indicators are divided into four dimensions: Education/scientific research and development, Technical performance, Economy, Social benefit. These 4 dimensions, each one links at the source, upper, middle and lower territory of the BDS industry. There are no major omissions. That follows comprehensive and representative principle; The four dimensions conform to the orthogonality concept of linear algebra, no overlap, follow the independence principle; After subdividing the first-level indicators to the third level indicators, all indicators are quantifiable, measurable. And eliminate indicators of unavailable data, or redesign the alternative indicators, ensure the comprehensiveness of the indicators. For instance, the “Beidou dual-carbon monitoring” indicators, in order to get the mileage monitoring of environmental pollution caused by traditional fuel vehicles, but many vehicles are not equipped with BDS navigation and positioning terminals, so unable to directly monitor these vehicles with the BDS technology, therefore, the specially designed fuel consumption is converted

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into the BDS monitoring mileage, and then, compared with the installation of the BDS navigation and positioning terminal to monitor the mileage of new energy vehicles, The “Beidou dual-carbon” monitoring indicator has been constructed. So that the indicator database of BDI is constructed, selected step by step, classified and one by one according to the above methods, and finally, the basic prototype of 4 first-level indicators, 19s-level indicators and 48 third-level monitoring indicators is formed. The indicators would be reviewed by BDTT experts every year, and individual indicators could be adjusted accordingly. BDI calculation formula after data normalization: BDI (x) =

p 

(wk ·

k=1

t 

ai )

i=1

Weight allocation formula: Level-1: w(i) = 1/n ∗ 100% Level-2: w(j) = w(i) ∗ z/y Level-3: w(k) = w(j) /z t: Number of sample data units x: The annual logo, from 2016 to 2021 a: The sample data w: Weight n = 4, m = 19, p = 48: the number of three levels indicators y: The number of level-3 indicators under the level-1 index z: The number of level-3 indicators under the level-2 index i = 1 to n, j = 1 to m, and k = 1 to p Optimization iteration of indicators weights adopts the Delphi method. 2.4 Data Sources In order to ensure the accuracy and comprehensive of the monitoring data, we queried data from the public database of authorities, such as China Network (https://www.cnki. net/), BDS related statistical reports of the Cyberspace Administration of China, Sampling data of the BDS industry head units mainly from: universities, research institutes, listed companies, state-owned enterprises, high-tech enterprises, institutional investors, BDS industrial park and overseas representatives. 2.5 Construction of the BDTT BDTT experts mainly come from the university department dean, scientific research institute director, state owned enterprise information technology department manager, listed company CTO, directors of institutional investor, provincial local government BDS industry related CPPCC member/NPC member/Party representatives. The experts has been divided into 10 professional groups: • BDS Frontier technology Research Group • BDS Safety Application Research Group

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BDS Big Data Research Group BDS Development Strategy and Industrial Policy Research Group BDS Financial Application Research Group BDS Intelligent Application Research Group BDS Industry Investment Research Group BDS Application Innovation and Incubation Research Group BDS Application Research Group for Key Industries BDS Mass Application Research Group.

2.6 BDI Report Form The research team sends “BDI report” to the State-owned Assets Supervision and Administration Commission of the State Council, Cyberspace Administration of China, China Satellite Navigation Office. The report would be released publicly at an appropriate time. The report composes of three parts: • BDI indicator monitoring charts; • Interpretation and analysis of the indicators monitoring results and data, as well as the bottlenecks or obstacles to the development of the BDS industry found; • BDTT expert opinions and suggestions. The content and form of the BDI report samples are briefly lists as follows. The content and form of the BDI report are briefly described in the following chapters, and the meanings of words, arrows or circles highlighted with difference colors are as follows: • • • •

Green logo: means that the indicator is healthy and valuable Colourless description: means that the index is normal White note: indicates that the index changes, need to be further observed Blue reminder: indicates that the indicator is abnormal, to remind attention, need to adjust the strategy • Yellow alert: means that the index is not normal, to pay attention to, need to improve the methods • Red warning: It indicates serious problems with the index, and it needs to be vigilant and take action. Overall indicator See Fig. 1. Figure 1 Analytic Report:. Year

Interpretation (phenomenon)

Study and judgment (reason)

2016–17

The BDI has remained almost unchanged

Restricted to the BDS-2 performance and service scope

2017–18

The BDI grew sharply by 22.1%

The BDS-3 launched, greatly improving the performance and service scope (continued)

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(continued) Year

Interpretation (phenomenon)

Study and judgment (reason)

2018–19

The BDI fell suddenly

Affected by the trade war between China and the United States

2019–21

The BDI resumed growth by 10.3%

Due to the COVID-19 pandemic, the growth rate was lower than that in 2017–18

BDTT Experts Expert comments and suggestions: ➀ It is found that the main factors affecting the changes of the BDI (impact the healthy of the BDS industry) in the past five years are: International political situation, Domestic economic development, the level of scientific and technological progress, and the state of COVID-19 ➁ In order to promote the sustainable and healthy development of BDS industry, it is suggested that the relevant decision-making bodies can consider formulating the development strategy from the above four influencing factors, such as • Develop a win-win cooperation solution and peaceful development strategy that can break through the international political influence for promoting the internationalization of BDS industry; • Plan the development outline of BDS industry “new infrastructure” and public demand key areas internally for promoting BDS industry scale; • Introduce BDS technology innovation and business model innovation incentives for promoting BDS industry marketization; • Study and formulate the BDS business expansion action plan that can effectively avoid and adapt to the long-term impact of COVID-19 for promoting the sustainable development of BDS industry

Fig. 1. The BDI overall development trend chart

Level-1 monitoring indicators See Figs. 2 and 3. Figures 2 and 3 Analytic Report:

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Fig. 2. Radar diagram of level-1 index

Fig. 3. Trend chart of level-1 index

Monitoring results of level-1 index radar diagram Year

Interpretation (phenomenon)

Study and judgment (reason)

2016 2017

Technical performance index and social benefit index are short board

Technical performance index will affect the social benefit index

2018

Social benefit index and economy index are the short The improvement of board technical performance index has a hysteresis effect on the social benefit index and economy index

2019

Economy index is the short board

The hysteresis effect on economy is longer than the social benefit (continued)

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(continued) Monitoring results of level-1 index radar diagram 2020 2021

Education/scientific R&D index is the short board

Social benefit index and economy index appear synchronous growth correlation effect

Monitoring results of level-1 index trend chart Indicators

Interpretation (phenomenon)

Study and judgment (reason)

Education/Scientific R&D index

Continuous declined sharply since 2018

The decline would have a negative impact on other indexes, would appear in the next few years; identified as a yellow warning

Technical Performance index

Increased in 2018 and then remained almost same for years

This index does not grow for a long time, it will become the bottleneck of the BDS industry in the future; identified as a blue reminder

Economy index

Before 2018, it was basically stable, with a sharp decline in 2019 and a rebound back to resume growth in 2020

The fluctuations of this index impacted by performance improvement with the BDS3 replaced BDS2, the trade war between China and the United States and the COVID-19 epidemic

Social Benefit index

It remained basically stable until 2018, and began to grow substantially after 2019

This index has shown a good development trend. The national investment in the BDS industry and infrastructure has achieved good social benefits, which is similar to the national input-output model of urban highway transportation facilities; identified as a green logo (continued)

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(continued) Monitoring results of level-1 index radar diagram BDTT Experts Expert comments and suggestions: ➀ After analysis and research, it is discovered the law that there are mutual influence between the four level-1 indexes and exist hysteresis effect. With the law could predict the future development trend of BDS industry ➁ According to the yellow warning of the Education/Scientific R&D index, three-year sustained sharp decline from 2018, It shows that the scientific research input and output of BDS application development has declined sharply, It is concluded that the competitiveness of BDS technology application and development will decline in the next few years, Long-term development would be not meet the expectations; Accompany with the superposition effect of the blue reminder of the Technical Performance index, It will become the bottleneck of the BDS industry in the next few years (In market survey on the sample units of the BDI, found the BDS business revenue forecast in 2022–23 substantially reducing, verified the accuracy of the evaluation); The warning of these two indicators, remind the relevant functional departments responsible for the development of the BDS industry to pay attention to it, Further research is recommended, Timely introduction of corresponding regulatory policies; To learn more about the details and root cause of the continuous decline, the level 2 and level 3 indicators to analyze this dimension need to be viewed ➂ Through the study of the the four BDI indicators and comparative analysis with other industries, found that BDS industry is more conform to the law of political economy development, show less the law of the market economy. If wanting to push the marketization of BDS industry, need to create more market economy development environment and conditions for BDS industry

Level-2 monitoring indicators The level-2 index analysis method is similar to the level-1 index, and it is no longer specified here. Level-3 monitoring indicators See Figs. 4, 5 and 6.

Fig. 4. Radar diagram of the level-3 indicators of BDS Education/R&D Index

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Fig. 5. Comparison of the trend of BDS Education/R&D level-3 Index

Fig. 6. Trend of the level-3 indicators of BDS Education/R&D Index

Figures 4, 5 and 6 Analytic Report: The analysis method of the level-3 radar index and the comparison chart is similar to that of the level-1 index. So only the report samples of the trend chart analysis and expert suggestions parts are listed below: Monitoring results of level-3 indicators trend chart Indicators

Interpretation (phenomenon)

Study and judgment (reason)

China’s financial investment in Since 2016, there has been a scientific research steady growth trend

Identified as a green logo

Thesis

It began to decline in 2021

Identified as a yellow alert

Patent application

In 2017, it began to show a downward development trend

Identified as a yellow alert

The Beidou cup entries

In 2016, it began to show a downward development trend

Identified as a yellow alert

Navigation annual conference exhibitors

In 2016, it began to show a downward development trend

Identified as a yellow alert

Scientific and technological achievement

It began to decline sharply in Identified as a red warning 2017, and dropped to 0 in 2021 (continued)

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(continued) Monitoring results of level-3 indicators trend chart Indicators

Interpretation (phenomenon)

BDS R&D Investment

Sample data have not yet been collected

Study and judgment (reason)

BDTT Experts Expert comments and suggestions: ➀ The main level-3 indicators that lead to the decline of the level-1 Education/Scientific R&D index include: BDS Thesis, Patent, Scientific and Technological Achievements, Beidou Cup Entries, Navigation Annual Conference Exhibitors. In particular, Scientific and Technological Achievements indicator declined the most and fall to 0 in 2021. This shows that there are big problems in BDS application technology innovation, identified as a red warning; Need to attract the attention of the relevant departments, to do further in-depth investigation and research finding the root cause and taking actions. To restore the scientific research and innovation capacity of the BDS industry to above the normal level otherwise, it will affect the long-term sustainable development of the BDS industry ➁ The Academic Journal Articles, Newspaper Media Reports and International Training Personnel indicators fluctuated sharply in some years, which were identified as white attention, indicating that there are promotion activities in these three aspects, and the unstable policy, which is not conducive to the sustainable development of the BDS industry, and the industry needs sustained and stable policies for development ➂ China’s Fiscal Research Investment indicator is identified as green logo telling us that China in the scientific research investment overall is increasing, in the health good momentum. BDS R&D investment indicator has not yet to collect data, if this indicator is lower than China’s Fiscal Research Investment indicator, hints BDS would be face more challenge by competition technology. This indicator is very critical to analyze and predict the future long-term development trend, so hope to get the support of relevant departments, organize the collection of sample data

The analysis method of the other level-3 indicators of three level-1 index dimensions is similar and no longer described.

3 Achievements • Establish the BDI industrial health monitoring indicator database, index model and algorithm; • Establish the BDI data analysis system; • Establish the BDTT expert database; • Establish quantitative health monitoring standards for BDS industry; • Delivery the BDI Report.

4 BDI Value Mining and Scenario Application Research The research work on the construction of the BDI system also includes the BDI value exploration and the open exploration of the scenario application. Some research cases are as follows.

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4.1 Social Value Mining and Application: “BeiDou Low Carbon Monitor Index” See Fig. 7.

Fig. 7. Trend chart of “BeiDou low carbon monitor index”

The “BeiDou low carbon monitor index” is calculated by applying BDS technology to track green travel mileages of new energy vehicles and shared bikes versus green travel mileages of fuel vehicles, so that could monitoring urban transportation carbon emission status and trends, then providing scientific data for the government decision-maker to formulate green and low-carbon travel policies. In order to promote “BeiDou low carbon monitor index” protecting the earth, human survival community with BDS technology and spirit. State-owned Assets Supervision and Administration Commission of the State Council, Cyberspace Administration of China, China Satellite Navigation Office support government allying new energy vehicle enterprises to release The initial written proposal of “promoting low-carbon and green travel with BDS technology”. 4.2 Economic Value Mining and Application: “BDS Investment Index” “BDS investment index” collects the BDS industry top 10 enterprises and high quality projects together, build the BDS index fund and investment prediction model, could avoid state owned investment decision making risk on single BDS project. That could be helpful for state-owned large capital inflow into the BDS industry, also could help government to make the national macro-control for BDS industry as capital leverage tools. 4.3 Scientific and Technological Value Mining and Application: “BDS Scientific Research Index” “BDS scientific research index” based on “BDS application development and innovation laboratory”, reference to Stanford university IDEO-Design Thinking-StartX-LASER innovation incubation model, build the incubation for BDS innovation projects, that can improve the transformation rate. At present, more cooperation and demonstration of central enterprises are being carried out. BeiDou Application Development Institute allies the members of SASAC state owned enterprises BDS collaborative development platform, builds “BDS Application and Technology Innovation Laboratory”, reference “BDS scientific research index”,

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select potential BDS scientific research project into the incubator refer to Stanford university innovation incubation model. After finished two incubating testing, found that could promote the transformation of scientific and technical result. More than 5 projects from state owned enterprises are selected and incubating in this laboratory. 4.4 Commercial Value Mining and Application: BDTT The BDTT experts can help companies to design new business model. For example, BDTT experts help two BDS business related subsidiary of China North Industries Group Corporation Limited designed 2B and 2C new business model referenced the IBM and China Merchants Group. Remarkable results have been achieved. 4.5 Mining and Application of Industrial Chain Ecological Value: Research on BDS Industry Derivative Business The BDI sample unit of financial institutions, based on BDI data and report, designed the loan service promotion and BDS payment system for clients of petroleum refining industry, and developed supply chain financial business for the BDS industrial park, to solve the financing difficult problem for the small and medium-sized enterprise.

5 Conclusion At present, the BDI modeling work has been completed, and 89.6% of the sample data has been collected, the BDS industry health monitor function has been constructed. Nearly 30 experts applied to join the BDTT, and BDTT could leverage nearly 60 academicians to participate BDI data analyze and problem solving. Nearly 50 leading sample units participating in the BDI system construction and application innovation. More than 5 state owned enterprises join “BDS Application Development and Technology Innovation Laboratory”start the research and develop the BDS industry solutions and applications reference the BDI system. We are looking forward more relevant units and experts to participate in improving the the BDI system. You are welcome to find out and correct the shortcomings in the paper. Acknowledgement. Special thanks for the guidance of Zhao Gang, former president of Beidou Application Development Research Institute.

References 1. GNSS and LBS Association of China Homepage, http://www.glac.org.cn/, “China Satellite Navigation and Location Service Industry Development White Paper”[R], GNSS and LBS Association of China (2022) 2. China Satellite Navigation Office homepage, http://www.beidou.gov.cn/yw/xwzx/202211/t20 221104_24827.html, “China’s BDS Navigation Satellite System in the New Era” white paper, The State Council Information Office of the People’s Republic of China (2022)

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3. Clark, J., Perrault, R.: Artificial intelligence index report 2022. HAI of Stanford University (2022) 4. Fan, G., Wanda Guo guide: “Global Financial Centers Index”. Z/Yen Group (British thinktank)&CDI (2022) 5. Weihua, M.A., Song, Z.P.: A-share listed company sustainable development value assessment report. Social Science Literature Press (2021) 6. Yang, C., Chen, G., Zheng. H.: Intelligent operation, maintenance and practice of the BDS navigation satellite system. China Aerospace Press (2020) 7. China Satellite Navigation Office: BDS Navigation Satellite System Open Service Performance Standard (3.0). China Satellite Navigation Office (2021) 8. Pan, J.: DIIS theory and methodology in think tanks. Science Press (2019) 9. Shi, D., An, S., Ni, B.: Research on basic theory and application method of defense critical technology selection. Defense Industry Press (2016) 10. Qing, H.: Evaluation index system for think tank experts. Economic Management Press (2019)

Design and Implementation of Integrated Navigation and Positioning System for Towed Streamer Marine Seismic Exploration Haonan Zhang1,2,3 , Kaiwei Sang1 , Cuilin Kuang1(B) , Chufeng Duan1 , and Baocai Yang1 1 School of Geoscience and Info-Physics, Central South University, Changsha, China

[email protected]

2 China Oilfield Services Limited Geophysical Division, Tianjin, China 3 National Engineering Laboratory for Offshore Oil Exploration, Beijing, China

Abstract. The integrated navigation system serves as the command-and-control center for the offshore towed streamer seismic exploration, and its positioning results of seismic sources and detector array are also the key to inversion of seabed geological structure using seismic data. In recent decades, China’s marine geophysical exploration integrated navigation system has been reliant on imports, which is expensive and constrained in key technologies. Therefore, to break the technical blockade imposed by foreign geophysical manufacturers and safeguarding the country’s energy security, it is of great strategic significance to independently carry out the research and development of the integrated navigation system for offshore streamer seismic exploration. This research presents critical algorithms for streamer positioning data processing in real-time, near-real-time, and post-processing scenarios, respectively. And the basic architecture and function modules of the integrated navigation system developed are given based on the requirement analysis. Furthermore, the system is tested and verified using both simulation and measured data. The results demonstrate that the shot prediction accuracy of the system is better than 0.5 m in the along line direction, and the streamer positioning accuracy with simulation data in real time, near real time and post processing are better than 6 m, 3 m and 2.2 m, respectively. Additionally, the streamer positioning results of the measured data are close to those of mainstream foreign commercial software, indicating that the system meets the operation requirements of offshore streamer seismic exploration. At present, the system has been formally installed and implemented on some geophysical exploration vessels, and has achieved good application results in the exploration in South China Sea and Bohai Sea. Keywords: Seismic exploration · Towed streamer · Integrated navigation system · Navigation and positioning · Shot prediction

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 201–215, 2024. https://doi.org/10.1007/978-981-99-6928-9_18

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1 Introduction The ocean is a significant field for the exploration and development of oil and gas in the future. Seismic exploration, including towed streamer and ocean bottom seismic, is the most widely predominant geophysical prospecting method, while towed streamer seismic exploration is currently the most cost-effective offshore exploration technology worldwide [1, 2]. During exploration, the vessel drags the gun arrays (seismic source) and streamers sailing along the predetermined survey line, and the gun array excites the seismic waves at every shot point designed. The seismic wave is reflected or refracted when it encounters the seabed rock interface and then acquired by the detectors on the streamer. The geological structure and stratigraphic characteristics of the seabed can be determined through the analysis of seismic data, so as to achieve the purpose of detecting marine oil and gas. The positioning results of seismic detectors directly affect the accuracy and reliability of seismic inversion, and seismic data are worthless without accurate position of detectors. Therefore, achieving high-precision positioning of seismic detectors on the streamer is the basis of seismic exploration data analysis. China’s marine seismic exploration started late, lacking accumulation of relevant technology and equipment, and so far most streamer navigation and positioning software/systems used in domestic marine seismic exploration were imported. The adoption of these imported software and systems entails a substantial financial burden, given their high acquisition costs, recurring licensing fees, and significant maintenance expenses. Moreover, their use carries the potential risk of authorization suspension, further exacerbating the financial risk involved. In recent years, China’s investment in seismic exploration equipment research and development has gradually increased, e.g., Zhou et al. [3] developed a 2D towed streamer navigation and positioning system, and the difference between the positioning results and foreign software was less than 10 m; Yi [4] established a complete set of streamer navigation and positioning data processing algorithms and developed a data processing software, and the difference between the positioning results and foreign software was less than 5 m; Cao et al. [5] introduced the integrated navigation system developed and indicated the positioning results met the requirements of 2D exploration. However, the current domestic mature software and systems that developed independently are still scarce, few of which can be put into practical application. Therefore, it is imperative to devise a viable towed streamer integrated navigation system that encompasses autonomous intellectual property to surmount technological embargoes, propel the progression of native marine geophysical exploration apparatus, and uphold the country’s energy security. This paper presents the fundamental data processing algorithms employed in realtime, near-real-time, and post-processing scenarios for streamer navigation and positioning in offshore seismic exploration. Then, a comprehensive overview of the basic architecture and functional modules of the developed integrated navigation system is given. Finally, the positioning accuracy and robustness of the system are tested using both simulation and measured data.

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2 Requirements Analysis At present, the offshore seismic exploration generally adopts multi-streamer operation, and the commonly-used configuration of exploration systems is shown in Fig. 1. Differential GNSS (DGNSS) on the exploration vessel is mainly utilized to obtain the absolute position of the vessel, while relative GNSS (RGNSS) is mainly used to transfer the position reference to the gun array and streamer tails [6, 7]. Each streamer is several kilometers in length and typically equipped with numerous positioning sensors, such as compasses and acoustic transducers. The compasses are utilized to acquire the magnetic azimuth of the streamer tangent at that place, which are generally installed at equal intervals on the streamer. The acoustic transducers are utilized for ranging and generally establish an acoustic ranging network. The towed streamer navigation and positioning data are usually characterized by large amount, various types, and unstable quality. According to the operation requirements of different scenarios, the integrated navigation system can be divided into real-time, near-real-time and post-processing modes for data processing. GEO Towed streamer

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Fig. 1. Schematic diagram of the towed streamer exploration positioning network

2.1 Real-Time Navigation and Positioning Scene The integrated navigation system plays a crucial role in real time exploration operations. Specifically, it is responsible for calculating the positions of the exploration vessel and gun arrays, predicting the time to next shot based on pre-set survey lines and current vessel speed, and determining the position and shape of the towed streamer in real time. The shot prediction is used to control the excitation of seismic waves when the gun array reaches the designated position, which is the core of exploration. Additionally, the calculation of towed streamer positioning is primarily used for displaying the streamers’ shape in real time, providing the necessary reference for exploration vessel operations, including correcting direction, steering, obstacle avoidance, etc. 2.2 Near-real-time Navigation and Positioning Scene The available data for real-time positioning are often limited and contain missing values and other issues that impact its continuity. Furthermore, these data are typically acquired with strong noise and gross errors, which can be challenging to effectively eliminate.

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Manually processing the positioning data after exploration can improve the positioning accuracy, however it can be time-consuming and tedious when this process needs to be repeated at every survey line. To enhance the towed streamer positioning accuracy without losing too much processing efficiency, the integrated navigation system can perform near-real-time calculations in the background during real-time operations. By using a near-real-time mode, observations can be cached and processed together after accumulating a sufficient quantity, resulting in higher-precision towed streamer positioning results upon survey line completion. 2.3 Positioning Data Post-processing Scene Some survey lines have substandard quality control after near-real-time processing. To improve the positioning results for these lines, the observations of the entire line are required to be reprocessed by post-processing, so that gross errors in the data sequence can be manually eliminated, abnormal sensors can be manually disabled, and users can choose different data preprocessing algorithms and network adjustment models according to the actual situation. The data can be iteratively processed to improve the streamer positioning accuracy [8].

3 Design of Crucial Algorithms The towed streamer navigation and positioning data processing algorithm is the core of the integrated system. The efficiency, accuracy and robustness of the algorithm significantly exhibit a considerable impact on the seismic detector positioning results, and play a pivotal role in guaranteeing the safety and augmenting the accomplishment rate of the subsequent exploration. For different data processing scenes, the data processing methods used are also different. The following section will describe the key algorithms of the integrated navigation system in real-time, near-real-time scene, and post-processing scene. 3.1 Real-Time Algorithm In the real-time scene, it is imperative to conduct shot prediction and real-time streamer positioning to ensure the uninterrupted advancement of exploration operations. The realtime algorithm adopts a fixed-length sliding window to cache a small amount of data, and the length of the data sliding window for each sensor is 12. Regardless of shot prediction or streamer positioning calculation, the present calculation epoch may not precisely correspond with the observation epoch of the positioning sensor. Consequently, it is necessary to utilize cached data within the sliding window to extrapolate the observations to the present calculation epoch before the calculation. 3.1.1 Extrapolation of Observations In real-time towed streamer positioning scene, massive observations are generated by the streamer system momentarily, with observation epochs preceding the current computation time. To obtain accurate positioning results, the observations need to be extrapolated. When a sufficient amount of historical data is cached, polynomial extrapolation

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can be utilized. The function L(t) of the observations with respect to the epoch t can be expressed as follows: L(t) = a0 + a1 t + a2 t 2 + · · · + an t n

(1)

where ai (i = 0, 1, 2, · · · , n) denotes the polynomial coefficients, which can be fitted using data in the sliding window, and n represents the polynomial order. To ensure the stability of extrapolated observations, the time interval between the original observations and the current time is usually controlled within 240 s, and the polynomial order n does not exceed half of the original data number. 3.1.2 Shot Prediction Shot prediction is a key algorithm for real-time operations. The towed streamer vessel navigates along the pre-set survey line, and fires shot is triggered when the shot reference point reaches the position of the pre-set shot point (as shown in Fig. 2). The shot prediction algorithm needs to calculate the current position and velocity of the shot reference point, and predict the time to reach the next pre-set shot point. The integrated navigation system then prepares to trigger the shot ahead of the predicted time.

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Fig. 2. Schematic diagram of shot point prediction

3.1.3 Streamer Positioning Method In real-time scene, to efficiently compute, display, and fully utilize observations, a curve fitting model is adopted for the streamer positioning calculation solution [9]. As shown in Fig. 3, the offset of each sensor on the streamer from the starting point of the streamer is regarded as the independent variable, and the coordinates of the sensors are regarded as the dependent variables. The polynomial function relationship can be established, and the coefficients of the polynomial curve are the parameters to be estimated in the model. The observation error equation is constructed using the approximation of the estimated parameters, and then the parameters correction is estimated. IGG-III scheme is used for robustness estimation [14]. The relationship between point i on the streamer and its curve offset si is expressed by the polynomial: ⎤ ⎡ ⎡ k ⎤ ⎡ T ⎤ ⎤ fx (si ) s ak Si A xi N  ⎣ sk bk ⎦ = ⎣ ST B ⎦ ri = f (si ) = ⎣ yi ⎦ = ⎣ fy (si ) ⎦ = i k=0 fz (si ) zi sk ck STi C ⎡

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In the formula, ri is the coordinate vector of point i, STi = [si0 , si1 , · · · , siN ] represents the offset of the curve. N as the polynomial order, A = [a0 , a1 , · · · , aN ]T , B = [b0 , b1 , · · · , bN ]T , C = [c0 , c1 , · · · , cN ]T represent the polynomial coefficients corresponding to xi , yi , zi coordinate components respectively. The distance observation equation is given by:   (3) di,j = f (si ) − f sj  In the formula, di,j represents the distance between point i and point j on the streamer. The corresponding error equation is given by the following formula, where STi,j = STi − STj , A0 , B0 and C 0 are the approximate values of the parameters to be estimated corresponding to the x, y and z coordinate components, respectively. δA, δB and δC are the corresponding parameter corrections. ldi,j is a constant term. vdi,j =

STi,j A0 STi,j ST B0 ST δA + i,jdi,j i,j δB di,j

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The azimuth observation equation is given by: tan(αi ) =



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In the formula, αi represents the azimuth observation of point i, and fx (si ) and fy (si ) are the first derivative of the polynomial function of the x and y coordinate components at point i, respectively. The corresponding error equation is given by the following formula. K i = Si STj A, where A = diag(0, 1, 2 · ··, N ), lαi is a constant term vα =

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The depth observation equation is given by: hi = −fz (si )

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The corresponding error equation is given by: vhi = −STi δC − lhi

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Compared with other traditional models, the polynomial fitting model is more rigorous, and the coordinates of the detectors can be obtained by simply substituting its offset s along the streamer [9]. 3.2 Near-real-time Algorithm To process positioning data more efficiently and obtain higher-quality streamer positioning results, near-real-time algorithm is applied. Near-real-time algorithm can cache raw observations for 60 shots and process them together. To ensure smooth processing results, 30 shots of overlapping data are retained during each processing iteration. Pre-processing algorithms detect gross errors, filter noise, and adaptively weight observations based on previous positioning results. Robust filtering is also incorporated into the calculation to improve the positioning accuracy. 3.2.1 Data Adaptive Weighting Algorithm The variance matrix of the observations used in the network adjustment is generally unknown, and the stochastic model of the observations generally uses the weight matrix instead, which is commonly determined based on the nominal precision of the sensors. However, there are different types of observations for streamers positioning, and it is difficult to reasonably determine the weight between them. Variance component estimation offers a solution to this issue. This method can estimate the variance components of different types of observation by residuals, and the weights is adjusted based on the estimated variance components to refine the stochastic model. This iterative process continues until the weights of different observation types converge to rational values. Assuming that the observation vector consists of two types of independent observations, namely l 1 and l 2 , with corresponding weight matrices of P 1 and P 2 , and the error equations for these observations are V 1 = B1 x1 − l 1 and V 2 = B2 x2 − l 2 , respectively, which are related by the following equations:







 B1 P1 0 l V1 ,B = ,P = ,l = 1 (9) V = V2 B2 l2 0 P2



N = BT PB = BT1 P 1 B1 + BT2 P 2 B2 = N 1 + N 2

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The variance component σ 201 and σ 202 of observations l 1 and l 2 are estimated by:

σ 201 =





V T1 P 1 V 1 , σ 202 n1 −tr(N −1 N 1 )

=

V T2 P 2 V 2 n2 −tr(N −1 N 2 )

where n1 and n2 are the number of observations l 1 and l 2 respectively.

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After obtaining σ 201 and σ 202 , the weights of l 1 and l 2 are adjusted based on the following formula: c c Pˆ 1 = 2 P1 , Pˆ 2 = 2 P2 (12) σˆ 01 σˆ 02



where c is a constant, generally chosen to be either σ 201 or σ 202 ; P 1 , P 2 are the initial weights, and P 1 , P 2 are the weights adjusted. By iterative solution until the ratio of σ 201 and σ 202 is close to 1.











3.2.2 Robust Adaptive Filtering Algorithm While the zero-order polynomial coefficient of the streamer curve changes with the forward sailing of the vessel, other high-order items of the curve change relatively slowly. The prediction of streamer coordinates is converted into virtual observations and then a generalized least squares adjustment is performed. Assume that the node coordinate at offset s on the streamer as f (s, tk−1 ) = φβ tk−1 

T  of at epoch tk−1 , where φ = diag ST , ST , ST , β tk−1 = Atk−1 , Btk−1 , C tk −1 ,  T T T   S = s0 s1 · · · sn , A = a0 a1 · · · an , B = b0 b1 · · · bn , C = T  c0 c1 · · · cn . The virtual coordinate observation of the node at offset s on the streamer at epoch tk−1 is: f − (s, tk ) = If (s, tk−1 ) + W k

(13)

where I is the identity matrix, W k ∼ N(0, σ 2 QW k ) is the system noise, QW k = diag(psd 2x t, psd 2y t, psd 2z t), and psd is the power spectral density. The covariance matrix of the virtual coordinate observation is: Qf − = φ T Qβ t tk

k−1

φ + QW k

(14)

The virtual coordinate observations are added to each compass on the streamer, and the error equation is: V ftk = φβ tk − f − (s, tk )

(15)

3.3 Post-processing Algorithm The post-processing algorithm aims to improve the streamer positioning accuracy by processing a full set of P2/94 observations after the exploration is completed. The processing mainly involves data preprocessing and streamer positioning. After the positioning data is imported, a series of preprocessing methods are applied, and the abnormal data can be manually disabled. The preprocessed observations are then input to the network adjustment. The network adjustment can fuse the observations to solve the streamer’s shape and position, and users can perform further quality control based on the residuals. If abnormal data is detected, it can be manually removed and the adjustment results are updated through iterative estimation.

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3.3.1 Data Preprocessing The data preprocessing algorithm is essential for obtaining high-precision navigation and positioning results in complex offshore environments. The algorithm includes gross error detection, denoising, and data standardization (epoch synchronization, interpolation, and extrapolation) [8]. The median is less sensitive to changes in the data sequence, and the gradient calculated by the median filtered observations can well reflect the change of data. The gross error detection algorithm compares the gradient in the original observation sequence with the median filtered observations. It performs both forward and backward detections with an adaptive sampling window, and an observation is identified as gross error only if its gradient difference exceeds the predetermined threshold in both detections. Filtering and denoising can smooth and reduce noise in the observations sequence. To effectively suppress high-frequency components and eliminate noise in the data, a low-pass Wiener filter is employed. The filter estimates the noise power by utilizing the frequency components higher than the cut-off frequency. The weight of each frequency component is determined by the ratio of the signal power to the noise power at that frequency. Specifically, if the total power of the signal is denoted as Pf and the noise power at a given frequency f is Nf , the weight of the corresponding frequency component is calculated as (Pf − Nf )/Pf . When the signal-to-noise ratio is high and the signal is much stronger than the noise, Pf is significantly larger than Nf , and the filter tends to approach 1. Conversely, when the signal is weak and the noise is comparable in magnitude to the signal, Pf is close to Nf , and the filter tends to approach 0, which is expressed as:  P −N f f f < fcutoff Pf (16) w(f ) = 0 f ≥ fcutoff

Fig. 4. The results of the observations of the compass after gross error elimination and noise reduction

It can be seen from Fig. 4 that after gross error elimination and the denoising filtering, the gross errors were effectively eliminated, and the data sequence became smoother.

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3.3.2 Network Adjustment Models In addition to the curve polynomial fitting model mentioned above, the network adjustment algorithm includes the arc model and the curve integral model [10, 11]. The overall idea of the arc model algorithm is to firstly divide the entire streamer into several discrete circular arcs based on the compass, regard the reading of the compass as the tangent azimuth of the point, and calculate the coordinates of other sensors one by one from the end of the streamer, to obtain an approximate streamer shape. Subsequently, the streamer shape is further adjusted based on the acoustic network adjustment. The acoustic network adjustment treats acoustic nodes as the parameters to be estimated and performs a global adjustment of the entire network. The curve integral model fits the streamer shape using the compass and acoustic observations, and then determines the nodes’ coordinates through coordinate integration along the towed streamer. The azimuth angle α(S) of the towed streamer is established through polynomial fitting [12, 13]. Assuming that the offset of a particular point on the towed streamer is known as s0 , and its coordinate (x0 , y0 ) is the coordinates at a particular point (x, y) on the towed streamer can be expressed as:  s x = x0 + s0 cosα(s)ds s (17) y = y0 + s0 sinα(s)ds

4 System Implementation Based on the aforementioned requirements analysis and key algorithms, the comprehensive marine navigation and positioning system is developed and implemented using the Qt platform, as shown in Fig. 5. The system mainly consists of the following modules: (1) DSM (Data Server Module): DSM is mainly responsible for forwarding data and messages for other modules in the integrated navigation system during exploration operations, which is the basis for data transmission among various modules. The observations collected by various positioning sensor will be forwarded to the required modules through DSM. At the same time, the information output by various modules is also forwarded to the corresponding modules or directly stored in the database through DSM. (2) NCM (Network Calculation Module): NCM is mainly responsible for invoking various data processing algorithms to perform network calculation on the received navigation and positioning data, and outputting the calculation results to DSM. Both shot prediction and towed streamer positioning rely on NCM for calculation. (3) SCM (System Configuration Module): SCM is mainly responsible for configuring the integrated navigation system according to the actual operation situation, including the configuration of exploration and vessels, streamers, seismic sources, positioning sensors, etc. SCM allows for flexible addition and removal of various operational equipment. (4) DM (Display Module): DM is mainly responsible for the real-time display of the network calculation results of the integrated navigation system and various observations. The important information such as the current survey line information, vessel

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position information, the position of the shot reference point and the shape of the streamer can be updated in real time through DM, which is an important reference for operators to perform various operations. PM (Plan Module): PM is mainly responsible for the setting of the pre-set survey line and the planning of the turning path of the survey vessel, and the set path will be displayed in DM. RCM (Real-time Control Module): RCM is mainly responsible for real-time control of the exploration system, including changing the state of the shot, retracting and releasing the streamer, removing the positioning sensor, and re-calculating operations. DGM (Diagnostic Module): DGM is mainly responsible for monitoring the data flow of the integrated navigation system and the operational status of other modules in the exploration operation, and summarizing the warnings, errors and other messages of each module. PPM (Post Processing Module): PPM is mainly responsible for post-processing the navigation and positioning data recorded in real time by the integrated navigation system, which is generally used after the survey lines is completed.

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Fig. 5. Architecture diagram of integrated navigation system

5 System Verification The simulation data and actual measurement data are utilized for testing, and the test results are statistically analyzed to validate the accuracy and reliability of the integrated navigation system. 5.1 Simulation Data Experiment Since the real coordinates of the towed streamer cannot be obtained by offshore exploration, the observations are simulated by the self-developed simulation platform, and

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the real-time, near-real-time and post-processing algorithms are used to calculate them respectively. The simulation operation is configured with 6-streamer, each streamer is 7km in length, the tail buoy and the gun array are mounted with RGPS, the installation distance of the detectors is 12.5m, the acoustic network is configured as the front and rear acoustic networks, the installation interval of the compass is 300m, and the speed of vessel is set to 2m/s, regardless of ocean currents, go straight at a constant speed, and the direction of the survey line is oriented towards the north, comprising a total of 200 shot epochs. Real-time and near-real-time algorithms are utilized to calculate the simulation data, and the simulation data files are imported into the post-processing module for positioning calculation. Manual configuration of preprocessing algorithm parameters is required for the post-processing calculation, including the length of the sliding window for gross error detection, the cut-off frequency of the low-pass Wiener filter, and the time interval for epoch synchronization interpolation. The network adjustment calculations utilize curve polynomial fitting models, and the calculation results are compared with the simulated results.

Fig. 6. The average positioning deviation of each epoch in three positioning scenarios

The comparison of the average point deviation of the detectors in each gun epoch among the three algorithms presents that the post-processing algorithm has the best positioning result and the real-time result is the worst in Fig. 6. The relevant statistical results are presented in Table 1, from which it can be seen that the average positioning deviation of the real-time algorithm is less than 6 m, the standard deviation is less than 0.5 m, and the maximum value is less than 12 m; the average positioning deviation of near-real-time algorithm and post-processing algorithm is less than 3 m, the standard deviation is less than 1 m, and the maximum value is less than 1.5 m. The post-processing algorithm produces more consistent and accurate results, while the near-real-time algorithm can noticeably enhance positioning precision. However, it still falls short of the post-processing algorithm that has undergone manual adjustments. 5.2 Measured Data Experimental Validation The shot prediction algorithm was verified using measured data from the Bohai Sea area, while the positioning algorithm was verified using measured data from the South China Sea. Moreover, the positioning results were compared with the calculation results obtained from the foreign mainstream commercial software Orca.

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Table 1. The statistics of the average coordinate deviation of the detectors Average value (m)

Standard deviation (m)

Maximum value (m)

Minimum value (m)

Real-time

5.91

1.49

11.26

3.48

Near-real-time

2.99

0.86

6.64

1.45

Post-processing

2.15

0.49

3.67

1.13

5.2.1 The Result of Shot Prediction The actual measurement data in 2022 of a certain working area in Bohai Sea was used for verification to validate the shot prediction algorithm. The pre-set survey line is southeastward, with the bearing azimuth is 160°, the designed shot interval is 25m, the vessel speed is approximately 2m/s. Two gun arrays are mounted, and the Common Mean Point (CMP) is used as the shot reference point. As shown in Fig. 7, the predicted deviation of the shot points indicates that the majority of epochs have a deviation better than 0.5 m, with the maximum deviation being less than 2 m.

Fig. 7. Shot point prediction deviation

5.2.2 The Result of Towed Streamer Positioning To further verify the positioning performance of the integrated navigation system, measured data from a certain working area in the South China Sea in 2019 were utilized. The total of 60 3D exploration survey lines were selected for real-time positioning and calculation testing, with the azimuth angle of each survey line is 149° or 329° (adjacent survey lines were operated in reverse directions), and each survey line was nearly 33 km long, containing about 1700 shots. The survey was conducted using a 6-streamer configuration, with each streamer about 7 km in length, the tail buoy and the gun array mounted with RGPS, the detectors installation spacing being 12.5m, and the acoustic network configured as front and rear acoustic networks in Fig. 8. The compass is installed at intervals of 300m. The real-time calculation results of 60 survey lines were compared with those of Orca, and the deviation of streamer positioning results of each shot epoch of 60 survey lines relative to that of Orca is counted, and the positioning deviation is

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projected to DA (Distance along line Delta) and DC (Distance off line Delta). The results are shown in Table 2. Tail buoy

Compass

Gun array Vessel

RGNSS DGNSS Base station Acoustic Transducer

Fig. 8. Schematic diagram of the configuration for the measured data of the South China Sea Table 2. Statistics of survey line positioning deviation Average value (m)

Standard deviation (m)

Maximum value(m)

Minimum value(m)

DA

1.38

0.23

2.00

1.06

DC

2.74

0.43

3.91

2.07

The results in Table 2 show that the average DA deviation bias for all survey lines is less than 2 m, the standard deviation is less than 0.5 m, and the maximum value is less than 2 m. Similarly, the average DC deviation bias is less than 3 m, the standard deviation is less than 0.5 m and the maximum is less than 4 m. As illustrated in Fig. 9, the variations in DA and DC deviation bias for each survey line demonstrate stable real-time positioning results are consistent with Orca’s solution, as shown in Fig. 9.

Fig. 9. Average positioning deviation of survey lines

6 Conclusion Based on the requirements of towed streamer navigation, this paper gives the key algorithms in real-time, near-real-time and post-processing scenarios for solving the problems in data processing. The integrated navigation system is designed and developed,

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and the performance of the system is verified by simulation data and measured data. The results show that the shot prediction accuracy is better than 0.5 m in the along-line direction, the streamer positioning accuracy in real time, near real time and post processing with simulation data are better than 6 m, 3 m and 2.2 m respectively. Similarly, the streamer positioning results of the measured data are close to foreign mainstream software, indicating the system meets offshore streamer seismic exploration requirements. At present, the system has been formally installed and put into use on some geophysical exploration vessels, and has achieved good application results in the actual production in South China Sea and Bohai Sea.

References 1. Wang, X., Quan, H., Liu, J. et al.: New progress of offshore oil and gas seismic exploration technology, pp. 1–7. Petroleum Industry Press, Beijing (2017) 2. Wang, S., Yang, K., Tang, J.: New technology and application of marine seismic exploration, pp. 8–25. Petroleum Industry Press, Beijing (2016) 3. Zhou, B., Song, W., Yi, W.: Navigation data processing for deep-sea exploration. Geomatics Inf. Sci. Wuhan Univ. 35(06), 705–707 (2010) 4. Yi, C.: Study on key techniques of navigation & positioning data processing and system development in marine seismic streamer operation. Wuhan University, Wuhan (2013) 5. Cao, G., Zhao, X., Fang, S. et al.: Research of the technology for deep sea towed streamer exploration navigation and its application. Equipment Geophys. Prospect. 24(03), 151–155 (2014) 6. Zhang, H., Ruan, F., Hu, G. et al.: Key positioning algorithm of marine 3D towed streamer integrated navigation system. J. Geomatics Sci. Technol. 36(05), 441–446 (2019) 7. Zhang, H., Hu, G., Fan, Z. et al.: Vessel and Buoy Positioning System Based on RT-PPP. J. Geomatics Sci. Technol. 36(03), 233–237 (2019) 8. Yao, Y., Yi, W., Song, W.: Processing methods for navigation data of offshore towed streamer exploration. Geomatics Inf. Sci. Wuhan Univ. 35(6), 698–701 (2010) 9. Yu, W., Wu. P., Zhang, H. et al.: Offshore towed-streamer seismic positioning based on polynomial curve fitting. Acta Geodaetica et Cartographica Sinica 51(05), 772–780 (2022) 10. Yi, C., Cao, G., Fang S. et al.: Fitting of Offshore Towed Streamer Shapes. Geomatics Inf. Sci. Wuhan Univ. 35(6), 702–704 (2010) 11. Kong, Z., Lai, Z.: Research on seismic navigation and localization algorithm. Bull. Sur-veying and Mapping S1, 17–21 (2018) 12. Duan, C., Zhang, H., Kuang, C. et al.: Multi-streamer positioning algorithm based on curvilinear integral for seismic exploration. Oil Geophys. Prospect. 57(06), 1317–1324, 1257 (2022) 13. Duan, C., Zhang, H., Kuang, C. et al.: Design and realization of a marine 3D towed-streamer navigation and positioning data processing system. Geophys. Prospect. Petroleum 62(01), 80–86, 129 (2023) 14. Yang, Y.: Robust LS estimation for classical adjustment models. J. Pla Institute Surveying & Mapping 02, 77–82 (1994)

Analysis of GNSS Coordinate Time Series in North China by Independent Component Analysis Guanghong Lan and Kaihua Ding(B) School of Geography and Information Engineering, China University of Geosciences, Wuhan 430074, China [email protected] Abstract. Common mode error (CME), as a kind of non-tectonic motion, is one of the most important error sources in Global Navigation Satellite System (GNSS) coordinate time series. In order to obtain a precise and reliable velocity at a station, the influence of CME should be removed or decreased. In this paper, independent component analysis (ICA) method is applied to extract CMEs and analyze their influences on the coordinate time series based on 24 GNSS reference stations in North China during 2011–2020 period. The results indicate that, (1) After CMEs filtered out by the ICA, the average correlation coefficients between the residual time series decrease from previously 0.5–0.7 to −0.04 in east, north and up directions at stations, implying that the strong correlation between the residual time series at stations is significantly reduced by the ICA filtering. (2) The RMS of residual time series is effectively suppressed after the ICA filtering, with the RMS decreasing about 43.95%, 52.25% and 38.13% in east, north and up direction, respectively. (3) The averages of uncertainties of velocity estimations are decreasing from 0.30, 0.27 and 0.42 mm/yr to 0.12, 0.09 and 0.22 mm/yr in east, north and up direction before and after the ICA filtering, respectively, showing that the precision of the velocity estimation is improved about 60%, 69% and 49% in the three directions. Therefore, it is necessary to do the filtering among the GNSS coordinate time series to remove the effect of CME and the ICA is demonstrated to be an effective method to apply the filtering, so as to extract the precise tectonic motion in North China. Keywords: North China · GNSS coordinate time series · ICA · CME

1 Introduction With the continuously increasing observation duration of reference stations from the Crustal Movement Observation Network of China (CMONOC), the Global Navigation Satellite System (GNSS) coordinate time series data is accumulated more and more, thus it provides a great opportunity to carry out the detailed study on crustal movement for these stations and related regions [1–3], including both the tectonic and non-tectonic movement signals. In order to analyze the accurate tectonic motions of stations, it is necessary to study the non-tectonic signals existing in the time series and get them removed from the time series [4, 5]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 216–230, 2024. https://doi.org/10.1007/978-981-99-6928-9_19

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Such non-tectonic signals are mainly composed of time-related errors and spacerelated errors, and space-related errors are usually called common mode errors (CMEs) [6–9]. As verified by previous studies, CME can’t be ignored in the process of establishing sub-millimeter high-precision velocity field [1, 10, 11], thus many different spatial filtering methods are proposed to filter out CME in GNSS coordinate time series, so as to improve the SNR of tectonic signals in GNSS coordinate time series. Among them, the stacking filtering method is based on the uniform distribution of CME in space. For the GNSS network in a small area, the observation environment of the station is roughly same, and the CME is evenly distributed in space, so it is effective to use this method to filter out the CME of the station [6, 12]. However, for large-area GNSS networks, the stacking filtering method is no longer applicable, since the assumption that CME is spatially uniformly distributed is not guaranteed, due to different observation environments between the stations. In order to overcome this disadvantage, an improved stacking filtering, the correlation weighted stacking filtering method is introduced by taking the correlation coefficient as the weight factor to filter out CME [13, 14]. A decomposition method proposed by Dong et al. [9], combines principal component analysis (PCA) and Karhunen-Loeve expansion (KLE) to filter CME. It is more rigorous in calculation theory, and does not assume that CME is uniformly distributed in space, so it is suitable for the large-area GNSS networks. However, PCA is based on the second-order statistics of variance and covariance, and its potential assumption is that CME obeys Gaussian distribution. Actually, CME contains coloured noise and does not completely obey the normal distribution, thus the principal components contains signals from different sources, which may produce false spatial features [7, 15, 16]. A blind source signal separation method, independent component analysis (ICA) can get these problems well solved, by using the high-order statistics information of residual matrix to separate statistically independent non-Gaussian signals [8]. Ming et al. [8] and Zhou et al. [17] applied ICA to filter out regional CME, and achieved good results. In this paper, we apply the ICA method to decompose the coordinate time series during the 2011–2020 period of 24 GNSS stations in North China, then analyze the spatial and temporal distribution characteristics of each independent component (IC), so as to discuss the influence of CME on the velocity and velocity uncertainty of GNSS stations in North China, and finally extract the accurate crustal movement field in North China.

2 Data and Methods 2.1 GNSS Coordinate Time Series We followed the processing strategy of Ding et al. [18] to process the observations of 24 GNSS stations from CMONOC in North China during the 2011–2020 period, and finally obtained the daily coordinate time series for each station. Due to the failure of the equipment or the influence of observation conditions, there are data losses in the time series at stations. The average data loss rate of all stations is 6.07%, and the station SXKL has the largest data loss rate of 26.47%, illustrated in Fig. 1. In addition, we the triple quartile spacing statistic method to remove outliers in the time series, causing

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some minor data loss. However, the long period coordinate time series with low data loss rate provides a good database to carry out the following study.

Fig. 1. Distribution and data loss of GNSS stations in the study area.

2.2 Coordinate Time Series Fitting Model GNSS coordinate time series usually includes a long-period linear motion caused by crustal movement and periodic motions caused by environmental loads such as seasonal atmospheric variations and land water migration. Therefore, we adopted widely used GNSS coordinate time series function model as follows to fit the coordinate time series [19]. y(ti ) = a + bti + c sin(2π ti ) + d cos(2π ti ) +e sin(4π ti ) + f cos(4π ti ) +

ng  j=1

  gj H ti − Tj + v(ti )

(1)

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in which, y is the coordinate time series in east, north or up direction at each station, ti is the observation time with the unit of decimal years, a is the initial position of the station, b is the linear movement rate, c, d, e and f are the coefficients of the annual and semiannual periodic terms, respectively, ng is the number of offsets in the time series, g is the amplitude of the offset, H is a heaviside function, and v is the fitting residual. 2.3 Noise Analysis on Residual Coordinate Time Series GNSS coordinate time series contains not only time-independent white noise, but also time-dependent colored noise, thus both the white noise and colored noise should be considered in constructing the stochastic model of the time series. If the colored noise is neglected, the estimated station velocity and its uncertainty will be biased [20–23]. Usually, the spectral index can be used to analyze the type of colored noise. The calculation formula of spectral index is as follows:  α f (2) P(f ) = p0 f0 in which, P(f) is the power spectral density of the time series, f is the frequency, α is the spectral index, and P0 and f0 are constants. When α is an integer, the observed noise corresponds to some special noise types [23]. If α equals 0, the observation noise corresponds to white noise (WN); when α is equal to −1, the observation noise corresponds to flicker noise (FN); when α is equal to −2, the observed noise corresponds to the random walk noise (RW). Figure 2 shows the statistical histogram of power-law (PN) spectral indices in east, north and up direction at all stations. It can be seen that the average spectral indices in each direction are close to −1, and the average spectral indices are −0.97, −0.90 and −0.74, in east, north and up direction, respectively. Due to that the optimal noise model may vary in different GNSS networks [20, 24, 25], we analyzed the optimal noise combination for the network in this study, from serval noise combination models, including white noise (WN), white noise + flicker noise (WN + FN), white noise + random walk noise (WN + RW), white noise + power-law noise (WN + PN), and white noise + flicker noise + random walk noise (WN + FN + RW). It should be stated that the WN is considered for the comparative analysis, although the noise can’t be represented by the white noise only in the actual cases. We used the Hector software to fit the obtained coordinate time series to decide the optimal noise combination model according to Bayesian Information Criterion (BIC) information criterion [26]. The noise combination model is regarded as the optimal if the corresponding BIC value is the smallest among the considered models [15]. The calculation method of BIC value is as follows: BIC = 2 ln(L) + k ln(N )

(3)

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Fig. 2. Statistical histograms of the spectral index at stations in East (a), North (b) and Up (c) direction, respectively.

in which, k is the sum of the noise model parameters, the design matrix H and the variance of the original driving white noise, N is the number of epochs in the time series, and ln(L) is the logarithm of the maximum likelihood value corresponding to the noise combination model. The calculation formula is as follows, 1 (4) ln(L) = − [N ln(2π) + ln det(C) + vT C−1 v] 2 in which, v is the fitting residual, and C is the sum of the covariance of the noise combination model. 2.4 Spatial Noise Analysis of Residual Time Series ICA is a blind source signal separation method, which can use the high-order statistics information of GNSS coordinate time series residual matrix to separate statistically independent non-Gaussian signals from the time series. Assuming that the coordinate residual time series matrix X is calculated by fitting the observed coordinate time series based on the function model as Eq. (1) and the optimal noise combination model, it can be decomposed as the following equation, T Xm×n = Pm×n Vn×n

(5)

in which, the determinant P represents the principal components, and the determinant V is the eigenvector. P and V are sorted in descending order. In order to determine number of statistically significant principal components, we used the parallel analysis (PA) test to analyze the coordinate residual time series matrix [8, 27]. If the first r principal components obtained by PA are statistically significant, then Eq. (5) can be further expressed as follows: T Xm×n = Pm×r Vr×n

(6)

Although the principal components in P are not related to each other, they are not independent. Therefore, the unitary matrix W is further used to rotate the P matrix as following: T T Xm×n = Pm×r Wr×r Wr×r Vr×n

= Sm×r ATr×n

(7)

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in which, S is the source signal matrix, and each column represents an independent source signal, also known as time response. A is a spatial response matrix and each row represents a spatial response factor vector. Thus, the Eq. (7) can be further abbreviated as: X = AS

(8)

Because CMEs are correlated in spatial domain, independent source signals and spatial responses can be calculated by using independent temporal ICA of each source signal in temporal domain. Here, we used the FastICA algorithm to do the calculation, since it is a fast optimization iterative algorithm with good stability, which can make full use of the high-order statistics information of the matrix to separate statistically independent non-Gaussian signals with significant advantages in computational efficiency, robustness and convergence speed [8, 28–30]. Besides, it is necessary to judge whether the signal is a CME signal according to the distribution characteristics of the spatial response factor of the signal. If the station response factor has obvious spatial distribution characteristics, the signal is considered to be a CME signal, and the CME of the station can be calculated by the following formula [8]: CMEICA =

R 

Aj Sj

(9)

j=1

in which, R is the number of signals with obvious spatial distribution characteristics, Sj is the CME signal, and Aj is the spatial response factor vector corresponding to the CME signal.

3 Results and Analysis 3.1 Noise Model of GNSS Residual Coordinate Time Series The proportion of the optimal noise combination model is calculated before and after the filtering in east, north and up direction, respectively, illustrated in Fig. 3. Before the filtering, the optimal noise combination models are WN + FN, WN + FN and WN + PN in east, north and up direction, respectively, indicated by the largest sector in the small circle, while after the filtering, the optimal noise combination model becomes WN + FN for each direction, indicated by the largest sector in the large circle. Therefore, we used the functional model as Eq. (1) and the optimal stochastic model WN + FN to fit GNSS coordinate time series, so as to calculate the corresponding residual time series. Since data loss would cause failure in applying the ICA filtering, it is necessary to interpolate the missing data before the filtering. In this study, we used the RegEM interpolation method to solve this issue, because it is a data-driven interpolation method, which has been proven to be good and effective and widely used in missing data interpolation processing [8, 31–33].

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Fig. 3. The proportion of the optimal noise combination model of the residual coordinate time series in East (a), North (b) and Up (c) direction before and after filtering, respectively.

3.2 Spatiotemporal Decomposition by ICA and CME Signal Identification The independent components will be biased if the abnormal stations are not removed before the application of the ICA [8], since ICA has good sensitivity to abnormal stations. Firstly, we used the ICA to decompose the residual coordinate time series matrix. Secondly, we identified abnormal stations according to the distribution of spatial response factors. If the spatial response of a station is abnormally large, and the spatial response of its adjacent stations is close to zero, the station is regarded as an abnormal station and should be excluded [34]. Finally, we excluded stations HECX and TJWQ for that their vertical velocities are extremely large, due to the land subsidence caused by excessive exploitation of groundwater [35, 36]. After removing abnormal stations, the residual matrix is tested by the PA to determine the number of principal components. We randomly simulated residual matrix for 1000 times and calculated the mean of their eigenvalues, then compared it with the eigenvalue of the observed residual matrix, and finally found that the first 1, 1 and 2 principal components in east, north and up direction are statistically significant when the significant level of the PA test is set to 1% [7]. The PA test results are shown in Fig. 4.

Fig. 4. The PA test results of East (a), North (b) and Up (c) direction.

In order to determine the number of independent components, we also calculated the eigenvalues of the first 10 principal components and their cumulative contribution rate

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in east, north and up direction, respectively, illustrated in Fig. 5. It can be seen that the eigenvalue of the first principal component accounts for the largest proportion of the total eigenvalues in each direction, and contribution rates are 60%, 70% and 54% in east, north and up direction, respectively, while these values are 6%, 5% and 7% for the second principal component and 5%, 4% and 4% for the third principal component in east, north, and up direction, respectively. However, the second-order or even higher-order principal components still have significant eigenvalues, implying that the information of the residual matrix has spread to other principal components, especially in up direction [34]. Therefore, we determined the number of independent components to be three in each direction to implement the subsequent ICA filtering.

Fig. 5. The cumulative contribution percentage of the first 10 principal components.

We calculated the contribution rates of independent components and sorted them in descending order by the following equation [37], rk =

Ak Sk 

n 

× 100%

(10)

Ak Sk 

k=1

in which, ||·|| denotes the F norm, Sk is the CME signal, Ak is the spatial response vector corresponding to the CME signal. Figure 6 shows the ICA analysis results in east, north and up direction, respectively. In order to make the results more intuitive, the spatial response of each IC is normalized by the maximum value of the absolute value of all the spatial responses, which is also convenient to detect the possible CME. CME is a spatially dependent error, and its source has not been determined yet. The possible sources include the reference frame error, GNSS system error and environmental

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Fig. 6. The temporal responses and spatial responses of ICs in East (top), North (middle) and Up (bottom), respectively. In each subplot, the temporal and spatial responses of ICs are indicated in the upper and lower panel, respectively. The legend marks 25% of the spatial response of the station. The blue and red arrows represent the positive and negative spatial responses with magnitude scaled by the legend at stations, respectively. The yellow dots represent the removed abnormal stations.

load, and so on [1, 4, 8]. Therefore, it is generally believed that if spatial responses of all stations are in the same direction and roughly equal [9] or if there is a clear and smooth transition between the positive and negative spatial responses [38], the corresponding signal may be a CME signal. As shown in Fig. 6, most of the spatial responses of the three ICs have the same direction with roughly equivalent amount in both east and north direction, while in the up direction, the first two have the similar responses and the third has a clear and smooth transition from northeast to southwest. In order to identify the CME signal, the spatial analysis method is used to analyze the envelope polygon composed of stations with positive and negative spatial responses [8]. This method considers both the distribution and amount of the spatial responses, demonstrating the

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reference significance to some extent, but it has certain subjectivity and may not be applicable to small-area GNSS networks [9]. By comparison, Dong et al. determined the CME signal by the PCA according to the following criteria, if most stations (more than 50%) have a significant normalized response (greater than 25%) and the eigenvalue of the mode exceeds 1% of the total eigenvalue, the mode is considered to be caused by the CME [9]. Although it does not take into account the spatial distribution of stations, it gives a clear criterion. Therefore, we followed the criteria proposed by Dong et al. to identify the CME signal. And the three ICs meet the criteria and are regarded to be CME signals in east, north and up direction, respectively. 3.3 The Influence of CME on GNSS Coordinate Time Series The existence of CME has the influence on the distribution of the optimal noise combination and also the amplitude of each noise in the combination, thus further affects the estimation of station velocity and its uncertainty from the GNSS coordinate time series. In order to analyze the influence of CME on correlation coefficients between stations, RMS value of residual time series, estimation of station velocity and its uncertainty, we calculated the variations of these values before and after the ICA filtering. Figure 7 shows the variation of correlation coefficients derived from residual time series between stations before and after the ICA filtering. It’s obvious that residual time series are highly correlated before the filtering with coefficients of 0.58, 0.67 and 0.49 in east, north and up direction, respectively, while the correlation is significantly reduced after the filtering with coefficients varying from −0.2 to 0.2 with mean of about 0, indicating that the correlations between the stations are largely removed from highly correlated before the filtering to weakly corelated after the filtering. It also implies that the ICA filtering is feasible and effective in extracting CMEs from residual coordinate time series in North China. In addition, we calculated Root Mean Square (RMS) of the residual time series before and after the filtering and further calculated the reduction ratio by using the following equation,   RMSbefore − RMSafter × 100% (11) RMSratio = RMSbefore in which, RMSbefore and RMSafter represent the RMS of residual time series before and after the filtering, respectively. Figure 8 shows the reduction ratio of RMS of residual time series after the filtering. It can be seen that the RMS after the filtering is largely reduced with reduction ratio of 43.95%, 52.25% and 38.13% in east, north, and up direction, respectively, indicating that the noise of the residual time series is effectively suppressed by the ICA filtering. Figure 9 shows the horizontal and vertical velocity field from GNSS stations in North China after the filtering and the differentiated velocity field in comparison with that after filtering (unfiltered minus filtered). It can be found that the horizontal movement of the stations is relatively stable at a south-eastward velocity of 30 mm/yr in North China, while the vertical motion shows obvious differences between the southern and northern regions with larger amplitudes at the southern stations. A significant subsidence is observed at

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Fig. 7. The left panel is the change of correlation coefficient with the distance between stations before and after filtering, and the right panel is the statistical histogram and normal distribution fitting curve of correlation coefficient before and after filtering. The E, N and U components are represented from top to bottom respectively.

Fig. 8. RMS reduction percentage of residual time series at each station after the filtering in East (a), North (b) and Up (c) direction, respectively. The histogram in subplot is a statistical histogram of RMS reduction percentages at all stations.

stations HECX, TJBH and TJWQ with the rate of −30.37, −15.93 and −38.98 mm/yr, respectively, while a slight uplift is recorded at other stations, which is consistent with other geodetic results by levelling [40], InSAR [41] and GRACE [36] techniques. In addition, the variation of the velocity and its uncertainty is also analyzed by comprising them before and after the filtering. The differentiated velocity is small at majority of stations with the maximum, minimum and mean of 0.40, 0.00 and 0.10 mm/yr in east direction, 0.24, 0.00 and 0.08 mm/yr in north direction, 0.58, 0.01 and 0.14 mm/yr in up direction, respectively. The velocity uncertainty is significantly decreased with mean from 0.30, 0.27 and 0.42 mm/yr to 0.12, 0.09 and 0.22 mm/yr before and after the filtering

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in east, north and up direction, respectively, indicating that CME cannot be ignored when solving for the accurate station velocity and the precision of estimated velocity can be significantly improved after filtering the CME. Therefore, it’s essential to do the ICA filtering in solving for the velocity field with precision at sub-millimeter or higher level [1, 4, 39].

Fig. 9. The horizontal and vertical velocity field graphs of GNSS stations in North China after filtering and the velocity difference graphs before and after filtering (unfiltered minus filtered). In the figure, the blue arrow represents the velocity of the stations after filtering, and the red arrow represents the velocity difference of the stations before and after filtering. (a) and (b) represent the horizontal and vertical directions of the stations respectively.

4 Conclusions and Prospect Based on the GNSS coordinate time series between 2011 and 2020 at 24 stations from CMONOC in North China, we used the ICA method to implement the time series analysis, extract the possible CME, and further analyze its influence on the time series. We finally drew the following conclusions: 1. Before and after the ICA filtering, the optimal noise combination models are WN + FN in east and north direction, while the optimal model varies from WN + PN before the filtering to WN + FN after the filtering in up direction. 2. After the ICA filtering, correlations between residual time series at stations are significantly reduced with mean coefficients decreasing from 0.5–0.7 before the filtering to −0.04 after the filtering in each direction. 3. RMSs of the residual time series decrease from 3.13, 2.29 and 5.50 mm before the filtering to 1.76, 1.10 and 3.47 mm after the filtering with reduction rate of 43.95%, 52.25% and 38.13% in east, north and up direction, respectively, implying that the noise of time series is supressed efficiently if CME is removed.

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4. No obvious variations are observed between station velocities before and after the ICA filtering, while the mean of uncertainties varying from 0.30, 0.27 and 0.42 mm/yr before the filtering to 0.12, 0.09 and 0.22 mm/yr after the filtering with reduction rate of 60%, 69% and 49% in east, north and up direction, respectively, implying that it is essential to carry out the CME study and the ICA method is feasible to filter the CME, so as to solve for station velocity with higher precision. GNSS coordinate time series can provide important data support for the study of crustal movement and the establishment of reference frame. Although this paper has studied the influence of CME on GNSS coordinate time series, it does not study the source of CME. Therefore, it is necessary to carry out relevant research work on the source of CME.

References 1. Jiang, W., Wang, K., Li, Z., Zhou, X., Ma, Y., Ma, J.: Prospect and theory of GNSS coordinate time series analysis. Geomat. Inf. Sci. Wuhan Univ. 43(12), 2112–2123 (2018) 2. Gan, W., Zhang, R., Zhang, Y., Tang, F.: Development of the crustal movement observation network in China and its applications. Recent Dev. World Seism. 343(7), 43–52 (2007) 3. Sheng, C., Gan, W., Liang, S., Chen, W., Xiao, G.: Identification and elimination of nontectonic crustal deformation caused by land water from GPS time series in the western Yunnan province based on GRACE observations. Chin. J. Geophys. 57(1), 42–52 (2014) 4. Wang, M., Shen, Z., Dong, D.: Effects of non-tectonic crustal deformation on continuous GPS position time series and correction to them. Chin. J. Geophys. 48(5), 1045–1052 (2005) 5. Yuan, L., et al.: Characteristics of daily position time series from the Hong Kong GPS fiducial network. Chin. J. Geophys. 51(5), 1372–1384 (2008) 6. Wdowinski, S., Bock, Y., Zhang, J., Fang, P., Genrich, J.: Southern California permanent GPS geodetic array: spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. J. Geophys. Res.: Solid Earth 102(B8), 18057–18070 (1997) 7. Li, F., Li, W., Zhang, S., Lei, J., Zhang, Q., Yuan, L.: Spatiotemporal filtering for regional GNSS network in Antarctic Peninsula using independent component analysis. Chin. J. Geophys. 62(9), 3279–3295 (2019) 8. Ming, F., Yang, Y., Zeng, A., Zhao, B.: Spatiotemporal filtering for regional GPS network in China using independent component analysis. J. Geodesy 91(4), 419–440 (2017) 9. Dong, D., et al.: Spatiotemporal filtering using principal component analysis and KarhunenLoeve expansion approaches for regional GPS network analysis. J. Geophys. Res.: Solid Earth 111(B3), 3405–3421 (2006) 10. Yao, Y., Ran, Q., Zhang, B.: Influence of common mode error on the estimation velocity field of CMONOC’s stations. J. Geomat. 44(3), 1–6 (2019) 11. Langbein, J., Johnson, H.: Correlated errors in geodetic time series: implications for timedependent deformation. J. Geophys. Res.: Solid Earth 102(B1), 591–603 (1997) 12. Hu, S., Wu, J., Sun, Y.: Comparison among three spatiotemporal filtering methods for regional GPS networks analysis. J. Geod. Geodyn. 29(3), 95–99 (2009) 13. Xie, S., Pan, P., Zhou, X.: Research on common mode error extraction method for large-scale GPS network. Geomat. Inf. Sci. Wuhan Univ. 39(10), 1168–1173 (2014) 14. Tian, Y., Shen, Z.: Correlation weighted stacking filtering of common mode component in GPS observation network. Acta Seismol. Sin. 33(2), 198–208 (2011) 15. Ming, F.: Research on the GPS coordinate time series analysis. Strategic Support Force Information Engineering University (2018)

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16. Ming, F., Yang, Y., Zeng, A.: Analysis and comparison of common mode error extraction using principal component analysis and independent component analysis. J. Geod. Geodyn. 37(4), 385–389 (2017) 17. Zhou, W., Ding, K., Liu, P., Lan, G., Ming, Z.: Spatiotemporal filtering for continuous GPS coordinate time series in mainland China by using independent component analysis. Remote Sens. 14(12), 2904 (2022) 18. Ding, K., Freymueller, J.T., Wang, Q., Zou, R.: Coseismic and early postseismic deformation of the 5 January 2013 Craig Mw 7.5 earthquake from GPS static and kinematic solutions. Bull. Seismol. Soc. Am. 105 (2015) 19. Nikolaidis, R.: Observation of geodetic and seismic deformation with the Global Positioning System. University of California, San Diego (2002) 20. Tian, Y., Shen, Z., Li, P.: Analysis on correlated noise in continuous GPS observations. Acta Seismol. Sin. 6, 696–704 (2010) 21. Wu, W., Meng, G., Wu, J.: Noise in GPS coordinate time series for North China fiducial stations. J. Geod. Geodyn. 36(8), 708–713 (2016) 22. Jiang, Z., Zhang, P., Bi, J., Liu, L.: Velocity estimation on the colored noise properties of CORS network in China based on the CGCS2000 frame. Acta Geod. Cartogr. Sin. 39(4), 355–363 (2010) 23. Williams, S.D.P.: The effect of coloured noise on the uncertainties of rates estimated from geodetic time series. J. Geodesy 76(9), 483–494 (2003) 24. Ding, K., Ding, J., Li, Z., Wang, L.: Analysis on noise model of GNSS base station from CMONOC in Sichuan-Yunnan region. Sci. Surv. Mapp. 39(12), 56–60 (2014) 25. Huang, L., Fu, Y.: Analysis on the noises from continuously monitoring GPS sites. Acta Seismol. Sin. 29(2), 197–202 (2007) 26. Bos, M.S., Fernandes, R.M.S., Williams, S.D.P., Bastos, L.: Fast error analysis of continuous GNSS observations with missing data. J. Geodesy 87(4), 351–360 (2013) 27. Peres-Neto, P.R., Jackson, D.A., Somers, K.M.: How many principal components? Stopping rules for determining the number of non-trivial axes revisited. Comput. Stat. Data Anal. 49(4), 974–997 (2005) 28. Hyvarinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Networks 10(3), 626–634 (1999) 29. Hyvärinen, A., Oja, E.: Independent component analysis: algorithms and applications. Neural Netw. 13(4–5), 411–430 (2000) 30. Tichavsky, P., Koldovsky, Z., Oja, E.: Corrections to “performance analysis of the FastICA algorithm and Cramér-Rao bounds for linear independent component analysis.” IEEE Trans. Signal Process. 56(4), 1715–1716 (2008) 31. Wang, F., Lü, Z., Lü, H., Kuang, Y.: Application analysis of GPS coordinate time series interpolation based on RegEM algorithm. J. Geod. Geodyn. 40(1), 45–50 (2020) 32. Ming, F., Zeng, A., Gou, W., Xu, K.: Analysis of the sensitivity of data-driven interpolation algorithm to GNSS coordinate time series. Geomat. Sci. Eng. 36(5), 4–9 (2016) 33. Schneider, T.: Analysis of incomplete climate data: estimation of mean values and covariance matrices and imputation of missing values. J. Clim. 14(5), 853–871 (2001) 34. Yuan, P., Jiang, W., Wang, K., Sneeuw, N.: Effects of spatiotemporal filtering on the periodic signals and noise in the GPS position time series of the Crustal Movement Observation Network of China. Remote Sens. 10(9), 1472 (2018) 35. Zhang, T., Shen, W.B., Wu, W., Zhang, B., Pan, Y.: Recent surface deformation in the Tianjin area revealed by Sentinel-1A data. Remote Sens. 11(2), 130 (2019) 36. Li, S., Shen, W., Pan, Y., Zhang, T.: Surface seasonal mass changes and vertical crustal deformation in North China from GPS and GRACE measurements. Geod. Geodyn. 11(1), 46–55 (2020)

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A Machine-Learning-Based Missing Data Interpolation Method for GNSS Time Series Wenzong Gao(B)

, Charles Wang, and Yanming Feng

School of Computer Science, Queensland University of Technology, Brisbane 4000, Australia [email protected]

Abstract. The long-term GNSS time series contain abundant geodynamic and geophysical information. These time series are inevitably subject to random or continuous missing data caused by environmental or human activities. However, many mathematic methods cannot be directly applied to analyse these time series when missing data arise. Though some efforts have been made to interpolate the random missing data, the long gaps still cannot be interpolated properly. This paper seeks to apply machine learning (ML) models in missing data interpolation. These ML models are trained by using 12 site-motion-related physical variables, including the Sun’s and Moon’s coordinates, temperature, atmospheric pressure, and hydrology. Then the missing data are generated from these trained ML models. This method is tested on seven GNSS stations, and the results show that the interpolation precision can averagely reach 5.5 mm for 2-year gaps, and 4.9 mm for 1-year gaps. This new missing data interpolation method shows good performance in restoring incomplete time series, which will be helpful for further analysis of GNSS time series. Keywords: GNSS time series · Machine learning · Missing data interpolation · Gap bridging · Modelling

1 Introduction The coordinate time series collected from continuous Global Navigation Satellite System (GNSS) stations contain geodetic and geophysical signals which reflect, for example, the tectonic movement, and periodical changes of atmospheric and hydrologic loadings. Various analysis methods have been applied to extract and analyse these signals from the GNSS time series, including principal component analysis, spectral analysis, wavelet transform, and independent component analysis. The application of these methods is conditioned that the data points composing the time series should be distributed evenly, which means the missing data is not allowed. However, missing data in GNSS time series is inevitable due to environmental and human activities, such as bad observation conditions, replacement of the receiver antenna or power failures. In addition, the detection and removal of outliers also lead to missing data when pre-processing the time series. The period of the missing data can be from a single day to a few months. In this paper, to distinguish between short-term random missing data and long-term continuous missing © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 231–241, 2024. https://doi.org/10.1007/978-981-99-6928-9_20

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data, we refer to the latter as the gap. The interpolation for missing data is necessary before applying advanced analysis methods. In addition, the continuity of GNSS coordinate time series is important to maintain a regional or international terrestrial reference frame for various geodetic and navigation applications. There are some methods proposed for missing data interpolation. The linear-squaresbased method is a commonly used interpolation method that uses the linear squares (LS) to fit the time series to a known function and estimate the unknown parameters. For the GNSS time series, the function commonly consists of a trend term, annual and semiannual terms, and jumps. The LS-based method works well for the random missing with a short period. However, the LS-derived interpolated data could be unreliable when it comes the continuous missing data with a long period (gaps), for example, a few months. Singular spectrum analysis (SSA) is a widely used method to bridge the gaps in time series. This method does not require any prior knowledge of the time series and has been applied in the interpolation of sea-surface temperature time series, GNSS time series and gravity time series [6]. In addition, Liu et al. [11] developed a data interpolation software based on Kriged Kalman Filter method. The interpolation performance of the software was tested on four GNSS stations and results show that it can reach an average interpolation precision of 5.3 mm in the vertical direction for 100-day gaps. Bao et al. [1] applied the matrix completion method to interpolate 50-day gaps for 12 stations, and the interpolation precision ranges from 4 to 8 mm in vertical direction. These methods mentioned above interpolate the missing data by modelling the time series from the previous observations without considering the physical variables that cause GNSS site motions. We hypothesise that precise interpolation for long gaps can be realised by recognizing the relationship between GNSS time series and related physical variables. However, the relationship between them is too complex to be modelled by traditional methods. Gao et al. [7] proposed applying machine learning (ML) approaches to model the GNSS time series using 12 physical variables as inputs, including the variables related to the Sun’s and the Moon’s ephemerides, temperature, atmospheric pressure, pole tides, and hydrology. The ML models achieve the fitting precision of 3–5 mm, and the prediction precision of 4–7 mm for GNSS height time series. This paper proposes using the ML models to interpolate missing data in GNSS height time series. And we seek to answer two research questions: (1) how to interpolate the missing data using the ML method; (2) what interpolation precision this method can reach. The interpolation precision here means the Root Mean Square (RMS) of residuals between interpolated data and raw data. Section 2 describes the basic principle of ML and GBDT algorithm. Section 3 prepares the input and output data sets for ML training from the GNSS height time series and physical variables collected from various sources. In Sect. 4, the interpolation performance of ML models is presented and evaluated. Finally, Sect. 5 concludes the paper.

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2 Methodology for ML-Based Data Interpolation In a supervised ML problem, models are trained from training data set that consists of independent and identically distributed samples. The training data set can be represented as: DTrn = {(x1 , y1 ), (x2 , y2 ), ..., (xN , yN )}

(1)

where N is the number of samples, and xn ∈ R, n = 1, 2, ..., N , represents the input vector. Each xn consists of one or more features. For GNSS coordinate time series modelling, 12 features or variables were adopted as inputs xn and full details of these variables can be founded in our previous work [7]. In brief, the inputs include the time variable (t), y polar motion (Pnx and Pn ), the Sun’s coordinates (RASn , DECnS , DELSn ), the Moon’s coorM M dinates (RAn , DECn and DELM n ), surface temperature (TEMn ), surface atmospheric pressure (APn ), and hydrology (HYDn ). The input vector xn can be represented as y

xn = [ tn , Pnx , Pn , RASn , DECnS , DELSn , RAM n , T DECnM , DELM n , TEMn , APn , HYDn ] .

(2)

ML method is able to find the relationship between X = (x1 , x2 , ..., xN ) and Y = (y1 , y2 , ..., yN ), i.e., Y = f (X), where Y is the GNSS height time series in this case. Once the relationship is established, the missing data ym can be generated through ym = f (xm ), where xm is the corresponding input vector on the missing data epoch. Figure 1 shows the workflow of this study. Once the input matrix X consisting of physical variables and the corresponding output vector Y consisting of GNSS height coordinates have been collected and prepared, they are used as the training dataset. The ML model, i.e., Y = f (X), can be obtained by feeding the training dataset into ML learning system. Then missing data can be interpolated through ym = f (xm ). To evaluate the interpolation precision of this method, we artificially generated some gaps of which the true values are known. Then the interpolation performance of ML model can be tested on these gaps. The mapping relationship Y = f (X) could be different when different ML algorithms applied. The works from Gao et al. [7] indicate that LSTM, GBDT and SVM algorithms can achieve similar fitting and prediction performances. Therefore, using which ML algorithms is not a vital question. In this study, the GBDT algorithm is applied. GBDT uses the robust gradient boosting technique which converts weak learners (base learners) to strong ones in an iterative fashion [4, 5]. A boosting tree model can be represented as the additive model of decision trees 





















fM (x) =

M 

T (x; m )

(3)

m=1

where T (x; m ) is the decision tree with its parameters m ; and M is the number of trees.

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Fig. 1. Workflow for the study case

To construct a proper model, boosting algorithm is applied to fit the training data in a forward stage-wise manner: f0 (x) = 0 fm (x) = fm−1 (x) + T (x; m ), m = 1, 2, · · · , M M  fM (x) = T (x; m )

(4)

m=1 

In the m th step of the algorithm, parameters of m th decision tree m can be determined by minimising 

m = argmin m

N 

L(yi , fm−1 (xi ) + T (xi ; m ))

(5)

i=1

where fm−1 (xi ) represents the known current model, and L(y, f (x)) is the loss function which is usually the mean squared error (MSE):   2  L y, fm (x) = 21 y − fm (x) (6) = 21 [r − T (x; m )]2 where r = y − fm−1 (x) is the fitting residual of step m − 1. Equation 5 can be solved by iteratively creating a base learner T (x; m ) that points in the negative gradient direction:    ∂L y, f (x) (7) y˜ = − ∂f (x) f (x)=fm−1 (x)

y˜ is called as pseudo-residuals. The pseudo-residuals of previous base learner T (x; m−1 ) can be fitted by the current base learner T (x; m ), thus overcoming drawbacks of a weak learner. Following the forward stage-wise manner the desirable GBDT model can be finally built.

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3 Data Collection and Preparation The data sets collected for the supervised ML modelling problem can be classified into 2 kinds: the input and output data sets. In this study, the output data sets are the GNSS height time series, and the input data are the physical variables related to the variation of the time series. In this section, the input and output datasets will be introduced at length. 3.1 GNSS Height Time Series

Fig. 2. Distribution of the seven studied GNSS stations

The GNSS time series consist of daily PPP solutions are obtained from the Jet Propulsion Laboratory (JPL). The effect of solid earth tides is corrected when conducting PPP processing by GipsyX software [2]. Outliers in the time series are detected and removed, which causes missing data in the time series. Seven GNSS stations named MOBS, DARW, SYDN, PERT, CEDA, KARR, and HOB2 are selected as our study objects. As shown in Fig. 2, six Australian GNSS sites are close to the ocean which indicates that they could be affected by the ocean tide loading. The remaining site is in the mountains of Nevada in the United States. The 5-year height time series, from January 1, 2010 to January 1, 2015, which consists of a total of 1827 epochs, are collected from these seven stations. There are missing data points in the time series due to outlier removal or other reasons. As shown in Fig. 3, most of the missing data points are discrete. However, there are continuous missing data in the time series of PERT station, with a duration of 294 days. The missing data rates for the seven stations are 2.96%, 2.79%, 0.66%, 16.58%, 1.20%, 4.43%, and 1.8%, respectively. The missing data can be interpolated by means of the ML models. However, the interpolated data cannot be evaluated because the true values corresponding to the missing data are not known. Therefore, in addition to the missing data caused by the measurement failure, simulated gaps were added to evaluate the interpolation precision. To investigate the dependence of the interpolation performance on the location and duration of the gaps, these simulated gaps starts at different epochs on the time series, and have

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different durations. As indicated in Fig. 3, the gap duration for the MOBS, DARW and SYDN sites is two years. For the remaining four stations the gap is one year.

Fig. 3. Illustration of missing data epochs and simulated data gaps

3.2 Physical Variables To model the GNSS height time series using physical variables, it is important to understand what causes the GNSS site motions. The impact factors on GNSS site include solid earth tides loading, ocean tides, pole tide, and atmosphere loadings [13]. These tide loadings are generated by the forces from the Sun and the Moon. Though the solid earth tides were already corrected when processing the GNSS observations, there still be residuals and other tide loadings remained in the GNSS time series [15]. In addition to the tidal loadings, there are non-tidal motions of GNSS sites related to the temperature, atmosphere and hydrology. Adopted from our previous work [7], the relationship between GNSS site displacements and the variables related to the Sun and the Moon’s locations, pole motion, atmosphere pressure, temperature, and hydrology is displayed in Fig. 4. The Sun’s and Moon’s locations are related to tidal loadings including ocean tidal loading, atmospheric pressure loading, pole tide, and ocean pole tide. In addition to the Sun’s and Moon’s locations, the pole tide and ocean pole tide are also related to the polar coordinates. The other three physical variables, surface atmospheric pressure, surface temperature, and hydrological variable are used to represent the non-tidal atmospheric loading, hydrological loading and bedrock thermal expansion, respectively. Finally, time is also considered as one of the variables because the site motion is obviously related to time.

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Fig. 4. Relationships between GNSS site motions and input data sets adopted from Gao et al. [7]

The amplitudes and variations of the physical variables on the HOB2 station over the data period are shown in Fig. 5. It is observed that many variables change annually and some of them seem related to each other. For example, the hydrological variable consistently records at the minimum value when the temperature is the highest of the year. Figure 4 also indicates that the temperature not only directly causes the site deformation by means of the bedrock thermal expansion, but also indirectly affects site position by affecting atmospheric pressure and hydrology. Therefore, it is hard to build a model using the traditional method due to the complex relationships between the physical variables.

4 Results and Analysis The collected physical variables and height time series (missing data and simulated gaps are excluded) are used to train ML models. Table 1 shows the composition of the time series for each station. It indicates that 57.0%, 57.2%, 59.3%, 63.4%, 78.8%, 75.6%, and 78.2% of the time series for the seven stations are used as the output vector for ML training, respectively. The GBDT algorithm is implemented through the scikit-learn Python library [12]. Parameters are tuned by a grid search processing, and the result shows that the GBDT models achieve their best performance when employing 100 base learners, with their maximum depth of 3 and learning rate of 0.5. The trained models are applied to interpolate the missing data and bridge the simulated gaps. Interpolation precision can be evaluated by comparing the difference between ML-predicted values with the original ones when bridging the simulated gaps. Figure 6 demonstrated that the missing data points are properly interpolated (marked as red points). It can be noticed that there is a jump in the interpolated time series when bridging the raw gap for PERT station. This result is consistent with the time series analysis results derived from Heflin et al. [8] (https://sideshow.jpl.nasa.gov/post/tables/ table3.html) which indicates that there indeed is a jump between the two sides of the gap. The interpolation results for these random missing data points from ML models seem reasonable as comparing to other interpolation methods. But the interpolation precision

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Fig. 5. The inputs (physical variables) for HOB2 station

cannot be quantified because the observed samples of the missing data are unknown. Therefore, to further understand the interpolation performance of the ML models, some data gaps over each continuous data points are simulated. These simulated gaps were created in different positions of the time series and with 1-year and 2-year long durations, respectively. Figure 6 illustrates that the ML-generated time series for the simulated gaps have similar trends and periodic changes with the observed time series. The interpolation precision is also quantified by calculating the RMSE of the interpolated data. As shown in Table 1, the interpolation precision for the 2-year simulated gaps in the MOBS, DARW, and SYDN stations are 3.5, 6.4, and 6.5 mm, respectively, and for the 1-year simulated gaps in the PERT, CEDA, KARR and HOB2 stations are 4.7, 4.6, 5.1, and 5.0 mm, respectively. It is noted that the interpolation for the 2-year gap at MOBS station achieves the precision of 3.5mm, although only 57.0% of the whole time series effectively contributed to the ML training. The reasons affecting the interpolation precision of the proposed method, such as the training data set length or gap length, still need to be further studied.

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Table 1. Composition and the interpolation precision (IP) for each time series. Site

Data rate Missing data (%)

IP (mm) Simulated gaps (%)

Training data (%)

MOBS

3.0

40.0

57.0

3.5

DARW

2.8

40.0

57.2

6.4

SYDN

0.7

40.0

59.3

6.5

PERT

16.6

20.0

63.4

4.7

CEDA

1.2

20.0

78.8

4.6

KARR

4.4

20.0

75.6

5.1

HOB2

1.8

20.0

78.2

5.0

Fig. 6. Illustration of interpolation results for missing data and simulated data gaps

5 Conclusion The GNSS coordinate time series data from a vast number of globally distributed continuous GNSS stations is a great resource for geophysics and geodynamics studies. Time variation information of coordinates of GNSS references is essential for maintaining

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a terrestrial reference frames. However, many advanced mathematical analysis methods require continuity of the time series. Though many methods have been applied to interpolate the missing data, results rarely showed how these methods handle long-term gaps. This paper has proposed to use the ML models to generate the missing data and bridge long data gaps. These ML models are trained by applying site-motion-related physical variables as inputs, including a time variable, polar motion coordinates, Sun and Moon locations, temperature, atmospheric, and hydrologic parameters. The results have demonstrated that these ML models can interpolate the random missing data very well. In further experiments for interpolating long-term simulated gaps, the ML models can interpolated the gaps with the precisions of 3.5, 6.4, and 6.5 mm for 2-year gaps, and 4.7, 4.6, 5.1, and 5.0 mm for 1-year gaps. Compared with the Kriged Kalman Filter method and matrix completion method which achieve average interpolation precision of 5.3 mm for 100-day gaps and 5.6 mm for 50-day gaps, our method can interpolate longer gaps with higher precision. Overall, ML-based GNSS time series analysis show advantages of precise long-term interpolation and prediction. ML-based interpolation consumes more time on training model and need more data preparation work for various physical variables which are obtained from different resources and institutions. However, this limitation can be overcome through future development efforts for automated data collection.

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12. Pedregosa, F., et al.: Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12, 2825– 2830 (2011) 13. Petit, G., Luzum, B.: IERS conventions (2010). Tech. rep., Bureau International des Poids et mesures sevres (France) (2010) 14. Sun, R., Wang, G., Zhang, W., Hsu, L.T., Ochieng, W.Y.: A gradient boosting decision tree based GPS signal reception classification algorithm. Appl. Soft Comput. 86(105), 942 (2020) 15. Watson, C., Tregoning, P., Coleman, R.: Impact of solid earth tide models on GPS coordinate and tropospheric time series. Geophys. Res. Lett. 33(8) (2006) 16. Zheng, Y., Lu, C., Wu, Z., Liao, J., Zhang, Y., Wang, Q.: Machine learning-based model for real-time GNSS precipitable water vapor sensing. Geophys. Res. Lett. 49(3), e2021GL096408 (2022)

Construction of Beidou Space Time Technology Application Micromajor and Practice of Characteristic New Engineering Education Jianping Xing1(B) , Xingmei Yang1 , Chong Cao2 , Lingguo Meng1 , Yafei Ning1 , Hairui Liu3 , and Shengli Wang4 1 School of Microelectronics, Shandong University, Jinan 250101, China

[email protected], [email protected]

2 Global New Space Time Information Technology Research Institute, Beijing 100084, China 3 Shandong Muke Space Information Technology Co., Ltd., Jinan 250101, China 4 School of Oceanography, Shandong University of Science and Technology, Qingdao 266071,

China

Abstract. Beidou is widely used in various industries and fields of economic and social development. It is deeply integrated with big data, the Internet of Things, artificial intelligence and other emerging technologies, promoting the birth of a new business form of “Beidou + micro specialty”, and supporting the economic and social digital transformation and improving quality and efficiency. Beidou + micro specialty enables learners to have certain academic and professional qualities and industry employability in this field through flexible and systematic training. The micro specialty has built universal technologies, protocols, standards and systems such as integrated Beidou high-performance antenna, PPP precise single-point positioning, chip and terminal embedded development, integrated navigation, Beidou high-precision satellite-based enhancement [1], Beidou + SoC implementation, Beidou precise time service, Beidou + 5G, Beidou + AI, communication gateway cluster, UAV + digital twin processing, space-time security + data encryption, massive space-time data platform + APP processing, and pseudosatellite development frontier, As well as the system of typical cases of Beidou major demonstration projects (Beidou Kinetic Energy Project, Beidou Precision Transportation and Logistics (including high-speed field application), Beidou Precision Scene Monitoring, Beidou Smart Ship, Beidou Precision Agricultural Machinery and Agricultural Internet of Things Project, Beidou Smart Environmental Protection, Beidou Precision Time Service Network, Beidou + Quantum Security Integration, Beidou Police/Civil (such as school bus, tourism guide) Project, Beidou UAV + emergency rescue, etc.). The use of micro specialty mode to achieve more in-depth and efficient interdisciplinary integration can also better enhance the depth and width of talent training, and provide useful reference for the training of compound talents. Keywords: Beidou · Micro specialty · Integration

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 242–251, 2024. https://doi.org/10.1007/978-981-99-6928-9_21

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1 Introduction In 2020, China will independently build the global Beidou satellite navigation system, demonstrating its comprehensive national strength and technical strength, which not only can fundamentally get rid of the situation of being controlled, but also is of great significance for improving China’s international status and international influence. The Beidou system is also an engine to promote and promote economic and social development. It is the cornerstone of China’s new infrastructure for space and time security. The Beidou industry is worth 400 billion yuan each year, driving hundreds of millions of value-added industries. At present, there is a shortage of hundreds of thousands of Beidou professionals. Satellite navigation is a national important tool related to national security, economic development and industrial upgrading. All major countries and economies in the world have made great efforts to develop satellite navigation systems and cultivate talents. Beidou satellite navigation system is a satellite navigation system independently built and operated by China with a view to national security and the needs of economic and social development. It is also the third mature satellite navigation system after GPS and GLONASS [2]. Academician Sun Jiadong, the winner of the highest national science and technology award and the first chief designer of China’s Beidou system, once sent a message, “Beidou applications and Beidou industrialization are facing new challenges, but also ushering in the best historical opportunity period. The pattern and trend of Beidou’s ‘good use in the sky, good use on the ground’ are being built firmly!” At the same time, he also pointed out that “satellite navigation is breaking the boundaries of the industry… A new spacetime service system is being built, and a huge industry combining information services is being formed” [3]. At the end of 2017, on the fifth anniversary of the opening of Beidou System, Yang Changfeng, the current chief designer of Beidou System, proposed that “before 2035, China will build a new space-time system with Beidou System as the core, which covers the sky, the earth and the sea, is high-precision, safe, reliable, and intelligent.” The original intention of China’s Beidou development is to master and apply the national independent and controllable space-time benchmark. The future of China’s Beidou industry will move towards a new era of new space-time service development [4].

2 Key to the Development of Beidou Industry The establishment of China’s new space-time service system is actually a process of promoting the technological integration and industrial integration of Beidou and other fields based on Beidou. This development process may be arduous and long, but facing the complex and huge space-time information consumption demand in the information age, this development process of technology integration and industry integration is also a process that the Beidou industry must go through to comprehensively move towards a new space-time development stage. Only through such innovation and integrated development can China’s new space-time technology and service system formed in the future be guaranteed, and truly become an intelligent information service ecosystem with full source awareness, universal transmission, and ubiquitous services, so as to effectively

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face ubiquitous users and provide full space, multi means, interchangeable, highly reliable, and unlimited accurate space-time information. In the future, the development of China’s new space-time services will also promote the global application of China’s Beidou and truly become the world’s Beidou [5].

3 The Purpose of Setting Up Micro Specialty The micro specialty focuses on effectively making up for the problems of too narrow division, too narrow caliber and too long training period of university majors, strengthening the connection between undergraduate and graduate stage training, and improving the matching between professional training and employment and career development needs. The curriculum is generally high-level, cross cutting and challenging. Based on the comprehensive advantages of disciplines, micro specialty is a new school running mode exploration implemented to flexibly respond to the new needs of social and economic development, build a new interdisciplinary professional organization mode, promote the cross integration of disciplines and specialties, and promote the collaborative development of production, teaching, research and application. Micro specialty can use online, offline, online offline combination and other ways to carry out teaching. Students can obtain the micro professional certificate after completing the course and passing the examination. The construction of micro specialty is a specific measure taken by Shandong University to actively adapt to the needs of new technologies, new business formats, new models and new industries based on the comprehensive advantages of the whole university’s disciplines, accelerate the distribution of talent training in the future strategic areas, and is a diversified school running mode exploration implemented to build a new interdisciplinary professional organization mode, promote the interdisciplinary integration of disciplines and the coordinated development of industry, education, research and application. “Education is the foundation, theory is the foundation, application is the priority, and innovation is the soul”. It is grafted with new engineering and science, deeply integrates with talents in strategic fields such as artificial intelligence, integrated circuit, emergency, transportation, ocean, aerospace, agriculture, environmental protection, cyberspace security, and organically integrates innovation and entrepreneurship, general education, and professional education, so as to cultivate Beidou high-quality talents with innovative spirit, international vision, and strong practical ability.

4 Teaching Concept and Work Objectives of Micro Major 4.1 Teaching Concept With the change of technology, the main contradiction of learning in education is constantly adjusting; Technology has more flexible and diverse means of expression. For example, the educational meta universe has greatly enriched students’ sensory experience; Lifelong learning is inevitable, and continuous learning can keep up with the pace of the times. Zhu Zhiting, a lifelong professor of East China Normal University and director of the Research Center of Education Informatization System Engineering, believes

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that the current “skill first, knowledge second”, skill based education is universal and the “golden touch” of high-quality education in the new era; At the same time, we should focus on building a lifelong learning ecology and an open skills certification system. He advocates that “1 + X” will become the new trend of education in the future, including micro certification, micro degree, micro curriculum certificate and micro professional certificate. The expert also put forward new suggestions for the digital transformation of colleges and universities: support “digital study tours”, weaken the classification of disciplines, and strengthen the development of micro majors. 4.2 Work Objectives Based on the national independent Beidou chip algorithm, board terminal, communication gateway, protocol standard, software platform, map service and other “choke point” technical strategic needs, establish the country’s first Beidou new space-time strategy, new infrastructure, integrated chip, precise space-time, land sea integration, air land coordination and other critical areas of talent training micro professional mechanism, “education oriented, theory based, application oriented, innovation oriented” The new science is grafted, innovation and entrepreneurship, general education and professional education are organically integrated, and the barriers between schools, enterprises and departments are broken through. The whole process, wide coverage, universal benefits and sustainability are achieved, so as to achieve the transformation from “teacher centered” to “student centered”, from “teaching centered” to “learning centered”, from “supply centered” to “demand centered”, and cultivate innovative spirit, international vision Beidou high-quality talents with strong practical ability. Construction principles: independent breakthrough and innovation drive, science, education, industry and education industry synchronization, system engineering project practice, special and universal heterogeneous network cooperation, air ground cooperation, land sea integration, timespace integration and hierarchical services, integrated intelligent resources of courses and training, and the combination of virtual and real is true. Support the new infrastructure construction and industrial transformation of the new space-time industry of the country and guarantee the national security, and deeply integrate and cultivate talents in strategic fields such as artificial intelligence, integrated circuit, emergency, transportation, ocean, aerospace, agriculture, environmental protection, cyberspace security, etc.

5 Construction of Beidou Micro Professional Course System The training goal is the premise and foundation of the curriculum system. The curriculum system is the carrier and means to achieve the goal of talent training [6]. The curriculum design of Beidou micro specialty includes three credits of Beidou innovation and entrepreneurship course, two credits of Beidou general course, two credits of Beidou basic course, five credits of Beidou professional course and three credits of Beidou practical course. The main courses include: innovative engineering practice (prototype design), Beidou innovative design navigation (including information retrieval), GNSS principle and application, embedded system implementation, Beidou micro-system terminal (including typical prototype implementation), Beidou navigation communication monitoring system (including gateway cluster, system software

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engineering). Among them, practical teaching link: Beidou case engineering implementation (3 credits of Beidou practice course), including Beidou innovation project actual combat-participation in competitive/open 2 competitions, including C language application design - Beidou, single-chip microcomputer system implementation - Beidou, Beidou antenna and anti-interference application, Beidou ASIC/SoC/FPGA implementation, differential/grid enhanced network, integrated navigation and indoor and outdoor joint positioning, UAV digital twin processing, Beidou + space-time security and other technologies, protocols, standards and system integration project implementation. The main practice teaching method is to lead students to visit Beidou related enterprises and research institutes, experimental practice and competition, academic exchange (Fig. 1). Course Construction

Practice Teaching Innovative Education Big Data Simulation

Application Scene

Beidou New Space-Time Big Data Platform

Learning Feedback

User Analysis Industry Application Trend Prediction

Deep Learning ProductionEducation Integration

Fig. 1. General framework of Beidou space-time technology and application micro specialty tomatically.

Global optimization reconstructs the core knowledge points and ability requirements such as tandem double innovation and methods, and constructs a framework for the unity of knowledge and practice of tempering will quality. Explore problems, goals, value-oriented innovation/entrepreneurship two-dimensional spiral micro-class group/micro-professional micro-form, knowledge, ability, methods, practice, innovation & entrepreneurship, moral integration practice. Construction of Beidou space-time technology micro professional, Beidou space-time technology = innovative engineering practice + innovative design navigation + innovative methods + Beidou principle + navigation and communication monitoring + Beidou case + entrepreneurial practice + competition 20 credits (Table 1). Through online learning, we adopt diversified teaching modes such as online learning + live broadcast + roadshow, break through time and geographical restrictions, increase practical dimensions, and reduce conflicts with first-degree learning. It is a joint training of online minor courses based on high-quality online courses. Micro-degree certification: On the basis of completing 17 course credits online and offline, complete 3 credits of homework: writing 1 topic review, forming 1 project report, making 1 actual work (including prototype), writing 1 patent document, writing 1 academic paper (including English), making 1 presentation (including micro-video), participating in 1 competition (provincial and ministerial level or above), combining courses and competitions, taskdriven, innovating passports and growth files, and passing the assessment. The Beidou

Construction of Beidou Space Time Technology Application Table 1. Design of Beidou space-time technology and application training program. Course category

Course name

Score total

Total class hours

Innovation and entrepreneurship course 6 credits

Innovation engineering time (prototype design)

2

32

Innovative methods, intellectual 2 property and standardization Beidou (Beidou product + TRIZ). (Beidou hard technology + service)

48

Entrepreneurship practice - Beidou (based on Beidou hard technology entrepreneurship)

2

48

Beidou general course 2 credits

Beidou innovative design navigation (including information retrieval)

2

48

Beidou basic course 3 credits

Beidou GNSS positioning timing principle and network services (including observation data processing, NTP)

3

48

Beidou skills class 2 credits

Beidou + 5G artificial intelligence system, intelligent terminal implementation (including typical prototype implementation)

2

40

Beidou Beidou high-land network service, 2 professional course communication monitoring 4 credits platform implementation (including gateway cluster, system software engineering)

36

Beidou practice course 3 credits Beidou case engineering implementation Beidou case engineering implementation

Beidou new space-time + security smart application (multi-industry application, chip board-level integration)

2

36

Beidou innovation project actual combat-competition, including C language application design Beidou, single chip microcomputer system design - Beidou, ASIC Beidou baseband chip design. Beidou antenna and receiving chip, FPGA + Beidou, integrated navigation and indoor and outdoor joint positioning, HGIS-T + VR/AR + BIM, spatio-temporal big data processing

3

64

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micro-degree graduation certificate (Chinese and English) jointly issued by Shandong University and other universities can be obtained. The multidisciplinary cross-practice teaching organization mode with project training as the engine develops the design method of multidisciplinary integrated curriculum system. Construct a scientific training and competition practice education system based on multidisciplinary cross-cutting issues, and comprehensively improve the innovative practice ability of new engineering compound talents. The main practice teaching method is to lead students to visit Beidou related enterprises and research institutes, experimental practice and competition, academic exchange. Taking the “Beidou Smart Industry” micro-specialty as the carrier, the curriculum knowledge structure is optimized, the professional talent training program is optimized, professional talents, solves the problem that the traditional specialties such as new engineering, new science and innovative education are too finely divided, establishes the teaching practice system of major application + system theory + methodology + engineering, and innovates the intersection of methods, engineering, Beidou navigation, integrated circuit design, mathematical modeling and application, so as to efficiently transport professional and technical talents for the country (Fig. 2).

Principle Of Beidou GNSS

Knowledge Moral Character

Capacity Micro Specialty

Innovation

Method Practice

Beidou Case

Fig. 2. Construction of Beidou new space time microdiscipline

6 Implementation and Outcome Categories Held five seminars, and in the Ministry of Education Innovation Method Teaching Committee, Entrepreneurship Teaching Committee, Zhejiang University, Peking University and other reports, in Shandong University, Shandong University of Science and Technology, Shandong University of Science and Technology, Liaocheng University, Dezhou University, Shandong Agricultural Engineering College, Huayu University of Technology, Shandong Management College, Shandong Vocational College of Transportation and other promotion and application. The Beidou space-time technology and application results of micro-specialty are evaluated as the international advanced/domestic leading level by academicians Yang

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Yuanxi and Liu Jingnan. Liu Jiayi, the former secretary of the provincial party committee, approved the Beidou + double innovation report. Guo Shuqing, the former governor, Li Ganjie, the secretary of the provincial party committee, and Yang Dongqi, the deputy secretary, listened to the report. The innovative methods and competition contents of the achievements have been supported and affirmed by the national teaching masters Feng Lin, Hu Renjie, Lu Guodong and Sun Kangning, as well as the combination of innovative engineering practice courses and competitions with Peking University and the work of teaching materials have been recognized and evaluated by 20 + academicians/education experts at home and abroad, such as Yang Shuzi, Gao Song, Wang Zhonglin, Chen Jiaer, Li Peigen, Xu Zhihong, Yang Bin and Sun Hongbin. The relevant work has been reported more than 10 times in Qilu Evening News, Volkswagen, Jinan Times, and the official website of the school. Beidou + micro-specialty/micro-course group development was carried out with China Satellite Positioning Association, Peking University and Aerospace Academy of Chinese Academy of Sciences. Beidou new space-time science and education experimental network cooperation was carried out with Beijing University of Aeronautics and Astronautics, Aerospace Academy of Chinese Academy of Sciences/National Astronomical Observatory, Shandong Academy of Land Surveying and Mapping, Shandong Radio Monitoring Station, Shandong Tianxing Beidou Information Technology Co., Ltd., Qingdao Jerry Automation Co., Ltd., Shandong Muke Space Information Technology Co., Ltd. The application of “Beidou New Time and Space + Smart Industry” micro-specialty has been officially opened in Shandong University. The cumulative number of beneficiaries participating in radiation such as elective courses, competition participation, innovation and entrepreneurship activities has exceeded 10,000 people. At present, the total number of elective courses has reached 6,500 people. The first Beidou + double innovation and micro major in China was selected into the new engineering project. The core courses such as “Beidou Innovative Design Navigation” and “Entrepreneurship Foundation” have exceeded 20,000 in the past year, “Innovative Engineering Practice” has been opened by Shanda for more than 7 years, and 650 colleges and universities nationwide have 450,000. Beidou + curriculum and curriculum ideological and political education (developed and taught by the famous teacher team of Shandong Province) have benefited more than 12,000 people. Two seminars were held, and the certification model was promoted and applied in 10 colleges and universities such as Shanda, Shanke University, Shanjian University, Shanligong, Shannong Engineering, Shanguanyuan, Shangong, Shanjiaozhi, Jigongzhi and Yanzhi. The independent Beidou science and education system was selected into 100 typical cases of national colleges and universities to incubate and select Taishan leading talents. The person in charge of the project has won the title of Shandong Province’s famous teacher and Qilu’s most beautiful science and technology worker; he guided students to win awards, invention patents, publish 100+ papers, and complete about 50 Beidou projects, including Internet + National Gold Award, Challenge Cup National Silver Award, etc. 1060 entrepreneurs/52,000 school hours are empowered by two classes and one group of innovative elites/Qilu entrepreneurial pioneers/gold medal instructors in Jixia

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province. Joint Innovation Master Class, ICANx talks, Xingguang School Public Lectures 125 more than 15 million people. Empowerment has won the first prize of Shandong provincial and ministerial teaching achievement (ranking 1), and is currently recommending to apply for the national teaching achievement award. At present, it has been approved by the Ministry of Science and Technology of the National Science and Technology Support Plan of the Big Dipper kinetic energy major project, as well as the 2 million Beidou production and education collaborative education project of Shandong High-speed Group, as well as the Xingguang School, the provincial Big Dipper Mocking Science Expert Studio, and the provincial Beidou + AIOT digital twin training base.

7 Conclusion Based on the development of a series of Beidou, integrated GPS, GLONASS and other multi-system domestic navigation chips with completely independent property rights, it provides wide-area refined grading service technology for the integration of production and education, science and education, and cultivates high-end talents. Improve the integrated circuit, electronic information, software engineering, Internet of things, surveying and mapping disciplines such as new layout, connotation development, characteristic development, quality development. Key innovations include: 1. The creation of the country’s first national strategy for Beidou new space-time technology and application urgently needs micro-specialties to promote the optimization of the structure of disciplines and professional directions and the innovation of talent training models. 2. Develop invention science and education, industry and education, develop Beidou training equipment, innovation and entrepreneurship platform, and establish a teaching practice system of major application + system theory + methodology + engineering. 3. Construct a combination of virtual reality and augmented reality, task-driven, innovative methods, and establish a learning certification and credit recognition system. Micro-major can not only effectively expand students’ academic vision, but also enrich their knowledge reserves. More importantly, taking the initiative to choose their favorite micro-majors with a diversified knowledge system can activate students’ interest in learning, improve students’ learning efficiency, promote colleges and universities to effectively achieve education and teaching goals, and promote students’ all-round development [7]. The micro-specialty is not just a simple interdisciplinary, but refers to a set of core courses set up outside the undergraduate professional directory, focusing on a specific academic field, research direction or core literacy, so that learners can have a certain academic professionalism and industry competence through flexible and systematic training. Micro-major is an important innovation in reshaping teaching methods and teaching organization forms, reforming traditional talent training specifications and educational structure. It is an important means to comprehensively improve students’ ability to

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adapt to future development and solve complex problems. It can improve students’ knowledge structure, broaden students’ horizons, cultivate students’ sound character, improve students’ comprehensive ability, and further cultivate students’ critical thinking, dialectical thinking and three-dimensional thinking, so as to promote students’ excellent growth [8]. I believe that in the near future, there will be such a large number of waves, they do not forget the original aspiration, multi-inclusive, independent thinking, embrace the world, running on the world stage, in order to better the world, a better China and strive hard, how comforting and proud. Looking forward to learning and practicing in the experimental class of micro-professional and international organization talent pilot program, I hope that on the way to the future, I will not forget my original intention and live up to my expectations. Acknowledgements. This work is supported by the National Key Research and Development Program of China (No. 2021YFB1407001) and partly Shandong Hi-speed Group Co., Ltd. Express sincere thanks to it.

References 1. Zhang, W.: Positioning analysis of Beidou satellite-based augmentation in multiple scenarios. Power Inf. Commun. Technol. 20(12), 88–93 (2022). https://doi.org/10.16543/j.2095-641x.ele ctric.power.ict.2022.12.012 2. Cao, C.: Research on Beidou space-time service military civilian integration innovation system. Satell. Netw. (09), 12–18 (2017) 3. Gao, Z.: Accelerating the construction of new Beidou infrastructure to better enable economic development. Shanghai Secur. J. (007) (2023) 4. Cao, C., Li, D.: On the future development direction of Beidou is the new space time system. Digit. Commun. World (S1), 6–13 (2018) 5. Li, D.: China’s Beidou industry aimed at the development of new time and space services. Digit. Commun. World (06), 4–5 (2018) 6. Wang, X., Yang, W., Wang, Q., Yang, Y.: The construction of the micro professional curriculum system of “rail transit signal and control.” Educ. Teach. Forum (05), 35–37 (2019) 7. Ye, Q., Du, Q., Xiao, M.: Why more and more colleges and universities begin to set up micro majors. Sci. Technol. Dly. (006) (2022). https://doi.org/10.28502/n.cnki.nkjrb.2022.003116 8. Zhang, X.: Strengthen the construction of micro specialty to create a complete undergraduate education. China Soc. Sci. J. (008) (2022). https://doi.org/10.28131/n.cnki.ncshk.2022.001124

BDS Multi-frequency Soil Moisture Retrieval Considering the Amplitude Stability of Reflected Signal Huiyi Xian1,2,3 , Zhongpei Guan1,2,3 , Fei Shen1,2,3(B) , Xinyun Cao1,2,3 , and Yulong Ge4 1 School of Geographical Sciences, Nanjing Normal University, Nanjing, China

[email protected]

2 Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of

Education, Nanjing, China 3 Jiangsu Center for Collaborative Innovation in Geographical Information Resource

Development and Application, Nanjing, China 4 School of Marine Science and Engineering, Nanjing Normal University, Nanjing, China

Abstract. With the successful networking of BeiDou Navigation Satellite System (BDS), BDS B1I/B2I/B3I signals enriched GNSS-IR data sources. GNSS-IR technology used to monitor soil moisture content (SMC) is constantly developing, but there are still the following problems in the current research. Firstly, the elevation angle range used for inversion is mostly determined based on experience, ignoring the problem that the amplitude of reflected signal varies greatly within a certain elevation angle range due to the influence of antenna gain, soil roughness, which affects the inversion Performance; Secondly, using single-star data, the inversion accuracy of linear regression model established by least squares algorithm is poor. Therefore, this research proposed a BDS multi-frequency SMC inversion method that takes into account the amplitude stability of reflected signal. Based on the sliding window method, a stationary signal window is obtained intelligently as the data source for subsequent inversion. On this basis, joint inversion of multi-frequency signals is carried out. In addition, RANSAC algorithm is used to estimate model parameters to reduce noise interference. The experiment shows that (1) Using the window with stable amplitude change as the elevation angle range of the experiment is useful to improve the retrieval accuracy of SMC. Compared with the retrieval results of the empirical elevation angle range of 5–30°, the correlation coefficient increases in the range of 5.2–34.9%, and the root mean square error decreases in the range of 19.2–52.9%; (2) B1I/B2I/B3I triple-frequency signal fusion can reflect the soil moisture information near the measurement station more comprehensively; (3) Compared with the least square linear regression algorithm, the SMC estimate effect of RANSAC algorithm is better. Finally, the SMC was inverted using the delayed phase fusion of the BDS triple-frequency signal. The correlation coefficient can reach 0.9850, the root mean square error is 0.0066 cm3 /cm3 , and the average absolute error is 0.0053 cm3 /cm3 . Compared with the traditional method, this method has significantly improved. Keywords: BDS-IR · Reflected signal · Amplitude · Soil moisture · Signal to noise ratio · RANSAC algorithm © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 252–263, 2024. https://doi.org/10.1007/978-981-99-6928-9_22

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1 Introduction Soil moisture content (SMC) is a very important variable in the study of land energy cycle and water cycle [1, 2], one of the important factors determining drought, land degradation and vegetation cover. Traditional methods of SMC observation have many problems, such as waste of manpower and material resources, destruction of environment, limited time resolution and so on. GNSS-IR technology has the advantages of all-weather, continuity, low cost and abundant signal resources, which can overcome the shortcomings of traditional methods and is an effective supplement to existing measurement methods. Since 2008, Larson’s team has monitored SMC with the help of Signal-to-Noise Ratio (SNR) data of GPS system at low elevation angle, and conducted a series of experiments, proving that the delay phase parameter obtained by SNR reflection component has a strong correlation with SMC. It is sensitive to the variation trend of SMC within 1–6 cm vertical depth around the site [3–5]. With the continuous improvement of global satellite systems, GNSS-IR technology had a wealth of data sources. In terms of multi-frequency fusion, Jing et al. used the entropy method to integrate GPS L1/L2 dual-frequency data to improve the accuracy of inversion model [6], aiming at the problem that the current research only inversed at a single frequency. Sun et al. proposed an adaptive variance fusion algorithm for GPS three-frequency delay phase inversion, and the results show that the inversion accuracy is effectively improved [7]. Zhang et al. used the amplitude of SNR reflected signal to carry out weighted fusion of GPS/BDS multi-satellite delay phase, and the results show that the multi-satellite fusion inversion results can be used as a better estimation of the measured SMC [8]. In order to improve the accuracy of retrieval and reduce the difficulty of data screening, Li et al. designed a GNSS-IR SMC retrieval method based on robust estimation of multi-system and multi-satellite combination [9]. Lv et al. combined GNSS multipath and SNR information to propose a nonlinear regression model with multiple adaptive regression splines considering vegetation impact correction and multi-star fusion [10]. Chen et al. used PCA to reduce the dimensions of the amplitude and phase of the reflected signal, and used the entropy method and prior information to weigh the GNSS multifrequency. The results showed that this method could better reflect the SMC fluctuations [11]. Shen et al. proposed an inversion method based on two different revisit period satellites, BDS IGSO and MEO, and proved that MEO satellite has advantages in SMC inversion [12]. The above studies mostly focus on the inversion method, while the choice of parameters such as satellite elevation angle range and signal frequency in the process will have an impact on the inversion results. In terms of parameter optimization, Luo et al. analyzed the impact of terrain, signal frequency and other factors on the inversion quality, and verified that the inversion effect of SNR data of 5–25° elevation angle is better [13]; Zhu et al. used the control variable method to study the influence of parameter selection on inversion. Experiments show that the parameters of elevation angle range between 5 and 30° and the length greater than 15° can obtain better inversion results [14]. However, there are still the following problems in the current research. Firstly, previous studies lacked the validation of the multi-frequency inversion effect of the BDS; Secondly, the selection of elevation angle range is random and empirical, and there is a lack of valid elevation angle selection method; Thirdly, the traditional least square linear

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regression algorithm has poor robustness and the established model is unstable. Therefore, this research proposed a BDS multi-frequency SMC inversion method considering reflected signal amplitude stability. The purpose of this research is to evaluate the potential of BDS multi-frequency delayed phase data to retrieve SMC. The sliding window method to determine the elevation angle range and the RANSAC algorithm to estimate model parameters are introduced. The effectiveness of this method is verified by data collected by the Agricultural Ecology Experiment Station of the Chinese Academy of Sciences. Then, the inversion results are compared with those of traditional methods. Finally, the findings of this research are summarized from different aspects.

2 Method 2.1 BDS-IR Principle and Multi-satellite Inversion Model The BDS signal received by a single antenna of the receiver includes the direct component and the reflected multipath component, and the geometric relationship is shown in Fig. 1 (left). Since the frequency of the direct component and the reflected signal are approximately the same under ground-based conditions, but the propagation path length is different, these two components will have relatively stable interference at the receiver antenna, forming interference signals. It can be seen from the Fig. 1 (right) that the interference oscillation phenomenon is very obvious at low elevation angle.

Fig. 1. Geometric relation of direct reflection signal (left), schematic diagram of SNR data (right)

In the receiver, because the strength of the direct signal is different from that of the reflected signal, the data recording SNR is expressed in logarithmic decibel (dB), so it is necessary to convert the data into a linear ratio before calculating. SNR = 10SNRdB /20

(1)

The mathematical model of SNR is defined as follows: SNR = A2d + A2m + 2Ad Am cos ψ

(2)

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where, Ad and Am represent the amplitude of direct and reflected signals respectively, and ψ represents the phase difference between direct and reflected signals. The overall variation trend is determined by the amplitude of the direct signal Ad , while the periodic oscillation is determined by the amplitude of the reflected signal Am . Only the reflection signal superimposed on the direct signal is related to the ground reflection characteristics, so the direct component must be eliminated first. The approximate value of the direct signal is obtained by quadratic polynomial fitting, and the difference between SNR and the approximate value is the reflection component DSNR. DSNR can be fitted with cosine function [15].   4π H sin θ + ϕ (3) DSNR = A cos λ where, A represents the amplitude of the reflected signal, H is the equivalent height of the receiver antenna, and its change will be affected by the penetration depth of the electromagnetic wave and the change of the dielectric property of the reflector. λ refers to the wavelength of GNSS satellite signal, θ represents the elevation angle of satellite and ϕ is the initial phase.   {DSNR(t, m)} = φ = φm1 , φm2 , φm3 ...φmt0 (4) where, DSNR represents the reflected signal sequence, t represents the SNR data on the t day, and m represents the arc number. For the m satellite arc, the delayed phase sequence calculated by the least square method on days 1 to t 0 . In order to analyse the relative changes of different satellite characteristic parameters laterally, the phase delay is zeroed out: φ = φ − φ 30%

(5)

where, φ 30% represents the average of 30% of the lowest value of the time series of phase values. After zeroing, the arithmetic average is taken by day to get the final single-frequency delay phase, so as to reflect the change of SMC: ϕt0 =

φ1t0 + φ2t0 + φ3t0 + ... + φmt0 m

(6)

According to the linear correlation between delay phase and SMC, SMC can be estimated by the following formula [16]: SMC = S × ϕ + SMCres

(7)

ϕ is a delayed phase time series after fusion, SMC is the true value. S and SMCres can be obtained through model calculation. 2.2 Slide the Window to Select the Elevation Angle Range Due to the influence of antenna gain, surface roughness and dielectric properties, the amplitude of reflected signal at low elevation angle varies greatly (see Fig. 2). Large

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Fig. 2. Schematic diagram of BDS triple-frequency (B1I/B2I/B3I) DSNR

amplitude variation is not conducive to spectrum analysis and cosine function fitting. Therefore, considering the influence of the amplitude variation of reflected signal on the characteristics of fitted signal, it is helpful to select the elevation angle range with stable amplitude variation and moderate length to improve the SMC inversion effect. In this research, the sliding window method is used to process the SNR data of 5–35°. The window length is 15° and the step size is 5°. The Levenberg-Marquardt algorithm is used to fit the reflected signal, and the variance of amplitude change within the window (Ampchange ) is calculated as the parameter to measure the amplitude change. n 

Ampchange =

(Ampi − Amp)2

i=1

n

(8)

where, Ampi represents the amplitude of the i wave in the window, Amp represents the average amplitude, and n indicates the wave number in the window. The smaller the value of Ampchange is, the more stable the amplitude variation is. The window with the smallest value of Ampchange is the appropriate elevation angle range.

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2.3 RANSAC Algorithm The RANdom Sample Consensus (RANSAC) algorithm estimates the parameters of the mathematical model from a set of observed data containing outliers in an iterative way. The RANSAC algorithm assumes that the data contains both correct and abnormal data. Correct data is denoted as inliers and abnormal data as outliers [17]. The probability of the interior point in the whole data set is t: t=

ninliers ninliers + noutliers

(9)

To simplify, we can get that the probability that n points are all inner points is t n , and the probability that at least one of n points is outer points is Pout Pout = 1 − t n

(10)

(1 − t n )k represents the case that no full interior points are found in k times of random sampling. In this case, the wrong solution is obtained, and then the probability P of the correct solution is: k P = 1 − Pout

(11)

k represents the number of iterations, that is, the number of randomly selecting m points to calculate the model. P is the probability of getting the correct solution under these parameters. Interior point probability t is a prior value. Even if t is too optimistic, the probability P of the correct solution can be guaranteed by increasing the number of iterations k. Similarly, we can calculate the number of iterations k through the following formula, that is, we assume that the correct probability is P: k=

log(1 − P) log(Pout )

(12)

In data sets with errors, the RANSAC algorithm can perform linear fitting after removing noise, and the results are better than the least squares algorithm (Fig. 3). 2.4 Process of Inversion SMC inversion based on BDS triple-frequency signal includes the following seven steps, and the process is shown in Fig. 4: (1) Acquisition of observation data. According to observation files, satellite ephemeris files and other documents, obtain standard format data including satellite azimuth, elevation angle, signal to noise ratio and other key contents. (2) Decomposition of the trend and interferometric item of SNR. Select SNR data with appropriate elevation angle range, and remove the direct component of SNR through second-order polynomial to obtain the reflection component. The reflection component is denoised by Savitzky-Golay filtering.

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Fig. 3. Comparison between RANSAC and least square

(3) Signal feature estimation. Lomb-Scargle spectrum analysis was used to extract the frequency of the reflection component, and nonlinear least square fitting was used to obtain the amplitude and phase of the reflection component. (4) BDS multi-frequency phase data fusion. The satellite arcs were clustered according to satellite PRN and azimuth angle. After clustering, the delay phase was zeroed out, and then the delay phase of each satellite arcs was fused with equal weights. (5) Division of test sets and verification sets. After the above processing, a total of 40 groups of data were obtained, and the experimental data were divided into two groups according to the ratio of 4:1, the training set was from day 26 to day 57, and the test set was from day 58 to day 65. Training set and test set are mutually exclusive without intersection. (6) RANSAC model inversion. The multi-frequency fusion phase of the training set was taken as the input item and SMC as the output item. The model parameters were estimated by RANSAC algorithm, and the test set was used for verification. (7) Evaluation of accuracy. The SMC retrieved from phase values after fusion was compared the in situ soil moisture, and the inversion accuracy was verified by root mean square error (RMSE) and mean absolute error (MAE).

3 Experiment and Result 3.1 Data Source The experimental site is located in the Agricultural Ecology Experimental Station of Chinese Academy of Sciences (35.019°N, 114.548°E) in Fengqiu county, Xinxiang City, Henan Province. The details around the station are shown in Fig. 5 (left). The terrain around the site was flat, and no crops were planted in the field during the experiment, which was used for GNSS-IR SMC monitoring experiment. The experimental receiver model is Sinan M300 Pro II, the antenna type is AT500, and a temporal resolution is 15 s. The types of BDS signals received by the receiver are B1I, B2I and B3I. The ground SMC was measured by the M1X soil temperature and humidity monitor installed at a

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Model

Observation files Navigation files

Original SNR

Reflected signal

Multi-frequency data Soil moisture

1.Data extraction 2.Data preprocessing

1.Slide window to calculate elevation angle range 2.Direct signal is fitted by second-order polynomial 3.SG filter

1.L-S spectrum analysis 2.Nonlinear least squares fitting

1.Equal weight fusion 2.RANSAC algorithm

SNR data Azimuth data Elevation angle data Observation time data

Direct signal Reflected signal

Frequency amplitude Delay phase

Multi-star inversion model based on BDS triple-frequency signal

Fig. 4. Soil moisture inversion process

depth of 5 cm. The sensor was developed by Nanjing Institute of Soil Science, Chinese Academy of Sciences, and can provide SMC measurement every 1 h. The data used in this research are BDS satellite observation data and SMC data collected from January 26, 2021 to March 6, 2021. The changes of SMC and precipitation at the site during the experiment are shown in Fig. 5 (right).

Fig. 5. Layout diagram of Henan survey (left), station schematic diagram of soil moisture and precipitation at the station (right)

3.2 Result Analysis In previous studies, SNR data ranging from 5 to 30° were generally selected for inversion according to experience. In this research, the SNR data in the elevation angle range obtained by sliding window method is used for inversion. As can be seen from Table 1, the results of the inversion of the BDS triple-frequency signal with the new elevation angle range were generally better than the empirical elevation angle range in various indicators. Differences in signal wavelength, penetration capability, and SNR quality among the BDS triple-frequencies cause varying inversion effects. The B1I frequency increased the most, the average of correlation coefficient increased by 34.87%, the average of

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RMSE decreased by 52.90%, and the average of MAE decreased by 51.55%. B2I and B3I have comparable effect enhancement. Table 1. Type of BDS signal received by Henan station. Band

Elevation (°)

R

RMSE (cm3 /cm3 )

MAE (cm3 /cm3 )

B1I

5–30

0.5271

0.0879

0.0774

20–35

0.7109

0.0414

0.0375

B2I

5–30

0.7133

0.0595

0.0573

20–35

0.7503

0.0481

0.0455

B3I

5–30

0.6194

0.0698

0.0674

20–35

0.6752

0.0541

0.0513

The delay phases of 20–35° BDS triple-frequency SNR data are fused with equal weight, and RANSAC algorithm is used to estimate model parameters. Table 2 shows that the RANSAC algorithm can improve the anti-interference ability of the model. Compared with the least square algorithm, the robustness is enhanced, and both RMSE and MAE are reduced by 27.47% and 31.17% respectively. Table 2. Comparison of results between RANSAC and least square algorithm. Method

RMSE (cm3 /cm3 )

MAE (cm3 /cm3 )

Least square linear regression

0.0091

0.0077

RANSAC

0.0066

0.0053

Figure 6 shows the inversion effects of the traditional linear regression method using 5–30° SNR data and the proposed method in this research. It can be seen that both of them reflect the change trend of SMC in the training set well, but the performance of the traditional method is poor in the test set. Since the 58th day, the reverse trend of soil change appears and the error increases gradually. The inversion results of both the training set and the test set are close to the real value. Figure 7 is the statistical diagram of the error distribution of the test set of the two methods. The error of the traditional method fluctuates within −0.02–0.06 cm3 /cm3 , with poor stability, while the inversion error of the method in this research is evenly distributed and varies within −0.02–0.02 cm3 /cm3 . As can be seen from Table 3, the traditional unary linear regression method and the proposed method were evaluated by RMSE and MAE, and the proposed method was superior to the traditional method in each index. The inversion values are highly correlated with in situ soil moisture with a correlation coefficient of 0.9850, RMSE of 0.0066 cm3 /cm3 and MAE of 0.0053 cm3 /cm3 .

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Fig. 6. Inversion effect with traditional method (left), inversion effect with proposed method (right)

Fig. 7. Error distribution of test set with traditional method (left), error distribution of test set with proposed method (right)

Table 3. Comparison of the results between the traditional method and the proposed method. Method

RMSE (cm3 /cm3 )

MAE (cm3 /cm3 )

Traditional method

0.0201

0.0140

Proposed method

0.0066

0.0053

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4 Discussion and Conclusion Based on GNSS-IR technology, this research proposed a SMC retrieval method using BDS triple-frequency delay phase fusion data, clarified the data processing process, and verified the effectiveness of the proposed method. In summary, the following conclusions can be drawn: (1) Compared to using SNR data of 5–30° directly, the cosine function is more accurate when fitting the original DSNR using an elevation angle range with a smooth variation in the amplitude of the DSNR, and the obtained delay phase can reflect the changes of SMC after precipitation. (2) Fusing BDS multi-satellite and triple-frequency delay phase can make full use of the differences and complementarities of satellite data of different frequencies and orbits to improve the quality of fusion phase, and hence the accuracy and reliability of the inversion. (3) RANSAC regression is more robust than the traditional least square linear regression. It can find the optimal model parameters in the case of noise, and its RMSE is reduced by 27.47%. In summary, this research verifies the feasibility and effectiveness of BDS triplefrequency signal in SMC inversion, laying a foundation for the subsequent application of BDS in continuous SMC monitoring and drought disaster warning. However, the station environment is relatively simple and does not need to consider the influence of vegetation and topography. The next research focus will be the inversion method of SMC in complex environment. Acknowledgement. This research is supported by the Natural Science Foundation of China (NSFC) Project (Grant Nos. 42077003); Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant Nos. SJCX22_0553).

References 1. Lin, Z.H., Yang, X.S., Guo, Y.F.: Sensitivity of land surface process model to initial soil moisture. Clim. Environ. Res. 6(2), 240–248 (2001) 2. Liu, Z.M., Zhang, B., Yan, M., et al.: Some research advances and trends on soil moisture and drought monitoring by remote sensing. Adv. Earth Sci. 18(4), 576–583 (2003) 3. Bilich, A., Larson, K.M.: Mapping the GPS multipath environment using the signal-to-noise ratio (SNR). Radio Sci. 42, RS6003 (2007) 4. Larson, K.M., Small, E.E., Gutmann, E.D., et al.: Use of GPS receivers as a soil moisture network for water cycle studies. Geophys. Res. Lett. 35(24), 851–854 (2008) 5. Chew, C.C., Small, E.E., Larson, K.M., et al.: Effects of near-surface soil moisture on GPS SNR data: development of a retrieval algorithm for soil moisture. IEEE Trans. Geosci. Remote Sens. 52(1), 537–543 (2013) 6. Jing, L.L., Yang, L., Han, M.T., et al.: Soil moisture inversion method based on GNSS-IR dual frequency data fusion. J. Beijing Univ. Aeronaut. Astronaut. 45(6), 1248–1255 (2019) 7. Sun, B., Liang, Y., Han, M.T., et al.: A method for GNSS-IR soil moisture inversion based on GPS multi-satellite and triple-frequency data fusion. J. Beijing Univ. Aeronaut. Astronaut. 46(6), 1089–1096 (2020)

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8. Zhang, S.C., Wang, T., Wang, L.X., et al.: Research on variation of soil moisture retrieval by BDS/GPS. Sci. Surv. Mapp. 46(7), 7–14 (2021) 9. Li, T., Zhang, X.Y., Deng, X.D., et al.: GNSS-MR soil moisture retrieval considering the multipath environments differences and gross error. Natl. Remote Sens. Bull. 25(6), 1324– 1337 (2021) 10. Lv, J.C., Zhang, R., Tu, J.S., et al.: A GNSS-IR method for retrieving soil moisture content from integrated multi-satellite data that accounts for the impact of vegetation moisture content. Remote Sens. 13, 2442 (2021) 11. Chen, K., Cao, X.Y., Shen, F., et al.: An improved method of soil moisture retrieval using multi-frequency SNR data. Remote Sens. 13(18), 3725 (2021) 12. Shen, F., Sui, M.M., Zhu, Y.F., et al.: Using BDS MEO and IGSO satellite SNR observations to measure soil moisture fluctuations based on the satellite repeat period. Remote Sens. 13(19), 3967 (2021) 13. Luo, C.X.: Soil moisture retrievals using GPS signal-to-noise ratio observations. Southwest Jiaotong University (2018) 14. Zhu, Y.F.: Soil moisture retrieval using BDS signal-to-noise ratio observations. Nanjing Normal University (2021) 15. Larson, K.M., Small, E.E., Braun, J.J., et al.: GPS multipath and its relation to near-surface soil moisture content. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 3(1), 91–99 (2010) 16. Vey, S., Güntner, A., Wickert, J., et al.: Long-term soil moisture dynamics derived from GNSS interferometric reflectometry: a case study for Sutherland, South Africa. GPS Solut. 20(4), 641–654 (2016) 17. Xu, Y., An, W.F.: Visual SLAM based on the improved RANSAC algorithm. J. Tianjin Univ. (Sci. Technol.) 53(10), 1069–1076 (2020)

The Evaluation Analysis of RDSS Timing Service for Beidou-3 Xianglei Wang(B) , Teng Han, and Chao Xie Beijing Satellite Navigation Center, Beijing, China [email protected]

Abstract. Beidou-3 system has been officially built and provides services to users all over the world. RDSS time service is a time service method provided by Beidou3. In this paper, the basic principles of RDSS one-way time service and RDSS twoway time service are discussed in detail, the monitoring and evaluation methods of RDSS time service are deeply studied, and the measured data are compared and analyzed. The experimental results show that the service accuracy of Beidou-3 is better than the published index requirements, among which the RMS of one-way service accuracy of RDSS is better than 3 ns, and the RMS of two-way service accuracy of RDSS is better than 2 ns. Compared with Beidou-2 RDSS, Beidou-3 has improved and optimized the service accuracy of RDSS, and the beam switching in the process of RDSS service will cause the fluctuation of service results, which can reach tens of nanoseconds in one-way service and several nanoseconds in two-way service. Keywords: RDSS · Two-way timing · One-way timing · Timing monitoring · Monitoring and evaluation

1 Introduction 1.1 A Subsection Sample At present, the United States, Russia, China and Europe all have their own global satellite navigation systems, while Japan and India are actively developing regional satellite navigation systems, forming a pattern of “four big ones and two small ones”. Beidou-3 system is a major strategic project of our country [1]. It was opened in 2020 and provided services to the whole world. Besides the traditional real-time positioning, navigation and timing services, it can also provide location reporting services [2]. This is also the biggest feature and advantage of Beidou satellite navigation system, which is different from other satellite navigation systems in the world [3, 4]. Beidou satellite navigation system provides both RDSS and RNSS service systems, and also provides RNSS time service and RDSS time service correspondingly. RDSS time service is a unique service of Beidou, and there is no experience to learn from in foreign countries [5, 6]. Studying the monitoring and evaluation method of RDSS time service is of great benefit to Beidou in improving its service performance. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 264–272, 2024. https://doi.org/10.1007/978-981-99-6928-9_23

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Satellite time service means has become the most widely used time service means. RDSS time service can be divided into RDSS one-way time service and RDSS twoway time service. The main difference is different propagation delay. Based on the measured data, this paper systematically studies the monitoring and evaluation methods of RDSS one-way time service and RDSS two-way time service, in order to change the habit of using GPS for time service users in China, eliminate the differences in users’ understanding of RDSS time service, and provide some reference for RDSS time service users.

2 Beidou RDSS Timing Principle 2.1 RDSS One-Way Time Service One-way time service of Beidou satellite is that the satellite transponder forwards the outbound signal sent by the ground control center to the user, that is, the main atomic clock of Beidou ground control center controls and generates the frequency, coding rate, phase and navigation message of the satellite navigation signal, which is sent to Beidou satellite by the ground control center, and Beidou satellite forwards the signal to the user terminal in the downlink, and the terminal outputs 1 PPS and TOD time information to complete the one-way time service of RDSS. Because RDSS satellite transparently forwards outbound signals, the difference between local time and UTC time obtained by time service terminal also includes the propagation delay of uplink signals and the zero value of satellite transponder. The uplink propagation delay can be obtained from the RDSS outbound message [7, 8]. TJST−UTC = TJST−GNT + TGNT−UTC

(1)

TJST−GNT = Tmeasure − Tdown − Tother − Tup

(2)

TJST-UTC is the difference between local time and UTC time; TJST-GNT is the difference between local time and RDSS system time, Tmeasure is the pseudo-range time transmitted from RDSS ground center station to the time service terminal via satellite, which is measured by the time service terminal. Tdown is the space geometric propagation delay from RDSS satellite to the time service terminal, and Tother is other time delay related content, including ionosphere, troposphere, equipment zero value, transponder time delay, etc. Tup is the uplink propagation delay from the ground central station of RDSS system to RDSS satellite, which can be obtained from the outbound message of RDSS, and TGNT-UTC is the difference between satellite navigation system time and UTC time. 2.2 RDSS Bidirectional Time Service Beidou two-way time service is a licensed user’s initiative time service mode, which requires the user terminal to have the ability to receive outbound signals and respond to inbound signals [9]. Through the round-trip measurement with the ground central

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station, the time difference between the time service terminal and the ground central station can be obtained by the central station, which can avoid the one-way time service deviation caused by many uncertain factors such as antenna position error of the time service terminal, ionosphere/troposphere reconstruction defects, etc. Compared with RDSS one-way time service, two-way time service has higher time service accuracy. RDSS two-way time service is a kind of time service application initiated by the time service terminal [10]. The time service terminal interacts with the ground central station, and sends the time application to the ground central station. The ground central station calculates the time difference between it and the time service terminal, and broadcasts it to the time service terminal through the outbound signal. The forward propagation delay information returned by the time service terminal is the difference TGNT-UTC between RDSS system time and UTC time, and the local time is corrected to synchronize with UTC time to complete the two-way time service (Fig. 1).

Fig. 1. Schematic diagram of RDSS two-way time service

The time stamp information sent by the ground control center is sent back to the ground control center after two uplink and downlink transmissions. For example, assuming that the user terminal forwarding delay and satellite forwarding delay have been calibrated, and the ground control center’s transmitting delay and receiving delay are recorded as sum respectively, the two-way transmission delay, the forward transmission delay and the reverse transmission delay of the signal are τfz and τrz , the delay of signal two-way transmission is τdual , the delay of forward transmission is τf , the delay of reverse transmission is τr . τdual = τf + τr + τfz + τrz τf = τfup + τfdown + τfz

(3)

τr = τrup + τrdown + τrz If the position of satellite during the signal two-way transmission, and the delay between forward and reverse is stay the same. In fact, the satellite drifted greatly during

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τfdown + τrup , which will lead to a certain delay deviation between the forward and reverse transmission delays τdiff . The ground control center can calculate τdiff according to the satellite ephemeris and user coordinates, and further obtain the forward signal transmission delay. τdual + τdiff + τfz − τrz (4) τf = τfup + τfdown + τfz = 2 Therefore, the user can calculate the time deviation between the local clock and BDT according to the received forward transmission delay parameters. tBDT = τtotal + τf + τint

(5)

3 Beidou RDSS Time Service Monitoring Principle 3.1 RDSS One-Way Time Service The basic method of time service monitoring is shown in Fig. 2.

Fig. 2. RDSS one-way timing accuracy evaluation diagram

(1) Beidou one-way time service calculates the deviation TJST-BDT between Beidou satellite broadcast time and receiver time through pseudo-range correction. T JST−BDT = Tmeasure − Tdown − Tother ρ/c − r/c − τclk − τrela − τion − τtrop − τsag − τJS

(6)

Among them, ρ is pseudo-range from satellite to receiver, r is geometric path delay from satellite to receiver calculated by ephemeris, τclk satellite clock error, τrela is relativistic effect correction, τion is ionospheric delay, τtrop is tropospheric delay, τsag is sagnac correction and τJS is receiver delay. The Beidou broadcast message contains the time deviation between BDT and UTC(BSNC), and the time deviation TJST-UTC(BSNC) between the receiver and UTC (BSNC) can be calculated by this parameter, as shown in formula (7). TJST−UTC(BSNC) = TJST−BDT − TUTC(BSNC)−BDT

(7)

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(2) After the time service monitoring receiver compensates the measured time deviation TJST-UTC (BSNC) to local time TJST , it will recover a certain standard time signal obtained by receiving Beidou RNSS signal, as shown in formula (8). TREV_UTC(BSNC) = TJST − TJST−UTC(BSNC)

(8)

Measuring the time difference between local UTC(BSNC) and a certain standard time service signal TREV_UTC(BSNC) output by the service monitoring receiver can evaluate and analyze the deviation of a certain standard time transmitted by Beidou. 3.2 RDSS Two-Way Time Service (1) Beidou RDSS bidirectional time service monitoring receiver works in bidirectional time service mode, and completes the inbound application of RDSS bidirectional time service according to the specified service frequency, inbound signal transmission power and inbound information rate. The central station calculates the round-trip time of the signal 2, and calculates the forward propagation delay value of the signal from the center to the receiving of the monitoring receiver τ2, and then sends it to the monitoring receiver as a bidirectional timing delay correction value. The principle of receiver bidirectional clock difference acquisition is shown Fig. 3, and the monitoring receiver can obtain the clock error TJST-BDT between local clock and center time BDT according to formula (9). TJST −BDT = 1 − 1 − τ 2 − nt = ρ − τ2

(9)

Fig. 3. RDSS two-way timing accuracy evaluation diagram

Among them, ρ = 1 − 1 − nt is the pseudo-range, n is generally the whole second time of the signal, and the broadcast message of Beidou contains the time deviation between BDT and UTC(BSNC). Through this parameter, the time deviation TJST-UTC(BSNC) between the receiver and UTC (BSNC) can be calculated, as shown in formula (10). TJST−UTC(BSNC) = TJST−BDT − TUTC(BSNC)−BDT

(10)

(2) After compensating the measured time deviation TJST-UTC (BSNC) to the local time TJST , the time monitoring receiver will recover a certain standard time signal obtained by Beidou RDSS bidirectional time service, as shown in formula (11). TREV_UTC(CMTC) = TJST − TJST−UTC(BSNC)

(11)

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(3) The counter measures the time difference between the local UTC(BSNC) and the time service signal TREV_UTC(BSNC) of a certain standard time output by the time service monitoring receiver to evaluate and analyze the deviation of a certain standard time transmitted by Beidou RDSS.

4 Analysis of Measured Data The experimental analysis data here comes from the measured data of Beidou-3 and Beidou-2 time-service receivers. The test time is October 1, 2021, the test length is 24 h, the sampling frequency of raw data is 1 s, the one-way result is 1 result in 1 s, and the two-way result is 1 result in 20 s. The reference time in the test is UTC(BSNC), and the input signals are 10 MHz and 1 pps. In order to analyze the timing results of Beidou system RDSS, one-way and two-way timing results of Beidou No.3 RDSS are given here. In order to compare the timing results of Beidou No.2 and Beidou No.3, one-way and two-way timing results of Beidou No.2 RDSS are also given here. The results are shown in Figs. 4, 5, 6, 7, 8, and 9.

Fig. 4. RDSS one-way timing results of the 4th beam of BDS-3 satellite 59

Fig. 5. RDSS one-way timing results of the 2th beam of BDS-3 satellite 60

Figures 4 and 5 show the one-way time service results of Beidou-3 No.59 satellite 4 beam and No.60 satellite 2 beam, with RMS of 2.4 ns and 1.9 ns respectively. Figures 6 and 7 show the two-way time service results of Beidou-3 satellite No.59 beam and Beidou-60 satellite No.6 beam, with RMS of 1.6 ns and 1.3 ns respectively.

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Fig. 6. RDSS two-way timing results of the 4th beam of BDS-3 satellite 59

Fig. 7. RDSS two-way timing results of the 6th beam of BDS-3 satellite 60

Fig. 8. RDSS one-way timing results of BDS-2

To compare the timing results of Beidou-2 and Beidou-3, the one-way timing results of 11-beam RDSS of Beidou-2 09 satellite and the two-way timing results of 10-beam RDSS of Beidou-2 08 satellite are shown in Figs. 8 and 9, with RMS of 4.1 ns and 2.7 ns respectively. Through the analysis of the results here, the following conclusions can be drawn: (1) The accuracy of Beidou-3 time service is all better than the published index requirements, among which the accuracy RMS of RDSS two-way time service results is better than 2 ns, and that of RDSS one-way time service results is better than 3 ns;

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Fig. 9. RDSS two-way timing results of BDS-2

(2) Beidou-3 RDSS timing results are better than Beidou-2 RDSS timing results, mainly because Beidou-3 improved the one-way timing algorithm of RDSS, which improved the timing accuracy of Beidou-3, and Beidou-2 timing results still had fluctuation errors with days as cycles; (3) The two-way service result of RDSS is better than the one-way service result of RDSS, and the errors of one-way service mainly include the central station transmission delay, satellite transmission delay, user receiver delay and other error model correction errors; (4) During the time service of Beidou-3 and Beidou-2, switching beams will cause the fluctuation of the time service results, which may reach tens of nanoseconds. These fluctuations are mainly caused by the inconsistency of the time delay correction of different beams. At the same time, due to the error of the fitting algorithm in the orbit of the orbiting satellite, the time service results will fluctuate in different degrees, and the fluctuation of beam switching of Beidou-3 is smaller than that of Beidou-2.

References 1. Yang, Y., Xu, Y., Li, J., et al.: Progress and performance evaluation of Beidou global navigation satellite system: data analysis based on BDS-3 demonstration system. Sci. Sin. (Terrae) 48(5), 584–594 (2018) (in Chinese) 2. China Satellite Navigation Office: BeiDou navigation satellite system open service performance standard (version 2.0). China Satellite Navigation Office, Beijing (2018) (in Chinese) 3. Liu, J., Cao, C.: Development status and trend of global navigation satellite system. J. Navig. Position 8(1), 1–8 (2020) (in Chinese) 4. Zhang, P., Tu, R., Guang, W., et al.: BDS-3 time frequency transfer method and its performance analysis. Navig. Position Timing 7(5), 58–64 (2020) (in Chinese) 5. China Satellite Navigation Office: The application service architecture of Beidou navigation satellite system. China Satellite Navigation Office, Beijing (2019) (in Chinese) 6. Liu, L., Han, C.: Two way satellite time transfer and its error analysis. Prog. Astron. 22(3), 219–226 (2004) 7. Tan, S.: The Engineering of Satellite Navigation and Positioning. National Defense Industry Press, Beijing (2010) (in Chinese)

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8. Guo, X.: Research on RNSS timing monitoring and abnormal diagnosis method. In: Proceeding of the 8th China Satellite Navigation Academic Annual Conference-S08 Test Evaluation Technology. Chinese Satellite Navigation System Management Office Academic Exchange Center (2017) 9. Liu, J., Li, H., Zhu, X., et al.: Research on two-way zero test method of RDSS receiver. Sci. Surv. Mapp. 39(4), 135–138 (2014) 10. Wang, T.: Research on time service performance evaluation of Beidou satellite navigation system. Changan University, Xian (2014) (in Chinese)

Identification of Tropopause Height Using COSMIC-2 Occultation Atmospheric Refractivity Ting Ni1 , Hang Guo1 , Jian Xiong2(B) , Longfei Lv1 , and Zihan Wan1 1 School of Information Engineering, Nanchang University, Nanchang 330000, China 2 School of Advanced Manufacturing, Nanchang University, Nanchang 330000, China

[email protected]

Abstract. The radio occultation (RO) observation data provided by the second generation of The Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) were used to study and verify the method of determining the tropopause height based on atmospheric refractivity covariance transform. The principle of selecting the scale factor a in the atmospheric refractivity covariance transform is discussed based on the occultation events of GPS and GLONASS. It is found that the vertical variation of the refractivity in the lower troposphere region is smoother when a is taken as 30 km, and the prominent peaks of the refractivity profiles are more conducive to the determination of the tropopause. Comparing the atmospheric refractivity with the covariance-transformed atmospheric refractivity, it is found that the change of latter is more obvious and prominent, which can be used for the determination of the tropopause. According to the RO data in the low, middle and high latitudes, the tropopause heights obtained by the atmospheric refractivity covariance transform was compared with the cold point tropopause (CPT) and the temperature lapse rate tropopause (LRT) heights determined by the occultation temperature profile in the same occultation event, and the results show that there is a remarkable consistency between the three results at different latitudes, which means that the method used to determine the tropopause height after the covariance transformation of the atmospheric refractivity is feasible. Keywords: Tropopause · Radio occultation · Atmospheric refractivity · Covariance transform

1 Introduction As the transition region between the troposphere and the stratosphere, the tropopause is subject to frequent water vapour exchange, energy transfer and other activities [1]. The characteristics of parameters in the tropopause are related to stratosphere-tropopause exchange as well as climate variability and change [2, 3], the tropopause height is also very sensitive to the changes in climate, that can even be considered as the “fingerprint” of climate change [4]. Therefore, the tropopause is vital for the study of climate change and atmospheric circulation [5, 6]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 273–282, 2024. https://doi.org/10.1007/978-981-99-6928-9_24

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The initial definition of tropopause was defined by the World Meteorological Organization (WMO) in 1957 as the lowest altitude above the 500 hPa isobar where the temperature decrement rate is arrive at or below 2 °C/km and where the average temperature decrement rate within the upper 2 km of this altitude does not exceed 2 °C/km, which is commonly referred to as the “thermodynamic” definition of the tropopause [7], also known as the LRT. Another thermodynamic criterion was also used for the definition of tropopause, the CPT, which is defined as the location corresponding to the lowest point of temperature on the vertical temperature profile [8]. In general, we will get diverse tropopause height by diverse calculation methods [9–11]. Data from the European Centre for Medium-Range Weather Forecasts (ECWMF) have been applied to the localization of tropopause for a long time [12]. The advantage of radio sounding technology is that sounding data is excellent in terms of vertical resolution and accuracy, but the temporal and spatial resolution is unsatisfactory. It is also difficult to get sounding data in polar and oceanic regions, and the bias owing to instrument variability is difficult to estimate [13]. The identification of the tropopause in reanalysis is limited by the low vertical resolution and model bias. The launch of the proof-of-concept mission Global Positioning System/Meteorology (GPS/MET) in 1995 began a revolution in profiling earth’s atmosphere through RO data [14, 15]. In recent years, satellite-based RO has become an innovative and powerful technology for obtaining atmospheric parameter profiles with global coverage with longterm stable, all-weather, high precision and vertical resolution [16]. RO data are ideal for studying changes in the tropopause. Previous studies have focused on determining the tropopause height from occultation temperature profiles and then analysing the global distribution and variability of top tropospheric parameters [17, 18]. In 2009, Lewis [19] proposed a method for estimating tropopause based on the covariance transformation of occultation curve angle, and the new method was considered more robust by comparing with traditional CPT and LRT. However, a number of RO data do not contain curved angle information, so this method is difficult to study the long-term trend of tropopause. Mean temperature and mean water vapour content are two important indicators of global climate change. The vertical profile of the atmospheric refractivity depends on local pressure, temperature and humidity. Meanwhile, temperature and humidity data for the region can also be extracted from atmospheric refractivity profile information from the RO data. Therefore, the atmospheric refractivity profile can be used as an indicator of global climate change, to provide another way to detect global climate [20]. Then, Xia et al. [21] proposed that the atmospheric refractivity covariance transform could also be used to determine the height of tropopause. The refractivity tropopause height was compared with the bending angle tropopause, CPT and LRT heights derived from RO and radiosonde data and revealed a good consistency. With the start of the second generation of COSMIC, six COSMIC-2 satellites were launched on 25 June 2019 successfully. This paper introduces the principle of using RO data to obtain the atmospheric refractivity, investigates the value of the scale factor a in the covariance transformation of the atmospheric refractivity using GPS and GLONASS occultation events from the COSMIC-2 occultation observations, and analyses the feasibility of determining the tropopause height from the covariance-transformed atmospheric refractivity.

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2 Determine the Height of Tropopause 2.1 Atmospheric Refractivity Profile In general, there are two ways to obtain the atmospheric refractivity profile, one is calculated from the temperature, pressure and relative humidity in the radiosonde data, anther is obtained from the RO data through the geometric relationship among low-orbit satellites, the Global Navigation Satellite System (GNSS) satellites and the earth at the time of the occultation event. In this paper, the second method is used to calculate the atmospheric refractivity profile. The basic principle is as follows (take a GPS satellite as an example).

Fig. 1. Geometric relationship between low-orbit satellites, GPS satellites, and earth during occultation events

As shown in Fig. 1, α is the curve angle between the front and back of the satellite signal propagation direction through the atmosphere, and θ is the angle between the loworbit satellite and the GPS satellite and the geocentric connection. φG and φL represent the angle between the satellite’s exit and incident signals and the low-orbit satellite and GPS satellites in a straight line. The unit of each of the above parameters is degrees. α = θ + ϕG + θL − π

(1)

The bending angle based on Snell’s law of refraction can be expressed as: a = rG sinϕG = rL sinϕL

(2)

where a is the collision parameter, rG and rL represent the straight-line distance from Earth to low-orbit satellites and GPS satellites, the units for the three parameters are km. The values of the collision parameter a and the bending angle α can be obtained by iterative calculation. Assuming that the earth’s atmosphere is spherically symmetrical, when the collision parameter is a0 , the bending angle of the signal propagation path is: ∞ α(a0 ) = 2a0 a0

1 d lnn(a) . .da da a2 − a0 2

(3)

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After the Abel integral, the refractive index of the earth’s atmosphere can be obtained: ⎤ ⎡ ∞ 1 α(a) ⎦ (4) n(a0 ) = exp⎣ .  π a2 − a0 2 a0

In space-based occultation observations, the orbital altitude of low-orbit satellites usually does not exceed 1000 km. Therefore, the refractivity of the earth’s atmosphere between the orbital altitude of a low-orbit satellite and the upper integral limit of formula (3) is considered to be constant 1. The maximum number of points in the above equation can be replaced with rL . The refractivity of the earth’s atmosphere at the time of the occultation event can be expressed as: N = 106 (n(a) − 1)

(5)

2.2 Atmospheric Refractivity Covariance Transforms Generally, the temperature decreases with the increase of troposphere height and the increases with the increase of stratospheric height, so the concept of CPT is proposed, and the turning point of the temperature profile is the tropopause height. The method is easy to understand and simple to operate, allowing the determination of tropopause height from a single temperature distribution alone, but CPT is only suitable for tropical regions where aerial convective activity is relatively simple. The LRT defined by OWM, can be used worldwide to determine the position of the tropopause. In this paper, the atmospheric refractivity covariance transform is used to determine the tropopause height by the vertical distribution of the atmospheric refractivity after the covariance transform. The basic algorithm is as follows: In 1993, Gamage and Hagelberg proposed to use wavelet covariance transform to detect step changes [22]. In this method, N (z) is used to represent the vertical distribution of the atmospheric refractivity with altitude, where N represents the atmospheric refractivity, where z represents height. The natural logarithm of the vertical distribution of the refractivity is f (z) = ln[N (z)]. The localized covariance transform Wf (a, b) of data in f (z) using a basis function h is defined as follows: 1 Wf (a, b) = a

z1

 z−b dz f (z)h a

(6)

z2

where a is the scale factor and b is the height involved in the calculation, z1 and z2 are the upper and lower bounds corresponding to the effective gradient interval. Their units are km. Meanwhile, the a that appears later represents the scale factor all the time. h( z−b a ) is a gradient function of the natural logarithm f (z) of the atmospheric refractivity distribution, which is defined as:

 z−b f (z) − f (b), b − a2 < z < b + a2 = h (7) 0, z < b − a2 or b > b + a2 a

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The result of the atmospheric refractivity covariance transforms, Wf (a, b), varies with altitude. When a maximum value of Wf (a, b) is obtained at a certain height b, it reflects a step change in the refractivity function at that height, and it is considered that the height b corresponding to the maximum value of Wf (a, b) is the tropopause height. In this paper, the tropopause height determined by the method is denoted as TPH(N).

3 Experiments and Analysis 3.1 Determine the Reasonable Value of the Scale Factor a In the application of atmospheric refractivity covariance transform, the value of scale factor a affects the determination of the tropopause height. In previous studies, the atmospheric refractivity covariance transformation generally took the empirical value of 25 km for a [21]. In this paper, the occultation event observed by COSMIC-2 are used as examples to study the changes of Wf (a, b) under different values of a and the influence of a values on the determination of tropopause height.

Fig. 2. Variation of Wf (a, b) with altitude at different values of a (using GPS RO data from the COSMIC-2 satellite survey over 33.99°N, 60.26°E at 00:34 on 15 August 2020).

Figure 2 shows the Wf (a, b) profiles at different values of a based on the GPS occultation event detected by the COSMIC-2 low-orbit satellite. As can be seen from the

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figure, the maximum value of the Wf (a, b) profile of the six subfigures in Fig. 2 corresponds to the height of about 18 km. When a were taken at different values (a = 5, 10, 15, 20, 25, 30 km), the tropopause heights were determined by the atmospheric refractivity covariance transform to be 18.2 km, 18.05 km, 18 km, 18 km, 18 km and 18 km, respectively. As shown in subfigures (a), (b) and (c), when the value of a is small (a = 5, 10, 15 km), the Wf (a, b) profile has large amplitude jitter in the lower troposphere below the tropopause height, which is generally affected by the combined effect of the temperature and humidity of the lower troposphere atmosphere, these amplitude jitter reflect small-scale changes in large temperature humidity, in which case the determination of the tropopause height may be affected by the stable inversion layer in the troposphere. By comparing the six subfigures in Fig. 2, it can be found that when a is 30 km, the changes of the lower tropospheric Wf (a, b) are Smoother, which can basically filter the small-scale changes caused by the temperature and humidity of the lower tropospheric atmosphere. Moreover, the value of Wf (a, b) in the stratospheric is significantly different from that near the tropopause, which is convenient for determining the height of the tropopause by Wf (a, b) peak. By comprehensive consideration, 30 km may be a more suitable choice than 25 km for the value of a.

Fig. 3. Variation of Wf (a, b) with altitude at different values of a (using GLONASS RO data from the COSMIC-2 satellite survey over 8.52°S, 22.8°E at 06:34 on 10 July 2020).

Figure 3 shows the Wf (a, b) profiles at different values of a based on the GPS occultation event detected by the COSMIC-2 low-orbit satellite. It can be seen that the Wf (a, b) profiles of the six subfigures in Fig. 3 have obvious protrusions at 16 km. The tropopause heights under different values of a were 16.7 km, 16.6 km, 16.8 km, 16.6 km, 16.6 km and 16.7 km, respectively. When the value of a is taken differently, the change of Wf (a, b) with altitude is similar to that of GPS occultation events, and both occultation events indicate that a = 30 km is a better choice when determining the tropopause height by atmospheric refractivity covariance transform. 3.2 Verification of Feasibility The feasibility of the atmospheric refractivity covariance transformation for determining the tropopause height when the scale factor a is 30 km is verified by analysing the

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variation of the atmospheric refractivity and comparing the heights of TPH(N), CPT and RLT, using the observed occultation event of the COSMIC-2 satellite over (36.34°N, 123.22°W) at 00:26 on 10 July 2020 as an example.

Fig. 4. The atmospheric refractivity before and after the covariance transformation changes with altitude.

Figure 4 shows the vertical distributions of atmospheric refractivity and covariance transformed atmospheric refractivity. The solid red line on the left is the refractivity profile, and the solid blue line on the right is the profile of refractivity after covariance transform. As we can see from the figure on the left, the atmospheric refractivity varies gently over the elevation range. Therefore, it is difficult to judge the mutation in the height of the tropopause from the refractivity profile alone. However, the atmospheric refractivity profile will produce drastic changes after local covariance transform, and it can be found that there is a maximum values and obvious mutations in its vertical distribution, which proves that the covariance transform can detect small changes in the refractivity profile well, thereby proving the feasibility of the refractivity covariance transform to determine the tropopause height. In order to further verify the effectiveness of using the atmospheric refractivity covariance transform to determine the tropopause height, three occultation events were selected at low, middle and high latitudes, and the tropopause heights measured by atmospheric refractivity covariance transform based on RO data was compared with the CPT and LRT heights measured by the temperature profile of the same occultation event. Figure 5 is the comparison results at low, medium and high latitudes, where the subfigures (a) and (b), (c) and (d), (e) and (f) correspond to low latitudes, middle latitudes and high latitudes, respectively, and the specific information of occultation events has been marked in the figure. The subfigures (a), (c) and (e) in Fig. 5 show the change in the vertical temperature of the atmosphere obtained from RO data, from which we can determine the positions of CPT and LRT. The dotted lines in subfigures (b), (d) and (f) correspond to the tropopause height determined by the atmospheric refractivity covariance transform. As we can be seen from subfigures (b), (d) and (f), there is a

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significant and unique maximum value in the profile of Wf (a, b) in each subfigure, and the height corresponding to this maximum is the tropopause height.

Fig. 5. Tropopause heights determined at low, middle, and high latitudes using occultation temperature profiles and atmospheric refractivity profiles.

Table 1. The tropopause heights at different latitudes Latitude

TPH(N)/km

CPT height/km

LRT height/km

21.69°N

16.45

16.47

15.93

30.67°S

10.91

11.75

11.12

61.04°N

16.7

16.6

14.6

As shown in Table 1, the LRT heights at different latitudes are 15.93 km, 11.12 km and 14.6 km, respectively. The CPT heights are 16.47 km, 11.75 km and 16.6 km, respectively. The TPH(N) are 16.45 km, 10.91 km and 16.7 km, respectively. Through analysis and comparison, it can be found that in the two occultation events that occurred at low and middle latitudes, the tropopause heights estimated by the three methods are basically consistent, and their gaps were less than 1 km. In the occultation event that occurred at high latitude, the gap between TPH(N) and CPT height is only 0.1 km, the LRT is about 2 km lower than them. In Fig. 5, it is easy to detect that TPH(N) is closer to

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CPT height and higher than LRT, that is due to LRT height represents the lowest possible value of tropopause height, while TPH(N) and CPT height generally represent the height of the most obvious transition layer between the troposphere and stratosphere. Generally, the tropopause heights estimated by the three methods are well consistent at different latitudes, indicating that the atmospheric refractivity covariance transform based on RO data is an effective method for determining the tropopause height.

4 Summary This paper presents and analyses a new method for calculating the tropopause height based on the atmospheric refractivity covariance transform. The atmospheric refractivity is transformed by covariance to obtain Wf (a, b), and its change is more visible than the atmospheric refractivity, with distinct peaks. The upper protruding peak of the Wf (a, b) profile reflects the transition from the troposphere to the stratosphere, allowing the tropopause height to be determined. The selection of scale factor a in the atmospheric refractivity covariance transform is also discussed and analyzed based on different occultation events. GPS and GLONASS occultation data were used to analyze the changes of the Wf (a, b) profile at different a and found that when a takes 30 km, the Wf (a, b) profile is smoother, which can basically filter out small-scale changes caused by the temperature and humidity of the lower troposphere atmosphere. At the same time, the tropopause height can be determined by the obvious peak. 30 km is more suitable for the value of a in atmospheric refractivity covariance transform than the empirical value 25 km. The occultation temperature profiles and atmospheric refractivity profiles were obtained by using the RO data in low, middle and high latitudes, and TPH(N) were compared with CPT and LRT heights, and it was found that the three results were highly consistent and consistent at different latitudes. The results further demonstrate the effectiveness of using the atmospheric refractivity covariance transform to determine the tropopause height when a is 30 km. In conclusion, the atmospheric refractivity covariance transform can provide a reliable new option for studying the spatiotemporal variation characteristics of global tropopause height, and further enrich the practicability of occultation technology. Acknowledgements. Thanks to the National Natural Science Foundations of China (41764002, 62263023 and 62161002) and the Graduate Innovation Special Fund of Jiangxi province (YC2022S019) for their support for this paper. Meanwhile, thanks to the COSMIC Data Analysis and Archive Center (CDAAC) for the free data.

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4. Santer, B.D., Wehner, M.F., Wigley, T.M.L., et al.: Contributions of anthropogenic and natural forcing to recent tropopause height changes. Science 301(5632), 479–483 (2003) 5. Gettelman, A.: A climatology of the tropical tropopause layer. J. Meteorol. Soc. Jpn. Ser. II 80(4B), 911–924 (2002) 6. Wang, W., Matthes, K., Schmidt, T., et al.: Recent variability of the tropical tropopause inversion layer. Geophys. Res. Lett. 40(23), 6308–6313 (2013) 7. World Meteorological Organization (WMO): Definition of the tropopause. WMO Bull. 6, Geneva, Switzerland (1957) 8. Highwood, E.J., Hoskins, B.J.: The tropical tropopause. Q. J. R. Meteorol. Soc. 124(549), 1579–1604 (1998) 9. Pan, L.L., Honomichl, S.B., Bui, T.V., et al.: Lapse rate or cold point: the tropical tropopause identified by in situ trace gas measurements. Geophys. Res. Lett. 45(19), 10756–10763 (2018) 10. Schmidt, T., Wickert, J., Beyerle, G., et al.: Tropical tropopause parameters derived from GPS radio occultation measurements with CHAMP. J. Geophys. Res.: Atmos. 109(D13) (2004) 11. Borsche, M., Kirchengast, G., Foelsche, U.: Tropical tropopause climatology as observed with radio occultation measurements from CHAMP compared to ECMWF and NCEP analyses. Geophys. Res. Lett. 34(3) (2007) 12. Xian, T., Homeyer, C.R.: Global tropopause altitudes in radiosondes and reanalyses. Atmos. Chem. Phys. 19(8), 5661–5678 (2019) 13. Seidel, D.J., Ross, R.J., Angell, J.K., et al.: Climatological characteristics of the tropical tropopause as revealed by radiosondes. J. Geophys. Res.: Atmos. 106(D8), 7857–7878 (2001) 14. Kursinski, E.R., Hajj, G.A., Bertiger, W.I., et al.: Initial results of radio occultation observations of Earth’s atmosphere using the Global Positioning System. Science 271(5252), 1107–1110 (1996) 15. Melbourne, W.G., Davis, E.S., Duncan, C.B., et al.: The application of spaceborne GPS to atmospheric limb sounding and global change monitoring (1994) 16. Kursinski, E.R., Hajj, G.A., Schofield, J.T., et al.: Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res.: Atmos. 102(D19), 23429–23465 (1997) 17. Schmidt, T., Wickert, J., Beyerle, G., et al.: Global tropopause height trends estimated from GPS radio occultation data. Geophys. Res. Lett. 35(11) (2008) 18. Xu, X., Luo, J., Zhang, K.: An analysis of the structure and variation of the tropopause over China with GPS radio occultation data. J. Navig. 64(S1), S103–S111 (2011) 19. Lewis, H.W.: A robust method for tropopause altitude identification using GPS radio occultation data. Geophys. Res. Lett. 36(12) (2009) 20. Yuan, L.L., Anthes, R.A., Ware, R.H., et al.: Sensing climate change using the global positioning system. J. Geophys. Res.: Atmos. 98(D8), 14925–14937 (1993) 21. Xia, P., Shan, Y., Ye, S., et al.: Identification of tropopause height with atmospheric refractivity. J. Atmos. Sci. 78(1), 3–16 (2021) 22. Gamage, N., Hagelberg, C.: Detection and analysis of microfronts and associated coherent events using localized transforms. J. Atmos. Sci. 50(5), 750–756 (1993)

Research on the Application Service System of BeiDou Navigation Satellite System Mudan Su, Jun Lu, Yeye Sui(B) , and Xiangyi Zhang Beijing Institute of Tracking and Communication Technology, Beijing, China [email protected]

Abstract. As BDS-3 satellite navigation system has been built and put into use for more than two years, the application of BeiDou satellite navigation system has gradually presented a prosperous trend. In order to further promote the marketization, industrialization and internationalization of BeiDou application, this paper conducts research on the application service system of BeiDou Navigation Satellite system. Through making a conceptual analysis of BDS scale application and public application service, this paper lays a theoretical foundation for BDS largescale application. A definition of BDS application service system is demonstrated in the perspective of BDS users. The BDS application service system architecture is designed at the same time, which clarifies the function of each component. This paper also discusses the progress at this stage, and puts forward suggestions for further improvement. Keywords: BDS · Application service · System architecture · Scale application

1 Introduction In 2020, BDS-3 system was built and put into use [1]. Compared with BDS2, its performance is further improved and its functions is expanded. The BDS-3 system has two functions including navigation and positioning as well as data communication, and provides users with seven kinds of services. In 2021, China incorporates the major project of Beidou industrialization into Fourteenth Five Year Plan for National Economic and Social Development [2]. In the same year, Xi Jinping sent a congratulatory letter to the first Beidou International Summit on Scale Application, pointing out that “the scale application of Beidou navigation satellite system has entered a critical stage of marketization, industrialization and international development”. At present, BDS has been widely used in all walks of life, as well as mass consumption/sharing economy and people’s livelihood. In 2021, total output value of China’s satellite navigation and location service industry reached 469 billion, and shipment of smart phones with satellite navigation and positioning functions reached 343 million [3]. In order to promote the large-scale application of BDS-3 system, and realize “convenience usage” and “fully utilization” of BDS-3 system at the same time, it is necessary to carry out research on the application service system of BDS. The application service system could establish a solid foundation for the large-scale application of BDS-3 © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 283–292, 2024. https://doi.org/10.1007/978-981-99-6928-9_25

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system and maximize the benefits of the BDS by clarifying the concept, analyzing the composition, finding gaps and making up for deficiencies. Application service system refers to a whole composition of a series of key elements related to its extensive application services around a system or a capability. The “application services” can be understood as “applications and services” or “services of applications”. No matter how you understand it, you need to analyze the problem from the point of view of the end users. For BDS, we might as well understand it in the broad scope of applications and services.

2 Overall Architecture of BDS-3 System Application Services On the basis of BDS engineering construction, the overall architecture of BDS application services which runs through all aspects from the system to users is constructed from the perspective of users (as shown in Fig. 1). It includes the basic layer, service layer, application layer and ecological security domain, forming the overall pattern of “one system, seven services, multiple operators, two user levels and two market directions”.

Fig. 1. Overall architecture of BDS-3 system application services

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The basic layer is the physical foundation for providing application services, consisting of five operation systems, namely satellite, ground operation control, TT&C, inter satellite link operation management and ground augmentation. The service layer is the bridge between the system and users. It contains supporting facilities, service documents, information distribution, monitoring and evaluation, feedback mechanism and other key elements. On the basis of supporting facilities, service documents and information distribution mainly support public announcement tasks, while the monitoring, evaluation and feedback mechanism mainly supports internal feedback tasks. The two tasks cooperate to complete the closed-loop, promote the repeated iteration of system construction and user needs, and thus promote the construction and development of the BDS-3 system. The application layer is a direct reflection of the effectiveness of the BDS-3 system. It mainly includes abroad user market and internal user market. It is divided into two user levels: equipment manufacturers and end users at the same time. The ecological security domain is the ecological environment for large-scale applications and industrial applications are based, which mainly includes policies and regulations, standards and specifications, intellectual property rights, etc. These will create a beneficial ecological environment for the healthy, orderly and benign development of China’s satellite navigation applications.

3 Design of BDS-3 System Application Service System 3.1 Research Ideas In order to further clarify the elements of the BDS-3 system application service system, we try to extract the key elements by analyzing the service process for users, which mainly includes three steps. The first step is to identify users of the BDS-3 system, the second step is to analyze the specific process to meet the needs, and the third step is to extract the relevant elements which need to be provided externally in each link of the process. Identify users of BDS-3 system: According to the overall architecture of BDS-3 system application services, the application layer is divided into two levels: equipment manufacturers and end users. The demand of equipment manufacturers is relatively focused and clear. The key point is that the main technical status related to the system in the production process needs to be supported by the interface control document. Therefore, we mainly analyze from the perspective of the end users who directly use BDS-3 system services. Analyze the specific process: The process of end users using services mainly includes four steps. First, the user decides to use the BDS-3 service. This requires relevant departments to provide system service performance specifications to support users’ judgment. Second, the user configures the device. This requires the equipment manufacturers to provide equipment that can receive and use BDS-3 system services. Third, users can register to access the network and use four services, namely, ground augmentation, regional short message communication, global short message communication and international search and rescue. This requires the service platform to provide various guarantees such as network access and data information, as well as the user guide to clarify the specific

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use process. Fourth, the BDS-3 system should be integrated into the user system for normal use, which requires stable operation and normal transmission of signals. Extract relevant elements: To sum up, building the application service system of the BDS-3 system is to provide users with a stable operating service platform, reliable and efficient service files, and high-quality product terminals on the basis of the stable operation of the BDS-3 system. At the same time, it is necessary to establish an information distribution and feedback mechanism to optimize and improve services, and a detection and certification mechanism to ensure that product quality is controllable. In order to ensure the efficient operation of the above elements and mechanisms, it is also necessary to build a clear responsibility system and create an ecosystem that adapts to the benign development of large-scale applications. 3.2 Architecture According to the above research and specific analysis, we formed the BDS-3 application service system as shown in the Fig. 2. From the logical perspective, the application service system of BDS-3 system includes three parts and seven elements. The first part is the core elements directly facing users, namely service platform, service documents and service products. The second part is to ensure that the first part optimizes the trusted mechanism elements, namely the distribution and feedback mechanism and the detection and certification mechanism. The third part is the assurance factors to ensure the sound development of the first two parts, namely, the ecosystem and the responsibility system. In terms of attributes, it can be considered as including two parts and seven elements. The combination of Part II and Part III is collectively referred to as the safeguard element. 3.3 Core Elements 3.3.1 Service Platform The service platform is a unified window that directly provides services for users and is deployed in a distributed manner. It consists of satellite-based augmentation service platform, ground augmentation service platform, regional short message communication service platform, global short message communication service platform, international search and rescue service platform, etc. The satellite-based augmentation service platform is the external window of satellitebased augmentation services, which provides users with civil aviation airworthiness certification, promotion of international standards, system performance evaluation, and promotion and application of satellite-based augmentation services. The ground augmentation service platform is the external window of ground augmentation services, providing users with services such as consultation, application, registration, charging, information announcement and opinion collection of various ground augmentation services. The regional short message communication service platform realizes the unified management, application, registration, annotation, use, etc. of the regional short message public service, and supports the market-oriented operation and efficiency of the regional short message communication service. The global short message communication service platform provides users with the application, registration, annotation and use guarantee

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Fig. 2. Application service architecture of BDS-3 system

of global short message communication services. The international search and rescue service platform provides users with access and distribution of distress alarm information, and reports the operation status information of BDS3 search and rescue payload to the International Search and Rescue Satellite Organization. In order to provide services more smoothly, a series of process specification files can be formed by referring to mature models such as mobile communication and released to users. 3.3.2 Service Document The service document refers to the relevant technical and guiding documents used to define the system service performance, support the R&D of user terminals, and facilitate users to use the system. It mainly includes interface control documents, service performance specifications, user guidance documents and other series of documents [4]. The interface control document mainly defines the basic characteristics of the space signal between the orbiting satellite and the user, as well as the ranging code characteristics, message structure, message parameters, algorithms and other system technical states related to the system functions. It is the basis for the development of user equipment such as the Beidou chip and the complete machine. The service performance specification mainly provides the types of services that the BDS can provide, as well as the performance characteristics and performance indicators of various services. It is the basis for users to decide whether to choose to use the BDS. The user guidance documents is mainly used to help users understand the procedures involved in the use of relevant

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services and guide them to complete the application, registration, annotation and use of services [4]. 3.3.3 Service Products Service products refer to all kinds of products that support users’ ability to use the BDS, including antennas, chips, boards, terminals and their firmware or software. With progress of science and technology and upgrading of electronic products, products are gradually developing towards direction of miniaturization/low power consumption/high performance/intelligence, to meet people’s yearning and pursuit of quality of life. 3.4 Assurance Factors 3.4.1 Distribution and Feedback Mechanism The distribution and feedback mechanism is an effective way to promote communication between the BDS and users. It mainly includes system information distribution mechanism and user feedback and response mechanism. The information distribution mechanism will inform users of the service platform information, service documents, service products information and other information of the BDS which closely related to users in an appropriate way, in order to help users use the functions of the BDS more effectively. The user feedback and response mechanism establishes a stable user information collection channel, pays attention to user concerns, responds to the needs of global users in a timely and efficient manner, and continuously optimizes and improves service capabilities to provide the best Beidou application service experience for global users. 3.4.2 Detection and Certification Mechanism The detection and certification mechanism is an effective means to ensure that the quality of Beidou application products is controllable. It standardizes the industrialized and market-oriented operation of service products by strictly controlling the quality of products. 3.4.3 Ecosystem The ecosystem is the sum of the external environment and factors that regulate and affect the construction and development of the Beidou application service system, including policies and regulations, standardization specifications, intellectual property rights, talent and technology, etc. Policies and regulations are a series of laws and policies formulated by national and local government departments to promote the sound and healthy development of Beidou application industry. Standards and specifications are the basic support for standardizing the development of industrial standardization and implementing various inspection and evaluation. Intellectual property is an important guarantee for the industry to be independent and controllable and have strong competitiveness. Talent technology is an important guarantee for the efficient development of industrial science and maintaining

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the momentum of development. In addition, ecosystem also includes market, capital and other factors. 3.4.4 Responsibility System The responsibility system is the basis for the implementation of all the above elements. On the premise of clear responsibilities, all relevant parties can perform their duties and work together to improve the capabilities. The importance of the responsibility system is self-evident. The responsible parties involved in the BDS application service architecture responsibility system include system suppliers, service suppliers, product suppliers, and relevant national departments. The system supplier is mainly responsible for the efficient implementation and maintenance of matters related to the BDS itself, such as the stable operation of the BDS, the updating and iteration of system interface control documents and service performance specifications, and the establishment of a distribution and feedback mechanism. The service provider is mainly responsible for providing application services and supporting contents, such as the construction and operation of the service platform, the preparation and release of user guide documents, etc. Product suppliers are mainly responsible for providing end users with products that have Beidou service capabilities and meet their needs, including the entire chain of production process, such as demand research, research and development, production, after-sales service. The relevant national departments implement the inspection and certification mechanism and build an ecosystem according to the existing division of labor.

4 Progress 4.1 Core Elements In terms of service platform, the satellite-based augmentation service platform has been able to provide initial services and provide industry application verification for civil aviation. The ground augmentation service platform has steadily provided real-time meter, decimeter, centimeter and post processing millimeter level positioning augmentation services. The regional short message service platform has been able to provide public services, providing nearly 200000 measured services for more than 100000 mobile phone users with short message communication functions. In terms of service documents, 15 interface control documents have been publicly released in Chinese and English, and 10 documents are currently in use, covering five categories of services: positioning, navigation and time service, satellite-based augmentation, ground augmentation, precise point positioning and international search and rescue [5]. The service performance specification has issued three versions, the latest version is version 3.0, which gives the main performance of five types of services, namely, positioning navigation time service, international search and rescue, precise point positioning, regional short message communication and ground augmentation [6]. User guidance document has not been officially released. There is an urgent need to coordinate and refine the service process, improve the guidance documents and release

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them as soon as possible. The above documents will be upgraded simultaneously with the development of system construction. In terms of service products, in order to promote the development of BDS civil industrialization, the Beidou Satellite Navigation System Management Office has organized and carried out high-quality research and development of BDS civil basic products in the way of “sunshine bidding and dynamic selection”. According to the comparison test, the Recommended Directory of BDS-3 Civil Basic Products (Version 1.0) was released in September 2020, which includes five categories of 24 products [7], including RNSS RF baseband integrated chip, dual frequency multi system high-precision RF baseband integrated chip, multi-mode multi frequency broadband RF chip, multi-mode multi frequency high-precision antenna, multi-mode multi frequency high-precision module, etc. Different industries can choose different products according to the actual situation. With the completion of BDS-3, the civil market in various industries and fields has further flourished, and the chip design and manufacturing technology has further improved. Civil products have achieved leapfrog development in performance and technology. The chip technology has been improved from 130 nm to 12 nm, and the size has been reduced from more than 150–5 mm2 . By the end of 2021, the sales volume of domestic Beidou compatible chip modules will exceed 200 million pieces. The total shipment volume of domestic centimeter level high-precision chips, modules and boards will exceed 1.2 million pieces, and the total number of terminal products with Beidou positioning function will exceed 1.2 billion sets [3]. 4.2 Assurance Factors In terms of information distribution and feedback mechanism, the official website of Beidou Satellite Navigation System (www.beidou.gov) and official WeChat official account have been established, on which the interface control documents, service performance specifications and other important information of the system have been publicly released. The official website will timely release the system construction and development plan, system constellation status, and parameters required for high-precision applications, and report information such as in orbit satellite plans and unplanned outages, according to the system construction development and actual operation. BDS has set up special mailboxes for system interfaces ([email protected]) and services (BDServices@ beidou.gov.cn), which is used to collect global user feedback and suggestions. At the same time, a regular research and timely response mechanism has been established to respond to users’ concerns. In terms of detection and certification mechanism, BDS Management Office released the “Recommended Directory of BDS-3 Civil Basic Products (Version 1.0)”, which sounded the prelude to the testing and certification of Beidou products. They also worked with relevant national departments to vigorously promote the establishment of detection and certification mechanism and Beidou basic product standard system. In August 2021, the State Administration of Market Supervision and Administration issued “the Opinions on the Implementation of Beidou Basic Product Certification”, which provided the top-level design of basic product certification and laid a solid foundation for orderly promotion of basic product certification [8]. “The Beidou Basic Product Certification Rules” was issued in September of that year, which defined the certification mode of

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“type test, initial factory inspection and supervision after certification” and the management requirements for certification marks. Based on this guidance, the first batch of Beidou basic products were initially certified [9], and “the Beidou Basic Product Certification Catalog (the first batch)” was formed and released, covering seven basic products in four categories: chip, antenna, module, and board, which guarantees the provision of high-quality Beidou products and services [10]. In the future, based on the certification system of Beidou basic products, BDS Management Office will try to gradually expand to Beidou application terminals and the whole industrial chain products. The ecological system and responsibility system have been initially completed with the development of the industry. In terms of policies and regulations, national government departments have successively issued policies to support the development of Beidou application industry. In 2013, the General Office of the State Council issued “the Medium and Long-term Development Project for the National Satellite Navigation Industry”. In 2021, the China Satellite Navigation System Management Office released “the Report on the Legal Construction of Beidou Satellite Navigation System”. In 2021, the industrial application of Beidou was written into the “Fourteenth Five Year Plan” and the Vision Outline for 2035. Local governments have also introduced the development plans and methods of satellite navigation industry to adapt to their own regions. In terms of standards and specifications, China has established the Beidou Satellite Navigation Standardization Technical Committee, formulated and updated “the Beidou Satellite Navigation Standard System (Version 2.0)”. It also organized the formulation of more than 100 military and civilian application standards [11], and expanded them to international civil aviation, international maritime, international mobile communications and other fields, further promoting the scientific development of Beidou standardization. In terms of intellectual property, the national government has established a green channel for priority review of Beidou patents, and the efficiency of intellectual property services has been constantly improved. By the end of 2021, China’s total number of satellite navigation patent applications (including invention patents and utility model patents) has exceeded 98000, maintaining a leading position in the world.

5 Outlook At present, BDS application service system has been preliminarily constructed, and Beidou large-scale application has entered a new stage. With development of BDS, its applications and services will inevitably continue to upgrade, and BDS application and service system will also continue to improve. In face of the urgent need for largescale applications, in order to facilitate global users to understand, comprehend and use Beidou better, and make the high-quality services of BDS benefit global users, it is urgent to build the service platform, improve the system service documents, issue user guidelines, standardize service processes and strengthen the rule of law focusing on the satellite navigation. At the same time, increasing the global layout of core high-value basic patents, creating a benign ecosystem with reasonable structure, complete elements, diverse means, smooth interaction, efficient operation and strong guarantee, and forming a unique competitive advantage are also pressing. In this way, users all over the world can enjoy fast, accurate, convenient, reliable and diversified systematic services. This

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could also promote the healthy and rapid development of the Beidou industry, push the development of BDS towards the goal of large-scale and international application, and make new contributions to the construction of a global community with a shared future for mankind.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Beidou global satellite navigation system officially opened. Interface News The Fourteenth Five Year Plan and the Outline of the Vision Goals for 2035.20210312 Industrial White Paper (2022) The Application Service Architecture of BeiDou Navigation Satellite System (1.0). China Satellite Navigation Office (2019) www.beidou.gov. Accessed 21 Feb 2022 China Satellite Navigation Office. BeiDou Navigation Satellite System Open Service Performance Standard. (2021) Recommended Directory of Beidou No. 3 Civil Basic Products (Version 1.0). China Satellite Navigation Office December, 2020 Opinions on the Implementation of Beidou Basic Product Certification. State Administration for Market Regulation (2021) Beidou Basic Product Certification Rules. State Administration for Market Regulation (2021) Beidou Basic Product Certification Catalog (the first batch). State Administration for Market Regulation Beidou Satellite Navigation Standard System (Version 2.0). China Satellite Navigation Office (2022)

PNT Architectures and New Technologies

NLOS Positioning Optimization Method Based on Unknown Location IRS Yuchen Jiang(B) , Lu Yin, and Zhongliang Deng School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China [email protected]

Abstract. The intelligent reflecting surface (IRS) is similar to an antenna array, which consists of multiple reflecting units. By controlling the phase shift of each reflecting unit, the direction of beam reflection is changed based on the analog beam fugacity theory, thus achieving the purpose of enhancing or constructing a channel. Therefore, IRS has great advantages in solving the channel estimation problem under non-line-of-sight (NLOS) conditions. For this characteristic, this paper proposes a localization method based on compressed sensing technology for the case where the relative position of IRS and base station is unknown, using NLOS path signals for second-order position estimation, first deriving rough localization parameters for IRS cascade channel estimation, and then conducting a joint phase configuration of IRS reflecting The phase configuration of the unit is jointly optimized, and then the second-order precise position estimation is performed. The results show that the proposed method is applicable to the NLOS positioning system with unknown IRS position, and due to the optimization capability of the IRS for the beam, the success rate of the positioning solution is improved by more than 20% and the positioning error is reduced by more than 40%. Keywords: Wireless positioning · Intelligent reflecting surface · Non-line-of-sight

1 Introduction In future communication systems, positioning technology will be integrated into the communication system as an essential function. Compared with independent positioning and communication systems, joint positioning and communication systems can improve spectrum and power utilization efficiency and reduce overhead by sharing physical platforms and spectrum resources [1]. Therefore, there is an increasing interest in different types of joint positioning and communication systems. For example, the multi-scale non-orthogonal multiple access technique in [2] is flexibly configured for different positioning users to obtain higher ranging accuracy, lower positioning delay, less resource consumption, and better signal coverage. The authors in [3] investigated integrated radar and communication systems to reduce localization errors and increase channel capacity. Although the above studies can provide both positioning and communication services and reduce resource overhead, some key issues remain to be further explored: how to © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 295–304, 2024. https://doi.org/10.1007/978-981-99-6928-9_26

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guarantee positioning services when the line-of-sight link is completely blocked; and how to guarantee positioning performance with lower resource consumption. Recently, intelligent reflective surfaces (IRS) have attracted significant attention as new technology to create an ideal path and reflect the incident signal to the receiver by phase shifting of passive reflective elements without any additional power or spectrum consumption [4]. Specifically, by jointly designing a base station beamforming and IRS configuration with continuous phase shift, IRS-based communication systems can effectively increase system throughput and reduce energy consumption [5]. Furthermore, [6] pointed out that IRS with limited discrete phase shifts can also ensure communication performance and energy efficiency. For the demand of localization services, [7] is used to improve the discriminative received signal strength (RSS) of adjacent locations in indoor localization scenarios. In [8], the case of a terminal located on the IRS center vertical is considered, and then the Fisher information matrix and the Cramer-Rao lower bound are derived to analyze the potential of IRS-assisted wireless localization. In [9], a localization system with dual IRS is proposed and a method for channel estimation using IRS is dis-cussed. The inclusion of IRS can effectively utilize the NLOS path and improve the robustness of the localization system compared to traditional elimination methods for solving the NLOS problem such as antenna design, receiver baseband signal processing, filtering techniques, and spatial information compensation [10–13], which result in significant resource consumption. The aforementioned studies show that the problems of LOS blocking and resource limitations can be overcome by introducing IRS into existing communication and localization systems. However, in the above studies, the IRS is mainly used as a known relay anchor point in the communication system and the location of the IRS is fixed and known. In some emergency rescue scenarios, IRS is temporarily deployed as a solution to establish a channel. The location of IRS is not precise with respect to the base station, and establish NLOS communication links through IRS in an unknown channel environment by transmitting beam scanning from the base station.In this paper, an IRS-assisted localization system completely obscured is considered for the above scenario. The main works are as follows. 1. We consider an IRS-assisted NLOS localization system that uses com-pressed sensing techniques combined with IRS beamforming gains to improve localization accuracy. 2. We propose the Unknown Anchor Optimized Positioning (UAOP) meth-od, which effectively implements cascaded channel scanning, terminal position estimation, and optimal solution of positioning results when the IRS position is unknown. 3. For the subproblem of optimized signal-to-noise ratio, we use the initial positioning parameters to optimize the phase of transmit antenna and IRSs elements, and then improve the received signal-to-noise ratio by beamforming.

2 System Model As shown in Fig. 1, the base station (BS) transmits beams in different directions to detect the unknown IRS and establishes a channel with the mobile terminal (MT) obscured by the obstacle through multiple reflection paths. The reflected beam angle θr is changed by adjusting the phase shift setting of the IRS reflector element, i.e., the phase shift

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Fig. 1. IRSs positioning system model

  matrix is  = diag ejφ1 , ejφ2 , . . . , ejφNm . where φn ∈ [−π, π ] denotes the phase shift of the reflector elements and Nm is the number of reflector units. The phase shift matrix is integrated into the cascade channel H2H H1 , where H1 and H2 represent the transmit and reflective channels. Therefore, the received signal can be expressed as  H2H H1 )ωs + z (1) y=( IRS

The overall channel from BS to MT is the sum of all cascaded channels through the IRS, ω denotes the beam assignment matrix of the BS, s denotes the transmitted symbols, and z is the additive white Gaussian noise with independent homogeneous distribution. Also, for the localization problem of the system, it is necessary to obtain information about the path distance r contained in the channel, the incidence angle θi of the electromagnetic wave to the IRS, the observation angle θs to the MT, etc. So for the overall channel, we have respectively H1 = T1 AM ,T (θi )AH T ,M (θi )

(2)

H2 = T2 AM ,T (θs )AH T ,M (θs )

(3)

where the phase difference T 1 , T 2 generated by the electromagnetic wave propagation distance and contains the BS-IRS and IRS-MT distance information. AM ,T and AT ,M denote the array antenna response matrices [14] at the transmitter and receiver ends, respectively, containing the angular information required for localization.

3 The Proposed Method 3.1 Angular Domain Channel Representation In view of the cascaded channel angle information θi and θs are not correlated. The angle domain of the overall channel H2H H1 is discretized from the two dimensions.  H2H H1 )A˜ I (4) HA = A˜ H R( IRS

where A˜ R , A˜ I are the response matrices of BS and MT in the angle domain, respectively.   Sets the resolution of the discrete representation Nb , that is, the angle domain − π2 , π2 divided into Nb grids to discretely represent that channel. Based on traditional MIMO channel response matrix, the angle domain response matrix are d

−j2π λ A˜ I = e



 β×θ˜i 

θ˜i = [0, 1, . . . , Nt − 1]

(5)

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−j2π λ A˜ R = e



 β×θ˜r 

θ˜r = [0, 1, ..., Nr − 1]

(6)

where β = [−Nb /2, −Nb /2 + 1, ..., Nb /2 − 1], and −j2π dλ is the unit phase difference. As shown in Fig. 2, the channels in the angle domain indicate the presence of peaks, each peak representing an NLOS channel established by the IRS, and the locations of the peaks include θi , θs . HA can be considered as sparse [15]. Therefore, it is possible to estimate HA as to further estimate and calculate the included positioning parameters such as angle, distance. In the positioning system of this paper, firstly, L random beams scan and detect the channel environment, and estimate the channel matrix according to the received signals. The received signal expression in the angle domain is yr = [(A˜ R ωs)T ⊗ A˜ I ]vec(HA ) + z

(7)

where ⊗ denoting the Kronecker product, vec represents the vectorization of a matrix. Thus, the parameter estimation problem in this paper can be transformed into the signal recovery problem in compressed sensing theory, and the location information contained in the channel matrix can be obtained by using the reconstruction algorithm. Define the sensing matrix = (A˜ R ωs)T ⊗ A˜ I , sparse channel vector hA = vec(HA ) Thus, a typical signal recovery problem yr = hA + z in compressed sensing theory is obtained. 3.2 Joint Optimization Positioning Method Based on the traditional Orthogonal Matching Pursuit (OMP) algorithm, the UAOP method consists of four steps: rough localization parameter estimation, joint IRS phase optimization, quadratic exact estimation, and position solving. For the algorithm of location parameter estimation, the support set is also orthogonalized, so that the whole iterative process is completely in the orthogonal domain, and finally calculated hA by QR decomposition. The method avoids the calculation error of large-scale sparse matrix inversion in the least square method in the traditional OMP algorithm. In the IRS positioning system of this paper, BS transmits OFDM signal containing N subcarriers. The input to the algorithm includes the sensing matrix and the serialized received signal yr . Initialize the iteration counter  = 1. For each subcarrier n = 1, 2, ..., N , initialize the orthogonal coefficient vector χn = 0. Support set ϒ is an empty set, the residual vector rn,−1 = 0, rn,0 = yr . εn,i is the i-th column of . Firstly, the residual of each signal is correlated with each column of the observation matrix, and the index value of the most correlated column is taken n N −1 r  n,-1 , εn,i  n = argmax (8) εn,i 2 n=0

The support set is then updated to include the most relevant array of sensing matrices ϒ = [ϒεn,n ]. And the added column vector of the support set is orthogonalized with the original support set as follows σn, = εn,n −

-1  εn,n , σn,t  t=0

σn,t 22

σn,t

(9)

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Finally, the residuals are updated in the orthogonal domain.

χn =

rn,−1 , σn, 

(10)

σn, 22

rn, = rn,−1 − χ n σn,

(11)

The above steps (8)–(11) are iterated until the residual term is lower than the threshold or reaches the maximum number of iterations, i.e., the number of columns of the sensing matrix. And the index coordinates of the peak value in the channel angle domain repren sentation are obtained through the support set index obtained by iteration ni, =  Nb , ns, = mod (n − 1, Nb ) + 1. so that the estimated values of the corresponding incident angle and observation angle are obtained  λ ni, − Nb /2 (12) θ i = arcsin d Nb  λ ns, − Nb /2 (13) θ s = arcsin d Nb



For the estimation of path distance, the original columnvector set corresponding to the  support set is obtained by QR decomposition. P = εn,n1 , ..., εn,nP And the set of column vectors after orthogonalization n = [σn,1 , ..., σn,P ] Represented as P =

n Rn Therefore, the upper triangular matrix can be obtained Rn , then yr = n Rn hA , and known yr = n χ n , so hA = R−1 n χ n The path length relayed by the IRS is calculated according to the mean value of the phase difference of each adjacent subcarrier r



r=





    1 N NTs c × ϕ hA [n] − ϕ hA [n − 1] n=2 2π N −1



(14)

Ts is the signal sampling interval, i.e. 1/B, ϕ represents the phase of complex number. Adjusting the phase shift configuration matrix  of the IRS according to the positioning parameters after the first rough positioning parameter estimation is finished, thus passing the beam through the reflection angle θr adjust to observation angle θs . Through Snell’s law, the relationship between the incident angle and the reflection angle of the beam and the phase shift of the IRS reflection element is derived as follows. k(sin(θi ) − sin(θr )) =

d φ(x) dx

(15)

where k is a constant and x is the distance of the IRS cell from the IRS center. The phase setting of the IRS reflection unit can be calculated. After the above initial parameter estimation, the estimated θ s can be used to reconfigure IRSs and then estimate that positioning parameter again. Because the approximate position of the index in the channel matrix is known, as shown in Fig. 2, the sensing matrix array corresponding to the index in the red frame range is calculated for the second positioning, which greatly reduces the amount of calculation, and can improve the resolution of channel representation.

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Finally, according to the geometric relationship of the positioning system, each parameter can be expressed as the following relationship l2 l1 + =r cosθi cosθs

(16)

Therefore, two NLOS paths generated by two IRSs are used to solve two unknowns. l1 And l2 . The final MT position coordinates can be expressed as 1 P (17) [l 1 tanθ i,p − l 2 cotθ s,p ] x= p=1 P















y = l1 − l2

(18)

4 Analysis of Simulation Results

Fig. 2. Channel representation in the angular domain

Fig. 3. Path loss of cascaded channels reflected by IRS

In order to verify the feasibility of the proposed method and the improvement of positioning performance, we compare the mean square error (RMSE) of channel estimation between the proposed method and the traditional OMP method. Unless otherwise specified, the main parameter values in the simulation are: carrier frequency fc = 3GHz, channel bandwidth B = 10MHz, light speed C = 299792458 m/s, number of transmitting and receiving antennas Nt =Nr = 32, number of subcarriers N = 10.The positions of BS and MT are respectively set as posBS = [0, 0] and posMT = [40, −10]. The location of the IRS is [20, 20]. The gain of the antenna system is GT =GR =10dB. The dimensions of the IRS are a = b = 10λ, the number of transmitted beams L = 40, the system noise is 0 dBm.100 Monte-Carlo experiments were performed separately at each condition.

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Fig. 4. RMSE of incident angle, observed angle and path distance estimates

Fig. 5. Positioning accuracy and solution success rate

Fig. 6. Effect of parameters B, L, N t and N b on positioning accuracy and success rate

Fig. 7. Comparison of calculation time before and after optimization of the proposed method

Firstly, we analyze the path loss. According to the propagation law of electromagnetic waves, after being reflected by the IRS, when the reflection angle is the same as the MT observation angle, the loss is minimal [17]. As shown in Fig. 3, as the size of the IRS increases, the overall gain increases, but the width of the beam becomes narrower and the number becomes larger. Then, the parameter estimation results as shown in Fig. 4, the RMSE of the estimated values is greatly reduced with the proposed method. However, limited by the resolution of discrete sparse domain, the error of angle estimation cannot be reduced after converging

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to a minimum value with the increase of PT . Under the condition of low PT , the advantage of proposed method is more obvious. The positioning solution is carried out under the condition of different PT , and the threshold for the successful solution is 10 m. The positioning error and the success rate of solution are shown in Fig. 5. Due to the configuration optimization of IRS in UAOP method, the path loss of the whole system is reduced, so that the received signal can meet the requirements of accurate positioning estimation. When the PT is lower than −5 dBW, the traditional OMP channel estimation method cannot be successfully solved even once in 100 Monte Carlo experiments, while the UAOP method still has a certain success rate and maintains a high positioning accuracy. It is worth noting that the positioning error decreases significantly when PT is −8 dBW, but the error increases again when the PT is −7 dBW and −6 dBW. After analysis, due to the increase of the success rate of calculation, more data with large errors but not exceeding the threshold are counted. According to the previous analysis of the success rate of solution, the influence of other parameters is analyzed under the condition that PT is set to -5dBW, so that the influence of other parameters will not be covered up, the success rate have not reached the limit due to the high PT . As shown in Fig. 6, when the bandwidth is lower than 6 MHz, the success rate is very low due to the large parameter estimation error. When the bandwidth is between 10 and 18 MHz, the positioning error is low and the success rate of positioning solution is at a high level. When the bandwidth is further increased to more than 18 MHz, the positioning performance suddenly and greatly degrades. Because increasing the bandwidth shorten the sampling interval Ts and it is less than the propagation time of the electromagnetic wave along the positioning path, the distance estimation cannot be carried out through the subcarrier phase difference. The influence of the number of transmit beams is shown in Fig. 6. When L is less than 10, the channel information is not sufficiently obtained, so the success rate is low. With the increase of L, the success rate of solution is gradually close to 100%, and the positioning error is always kept within 1 m, but the dimension of the sensing matrix is larger with larger L, so in practical applications, it is necessary to consider the balance between computing resources and positioning accuracy. Figure 6 shows the effect of the number of BS antennas. In order to achieve the ideal positioning accuracy, the number of transmitting and receiving antennas of the MIMO positioning system in this paper should be set at more than 20. The angle domain resolution Nb is analyzed statistically in Fig. 6, it is obvious that the higher the resolution has higher positioning accuracy and success rate. However, as mentioned in the analysis of L, the improvement of Nb will also lead to a large consumption of computing resources. However, the proposed method reduces the range of the sensing matrix according to the roughly estimated parameter position in the secondary estimation, which greatly reduces the amount of calculation, as shown in Fig. 7. The proposed optimization positioning method reduces the calculation time by an order of magnitude.

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5 Conclusion In this paper, we propose an IRS-aided NLOS location system based unknown anchor optimization location (UAOP) method and compare the proposed method with the conventional OMP channel estimation method. The results show that the proposed method can greatly improve the channel detection ability, thus greatly improve the positioning results, and can still maintain its performance in high noise environment. Therefore, the application range is greatly broadened. The results show that the bandwidth and the number of transmitted beams should be in a reasonable range, so that the location error can be kept at a stable and low level, and the success rate of location solution is very high, while the resolution expressed in the angle domain, that is, the beam dictionary, has a great influence on the location results, and in order to solve the problem of excessive calculation caused by improving the resolution. The range of the beam dictionary is reduced in the second accurate estimation, and the calculation amount is greatly reduced. Acknowledgement. This work is financially supported by National Key R&D Program of China (No. 2022YFB2601801) and by National Key R&D Program of China (No. 2022YFB3904502).

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11. Lu, R., Chen, W., Dong, D., et al.: Multipath mitigation in GNSS precise point positioning based on trend-surface analysis and multipath hemispherical map [J]. GPS Solut. 25(3), 119 (2021) 12. Fang, L., Wan, H.R., Yi, J.X., et al.: Modulation compensation of extended phase canceling batch clutter suppression algorithm for external radiation source radar [J]. J. Electron. Inf. 36(1), 209–214 (2014) 13. Cui, B.B., Chen, X.Y.: A GPS multipath effect suppression method based on an improved EMD algorithm[J]. Chin. J. Inert. Technol. 22(3), 346–351 (2014) 14. Heath, R.W., Gonzalez-Prelcic, N., Rangan, S., Roh, W., Sayeed, A.M.: An overview of signal processing techniques for millimeter wave MIMO systems. IEEE J. Sel. Top. Signal Process. 10(3), 436–453 (2016) 15. Johnson, D.H., Dudgeon, D.E.: Prentice-hall signal processing series: Array signal processing [M]. PTR Prentice Hall, Upper Saddle River, NJ (1993) 16. Duarte, M., Sarvotham, S., Baron, D., et al.: Distributed compressed sensing of jointly sparse signals[C]. In: Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers. [S.l.], IEEE (2005) 17. Ozdogan, O., Bjornson, E., Larsson, E.G.: Intelligent reflecting surfaces. Phys. Propag. Pathloss Model. (2019)

UWB/INS Integrated Positioning Method Considering Time Latency and NLOS Errors Xiaoji Dai1 , Tianhe Xu2 , Min Li2(B) , Tianyou Jiang2 , and Linghan Yao2 1 Zhengzhou Economy and Trade School, Zhengzhou 450000, China 2 School of Space Sciences and Physics, Shandong University, Weihai 264209, China

[email protected]

Abstract. Ultra-wideband (UWB) positioning technology has currently become a research hotspot for local small-scale positioning and navigation due to its advantages of high accuracy and wide bandwidth. The UWB positioning accuracy based on time of arrival (TOA) can theoretically reach centimeter level accuracy. However, due to the susceptibility of UWB signals to system time latency and non line of sight (NLOS) errors during propagation, it is difficult to achieve the expected positioning accuracy. Based on the method of broadcasting clock differencing approach in GNSS positioning, a UWB time synchronization station is established. Time differencing observation information is used to calibrate the time latency of the base station relative to the main base station. The unknown parameters include tag position information and equivalent time delay latency. The UWB/INS tightly coupled model combines Kalman filtering with ranging innovation vector to reduce the impact of UWB NLOS errors on positioning accuracy by multi-factor adaptive adjustment of the weight of UWB ranging information containing NLOS errors. The impact of time latency is also considered. The experimental results show that the static UWB positioning plane accuracy can reach centimeter level by considering the time latency. The tightly coupled UWB/INS positioning, considering both time latency and NLOS errors, can effectively reduce the influence of system time latency and NLOS errors on positioning accuracy. The positioning accuracy and stability are further improved compared with the conventional UWB/INS combination. Keywords: UWB · INS · Time latency · NLOS error · Multi-factor adaptive adjustment · Tightly coupled

1 Introduction Recently, the use of UWB sensors for indoor localization has gained attention as an alternative to Global Navigation Satellite System (GNSS) in indoor complex environment. However, UWB-based positioning requires pre-installed UWB anchor points with known precise position information as reference stations. Additionally, UWB distance measurement can be challenging in NLOS environments where obstacles or walls obstruct the signal path, leading to large errors. Two broad categories of NLOS error handling methods including data signal feature identification methods and adaptive filtering methods are developed. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 305–319, 2024. https://doi.org/10.1007/978-981-99-6928-9_27

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In the data signal feature identification method, a support vector data description learner with outliers is trained to recognize NLOS signals using the classical imbalance characteristic, resulting in better performance than traditional machine learning method [1]. Random forest models are used to discriminate NLOS signals, and TOA observations containing NLOS are equated to the average of TOA observations and computed values, resulting in a non-visual recognition rate of 98.6% and a 52–55% improvement in localization accuracy compared to the least square localization method [2]. A fuzzy clustering recognition method based on the principal component analysis model and fuzzy C-mean algorithm achieves a 92% recognition rate of NLOS signals [3]. Adaptive filtering methods combining un-differenced estimation theory with Kalman filter have improved navigation accuracy from 2.5 m to within 0.09 m [4]. A robust unscented Kalman filter with generalized likelihood estimation is proposed to attenuate the effects of measurement outliers and system perturbations on state estimation, resulting in reduced error peaks in coordinate estimation and faster convergence than conventional unscented Kalman filter [5]. Systematic time latency in UWB system is another factor affecting positioning accuracy. The symmetrical double-sided clock synchronization algorithm is proposed to address low time synchronization accuracy and inconsistent message processing delay of UWB sensors, resulting in a synchronization accuracy of 1.2 ns [6]. To address systematic errors in UWB positioning algorithms, phase center offset (PCO) calibration and multi-point time latency determination (MTLD) methods of UWB antenna are proposed, resulting in a 10 and 44% improvement, respectively [7]. However, the UWB sensor localization has limitations in that it cannot obtain attitude information of the target, and multi-sensor fusion is necessary to solve the UWB NLOS problem. For the first time, UWB was combined with an inertial navigation system (INS) to determine the attitude of the combined system [8]. The combination of UWB under the IEEE802.15.4a standard with 6-degree-of-freedom inertial measurement elements for indoor positioning, along with data transmission using the communication function of UWB, yielded higher positioning accuracy than that of the inertial navigation system alone [9]. Researches have focused on identifying NLOS errors, weakening the effect of NLOS errors on localization, and studying INS-assisted localization when UWB ranging information is not available [10, 11]. Based on the dynamical model of quaternion and position, and the UWB observation equations, the mathematical expressions of the dynamic errors-in-variables model of UWB/INS are derived. The computational complexity of the generalized overall Kalman filter method and strategies to improve the computational efficiency of the unscented overall Kalman filter method are also provided [12]. To overcome these problems, this paper proposes a UWB/INS tightly coupled localization method that takes into account the time latency and NLOS error. This method tightly integrates UWB sensors and inertial measurement unit (IMU) sensors, establishes a tightly coupled UWB/INS model that takes into account the time latency and NLOS error, compensates the UWB ranging information using time-synchronized station time differencing observations, uses the UWB tag equivalent time latency as the parameter to be solved, and combines Kalman filtering with the ranging new information vector to adjust the UWB range with NLOS error by multi-factor adaptive adjustment of the

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weight of UWB ranging information containing NLOS errors. This improves the position estimation performance and provides target attitude information.

2 UWB Observation Equations Taking into Account the Time Latency The basic observation of the UWB sensor based on Time of Arrival (TOA) is the distance between the tag and the base station, which is calculated by recording the time of pulse signal propagation from the tag to the base station. However, when performing tag-side positioning, the distance observation is affected by various errors related to the base station and the tag, as well as those related to pulse signal propagation. In particular, the time latency between the base station and the tag can significantly affect positioning accuracy, and its error impact needs to be considered. The UWB TOA observation equation can be modeled as follows: i = r i + cδtr + cδtb + ε˜ ρi ρUWB

(1)

i where ρUWB is the observed distance between base station i and the tag; r i is the geometric distance between base station i and the tag; cδtr is the time latency of the tag; cδtb is the time latency of base station i; ε˜ ρi is other noise. Similarly, using base station 0 as the reference master base station, the UWB time difference of arrival (TDOA) observation equation can be modeled as 0i = r 0i + ctb0i + ε˜ ρ0i ρUWB

(2)

0i where ρUWB is the time difference observation between base station i and primary base station 0; r 0i is the time difference geometric distance between base station i and primary base station 0; ctb0i is the time latency of base station i with respect to primary base station 0, ctb0i = cδtb − cδtb0 , cδtb0 is the time latency of primary base station 0; ε˜ ρ0i is other noise. Since the time latency ctb0i of base station i with respect to the primary base station 0 can be calibrated in advance or broadcasted in real time by establishing a time synchronization station, the time latency ctb0i is taken as a known value in the positioning process and substituted into the equation, the UWB TOA observation equation is i − ctb0i = r i + cδt r + ε˜ ρi ρUWB

(3)

where cδt r is the tag equivalent time latency, cδt r = cδtr + cδtb0 . Equation (3) proposes a method for utilizing GNSS navigation and positioning by broadcasting the clock difference. This method involves establishing a UWB time synchronization station and using a certain clock-stabilized base station of UWB as the main base station. The time difference observation between the base station and the main base station is then used to calibrate in advance or to broadcast the time latency of the base station relative to the main base station in real-time. The solution result obtained through this method contains tag position information and equivalent time latency. To model the time latency of the UWB system, the delay deviation on positioning accuracy of the UWB system can be fully weakened. This modeling approach is effective in reducing the impact of delay deviation on the accuracy of the UWB system’s positioning.

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3 Tightly Coupled UWB/INS Positioning Considering the Time Latency and NLOS Errors NLOS refers to the situation where the direct signal propagation path between the signal transmitter and receiver is blocked, and the signal reaches the receiver through a reflected, diffracted path or by penetrating an obstacle. In challenging environments, NLOS propagation leads to longer signal flight times and more severe energy attenuation than direct signals, resulting in NLOS distance errors for both arrival signal strength and arrival time-based distance estimation methods. If observations with NLOS errors are directly used for UWB indoor positioning, the accuracy of the positioning will be greatly affected, and fusing IMU information is an ideal solution. In a previous study [13], IMU acceleration information was used as the system input in a tightly coupled UWB/INS model. The constant acceleration model was used as the system state of motion equation for filtering. However, this method cannot provide the attitude information of the target, and the angular velocity and acceleration measurements of low-cost commercial IMUs are often noisy due to factors such as temperature, operation duration, and mechanical vibration. Integrating acceleration directly from the IMU may lead to worse results than the constant velocity or constant acceleration assumptions. Therefore, this study proposes a tightly coupled UWB/INS method that takes into account time latency. The system state variables are defined as position error, velocity error, attitude error, gyroscope and accelerometer zero bias error, and tag equivalent time latency, with a dimension of 16 × 1. This approach improves the accuracy of positioning and overcomes the limitations of the previous method. T  δx(t) = (δpn )T (δvn )T φ T bTg bTa cδt r

(4)

where δpn is the position error in n-system, dimension 3 × 1; δvn is the velocity error in n-system, dimension 3 × 1; φ is the attitude error, dimension 3 × 1; bg is the gyroscope zero bias error, dimension 3 × 1; ba is the accelerometer zero bias error, dimension 3 × 1; cδt r is the tag equivalent time latency. Using the error vector as the system state variable is beneficial to estimate the INS solution error and the IMU sensor zero bias error, to correct the INS solution result, and to compensate the IMU zero bias. The error differential equation of the system state variable taking into account the time latency is. δ x˙ (t) = F(t)δx(t) + G(t)w(t)

(5)

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where F is the system matrix of error differential equations, as shown in Eq. (6), the dimension is 16 × 16; w is the process noise of the corresponding state, as shown in Eq. (7), where wv denotes the white noise of accelerometer measurement, wφ denotes the white noise of gyroscope measurement, wgb and wab denotes the zero bias noise of accelerometer and gyroscope, respectively; G is the process noise transfer matrix, as shown in Eq. (8). ⎡ ⎤ 0 I 3×3  0   0 0 0 ⎢ ⎥ C nb f b × 0 C nb 0 ⎥ ⎢0 0 ⎢ ⎥ ⎢0 0 0 −C nb 0 0⎥ ⎢ ⎥ (6) F=⎢ −1 0 0⎥ 0 ⎢0 0 ⎥ Tgb I 3×3 ⎢ ⎥ −1 ⎣0 0 ⎦ 0 0 T I3×3 0 ab

0 0

0

0



w = 01×3 wTv wTφ wTgb wTab 0 ⎡

0 0 ⎢ 0 Cn ⎢ b ⎢ ⎢0 0 G=⎢ ⎢0 0 ⎢ ⎣0 0 0 0

0 0 C nb 0 0 0

0 T

0

⎤ 0 0⎥ ⎥ ⎥ 0⎥ ⎥ 0⎥ I 3×3 ⎥ 0 I 3×3 0 ⎦ 0 0 0 0 0 0

0 0 0 0

(7)

(8)

To facilitate the use of the discrete-time Kalman filter, the error differential equation for the system state variables is discretized and the discrete-time system state equation is constructed as follows. δxk = Φ k δxk−1 +wk−1

(9)

where Φ k is the discrete-time system state transfer matrix, which can be simplified to Φ k ≈ I +F(tk−1 )t, when F does not vary drastically in t, t is the discrete time interval; wk−1 is the discretized time process noise. Qk is the discrete-time state noise covariance array, which can be simplified to a trapezoidal integral as Qk ≈

 1 Φ k G(tk−1 )q(tk−1 )GT (tk−1 )Φ Tk + G(tk )q(tk )GT (tk ) t 2

(10)

where q is the IMU sensor power spectral density. From the INS navigation results and the pole arm measurements, the UWB tag antenna center position is deduced as p = pnI + C nb l b − vnI δt

(11)

where pnI is the INS position; l b is the pole arm measurement; vnI δt is the position error caused by the UWB and IMU time asynchrony.

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The approximate distance between the center position of the UWB tag antenna and the UWB base station position deduced from the INS navigation result and the pole arm measurement can be expressed as r i = (pe − pei )2 + (pn − pni )2 + (pu − pui )2 (12) where pe , pn and pu are the E, N, and U directions of the UWB tag antenna center positions derived from the INS navigation results; pei , pni and pui are the E, N, and U directions of base station i, respectively. The UWB/INS tightly coupled measurement equation that takes into account the time latency is zk = H k δxk + V k

(13)

i −ctb0i ); H k is the measurement where zk is the measurement information, zk = r i −(ρUWB matrix, as shown in Eq. (14); V k is the measurement noise, which conforms to the Gaussian distribution; Rk is the measurement noise covariance, Rk = σr2 I , represents the measurement noise between the UWB sensor tag and the base station.   Hk = Jk 0 0 0 0 1 ,   (14) i i i e pn −pn pu −pu J k = pe −p i i i r

r

r

In challenging environments, NLOS propagation can result in longer signal flight times and more severe energy attenuation than direct signals, leading to NLOS distance errors for both arrival signal strength and arrival time-based distance estimation methods. While fusing IMU information can help weaken the effect of NLOS errors on localization results, there is a lack of effective methods to accurately estimate the magnitude of NLOS distance error. Moreover, simply adding IMU information with a constant covariance may become less useful as the NLOS error duration increases, eventually pulling the INS solution out of alignment. To address these challenges, this paper proposes a multi-factor adaptive filtering approach for UWB/INS positioning based on a tightly coupled UWB/INS model that accounts for time latency. This approach adaptively adjusts the weight of each observation based on its reliability to avoid the impact of reliable observations losing their usefulness due to larger errors. Constructed inspection information εi   −1 εi = εi Qvv εi (15) i,i

where εi is the new interest vector of the tightly coupled system; Qvv is the covariance matrix of the new interest vector of the system, Qvv = H k P k H Tk + Rk . Construct the equivalence weight factor αi ⎧ ⎪ 1, |εi |c1 ⎪ ⎪ ⎨ |εi | , c |ε |c 1 i 2 c1 αi = (16) ⎪ | |ε i > c2 ⎪ ⎪ ∞, ⎩

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where c1, c2 are the multi-factor array test thresholds, which are obtained from the law of taking the test information in the line-of-sight environment. α k = diag[α1 α2 · · · αi ], α k is the equivalent multi-factor array of observations at time k. Then the system measurement noise equivalent covariance matrix is Rk = α k Rk

(17)

where Rk is the system measurement noise equivalent covariance matrix at time k. The UWB/INS tightly coupled positioning algorithm, which considers the time latency and NLOS error, combines the advantages of INS and UWB. INS can provide high accuracy position information in a short period of time and overcome the limitation of the single UWB sensor not being able to obtain the target attitude information. On the other hand, UWB can suppress INS divergence and consider the influence of time latency and NLOS error on the position estimation, making it more robust. The overall flow of the UWB/INS tightly coupled positioning system that considers the time latency and NLOS error is shown in Fig. 1.

Fig. 1. UWB/INS tightly coupled positioning process

4 Experiments and Results Analysis 4.1 Experimental Description In this study, static and dynamic experiments were designed to evaluate the positioning accuracy of an UWB. The experimental scene and platform are shown in the Fig. 2. The static test site was located in the connecting corridor of the Wen-tian Building in Shandong University in Weihai, with a test site of approximately 100 m2 . Three UWB base stations and one time-synchronous station were deployed for the experiment. The dynamic test site was situated on the soccer field of Shandong University, covering an

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area of approximately 1600 m2 . Four UWB base stations and one time synchronization station was deployed for the dynamic experiment. The power spectral density of UWB sensors was in the range of −26 to −13 dB/MHz, and the tag sampling frequency was set to 50 Hz. In the static experiment, the reference true value of the test point was measured by the ZTS-420 total station, which provided a reference of 2 mm accuracy. In the dynamic experiment, the reference true value was measured by the GNSS RTK solution, which provided a reference of centimeter-level accuracy.

Fig. 2. Experimental scene and platform

4.2 Static Experiment Static test were conducted to evaluate the static positioning accuracy of UWB, taking into account time latency. In Fig. 2(a), eight static test points were set up at the test site. The conventional UWB EKF algorithm was compared with the UWB EKF algorithm that considers time latency from the perspective of positioning accuracy. Table 1 shows the root mean square error (RMSE) of E and N direction coordinates of the eight static test points. The RMSE of the conventional UWB EKF algorithm for planar localization is 0.187 m, while the RMSE of the UWB EKF algorithm that accounts for time-delay bias is 0.073 m. The experimental results demonstrate that the average error of the UWB EKF algorithm with delay bias is 60.1% lower than that of the conventional UWB EKF algorithm. Furthermore, Fig. 3 shows the cumulative distribution function curves of the plane position of the static test points. The 50, 90%, and maximum error of the plane positioning results of the conventional UWB EKF algorithm are 0.184 m, 0.209 m, and 0.346 m, respectively. The results indicate that the UWB EKF algorithm that considers time latency of the UWB sensor system can largely solve the loss of positioning accuracy caused by the system’s time latency. The planar positioning accuracy of the UWB EKF algorithm can reach the centimeter level under good observation conditions.

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Table 1. RMSE of static test point Algorithm

Point 1

Point 2

Point 3

Point 4

Point 5 Point 6

Conventional E-RMSE(m) 0.246 0.372 0.341 0.265 0.202 EKF N-RMSE(m) 0.053 0.053 0.075 0.076 0.115 EKF (Consider latency)

E-RMSE(m)

0.121 0.064 0.141 0.090 0.151

N-RMSE(m) 0.032 0.031 0.050 0.021 0.0339

Point 7

Point 8

0.169 0.157 0.113 0.092 0.078 0.051 0.107 0.074 0.074 0.024 0.027 0.037

Fig. 3. Static test plane error CDF curve

4.3 Dynamic Experiments The experimental setup was installed on a test cart and included four UWB base stations, one UWB time synchronization station, and one UWB tag equipped with a UWB sensor from Nooploop company, providing range accuracy up to 10 cm. The system also utilized a PwrPak7-E2 receiver, consisting of a NovAtel OEM7700 receiver and an Epson G370N Micro Electro Mechanical Systems (MEMS) IMU. The experimental platform is illustrated in Fig. 2(c), with the UWB tag positioned on the same vertical axis as GNSS antenna. The performance parameters of the inertial sensors are listed in Table 2. Table 2. Epson G370N MEMS IMU sensor performance parameters Input range

Bias stability

Gyroscope

±450°/s

0.8°/h

Accelerometer

±10 g

0.01 mg

Random walk √ 0.06°/ hr √ 0.025 m/s hr

Maximum output 200 Hz 200 Hz

The dynamic test was conducted to evaluate the dynamic positioning accuracy of the UWB/INS tightly coupled algorithm and compare it with the conventional UWB/INS

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combination, considering the time latency and NLOS error. The trajectory of the dynamic test, as shown in Fig. 2(b), was defined based on the GNSS RTK solution results, which served as the reference true value. During the test, the experimental device mounted on the test cart was pushed along the predefined trajectory at a constant speed, and the GNSS receiver observation data, UWB sensor TOA data, and IMU sensor data were recorded. The number of visible satellites in the GNSS was reflected in Fig. 4(a). The GNSS receivers provided high-quality results due to their wide field of view, allowing each ephemeris element to track signals from more than four satellites. This feature helped to provide accurate reference positioning results during the test. The GNSS RTK positioning results, which were used as the true reference, had standard deviations of 0.025 m, 0.019 m, and 0.019 m for the E, N and U directions, respectively, as shown in Fig. 4(b). These values reflected the observation accuracy of the coordinate 3D components. To analyze the quality of GNSS data as a whole, the GNSS accuracy factor plot was presented in Fig. 4(c). The root mean square (RMS) of GDOP, PDOP, HDOP, and VDOP were 1.635, 1.413, 0.761, and 1.184, respectively, which were suitable for most applications except for the most sensitive ones.

Fig. 4. The analysis of GNSS data quality

The dynamic test trajectory is divided into two parts. Track I is the positioning test trajectory in the pure LOS environment, and track II is the positioning test trajectory in the NLOS error challenge environment. The trajectory results of Track I in the pure LOS environment are shown in Fig. 5. The combined UWB/INS tight localization method takes into account the time latency of the UWB sensor system, and as shown in the trajectory results, the localization trajectory is closer to the reference trajectory. Additionally, the localization trajectory is smoother than that of UWB alone. The RMSE values for the east, north, and up directions of the UWB/INS tightly coupled system were found to be 0.093 m, 0.062 m, and 0.898 m, respectively. These values are 38.8, 35.4, and 53.5% higher than those of the conventional UWB/INS tightly coupled system. The main reason for this difference in performance is attributed to the fact that the UWB sensor in the dynamic test trajectory is limited to LOS observations.

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Fig. 5. Positioning trajectory of trajectory I in pure LOS environment

As a result, the positioning accuracy of the UWB/INS tightly coupled system is primarily dependent on the UWB sensor’s positioning accuracy (Table 3). Table 3. RMSE of E, N and U for different positioning methods of trajectory I Algorithm

E-RMSE (m)

N-RMSE (m)

U-RMSE (m)

UWB EKF

0.155

0.097

1.933

UWB EKF (consider latency)

0.097

0.070

1.034

UWB/INS TC

0.152

0.096

1.931

UWB/INS TC (consider latency)

0.093

0.062

0.898

The cumulative distribution function curve of the plane position for trajectory one is given in Fig. 6. From the experimental results of trajectory I, the 50, 90% and maximum errors of the conventional UWB/INS tightly coupled are 0.155 m, 0.283 m and 0.781 m, respectively, while the 50, 90% and maximum errors of the UWB/INS tightly coupled algorithm taking into account the time latency are 0.089 m, 0.175 m and 0.645 m, respectively. The UWB/INS tightly coupled algorithm can also largely solve the loss of positioning accuracy caused by the time latency of the system, and its plane positioning accuracy can be improved by 37.8% compared with the conventional UWB/INS tightly coupled, and it can provide attitude information, as shown in Fig. 7, to make up for the shortage of single UWB sensor positioning. Apart from providing attitude information, another significant advantage of the UWB/INS tightly coupled algorithm is its ability to offer reliable position estimation even when the UWB positioning estimation error is substantial, or the UWB positioning solution is temporarily lost. In dynamic test trajectory II, NLOS errors in some ephemeris elements occur due to pedestrian and obstacle occlusions, which can last for varying durations. The results of the dynamic test trajectory II with NLOS errors are presented in Fig. 8. From the trajectory results, it is observed that the conventional UWB trajectory deviates from the reference trajectory due to NLOS errors caused by pedestrian and obstacle

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Fig. 6. CDF of trajectory I plane position

Fig. 7. Attitude of dynamic trajectory I

occlusions. However, for longer epochs of NLOS error-induced deviation of position estimation, the conventional UWB/INS tightly coupled algorithm is unable to adjust the weights between UWB sensors and IMU sensors adaptively, leading to scattered IMU position estimation. Thus, the maximum potential of the UWB/INS tightly coupled algorithm cannot be exploited. The UWB/INS tightly coupled algorithm with NLOS error is a multi-factor adaptive method that makes full use of UWB sensor ranging information and adaptively adjusts the weights between the UWB sensor and IMU sensor. Thus, the localization trajectory can be better corrected, whether it is a short NLOS error or a longer one. The UWB/INS tightly coupled algorithm that considers time latency and NLOS error is based on the above method to fully consider the influence of UWB system time latency on position estimation. Its positioning trajectory is more consistent with the reference true value trajectory. Table 4 shows the RMSEs of the E, N and U directions of the UWB/INS tightly coupled algorithm that takes into account time latency and NLOS error. Compared to the conventional UWB/INS tightly coupled system, the UWB/INS tightly coupled algorithm improves the accuracy by 49.0%, 84.7%, and 49.2%, respectively. Compared

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to the UWB/INS tightly coupled system that only takes into account NLOS error, the conventional UWB/INS tightly coupled algorithm enhances the accuracy by 33.8%, 49.1%, and 37.2%, respectively. These findings indicate that the conventional UWB/INS tightly coupled algorithm cannot adaptively adjust the weights between UWB sensors and IMU sensors to reach the optimal solution for longer NLOS error epochs.

Fig. 8. Positioning trajectory of dynamic test trajectory II with NLOS error

Table 4. RMSE of E, N and U for different positioning methods of trajectory II Algorithm

E-RMSE (m)

N-RMSE (m)

U-RMSE (m)

UWB EKF

0.197

0.385

2.139

UWB/INS TC

0.196

0.378

2.134

TC (consider NLOS)

0.151

0.114

1.726

TC (consider NLOS + latency)

0.100

0.058

1.084

The estimation errors of the east, north, and up directional positions of test trajectory II are presented in Fig. 9. The conventional UWB system exhibits an average error of 0.433 m and a maximum error of 8.45 m in plane positioning. In comparison, the conventional UWB/INS tightly coupled system shows an average error of 0.426 m and a maximum error of 4.88 m. On the other hand, the UWB/INS tightly coupled system that only accounts for NLOS errors achieves an average error of 0.189 m and a maximum error of 0.579 m, while the UWB/INS tightly coupled system that accounts for both time

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latency and NLOS errors achieves the same level of accuracy. These results indicate that the UWB/INS tightly coupled algorithm can effectively suppress both the time latency and NLOS errors of the UWB sensor system, resulting in significantly improved positioning accuracy and stability.

Fig. 9. Errors in the three-directional positions of E, N and U for test trajectory II

5 Conclusion This paper investigates the UWB/INS tightly coupled positioning method based on UWB and IMU sensors. The proposed algorithm takes into account the time latency and NLOS error to improve the positioning accuracy and stability of the system. The complementarity of INS and UWB TOA is fully utilized to consider the impact of system time latency and NLOS error on the positioning estimation accuracy. Experimental results demonstrate that the proposed UWB positioning method, taking into account the time latency, achieves a plane accuracy of 0.073 m in static tests, which is 60.1% better than that of the conventional UWB positioning method. In dynamic tests, the proposed method achieves a plane accuracy of 0.120 m, which is 34.6% better than that of the conventional UWB positioning method. The proposed UWB/INS tightly coupled positioning method, taking into account the time latency, achieves a plane accuracy of 0.112 m in pure LOS dynamic tests, which is 37.8% better than the conventional UWB/INS tightly coupled positioning method. Moreover, the proposed UWB/INS tightly coupled positioning method, which takes into account the time latency and NLOS error, achieves a plane accuracy of 0.124 m in dynamic tests with NLOS environment, which is 72.9% better than the conventional UWB/INS tightly coupled positioning method and 38.9% better than the UWB/INS

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tightly coupled positioning method that only takes into account the NLOS error. The UWB/INS tightly coupled positioning method that takes into account the time latency and NLOS error has better robustness and is more suitable for complex environments. Overall, the proposed UWB/INS tightly coupled positioning method shows improved accuracy and robustness compared to conventional UWB positioning methods and is well-suited for various practical applications. Acknowledgements. The study is funded by National Key Research and Development Program of China (2020YFB0505800 and 2020YFB0505804), the National Natural Science Foundation of China (Grant No. 42204015, and 42192534), and the Natural Science Foundation of Shandong Province (ZR2022QD094).

References 1. Zhimin, M., Luwen, Z., Shiwei, T., et al.: Class imbalance learning for identifying NLOS in UWB positioning [J]. J. Signal Process. 32(01), 8–13 (2016) 2. Zeng, L., Peng, C., Liu, H.: UWB indoor positioning algorithm based on NLOS identification [J]. J. Comput. Appl. 38(S1), 131–134+139 (2018) 3. Cui, H.: Non-line-of-sight obstacle recognition and error compensation for UWB Indoor positioning [D]. China Univ. Min. Technol. (2020) 4. Tao, L.I.U., Aigong, X.U., Xin, S.U.I.: UWB navigation and positioning based on adaptive robust KF-UKF [J]. Sci. Surv. Mapp. 42(12), 104–111 (2017) 5. Cheng, Y.A.N.G., Wenzhong, S.H.I., Wu, C.H.E.N.: Robust M-M unscented Kalman filtering for GPS/IMU navigation [J]. J. Geodesy 93(8), 1093–1104 (2019) 6. Ge, L.: Reserch on high precision indoor location and clock synchronization algorithms based on UWB [D]. Beijing Univ. Posts Telecommun. (2019) 7. Liu, T., Li, B., Yang, L.: Phase center offset calibration and multi-point time latency determination for UWB location [J]. IEEE Internet Things J. (2022) 8. Hol, J.D., Dijkstra, F., Luinge, H., et al.: Tightly coupled UWB/IMU pose estimation[C]//2009, pp. 688–692. In: IEEE International Conference on Ultra-Wideband. IEEE (2009) 9. Ye, T., Tedesco, S., Walsh, M., et al.: Fully-coupled hybrid IEEE 802.15. 4a UWB/IMU position estimation in indoor environments [C]. In: 25th IET Irish Signals and Systems Conference 2014 and 2014 China-Ireland International Conference on Information and Communications Technologies (ISSC 2014/CIICT 2014), pp. 53–58. IET (2014) 10. Qigao, F.A.N., Biwen, S.U.N., Yan, S.U.N., et al.: Data fusion for indoor mobile robot positioning based on tightly coupled INS/UWB [J]. J. Navig. 70(5), 1079–1097 (2017) 11. Aigong, X.U., Tao, L.I.U., Xin, S.U.I., et al.: Indoor positioning and attitude determination method based on UWB/INS tightly coupled [J]. J. Navig. Position. 5(2), 14–19 (2017) 12. Yu, H.: Research on the models and methods of ultra-wideband/GNSS/SINS integrated positioning [D]. China Univ. Min. Technol. (2020) 13. Li, J., Bi, Y., Li, K., et al.: Accurate 3D localization for MAV swarms by UWB and IMU fusion[C]. In: 2018 IEEE 14th International Conference on Control and Automation (ICCA), pp. 100–105. IEEE (2018)

A Gaussian Process Surrogate Model Assisted Multi-optimization Algorithm for Pulsar Period Searching Yusong Wang, Yidi Wang(B) , and Wei Zheng National University of Defense Technology, Changsha 410073, China [email protected]

Abstract. In recent years, X-ray pulsar-based navigation and timing have been widely concerned. Period searching is a key technique of pulsar navigation and pulsar timing. Since the pulsar signal is extremely weak, an accurate result of pulsar period requires a large amount of pulsar photons. However, the current method for pulsar period searching is of high computational cost when the amount of pulsar photons is very large. In this paper, we propose a Gaussian process (GP) surrogate model assisted multi-optimization algorithm to reduce the computational cost of period searching. In this algorithm, GP with low computational cost is used as a surrogate of the objective function of period searching. Besides, the proposed multi-optimization algorithm combines the advantages of Particle swarm optimization (PSO) and Cross-Entropy (CE) algorithm, which guarantees the accuracy of algorithm. The performance of the proposed algorithm is verified by the experiments with the simulation dada of PSR B1821-24 and Crab pulsar. Experiment results shows that the proposed method can efficiently reduce the computation cost while remains the accuracy of period searching. Besides, the proposed algorithm has good universality that can be used in different period searching method such as the epoch folding method and the MLE method. Keywords: Pulsar period search · Gaussian process · Particle swarm optimization · Cross-entropy algorithm

1 Introduction A pulsar is a kind of high-speed rotating neutron star. Most pulsars are about 1.4 solar mass and 20 km in diameter [1]. Since the rotating period of pulsars are extremely stable, pulsars could radiate photon signal with stable period [2]. Thus, the pulsars are called as natural beacons in the universe. Also, pulsars play important roles in studying for gravitational waves detecting, establishment of timing reference and autonomous navigation for space vehicle [3–5]. Since the X-ray radiation can be utilized by smallsized detectors, the space vehicle utilizes X-ray signal of pulsars in pulsar navigation [6]. In recent years, verification of pulsar navigation and pulsar timing have been realized based on the observation data of space observation stations [7, 8]. © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 320–330, 2024. https://doi.org/10.1007/978-981-99-6928-9_28

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In this paper, the period search of pulsar is relevant to pulsar navigation and pulsar timing on space vehicles. In pulsar timing task, the timing parameters are calculated by handling pulse TOAs (Time of Arrival) of pulse [9]. However, the pulsar signal is so weak that a space vehicle could only record a series of photon TOAs rather than a continuous pulsed signal. Thus, we must search the period of pulsar and recover the profile before calculating the pulse TOA. What’s more, period search is also necessary in pulsar navigation. The principle of pulsar navigation is as follows: the position of vehicle along the direction of pulsar could be calculated by handling the pulse TOA predicted at SSB (Solar System Barycenter) with that at vehicle, and the position of vehicle could be determined by observing three pulsars [10]. Since the vehicle performs orbital motions, the pulsar signal recorded by vehicle contains a time-varying Doppler frequency. In the autonomous navigation mission, the position and velocity of vehicle are unknown. Thus, the impact of introduced Doppler frequency could not be eliminated directly. In order to reduce the impact of the Doppler frequency, we should search the period of recorded pulsar signal. Currently, most pulsar period search method is based on the epoch folding method [11]. The pulse profile is recovered by epoch folding at a class of predicted periods, 2 and the period of pulse signal could be identified by the test statistics such as χ 2 , Zm 2 and Um [12–14]. However, in the period search method that based on epoch method, the test statistics should be calculated on each period in the predicted domain, which leads to a large computational cost. The computational cost is mainly manifested in two aspects. On the one hand, the predicted domain of period must be divided into many grids, and the number of calculated times of test statistic is equal to the number of grids. On the other hand, the accuracy of period is increase with the photon number, and the computational cost of calculating test statistic is also increase with photon number. Thus, in order to obtain pulsar signal period with high precision, the calculated time of test statistic and the computational cost of calculating test statistic are both large, which leads to a large computational cost of period search of pulsar signal. Besides, for pulsar timing task, since the exact position of the detector is known, a maximum likelihood estimator (MLE) method [15] can also be used to estimate the period of pulsar signal. However, the computational cost of this method is much higher than that of the epoch folding method. Therefore, this method is not widely used. In this paper, we reduce the computational cost of period search in two aspects. On the one hand, instead of the grid search, we use the optimization algorithm to obtain optimal period of pulsar signal. Swarm intelligence optimization is a promising optimization technique developed in recent decades [16, 17]. PSO is invented in 1995 with reference to birds’ social behavior [18]. Compare with other swarm optimization such as cuckoo search algorithm [19] and bat algorithm [20], PSO has better adaptability. CE method was motivated for solving the rare event simulation problem originally, and later the CE algorithm was successfully applied to solve the optimization problem [21]. In this paper, we derived a multi-optimization algorithm which combines the advantages of PSO and CE algorithm. On the other hand, since the computational cost of calculating objective function is very high, we intend to use a surrogate model with low computational cost to approximate the objective function in the period domain. Gaussian process (GP) could provide the estimated uncertainty of the function approximation [22]. Therefore, GP

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could facilitate the exploration of improvement in the surrogate model with highest probability. Besides, GP has been introduced to assisted PSO to improve the efficiency of the algorithm. In this paper, we introduce the GP to the CE/PSO multi-optimization algorithm and proposed a Gaussian process surrogate model assisted multi-optimization algorithm for pulsar period searching. This paper is structured as follows: the relevant woks including epoch folding method, MLE method, PSO, CE and GP are introduced in Sect. 2; Sect. 3 shows the proposed gaussian process surrogate model assisted multi-optimization algorithm; Experiments with simulation data of pulsars are performed to verify the validity and efficiency of the proposed algorithm in Sect. 4. Finally, Sect. 5 presents the conclusions.

2 Related works 2.1 Period Search Based on Epoch Folding Method Epoch folding method is a widely applied method which recovers the pulse profile from photons of pulsar signal. Assuming that the period of pulsar is P and the observation period of pulsar consists NP pulsar periods. Thus, the observation period Tobs has the form of Tobs ≈ NP ·P. Besides, the period of pulsar is split into Nb bins and each bin lasts Tb [23]. The epoch folding method folds NP pulsar periods into one period and counts the number of photons in each bin. Thus, we could obtain the magnitude of empirical profile. The magnitude in the ith bin i ∈ [1, Nb ], λ˜ (Ti ) is as the form of [23]. λ˜ (Ti ) =

Np 1  cj (Ti ) Np Tb

(1)

j=1

where Ti repsents the center of the ith bin and cj is the counted photons number of the ith bin in the jth period. After recovering the profile of pulsar signal, the period could be searched by test 2 and U 2 . In this paper, we use χ 2 as the test statistic. statistics such as χ 2 , Zm m 2.2 Period Search Based on the MLE The photon TOAs {tk }N k=1 obeys a non-homogeneous Poisson process with a periodic rate function λ(t). λ(t) is as the form of [24]. λ(t) = β + αh(φdet (t))

(2)

where α is average signal count rates, β represents the total background count rates. h(·) is defined as a normalized profile function and φdet (t) is the pulsar signal phase. φdet (t) can be modeled as [25]. φdet (t) = q + f (t − t0 ) where f is the frequency of the pulsar (f = 1/P), and q is the initial phase at t0 .

(3)

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The MLE method estimates q and f by solving the optimization problem [25]. (ˆq, fˆ ) = arg max q,f

N 

ln λ(tk ).

(4)

k=1

When q is known, f could be estimated by the MLE method. 2.3 Gaussian Process Gaussian process has good performance of approximation of the objective function and has been strict theoretical fundamentals [26]. The Gaussian process could be described by mean function and covariance function [27]. f (x) ∼ GP(m(x), k(x, x ))

(5)

where m(x) = E[f (x)] and k(x, x ) = E[(f (x) − m(x))(f (x ) − m(x ))]. Usually, we assume that m(x) = 0. Gaussian process represents a group of random variables, which has the property that any finite random variables satisfy a joint Gaussian distribution. Assume that we have a train set D = {x, y}, x = {x1 , x2 , ..., xn }, y = {y1 , y2 , ..., yn }, y = f (x) + ε , εis white Gaussian noise and ε N (0, ∂ 2 ). The priori probability distribution is as the form of p(f|x) = N (f|m, K) p(y|f) = N (0, ∂ 2 I)

(6)

where m = m(x) = {m(x1 ), m(x2 ), ..., m(xn )} and K = k(x, x ). The output f ∗ on test point x∗ follows the posterior probability distribution:  p(f∗ |x∗ ) = p(f∗ |x∗ , f)p(f|x, y)d f (7) = N (f∗ |μ∗ , Σ∗ ) Based on the GP, there is the following joint distribution:       m y Σ K∗ ∼N , f∗ K∗T K∗∗ m∗

(8)

where Σ = K + ∂ 2 I, m∗ = m(x∗ ) , K∗ = k(x, x∗ ) , K∗∗ = k(x∗ , x∗ ) and we have μ∗ = m∗ + K∗T Σ −1 (y − m) Σ∗ = K∗∗ − K∗T Σ −1 K∗

(9)

Usually, we assume that m(x) = 0, and we have μ∗ = K∗T Σ −1 y Σ∗ = K∗∗ − K∗T Σ −1 K∗

(10)

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In this paper the covariance function k(xi , xj ) is as the form of  (xi − xj )(xi − xj )T 2 k(xi , xj ) = σf exp − 2l 2

(11)

The hyper-parameters  = {σf2 , l} could be optimized by a log-likelihood function [27]. n 1 1 L = log p(yx, ) = − yT Σ −1 y − log detΣ − log 2π 2 2 2

(12)

3 Gaussian Process Surrogate Model Assisted Multi-optimization Algorithm In this section the proposal of Gaussian process surrogate model assisted multioptimization algorithm is shown. In order to reduce the calculation times of objective function, the GP is utilized to approximate the real objective function. Besides, we propose a multi-optimization algorithm which combines the advantages of PSO and CE algorithm. In this algorithm, the multi-optimization algorithm is used to determine the best promising solution with the aid of GP model. Once the new solution is conducted, the solution and the real function value of it are added to the database.

Fig. 1. The flow chart of Gaussian process surrogate model assisted multi-optimization algorithm.

As shown in Fig. 1, the Gaussian process surrogate model assisted multi-optimization algorithm works as follows:

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Step 1: Initializing database: Sampling N solutions and calculate the real function values of the solutions. Step 2: If the stopping criterion is met, stop the algorithm, otherwise go to next step. Step 3: Select the M best solutions with the best function values as the initial population of PSO and CE. Step 4: Apply the PSO and CE to generate M child solutions and go to next step. Step 5: Take the database to train the GP model. Evaluate the function value by GP model. Find the best promising solution of child solutions and go to Step 5. Step 6: Update the database by adding the estimated best solution and its real function value into database. In the Gaussian process surrogate model assisted multi-optimization algorithm, the estimated best promising solution is evaluated by GP model. Thus, the number of real function evaluations can be reduced greatly. Since the computational cost of evaluating GP model is much lower than evaluating real function, the proposed algorithm could reduce the computational cost greatly. Besides, the multi-optimization algorithm combines the advantages of CE and PSO, which could provide better performance than CE or PSO.

4 Experiments In this section, we use real data from NICER of Crab pulsar and simulation data of Crab pulsar and PSR B1821-24 to verify the performance of the proposed Gaussian process surrogate model assisted multi-optimization algorithm. The RMS (root mean square) error of frequency f from 1000 Monte Carlo trials is defined as the evaluation criterion of the accuracy of the proposed algorithm. The CPU time cost is defined as the evaluation criterion of computational cost. The computation environment comprises Intel Core [email protected] GHZ, Python 3.8 and memory of 8G. The PSR B1821-24 and Crab are chosen as the observe pulsar, the parameters of it are shown in Table 1 [28] and the profile is shown in Figs. 2 and 3.

Fig. 2. Template of PSR B1821-24.

At first, we use the simulation data of PSR B1821-24 to compare the performance of the proposed Gaussian process surrogate model assisted multi-optimization algorithm

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Fig. 3. Template of Crab pulsar.

Table 1. Simulation parameters of PSR B1821-24 and Crab [28, 29]. Name PSR B1821–24 Crab

Period/ms 3.05 33.4

α/ph·s-1 0.093 660

β/ph·s-1 0.22 13860.2

with GP-PSO and GP-CE algorithm. The difference between the proposed algorithm, GP-PSO and GP-CE is Step 4 in Sect. 3. For GP-PSO, the child solutions are generated by PSO. And in GP-CE, the child solutions are generated by CE algorithm. Assuming that the observation period of PSR B1821-24 is 3000s, the parameters of PSO are set as c1 = c2 = 2, w = 0.1. Choosing the objective function of MLE, Fig. 4 shows the estimated error of f for GP-CE, GP-PSO and the proposed Gaussian process surrogate model assisted multi-optimization algorithm. In the remainder of this paper, the proposed Gaussian process surrogate model assisted multi-optimization algorithm is referred as the GP-multi algorithm. As shown in Fig. 4, the convergence speed of GP-CE and GPmulti algorithm is faster than GP-PSO. And the accuracy of GP-PSO and GP-multi algorithm is higher than GP-CE. Figure 5 shows the estimated error of f for the three algorithms based on the objective function of epoch folding method. The convergence speed as well as the accuracy of GP-CE and GP-multi algorithm both better than that of PSO. Therefore, for different objective function based on epoch folding method and MLE method, GP-multi algorithm has better performance than GP-CE and GP-PSO. In the proposed GP-multi algorithm, the child solutions are generated by PSO and CE. Thus, the GP-multi algorithm combines the advantages of GP-CE and GP-PSO, and has the characteristics of high accuracy and fast convergence. Next, we process the simulation data of Crab pulsar. Based on the epoch folding method, we compare the accuracy and computational cos of GP-multi algorithm with PSO and CE algorithm. Figure 6 shows the RMS of f for GP-multi algorithm, PSO and CE algorithm. The RMS of f for the three algorithms are similar and gradually decrease. With the increase of the observation period. It means that the accuracy of the three algorithms is similar.

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Fig. 4. Convergence of the GP-multi algorithm for objective function of MLE method.

Fig. 5. Convergence of the GP-multi algorithm for objective function of the epoch folding method.

As shown in Fig. 7, the CPU time of the three algorithms is increase with the increase of the observation period of pulsar. However, the increase speed of CPU time of the GPmulti algorithm is much lower than other algorithms. When the observation period is 3000s, the computation cost of the proposed GP-multi algorithm is about 13.5% of the PSO and CE algorithm. It is because that the GP-multi algorithm utilizes GP model to evaluate the promising child solution instead of utilizing the real function. Since the computational cost of real function rapidly increase with the increase of observation period, the CPU time of PSO and CE also increase fast. Thus, the obviousness of the advantage of the GP-multi algorithm is increase with the increase of observation period. Assuming that the observation period of Crab pulsar is 500s. We use CE, PSO and GP-multi algorithm to estimate f of pulsar signal objective function of epoch folding method and MLE method respectively. As shown in Figs. 8 and 9, the estimated accuracy of MLE method is better than that of the epoch folding method with χ 2 as the test statistic. However, the computational cost of MLE method also higher. For MLE method and the epoch folding method, the estimated accuracy of the proposed GP-multi algorithm is similar to the accuracy of other algorithms, and the computational cost of GP-multi algorithm is much lower than other algorithms. It means than the proposed can be used in both MLE method and the epoch method.

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Fig. 6. Estimation Error of f for GP-multi algorithm, PSO and CE algorithm.

Fig. 7. CPU time for GP-multi algorithm, PSO and CE algorithm.

Fig. 8. Estimation Error of f for GP-multi algorithm, PSO and CE algorithm.

5 Conculations In order to reduce the computational cost of pulsar period searching, we a Gaussian process surrogate model assisted multi-optimization algorithm in this paper. The GP model with lower computational cost is used to as a surrogate of the objective function. Therefore, the optimization is mainly based on the GP model, avoiding evaluate the objective function directly. In addition, the proposed multi-optimization algorithm combines the advantages of PSO and CE algorithm, and has the characteristics of high

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Fig. 9. CPU time for GP-multi algorithm, PSO and CE algorithm.

accuracy and fast convergence. Simulation results shows that the proposed GP-multi algorithm can reduce the computational cost while retains accuracy of period searching. For the data of Crab pulsar with observation period of 3000 s, the computation cost of the proposed GP-multi algorithm is about 13.5% of the PSO and CE algorithm. In addition, the proposed GP-multi algorithm can be applied to objective function of different period searching method.

References 1. Sheikh, S.I., Pines, D.J., Ray, P.S., Wood, K.S., Lovellette, M.N., et al.: Spacecraft navigation using X-ray pulsars. J. Guid. Control. Dyn. 29, 49–63 (2006) 2. Zheng, W., Wang, Y.D.: X-ray Pulsar-based Navigation: Theory and Applications, pp. 1–24. Springer Singapore, Singapore (2020) 3. Hobbs, G.B., Bailes, M., Bhat, N.D.R., et al.: Gravitational-wave detection using pulsars: status of the Parkes pulsar timing array project. Publ. Astron. Soc. Australla 26, 103–109 (2009) 4. Desvignes, G., Caballero, R.N., Lentati, L., et al.: High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array. Mon. Not. R. Astron. Soc. 458, 3341–3380 (2016) 5. Emadzadeh, A.A., Speyer, J.L.: Relative navigation between two spacecraft using X-ray pulsars. IEEE Trans. Control Syst. Technol. 19, 1021–1035 (2011) 6. Emadzadeh A.A., Speyer J.L.: Navigation in Space by X-ray Pulsars, pp. 3–12 Springer New York, New York, NY (2011) 7. Deneva, J.S., Ray, P.S., Lommen, A., et al.: Large high-precision X-ray timing of three millisecond pulsars with nicer: stability estimates and comparison with radio. Astrophys. J. 874 (2019) 8. Mitchell, J.W., Winternitz, L.B., Hassouneh, M.A., et al.: SEXTANT X-ray pulsar navigation demonstration: initial on-orbit results. Guidance, Navigation, and Control 2018, PTS I-II: Advance in the Astronautical Sciences, pp. 1229–1240. (2018) 9. Manchester, R.N.: Pulsar timing arrays and their applications. Radio Pulsars: An Astrophysical Key to Unlock the Secrets of the Universe, pp. 65–72. (2011) 10. Wang, Y.D., Zheng, W., Sun, S.M., Li, L.: X-ray pulsar-based navigation using timedifferenced measurement. Aerosp. Sci. Technol. 36, 27–35 (2014) 11. Sun, H.F., Sun, X., Fang, H.Y., Shen, L.R., Cong, S.P., et al.: Building X-ray pulsar timing model without the use of radio parameters. Acta Astronaut. 143, 155–162 (2018)

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12. Jager, O., Raubenheimer, B., Swanepoel, J.: A poweful test for weak periodic signals with unknown light curve shape in sparse data. Astron. Astrophys. 221, 180–190 (1989) 13. Leahy, D., Elsner, R., Weisskopf, M.: On searches for periodic pulsed emission - The Rayleigh test compared to epoch folding. Astrophys. J. 272 (1983) 14. Protheroe, R., Clay, R.: First observation of ultra-high-energy γ rays from LMC X-4. Nature 315, 205–207 (1985) 15. Emadzadeh, A.A., Speyer, J.L., Golshan, A.: Asymptotically efficient estimation of pulse time delay for X-ray pulsar based relative navigation. AIAA Guidance, Navigation, and Control Conference, American Institute of Aeronautics and Astronautics (2009) 16. Rao, A.R.M., Sivasubramanian, K.: Multi-objective optimal design of fuzzy logic controller using a self configurable swarm intelligence algorithm. Comput. Struct. 86, 2141–2154 (2008) 17. Gandomi, A.H., Kashani, A.R., Roke, D.A., Mousavi, M.: Optimization of retaining wall design using recent swarm intelligence techniques. Eng. Struct. 103, 72–84 (2015) 18. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95—International Conference on Neural Networks, pp. 1944, 1942–1948. (1995) 19. Cui, Z., Sun, B., Wang, G., Xue, Y., Chen, J.: A novel oriented cuckoo search algorithm to improve DV-Hop performance for cyber–physical systems. J. Parallel Distrib. Comput. 103, 42–52 (2017) 20. Cai, X.J., Gao, X.Z., Xue, Y.: Improved bat algorithm with optimal forage strategy and random disturbance strategy. Int. J. Bio-Inspired Comput. 8, 205–214 (2016) 21. De Boer, P.T., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A tutorial on the cross-entropy method. Ann. Oper. Res. 134, 19–67 (2005) 22. Liu, B., Zhang, Q.F., Gielen, G.G.E.: A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Trans. Evol. Comput. 18, 180–192 (2014) 23. Emadzadeh, A.A., Speyer, J.L.: X-ray pulsar-based relative navigation using epoch folding. IEEE Trans. Aerosp. Electrontic Syst. 47, 2317–2328 (2011) 24. Emadzadeh, A.A., Speyer, J.L.: On Modeling and pulse phase estimation of X-ray pulsars. IEEE Trans. Signal Process. 58, 4484–4495 (2010) 25. Winternitz, L.M.B., Hassouneh, M.A., Mitchell, J.W., et al.: X-ray pulsar navigation algorithms and testbed for SEXTANT. IEEE Aerospace Conference Proceedings, pp. 1–14. (2015) 26. MacKay, D.: Introduction to Gaussian processes. NATO Adv. Stud. Inst. Ser. F Comput. Syst. Sci. 168 (1998) 27. Zhang, Y., Li, H.Y., Bao, E.H., Zhang, L., Yu, A.P.: A hybrid global optimization algorithm based on particle swarm optimization and Gaussian process. Int. J. Comput. Intell. Syst. 12, 1270–1281 (2019) 28. Wang, Y.D., Zheng, W.: Pulse phase estimation of X-ray pulsar with the aid of vehicle orbital dynamics. J. Navig. 69, 414–432 (2015) 29. Wang, Y.D., Zheng, W.: Pulsar phase and Doppler frequency estimation for XNAV using on-orbit epoch folding. IEEE Trans. Aerosp. Electrontic Syst. 52, 2210–2219 (2016)

GNSS-5G-SINS Resilient Integrated Navigation Algorithm for Indoor and Outdoor Seamless Environment Tianyou Jiang1 , Tianhe Xu1 , Wenfeng Nie1 , Xiaoji Dai1 , Linghan Yao1 , and Fan Gao1,2(B) 1 School of Space Science and Physics, Shandong University, Weihai 264209, China

[email protected] 2 Shandong Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment,

Weihai 264209, China

Abstract. At present, the accuracy and reliability of Global Navigation Satellite Systems (GNSS) in complex environments have not been able to meet the demands of seamless location services both indoors and outdoors. The 5G cellular network provides technical characteristics of ultra-dense networking, large bandwidth, and large-scale array antenna, which can offer wide-area and highprecision information on Time of Arrival (ToA) and Angle of Arrival (AoA). This paper proposes an adaptive integrated navigation algorithm based on a federated Kalman filter, integrating three sensors-GNSS/5G base station/Strap-down Inertial Navigation System (GNSS-5G-SINS) - to resolve the signal blocking issue in the indoor-outdoor transition environment. To overcome frequent out-of-lock and non-line-of-sight errors of the satellite in the indoor-outdoor seamless environment, this algorithm realizes the tight combination of observed values in the sub-filter and designs a fault detection and processing module to suppress the influence of abnormal observed values on the system. Finally, the main filter fuses information from each sub-filter and distributes dynamic information according to the quality of observed values. Experimental tests demonstrate that the proposed scheme improves the accuracy and stability of the navigation system. Under the partial lock-out of the satellite, the proposed algorithm reduces the positioning error by 68% compared with the GNSS-SINS compact combination, and the Root Mean Square Error (RMSE) reached 0.37m in the indoor environment. These results indicate that the new 5G technology has the potential to offer relatively high precision positioning services. Keywords: 5G positioning · Indoor and outdoor seamless · Fault handing · Federated filtering · Integrated navigation

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1 Introduction With the proliferation of mobile Internet, Internet of Things (IoT) applications, and smart transportation, the demand for Location-Based Services (LBS) is increasing [1]. At the same time, the increasing level of urbanization and underground space development necessitates that LBS meet the demand for high accuracy and robust positioning in various scenarios, both indoors and outdoors [2]. In navigation systems, a single sensor is often unable to meet the performance requirements for seamless indoor-outdoor localization. Therefore, combined navigation technology with heterogeneous multi-source sensors can leverage the strengths and overcome the limitations, exploiting the advantages of each subsystem, and improving the robustness of the system [3]. The Global Navigation Satellite System (GNSS) is a ubiquitous source of outdoor navigation information that can provide global-scale services with centi-meter-level accuracy or higher in areas with good satellite visibility [4]. However, in common environments such as urban canyons, tunnels, and streets with trees, satellite visibility decreases and multipath effects occur, resulting in a sharp deterioration in positioning accuracy and system malfunction [5]. The Strap-down Inertial Navigation System (SINS) uses the data acquired by a plus meter and gyroscope to obtain attitude, velocity and position information after integration operations. As an autonomous navigation system, it has the advantages of fast measurement update frequency, complete measurement information, and freedom from external interference, but it requires external initialization information before working, and the navigation error also increases incrementally with time [6]. Therefore, SINS is often used in conjunction with GNSS, and the undesirable effects of GNSS short-time loss of lock can be weakened by a combination of loose and tight algorithms [7]. The Global Navigation Satellite System (GNSS) provides ubiquitous outdoor navigation services with centi-meter-level accuracy in good satellite visibility conditions. However, in common environments such as urban canyons, tunnels, and street trees, satellite visibility decreases, leading to a sharp deterioration in positioning accuracy and system performance. This problem can be addressed by the introduction of 5th Generation Mobile Communication Technology (5G), which provides new technology support for navigation [8]. The massive MIMO, large bandwidth, and milli-meter wave technologies of 5G base stations make high-accuracy positioning possible, while Ultra-Dense Network (UDN) and indoor-outdoor scene separation technologies support seamless indoor and outdoor coverage [9]. At the signal level, the 5G Channel State Information (CSI) can be used for localization using Time of Arrival (ToA) and Angle of Arrival (AoA) measurements [10]. The JADE-ESPRIT algorithm, based on the rotation-invariant property among subarrays, can estimate ToA and AOA in 3D space with a balance of efficiency and accuracy. At the hardware level, mMIMO technology uses tens or even hundreds of antennas at the base station end, which improves the measurement accuracy of ToA and AoA and reduces interference using beam assignment techniques. Millimeter wave technology uses a higher frequency band, providing a larger bandwidth and solving the problem of sub-6 GHz spectrum resource constraint. UDN high-density deployment of micro-skin base stations shortens the base station spacing, increasing the

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probability of Line Of Sight (LOS) between users and base stations and reducing Non Line Of Sight (NLOS) errors. Indoor-outdoor scene separation allows indoor users to connect to the outside through indoor antennas, reducing the signal penetration loss. This paper selects the JADE-ESPRIT algorithm for joint estimation of ToA and AoA, which has a balance of efficiency and accuracy, and can estimate these parameters in 3D space. In conclusion, Global Navigation Satellite System (GNSS) has high accuracy under good observation conditions, 5G base station provides good navigation capability for both indoor and outdoor scenes, and Strapdown Inertial Navigation System (SINS) has certain autonomous navigation capability. In order to combine the advantages of these three systems, this paper proposes an adaptive combined navigation algorithm based on the federal Kalman filter. Firstly, the algorithm implements the tight combination of GNSS-SINS and 5G-SINS at the observation level in the sub-filter. To suppress NonLine Of Sight (NLOS) errors, the observations are detected before entering the sub-filter, and the weights of the observations are adaptively adjusted by constructing a variance expansion factor. This algorithm can effectively improve the positioning accuracy and robustness of the system.

2 GNSS-5G-SINS Integration Navigation System The overall architecture of the GNSS-5G-SINS combined navigation system designed in this paper is shown in Fig. 1, which consists of five modules: SINS, 5G, GNSS, fault detection and processing, and filter fusion. SINS is used as a reference navigation source to fuse with GNSS and 5G, respectively, to form separate sub-filters. GNSS is usually solved under Earth-Centered, Earth Fixed (ECEF) system, while 5G base station is positioned under station centered system, so in this paper, the state vectors are converted to ECEF for processing before information fusion. Usually, the output frequency of SINS is higher, while the output frequency of GNSS and 5G is lower. In this paper, by aligning the timestamps of 5G and GNSS, the lower output frequency is selected for time synchronization during information fusion.

Fig. 1. The architecture of the proposed navigation system.

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2.1 State Equation The system state equation is established with respect to the type of inertial sensor error, the combination method and the choice of the coordinate system. For multi-source sensors, the fusion of the common parts of the different state vectors should also be considered. In this paper, the 15-dimensional state vector constructed under ECEF is e e e , δveb , δreb , ba , bg ]Tt Xt = [δψeb

(1)

e is the attitude angle error along X, where Xt is the system state vector at moment t; δψeb e Y, and Z directions under ECEF; δveb is the velocity error along X, Y, and Z directions; e is the position error along X, Y, and Z directions; b and b are the accelerometer δreb a g and gyroscope errors along X, Y, and Z directions under the carrier coordinate system, respectively. The equation of state of the navigation system is

Xt+1 = Ft Xt + Wt

(2)

where Ft is the state transfer matrix, the specific formula can be referred to the literature; Wt = [wra , wrg , wbad , wbgd ]Tt is the process noise vector, Q is the process noise vector, containing the random white noise wra , wrg of the accelerometer and gyroscope and the zero-bias random wandering process noise wbad , wbgd . 2.2 Measurement Equation The GNSS-SINS and 5G-SINS sub-filters allow for the correction of the system state vector through their respective measurement equations. The GNSS observation vector includes the pseudo range and pseudo range rate, and when the measurement update is performed, the observation new information is obtained by differentiating it from the observation value obtained through the SINS projection ⎤ ⎡ GNSS SINS ρ1,t − ρ1,t ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ ⎢ GNSS SINS ⎥ ⎥ ⎢ ρ − ρ i,t i,t ⎥ = H GNSS Xt + V GNSS YtGNSS = ⎢ (3) t t ⎢ GNSS SINS ⎥ ⎢ ρ˙1,t − ρ˙1,t ⎥ ⎥ ⎢ ⎥ ⎢ .. ⎥ ⎢ . ⎦ ⎣ GNSS SINS − ρ˙i,t ρ˙i,t

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GNSS and ρ˙ GNSS are the pseudo-range and where YtGNSS is the observation vector: ρi,t i,t SINS and ρ˙ SINS are pseudo-range rate of the ith satellite observed by GNSS at time t: ρi,t i,t the pseudo-range and pseudo-range rate of the ith satellite projected by SINS at time t; HtGNSS is the measurement relationship matrix, expressed as ⎤ ⎡ 01,3 , 01,3 , I1,t , 01,3 , 01,3 ⎡ ⎤ SINS T ⎥ ⎢ ∂ρ i,t .. ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ . ⎢ ∂x ⎥ ⎥ ⎢ ⎢ SINS ⎥ ⎢ 0 ,0 ,I ,0 ,0 ⎥ ⎢ ∂ρi,t ⎥ ⎢ 1,3 1,3 i,t 1,3 1,3 ⎥ ⎥ HtGNSS = ⎢ (4) ⎥, Ii,t = ⎢ ⎢ ⎥ ⎢ 01,3 , I1,t , 01,3 , 01,3 , 01,3 ⎥ ⎢ ∂y ⎥ ⎥ ⎢ ⎢ SINS ⎥ ⎥ ⎢ ⎣ ∂ρi,t ⎦ .. ⎥ ⎢ . ⎦ ⎣ ∂z 01,3 , Ii,t , 01,3 , 01,3 , 01,3

VtGNSS = [vρ , vρ˙ ]Tt is the measurement noise vector, which contains the measurement noise of pseudo-range and pseudo-range rate. The observation vector of 5G base station includes ToA and AoA, while AOA contains Azimuth (Azi) and Elevation (Ele). The measurement equation of 5G-SINS tight combination system is SINS ⎤ TOA5G 1,t − TOA1,t ⎥ ⎢ .. ⎥ ⎢ . ⎥ ⎢ ⎥ ⎢ ⎢ TOA5G − TOASINS ⎥ ⎢ i,t i,t ⎥ ⎥ ⎢ ⎢ Azi5G − AziSINS ⎥ ⎥ ⎢ 1,t 1,t ⎥ ⎢ ⎥ ⎢ . .. =⎢ ⎥ = Ht5G Xt + Vt5G ⎥ ⎢ ⎢ 5G SINS ⎥ ⎥ ⎢ Azii,t − Azi i,t ⎥ ⎢ ⎥ ⎢ 5G SINS ⎢ Ele1,t − Ele1,t ⎥ ⎥ ⎢ ⎥ ⎢ .. ⎥ ⎢ . ⎦ ⎣

⎡

Yt5G

(5)

5G SINS Elei,t − Elei,t 5G 5G where Yt5G is the observation vector: TOA5G i,t , Azii,t , Elei,t are the ToA, Azi, Ele of the SINS SINS are the ToA, Azi, Ele of ith base station observation at time t; TOASINS i,t , Azii,t , Elei,t 5G the first base station projected by SINS at time t; Ht is the measurement relationship matrix, expressed as

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⎤ TOA 01,3 , 01,3 , I1,t , 01,3 , 01,3 ⎥ ⎢ .. ⎥ ⎢ . ⎥ ⎢ ⎥ ⎢ ⎢ 0 , 0 , I TOA , 0 , 0 ⎥ ⎢ 1,3 1,3 i,t 1,3 1,3 ⎥ ⎥ ⎢ ⎢ 0 , 0 , I Azi , 0 , 0 ⎥ ⎢ 1,3 1,3 1,t 1,3 1,3 ⎥ ⎥ ⎢ ⎥ ⎢ .. =⎢ ⎥, . ⎥ ⎢ ⎥ ⎢ Azi ⎢ 01,3 , 01,3 , Ii,t , 0 , 0 1,3 1,3 ⎥ ⎥ ⎢ ⎥ ⎢ Ele ⎢ 01,3 , 01,3 , I1,t , 01,3 , 01,3 ⎥ ⎥ ⎢ ⎥ ⎢ .. ⎥ ⎢ . ⎦ ⎣ ⎡

Ht5G

TOA Ii,t

(6)

Ele , 01,3 , 01,3 01,3 , 01,3 , Ii,t ⎡ ⎡ ⎡ ⎤T ⎤ SINS ⎤T SINS T ∂Azii,t ∂TOASINS ∂Elei,t i,t ⎢ ⎢ ⎢ ⎥ ⎥ ⎥ ∂x ⎥ ⎢ ⎢ ⎢ ⎥ ∂x ∂x ⎥ ⎢ ⎢ ⎢ ⎥ ⎥ ⎥ SINS SINS ⎥ ⎢ ∂TOASINS ⎢ ∂Azii,t ⎥ Ele ⎢ ∂Elei,t ⎥ i,t ⎥ , I Azi = ⎢ ⎥ ⎥ ,I = ⎢ =⎢ i,t ⎢ ⎢ ⎢ ⎥ i,t ⎥ ∂y ⎥ ∂y ∂y ⎥ ⎢ ⎢ ⎢ ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ ⎥ ⎥ SINS ⎦ ⎣ ∂TOASINS ⎣ ⎣ ∂Elei,t ⎦ ⎦ i,t 0 ∂z ∂z

Vt5G = [vTOA , vAzi , vEle ]Tt is the measurement noise vector, which contains the measurement noise of ToA and AoA. 2.3 Information Fusion and Distribution By discretizing the state equation and the measurement equation given above, the subfilter time update process is Xˆ i,k+1/k = Fi,k+1/k Xˆ i,k T Pi,k+1/k = Fi,k+1/k Pi,k Fi,k+1/k + Qi,k , i = 1, 2

(7)

Each sub-filter is independently measured and updated as T T Ki,k+1 = Pi,k+1/k Hi,k+1 (Hi,k+1 Pi,k+1/k Hi,k+1 + Ri,k+1 )−1

Xˆ i,k+1 = Xˆ i,k+1/k + Ki,k+1 (Yi,k+1 − Hi,k+1 Xˆ i,k+1/k ) Pi,k+1 = (I − Ki,k+1 Hi,k+1 )Pi,k+1/k , i = 1, 2

(8)

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where Pi,k is the state error covariance matrix; Qi,k is the process noise covariance matrix; Ri,k is the measurement noise covariance matrix; Ki,k is the Kalman gain matrix; the subscripts i and k denote the corresponding sub-filters and the discretization time, respectively. The local optimal solution of each sub-filter is fused to obtain the main filter fusion equation as Pg,k =

Xˆ g,k



−1 Pi,k

−1

−1  −1 Qg,k = Qi,k −1 ˆ = Pg,k Xi,k ), i = 1, 2 (Pi,k

(9)

Only time updates are performed in the main filter, and the global optimal estimate Xˆ g,k , the state error covariance matrix Pg,k , and the system noise covariance matrix Qg,k in Eq. (9) are fed back to each sub-filter according to certain information allocation criterion. The information allocation criterion can be expressed as Xˆ i,k = Xˆ g,k Pi,k = βi−1 Pg,k

(10)

Qi,k = βi−1 Qg,k , i = 1, 2 where β represents the information distribution coefficient, whose value is related to the overall performance of the federal filter, and satisfies the following information conservation principle N

βi = 1, N = 2

(11)

i=1

In this paper, the size β is dynamically adjusted according to the GNSS geometric accuracy factor and the carrier-to-noise ratio to improve the fault isolation of the subfilter, and the global filtering accuracy after fusion can also be improved. 2.4 Fault Detection and Handling GNSS and 5G observations in indoor and outdoor seamless environments are susceptible to NLOS errors, which in turn affect the positioning accuracy of the whole system. In this paper, the mode |δYi,k | = |Yi,k − Hi,k Xˆ i,k/k−1 | of the observed innovation is used as the test value, and the χ 2 distribution is used to construct the fault detection threshold to

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identify the NLOS error. When the measurement information is normal, δYi,k is Gaussian white noise and obeys a normal distribution with a mean value of 0; when the system is faulty, the mean value of δYi,k is no longer 0, and the system fault can be judged by hypothesis testing. The construct hypothesis testing statistic is T −1 Ci,k δYi,k Ti,k = δYi,k

(12)

T +R is the covariance matrix of the observed innovation. where Ci,k = Hi,k Pi,k/k−1 Hi,k i,k Ti,k with degree of freedom n (n is the dimensionality of the observation vector) χ 2 distribution. Taking the significance level as Ti,k χ 2 (n), then the threshold value for determining the occurrence of failure in the system is

TD = χα2 (n)

(13)

When Ti,k ≤ TD , the system is judged to be currently free of anomalies, and vice versa, the current ephemeral observations are judged to contain errors. In this paper, we weaken the observation error by constructing the variance expansion factor αi,k , that is ⎧ ⎨ 1, |δYi,k | ≤ TD (14) αi,k = |δYi,k | ⎩ , |δYi,k | > TD TD The αi,k vector in the above equation is diagonalized to obtain diag(αi,k ), then the modified system measurement noise covariance matrix is R˜ i,k = diag(αi,k )Ri,k

(15)

By substituting R˜ i,k into Eq. (8), the weight of the observations in the measurement update can be adjusted adaptively according to the quality of the observations, thus making the filtering results smoother and more accurate.

3 Experimental Results and Analysis 3.1 Experimental Conditions and Simulation Setup In this paper, we design experiments to verify the effectiveness of GNSS-5G-SINS combined navigation algorithm, in which GNSS-SINS uses the measured data and 5G signal is simulated with full area coverage. The experimental site was selected in the soccer field of Weihai campus of Shandong University as shown in Fig. 2 (left), with a range of about 70m × 100m, and the starting and ending points of the carrier operation were represented by “triangle” and “circle” respectively. The red box area simulates the “indoor aisle” observation environment.

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Fig. 2. Test environment and the trajectory (left) and the experimental platform (right).

The experimental equipment is mounted on a dolly, as shown in Fig. 2 (right). The main performance parameters of the IMU are shown in Table 1. The measurement update frequency of GNSS is 1 Hz and the update frequency of SINS is 200 Hz. The carrier reference trajectory is obtained by NovAtel IE 8.9 post-processing software through RTK-INS tight combined positioning mode with centi-meter-level accuracy. In order to simulate the indoor 5G micro-base station environment, the simulated base station antenna adopts a large-scale Uniform Plane Array (UPA), which is placed at the four vertices (yellow pentagram) in the simulated “indoor aisle” area (red box) and obeys a uniform distribution of 5 ~ 15m in height. The 5G simulation terminal is coincident with the GNSS antenna phase center, and the 5G Channel State Information Reference Signal (CSI-RS) is generated according to the carrier reference trajectory and pre-set parameters, and the signal transmission frequency is 1 Hz. 5G new radio channel parameters are set in Table 2. Table 1. Main performance parameters of IMU. Sensor type

Parameters

Value

Accelerometer

bias uncertainty

2mg

bias stability

0.01mg

Gyroscope

noise PSD

√ 0.025m/s/ hr

bias uncertainty

360deg/hr

bias stability

0.8deg/hr √ 0.06deg/ hr

noise PSD

3.2 5G Navigation Performance Evaluation In order to evaluate the improvement in positioning accuracy brought by the new 5G technology, simulations are performed for different sizes of mMIMO antennas and different bandwidths of signals, respectively.

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Parameters

Value

mMIMO antenna

UPA(12 × 12)

Array element spacing

5mm

Center frequency

28GHz

Bandwidth

200MHz

Frequency points

201

SNR

10dB

Fig. 3. ToA/AoA RMSE with different number of antennas (left) and different bandwidth (right).

The Root Mean Square Error (RMSE) of ToA/AoA estimation was evaluated using 64, 144, and 256 antennas. The results depicted in Fig. 3 (left) illustrate that the estimation accuracy significantly improves with an increase in the array size. This is due to the phase shift in the delayed space domain caused by the incoming wave incident at a specific angle, which contains the angular time delay information, and an increased number of elements enables more accurate calculation of the phase shift. The estimation accuracy of ToA/AoA was also calculated at bandwidths of 200, 400, and 800 MHz, as depicted in Fig. 3 (right). The results show that increasing the bandwidth improves the estimation accuracy when the number of frequency points is constant. This is because a larger bandwidth increases the frequency interval between frequency points, resulting in more significant time-domain phase shifts that can be solved effectively.

Fig. 4. 5G WDOP during the experiment.

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Fig. 5. Position bias by 5G solution.

In addition to the above factors, the base station layout has a large impact on the positioning accuracy. The Weighting Dilution of Precision (WDOP) factors for horizontal and vertical directions are given in Fig. 4, respectively [11]. The 5G positioning error sequence obtained based on the setting conditions in Table 2 is shown in Fig. 5. In general, the positioning error of the carrier is larger at the beginning of the operation, which is due to the fact that the base stations are all distributed on one side relative to the terminals, resulting in larger WDOP values. As it gradually approaches the “indoor area”, the WDOP value decreases and the positioning error gradually decreases. In addition, Table 3 shows that the vertical position error is larger because the base station is distributed above the carrier during the whole motion and the geometric change is not obvious, which leads to the low estimation accuracy of the altitude angle and finally affects the positioning results. Table 3. 5G positioning and ToA/AoA RMSE. Position RMSE

ToA/AoA RMSE

N/m

E/m

D/m

ToA/m

Azi/deg

Ele/deg

0.12

0.11

0.22

0.25

0.0042

0.032

3.3 GNSS-5G-SINS Navigation Performance Evaluation In this paper, we simulate a scenario by configuring the reception signal through a GNSS observation file. Specifically, when the carrier approaches the “indoor aisle” area, some of the forward satellite signals cannot be received, and only the backward and zenith direction satellites are visible. Moreover, when the carrier enters the “indoor aisle”, all

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satellite signals are lost. In addition, we simulate the NLOS observation environment in the outdoor part of the ephemeris with some base stations (1–2), based on the simulated 5G signals in the previous section. Here, the GNSS solution mode is RTK, and the reference stations are placed on the roof of the Wentian-building of the Weihai Campus of Shandong University, approximately 400 m apart. Figure 6 shows the comparison between the proposed GNSS-5G-SINS combined navigation system and the reference trajectory. Additionally, we provide trajectories obtained by the GNSS-SINS tight combined navigation system and the GNSS-5G-SINS combined navigation system without considering fault detection and handling. Table 4 shows the statistical results of the positioning errors for the above two positioning methods in different scenarios. Moreover, Fig. 7 shows the position error sequence of the GNSS-SINS system, Fig. 8 shows the position error sequence of the GNSS-5G-SINS system without considering the fault detection and processing module, and Fig. 9 shows the position error sequence of the proposed GNSS-5G-SINS system.

Fig. 6. Reference trajectories and trajectories by different algorithms.

The results demonstrate that the proposed GNSS-5G-SINS combined navigation system achieves comparable performance to the GNSS-SINS system in the outdoor environment, with an RMSE of 0.04 m. However, when some 5G base stations are in NLOS environments, the system’s overall filtering accuracy decreases due to observation contamination. Nevertheless, the fault detection and processing module of the proposed algorithm can effectively detect and isolate NLOS errors from some base stations, thereby significantly improving the system accuracy. It is important to note that when all 5G base stations are in NLOS environments, the errors cannot be suppressed by this module. In the indoor-outdoor transition area, the positioning error for the GNSS-5G-SINS system is almost the same as other normal time periods, but with a 68% improvement in positioning accuracy compared to the GNSS-SINS system. Furthermore, the proposed algorithm dynamically fuses GNSS and base station observation information according to the state error covariance provided by each sub-filter during satellite observable time,

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dynamically distributes the fused information based on the satellite positioning accuracy factor and signal load-to-noise ratio, and achieves the effect of “1 + 1 > 2”. These results indicate that the proposed algorithm can obtain optimal solutions for the system with a small number of GNSS observations and has strong robustness. After the satellites are completely lost, the GNSS-SINS system enters pure inertial guidance mode, maintaining a stable position accuracy for a short period of time before gradually dispersing to a maximum error of 57.6 m. When satellite observability returns to normal levels, the positioning accuracy does not immediately return to normal, but rather experiences a gradual convergence process, which is a characteristic of GNSSSINS tight integration. In contrast, the GNSS-5G-SINS system automatically degrades to 5G-SINS mode during this period, with a positioning RMSE of 0.37 m, which can be continuously constrained within a certain range.

Fig. 7. Position bias by GNSS-SINS TC solution.

Fig. 8. Position bias by GNSS-5G-SINS with Non-fault detection and processing module solution.

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Fig. 9. Position bias by proposed GNSS-5G-SINS solution.

Table 4. Positioning errors of each method with different scenarios. Error(m)

outdoor transition indoor

GNSS-SINS

GNSS-5G-SINS (NLOS)

Proposed

RMSE

MAX

RMSE

MAX

RMSE

MAX

0.04

0.13

0.49

1.07

0.06

0.11

0.24

0.04

0.12

0.04

0.12

0.37

0.83

0.37

0.83

0.14 43.2

57.6

4 Conclusion This paper proposes a combined GNSS-5G-SINS navigation algorithm for seamless indoor-outdoor environments that effectively addresses the problems of unstable system operation and low positioning accuracy caused by satellite out-of-lock and non-lineof-sight (NLOS) errors. The algorithm adopts a federated Kalman filter architecture, enabling tight combination at the observation level in the sub-filter without the need for the subsystem to solve the position information separately. An adaptive fault detection and processing module is designed to suppress the impact of abnormal observations on the system. The time-updated values of the sub-filters are fused by the main filter, and dynamic information distribution is carried out, taking into account the quality of the observations. Outdoor semi-realistic and semi-simulation experiments demonstrate that the proposed algorithm effectively isolates NLOS errors. The algorithm improves positioning accuracy by approximately 68% compared to the GNSS-SINS tight combination navigation system under partial satellite loss in the indoor-outdoor transition area. The positioning RMSE reaches 0.37m in the indoor environment, demonstrating that the new 5G technology has the potential to provide higher accuracy positioning services. Acknowledgements. The study is funded by National Key Research and Development Program of China (2020YFB0505800 and 200YFB0505804).

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References 1. Zhang, Z., Wu, L., Zhang, Z., et al.: AoA-and-amplitude fingerprint based indoor intelligent localization scheme for 5g wireless communications. In: 2021 13th International Conference on Wireless Communications and Signal Processing (WCSP). IEEE (2021) 2. Chen, W.: Research on GPS/Self-Contained Sensors Based Seamless Outdoor/Indoor Pedestrian Positioning Algorithm[D]. University of Science and Technology of China, Hefei (2010) 3. Fei, L.I.U.: Research on high-precision seamless positioning model and method based on multi-sensor fusion[J]. Acta Geodaetica et Cartographica Sinica 50(12), 1780 (2021) 4. Li, X.: Rapid Ambiguity Resolution in GNSS Precise Point Positioning[D]. WuHan University, Wuhan (2013) 5. Feng, Z.H.U.: GNSS/SINS/Vision Multi-sensors Integration For Precise Positioning and Orientation Determination[D]. WuHan University, Wuhan (2019) 6. Groves, P.D.: Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems (Second Edition) [M]. ARTECH HOUSE, London (2013) 7. Zhang, C., Lyu, Z., Ke, Y., Tian, A.H., Dan, H.: Comparison of GNSS/INS loosely coupled and tightly coupled systems under spoofing interference [J/OL]. J. Navig. Position. 8. Liu, J., Gao, K., Guo, W., Cui, J., Guo, C.: Role, path, and vision of “5G + BDS/GNSS”. Satell. Navig. 1(1) (2020) 9. Zhang, P., Chen, H.: A survey of positioning technology for 5G [J]. J. Beijing Univ. Posts Telecommun. 41(5) (2018) 10. Shahmansoori, A., Garcia, G.E., Destino, G., Seco-Granados, G., Wymeersch, H.: Position and orientation estimation through millimeter-wave MIMO in 5G systems. IEEE Trans. Wireless Commun. 17(3), 1822–1835 (2018) 11. Deng, Z., Ma, Z.: et al.: Optimal geometric layout of outdoor base station for TC-OFDM positioning system [A]. The CSNC management office, academic exchange center. Proceedings of the 12th CSNC-S09 User Terminal Technology[C]. The CSNC Management Office, Academic Exchange Center: Organizing Committee of the CSNC, p. 6. (2021)

Three-Dimensional Station Distribution Design for TDOA Positioning System of Sea Launch Site Maolin Chen1 , Xianglu Li1(B) , Changjiang Liu2 , Zhengyu Ji1 , and Yimao Sun3 1 Institute of Electronic Engineering, China Academy of Engineering Physics, Sichuan

Province, Mianyang City, China [email protected] 2 Troop of PLA, Sichuan Province, Chengdu City 78090, China 3 School of Computer Science, Sichuan University, Sichuan Province, Chengdu City, China

Abstract. In recent years, USA, Russia and China have carried out many sea launch and recovery experiments, sea launch site exhibits better safety and economical efficiency compared with land launch site, which can provide launch service for spacecraft with different orbits. GNSS/INS integrated navigation system is adopted by rockets to acquire positioning results, nevertheless, owing to the inherit vulnerability of GNSS and possible INS failure, other navigation system is required to offer independent multi-source positioning data. TDOA positioning system is able to calculate rocket’s position utilizing time measurement data from telemetering signals, on one hand, the reliability can be promoted, and on the other hand, real-time central monitoring can be achieved, which aroused an increasing number of interests. However, present TDOA system usually apply land stations to obtain time measurements and localization results, because the characteristics of flat station distribution along the vertical direction, the vertical positioning precision cannot be satisfactory, especially for the need of rocket recovery on the sea launch site. To solve this problem, this work first discusses the precision influence of different surveying ships distribution layouts, “T” shape distribution is recommended for surveying ships according to evaluation results, then introduces air-based surveying station into TDOA positioning system to improve vertical localization accuracy, probes the performance variation utilizing different UAVs, including tethered UAV, multi-rotor UAV, medium-scale vertical takeoff and landing fixed wing UAV and large-scale fixed wing UAV, confirms the optimal UAV height in the rocket recovery key area under 10 km height, then researches on surveying station optimal distribution layout strategy according to predefined trajectory. This work can enhance the positioning precision and reliability, and provide three-dimensional surveying station distribution guidance in sea launch site. Keywords: Rocket sea launch · TDOA positioning · Three-dimensional station distribution · Positioning precision evaluation · Air-based survey station

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 346–357, 2024. https://doi.org/10.1007/978-981-99-6928-9_30

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1 Introduction Sea launch refers to the launch method of transferring a carrier rocket to a sea launch platform and driving it to a predetermined sea area for launch [1]. At present, the rocket mostly uses GNSS/INS integrated navigation to achieve high-precision positioning [2], and the positioning data is transmitted back to the measurement and control center through the telemetry link. Due to the inherent vulnerability of GNSS [3, 4], it is highly susceptible to intentional and unintentional interference when launched on the high seas, and INS may also fail to obtain correct positioning results due to accidental failure. This requires the establishment of a redundant positioning system at the sea launch site to improve the positioning accuracy and reliability of rocket launches. Especially in recent years, the recyclable rocket launch mission represented by the American company SpaceX [5], in the altitude range below 10 km of rocket recovery, has higher requirements for positioning accuracy and reliability, otherwise it is very likely that a large safety accident may occur and lead to rocket recovery failure [6]. The time difference of arrival (TDOA) positioning system can use several telemetering stations to receive rocket telemetry signals, solve the obtained time measurement data, and obtain real-time position, speed and other information of the rocket [7], which can be used as a supplement to and a redundant backup of the GNSS/INS integrated navigation system. However, the telemetering stations of the current TDOA system are arranged at similar elevations on the earth’s surface, which makes the elevation positioning accuracy of the target poor [8], and cannot meet the requirements of positioning in the process of rocket launching and recovering, especially high-precision elevation positioning. In order to improve the elevation positioning accuracy of the TDOA positioning system of the sea launch site in rocket launch and recovery, this paper proposes to use the Unmanned Aerial Vehicle (UAV) as the space-based telemetering station, and analyzes four kinds of typical UAVs, including tethered UAV, rotary wing UAV, medium-sized fixed-wing vertical take-off and landing (VTOL) UAV, and large-sized long-endurance UAV, and evaluates the influence of the application scenarios and working altitudes of these types of UAVs on the positioning accuracy. Then, the typical station layout scheme and the influence of the layout change on the positioning accuracy are analyzed. Finally, the optimal station generation strategy based on launch and recovery trajectory is discussed.

2 TDOA Principle and Precision Index 2.1 TDOA Positioning Principle Similar to GNSS (Global Navigation Satellite System), the TDOA positioning system also requires at least four time observations to calculate positioning results, usually one main station and several substations are defined. Set the position of the main station is (x0 , y0 , z0 ), the position of the i-th substation is (xi , yi , zi ), subtract the time measurement from the target to this substation and to the main station, the distance difference ri

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between the main station and the substation can be obtained [9]:  ri = (x − xi )2 + (y − yi )2 + (z − zi )2  − (x − x0 )2 + (y − y0 )2 + (z − z0 )2

(1)

When the number of substations is N(N > 3), the position of the target can be obtained by solving the three unknowns values x, y, and z by connecting the equation system composed of Eq. (1). 2.2 DOP Based Positioning Precision Evaluation The target positioning accuracy related to the spatial geometric distribution of telemetering stations is usually expressed by GDOP (Geometric Dilution of Precision), and the larger the GDOP value, the lower the positioning accuracy. At the same time, HDOP (Horizontal Dilution of Precision) and VDOP (Vertical Dilution of Precision) are used to express the horizontal positioning accuracy and the vertical positioning accuracy, respectively [10].  (2) GDOP = δx2 + δy2 + δz2 HDOP =



δx2 + δy2

VDOP =



δz2

(3) (4)

where, δx , δy and δz are standard deviations of positioning errors in x, y and z directions.

3 Three-Dimensional Station Distribution Design 3.1 Telemetering Ship Distribution Design A variety of station distribution forms have already been proposed by former researchers, such as square, diamond, flat diamond, T-shape, and Y-shape, to evaluate the GDOP values under these five station distributions, the distance between mesurement stations is set to 10 km, the elevation of the evaluation plane is 3 km, and the coordinates of telemetering stations are shown in Table 1. It can be found that the “T” shape station distribution scheme is suitable for highprecision positioning of rockets from the sea launch site with preset trajectory due to its good directionality of DOP distribution, high positioning accuracy near the main station, and the same expansion direction with better performance when HDOP and VDOP expand to the periphery (Figs. 1, 2, 3, 4 and 5).

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Table 1. Distribution layout of TDOA surveying stations Station Distribution

Main station

Substtion1

Substation2

Substation3

Square

(−5, 5, 0)

Diamond

(0, 4, 0)

(5, 5, 0)

(−5, −5, 0)

(5, −5, 0)

(8.2, 0, 0)

(0, −4, 0)

(−8.2, 0, 0)

Flat diamond

(−2, 4, 0)

(8.2, 0, 0)

(2, −4, 0)

(−8.2, 0, 0)

T-shape

(0, 0, 0)

(−10, 0, 0)

(10, 0, 0)

(0, −10, 0)

Y-shape

(0, 0, 0)

(−7.1, 7.1, 0)

(7.1, 7.1, 0)

(0, −10, 0)

Fig. 1. HDOP and VDOP of square distribution

Fig. 2. HDOP and VDOP of diamond distribution

3.2 UAV Based Telemetering Station Analysis UAV can be used as telemetering station to improve the vertical positioning precision, four kinds of UAVs can be adopted in TDOA system at sea launch site, mainly including tethered UAV, rotor UAV, medium-sized fixed-wing VTOL UAV and large long-endurance UAV, the characteristics of those UAVs are analyzed in following Table 2.

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Fig. 3. HDOP and VDOP of flat diamond distribution

Fig. 4. HDOP and VDOP of “T” shape distribution

Fig. 5. HDOP and VDOP of “Y” shape distribution

By analyzing the characteristics of the above four typical UAVs in Table 2, the cruising track in the application scenario of the sea launch site can be obtained as follows:

Below 30 kg

Above 12 h

Simple operation, long working Simple operation, economy hours

Load

Working hours

Merit

Below 30 min

Below 30 kg

1000

300

Max height (m)

Takes off from the sea launch platform or the supporting ship before the rocket launch test and hovers at a predetermined altitude, landing after the mission

Takes off from the sea launch platform before the rocket launch test and hovers at a predetermined altitude, landing after the mission

Rotor UAV

Usage

Tethered UAV

Specification Type

Long working hours

Above 4 h

Below 30 kg

4000

Before the rocket launch test, takes off from the launch platform or supporting ship relying on the rotor, hovers by the fixed-wing during the mission, and lands with the rotor after the mission

(continued)

Long Working hours, high reliability

Above 10 h

Above 100 kg

9000

Takes off from a land airfield, flies a long distance to the area of the sea launch site, hovers around a fixed point during the mission, and return to the land airfield after the mission to land

Medium-sized fixed-wing VTOL Large long-endurance UAV UAV

Table 2. UAV types and specification analysis Three-Dimensional Station Distribution Design for TDOA Positioning System 351

Legend

Drawback

High price

Tethered UAV

Specification Type

Short working hours

Rotor UAV Complex operation, low reliability

Very high price, Require professional pilot

Medium-sized fixed-wing VTOL Large long-endurance UAV UAV

Table 2. (continued)

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(1) Tethered UAV hovers at an altitude of 300 m on the side of the launch platform; (2) Rotor UAV hovers at an altitude of 1000 m on the side of the launch platform; (3) Medium-sized fixed-wing VTOL UAV hovers around the launch platform at an altitude of 4000 m at a radius of 1500 m; (4) Large long-endurance fixed-wing UAV hovers around the launch platform at an altitude of 9000 m at a radius of 1500 m. 3.3 Positioning Influence Analysis of UAV Telemetering Station Four measurement ships in the TDOA positioning system adopts “T” shape station distribution scheme, and VDOP is evaluated in five situations, including without UAV-based telemetering station, tethered UAV, rotor UAV, medium-sized fixed-wing VTOL UAV, and large long-endurance UAV, corresponding results are demonstrated in following Fig. 6. In Fig. 6, the green dots represent the horizontal projection point of the UAV-based telemetering stations, following results can be found: (1) The adoption of UAV-based telemetering station can greatly improve the vertical positioning accuracy of the TDOA positioning system at low altitudes; (2) The higher the height of the UAV-based telemetering station within a certain range, the more obvious the improvement in vertical positioning precision; (3) The height increasement of the UAV-based telemetering station from 4000 to 9000 m has limited improvement in vertical positioning precision. In order to deeply evaluate the impact of the altitude of the UAV-based telemetering station above 1000 m on the improvement of vertical positioning accuracy at low altitude, (0 m, -1000 m, 100 m) was selected as the evaluation point, and the horizontal position of the UAV was located at (0 m, 1500 m), and the altitude of the UAV ranges from 1000 to 9000 m. Figure 7 shows the VDOP values at the evaluation point as a function of the altitude of the UAV. It can be seen from Fig. 8 that when the UAV is below 4 km, the VDOP at the evaluation point decreases significantly with the increase of the altitude of the UAV, and when the altitude of the UAV is above 4 km, the impact on VDOP is small. In order to further evaluate the influence of the horizontal distance of the UAV-based telemetering station from the launch platform on VDOP, the horizontal position of the UAV is located at (0 m, 500 m), and the VDOP value at the evaluation point changes with the height of the UAV are shown in Fig. 8. Comparing Fig. 8 with 7, it can be found that the closer the horizontal distance between the UAV-based telemetering station and the sea launch platform, the more obvious the improvement of the vertical positioning precision, especially in the area near the launch platform.

4 Trajectory Based Station Distribution Strategy Optimization As can be seen from Fig. 4, in order to obtain better horizontal and vertical positioning precision, the vertical edge of the “T” shape should follow the direction of movement after the rocket launch as much as possible.

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Fig. 6. VDOP distributions of different UAV-based telemetering stations at 100m height

In order to verify the effectiveness of the above station layout strategy, a preset launch trajectory is used for verification, and Fig. 9 shows the typical preset launch trajectory and the positions of measurement stations after the optimal arrangement process. (that is the vertical edge of the “T” shape along the direction of movement of the rocket after launch). By combining the DOP and distance difference measurement accuracy (set to 2.5 m in this work), the positioning accuracy along the typical emission trajectory below 10 km

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Fig. 7. VDOP variation with different UAV-based telemetering station heights at the defined evaluation point (Horizontal distance = 1500 m)

Fig. 8. VDOP variation with different UAV-based telemetering station heights at the defined evaluation point (Horizontal distance = 500 m)

is evaluated, and the positioning error variation curve with elevation can be obtained as shown in Fig. 10. In order to compare with the positioning accuracy under the condition of optimized stationing as shown in above Figs. 9, 11 and 12 respectively show the distribution of measurement stations and the corresponding positioning accuracy when the layout is not optimized.

Fig. 9. Typical launch trajectory and optimized measurement station layout

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Fig. 10. Variation curve of positioning accuracy with elevation

Comparing Figs. 10 with 12, it can be seen that after the station position optimizing process, the positioning accuracy below 10 km is below 45 m, but if the measurement station is not optimally arranged, the positioning error can exceed 200 m at most.

Fig. 11. Typical launch trajectory and unoptimized measurement station layout

Fig. 12. Variation curve of positioning accuracy with elevation (unoptimized station layout)

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5 Conclusions Some conclusions can be reached from this work: (1) “T” shape station distribution scheme is suitable for high-precision positioning of rockets from the sea launch site with preset trajectory; (2) When the UAV is below 4 km, the VDOP at the evaluation point decreases significantly with the increase of the altitude of the UAV, and at the same time, the closer the horizontal distance between the UAV-based telemetering station and the sea launch platform, the more obvious the improvement of the vertical positioning precision; (3) The vertical edge of the “T” shape is encouraged to follow the direction of rocket launch trajectory in order to obtain better horizontal and vertical positioning precision. The positioning of the measurement station itself has a great influence on the positioning accuracy of the TDOA system on the target, in future work, the authors will research on cooperative positioning method to provide relative positioning information to measurement stations in GNSS denied environment, as well as multi-source fusion positioning method to meet the requirements of positioning accuracy and continuity in rocket sea launches.

References 1. Volodymyr, H., Volodymyr, S., Anatolii, S.: Risks and potential advances in operation recovery of sea launch international space rocket complex. Strategic Priorities 44(3), 5–11 (2017) 2. Trigo, G.F., Theil, S., Vandersteen, J., Bennani, S., Roux, C.: Robust tightly coupled hybrid navigation for space transportation. J. Spacecr. Rocket. 56(2), 596–609 (2019) 3. Chen, Y., Zhan, X.: GNSS vulnerability reliable assessment and its substitution with visual– inertial navigation. Aerospace Systems 4(3), 179–189 (2021) 4. Chen, M.L., Zhan, X., Liu, B., Yuan, W.: GNSS vulnerability network risk assessment and alleviation strategies considering efficiency cost. J. Aeronaut. Astronaut. Aviat 50(2), 161–173 (2018) 5. Wang, C., Song, Z.: Trajectory optimization for reusable rocket landing. In: 2018 IEEE CSAA Guidance, Navigation and Control Conference (CGNCC), pp. 1–6. (2018) 6. Blackmore, L.: Autonomous precision landing of space rockets. In: Frontiers of Engineering: Reports on Leading-Edge Engineering from the 2016 Symposium, vol. 46, pp. 15–20. The Bridge, Washington, DC (2016) 7. Nan, X., Futang, Z.: Performance analysis of reentry TDOA positioning system. International Foundation for Telemetering (2009) 8. Wang, Q., Li, B., Rizos, C.: Dilution of precision in three dimensional angle-of-arrival positioning systems. Journal of Electrical Engineering & Technology 14(6), 2583–2593 (2019) 9. Ma, X., Ballal, T., Chen, H., Aldayel, O., Al-Naffouri, T.Y.: A maximum-likelihood tdoa localization algorithm using difference-of-convex programming. IEEE Signal Process. Lett. 28, 309–313 (2021) 10. Wang, H., Deng, Z., Zheng, X., Fu, X.: DOP Analysis for indoor hybrid TDOA/TOA positioning based on mobile communication network. In: China Satellite Navigation Conference (CSNC 2021) Proceedings, pp. 576–585). Springer, Singapore (2021)

An Improved DOA Estimation Method Based on Sparse Reconstruction Jiahao Yang(B) , Zhongliang Deng, Zhichao Zang, and Biao Lei Beijing University of Posts and Telecommunications, BUPT, Beijing, China [email protected]

Abstract. With the development of millimeter wave technology and the increasingly complex electromagnetic environment, the traditional method of DOA estimation based on subspace technology can not meet the high-precision position requirements of space-time networks in various application scenarios. For this reason, scholars have introduced compressed sensing and sparse reconstruction technology into the problem of array signal estimation, and used sparse Bayesian (SBL) reconstruction based methods to estimate the angle of arrival (DOA), which often faces the problems of estimation performance and computation adjustment. In this paper, we propose a Bayesian grid iteration algorithm with low computational complexity while ensuring high estimation performance. Firstly, the SBL with the lowest computational complexity is used for rough estimation of the direction of arrival, and the grid is divided unevenly according to the rough estimation results. After the grid division termination condition is reached, the MDL criterion is used to estimate the number of sources, and the signal is decomposed into SVD. Finally, the updated grid division is combined with the SVD decomposition results, and the DOA is fine estimated using Root SBL. Simulation results show that this algorithm has low computational complexity and high estimation performance. Keywords: Sparse reconstruction · DOA estimate · Dynamic mesh generation

1 Introduction In recent years, countries have carried out a major layout of time-space service system. 5G time-space service construction has key requirements such as high coverage, high reliability, high positioning accuracy, and high security. When the positioning environment is faced with deception jamming or single base station positioning, only time difference of arrival (TDOA) cannot be used to achieve high-precision position estimation [1]. Direction of arrival (DOA) measurement is an important research direction in signal source integrity assurance, and has an important application in high-precision space-time network construction. At present, with the development of millimeter wave technology and the increasingly complex electromagnetic environment, the traditional subspace based direction of arrival (DOA) estimation technology [2, 3] has poor performance in small beat, low signal-to-noise ratio, correlation signal detection and other © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 358–367, 2024. https://doi.org/10.1007/978-981-99-6928-9_31

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aspects. After the emergence of compressed sensing theory [4, 5], scholars introduced sparse reconstruction theory into DOA estimation and proposed many algorithms with good performance. Reference [6] proposed a l1 norm reconstruction algorithm based on SVD decomposition, which can be directly used for DOA estimation of single snapshot signal, and has good estimation performance in the case of signal correlation. Although l1 norm is used to relax the l0 norm problem, solving this kind of convex optimization problems inevitably faces the problem of computational complexity. Then the SBL algorithm [7] was introduced from the field of machine learning to the field of sparse signal recovery [8, 9]. Reference [9] proposed a correlation vector machine based DOA estimation algorithm (RVM-DOA), which has better global convergence than the l1 norm sparse reconstruction method. SBL algorithm is to divide the airspace into equal intervals and estimate the angle of arrival. Because of the contradiction between the discontinuity and finiteness of interval division and the infinity and continuity of the direction of arrival of signal, the problem of off grid error is inevitable. If the spatial grid is divided more closely, it will not meet the RIP criteria [10] and increase the computational load. Reference [11] proposed an off grid DOA estimation algorithm (OGSBL), which uses Taylor interpolation approximation to reduce the off grid error. Although this algorithm uses SVD decomposition, the calculation is still complex. Reference [12] improved the OGSBL algorithm by using a linear interpolation algorithm to estimate the off grid error, which has a lower computational complexity than OGSBL in the case of large snapshots. Reference [13] proposed the Root SBL DOA estimation algorithm for dynamic grids, which uses the method of polynomial root to dynamically partition the space, greatly reducing the computational complexity. However, the discrimination of space adjacent signals is not high and depends on the initial grid division. Reference [14] proposed a DOA estimation method for near end splitting of grids (GEDOA), which aims to reduce the computational effort by non-uniform dividing the spatial grids of Taylor interpolation algorithm. However, this algorithm is greatly affected by the signal-to-noise ratio, and the estimation accuracy is still affected by the grid division. In this paper, a DOA estimation method based on non-uniform spatial grid division and dynamic solution is proposed. Firstly, the SBL algorithm is used to estimate the direction of arrival of the signal roughly, and the uneven space is divided according to the result of the rough estimation. According to the rough estimation results, the Root SBL is used to fine estimate the direction of arrival of the signal, and the number of sources and SVD decomposition are performed on the signal before the fine estimation to reduce the computational complexity and improve the estimation performance under low SNR.

2 System Model 2.1 Array Signal Receiving Model This paper assumes that the signal is a far field narrowband signal, and the signal acceptance model of the antenna array [15] is shown in Fig. 1.

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Fig. 1. Array signal receiving model

Assuming that K far-field narrowband signals are injected, the antenna array is a Uniform Liner Array (ULA) with M elements, and the element spacing is d = λ/2, λ is the wavelength of the signal carrier. At time t, k signals are incident at the angle of θ (θ1 , ..., θk ), and the signals received by the array are y(t) =

k 

am (θi )si (t) + n(t)

(1)

i=1

a(θk ) = [1, .., exp(−i2π fDsin(θk )/c)]T is the array steering vector, D is the wave path difference, s(ti ) = [s1 , ..., sk ]T is the incident signal vector. Expand to multi snapshot situation Y = AS + N

(2)

Y = [y(t1 ), ..., y(tl )]T , A = (a(θ1 ), ..., a(θk )), S = [s(t1 ), ..., s(tl )], N = (n(t1 ), ...n(tl )) are array output matrix, signal guidance matrix and signal noise matrix respectively. 2.2 DOA Estimation Model Based on Sparse Reconstruction Millimeter wave MIMO signals have significant sparsity in the angular domain, and can be estimated through sparse signal restoration. Based on this, the whole signal space [−90◦ , 90◦ ] is divided equally in the angle domain to generate N spatial grids θ = [θ1 , ..., θN ]. From this, we can get a super complete dictionary A¯ = [a(θ1 ), ..., a(θN )], Then Eq. (2) can be re expressed as Y = A¯ S¯ + N

(3)

where S¯ is a sparse signal represented by a super complete dictionary. For sparse Bayesian reconstruction signal model, Y is the observation data, A¯ is the observation matrix, S¯ is the sparse signal to be calculated, N is the Gaussian noise with mean value of 0 and variance of σ 2 . Introduction of super parameters γ = [γ1 , ..., γN ]T , assuming sparse signal S¯ ∼ N (0, )

(4)

N (0, ) represents the Gaussian distribution with mean value of 0 and variance of, where  = diag(γ ). It can be seen that the probability density of S¯ and the likelihood function of signal Y obey Gaussian distribution. ¯ ¯ ) = |π |−L exp(−tr(S¯ H  −1 S)) p(S|γ

(5)

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¯ σ ) = |π σ IM |−L exp(−σ Y − A¯ S ¯ 2F ) P(Y |S;

(6)

The posterior probability of signal S¯ can be known from Bayesian formula   ¯ ; γ , σ ) = π  ¯ −L exp(−tr[(S¯ − μ ¯ )H  −1 (S¯ − μ ¯ )]) p(S|Y S S S S¯

(7)

where μS¯ =  A¯ H X−1 Y

(8)

¯ S¯ =  −  A¯ H X−1 A

(9)

¯ A¯ H X = σ I + S

(10)

¯ where only the position corresponding to the μS¯ is the estimated value of signal S, direction of arrival of the signal has a significant non-zero value, then the reconstruction problem of sparse signal is converted into solving the maximum a posteriori probability ¯ of signal S.

3 DOA Estimation Process and Method 3.1 Super Parameter Update Iteration The super parameter γ and signal S¯ share the sparsity. Only when γ can well reflect the signal sparsity, the estimation result will be accurate. Therefore, it is necessary to update and iterate the super parameter γ to maximize the likelihood function of Y with respect to γ . p(Y |γ , σ ) = |π X |−N exp(−tr(Y H X−1 Y ))

(11)

Take the logarithm of Eq. (11) and omit the term irrelevant to γ . 

L(γ , σ ) = In(X ) + tr(X−1 R)

(12)



where R represents the covariance matrix of the array received signal. The estimation value of the super parameter can be obtained by solving the minimum value of Eq. (12). EM (Expectation Maximization) algorithm is used to update the super parameters. In the E-Step process, μS¯ and S¯ are obtained by maximizing the posterior probability of signal A, and the super parameters are updated iteratively in the M-Step process. In order to ensure the integrity of the method, σ is updated at the same time. The two super parameter iteration formulas are as follows 2

γni+1 = μiS¯ 2 /N + (Si¯ )(n,n) σ i+1 =

2 F

Y − AμiS¯  + σ (N −

N n=1

(13) ( i¯ )(n,n) S

γni+1

)

(14) M When the iteration result meets the set convergence condition, γ is the estimation result of signal power and μS¯ have the same sparsity. The DOA estimation result can be obtained by searching the spectral peak of the two parameters.

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3.2 Grid Iteration The space domain grid division interval is set to θ = 6◦ . Although the calculation amount is reduced due to the large grid division, there is a large off grid error. Therefore, the grid iteration process is added in the update process of super parameter γ to realize the non-uniform grid division, that is, only the grid where the source is located is finely divided. Usually, the spectral peak is composed of two consecutive significant nonzero spectral peaks, so K spectral peaks are selected and their adjacent spectral values are roughly estimated.   (q) (q) γk,1 γk,2   θk =  θ¯k +  θ¯k (15) (q) (q) (q) (q) γk,1 + γk,2 γk,1 + γk,2 

where, θ¯k and θ¯k are the left and right angle values of the kth spectral peak respectively, (q) (q) and the corresponding amplitudes are γk,1 and γk,2 respectively. The grid iteration is performed based on the rough estimation results of the above signal direction. If the rough estimation angle is less than the angle value corresponding to the spectral peak, add a new grid on the left side, otherwise add it on the right side, and set the angle of each grid iteration to R. θnew = angle(ii) ± R

(16)

R = R/step

(17)

where, angle (ii) is the initial division angle value corresponding to the spectral peak, and ii is the index of the corresponding spectral peak angle value. After a division of k spectral peaks, the iteration angle value R is updated. Step is a self setting parameter, which can be adjusted according to the needs. After the grid is updated, the super complete dictionaries A¯ and γ are required. Suppose that the new angle value generated by grid iteration is, the original angle value is θ1 (θlast ), and the corresponding γ isγ1 ,γ2 ,γlast . To ensure the consistency of Y prior probability of over signal. γ1 = γ2 = γlast /2

(18)

The grid update does not affect the noise prior, so can continue to use. The grid iteration termination setting is that the minimum interval between grids is less than the set value Rmin or the number of iterations N is greater than the set value Nmax. Reference [14] of this paper sets the maximum number of iterations as 2M-2. 3.3 DOA Fine Estimation The algorithm flow is shown in Table 1. In order to reduce the impact of noise on estimation performance, the received signal is decomposed into SVD before DOA fine

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estimation, i.e., Y = SVD. D = [D1 D2 ], D1 and D2 are the first K columns and the last T-K columns of D. According to the knowledge of the signal subspace, the first K columns store most of the information of the signal. If YSSV = YD1 , SSSV = SD1, NSSV = ND1 , we can get Yssv = ASssv + Nssv

(19)

SVD decomposition can not only reduce the noise to gain the estimation performance, but also reduce the computational complexity of the algorithm. The information before and after SVD decomposition is divided by K column, and K is the number of signal sources to be estimated. To ensure the accuracy of SVD decomposition, MDL criterion is introduced to estimate the number of signal sources. Finally, the Root SBL algorithm in reference [18] is used for solution. The Root SBL algorithm also regards the grid as a dynamic parameter, and updates the position of the angle through multiple root seeking, in order to reduce the off grid error. Table 1. Grid iteration algorithm process Input

¯ θ, Y, A,

Output

Signal doa estimation results and grid θ

1

initialization γ ,σ , θ,R Iteration number i, convergence threshold tol

2

for

3

update μS¯ and S¯

4

Update super parameters γ , σ

5

If N < Nmax ||R > Rmin

6

Screen spectral peaks and perform rough grid estimation (Formula 15)

7

Perform grid iteration (16) ¯ γ , R, N Update A,

8 9

Endif

10

MDL criterion for source number estimation

11

SVD decomposition of Y

12

DOA fine estimation using root SBL

4 Simulation Experiment and Result Analysis 4.1 Evaluation Criteria In this paper, the root mean square error generated by Monte Carlo experiment is used to evaluate the accuracy of DOA estimation. The number of experiments is 100. The incident signal is incoherent far-field narrowband signal. Simulating hardware and software configuration: The simulation is completed on a desktop computer with Core i5

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11 generation and 2.6 GHz main frequency, Windows 10 operating system. And the simulation tool is MATLAB R2021b.  2 1 p K   (20) RMSE = θ p,k − θk  P=1 k=1 KP 

where, K is the number of signal sources to be estimated, P is the number of Monte Carlo experiments, θp,k is the k-th signal estimation angle of the p-th experiment, and θk is the incidence angle of the k-th signal. Resolution success rate: assuming that there are K incident signals, the incidence angle  is θ = (θ1 , ..., θk ), and the estimated value is θ = (θ 1 , ..., θ k ), then   ∀i ∈ [1, K], θ i − θi  < 1◦ , it is considered that the estimation is successful. 







4.2 Simulation Experiment Influence of snr estimation performance ◦

◦

Setting of simulation experiment conditions: the incidence angle is [−22.8 , 15.4 ], the number of snapshots is 200, the number of array elements is 8, the initial grid interval ◦ is 6 , and the signal to noise ratio is SNR = [−16:4:12]. Analysis of experimental results: Fig. 2 shows that the proposed GRSBL has smaller root mean square error and higher estimation accuracy than GEDOA algorithm at the same signal-to-noise ratio. Here, it is found that the root mean square error is the smallest due to the SBL algorithm’s constraints on meshing and its robustness. However, in combination with Fig. 3, it can be found that although the root mean square error of SBL is small, the estimation accuracy is not high because of the outlier error, which is the same reason for OGSBL algorithm. From Fig. 3, GRSBL has a higher estimated success rate than GEDOA at low SNR. Figure 4 shows the running time of 100 Monte Carlo experiments. To ensure the same estimation accuracy, the grid interval of SBL and OGSBL algorithms is set to 1, while the rest are unchanged. From this diagram, the algorithm presented in this paper has the lowest computational complexity while guaranteeing the same estimation accuracy. Influence of snapshot number on estimation performance ◦

◦

Setting of simulation experiment conditions: the incidence angle is [−22.8 , 15.4 ], ◦ SNR is 5, the number of elements is 8, the initial grid interval is 6 , and the number of snapshots is T = [10:20:200]. Analysis of experimental results: From Fig. 5, we can see that the root mean square error of GRSBL proposed in this paper decreases sharply with the increase of the number of snapshots, while it is the smallest with the same number of snapshots and has higher estimation accuracy than GEDOA algorithm. From Fig. 6, the GRSBL algorithm has the highest estimated success rate with a small number of snapshots. Figure 7 shows the running time of 100 Monte Carlo experiments. Similarly, for contrast, the grid interval of SBL and OGSBL algorithms is set to 1, while the rest remain unchanged. It can be seen that the proposed algorithm has better estimation performance and lower computational complexity.

An Improved DOA Estimation Method Based on Sparse Reconstruction

Fig. 2. Relationship between signal to noise ratio and root mean square error

Fig. 3. Relationship between signal to noise ratio and resolution success rate

Fig. 4. Relationship between signal to noise ratio and running time

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Fig. 5. Relationship between snapshots and the root mean square error

Fig. 6. Relationship between snapshots and resolution success rate

Fig. 7. Relationship between snapshots and running time

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5 Conclusion In this paper, a sparse Bayesian DOA estimation algorithm improved by grid iteration is proposed and simulated. First, in order to reduce the complexity of the algorithm, the simplest SBL algorithm is used for grid iteration. The simulation shows that the algorithm reduces the running time compared with the original algorithm. Secondly, in order to ensure the estimation accuracy, SVD decomposition is used to reduce the impact of noise and Root SBL is used for fine estimation to reduce the outlier error, so that the signal has a high estimation accuracy in the low SNR environment.

References 1. Zhongliang Deng, L., Yin, S.T., Liu, Y., Song, W.: Overview of key indoor positioning technologies. Navig. Position. Timing 5(03), 14–23 (2018) 2. Schmidt, R.: Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3) (1986) 3. Roy, R., Kailath, T.: ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7) (1989) 4. Candès, E.J.: The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathématique 346(9) (2008) 5. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4) (2006) 6. Malioutov, D., Cetin, M., Willsky, A.S.: A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. A Publ. IEEE Signal Process. Soc. 53(8) (2005) 7. Tipping, M.E.: Sparse bayesian learning and the relevance vector machine. J. Mach. Learn. Res. 1 (2001) 8. Wipf, D.P., Rao, B.D.: Sparse bayesian learning for basis selection. IEEE Trans. Signal Process. 52(8) (2004) 9. Liu, Z.: Array Processing Theory and Method Based on Signal Spatial Sparsity. National University of Defense Science and Technology (2012) 10. Candès, E.J.: The restricted isometry property and its implications for compressed sensing. Comptes rendus -Mathématique 346(9) (2008) 11. Yang, Z., Xie, L., Zhang, C.: Off-grid direction of arrival estimation using sparse bayesian inference. IEEE Trans. Signal Process. 61(1) (2013) 12. Wu, X., Zhu, W.P., Yan, J.: Direction of arrival estimation for off-grid signals based on sparse bayesian learning. IEEE Sens. J. 16(7) (2016) 13. Jisheng, D., Xu, B., Weichao, X., Chunqi, C.: Root sparse bayesian learning for off-grid DOA estimation. IEEE Signal Process. Lett. 24(1) (2017) 14. Qianli, W., Zhiqin, Z., Zhuming, C., Zaiping, N.: Grid evolution method for DOA estimation. IEEE Trans. Signal Process. 66(9) (2018) 15. Wang, Y., Hui, C., Yingning, P.: Spatial spectrum estimation theory and algorithm. Tsinghua University Press, Beijing (2004)

A Joint Adjustment Method for Precise GNSS/Acoustic Underwater Positioning Based on Single-Differenced Observations Zhen Sun, Zhenjie Wang(B) , and Zhixi Nie College of Oceanography and Space Informatics, China University of Petroleum (East China), Qingdao 266580, China [email protected]

Abstract. Global navigation satellite system/acoustic (GNSS/A) underwater positioning technique is widely used in the fields of marine scientific research and engineering applications. The conventional single-differenced (SD) positioning method generally treats the position of acoustic transducer obtained by GNSS positioning as known without error. However, error inevitably exists in the estimation of the transducer’s position determined by GNSS positioning, and the precision varies at different epochs. Ignoring the errors of acoustic transducer coordinates will lead to a worse estimation of the position of seafloor transponder. In this contribution, a joint adjustment method for precise GNSS/A underwater positioning is presented based on single-differenced observations. The positions of both transducer and transponder are treated as unknown parameters, and the positions of acoustic transducer are considered as virtual observations. The Helmert variance component estimation is used to adjust the weight ratio of two heterogeneous observations. To verify the performance of the proposed method, two field experiments were carried out. The lake experiment results show that the positioning accuracy with the proposed method can be improved by approximately 49% compared with the SD positioning method. The sea experiment results further demonstrate that the proposed method can perform much better than the SD positioning method, with the standard deviation values of coordinate components better than 0.06 m and the root mean square errors of the acoustic ranging residuals better than 0.02 m. Keywords: GNSS/A · Single-differenced positioning method · Joint adjustment method · Equivalent transformation

1 Introduction Global navigation satellite system/acoustic (GNSS/A) underwater positioning technique was first developed by the Scripps Institute of Oceanography, USA [1, 2]. It can accurately estimate the position of seafloor transponder by combining GNSS positioning of a sea surface observation platform with a set of acoustic ranging to seafloor transponder [3, 4]. Over the past years, this technique opens the door to bridge its ocean coverage © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 368–379, 2024. https://doi.org/10.1007/978-981-99-6928-9_32

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gap of the global reference frame (ITRF), and has produced a steady series of successful geodetic observations in seafloor deformation monitoring [5], seismic deformation acquisition [6], and plate movement measuring [7, 8]. GNSS/A underwater positioning is usually carried out by a research vessel sailing around a seafloor transponder. The position of acoustic transducer is obtained by using the relative relationship between GNSS antenna and acoustic transducer [9], while the position of GNSS antenna is provided by GNSS positioning [10]. The onboard transducer continuously broadcasts sound signals at a certain frequency to transponder and records the time of arrival while receiving the seafloor transponder’s feedback signal. The propagation time is transformed into acoustic ranging according to the ray-tracing method with a sound velocity structure obtained by sound velocity profilers [11]. Based on acoustic ranging measurements between acoustic transducer and seafloor transponder, the position of seafloor transponder is obtained by undifferenced positioning models [12]. However, the precision of seafloor transponder is significantly drop due to the influence of system errors including both hardware delay error and sound velocity error in acoustic ranging. To eliminate the effect of systematic errors, an underwater differenced positioning method was proposed [13]. Yang alerts that this positioning method may lose some positioning information in upward direction, resulting in a worse estimation in upward direction [14]. For minimize the influence of positioning information loss in upward direction, a mixed positioning model with differenced and undifferenced observations was developed [15]. Furthermore, Xue proved the differenced model is equivalent to the undifferenced model with a bias nuisance parameter, and proposed a dimension reduction algorithm to fast solve the Gauss–Markov model augmented with nuisance parameters [16]. The problem is that the conventional single differenced positioning methods treat the position of acoustic transducer obtained by GNSS positioning as known without error. However, there inevitably exists error in the estimation of transducer’s position determined by GNSS positioning, and the precision varies at different epochs. Such negligence will lead to a worse estimation of the position of seafloor transponder. In this contribution, a joint adjustment method is presented based on singledifferenced observations, in which the positions of both transducer and transponder are considered as parameters to be estimated, and the positions of acoustic transducer are treated as virtual observations. The paper is organized as follows. In Sect. 2, the conventional single-differenced positioning method is briefly introduced. In Sect. 3, the joint adjustment method is presented based on single-differenced observations. In Sect. 4, two field experiments are used to assess the performance of the proposed method. Finally, conclusions are drawn in the last section.

2 Introduction The schematic diagram of GNSS/A underwater single-differenced positioning method is shown in Fig. 1. Given that the position of acoustic transducer at two adjacent epochs are taken consecutively and are sufficiently close in space and time, then it is reasonable to assume that two acoustic rays between acoustic transducer and seafloor transponder go through the similar sound velocity structure. Consequence, the long period errors,

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Fig. 1. Schematic diagram of GNSS/A single-differenced positioning

due to the ocean tide, can be eliminated. Since acoustic ranging measurements of two adjacent epochs are taken on the same transponder, the influence of time delays in re-transmitting the signals back to acoustic transducer can be also reduced. Assuming that the acoustic ranging observations are ρ si at time ti and ρ si+1 attimeti+1 , the singledifferenced observation equation read as     ρi+1 − ρi = f xsi+1 , xr − f xsi , xr + εi+1,i (1)  s r where i = 1, 2, 3, . . . , n−1 is the observation sampling epoch; f xi , x is the  geometric  distance between acoustic transducer and seafloor transponder at time ti ; f xsi+1 , xr is the geometric distance between acoustic transducer and seafloor transponder at time ti+1 ; xsi = [xis , yis , zis ]T represents the coordinate vector of acoustic transduce at time ti ; s , y s , z s ]T represents the coordinate vector of acoustic transduce at time xsi+1 = [xi+1 i+1 i+1 r ti+1 ; x = [xr , yr , z r ] denotes the coordinate vector of seafloor transponder; and εi+1,i represents the measurement error. Ignoring the errors of acoustic transducer position, Eq. (1) is linearized as     ρi+1 − ρi − f xsi+1 , xr0 + f xsi , xr0 = ai+1,i dxr + εi+1,i (2)  where ai+1,i =

s x0r −xi+1   s f xi+1 ,xr0

−

s x0r −xis y0r −yi+1   f (xsi ,xr0 ) f xsi+1 ,xr0

−

s y0r −yis z0r −zi+1   f (xsi ,xr0 ) f xsi+1 ,xr0

−

z0r −zis f (xsi ,xr0 )

T ; and

xr0 = [x0r , y0r , z0r ]T is the initial position vector of seafloor transponder. With n observations to estimate the coordinates of the seafloor transponder, the linearized observation equations can be expressed as L = Adxr + ε

(3)

where dxr = [dxr , dyr , dz r ]T is the coordinate correction vector of seafloor transponder; L is the observed-minus-computed residual vector with a length of n − 1; ε is the error

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vector; and A is the design matrix with a size of (n − 1) × 3, namely, ⎡ (xr −xs ) ⎤ (x0r −x1s ) (y0r −y1s ) (z0r −z1s ) (y0r −y2s ) (z0r −z2s ) 0 2 f (x2s ,x0r ) − f (x1s ,x0r ) f (x2s ,x0r ) − f (x1s ,x0r ) f (x2s ,x0r ) − f (x1s ,x0r ) ⎢ (xr −xs ) (xr −xs ) ⎥ (y0r −y2s ) (z0r −z2s ) ⎥ (y0r −y3s ) (z0r −z3s ) ⎢ 0 3 0 2 ⎢ f (x3s ,x0r ) − f (xis ,x0r ) f (x3s ,x0r ) − f (x2s ,x0r ) f (x3s ,x0r ) − f (x2s ,x0r ) ⎥ ⎥ A=⎢ .. .. .. ⎢ ⎥ ⎢ ⎥ . . . ⎣ r s ⎦ r s r s r s (x0 −x(n−1) ) (y0r −yns ) (y0 −y(n−1) ) (z0r −zns ) (z0 −z(n−1) ) (x0 −xn ) − − − r s r r s r r s r s s s f (x ,x ) f (x ,x ) f (x ,x ) f (x ,x ) f (x ,x ) f (x ,x ) n

0

(n−1)

n

0

0

(n−1)

0

n

0

(n−1)

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(4)

0

Based on the least square adjustment method, the coordinate correction vector of seafloor transponder is estimated

−1 dxr = AT PA AT PL

(5)

where P = CT PL C is the weight of single-differenced observations; P L is the weight of acoustic ranging measurements, which can be determined by acoustic incident angle; and C is single-differenced operator with a size of (n − 1) × n, namely ⎤ −1 1 ⎥ ⎢ −1 1 ⎥ ⎢ C=⎢ .. .. ⎥ ⎣ . . ⎦ −1 1 ⎡

(6)

The estimated coordinates of seafloor transponder are calculated as follows: xr = xr0 + dxr



(7)

The conventional single-differenced positioning method generally treats the position of acoustic transducer obtained by GNSS positioning as known without error. However, error inevitably exists in the estimation of acoustic transducer’s position determined by GNSS positioning, and the precision varies at different epochs. Ignoring the errors of acoustic transducer coordinates will reduce the precision of seafloor transponder positioning.

3 Joint Adjustment Method Based on Differenced Observations 3.1 Positioning Model To reduce the effect of acoustic transducers’ coordinate errors on underwater positioning, a joint adjustment method for GNSS/A underwater precise positioning is presented based on single-differenced observations. Treating the positions of both acoustic transducer and seafloor transponder as unknown parameters in the acoustic ranging equation, the single-differenced observation equation is linearized as Li+1,i = bi+1 dxsi+1 − bi dxsi − ai+1,i dxr + εi+1,i

(8)

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 where bi+1 =

xs −xr −yr −z r ys zs

i+1,0 0  i+1,0 0  i+1,0 0  f xsi+1,0 ,xr0 f xsi+1,0 ,xr0 f xsi+1,0 ,xr0



ranging measurement at time ti+1 ; bi =

T is the linearized matrix of acoustic

xs −xr ys −yr z s −z r

i,0 0  i,0 0  i,0 0  f xsi,0 ,xr0 f xsi,0 ,xr0 f xsi,0 ,xr0

T is the linearized

s s s matrix of acoustic ranging measurement at time ti ; xsi+1,0 = [xi+1,0 , yi+1,0 , zi+1,0 ]T is s , y s , z s ]T is the initial position vector of acoustic transducer at time ti+1 ; xsi,0 = [xi,0 i,0 i,0 the initial position vector of acoustic transducer at time ti ; and εi+1,i is the measurement error. With n observations used to estimate the coordinates of seafloor transponder, the linearized observation equations are re-expressed as

L = Bdxs − Adxr + ε

(9)

where dxs = [dxs1 , dxs2 , · · · dxsn ]T is the coordinate correction vector of acoustic transducer; and B is the design matrix with a size of (n − 1) × 3n, namely, ⎤ ⎡ −b1 b2 ⎥ ⎢ −b2 b3 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ (10) B=⎢ ⎥ ⎥ ⎢ −bi bi+1 ⎥ ⎢ ⎦ ⎣ −bn−1 bn The acoustic transducer’s positions determined by GNSS positioning at different epochs can be introduced into virtual observations Lxs = Hdxs + ε xs

(11)

where Lxs is the virtual observation vector with a length of 3n; H is a block diagonal matrix with a size of 3n × 3n; H = blkdiag(E, E, . . . , E); E is an identity matrix with a size of 3 × 3; and εxs is the error vector. According to Eqs. (9) and (11), the equation system of the joint adjustment method based on single-differenced observations is expressed as  L = Bdxs + Adxr + ε (12) Lxs = Hdxs + ε xs Based on the least-square method, the following equations can be obtained   T B PB + H T P xs H dxs + BT PAdxr = BT PL + H T P xs Lxs AT PBdxs + AT PAdxr = AT PL

(13)

where P xs is the weight matrix of virtual observations, which is provided by GNSS positioning techniques. According to Eq. (13), both acoustic transducer and seafloor transponder coordinate corrections can be obtained according to the least-square method. However, when

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the positions of acoustic transducer as unknown parameters are estimated, it obviously enlarges the dimensions of the normal matrix, and requires a lot of computing resources. Assuming that with 500 observations to estimate the coordinates of seafloor transponder, the inverse of the normal matrix with a size of 1500 × 1500 is a computeintensive task that requires extensive calculations. Thus, an equivalent transformation is applied to normal equation to solve the problem of excessive calculation caused by too many parameters to be estimated. The first equation of Eq. (13) multiplied by M = −AT P 1 B(BT P 1 B + H T P xs H)−1 is added to the second equation of Eq. (13), we obtain

 AT PA + MBT PA dxr = AT PL + MBT PL + MH T P xs Lxs (14) Subsequently, the coordinate correction vector of seafloor transponder is estimated dxr = (AT PA + MBT PA)−1 (AT PL + MBT PL + MH T P xs Lxs )

(15)

Combing Eq. (15) with Eq. (7), we can obtain the estimated coordinates of seafloor transponder. 3.2 Stochastic Model The virtual observations and single-differenced observations are heterogeneous observations with different observation qualities and variance scales. Therefore, the Helmert variance component estimation is used to adjust the weight ratio of two heterogeneous observations. According to Eqs. (9) and (11), the equation system of the joint adjustment method based on single-differenced observations is expressed as  V = Bdxs + Adxr − L (16) V xs = Hdxs + 0dxr − Lxs where V xs is the residual vector of virtual observations; and V is the residual vector of acoustic ranging measurements. Then the corresponding Helmert type of variance component estimator is like ⎡

⎤



2      −1 N −1 N −1 N N −1 N n − 2tr N tr N + tr N 1 1 1 1 2 VT ⎢ ⎥ σˆ 12 s P xs V xs x

 

2 ⎦ 2 = ⎣ σˆ 2 V T PV tr N −1 N 1 N −1 N 2 n2 − 2tr N −1 N 2 + tr N −1 N 2

(17) where n1 = 3n; n2 = 3n − 3   T  H T P xs H 0 A PA AT PB N1 = ; ; N2 = 0 0 BT PA BT PB   T H P xs H + AT PA AT PB N= BT PB BT PA 

After solving variance component estimates of two heterogeneous observations, we re-estimate the coordinates of seafloor transponder in the same way as listed in Positioning model section.

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4 Results and Analysis In this section, field test data obtained from the Songhua Lake and South-Sea Experiment were applied to verify the validity of the proposed method. 4.1 Field Test in Songhua Lake The real data obtained from a lake trial carried out by Songhua Lake were processed to assess the precision of the proposed method. The scientific research vessel was equipped with a Kongsberg Simrad EM3000 multibeam system, Leica GNSS-1200 receivers, a Seatex MRU-05 motion reference unit, an AML sound speed, and a pressure transducer. The pressure transducer was fixed on seafloor transponder, and its precision was better than ±0.1% of depth. As shown in Fig. 2a, the terrain of the lake bed was measured by the multiband system. The average depth in the experimental area is 60 m. The sound velocity structure was obtained by the sound velocity profiler, and its accuracy was better than 0.1 m/s, as shown in Fig. 2b. The surface sound velocity was 1465.34 m/s. The stratified constant-gradient ray-tracing method was applied. Single transponder named C06 was placed in the lake bed.

Fig. 2. Topographic map of the lake bottom (left) and sound velocity profile (right)

The conventional single-differenced (SD) positioning method and the joint adjustment method based on single-differenced observations (SD-JA) were used to carry out seafloor transponder positioning. The positioning results with two methods are presented in Table 1. The standard deviation (STD) values of coordinate components with the SD method are on average 0.0215 m, 0.0325 m, and 0.4684 m in three directions, while the JA method has an STD of 0.0109 m, 0.0109 m, and 0.0052 m. It means the accuracy of seafloor transponder positioning with the conventional single-differenced positioning method is lower than that based on the SD-JA method. High-precision depth inverted by pressure gauge measurements is used as reference values to evaluate the performance of the proposed method. The positioning errors in the up direction with the SD-JA method is 0.0566 m. The accuracy of seafloor transponder positioning with the proposed method is on average improved by approximately 49% compared with the single-differenced (SD) positioning method. The acoustic-ranging residual and its corresponding distributions of the data set obtained by two positioning methods are shown in Fig. 4. Residual histogram features

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Table 1. Positioning coordinates and its positioning errors (unit: m) Method

Positioning coordinates

Bias_Up

East

North

Up

SD

315787.1018

4841969.9373

−60.6490

SD-JA

315787.1223

4841969.8593

−60.5926

STD East

North

Up

0.1130

0.0215

0.0325

0.4684

0.0566

0.0172

0.0153

0.2072

show that the probability densities of acoustic-ranging residuals with two methods are subordinate to normal distribution. The acoustic-ranging residuals in the SD-JA method are more concentrated than that based on the SD positioning method. The root mean square (RMS) values of acoustic-ranging residuals in two method are calculated to assess the precision of seafloor transponder positioning. The RMS value of acoustic-ranging residuals with the SD-JA method is 0.0475 m, while the SD method performs an RMS of 0.0553 m. This test indicates that a more stable positioning performance can be obtained with the proposed method (Fig. 3).

Fig. 3. The acoustic-ranging residual and its corresponding distributions of the data set obtained by two positioning methods. Blue and red bars present the single-differenced positioning method and the joint adjustment method based on single-differenced observations respectively.

4.2 Field Test in Songhua Lake An experiential trial performed in the South China Sea was used to verify the performance of the proposed method. The length of the science research vessel named “No. 18 Xiang Yang Hong” is 86.4 m, as shown in Fig. 4A. The onboard equipment including a GNSS antenna and a motion sensor was attached to the top of the pole, and an acoustic transducer was attached to the bottom of the pole. The transponder fixed by a shelter was placed on the seafloor, as shown in Fig. 4B. The seafloor transponder located at about 3000 m was measured by GNSS/A technique, and one cross-tracking line was laid out, as shown in Fig. 4C. The position of GNSS antenna was obtained by precise point positioning technique. The motion sensor of the MRU5 device from Kongsberg company was

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adopted to measure real-time attitude change of the science research vessel. It can provide documented roll and pitch precision of 0.02° RMS at a ±5° amplitude. The acoustic transducer installed at the port side of the vessel continuously broadcasted an acoustic signal to seafloor transponder and recorded the acoustic time of arrival while receiving seafloor transponder’s feedback signal. The sound velocity structure was obtained by the sound velocity profiler, and its accuracy is better than 0.025 m/s, as shown in Fig. 4D. The surface sound velocity was 1544.18 m/s. The stratified constant-gradient ray-tracing method was applied.

Fig. 4. The real data collected from a sea trial carried out in the South China Sea. The English alphabets of A, B, C and D represent science Research Vessel “No.18 Xiang Yang Hong, placement of transponder, the cross-tracking line, and the sound velocity profile.

Both the conventional single-differenced positioning method and the joint adjustment method based on single-differenced observations were used to carry out seafloor transponder positioning, and their positioning results are presented in Table 2. The standard deviation values of coordinate components in three directions with the SD method are invariably higher than those in the SD-JA method. It means that the accuracy of seafloor transponder positioning with the SD method is lower than that of the SD-JA method due to the influence of acoustic transducers’ coordinate various errors. The SD-JA method can stably and accurately estimate the position of seafloor transponder. The differences of N/E/U coordinate components between the SD method and SD-JA method are 0.0118 m, 0.0462 m, and 0.1046 m respectively. The square roots of the sum of variances in three directions with the SD-JA method is 0.0596 m, and improved

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by 0.1076 m compared with the conventional single-differenced positioning method. It indicates that a more stable positioning performance can be obtained with the proposed method. Table 2. Positioning coordinates and it’s precision (unit: m) Method

Positioning coordinates

Bias_Up

East

North

Up

SD

−153.4931

−148.0548

−3065.4197

SD-JA

−153.5049

−148.1010

−3065.5243

STD East

North

Up

0.0419

0.0443

0.1556

0.0419

0.0150

0.0157

0.0555

0.0150

To further investigate the performance of the proposed method, the residual comparison diagram and histogram of acoustic-ranging residual after adjustment are presented in Fig. 5. Residual histogram features show that the probability densities of acoustic-ranging residuals in two methods are subordinate to normal distribution. The acoustic-ranging residuals in the SD-JA method are more concentrated than that based on the single-differenced positioning method. The RMS of the acoustic-ranging residuals based on the SD-JA method is 0.0106 m, while the single-differenced positioning method performs an RMS of 0.0682 m. This test demonstrates the performance of the proposed method in seafloor transponder positioning.

Fig. 5. Acoustic-ranging residuals and its corresponding distributions of the data set obtained by two positioning methods. Blue and red bars present the single-differenced positioning method and the joint adjustment method based on single-differenced observations respectively.

5 Conclusions To improve the accuracy of seafloor transponder positioning based on the GNSS/A underwater positioning technique, a joint adjustment method for precise GNSS/A positioning is proposed based on single-differenced observations. The following conclusions are summarized:

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(1) The conventional single-differenced positioning method treats the coordinates of acoustic transducer obtained by GNSS positioning technique as known without error. However, there inevitably exists bias in the estimation of transducer’s position provided by GNSS positioning, and the precision varies at different epochs. Ignoring the errors of acoustic transducer’s coordinates will lead to a worse estimation of seafloor transponder’s position. (2) To improve the precision of seafloor transponder positioning, we propose a joint adjustment method based on single-differenced observations, in which the positions of both transducer and transponder are treated as unknown parameters, and the positions of the transducer are considered as virtual observations. Two field tests were carried out. The conventional single-differenced positioning method is likewise applied as a comparison. The accuracy of seafloor transponder positioning with the proposed is much better than that of the conventional single-differenced positioning method. The acoustic-ranging residuals in the proposed method are more concentrated than that in the conventional single-differenced positioning method for real data. Acknowledgments. This study was supported by the National Nature Science Foundation of China (No.42174020); Financially supported by Laoshan Laboratory (No.LSKJ202205101); Shandong Natural Science Foundation Project (ZR2021MD031).

References 1. Spiess, F.N.: Suboceanic geodetic measurements. IEEE Trans. Geosci. Remote Sens. GE23(4), 502–510 (1985). https://doi.org/10.1109/TGRS.1985.289441 2. Spiess, F.N., Chadwell, C.D., Hildebrand, J.A., et al.: Precise GPS/acoustic positioning of seafloor reference points for tectonic studies. Phys. Earth Planet. Inter. 108(2), 101–112 (1998). https://doi.org/10.1016/S0031-9201(98)00089-2 3. Fujita, M., Ishikawa, T., Mochizuki, M., et al.: GPS/acoustic seafloor geodetic observation: method of data analysis and its application. Earth Planets Space 58, 265–275 (2006). https:// doi.org/10.1186/BF03351923 4. Yang, Y., Qin, X.: Resilient observation models for seafloor geodetic positioning. J. Geodesy 95(7), 1–13 (2021). https://doi.org/10.1007/s00190-021-01531-7 5. Yamada, T., Ando, M., Keiichi., et al.: Error evaluation in acoustic positioning of a single transponder for seafloor crustal deformation measurements. Earth Planets Space 54(9), 871– 881 (2002). https://doi.org/10.1186/BF03352435 6. Kato, T., Terada, Y., Ito, K., et al.: Tsunami due to the 2004 September 5th off the Kii peninsula earthquake, Japan, recorded by a new GPS buoy. Earth Planets Space 57(4), 297–301 (2005). https://doi.org/10.1186/BF03352566 7. Watanabe, SI., Sato, M., Sata, Mariko., et al.: Evidence of viscoelastic deformation following the 2011 Tohoku-Oki earthquake was revealed from seafloor geodetic observation. Geophys. Res. Lett. 41, 5789–5796 (2014). https://doi.org/10.1002/2014GL 061134 8. Petersen, F., Kopp, H., Lange, D., et al.: Measuring tectonic seafloor deformation and strainbuild up with acoustic direct-path ranging. J. Geodyn. 124, 14–24 (2019). https://doi.org/10. 1016/j.jog.2019.01.002

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9. Chen, G., Liu, Y., Liu, X., et al.: Adjustment of transducer lever arm offset and sound speed bias for GNSS-acoustic positioning. Remote Sens. 11(13), 16000000000000006 (2019). https:// doi.org/10.3390/rs11131606 10. Nie, Z., Wang, B., Wang, Z., et al.: An offshore real-time precise point positioning technique based on a single set of BeiDou short-message communication devices. J. Geodesy 94, 78 (2020). https://doi.org/10.1007/s00190-020-01411-6 11. Chadwell, C.D., Sweeney, A.D.: Acoustic ray-trace equations for seafloor geodesy. Mar. Geodesy 33, 164–186 (2010). https://doi.org/10.1080/01490419.2010.492283 12. Sakic, P., Ballu, V., Royer, J., et al.: A multi-obsServation least-squares inversion for GNSSacoustic seafloor positioning. Remote Sens. 12, 1–19 (2020). https://doi.org/10.3390/rs1203 0448 13. Xu, P., Ando, M., Tadokoro, K., et al.: Precise three-dimensional seafloor geodetic deformation measurements using different techniques. Earth Planets Space 57(9), 795–808 (2005). https:// doi.org/10.1186/BF03351859 14. Yang, Y., Xu, T., Xue, S., et al.: Progresses and prospects in developing marine geodetic datum and marine navigation of China. Acta. Geod. Cartogr. Sin. 46, 1–8 (2017). https://doi. org/10.11947/j.AGCS.2017.20160519 15. Chen, G., Liu, Y., Liu, X., et al.: Improving GNSS-acoustic positioning by optimizing the ship’s track lines and observation combinations. J. Geodesy 94(6) (2020). https://doi.org/10. 1007/s00190-020-01389-1 16. Xue, S., Yang, Y., Yang, W.: Single-differenced models for GNSS-acoustic seafloor point positioning. J. Geodesy 96, 38 (2022). https://doi.org/10.1007/s00190-022-01613-0

A Doppler Frequency Shift Abrupt Processing Method for High-Speed Train Localization in Long Tunnel Scenarios Chengyang Huang(B) , Lu Yin, Zhongliang Deng, and Shinan Li Beijing University of Posts and Telecommunications, Beijing 100876, China [email protected]

Abstract. In recent years, it is of great significance to construct a high-precision positioning scheme for intelligent transportation in non-exposed space for allairspace spatiotemporal network to obtain continuous and accurate position information of high-speed trains. Due to the narrow tunnel environment, when the train quickly passes through the positioning base station (BS), serious Doppler frequency shift mutation will occur, which reduces the tracking accuracy and robustness of the carrier ring and seriously affects the positioning accuracy of the train. Therefore, an adaptive tracking loop based on feedback local error search structure (ATLBOFLESS) is designed. The simulation results show that the proposed method can effectively reduce the influence of Doppler shift mutation on the tracking accuracy and robustness of the carrier loop. Keywords: Tracking loop · Tunnel · High-speed trains · Local error search · Doppler shift mutation

1 Introduction With the rapid development of global digitalization, spatiotemporal information, positioning and navigation services have become important new infrastructures. The construction of spatiotemporal networks for all-airspace is applied to various high-precision industry scenarios such as smart transportation and smart factories [1]. At present, highspeed trains can achieve high-precision positioning outdoors through the Beidou navigation system [2], but in the long tunnel scenario, due to factors such as signal occlusion, trains usually use BS positioning to achieve high-precision positioning. Due to the narrow environment, the height of the BS layout is limited when using the BS positioning. Due to the small vertical distance between the BS and the train, the Doppler frequency shift between the train receiver and the passing BS will undergo a huge sudden change, which seriously affects the positioning accuracy of the high-speed train in the long tunnel scene, when the train passes the BS at high speed [3]. Therefore, the Doppler frequency shift mutation problem needs to be solved to improve the accuracy and stability of the positioning of the high-speed train in the long tunnel scenario. This paper mainly studies the processing method of Doppler frequency shift mutation phenomenon in the long tunnel scene. The train and the fixed BS usually maintain relative © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 380–390, 2024. https://doi.org/10.1007/978-981-99-6928-9_33

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motion, which leads to the Doppler effect. Due to the Doppler effect, the BS data received by the receiver usually has Doppler frequency deviation rather than the real transmitted data of the BS, which results in the carrier phase measurement value is not equal to the geometric distance between the receiver and the BS [3]. In order to reduce the influence of Doppler shift on positioning accuracy, the receiver usually adopts a tracking loop to obtain the exact value of Doppler shift. In tunnel scenarios, Doppler shift changes rapidly from positive to negative when the high-speed train passes the BS. For the traditional tracking loop with second-order frequency locking loop (FLL) assisted by third-order phase locking loop (PLL), the positive and negative mutations of Doppler frequency shift values in a short period of time lead to the surge of carrier tracking frequency errors and phase errors and even the loop lock-loss [4], which affects the measured value of carrier phase and reduces the accuracy of train positioning. In response to the above problems, algorithms such as Kalman filtering (KF) can usually be used to improve the tolerance of traditional tracking loops to high Doppler frequency shift rates [5]. However, the tracking error of the tracking loop based on Kalman filter is higher than that of the traditional tracking loop for the carrier frequency and carrier phase in the case of nonDoppler frequency shift abrupt change, and it will greatly increase the computational complexity of the entire loop. This paper proposes an adaptive tracking loop based on the feedback local error search structure. The error of the real-time position information of the receiver is reduced through the local error search structure, and it is accurately judged whether a Doppler frequency shift mutation occurs, thereby adaptively adjusting the type of the loop filter. Simulation results show that the proposed method can accurately predict the location of Doppler shift mutation and effectively reduce the influence of Doppler shift mutation on the tracking accuracy and robustness of carrier loop.

2 Train Doppler Shift For the fixed BS, the Doppler shift fd generated by the relative motion between the train receiver and the BS is as follows: v v fd = cosβ = fcosβ (1) λ c Among them, f is the transmission frequency of the BS signal, λ is the wavelength corresponding to f , v is the speed of the train, c is the speed of light, β is the incident Angle of the signal, representing the Angle between the movement direction of the receiver and the incident direction of the signal. In the train motion model accelerating uniformly with a straight track, the Doppler shift between the train and the fixed BS is shown in Fig. 1. When the receiver moves towards the fixed BS, the absolute value of the signal incident Angle β is less than 90°, and the Doppler shift fd is greater than 0 Hz. When the train motion direction is perpendicular to the signal incident direction, the Doppler shift fd is equal to 0 Hz. When the receiver moves away from the fixed BS, the absolute value of the signal incident Angle β is greater than 90°, then the Doppler shift fd is less than 0 Hz [6]. The time experienced by the Doppler shift mutation becomes smaller with the increase of train speed, and the change rate of Doppler shift becomes larger. The tracking error of traditional tracking loop increases and even loses lock, as shown in Table 1.

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Fig. 1. Doppler frequency shift diagram between train and fixed BS.

Table 1. Duration and effect of Doppler shift mutation. Horizontal position of BS (m)

Train speed when crossing BS (km/h)

Time of frequency shift mutation (ms)

Maximum error Influential time of carrier tracking of frequency shift results (Hz) mutation (ms)

0

0

\

\

0

100

84.6

700

71.17

515

200

120

600

143.22

845

300

147

520

215.10

817

400

169

450

Loss of lock

Loss of lock

500

190

400

Loss of lock

Loss of lock

3 Adaptive Tracking Loop Based on Feedback Local Error Search Structure The schematic of ATLBOFLESS is shown in Fig. 2:

Fig. 2. Schematic of the ATLBOFLESS

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3.1 Feedback Local Error Search Structure The feedback local error search structure mainly consists of positioning information feedback structure and local error search structure, as shown in Fig. 3.

Fig. 3. Feedback local error search structure

The function of the positioning information feedback structure is to feed the real-time positioning information of the receiver back to the tracking loop. In BS positioning, the position of BS is usually fixed coordinates. The train can obtain the position coordinates of each BS in advance through the communication signal. By comparing the real-time positioning coordinates of the receiver with the coordinates of the nearest BS in the direction of the train, the positioning information feedback structure predicts the position of the Doppler frequency mutation, so as to determine whether the tracking loop needs to be adjusted. The function of the local error search structure is to reduce the influence of receiver positioning error on the prediction of Doppler shift mutation. Due to the signal propagation environment and receiver error, the train positioning results usually have errors. When the positioning result is ahead of the true value, the error may cause the receiver to advance the predicted position of Doppler frequency mutation, causing the tracking loop to process the Doppler frequency mutation prematurely without processing the real Doppler frequency mutation. When the positioning result lags behind the true value, the error may cause the receiver to delay the predicted position of Doppler frequency mutation, resulting in the tracking loop not processing the real Doppler frequency mutation.

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At the k epoch time, the receiver will feedback the positioning result Xk0 of the positioning information feedback structure to the local error search module. The local search module takes Xk0 as the center and divides it according to the error search interval x, as follows:   (2) Xi, k = Xk0 + −Mopen , · · · , 0, · · · , Mopen x Among them, i represents the location of the positioning information, x represents the search interval of the positioning information, and Mopen determines the refined search range. Each error search unit Xi, k generate the corresponding carrier phase difference according to the relation between carrier phase difference and distance φ = λ−1 r + N . Thus, corresponding local replication signals SI (n) and SQ (n) are generated:   (3) SI (n) = clocal (n − τ)cos ωi, k nTs + ϕk0   SQ (n) = clocal (n − τ)sin ωi, k nTs + ϕk0

(4)

Among them, ϕk0 represents the initial value of carrier phase, ωi, k is the carrier angular frequency corresponding to Xi, k . The output value of the correlation calculation between the received signal and the signal generated by the error search unit is:      Tcoh cos ϕk − ϕk0 + nI (5) Ii (k) = AR(τk − τ)sinc ωd ,k − ωi, k 2     Tcoh  sin ϕk − ϕk0 + nQ Qi (k) = AR(τk − τ)sinc ωd ,k − ωi, k (6) 2 Among them, τk represents the pseudo-code phase difference between the received signal and the locally copied pseudo-code signal, ωd ,k represents the residual carrier frequency in the received signal, ϕk represents the carrier phase in the received signal, and nI and nQ represent the noise terms of channel I and channel Q respectively. After correlation operation, the total integrated energy of the signal can be expressed as:    Tcoh + nI 2 + nQ 2 (7) Vi (k) = Ii2 (k) + Qi 2 (k) = A2 R2 (τk − τ)sinc2 ωd ,k − ωi, k 2 Because of autocorrelation, the calculated output signal power is maximum when the local replicated signal matches the received signal exactly. By fitting the signal power of each discrete search unit, the position Xk of the maximum output signal power is obtained. Xk is the most accurate positioning information within the error range. 3.2 Second-Order FLL Assisted Third-Order PLL Based on Adaptive Q - Value Kalman Filter In this paper, the function of second-order FLL assisted third-order PLL based on adaptive Q - value KF is to deal with the influence of Doppler frequency shift on the tracking

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loop and improve the dynamic tolerance of the tracking loop [7]. The loop takes the frequency discrimination results ωe and phase detection results θe as the observed values of the adaptive Kalman filter (AKF). The loop adjusts the process noise variance Q according to the changes of the system, and combines the numerically controlled oscillator (NCO) of the second order FLL and the NCO of the third order PLL into a new adjustment NCO. The local replication signal is updated. Second-order FLL model based on KF. The state vector corresponding to the secondorder FLL is defined as X k : T  (8) Xk = fk f˙k Among them, fk represents carrier frequency and f˙k represents the rate of change of carrier frequency. The state transition vector is f ,k :  1 TL

k = (9) 0 1 The equation of state corresponding to the second-order FLL is: Xk = k Xk−1 + Wk−1

(10)

Among them, W k−1 is the process noise vector, and the power spectral density of process noise is qf . The observation matrix and observation equation corresponding to the second-order FLL are: H = [1 0]

(11)

Zk = HXk + Vk

(12)

Among them, V k is the observation noise vector. The measured residual of KF is: −





Zk − H X k = f e,k

(13)



Among them, f e,k is the output value of frequency discriminator. The specific prediction and correction process of Kalman filter is referred to the literature [7]. Third-Order PLL Model Based on KF. Define the state vector corresponding to the third-order PLL as X k : T  (14) Xk = ϕk ωk ω˙ k Among them, ϕk represents carrier phase, ωk represents angular frequency, ω˙ k represents angular frequency change rate. The state transition vector is k : ⎡ ⎤ 1 TL 0.5TL2 (15) p = ⎣ 0 1 TL ⎦ 0 0 1

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The equation of state corresponding to the third-order PLL is: Xk = k Xk−1 + Wk−1

(16)

Among them, W k−1 is the process noise vector, and the power spectral density of process noise is qp . The observation matrix and observation equation corresponding to the third-order PLL are: H = [1 0 0]

(17)

Zk = HXk + Vk

(18)

Among them, V k is the observation noise vector. The measured residual of KF is: −





Zk − H X k = ∅e,k

(19)



Among them, ∅e,k is the output value of phase discriminator. Adaptive Q Value Algorithm. Define the new sequence of information at time k as d k : ∧ dk = zk − z k,k−1 = zk − Hxk,k−1

(20)

That is, the new information sequence is the difference between the actual observation vector and the predicted observation vector at time k [8], and the variance of the corresponding new information sequence dk can be written as the variance of the new information Cdk , which can be expressed as:   (21) Cdk = E dk dkT = Rk + H P k,k−1 H T

Assuming that the new sequence dk has the properties of various states, for the estimation of Cdk , the maximum likelihood criterion is used and the sliding window method is adopted to get the estimated value of Cdk :  k−1 Cd −1 + k1 dk dkT , k ≤ W C dk = 1k k k (22) T j=k−W +1 dj dj , k > W W





Among them, W is the length of the sliding data window. Then, the process noise variance Q obtained by the new information variance estimation is: Qk−1 = Kk Cdk Kk T + Pk − APk−1 AT ≈ Kk Cdk Kk T

(23)

Fusion of Second-Order FLL and Third-Order PLL. By recombining the NCO of the second-order FLL based on KF and the NCO of the third-order PLL based on KF, the new NCO update equation can be written as follows:

˙ noc =

 1 ˙ noc,pll + 2π f˙ noc,fll

2



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   PLL ∅ Kk1 1 e,k FLL ˙k +∅ ¨ kT + + 2π f k + f˜ k + Kk1 f e,k

= T 2

387













(24)





˙ noc,pll for the NCO of third order PLL, f˙ noc,fll for the NCO of second order The

FLL [9].

4 Simulation Results and Analysis The ATLBOFLESS is simulated by MATLAB, and compared with the traditional frequency-locking assisted phase-locking algorithm. The simulation environment is set as follows: the layout position of the BS and the running trajectory of the train are shown in Fig. 4, and the initial position of the train is (20 m, 0 m, 0 m), respectively, under the two conditions of initial speed of 140 km/h, acceleration of 0.83 m/s2 and initial speed of 165 km/h and acceleration of 0.83 m/s2 . Each base station sends an on-off fusion signal with a carrier frequency of 2800 MHz. The power of the communication signal is 20 dB higher than the positioning signal, which is replaced by Gaussian white noise. The bandwidth and Power Spectral Density of thermal noise are 10 MHz and −174 dBm/Hz respectively [6]. In the above environment, the tracking loop of the traditional second-order FLL assisted by the third-order PLL and the ATLBOFLESS are used to track the BS signal. The tracking frequency and frequency error under the two methods was observed and analyzed.

Fig. 4. BS layout and train trajectory

Figures 5(a) and 6(a) respectively provide the tracking results of frequency and frequency error of the traditional tracking loop when the train passes through the No. 4 BS at a speed of 146 km/h. Figures 5(b) and 6(b) respectively provide the tracking results of the ATLBOFLESS under the same conditions. It can be clearly seen that when the Doppler translation rapidly changes from positive to negative, the tracking frequency of the traditional tracking loop fluctuates greatly and the frequency error has a jitter of 1300 ms, while this method has maintained a stable convergence state and the frequency error jitter time is reduced to about 300 ms. According to calculations, the tracking frequency root mean square error of the traditional tracking loop from 0 s to 10 s is 31.70 Hz, and the root mean square error of the tracking frequency and frequency error of this method is 12.75 Hz. Figures 7(a) and 8(a) respectively provide the tracking results of frequency and frequency error of the traditional tracking loop when the train passes through the No.

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Traditional Tracking Loop

b

ATLBOFLESS

Fig. 5. Comparison of signal frequency tracking results of PRN4 BS

ATLBOFLESS (3~8sε

Fig. 6. Comparison of signal frequency error tracking results of PRN4 BS

Traditional Tracking Loop

b

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Fig. 7. Comparison of signal frequency tracking results of PRN5 BS

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a

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b

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Fig. 8. Comparison of signal frequency tracking results of PRN5 BS

5 BS at a speed of 170 km/h. Figures 7(b) and 8(b) respectively provide the tracking results of the ATLBOFLESS under the same conditions. It can be clearly seen that when the Doppler frequency shift rapidly changes from positive to negative, the traditional tracking loop loses lockup, while the tracking frequency of this method has maintained a stable convergence state and the frequency error jitter time is about 200 ms. According to calculations, the tracking frequency root mean square error of the traditional tracking loop from 0 s to 10 s is 360.79 Hz, and the root mean square error of the tracking frequency of this method is 15.88 Hz. By comparing the above simulation results, it can be seen that the ATLBOFLESS can effectively reduce the influence of Doppler shift mutation on the tracking of train receiver signal when the train passes the BS, and improve the tracking accuracy and robustness of the receiver.

5 Conclusion In this paper, an adaptive tracking loop based on the feedback local error search structure is proposed. By introducing the feedback local error search structure and the discrete adaptive Q-value Kalman filter, the influence of the Doppler shift mutation on the train receiver signal tracking is effectively reduced. Simulation results show that the tracking loop can keep the tracking frequency in a stable convergence state during the abrupt Doppler shift, and the frequency error jitter time can be greatly reduced, which improves the tracking accuracy and robustness of the receiver. It is of great significance to realize stable and high precision positioning of high-speed trains in long tunnel scenarios. Acknowledgments. This work is financially supported by National Key R&D Program of China (No. 2022YFB2601801) and National Key R&D Program of China (No. 2022YFB3904702).

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References 1. Wang, P.: Tunnel positioning method for high speed trains based on communication signals. University of Electronic Science and Technology of China (2022) 2. Shi, Q., Liu, S., Shang, Q.: Precise positioning of high speed train based on tightly coupled GNSS/INS. Electron. Meas. Technol. 45(13), 7–13 (2022) 3. Fan, S., Rong, Z., Tian, H., et al.: High-precision indoor fast localization algorithm based on carrier phase. J. Commun. 43(01), 172–181 (2022) 4. Chen, Y., Wang, X., Chen, X., et al.: A novel combined control loop based on FLL-assistedPLL for highly dynamic tracking. In: 2021 International Wireless Communications and Mobile Computing, pp 1742–1747 (2021) 5. Bian, X.: Design and implementation of positioning receiver tracking algorithm for mobile network. Beijing University of Posts and Telecommunications (2019) 6. Xie, G.: GPS principle and receiver design, 2nd edn. Publishing House of Electronics Industry (2009) 7. Li, N., Jiang, H., Deng, Z., et al.: A carrier tracking loop method based on adaptive weight adjustment. In: The 9th China Satellite Navigation Annual Conference, pp 41–45 (2018) 8. Miao, J., Sun, Y., Liu, J., et al.: A Kalman filter based tracking loop in weak GPS signal processing. In: International Conference on Fuzzy Systems and Knowledge, pp 438–442 (2009) 9. Mo, J.: Research on key technologies of the navigation baseband signal processing for the communication and navigation integrated system. Beijing University of Posts and Telecommunications (2019)

An Innovation Sequence Variance Interference Detection Algorithm Based on Reference Noise Yichen Wang, Xiaohui Liu(B) , Chao Wen, and Zichen Xu National University of Defense Technology, Changsha, China [email protected]

Abstract. Spoofing interference poses a threat to the positioning and timing security of GNSS that cannot be ignored. In traditional spoofing interference detection algorithms, the spoofing rate is often regarded as an unknown constant, which is not consistent with the actual spoofing interference. For the case of spoofing rate jitter in actual spoofing interference, this paper proposes an innovation variance spoofing interference detection algorithm based on reference noise. The jittered spoofing rate is modelled as a random variable obeying non-zero mean Gaussian distribution, and the detection statistics of innovation sequence variance is constructed by comparing the reference noise variance in the stationary no-spoofing state with the innovation sequence variance in the motion state for spoofing interference detection. Simulation results show that the proposed method has high sensitivity and good detection performance for spoofing of jitter rate. Compared with the traditional method, the proposed algorithm has obvious advantages in detection speed under real spoofing environment. In addition, the proposed method is insensitive to the mean of spoofing rate and has positive detection performance especially for slow-varying deception. Keywords: Spoofing interference detection · Kalman filter · Reference noise · Sequence variance

1 Introduction Global Navigation Satellite System (GNSS) has been widely used in various industries such as transportation, electric power, finance, communication, agriculture, forestry, animal husbandry and fishery [1], which shows the great application value of GNSS. However, due to the low landing power of GNSS signal and the open structure of civil GNSS signal, GNSS navigation is vulnerable to deliberate spoofing jamming attacks [2], which seriously affects the positioning and timing security of user devices. Meanwhile, with the development of Software Defined Radio (SDR) technology, it is cheaper for individuals to generate simulated satellite navigation signals through SDR boards [3]. From the numerous incidents of unmanned aerial vehicles being spoofed, GNSS spoofing interference has gradually become a threat that cannot be ignored by GNSS civilian users. GNSS spoofing interference can be divided into forwarding spoofing and generating spoofing interference [4], where forwarding spoofing uses GNSS receivers to receive real © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 391–400, 2024. https://doi.org/10.1007/978-981-99-6928-9_34

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satellite signals and transmit them through local transmitting equipment after a certain delay. The delay of such interference signals can be easily identified and eliminated by receivers because they obviously lag real signals. Generative spoofing refers to spoofing signals generated by SDR module that are consistent with real satellite signals, whose duration can be dynamically adjusted according to needs, either ahead of or behind the authentic signal [5]. For this type of interference signal, it is difficult for the receiver to recognize and eliminate deception, which has become the research focus of spoofing interference detection technology at present. In spoofing detection technology, the method of assisting GNSS receiver by external devices has better detection performance due to the introduction of external redundant navigation information. Inertial Navigation System (INS) is an autonomous navigation device that is not affected by radio signals. GNSS/INS integrated navigation system has become a commonly used integrated navigation system. Combining detection theory, the GNSS/INS tightly coupled mode uses Kalman filter and other ways to integrate GNSS and INS measurement information which can be utilized for spoofing interference detection. The traditional theory of spoofing detection based on GNSS/INS tightly coupled system considers that the spoofing signal rate is an unknown constant, which causes non-zero change in the mean value of the innovation, so scholars have proposed spoof detection algorithms based on the innovation [6], the detection algorithm based on innovation chi-square [7], and the detection algorithm of innovation sequence [8], etc. In order to improve the detection speed of slow-varying spoofing interference, a spoofing interference detection algorithm based on Sequential Probability Ratio Test (SPRT) was proposed in the literature [9]. But in fact, due to factors such as environmental noise and various errors, there are variations in the spoofing signal rate applied to target receiver, and it is not reasonable to treat the spoofing rate as a constant. For the changing spoofing rate, this paper models it as a random variable obeying Gaussian distribution with non-zero mean and proposes a spoofing interference detection algorithm based on the variance of innovation sequence regarded as reference noise. Firstly, the motion state of vehicle is determined by INS output data, and when the carrier is in stationary state without spoofing interference, the innovation sequence is obtained as the reference noise and the statistical variance is set as priori variance of the noise in the spoof-free state. When vehicle moves, the variance of innovation sequence is estimated and compared with the priori variance to achieve the detection of spoofing interference. The proposed method is more sensitive to the detection of spoofing interference with varying spoofing rate and can improve the utilization of GNSS signals in non-continuous spoofing interference scenarios.

2 Deceptive Jamming and Detection System Model In this section, the pseudo-range slowly varying spoofing interference model and the Kalman filtering model of GNSS/INS tightly coupled system are introduced respectively, mainly to analyze the factors generating spoofing and show the unreasonableness of treating spoofing rate as a constant. Moreover, the traditional SPRT spoofing detection algorithm is briefly described.

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2.1 Slow-Varying Random Signal Spoofing Interference Model The transmission time of GNSS signals from satellite to the target receiver is [10]: toi =

roi + tiono + ttrop − tclck c

(1)

where roi is the distance from satellite to the target receiver, tiono and ttrop are the ionospheric delay and tropospheric delay, respectively, and tclck is the satellite clock difference, which is kept constant for a short time. The GNSS signal arrives at the spoofing receiver from the satellite and is processed to generate spoof signal, which eventually arrives at the target receiver in: tp = tsi +

r + tdeal c

(2)

tsi is the transmission time for the GNSS signal reaching the spoofing receiver, r is the distance from the spoofing signal transmitter to the target receiver, and tdeal is the processing time of the spoofing system after receiving the GNSS signal. When the code phase of real signal and spoofing signal are aligned [11], the spoofing starts and the target receiver position is pulled off by the change of spoofing signal pseudocode delay. Let the distance deviation between the deviated position and the real position be r , and at the deviated position, the distance between the GNSS signal and the target receiver is roi . The transmission time is toi , then the code delay compensation can be calculated by: τ  = toi  − tsi −

r − tdeal c

(3)

To simplify the analysis, the τ  is modelled as a first-order linear model, which can be expressed at the pseudo-range level by the following equation. i ρsi = ρau + a(t − ts )

(4)

Then the spoofing pseudo-range rate can be written as: i ρ˙si = ρ˙au +a

(5)

In this paper, the spoofing rate is randomly treated as a Gaussian distribution with non-zero mean, and the design of spoofing algorithm is based on this. 2.2 SPRT Algorithm Based on GNSS/INS Tightly Coupled Model From the GNSS/INS tightly coupled system theory [12], the state vector at the k th measurement moment is: T  xk = δpk , δvk , δφk , δωk , δfk ,bclk (6) Where δpk = [δϕk , δλk ,δhk ] is the position error vector, which consists of longitude, lat itude and altitude; δvk = δvE,k , δvN ,k , δvU ,k is the georeferenced velocity error vector;

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    δφk = δpk , δrk , δAk is the attitude error vector; δωk =  δωR,k , δωF,k , δωU ,k is the gyroscope zero bias error vector; δf k = δfR,k , δfF,k , δfU ,k is the accelerometer zero bias error vector; bclk =[δbr , δdr ] is the receiver clock difference and clock drift. The subscripts E, N , U represent the east, north, and sky components of the local geographic coordinate system, and the subscripts R, F, U represent the right, front, and top components of the vehicle coordinate system, respectively. The state and measurement equation of the system [13] can be written as:  xk = Φ k/k−1 xk−1 + wk−1 (7) z k = H k xk + vk The measurement vector zk is denoted as follows.    1  2 , · · · )T (ρG,k , ρG,k ρk = zk = 1 2 ρ˙ k (ρ˙G,k , ρ˙G,k , · · · )T

(8)

i , ρ˙ 1 (i = 1, 2,· · ·M , M is the number of observation satellites) are the observation ρG,k G,k of i th satellite pseudo-range and pseudo-range rate at time k, respectively. SPRT detection statistic is constructed using the innovation sequence of current and historical moments [9]. The innovation vector is defined as:

δzk = zk −H k xˆ − k

(9)

which includes the pseudo-range and pseudo-range rate innovation.The SPRT spoofing detection algorithm collects all the innovation sequences ft,j = δzt,j t = 1, 2,· · ·k . And the test statistic Tk,j is constructed as [14]: 2

Tk,j =

kf k,j 2 2σk,j

(10)

The detection threshold γ can be obtained from the false alarm rate α and the missed alarm rate β [15]: γ = ln

1−β α

(11)

3 Interference Detection Algorithm Based on Reference Noise Zero speed detection is performed based on the acceleration and angular velocity measurements firstly. If the carrier is detected to be stationary, it is easy to determine whether GNSS signal is spoofed. Since the variance of innovation only includes INS propagation error and observation noise under the condition of no deception, innovation free from spoof can be regarded as reference noise, and its variance can be counted as a priori information. When carrier moves, spoofing can be detected by comparing the variance of innovation sequence in the motion state with that of the reference noise in stationary state.

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3.1 Reference Noise Acquisition Based on Zero Velocity Detection The acquisition of reference noise is based on the static motion state, so it is necessary to determine the motion state of carrier first. The specific method is to use the acceleration and angular velocity output values from INS for zero-velocity detection. Zero velocity detection can be understood as a statistical detection problem of binary signal, defined as:  R0 : motion (12) R1 : stationary Using the Neyman-Pearson criterion to maximize detection probability PD with a given false alarm probability PFA = α, then the test statistic can be expressed as [16]: 2   yan  1 1  1    a yω 2 ) < γ   T (zn ) = ( 2 +  yk − g  k a 2     N σa σω yn k∈n

(13)

k∈n

Where σa2 , σω2 are the variance of acceleration and angular velocity measurements output from the IMU, varvecyak and yωk , are the acceleration and angular velocity in the three axes measured by the IMU at time k, respectively, N is the detection window length, and −a n+N −1 a g is the gravity constant. The estimated value y n =1/N· k=n yk is the average value of −a 2

−aT −a

acceleration within the detection window length N , and  y n  = y n y n represents binary norm operation. When Eq. (13) is true, hypothesis R1 holds. 3.2 Sequence Variance Spoofing Detection Algorithm based on Reference Noise j

j

Let the pseudo-range rate innovation of j th visible satellite at time k be δ ρ˙k , x[k]=δ ρ˙k , H0 is the no-spoof hypothesis and H1 is the spoof hypothesis, then the binary hypothesis model is:  H0 : x[k] = w[k] k = 0, 1, · · · , M (14) H1 : x[k] = s[k] + w[k] k = 0, 1, · · · , M where M is the length of the detection sequence, w[k] is the zero-mean Gaussian noise 2 , and s[k] is the zero-mean Gaussian distributed with known reference noise variance σwj signal with unknown variance σs2 introduced by the spoofed signal. Then the generalized likelihood ratio is: LG (x) = p(x; σˆ s2 , H1 )

1

p(x; σˆ s2 , H1 ) p(x; H0 ) 

= M /2 2 +σ 2π(σwj ˆ s2 )

 M

1 2 exp − x [n] 2 +σ 2(σwj ˆ s2 ) n=0

(15)

(16)

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Taking the logarithm of Eq. (16) and deriving it yields the MLE estimate of the spoofed signal variance σˆ s2

M 1 2 2 = x [n] − σwj M

(17)

n=0

Let σˆ s2+ = 1/M

M n=0

2 , where the superscript “ + ” means that if σ x2 [n] − σwj ˆ s2+ is

positive, then it is the MLE. If ln LG (x) = ln

p(x; σˆ s2 , H1 ) > ln γ p(x; H0 )

(18)

Then determine H1 is true. Taking the estimated value σˆ s2 into the log-likelihood ratio yields   M σˆ s2 σˆ s2 ln LG (x) = (19) ( 2 + 1) − ln( 2 + 1) − 1 2 σwj σwj 2 + 1, g(z)= z − lnz − 1 is a monotonically increasing function such Let z = σ 2s /σwj that for z > 1, its inverse g −1 exists. Then if 

2 [g −1 ( σˆ s2 > σwj

2 ln γ ) − 1] = γ  M

(20)

determine H1 is true. And the test statistic is exactly the estimate of variance σˆ s2 . When the number of samples is sufficiently large, the variance of innovation asymptotically satisfies the Gaussian distribution of the following equation. M 1 2 2 x [n] ∼N (σwj , var(w2 [n]/M )) M

(21)

n=0

where var(w2 [n]/M ) = 2σwj 4 /M . Finally, the threshold γ is calculated as follows:  4 2σwj 2 Q−1 (PFA ) + σwj (22) γ = M where Q−1 is the inverse Gaussian right-tailed probability function.

4 Simulation Results and Analysis 4.1 Experimental Design and Simulation Setup Two sets of simulation experiments are set up for the GNSS/INS tightly coupled system for slow-varying spoofing interference detection as follows.

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Experiment 1: Record 200s inertial sensor data including stationary and motion states for zero speed detection to verify the effectiveness of the zero speed detection algorithm. Experiment 2: Compare the detection time and reset time required for the two algorithms to return to the spoof-free state after the spoofing interference disappears. Meanwhile, the effect of spoofing signals on the localization results is observed as well. The settings of related sensor parameter in Experiment 1 and Experiment 2 are presented in Table 1. Table 1. Simulation parameters setup Parameter

Value

GNSS Pseudo-range measurement noise Standard Deviation

2.5 m

GNSS Pseudo-range rate measurement Noise Standard deviation

0.1 m/s

Gyroscope bias Gyroscope random noise

  (−9, 13, −8) ◦ /h   √ 0.01 ◦ / h

(900, − 1300, 800) mg √ 100 mg/ Hz

Accelerometer bias Accelerometer random noise

Spoofing is applied to the PRN01 satellite in Experiment 2, the settings of the slowvarying deception amount in the experiment are shown in Table 2. Table 2. Setting of spoofing amounts Index

Spoofing PRN

Application time

Mean

Variance

Experiment 2

PRN01

50–150 s

0.2 m/s

0.1 (m/s)2

PRN01

50–150 s

0.4 m/s

%1.%2 (m/s)2

4.2 Simulation Results and Analysis Experiment 1 Results and Analysis The real-time velocity of inertial sensor and zero speed detection results are shown in Fig. 1. The zero-speed detection rate is 99.73%, and the false detection rate is 1.7%. Experiment 2 Results and Analysis The curves of the deception test statistics with time for the SPRT algorithm and the algorithm proposed in this paper are shown in Figs. 2 and 3.

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1.2 1 0.8 0.6 0.4 0.2 0

0

20

40

60

80

100

120

140

160

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200

Fig. 1. Real-time speed and zero speed detection results

Fig. 2. Spoofing test statistics of two methods with 0.2 mean and 0.1 variance spoofing rate

Fig. 3. Spoofing test statistics of two methods with 0.4 mean and 0.05 variance spoofing rate

The results of the comparison between the two algorithms are shown in Table 3, showing the time when the test statistic is below the threshold after the spoofing interference disappears.

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Table 3. Comparison of detection time of deception disappearing Spoofing rate

SPRT algorithm

Proposed algorithm

0.2 m/s mean 0.1(m/s)2 variance 0.4 m/s mean 0.05(m/s)2 variance

–

16 s

–

15 s

During the presence of spoof interference, the maximum positioning error is 6.85 m for the D-axis, 3.47 m for the N-axis, and 0.921 m for the E-axis. To compare the detection speed of two algorithms, the detection time of both algorithms for different slow-moving deception are listed in Table 4. Table 4. Comparison of detection time of different slow spoofing Spoofing rate

SPRT algorithm

Proposed algorithm

0.2 m/s mean 0.1(m/s)2 variance

27 s

7s

0.4 m/s mean 0.05(m/s)2 variance

10 s

11 s

The detection time of SPRT algorithm for 0.2 m/s mean, 0.1(m/s)2 variance spoofing rate is 27 s and for 0.4 m/s mean, 0.05(m/s)2 variance is 10 s, while for the proposed method they are 7 s and 11 s, respectively. The proposed method is mainly affected by the variance of spoofing rate, and in practice it is impossible to control the variance of the spoofing rate. The larger the spoofing rate is, the greater the jitter will be. Therefore, in the real spoofing interference environment, the proposed method has obvious advantage in the detection speed.

5 Conclusion In this paper, the slow spoofing rate is regarded as a random variable subject to Gaussian distribution of non-zero mean, and combined with the variance of reference noise obtained in the case of zero velocity detection, an innovation variance spoofing detection algorithm is proposed which is suitable for multi-satellite spoofing and has good performance in the detection of slow spoofing. The simulation results show that the proposed algorithm has higher detection sensitivity when the spoofing rate variance is large compared with traditional SPRT slow-varying spoofing detection algorithm. Under the condition that the mean value of pseudo-range spoofing rate is 0.2 m/s, the variance is 0.1(m/s)2 , the detection time is improved by 20 s compared with the SPRT algorithm. When the spoofing disappears, the method in this paper can effectively identify it within 16 s, while the SPRT algorithm cannot. Additionally, the impact of spoofing interference on the localization results is small, and the maximum errors caused on the N, E and D axes are 3.47 m, 0.921 m and 6.85 m, respectively.

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References 1. Zhou, Y., Wang, S., Yang, W.: Overview of GNSS spoofed interference detection. Comput. Eng. Appl. 58(11), 12–22 (2022) 2. Lunlong, Z., Yongyu, L., Xueyan, L.: Based on KL divergence tightly integrated navigation deception interference detection method. Aerosp. Sci. Technol. 33(11), 76–83 (2022). https:// doi.org/10.19452/j.issn1007-5453.2022.11.011 3. Lu, D., Waizhen, Z., Lunlong, Z.: Inertial navigation system/rangefinder system-assisted autonomous detection algorithm for airborne GNSS spoofed interference. J. Electron. Inf. 44(9), 3195–3202 (2022) 4. Psiaki, M.L., Humphreys, T.E.: GNSS spoofing and detection. Proc. IEEE 104(6), 1258–1270 (2016) 5. Jafarnia-Jahromi, A., Broumandan, A., Nielsen, J., et al.: GPS vulnerability to spoofing threats and a review of antispoofing techniques. Int. J. Navig. Obs. 2012 (2012) 6. Ke, Y., Lv, Z.W., Zhou, W.L., Deng, X., Zhou, S.H.H., Ai, H.Y.: New interest-optimized anti-difference estimation spoof detection algorithm for GNSS/INS tight combination. Chin. J. Inert. Technol. 30(02), 272280 (2022). https://doi.org/10.13695/j.cnki.12-1222/o3.2022. 02.020 7. Lunlong, Z., Guipo, L.: Research on deceptive interference detection technology based on tight combination navigation. In: Proceedings of the Fifth Chinese Aviation Science and Technology Conference, pp 426–431 (2021). https://doi.org/10.26914/c.cnkihy.2021.064888 8. Tanıl, Ç., Khanafseh, S., Joerger, M., et al.: Kalman filter-based INS monitor to detect GNSS spoofers capable of tracking aircraft position. In: 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), pp 1027–1034. IEEE (2016) 9. Lunlong, Z., Liu Guipo, Y., Liang, Y., et al.: Adaptive SPRT-based slow-variant spoofing interference detection algorithm. Signal Process. 38(10), 2144–2154 (2022) 10. Ying, S., Hongyu, L., Shuyong, Z., et al.: Research on GPS generative spoofing interference method. Foreign electronic measurement technology, 8 (2018) 11. He, L., Li, W., Guo, C.J.: Research on generative spoofing interference. Comput. Appl. Res. 33(8), 2405–2408 (2016) 12. Groves, P.D.: Principles of GNSS, inertial, and multisensor integrated navigation systems, 2nd edition [Book review]. In: IEEE Aerospace and Electronic Systems Magazine, vol. 30, no. 2, pp. 26–27 (2015). https://doi.org/10.1109/MAES.2014.14110 13. Wu Zhijia, W., Wenqi, L.K., Kanghua, T.: Research on stepwise induced deception detection algorithm based on INS/GNSS tightly coupled combination. Navig. Position. Timing 6(01), 7–13 (2019). https://doi.org/10.19306/j.cnki.2095-8110.2019.01.002 14. Ceccato, M., Formaggio, F., Laurenti, N., et al.: Generalized likelihood ratio test for GNSS spoofing detection in devices with IMU. IEEE Trans. Inf. Forensics Secur. 16, 3496–3509 (2021) 15. Chen, H., Huang, W., Huang, J., et al.: Multi-fault condition monitoring of slurry pump with principle component analysis and sequential hypothesis test. Int. J. Pattern Recognit. Artif. Intell. 34(07), 2059019 (2020) 16. Yu, S., Feng, Z., Ligo, L. et al.: Improvement of zero-speed interval detection method in vehicle-mounted GNSS/SINS integrated navigation. Geoinf. Surv. Mapp. 41(6), 12–16 (2016)

Research on Shadow Matching Algorithm Based on Consistency Probability Weighting Xiang Lv(B) , Zhongliang Deng, and Nijun Ye Beijing University of Posts and Telecommunications, Beijing, China [email protected]

Abstract. Shadow matching method can effectively improve the positioning accuracy of street crossing direction in urban canyons. This paper discusses the selection method of search area where the matching initial positioning point is not too accurate. Aiming at the problem of insufficient positioning along the street, this paper discusses the matching method of satellite signals with fuzzy direction range along the street. On the basis of clustering shadow matching, the user’s position is finally determined through the weighted solution of different scores. Keyword: Shadow matching location of urban canyon

1 Introduction In recent years, GPS has been widely used in mobile terminals. Mobile terminals in open areas can achieve meter level or even decimeter level positioning accuracy [1], which provides extremely convenient services for our public life, regardless of personal location services, vehicle transportation and other industries. However, the urban environment is extremely bad in relatively open areas. Whether it is high-rise buildings, or vehicles, pedestrians, trees, it may have a greater impact on the positioning accuracy. This leads to multipath signal interference, signal attenuation, and non line of sight signal reception [2]. The positioning accuracy in urban environment needs to be further improved, especially the street accuracy. By building a 3D city model, many researches predict the visibility of satellites based on this to distinguish NLOS signals. Shadow matching is one of the typical algorithms, which determines the user’s position through the predicted satellite visibility and the visibility of receiving discrimination. Grove put forward this concept for the first time, and proved that the shadow matching algorithm can improve the cross street positioning accuracy through modeling, proposed a solution [3], and further carried out preliminary testing of the algorithm in London Urban Canyon, proposed two 3D model solutions, one is the 3D model library for regions with poor GPS positioning accuracy downloaded locally, which accounts for about 10% of the total; The other is to download map boundary data from the network server [4]. Wang et al. considered diffraction and reflection, interpolated the area with the highest score, provided a new scoring scheme, and tested it on a smart phone. The cross street accuracy was improved to 2 m at the selected test © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 401–410, 2024. https://doi.org/10.1007/978-981-99-6928-9_35

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point [5, 6]. Luo Huan et al. applied clustering algorithm to shadow matching [7]. Hu Hui et al. proposed SM algorithm based on EKF and SM algorithm based on particle filter [8, 9] on the basis of shadow matching algorithm and considering dynamic velocity information. Xia Jingping et al. proposed an improved SM algorithm based on high score weighting after analyzing the characteristics of the received signal SNR [10]. The research on the algorithm is mainly divided into two aspects: one is to improve the accuracy of satellite visibility prediction, and the other is to improve the shadow matching fraction mechanism to optimize the location determination. In addition, like fingerprint matching and location, there are also problems with large amount of computation. The current research regards all signals beside buildings as visible, but when there are buildings with a certain distance beside buildings, this will bring errors. This paper analyzes this and proposes an improved SM method based on consistency probability weighting according to the degree of satellite matching consistency.

2 Shadow Matching The terminal can receive satellite data, which includes pseudo range value, signal-tonoise ratio, etc. And according to the positioning time, the satellite position can be calculated according to the satellite ephemeris, and then the satellite azimuth angle and altitude angle can be calculated. In the streets with high-rise buildings, high-rise buildings will block some signals, resulting in the inability to receive signals from a satellite, or receive signals with low signal-to-noise ratio [11, 12]. As shown in Fig. 1, its principle is simply explained. The terminal is located at the crossing position according to whether it can receive the satellite data of the specified signal quality. The positioning process at a single epoch time is shown in Fig. 2, which is divided into the following steps.

Fig. 1. Shadow matching flowchart

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Fig. 2. Schematic diagram of signal acceptance

(1) Position initialization: preliminary positioning is carried out by GPS pseudo range measurement and least square method. The accuracy of preliminary positioning affects the matching accuracy and regional division after the algorithm. For the relatively open area, the initial positioning accuracy can reach meter level positioning, and the location of the terminal is generally located in the street. However, in the harsh area, the initial location may not be located in the street, which is also an aspect of this study. (2) Select the search area: search near the center of the initial positioning point P0. The search area is generally set as a rectangle, which is generally divided into 1m2 units. When the initial location cannot be located on the street, or the initial location is too close to the building, it will be carried out with P0 as the center, and the candidate point may reach the building. This article will be discussed later. (3) Visibility prediction: based on the candidate positions in the second step, for each position, calculate the azimuth and altitude of the satellite according to the GPS satellite ephemeris. Calculate the elevation of the building boundary at the satellite azimuth angle, compare this elevation angle with the satellite altitude angle, and if the altitude angle is greater than the critical elevation angle, predict that the satellite signal can be received. (4) Visibility observation: the SNR of the satellite signal received by the terminal receiver is higher than the threshold value, which proves that the signal can be directly received by the terminal, and the satellite is judged as visible; If the SNR is lower than the threshold value, it is the result of reflection or diffraction of the NLOS signal, which is judged as invisible. (5) Scoring of matching results: score according to the scoring diagram 3. After removing the satellite with the cut-off elevation (10°), score each position in the search area through the following scoring function [8].

fpos (j) =

n  i=1

fsat (i, j)

(2.1)

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where: f_ Pos (j) is the final position score of candidate position j, f_ Sat (i, j) is the scoring value of the satellite i at the candidate location j. The final scoring value is the cumulative score of each satellite (Fig. 3).

Fig. 3. Scoring diagram

(6) Position calculation: select the K points with the highest final score, and calculate the position according to KNN algorithm. X=

1 K · xi i=1 k

(2.2)

Y=

1 K yi · i=1 k

(2.3)

where xi and yi The cross street and along street coordinate values of K points are respectively averaged by KNN to obtain the final positioning results (X, Y).

3 Improved Shadow Matching Algorithm 3.1 Satellite Matching Considering Building Fuzzy Boundary In the process of matching, the traditional method calculates the satellite azimuth and elevation in this epoch through ephemeris, and uses 3D building model to calculate the boundary elevation of buildings in the same azimuth. If the satellite elevation in this azimuth is greater than the building boundary elevation, it is predicted that the satellite is visible. When a building is surrounded by tall buildings with a certain distance between buildings, it cannot be seen. Next, we will analyze the situation of tall buildings around the building and with a certain distance between buildings. First, consider the problem of judging this kind of situation. The system is established with point A as the coordinate origin. The X and Y directions are as shown in the figure. The coordinates of point P are P (X0, Y0). The length of the building is L, the width is W, and the height is H. The radio wave in the wireless distance is launched in parallel, and the azimuth angle is assumed to be (90° – 180°) reaches the critical point when P’G just intersects with point B. In this case, if the coordinates of P ’are (X1, Y1), then tan(π − α) = X/(L − Y), when the matching lattice moves to P, the coordinates meet tan (π − α) < X/(L − Y)。At this time, the arrival signal should be received in the P

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Fig. 4. Satellite signals outside the building boundary

point processing, so only SNR matching is performed. When SNR > threshold, it is determined that the matching is successful. The discriminant formulas for other azimuths are given.   X > tan(α) α 0, 90◦ Y

(3.2)

  W −X > tan(α − π ) α 180, 270◦ L−Y

(3.3)

  W −X > tan(2π − α) α ∈ 0, 90◦ Y

(3.4)

The above discussion is aimed at the open area near the building, considering the adjacent situation of two buildings with building spacing, as shown in Fig. 4. If the satellite azimuth is at (α 1, α 2), α 1 and α 2 are the critical azimuths of the two buildings respectively. According to the 3D building model, there is no occlusion within this range. It is only necessary to determine whether SNR is greater than the threshold. Azimuth greater than α 2 falls into the blocking range of building 2, which is matched with the critical elevation of building 2. Assume that the height of building 2 is H2, P (X0, Y0), the floor spacing is L1, the azimuth corner is in the front of the building, and the critical elevation angle is: θ = tan−1

H 2 ∗ sin(π − α) α ∈ (90, 180) X0

(3.5)

When it falls on the side of the building, θ = tan−1

−(H 2 ∗ − cos(α)) α ∈ (90, 180) L1 + AB − Y 0

(3.6)

The analysis does not consider the impact of the surrounding buildings: if the candidate point is at p, the azimuth of a satellite exceeds the PB boundary, and the satellite signal cannot be received due to the actual observation of the right building. The original scoring forecast can receive the satellite at this time. If the matching fails, no points will be added. When we consider the right building, we find that the elevation of the right building boundary is greater than the satellite elevation, the prediction is invisible, the matching

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is successful, and the correct matching result is obtained. The following Table 1 shows various situations, indicating that when the signal is observed, there is no blocking signal at the boundary of the two buildings, and the matching is normal. When no signal is observed, the building on the right blocks the signal, which is mismatched. Table 1. The influence of the buildings nearby on the results Buildings next to it are not considered

Buildings next to it are considered

The signal is observed

Match correctly

Match correctly

The signal is not observed

Match incorrectly

Match correctly

3.2 Positioning Solution Based on Consistency Probability Weighting Because the location can be ignored compared with the satellite distance, in fact, the satellite azimuth and elevation angle of each location in the search range are almost similar. Based on this assumption, this paper only needs to calculate the elevation of the building boundary at the corresponding location of each grid, and each grid carries its own elevation boundary information. At this time, for each match, it only needs to look up the table, reducing the calculation. The shadow matching scoring mechanism determines the optimal position, not necessarily the most accurate position. The higher the score, the higher the probability of approaching the location. We take the degree of final match with the observation star as the consistency probability, which is expressed as: Pi =

Ni Nall

(3.7)

Pi represents the consistency of matching at position i, Ni represents the number of satellites matched, which is the score in this paper. Nall represents all the stars observed at that time, and the maximum visible probability is 1 and the minimum is 0. The higher the probability, the higher the weight. Because the SNR of the terminal observation satellite will be affected by vehicles, pedestrians or trees, resulting in inaccurate observation, it may lead to inaccurate matching, and there may be an error for the wrong point. At this time, we use the clustering method to find the center coordinates of the region with the highest score and the second highest score, assuming (Xi, Yi), (Mj, Nj). According to the consistency probability formula, assuming that the consistency probability of the two regions is P1, P2, the final positioning result is: X=

k  i=1

 P2 P1 × Xi + × Mj P1 + P2 P1 + P2 H

j=1

(3.8)

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Y=

k  i=1

 P2 P1 × Yi + × Nj P1 + P2 P1 + P2

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H

(3.9)

j=1

Finally, (X, Y) is the final goal of improving SM. Because SM algorithm improves greatly in the street direction, and GPS has better accuracy in the street direction, (X_ sm, Y _ Gps) is the final coordinate.

4 Analysis of Experimental Results 4.1 Data Processing The text first collected data near Xueshi Dormitory Building of Beijing University of Posts and Telecommunications. The data was collected by Xiaomi mobile terminal and GNSS logger APP to verify the feasibility of matching the prediction and observation results. In a period of time, the types of buildings around are similar, the satellite movement changes little, and the SNR received by the same satellite should also change little. However, due to the large noise of the GNSS chip embedded in the mobile phone, trees and pedestrians in the urban canyon environment will cause SNR fluctuations. As shown in Fig. 5, blue is the SNR value of G21 satellite actually received by the terminal, which fluctuates greatly. In this paper, it is first filtered, and the filtering result is represented by the red line. It can be found that the SNR value received in the first 80 epochs is low because the satellite is in the blocked road section, and then enters the satellite open road section, and the SNR value rises. According to the observation, we observed the visible satellites with SNR greater than 34db and analyzed the matching feasibility. Figure 5c In d, 1 indicates successful matching and 0 indicates failed matching. According to the above two figures, the success rate of determination is obviously improved after filtering. 4.2 Selection of Search Area The experimental scene of this paper is selected in the area between Hongtong Building and Jiaosi Building of Beijing University of Posts and Telecommunications (as described in the above real map). The street is 40 m long, about 14 m wide, and the buildings are 18 m and 12 m high respectively. Figure 6 shows a 3D map model built with Baidu Maps, where building boundary points are selected, A (39° 57 38.50 ", 116° 20 57.76") B (39° 57 37.28 ", 116° 20 57.84") C (39° 57 37.22 ", 116° 20 57.26") D (39° 57 38.95 ", 116° 20 57.26"). Due to the positioning error, the initial longitude and latitude positioning coordinates are (39.960646325116.349401120) and the real coordinates are (39.960666226116.349251090). 4.3 Analysis of Matching Results The experiment models the selected street part, selects a 40 * 14 search area, and the final scoring chart of the experiment is shown in the figure. Different colors represent different scoring values, and the legend on the right shows the scores represented by

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a. Scene graph

b.SNR Filter diagram

c.Unfiltered matching renderings

d.filtered matching renderings

Fig. 5. SNR measurement scene and filter matching effect

Fig. 6. 3D model of test area

different colors. In Fig. 7, ✩ represents the real position, the real coordinates of which are given by the RTK equipment, ◯ represents the positioning points given by the original SM method, and * represents the positioning points given by the SM method based on the consistency probability weighting. The statistical alignment error is 0.7 m, which is 1.3 m higher than the traditional SM method and 11.78 m higher than the original

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GPS method. The direction error along the street of the two methods is equivalent, both of which are about 15 m, with a large difference compared with the original GPS positioning of 2.56 m, which is also a disadvantage of the SM method. Finally, take the street coordinates of the improved SM and the street coordinates of the GPS to get the SM-GPS fusion positioning results, as shown in the diamond box (Table 2). Table 2 Error statistics GPS

SM

Opposite street error/m

18.78

2

Error along the street/m

2.56

15.35

Improved SM

GPS + Improved SM

0.7

0.7

15.98

2.56

Fig. 7. Result scoring chart

5 Conclusion and Prospect Positioning in urban canyons is a hot topic in current research. This paper discusses the current situation of buildings with a certain space between buildings around them, and draws a conclusion that when the candidate location is affected by the adjacent buildings, it will cause a wrong match. After filtering the satellite data collected by the mobile phone terminal, the feasibility of SM algorithm is verified. Considering the consistency degree of the final scoring match, this paper proposes a SM method based on consistency probability weighting. Considering the matching error caused by inaccurate SNR measurement, the location result is obtained by using the consistency probability weighting of the highest score and the second highest score. The results show that the improved SM algorithm improves 1.3 m in the street direction, and has a large improvement compared with the traditional SM. However, the difference in the street direction is small or even slightly worse. This paper considers whether the satellite mainly distinguishes in the street direction or in the street direction. The secondary high value has a deviation in the street direction positioning, and the error increases after weighting.

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References 1. Kaishi, Z., Wenhai, J., Jianwen, L.: Analysis of GNSS positioning accuracy of android intelligent terminal. J. Wuhan Univ. (Information Science Edition) 44(10), 1472–1477 (2019). https://doi.org/10.13203/j.whugis20180085 2. Hsu, L.T., Gu, Y., Kamijo, S.: NLOS correction/exclusion for GNSS measurement using RAIM and city building models. Sensors 15(7), 17329–17349 (2015) 3. Groves, P.D.: Shadow matching: a new GNSS positioning technique for urban canyons. J. Navig. 64(3), 417–430 (2011) 4. Groves, P.D., Wang, L., Ziebart, M.: Shadow matching: improved GNSS accuracy in urban canyons. GPS World 23(2), 14–18 (2012) 5. Wang, L., Groves, P.D., Ziebart, M.K.: GNSS shadow matching: Improving urban positioning accuracy using a 3D city model with optimized visibility scoring scheme. NAVIGATION: J. Inst. Navig. 60(3), 195–207 (2013) 6. Wang, L., Groves, P.D., Ziebart, M.K.: Shadow matching: improving smartphone GNSS positioning in urban environments. In: China Satellite Navigation Conference (CSNC) 2013 Proceedings, pp. 613–621. Springer, Berlin, Heidelberg 7. Huan, L., Duojie, W., Chen, W.: An improved mobile phone shadow matching positioning method. J. Wuhan Univ. (Information Science Edition) 46(12), 1907–1915 (2021). https:// doi.org/10.13203/j.whugis20210275 8. Hui, H., Yujun, Y., Minhui, O.: An EKF based GPS/SM integrated positioning algorithm. Global Position. Syst. 41(02), 7–13+19 (2016). https://doi.org/10.13442/j.gnss.1008-9268. 2016.02.002 9. Hu Hui, O., Minhui, Y.Y.: Shadow matching/particle filter adaptive weighted combined localization algorithm. J Detect. Control 38(04), 82–87 (2016) 10. Xia Jingping, H., Hui, Y.Y., Minhui, O.: Research on improved shadow matching location algorithm based on high score weighting. Glob. Position. Syst. 42(06), 1–8 (2017). https:// doi.org/10.13442/j.gnss.1008-9268.2017.06.001 11. Bétaille, D., Peyret, F., Voyer, M.: Applying standard digital map data in map-aided, lane-level GNSS location. J. Navig. 68(5), 827–847 (2015) 12. Ng, H.F., Zhang, G., Hsu, L.T.: Robust GNSS shadow matching for smartphones in urban canyons. IEEE Sens. J. 21(16), 18307–18317 (2021)

Ubiquitous Localization and Trajectory Tracking Approach for GNSS Jammer Jiaxing Liu(B) , Jun Xie, and Linshan Xue China Academy of Space Technology, Beijing, China [email protected]

Abstract. It is more and more significant to quickly solve GNSS (Global Navigation Satellite System) jamming problem whenever and wherever possible. The dynamic jammer is more difficult to be localized, tracked and deactivated than the stationary one, so usually poses a greater threat. Based on thought of GNSS + Network (such as 5G mobile communication, Internet and Internet of Things) enabling, a new approach proposed in this paper generates the localization result of a dynamic or stationary jammer in real-time by fusion of the basic observation information, position information and factory data from GNSS and mobile communication integrated terminals. Then it obtains the trail of the jammer near real-time by reprocessing multi-epoch localization results. The structure and estimation method of jammer localization error sources are analyzed in depth, and further localization and trajectory tracking of a GNSS jammer for multiple typical moving scenes is simulated in this paper. Finally, an optimization strategy of the critical parameter is presented for multiple or unknown jammer dynamics. It shows through simulation and analysis that, the approach presented is accurate and stable; the localizing and tracking accuracy is insensitive to position error of receivers, and is slightly affected by receiver density; under typical situations, tracking accuracy of a single stationary and dynamic jammer is up to 30m and 50m or so respectively. Keywords: GNSS jamming event · Ubiquitous jammer localization · Jammer trajectory tracking · GNSS + Network enabling technology · Error source analysis

1 Introduction GNSS (Global Navigation Satellite System) is capable of supplying all-time, all-weather, hard real-time, high accuracy and low-cost position, navigation and timing service for global open space, and is successfully applied to mapping, engineering construction, transportation, agriculture, forestry, telecommunication, electric power, national defense and other industries, as well as mass consumption. However, GNSS services face lowcost, intentional or unintentional interference threat anytime and anywhere, such as inband interference caused by private electronic devices or amateur radio station, in-band

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or out-of-band interference caused by portable terminals for mobile satellite service, interference on non-cooperative users from pseudolites, dynamic or stationary intentional interference for avoiding monitoring, tracking, paying or that for regional control. Jammer aggravates accuracy, availability, continuity and integrity, while low accuracy, erroneous or missing position and timing results have adverse effects on the production and life of users, and may even cause malignant accidents. For example, navigation error derived by jamming may delay transportation, cause economic loss and even traffic accident. Drones need to acquire position, navigation and timing information by GNSS service. Small drones cost less and own poor anti-interference performance, so they are easy to be driven away from the target sites or trapped to wrong locations and as a result unable to perform tasks normally. GNSS receiver anti-interference technology requires high equipment configuration requirements and is not suitable for low-cost handheld, onboard, or airborne receivers. As an effective interference cancellation measure, jammer localization technology can reduce the configuration requirements of GNSS user receivers. The urgent problem to be solved is to be capable of using low-cost equipment to achieve wide range and high real-time jammer localization. TDOA (Time Difference of Arrival) determines the position of interference through the correlation calculation results of samples collected by multiple monitoring nodes, which requires monitoring nodes to keep accurate time synchronization and transmit signal sampling data mutually [1–3]. AOA (Angle of Arrival) determines the interference direction by the array antenna at monitoring node, and localize a jammer by the estimation results of AOA from multiple monitoring nodes [4, 5]. RSS (Received Signal Strength) can be used to jammer localization. The jammer localization method based on radio frequency front-end needs the front-end of the monitoring device to have jamming-to-noise ratio detection function [6]. The single-receiver synthetic method based on C/N0 [7] requests the receiver to additionally configure an integrated navigation unit to move around a jammer by large angles. The crowdsourcing centroid method based on C/N0 [7] requests the jammer to be at the geometrical center of the receivers with sum of squares jammer detector. The jammer localization method based on collection and training of signal samples [8] needs the samples and the jamming characteristics to be accordant, and the environment to be stable. For the methods afore, monitoring devices are complex, high-cost and unable to be supported by regular navigation receiver, consequently difficult to solve jamming threat anytime and anywhere and the jammer in movement. In recent years, with the vigorous development of the smart phone and wearable smart device market, as well as the progress of embedded GNSS receiver, GNSS single system/multi system dedicated chips, GNSS and mobile communication integrated chips and other technologies, mass consumer applications have emerged and dominated. According to the GNSS market report in 2019 [9], the global user holdings of GNSS terminals in 2019 reach 6.4 billion, about 0.8 per capita, including 3.4 billion in the Asia Pacific region, about 0.8 per capita. In 2019, among all kinds of terminals, consumer terminals accounted for about 90% of the total holdings, while professional terminals such as highway, UAV and seafaring accounted for only about 10% in total. Consumer

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terminals are mainly realized by smart phones and tablets, as well as personal tracking devices, wearable devices, digital cameras and portable computers. With the integration and development of GNSS, 4G/5G, Internet, IoT (Internet of Things), big data and other technologies, the GNSS enabling technology has been upgraded from a simple GNSS application technology to a combined GNSS + 5G/Internet/IoT application technology, which has constantly generated new applications and new businesses to meet the needs of the consumer and professional users. Based on the static GNSS jamming source location approach based on crowdsourcing carrier to noise ratio fusion [10], this paper presents a localization and trajectory tracking approach for a single dynamic GNSS jammer anytime and anywhere. The approach herein, a type of RSS method, utilizes the carrier-to-noise ratio measurements, positions, antenna gains and so on of the GNSS and mobile communication integrated terminals, and calculates the real-time position and movement trail of a jammer precisely. The new approach has a wide range of functions, high real-time performance and low equipment configuration requirements, compared with traditional ones. Aiming at typical jammer motion scenes such as static motion (simulating a fixed erected jammer), linear motion (simulating an onboard jammer travelling straight along a road, or an airborne jammer flying straight along a route) and square motion (simulating an onboard jammer turning at an intersection, or an airborne jammer turning at a corner of a building), this paper simulates, analyzes and optimizes jammer localization and tracking.

2 Localization and Tracking Approach 2.1 Observation Equation Carrier-to-noise ratio observation C/N0 is a basic observation generated by the baseband process part of GNSS receiver, which is defined as ratio of signal power to noise power density. In an interference environment, the carrier-to-noise ratio output of a user receiver includes signal, noise and jamming, namely equivalent carrier-to-noise ratio [11], the expression of which is 

C N0

j

j

eff,i

Ci,r  = N0 + Ji,r (QR)

(1) j

where, i is receiver serial number, j is satellite serial number, Ci,r is the received satellite j signal power by receiver i, N 0 is receiver noise power spectrum density, Ji,r is the received jamming power by receiver i, Q is anti-jam quality factor, R is spread spectrum code rate of satellite signal. Anti-jam quality factor Q is determined by spread spectrum code rate R and power spectrum density S S ( f ) of satellite signal, as well as jammer power spectrum density S J ( f ). Q≈

R

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∞

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When wide-band white noise jamming acts on BPSK modulated spread spectrum signal and covers its spectrum main lobe, Q ≈ R

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When the jamming power is significantly higher than the noise power, the receiver carrier-to-noise ratio declines substantially, even causing the tracking loop of the receiver unlock, so formula (1) can be approximated as:  j j Ci,r QR C = (4) N0 eff,i Ji,r Formula (4) is further expanded as:  j j j Ci,a Gi QR C =  2 N0 eff,i λ J 4πd GiJ i

(5)

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where λ is carrier length of the signal, Ci,a is satellite j signal power at the antenna aperture j

of receiver i, Gi is the antenna gain of receiver i toward satellite j, J is transmitting power of the jammer, di is the distance between the jammer and receiver i, GiJ is the antenna gain of receiver i toward the jammer. It can be obtained by sorting out (5) that   j  j j Ci,a Gi λ 2 J C (6) = N0 eff,i 4πdi QR GiJ According to formula (6), jammer localization can be supported by observing a single navigation satellite. Actually, a GNSS receiver completes its positioning depending on at least 4 satellites. In order to reduce the measurement error, the observation results of all n satellites could be used, and it can be obtained from formula (6) that n  j j C1,a G1 G1J  

  2 n  n 

C j C j di j=1 = (7) n  N N d j j 0 0 1 J eff,1 eff,i j=1 j=1 Ci,a Gi Gi j=1

For the receivers, navigation satellites and their signals which participate jammer localization, it is assumed that navigation signal powers from all the satellites at antenna apertures of all the receivers are equal (the situation where this assumption causes errors will be discussed in Chap. 3), which means formula (7) can be simplified to: n  j G1 G1J  

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C j C j di j=1 = (8) n  N N d j 0 0 1 J eff,1 eff,i j=1 j=1 Gi Gi j=1

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Observation equation for jammer localization can be derived from formula (8):

f (x, y, z) = F1,i (xi − x)2 + (yi − y)2 + (zi − z)2

− G1,i (x1 − x)2 + (y1 − y)2 + (z1 − z)2 = 0 (9) where F1,i

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G1 j Gi



G1J (11) GiJ

(x, y, z) is jammer coordinate, (xi , yi , zi ) is receiver i coordinate. 2.2 Single Epoch Localization The ubiquitous localization for GNSS jammer is based on the carrier-to-noise ratio and positioning information of receivers, so the epoch of ubiquitous localization for GNSS jammer is the epoch of observation data of receivers, usually 1 s. Apply the first order Taylor expansion to Eq. (9) to form the following linearized equation:       −f xJk , yJk , zJk = −2F1,i xi − xJk + 2G1,i x1 − xJk x     + −2F1,i yi − yJk + 2G1,i y1 − yJk y     + −2F1,i zi − zJk + 2G1,i z1 − zJk z (12)   where xJk , yJk , zJk is the k-th estimate of jammer coordinates, i = 2,3,…,m, and m is the total number of receivers involved in jammer localization. Solve the equation set according to Eq. (12) to obtain the k + 1st estimation:     xJk+1 , yJk+1 , zJk+1 = xJk + x, yJk + y, zJk + z (13) After meeting the convergence requirements, the localization solution of this epoch is completed, and the last coordinate estimation is the jammer localization result. The convergence requirements include Lower limit value of two norm of (x, y, z) and upper limit value of iteration calculation times. The GNSS receivers, with sudden drop of carrier-to-noise ratio and loop keeping tracking state, can be included into GNSS receiver sequence involved in jammer localization (short for receiver sequence). The receivers with loop unlocked or stopping to output carrier-to-noise ratio measurements should exit receiver sequence, whereas the receivers which restore loop lock and output carrier-to-noise ratio measurements

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continuously should rejoin. In a receiver sequence, the static receiver coordinate is predetermined by GNSS positioning or any other ways; the dynamic receiver coordinate could be the GNSS positioning results updated in real time. The widely distributed GNSS and mobile communication integrated terminals can transmit the navigation signal carrier-to-noise ratio and positioning information to the data processing center through direct transmission or transfer. The data processing center can be the Beidou system short message communication center station, mobile communication base station or mobile communication core network, or a special jammer localization and tracking center. The data processing center establishes and maintains the receiver sequence according to the jamming event, and uses the corresponding receiver observation data to determine the location and trail of jammer. 2.3 Multiple Epoch Tracking In principle, the real-time jammer localization can be realized through multiple single epoch localization in a short time interval. The receiver near the jammer cannot participate in the positioning process because of the loss of the tracking loop. The jammer causes the receiver close to it to lose its lock during the movement. At the same time, even if the receiver which previously lost its lock and was far away from it has the conditions for relocking, it needs to wait for a certain time to restabilize the loop tracking and output its own positioning results. The effect of instant exit and delayed rejoining of receiver leads to less receiver resources participating in dynamic jammer localization than those participating in static jammer localization under the same receiver environment, so the localization accuracy of the former is lower. In order to improve the localization accuracy of dynamic jammer and adapt to various dynamic characteristics, the quasi realtime trajectory tracking of jammer is realized by Norder least square fitting of the multiple epoch jammer localization results. The N-order least squares fitting expression is: ⎡

⎤

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1N 1N −1 pJ ,1 ⎢ ⎢ . ⎥ ⎢ 2N 2N −1 ⎢ . ⎥=⎢ . .. ⎣ . ⎦ ⎣ . . . pJ ,ep epN epN −1

⎤⎡ co1 ⎤ ⎥⎢ co2 ⎥ ⎥ ⎥⎢ ⎥ ⎥⎢ . ⎢ ⎦⎣ .. ⎥ ⎦ · · · ep0 coN +1 ··· ··· .. .

10 20 .. .

(14)

where, pJ ,1 , · · · , pJ ,ep represents someone dimension (x, y or z) coordinate of the multiple epoch jammer localization results; ep is the total number of epochs involved in the fitting, meeting ep > N + 1; co1 , co2 , · · · , coN +1 are coefficients of fitting polynomial. The coefficient sequence of fitting polynomial can be obtained by solving Eq. (14) with least squares, which is recorded as coe1 , coe2 , · · · , coeN +1 .

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The fitting result of someone dimension coordinate of the jammer is ⎤ ⎡ N N −1 1 1 pJfit,1 ⎥ ⎢ 2N 2N −1 ⎢ ⎢ .. ⎥ ⎢ ⎢ . ⎥=⎢ . .. ⎦ ⎣ .. ⎣ . N N pJfit,ep ep ep −1 ⎡

⎤⎡ coe ⎤ 1 e ⎥ ⎥⎢ co 2 ⎥ ⎥⎢ ⎥ ⎥⎢ . ⎢ ⎦⎣ .. ⎥ ⎦ e · · · ep0 coN +1 ··· ··· .. .

10 20 .. .

(15)

2.4 Error Source Analysis According to formula (9), (10) and (11), the error sources of the jammer localization equation include receiver positioning error (RPE) obtained by satellite navigation service and receiver carrier-to-noise ratio measurement error (CNOME). Besides, what needs attention is formula (8) requires that the navigation signal power from each satellite at the antenna aperture of each receiver is equal. However, actually signal transmitting power from different satellite are different to a certain extent, and signal landing power from the same satellite in different directions are also different to a certain extent. The differences above introduce signal transmitting power error (STPE) and signal landing power error (SLPE) to formula (8). Those errors could be included in carrier-to-noise ratio error. According to the factory test data of the receiver, the average gain of the receiving antenna in all directions can be obtained, which is substituted into formula (11). In fact, receiving antenna gain (RAG) of each receiver fluctuates in different directions, and the antenna gains of different receivers towards the direction of GNSS jammer are also different, causing receiving antenna gain error (RAGE). RAGE can be considered as a part of the carrier-to-noise ratio error. STPE, SLPE and RAGE are independent from each other, and are included in carrierto-noise ratio error by multiplying. The observation error including STPE, SLPE, RAGE and CNOME is called comprehensive carrier-to-noise ratio error (CCNOE), so as to distinguish from CNOME. The standard deviation of CCNOE measured in decibels is:  2 + σ2 + σ2 2 (16) σCCNO = σSTP SLP RAG + σCNOME where, σSTP , σSLP , σRAG and σCNOME is standard deviation of STPE, SLPE, RAGE and CNOME respectively. Imagine that STPE, SLPE, RAGE and CNOME are all uniformly distributed. In general, the distribution intervals of the above errors are [−2dB, 2dB], [−1dB, 1dB], [−2dB, 2dB] and [−2dB, 2dB]. According to the variance characteristics of uniform distribution, σSTP , σSLP , σRAG and σCNOME is 1.2dB, 0.6dB, 1.2dB and 1.2dB respectively. By substituting the above values into the formula (16), it can be obtained that the typical value of σCCNO is 2.1dB.

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3 Simulation and Optimization 3.1 Typical Scenes Simulation The following simulation conditions are adopted for various dynamic scenes of jammer: • There are three kinds of dynamic scenes of jammer, including static, linear motion and square motion. In the static scene, the jammer is localized for 20 times. In the linear motion scene, the motion speed of the jammer is set to 6 m/s, and the jammer is localized for 14 times. In the square motion scene, the square side length is set to 600 m, the motion speed of the jammer to 10 m/s, and the jammer is localized for 25 times. In all the scenes, the time interval between two adjacent jammer localizations is 10s; • The ground jammer interferes with the B1I signal of Beidou satellite navigation system using broadband white noise, with transmitting power 1mW and bandwidth 4.092 MHz; • 50 times of simulations are conducted for each dynamic scene of jammer, namely 50 samples used, among which the number, location distribution, positioning error and carrier-to-noise ratio error of receivers are different; • Under each dynamic scenes and samples, 200, 100 or 50 receivers near the jammer participate in jammer localization, which are randomly distributed within 2000 m in the east-west direction and 2000 m in the north-south direction; The receivers use the B1I signal to complete the positioning solution, with positioning errors in the east-west, north-south and up-down directions following the Gaussian distribution, and the standard deviation of the receiver positioning error (σRPE ) in each direction being 1 m, 5 m or 20 m; The standard deviation of comprehensive carrier-to-noise ratio error (σCCNO ) is 2dB or 3dB; • Four Beidou navigation satellites are used to participate in jammer localization; The landing power of the B1I signal is set to −158 dBW; The equivalent carrier-tonoise ratio threshold for the receiver to maintain loop tracking is set to 28 dBHz; The condition for relocking after a receiver loses lock is that the equivalent carrier-to-noise ratio remains above the threshold for 30 s. Static Scene of Jammer The simulation results of horizontal localization and tracking accuracy of static jammer are shown in Figs. 1, 2 and 3, where the abscissa is the fitting order and the ordinate is the horizontal localization and tracking accuracy. Jammer localization accuracy is defined as the root mean square value of the difference between the real-time localization result of the jammer and its true location. Jammer tracking accuracy is defined as the root mean square value of the difference between the localization fitting result of the jammer and its true location. Figure 1 shows the relationship between localization and tracking accuracy of static jammer and receiver positioning error (RPE), when the number of receivers is 200 and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue dots and red triangles correspond to σRPE in each direction, which

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are 1 m, 5 m and 20 m respectively. It can be seen that the 1m curve almost coincides with the 5m curve, and the accuracy in the 20m curve is only about 4% lower than that in the 1m curve. Localization and tracking accuracy of static jammer are not sensitive to RPE. 70

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Fig. 1. Relationship between localization and tracking accuracy of static jammer and RPE

Figure 2 shows the relationship between localization and tracking accuracy of static jammer and number of receivers, when σRPE in each direction is 5 m and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue dots and red triangles correspond to the numbers of receivers, which are 200, 100 and 50 respectively. It can be seen that number of receivers has a small impact on localization and tracking accuracy of static jammer. The tracking accuracy by 100 receivers is about 5% lower than that by 200 receivers, and the tracking accuracy by 50 receivers is about 18% lower than that by 200 receivers. 70

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Figure 3 shows the relationship between localization and tracking accuracy of static jammer and CCNOE, when the number of receivers is 200 and σRPE in each direction is 5 m. The dotted line represents the horizontal localization accuracy of jammer, and

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the solid line represents its horizontal tracking accuracy; the curves marked with green circles and red triangles correspond to σCCNO , which are 2dB and 3dB respectively. It can be seen that CCNOE has a significant impact on localization and tracking accuracy of static jammer, where the tracking accuracy with 3dB is about 41% lower than that with 2dB. 70

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Fig. 3. Relationship between localization and tracking accuracy of static jammer and CCNOE

It can be seen from Figs. 1, 2 and 3 that for static jammer, tracking accuracy is obviously better than localization accuracy. The lower the fitting order, the higher the tracking accuracy. In typical cases (with σCCNO 2dB), localization accuracy is approximately 56 m, tracking accuracy of 1st order fitting can reach about 30 m, and that of 5th order fitting can reach about 37 m. When the number of receivers is 50, σRPE in each direction is 5 m, and σCCNO is 2dB, the horizontal localization results of static jammer of a simulation sample are shown in Fig. 4. The jammer is at [0, 0] coordinate point, the light blue dots represent the receivers, the dark blue dots represent the horizontal localization results of the jammer, and the green dots represent the horizontal tracking results of the jammer of 1st order fitting. It can be seen that the tracking results are concentrated near the real location of the jammer. 1000 800

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Linear Motion Scene of Jammer The simulation results of horizontal localization and tracking accuracy of linear motion jammer are shown in Figs. 5, 6 and 7, where the abscissa is the fitting order and the ordinate is the horizontal localization and tracking accuracy. Figure 5 shows the relationship between localization and tracking accuracy of linear motion jammer and RPE, when the number of receivers is 200 and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue dots and red triangles correspond to σRPE in each direction, which are 1 m, 5 m and 20 m respectively. It can be seen that the 1m curve, the 5m curve and the 20 m curve almost coincide with each other. Localization and tracking accuracy of linear motion jammer are almost unaffected by RPE. 70

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Fig. 5. Relationship between accuracy of linear motion jammer and RPE

Figure 6 shows the relationship between localization and tracking accuracy of linear motion jammer and number of receivers, when σRPE in each direction is 5 m and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue dots and red triangles correspond to the numbers of receivers, which are 200, 100 and 50 respectively. It can be seen that number of receivers has a small impact on localization and tracking accuracy of linear motion jammer. The tracking accuracy by 100 receivers is about 4% lower than that by 200 receivers, and the tracking accuracy by 50 receivers is about 14% lower than that by 200 receivers. Figure 7 shows the relationship between localization and tracking accuracy of linear motion jammer and CCNOE, when the number of receivers is 200 and σRPE in each direction is 5 m. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles and red triangles correspond to σCCNO , which are 2dB and 3dB respectively. It can be seen that CCNOE has a significant impact on localization and tracking accuracy of linear motion jammer, where the tracking accuracy with 3dB is about 49% lower than that with 2dB. It can be seen from Figs. 5, 6 and 7 that for linear motion jammer, tracking accuracy is obviously better than localization accuracy. The lower the fitting order, the higher the

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tracking accuracy. In typical cases (with σCCNO 2dB), localization accuracy is approximately 64 m, tracking accuracy of 1st order fitting can reach about 40 m, and that of 5th order fitting can reach about 50 m. When the number of receivers is 50, σRPE in each direction is 5 m, and σCCNO is 2dB, the horizontal localization results of linear motion jammer of a simulation sample are shown in Fig. 8. The red dots represent the real location of the jammer, the light blue dots represent the receivers, the dark blue dots represent the horizontal localization results of the jammer, and green dots represent horizontal tracking results of the jammer of 1st order fitting. It can be seen that the tracking results are consistent with the linear motion trajectory of the jammer. Square Motion Scene of Jammer The simulation results of horizontal localization and tracking accuracy of square motion jammer are shown in Figs. 9, 10 and 11, where the abscissa is the fitting order and the ordinate is the horizontal localization and tracking accuracy. Figure 9 shows the relationship between localization and tracking accuracy of square motion jammer and RPE, when the number of receivers is 200 and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue

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Fig. 8. Horizontal localization results of linear motion jammer of a simulation sample

dots and red triangles correspond to σRPE in each direction, which are 1m, 5m and 20m respectively. It can be seen that the 1m curve, the 5m curve and the 20 m curve are almost coincident. Localization and tracking accuracy of square motion jammer are scarcely affected by RPE. 350

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Figure 10 shows the relationship between localization and tracking accuracy of square motion jammer and number of receivers, when σRPE in each direction is 5 m and σCCNO is 2dB. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles, blue dots and red triangles correspond to the numbers of receivers, which are 200, 100 and 50 respectively. It can be seen that number of receivers has a small impact on localization and tracking accuracy of square motion jammer. The tracking accuracy by 100 receivers is about 2% lower than that by 200 receivers, and the tracking accuracy by 50 receivers is about 6% lower than that by 200 receivers. Figure 11 shows the relationship between localization and tracking accuracy of square motion jammer and CCNOE, when the number of receivers is 200 and σRPE in each direction is 5 m. The dotted line represents the horizontal localization accuracy of jammer, and the solid line represents its horizontal tracking accuracy; the curves marked with green circles and red triangles correspond to σCCNO , which are 2dB and

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It can be seen from Figs. 9, 10 and 11 that for square motion jammer, tracking accuracy is obviously better than localization accuracy with appropriate fitting order. The tracking accuracy of 9th order fitting is highest. In typical cases (with σCCNO 2dB), localization accuracy is approximately 72 m, tracking accuracy of 9th order fitting can reach about 60 m, and that of 5th order fitting can reach about 70 m. When the number of receivers is 50, σRPE in each direction is 5 m, and σCCNO is 2dB, the horizontal localization results of square motion jammer of a simulation sample are shown in Fig. 12. The red dots represent the real location of the jammer, the light blue dots represent the receivers, the dark blue dots represent the horizontal localization results of the jammer, and green dots represent horizontal tracking results of the jammer of 5th order fitting. It can be seen that the tracking results are consistent with the square motion trajectory of the jammer.

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3.2 Approach Optimization In different jammer motion scenes, the fitting order to make tracking accuracy of jammer best is different. When the motion form of the jammer is unknown or difficult to determine, the fitting order is preferred to be 5. In typical cases, the tracking accuracy of static, linear and square motion jammer can reach about 37 m, 50 m and 70 m respectively, which is 34%, 22% and 3% higher than their respective localization accuracy. In the case of predicting or determining that the jammer is in static state or in linear motion, the fitting order is preferred to 1. In typical cases, the tracking accuracy of the static and linear motion jammer can reach about 30 m and 40 m respectively, which is about 46% and 38% higher than their respective localization accuracy. In the case of predicting or determining that the jammer is in square motion, the fitting order is preferred to 9. In typical cases, the tracking accuracy of the square motion jammer can reach about 60 m and about 17% higher than the localization accuracy.

4 Conclusion This paper exploits the potential of GNSS + Network enabling technology, and deeply studies the approach of precise localization and quasi real time tracking for satellite navigation jammer. Based on the optimization strategy of fitting order, the tracking accuracy of static or dynamic jammer is obviously better than the localization accuracy. The localization and tracking accuracy of jammer is not sensitive to the receiver positioning error, but is affected by the distribution density of receiver to a small extent, and is significantly affected by the comprehensive carrier-to-noise ratio error. When the optimal fitting order is selected in typical cases, the tracking accuracy of static, linear and square motion jammer can reach about 30 m, 40 m and 60 m respectively, which is about 46%, 38% and 17% higher than their respective localization accuracy.

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References 1. Myrna B. My.: Passive Geolocation of low-power emitters in urban environment using TDOA. In: Department of Electrical and Computer Engineering, Air Force Institute of Technology (2007) 2. Jonas, L., Dennis, M.A., Oscar, I., et al.: GNSS interference detection and localization using a network of low cost front-end modules. In: The 20th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 1165–1172 (2007) 3. Jahshan, A.B., Todd, E.H., Brent, M.L.: Development and demonstration of a TDOAbased GNSS interference signal localization system. In: IEEE/ION Position Location and Navigation Symposium (PLANS), pp. 455–469 (2012) 4. Ediz, C., Ryan, J.R.T., Matthew T., et al.: Interference detection and localization within the GNSS environmental monitoring system (GEMS)-system update and latest field test results. In: The 27th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 3449–3460 (2014) 5. Deng, P., Fan, P.Z.: An AOA assisted TOA positioning system. In: 2000 International Conference on Communication Technology Proceedings, vol. 2, pp. 1501–1504 6. Scott, L.: J911: the case for fast jammer detection and location using crowdsourcing approaches. In: The 24th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 1931–1940 (2011) 7. Daniele, B., Ciro, G., Andrej, S., et al.: Jammer localization: from crowdsourcing to synthetic detection. In: The 29th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 3107–3116 (2016) 8. Dongliang, L., Xin, C., Di, H.: Wide-area navigation band jamming signal monitoring and localization based on pattern recognition. In: The 9th China Satellite Navigation Conference (2018) 9. European GNSS Agency.: GSA GNSS Market Report, issue 6 (2019) 10. Jiaxing, L., Jun, X., Xu, Z., et al.: Jammer localization approach based on crowdsourcing carrier-to-noise density power ratio fusion. In: China Satellite Navigation Conference 2020 Proceedings, vol. III, pp. 604–612. Springer (2020) 11. John. W.B.: Effect of narrowband interference on receiver estimation of C/N0: theory. In: The 2001 National Technical Meeting of the Institute of Navigation, pp. 817–828 (2001)

Research on 3D Positioning Technology of UWB Single Base Station Jingjing Zhang1 , Lu Huang2 , Jia Su1(B) , Zihan Yang2 , and Qingwu Yi2 1 School of Information Science and Engineering, Hebei University of Science and Technology,

Hebei 050018, China [email protected] 2 State Key Laboratory of Satellite Navigation System and Equipment Technology, The 54th Research Institute of China Electronics Technology Group Corporation, Hebei 050081, China

Abstract. In recent years, in the context of smart cities and the internet of everything, with the rapid development of the intelligent indoor environment, the demand for indoor location services in many industries has become higher and higher, and the need for real-time location of personnel has become more and more urgent. In this paper, a UWB-based circular antenna array single base station is designed for indoor space single base station 3D positioning problem, and the joint Time of Arrival (TOA)/Angle of Arrival (AOA) positioning estimation algorithm is studied. In terms of direction finding, a five-array element direction finding model is established using a uniform circular array, and the Phase Difference of Arrival (PDOA) algorithm is combined to obtain the signal arrival angle information, and TOA is used to complete the distance measurement between the base station and the label, to achieve the calculation of label location information. Also, for the consideration of improving the accuracy of angle measurement, the ambiguity resolution method of antenna array element phase difference for long baseline is proposed. Finally, the system performance was tested and verified in the experimental environments. The results show that the UWB single base station can be used to achieve indoor 3D positioning, its positioning accuracy is better than 1m. Furthermore, the technology can effectively solve problems such as the high deployment cost of multiple base stations, complicated system construction, and so on in practical applications with more excellent application and promotion value. Keywords: UWB · Single base station · Antenna array · AOA · Ambiguity solution

1 Introduction With the rapid development of Internet of Things technology, intelligent mobile terminal technology and mobile computing technology, indoor positioning technology has become a popular topic for academic research and industrial applications [1, 2]. Also, Ultra Wideband (UWB) has unique advantages such as low transmit power, high transmission rate, strong penetration ability, strong anti-interference, and so on [3]. It has © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 427–437, 2024. https://doi.org/10.1007/978-981-99-6928-9_37

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gradually become an excellent choice for indoor positioning signal sources. Most UWB positioning systems use multiple base stations to achieve 2D or 3D positioning of users. In order to overcome the shortcomings of multiple reference base station systems in installation and deployment, time synchronization and other aspects, single base station positioning is one of the current development trends. Iwakiri and Kobayashi [4] utilized the antenna array time-domain smoothing method for joint TOA and AOA estimation of UWB signals, which gives AOA a resolution greater than 3°, but leads to a decrease in TOA resolution compared to the previous method. Ding [5] proposed a new idea of using the matrix beam algorithm to calculate the multipath time delay arriving at the different antennas, then determining the 2D position of the signal source according to the TOA and DOA models. However, it needs to satisfy the condition that the transceiver is far enough away and no longer holds for close position estimation. Smaoui et al. [6] proposed a new method for AOA estimation using a label with a single antenna and a reference point with a dual antenna. It simplified the tag design but with a slight increase in the complexity of the base station. To address the above problems, the paper changes the thinking and combines the unique advantages of UWB with the characteristics of single base station positioning, designs a UWB single base station with array antennas, uses a uniform circular array to establish a five-array element direction finding model to obtain signal angle information (azimuth angle and pitch angle). Also, the UWB accurate ranging information is fused to achieve tag positioning, further improving location information accuracy.

2 Related Work 2.1 UWB Common Positioning Methods UWB commonly used positioning methods include Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), and so on [7]. TOA positioning requires ranging based on the one-way propagation time of the signal at the base station and the node to be measured. In order to achieve accurate positioning, distance information between at least three and more base stations and the target to be measured is required. However, TOA positioning requires an asynchronous operation. If the base station clock accuracy is very high, the positioning accuracy can be up to centimetre-level. TDOA localization can be an excellent solution to the shortcomings of TOA localization, but it requires strict clock synchronization between anchor points. AOA positioning requires the installation of antenna arrays at the base station and is costly. In addition, the signal is vulnerable to reflection, refraction, and diffraction during transmission, but overall, AOA positioning has high accuracy. 2.2 Uniform Circular Array Direction Finding Model The commonly used array structures in direction finding include Uniform Linear Array (ULA) and Uniform Circular Array (UCA). Compared with the ULA, UCA can not only provide azimuth angle estimation over a range of 360°, but also carry out 2D direction finding estimation of azimuth and pitch angles [8]. A UCA direction finding model is

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established as shown in Fig. 1. The model contains M = 5 array elements antenna, uniformly distributed on a circle of radius R = 29.8 mm, and array element 0 is in the x-axis direction. The angle between the incident signal and the positive z-axis direction is recorded as the pitch angle ϕ ∈ [0, π/2). The angle between the projection of the signal on the xoy plane and the x-axis positive direction is noted as the azimuth angle θ ∈ [0, 2π ).

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Fig. 1. Schematic diagram of UCA direction finding model

With the coordinate origin as the reference point, the angle between the first m array element and the x-axis is γm = 2π m/M (m ∈ [0, M − 1]), and the coordinates of each array element are Pm = (R cos γm , R sin γm , 0). The propagation time delay difference τm between the arrival of the incident signal at array element m compared to the arrival at the reference point is shown in Eq. (1). The corresponding received phase difference φm (ϕ, θ ) is Eq. (2) compared to the reference point. τm = −

2πm R sin ϕ cos(θ − ) c M

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2πm 2πR sin ϕ cos(θ − ) λ M

(1) (2)

where, the signal wavelength is λ and the speed of light is c.

3 Description of Algorithm Details In this paper, a uniform circular antenna array single base station based on UWB is designed. Figure 2 shows the relevant information about the base station, and a fivearray element antenna is installed on the UWB single base station to realize the tag localization. Next, this section introduces the TOA/AOA joint localization estimation algorithm based on a uniform circular array in detail. Then, based on the characteristics of a circular array, the problem that the distance between antenna elements limits the accuracy of angle measurement is considered, and the ambiguity resolution algorithm of the element phase difference for the long baseline antenna is proposed.

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Inside of the antenna array

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Fig. 2. Schematic diagram of base station related information

3.1 The TOA/AOA Joint Localization Estimation Algorithm Based on a UCA The combination of UWB ranging and direction finding methods can rely on a single base station for the actual location estimation of the tag. The TOA method is used to obtain the distance d between the tag and the positioning base station. In the direction finding, a five-array element direction finding model is established using a UCA and combined with the Phase Difference of Arrival (PDOA) algorithm to obtain θ and ϕ of the tag. Therefore, d , θ , and ϕ can calculate the tag position information by combining the base station coordinate information. Suppose the spacing of the array element m and n (n < m) is dmn , and the geometric relationship of a uniform circular array is easy to obtain dmn = 2R sin[π(n − m)/M ]. According to Eq. (2), the phase difference φmn between the first n array element and the first m array element is obtained as Eq. (3).   2πm 2πn 2πR sin ϕ cos(θ − ) − cos(θ − ) (3) φmn = φn − φm = λ M M Assuming that m1 , n1 , m2 and n2 are four different array elements in a uniform circular array, where dm1 n1 is the distance between the array elements m1 and n1 , dm2 n2 is the distance between the array elements m2 and n2 . The θ and ϕ can be solved according to Eq. (4). ⎧ −1 ⎡ φm1 n1 ⎤  −1 α ⎪   ⎨ θ = tan π(n +m ) π(n +m ) 1 1 1 1 λ − sin α cos β dm1 n1 ⎦ M M ⎣ φ ⇒ =−  m2 n2 ⎪ β 2π cos π(n2M+m2 ) − sin π(n2M+m2 ) ⎩ dm n ϕ = sin−1 α 2 + β 2 2 2

(4) where, α = sin ϕ sin θ, β = sin ϕ cos θ . The phase difference φm1 n1 and φm2 n2 can be calculated with the help of φ = ((αA − βA − αB + βB + π ) mod 2π ) − π. For details, please refer to the literature [9] to realize the angle of arrival solution with the PDOA method. The location information (x0 , y0 , z0 ) of the positioning label can be calculated according to the trigonometric function relationship as shown in Eq. (5). ⎧ ⎪ ⎨ x0 = d sin ϕ cos θ y0 = d sin ϕ sin θ (5) ⎪ ⎩ z0 = d cos ϕ

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3.2 The Ambiguity Resolution Algorithm Based on the Phase Difference of Antenna Elements with Long Baseline In the previous section, the θ and ϕ were solved using only the phase difference between two sets of adjacent antenna array elements. No phase ambiguity is generated if the distance between adjacent array elements is less than half the signal’s wavelength. The longer the distance between the array elements, the longer the signal arrival time difference and the more significant the resulting phase difference, which is of great help in terms of improved angle measurement accuracy. However, when the array element spacing exceeds the signal half-wavelength, it causes phase ambiguity problems. In other words, there is a difference of 2kπ between the measured φ and theoretical values ϕ of the phase difference. To enhance the precision of angle measurement, this paper investigated the method of long baseline phase difference ambiguity resolution. The principle diagram of phase difference solution ambiguity based on long baseline antenna array elements are shown in Fig. 3, there are three antenna array elements k0 , k1 and k2 . The received signal phases are φ0 , φ1 and φ2 , respectively. Among them, the spacing between antennas k0 and k1 is less than half-wavelength of the signal, the spacing between antennas k1 and k2 is less than half-wavelength of the signal, and there is no ambiguity in the phase difference. The distance between antennas k0 and k2 exceeds half-wavelength of the signal, and there is ambiguity in the phase difference. Assuming that the distance between antennas k0 and k2 is d , the signal wavelength is λ, the phase ambiguity is k, and the   range of values of k is k ∈ rounddown(−(d /λ − 0.5)), roundup(d /λ − 0.5) . Assuming that the phase difference between k0 and k1 is measured as φ01 , the phase difference between k0 and k2 is measured as φ02 , and the phase difference between k1 and k2 is measured as φ12 , as in Eq. (6). ⎧ ⎨ φ01 = φ1 − φ0 (6) φ02 = φ2 − φ0 ⎩ φ12 = φ2 − φ1 Since there is phase ambiguity between antennas k0 and k2 , Eq. (7) can be obtained by a series of derivations. φ12 = ϕ02 − φ01 = φ02 +2kπ − φ01 ⇒ φ02 + 2kπ − φ12 − φ01 = 0 (7) The value of k that makes the equation closer to 0 is the phase difference ambiguity between the antenna k0 and k2 , by traversing the values of the ambiguity k.

4 Experimentation and Evaluation In this section, static positioning experiments were designed to evaluate the positioning precision of the UWB antenna array 3D positioning technology. At the same time, to raise the angle measurement precision, the ambiguity resolution algorithm of the long baseline phase difference proposed in this paper is verified. The experimental site is

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Fig. 3. Schematic diagram of the phase difference ambiguity resolution

Fig. 4. Diagram of experimental scenario

shown in Fig. 4 in the C7 AI test site of the 54th research institute. The center frequency of the transmitted signal of the tag is 4.0 GHz, and the half wavelength can be calculated as 37.5 mm. The base station is fixed at the height of 3.778 m, located directly above the test point 0. 4.1 Accuracy of Ranging For the ranging accuracy analysis, 31 test points are selected. The positioning tags are placed on the calibrated test points, and the straight-line distance between the tag and the base station is calculated by the distance formula. The linear distance between the tag and the base station is taken as the reference value, and compared with the ranging results of the simulation output, and the ranging error is calculated. The diagram of the ranging error bar is shown in Fig. 5, it can be seen that the mean values of the errors at different test points are different, and the ranging error is not linearly related to the distance. However, the error fluctuation at any test point is slight, and the overall ranging error tends to be 0.1 m. 4.2 Accuracy of Angle Measurement This paper randomly selects many test points for the angle measurement accuracy analysis, and the positioning tags are placed on the calibrated test points. The reference angle of the test points is calculated by arctangent function and compared with the angle measurement results of the simulation output. The diagram of the angle measurement

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Fig. 5. Diagram of ranging error bar

Fig. 6. Diagram of angle error bar

error bar is shown in Fig. 6. It can be seen that the mean and standard deviation of the angle measurement errors at different test points are different. Among the selected test points, the mean and standard deviation of the maximum angle measurement errors are 13.5750° and 6.9379°, respectively. In addition, the mean and standard deviation of the minimum angle measurement errors are 2.5367° and 0.8643°, respectively. For the phase angle measurement method, in addition to a suite of system errors that affect the angular accuracy, the length of the baseline between antenna elements also limits the accuracy to a large extent. In order to raise the angle measurement precision, the ambiguity resolution algorithm of the long baseline phase difference proposed in this paper is authenticated. The azimuth and pitch angle error estimates for a set of long baseline antenna elements and a set of short baseline antenna elements are shown in Fig. 7. The error estimation of azimuth and pitch angle for two long baseline antenna elements are shown in Fig. 8. As can be seen from the figures, whether it is a combination of antenna elements with one long and short baseline or two long baselines, the angle measurement algorithm’s azimuth and pitch estimation errors converge to 0°, with azimuth in range [0°, 360°) and pitch in range [0°, 90°). The correctness and effectiveness of the ambiguity resolution algorithm of element phase difference for long baseline antenna are verified.

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Fig. 7. Diagram of azimuth and pitch angle error estimation based on a set of long baseline antenna elements and a set of short baseline antenna elements: (a) 01–02 and 02–23 antenna pitch and azimuth estimation errors, (b) 02–04 and 02–12 antenna pitch and azimuth estimation errors

Fig. 8. Diagram of azimuth and pitch angle error estimation based on two groups of long baseline antenna elements: (a) 02–03 and 02–13 antenna pitch and azimuth estimation errors, (b) 02–24 and 02–14 antenna pitch and azimuth estimation errors

4.3 Accuracy of Positioning This paper randomly selects test points 2, 28, 29 and 31 for positioning accuracy analysis. Place the positioning label on the selected test points, compare the positioning reference values with the simulation output positioning results, and calculate the mean and standard deviation of the positioning errors. The positioning results and errors of the four test points are shown in Figs. 9 and 10, respectively. Moreover, the data of positioning errors are shown in Table 1. As can be seen in Fig. 9, the UWB positioning results for the four test sites are close to their own positioning benchmarks. From the data in Table 1 and Fig. 10, it can be seen that the maximum positioning error of test point 2 is 0.955 m, with a mean error value of 0.8591 m and a standard deviation of 0.0439 m. The maximum positioning error of test point 28 is 1.10 m, the mean error is 0.7716 m, and the standard deviation is 0.0955 m. The maximum positioning error at test point 29 is about 0.91 m, with a mean error value of 0.6239 m and a standard deviation of 0.0876 m. Furthermore, the maximum positioning error of test point 31 does not exceed 1.07 m, where the mean

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Fig. 9. Diagram of positioning results

Fig. 10. Diagram of positioning error

Table 1. Data of positioning error Test points

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2

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0.0955

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0.6239

0.0876

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0.1124

error is 0.7220 m, and the standard deviation is 0.1124 m. The positioning results are calculated by combining the ranging and angle measurement information, and the angle measurement errors of individual positions fluctuate considerably. However, according to the above analysis of the positioning error data, it can be obtained that the overall positioning accuracy of the positioning algorithm proposed in this paper is better than 1 m.

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5 Conclusion and Outlook This paper proposed the UWB single base station 3D positioning technology. In the first part, the challenges faced by current indoor positioning technology and the commonly used solutions are introduced, and the current snagging problems are summarised in this paper. In the second part, the direction finding model of five-array elements uniform circular array is mainly designed. In the third part, the details of the implementation of the algorithm are described in this paper, and the joint TOA/AOA localization estimation algorithm based on the uniform circular array is designed and proposed, and the information of azimuth angle and pitch angle are obtained by combining the PDOA algorithm in the direction finding. Aiming at the problem that the baseline between antenna elements limits the accuracy of angle measurement, the ambiguity resolution algorithm of long baseline phase difference is studied, further improving the positioning information’s accuracy. In the fourth part, the performance of the proposed algorithm is verified through extensive experiments. In the static experiments, the ranging error tends to be 0.1m, and the positioning accuracy is better than 1m, which has high positioning accuracy. Furthermore, according to the angle measurement errors of a group of long and short baselines and two groups of long baselines are close to 0°, which confirms the correctness and effectiveness of the proposed phase difference ambiguity resolution algorithm. In the coverage area, the problems of high deployment cost and poor environmental adaptability faced by multi-base station systems in practical applications can be effectively solved by the technology, and the system deployment efficiency is significantly improved, which has a more significant application and promotion value. In future studies, this paper will continue to find a method to suppress the ranging and angle measurement error based on the 3D positioning technology of UWB single base station, to achieve a more lightweight, more stable, reliable and low-cost indoor positioning solution.

References 1. Lymberopoulos, D., Liu, J.: The microsoft indoor localization competition: experiences and lessons learned. IEEE Signal Process. Mag. 34(5), 125–140 (2017) 2. Bi, J., Zhao, M., Yao, G., Cao, H., Feng, Y., Jiang, H., Chai, D.: PSOSVRPos: WiFi indoor positioning using SVR optimized by PSO. Expert Syst. Appl., Volume 222, 2023, 119778, ISSN 0957–4174 3. Alarifi, A., et al.: Ultra wideband indoor positioning technologies: analysis and recent advances. Sensors 16(5), 707 (2016) 4. Iwakiri, N., Kobayashi, T.: Joint TOA and AOA estimation of UWB signal using time domain smoothing. In: 2007 2nd International Symposium on Wireless Pervasive Computing. IEEE (2007) 5. Ding, R., Qian, Z., Wang, X.: UWB localization method based on TOA and DOA joint estimation. J. Electron. Inf. Technol. 02, 313–317 (2010) 6. Smaoui, N., Heydariaan, M., Gnawail, O.: Single-antenna aoa estimation with uwb radios. In: 2021 IEEE Wireless Communications and Networking Conference (WCNC), pp. 1–7. IEEE (2021) 7. Nouali, I.Y., Slimane, Z., Abdelmalek, A.: Change point detection-based TOA estimation in UWB indoor ranging systems. In: 2022 45th International Conference on Telecommunications and Signal Processing (TSP), pp. 329–332. IEEE (2022)

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8. Zhang, K., Shen, C., Bao, M., Vaniushkina, D., Kumushai, K., Zang, L.: Research on optimization algorithm based on PDOA. In: 2021 IEEE 21st International Conference on Communication Technology (ICCT), pp. 1427–1430. IEEE (2021) 9. Dotlic, I., Connell, A., Ma, H., Clancy, J., McLaughlin, M.: Angle of arrival estimation using decawave DW1000 integrated circuits. In: 2017 14th Workshop on Positioning, Navigation and Communications (WPNC), pp. 1–6. IEEE (2017)

Towards Cis-Lunar Navigation: Design and Analysis of a SmallSat System with Time-Transfer from BDS Xiao Chen1,2

, Zhongkai Zhang1(B) , Yong Zheng1 and Conghai Ruan1

, Zhanglei Chen1

1 Information Engineering University, Zhengzhou 450001, China

[email protected] 2 Xi’an Satellite Control Center, Xi’an 710043, China

Abstract. The Moon, as the only natural satellite of the Earth, is a crucial destination for human space exploration and serves as a foundation for deeper space exploration. Cis-lunar space offers vast opportunities for human expansion beyond the Earth’s land and ocean. The exploration, construction, and development of cislunar space demand enhanced cis-lunar space navigation. While GNSS navigation technology for the Earth and near-Earth space is well-established, extending it to cis-lunar space is the current stage. Small satellite technology development provides new ideas for efficient and rapid deployment of small satellite navigation constellations. To meet the cis-lunar space navigation demands, we propose a small space-based navigation system using BDS for time-transfer, based on Earth-Moon libration points orbits and small satellite platform. In this paper, we systematically study the multi-type orbital and navigation characteristics adopted, and design and analyze the architecture of the cis-lunar space small satellite navigation system using BDS timing. The proposed navigation constellation using multiple types of orbits, including DRO, NRHO, etc., is timed through BDS to compensate for the limited load of small satellites and the limited accuracy of the star clock. We analyze the observability of navigation constellations and evaluate the navigation performance of several constellation design cases using corresponding accuracy indicators. Our results verify the feasibility and preliminary performance of the proposed cis-lunar space small satellite navigation system using BDS as time-transfer, and provide a reference for BDS and GNSS to provide navigation services to cis-lunar space. We propose a new idea and method for cis-lunar space navigation that combines BDS navigation technology and small satellite platform, and which holds great promise for future space exploration. Keywords: Navigation · Earth-moon libration points · BDS · Time-transfer · DRO · NRHO

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 438–448, 2024. https://doi.org/10.1007/978-981-99-6928-9_38

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1 Introduction The exploration of the Moon has been a primary focus of human space exploration since the Apollo program, and it continues to be a crucial goal for space exploration. As more countries, including China, Europe, Japan, Russia, and the US, plan to return to the Moon, the need for reliable Position, Navigation, and Timing (PNT) services in cis-lunar space is becoming increasingly important to support crewed and robotic exploration activities. Global Navigation Satellite System (GNSS) is capable of providing precise PNT services anywhere on Earth’s surface or in near-Earth space. The GNSS constellation’s satellite clock accuracy is relatively high, and it can be continuously corrected by the ground segment. Therefore, it can be used as a source of time transfer. However, the SmallSat platform used in cis-lunar navigation constellations has some limitations, such as a small payload capacity, including the on-board clock, and limited capacity to monitor cis-lunar navigation satellites [1]. Due to the limited resources available for monitoring the earth-moon navigation constellation on Earth, the cis-lunar satellite requires less maintenance, including less orbit maintenance and clock correction. To improve the navigation accuracy of cis-lunar constellation based on SmallSat, this paper proposes to use high-precision BDS for time-transfer. The earth-moon libration-points orbits, such as Near-Rectilinear Halo Orbits (NRHOs) and Deep Space Resonance Orbits (DROs), can be used for the large-scale cis-lunar space. NASA’s Gateway program has selected the NRHO of the L2 southern family as its operational orbit [2]. NRHOs have neutral stability characteristics, which reduces the orbit maintenance cost. Similarly, DRO is expected to be autonomous, reducing its dependence on ground support. The DRO-based navigation system could provide broader coverage and higher signal intensities in cis-lunar space than those of the current GNSS system [3, 4]. Thus, this paper proposes to establish a small space-based navigation system for cis-lunar space using BDS for time-transfer under the SmallSat platform on the basis of earth-moon libration points orbits. This paper analyzes the visibility of satellites in different orbits in the cis-lunar constellation and the BDS constellation, obtaining the visible time ratio of SmallSat to more than one and more than four BDS satellites, as well as the Maximum Continuous Invisible (MCI), the maximum invisible time interval. By timing, this paper achieves the same time accuracy for the cis-lunar constellation of SmallSat as the BDS constellation, analyzing the cis-lunar constellation’s navigation coverage of the lunar surface and the lunar low-orbit LLO constellation by GDOP and navigation accuracy. The proposed system provides a new idea and method for cis-lunar space navigation and verifies the feasibility and preliminary performance of the cis-lunar space small satellite navigation system using BDS as time-transfer. The study also provides a reference for BDS and GNSS to provide navigation services to cis-lunar space.

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2 Background 2.1 CRTBP and Libration Points Orbits In the Earth-Moon space, the spacecraft is mainly affected by the Earth and the Moon, forming the Three-Body Problem. The three-body problem cannot be solved accurately, and it is usually simplified as a Circular Restricted Three-Body Problem (CRTBP). The libration point is described as the point of a small celestial body in space under the gravity of two main celestial bodies. At this time, the small object remains essentially stationary relative to the two main objects. In the earth-moon space, five special solutions can be derived from the restricted three-body problem in celestial mechanics. NRHO is a kind of periodic orbit, which belongs to the halo orbit family around L1/L2 point in the three-body system. Generally, it is a highly elliptical orbit in the CRTBP of the Earth-Moon L2 point, which is considered to be a special case of the halo orbit (near L1/L2) of the Earth-Moon system. NRHOs have good dynamic and geometric properties, which are almost constant visible on Earth and almost constant coverage of the Moon’s Antarctic region. This feature makes the orbit easy to control from the earth and cover the Moon’s South Pole. It is currently considered to be a potential orbit for manned deep space stations in the future. Different aspects of the moon’s NRHO orbit have been studied: Earth-NRHO transfer, station keeping and ground station visibility conditions. The feasibility of earth-moon round-trip activities is verified by using NRHO [5]. NRHO orbit is designed for lunar soft landing [6]. NRHO is analyzed for feasibility of orbit transfer to lunar surface [7]. It is analyzed that the visible conditions on and around the moon and the approximate performance of the user receiver when the NRHO orbit is used as a navigation constellation [8]. Distant Retrograde Orbit (DRO) family belongs to a special symmetric planar family of the CRTBP model. With increasing amplitudes, the Earth’s influence becomes more stronger and the shape of the DRO deviates more further from a circular orbit. For DROs very close to the Moon, the influence from the Earth is negligible, and the DROs are approximately retrograde circular orbits around the Moon in a two-body frame. As a result, the frequency of orbit control maneuvers can be smaller. The planar DROs are in the Moon’s orbit plane, having good coverage of the lunar surface except for the poles. The DRO orbit is more stable than the Collinear Libration Point orbit and is more suitable for navigation [9]. In order to increase the coverage of the lunar polar region, a small out-of-plane amplitude added to the DROs [10]. 2.2 BDS and Time Transfer BeiDou navigation System (BDS) is a GNSS independently developed by China, provided seven kinds of PNT services worldwide in 2018. Considering the integrity and coverage of the BDS constellation 3GEO + 3IGSO + 24MEO configuration, as well as the frequency bandwidth, this paper selects B3I as the timing signal, which is 1561.098 MHz. We design an architecture of Cis-Lunar Navigation SmallSat System (CLNSS), which uses the traditional BDS system to provide accurate timing correction for onboard clock. The BDS on-board atomic clock has high accuracy and is corrected by the monitoring ground stations at any time, so the time is more accurate. The onboard

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clock of SmallSat on the cis-lunar navigation constellation orbits has limited in function with lower grade of time accuracy. As shown in Fig. 1, we propose time transfer technology utilizes intermittently available BDS signals to mitigate the need for on-board clocks and to the need for extensive ground monitoring infrastructure on the Moon. In a reasonable time range, by receiving BDS time to update the time of the satellite-based clock, improve the accuracy of the earth-moon space navigation satellite clock, to meet the earth-moon space navigation accuracy requirements.

Fig. 1. Time transfer from BDS to CLNSS (not to scale).

3 Architecture & Method 3.1 Constellation Architecture Through the analysis of extensive case studies, we designed a cis-lunar space small satellite navigation system architecture using BDS timing, and systematically studied the multitype orbital and navigation characteristics used, considering the BDS transfer time to the earth-moon orbit. In particular, we design high-fidelity simulations of satellites for each earth-moon orbit type. For each type of modeling orbit, we design a case study by simulating the onboard clock. For each case study, we consider the start time epoch to be 1 Jan 2025 00:00:00.000 UTC and the experiment time duration to be 30 days. Our choice of cis-lunar orbits types (including DRO, NRHO and ELFO) for this work to establish a navigation SmallSat constellation. In our case study analysis, we define the earth-moon rotating frame along the instantaneous earth-moon position vector, the z-axis is along the instantaneous angular momentum vector of the Moon’s orbit around the Earth, and the y-axis completes the orthogonal system. The initial conditions of position and velocity in the Moon-centered earth-moon rotating frame. Specifically, in the earth-moon rotation frame, for NRHO L2 South, we refer to the previous literature [5] that solves for an NRHO in the ephemeris model (L2, radius of perigee to be 4500 km, South family) using a forward/backward shooting process to provide the following initial state vector at an initial time epoch. We create realistic simulations of these satellites

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in different earth-moon libration points orbits by leveraging the High Precision Orbit Propagator (HPOP). The HPOP generates and propagates accurate position and velocity solutions of the earth-moon orbit satellite by accounting for precise force models of Earth, the Sun and the Moon. In addition, in order to take advantage of the navigation performance of the DRO orbit closer to the moon, we found the orbit of DRO2 for the construction of the Earth-Moon navigation constellation. Where NRHO and DROs are in the Moon-centred synodic coordinates, and ELFOs are in the Moon-centred inertial coordinates. The ELFO constellation have four satellites. The true proximal angle of the reference star is 0°, and the spacing is 90°. The parameters of the ELFO constellation are shown in Table 1 and Fig. 2. Table 1. Orbit parameters in our case study analysis. Orbit type

Epoch (UTC)

rx (km)

ry (km)

rz (km)

NRHO

1 Jan 2025 00: 00: 00.000

−125.952

120.961

4357.681

−0.042

1.468

−0.003

−53080.5

0

0

0

0.490681

0 0

DRO1

vx (km/s)

vy (km/s)

vz (km/s)

−9761.09

0

0

0

0.736051

Orbit type

Epoch(UTC)

a (km)

e

i

ω



λ

ELFO_0

1 Jan 2025 00: 00: 00.000

11487.9

0.7

63.5

90

0

0

DRO2

ELFO_1

90

ELFO_2

180

ELFO_3

270

Fig. 2. Designed orbits in Moon-inertial frame.

The CLNSS consists of one NRHO orbiting satellite, two different DRO orbiting satellites, and four ELFO orbiting satellites with different phases in the same orbit. Through preliminary simulation analysis, when the cone half angle of the satellite sensor of the CLNSS set 30°, it can meet the coverage of the lunar surface and the near-moon space LLO constellation.

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4 Analysis and Results 4.1 Satellite Visibility and MCI Analysis For comparative analysis in this study, we define the following two validation metrics: • Satellite visibility. Satellite visibility refers to the percentage of time that the number of visible BDS satellites is greater than the set threshold. There is at least one satellite visibility, which is the minimum number of satellites required to estimate stellar clock bias and clock drift. There are at least four satellites visibility, which is the minimum number of satellites estimated to include the complete state of satellite position and velocity. • Maximum Continuous Invisibility (MCI). MCI is the maximum continuous time duration when no BDS satellite visible. The smaller the MCI value, the better. For the four orbit types considered in our case study, we showcase the number of visible BDS satellites by blue in Fig. 3a–d. Based on Table 2, we observe that NRHO achieves the greatest at least one satellite visibility, which is 100% of the total time, and also the greatest at least four satellite visibility, which is 100% of the total time. These observations related to NRHO seem reasonable since an earth-moon satellite in NRHO operates at high altitudes ranging between 4500 km–700000 km above the Moon’s surface, and thus experiences fewer occultations from Earth and the Moon. And the DRO achieves the greatest at least one satellite and least four satellites visibility, both of which are 100% of the total time. This is due to the orbital characteristics of the DRO far from the moon. However, DRO2 exhibits the Max MCI of 2839.74s, while the greatest at least one satellite visibility, which is 96.96% of the total time, and also the greatest at least four satellite visibility, which is 96.29% of the total time. Although the ELFO orbit is relatively high, but there are still blocked by the moon, and can’t receive the BDS signal, which exhibits the Max MCI of 3030.279s. Table 2. Comparison analysis across different orbit types. Orbit type

MCI (s)

Satellite visibility (%) ≥1

≥4

0

100.00%

100.00%

DRO1

0

100.00%

100.00%

DRO2

2840

96.96%

96.29%

ELFO_0

3030

99.66%

99.59%

NRHO

Based on the results of the above visibility analysis, the CLNSS and BDS can almost remain visible. In this case, BDS can be used to provide time synchronization service for CLNSS. By using BDS timing to improve its clock accuracy, the CLNSS enable the navigation for the Moon and the LLO constellation in near-moon space.

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(a) NRHO

(c) ELFO

(b) DRO1

(d) DRO2

Fig. 3. BDS satellite visibility across different orbit types.

4.2 Case Analysis for Moon By analyzing the coverage of CLNSS navigation satellites on the entire moon, the navigation ability of CLNSS on the lunar surface is studied. In the simulation analysis, parameter settings are shown in Table 3. The multi-coverage capability of the CLNSS to the entire moon was analyzed firstly, and then the GDOP and Navigation Accuracy analysis of the whole moon are analyzed. Table 3. Simulation settings of case analysis for Moon. Parameter

Values

Latitude/longitude step for the moon

6°

Simulation time step

300 s

Multiple coverage

0~7

The range uncertainty of the CLNSS sensor

5m

The range uncertainty of the lunar surface receiver

5m

Threshold of GDOP

6.0

Time transfer

BDS

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• Multiple coverage analysis. The CLNSS covers the Moon‘s South Pole very well. This is because NRHO and ELFO orbits’ satellites stay longer over the moon’s south pole, providing more navigation service time. In the 30-day simulation experiment, 6fold coverage can be achieved in most areas of the southern hemisphere of the moon, and the entire lunar surface can achieve 4-fold coverage. In terms of the duration of continuous navigation services, 4-fold coverage can be achieved continuously in the area south of 36° southern latitudes (see Fig. 4a). With the increase of latitude, the percentage of coverage time and the total coverage time decrease. The two indicators are lowest at the Moon’s North Pole, with a coverage time percentage of 45.18% and total coverage time of 13.6 days (see Fig. 4b). • GDOP. For navigation performance, GDOP < 6.0 can be considered relatively good navigation performance. The CLNSS has good navigation performance for most areas of the entire lunar surface, except for the area near the north pole (see Fig. 5). • Navigation Accuracy. For most lunar regions, the navigation accuracy is less than 100 m, especially in the Antarctic region. However, with the operation of CLNSS, the navigation accuracy of some lunar surface areas is still not very high. This is due to the constellation configuration problem of CLNSS. During the whole period, the number of CLNSS satellites over the region is small.

(a) Multiple coverage

(b) Latitude Coverage

Fig. 4. Multiple coverage and Latitude Coverage of CLNSS to Moon.

Fig. 5. Analysis of GDOP and Navigation Accuracy for Moon.

According to the above analysis, the CLNSS achieves at least six-fold coverage of satellite navigation signals in the southern hemisphere of the moon, and 100% navigation

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signal coverage in the region of south 36° south of the moon within 30 days. The navigation performance of the constellation meets the design requirements. GDOP and Navigation Accuracy can basically satisfy the navigation requirements of the moon. 4.3 Case Analysis for LLO In order to analyze the navigation performance of the CLNSS for lunar low-orbit satellites. We select the reference satellite in the LLO constellation as the observation satellite. The simulation settings of this case analysis are shown in Table 4, and the orbital parameters of LLO_0 in the lunar inertial frame are shown in Table 5. By analyzing the reference satellite of LLO, and receiving the navigation signal provided by the CLNSS, the navigation performance is analyzed by GDOP and Navigation Accuracy. Table 4. Simulation settings of case analysis for LLO. Parameter

Values

Satellite

LLO_0

Integration step

300 s

The range uncertainty of the CLNSS sensor

5m

The range uncertainty of the LLO receiver

5m

Threshold of GDOP

6.0

Time transfer

BDS

Table 5. Orbit parameters of LLO_0. Satellite

Epoch (UTC)

LLO_0

1Jan 2025 1838.19 00: 00: 00.000

a (km)

e

i

ω



λ

0.000409

90.015

123.859

256.221

0

• GDOP. The optimal GDOP value of the CLNSS for LLO is 1.6, with a large average value. In order to ensure better navigation performance, the segment with GDOP BERC th , BERd > BERth or i < Imax , return to step i . 2, otherwise stop the iteration and output the global optimal value Qbest

4 Numerical Results The simulation scenario is D2D signals multiplexing MS-NOMA signals uplink scenario shown in Fig. 1, the BS coordinate is (0, 0), the cell radius is 200 m, the number of PUsers is 20, The number of C-Users included in the bandwidth occupied by each P-User is 30, 50 and 80, and the total system bandwidths B = 18 MHz, 32 MHz and 50 MHz,

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respectively. The distances of all users are randomly selected from 10~200 m, the distance between D2D pairs is 20 m, the carrier frequency is f = 3.5 GHz, the communication subcarrier bandwidth fc is 30 kHz, the one-sided PSD of noise is 3*10–14 W/Hz, the maximum transmit power of C-Users and D-Users are 23 dBm and 20 dBm, respectively, the channel model is a free propagation model, the inertia weight w is 0.8, the learning factor c1 and c2 are 0.5, the number of particles Z is 300, the maximum number of iterations Imax is 50. Meanwhile, we compare the PSOBPA strategy with the average power allocation algorithm and repeat the Monte Carlo experiment 50 times. Figure 2 shows the variation of total system throughput with the power of P-users. It can be seen from Fig. 2 that the PSOBPA strategy has greater total system throughput than the average power allocation method at the same bandwidth, and the total system throughput increases with increasing bandwidth when using the same power allocation method. In addition, it shows that increasing the power of P-Users did not have a significant impact on the total system throughput when using the same algorithm and system bandwidth. Therefore, we set the signal power of P-Users in the MS-NOMA signal system to a fixed value (6 dBm). Then we allocate the signal power of the C-Users in the MS-NOMA signal system and the signal power of D-Users to maximize the total system throughput. Figure 3 shows the Cumulative Distribution Function (CDF) of SINR for C-users and D-Users using the PSOBPA strategy, it shows the overall SINR of D-users is better than that of C-users, that’s because the distance between D2D pairs is generally smaller, so a better SINR can be obtained.

Fig. 2. Total system throughput with the power of P-Users.

Table 1 displays total system throughput of two power allocation algorithms at different bandwidths. The results indicate that the PSOBPA strategy enhances the total system throughput by approximately 15% compared to the average power allocation algorithm, across three bandwidths (50 MHz, 32 MHz, and 18 MHz). Table 2 presents the average ranging accuracy of two power allocation algorithms at different bandwidths. It indicates that the PSOBPA strategy improves the ranging accuracy by approximately 4% compared to the average power allocation algorithm, across the same three bandwidths. Meanwhile, the average ranging error of all positioning users becomes smaller as the bandwidth increases.

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Fig. 3. The CDF of SINR for C-users and D-Users

Table 1. Total system throughput of two power allocation algorithms at different bandwidths. PSOBPA power allocation (Mbps)

Average power allocation (Mbps)

Total system throughput improvement (%)

50 MHz

326.21

283.64

15.01

32 MHz

203.12

177.27

14.58

18 MHz

120.85

105.01

15.08

Table 2. Average ranging accuracy of two power allocation algorithms at different bandwidths. PSOBPA power allocation (m)

Average power allocation (m)

Average ranging accuracy improvement (%)

50 MHz

0.41

0.43

4.65

32 MHz

0.67

0.70

4.29

18 MHz

1.07

1.12

4.47

Figure 4 shows the BER of all communication users when using the PSOBPA strategy. It can be seen from the figure that the BER of each C-User and each D-User is less than the predetermined BER threshold, indicating that the PSOBPA strategy can ensure the communication quality of all communication users. In Fig. 5, the ranging accuracy of each P-user using the PSOBPA strategy is displayed within three different bandwidths. It can be seen from Fig. 5 that the ranging errors become smaller as the bandwidth increases. Meanwhile, the ranging errors of all Pusers are smaller than the predetermined threshold under the corresponding bandwidths, which indicates that the PSOBPA strategy can ensure the ranging accuracy of all P-Users.

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Fig. 4. BER of all communication users over C-Sub.

Fig. 5. Ranging error of P-Users.

5 Summary Since existing studies do not consider the mutual interference between D2D and MSNOMA signals, in this paper, we study the power allocation strategy for D2D and MS-NOMA signals. We formulate an optimization problem that aims at maximize the total system throughput under the QoS requirement and power constraints. To solve this problem, we propose the PSOBPA strategy to allocate the signal power of the C-Users in the MS-NOMA signal system and the signal power of D-Users. Based on the numerical results, the proposed PSOBPA strategy can improve the total system throughput by roughly 15% and raise the average ranging accuracy by about 4% compared to the average power allocation algorithm using the same bandwidth. Acknowledgement. This work is financially supported by National Key R&D Program of China (No. 2022YFB2601801) and by National Key R&D Program of China (No. 2022YFB3904502).

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References 1. Liang, D.Z., Hanhua, W., Jingrong, L.: Status and trend of communication-navigation integration positioning technology. Navigat. Positioning Timing 9(2), 15–25 (2022) 2. Xuemin, H., Yang, Z., Xueting, X. et al.: Performance analysis of position verification system in 5G-based integration communication and navigation networks. Navigat. Positioning Timing 9(2), 65–72 (2022) 3. Xiaobin, L., Ping, Z., Minhao, L.: A method for selecting a multiplexing mode for device pass-through communication. Guangdong: CN108650661A, 2018/10/12 4. Yang, H., Alphones, A., Zhong, W.D., et al.: QoS-driven optimized design in a new integration visible light communication and positioning system. In: ICC 2020–2020 IEEE International Conference on Communications (ICC), pp. 1–6. IEEE, Dublin (2020) 5. Zhu, L., Liu, C., Yuan, J., et al.: Machine learning-based resource optimization for d2d communication underlaying networks. In: 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall), pp. 1–6. IEEE, Victoria (2020) 6. Li, R., Hong, P., Xue, K., et al.: Resource allocation for uplink NOMA-based D2D communication in energy harvesting scenario: a two-stage game approach. IEEE Trans. Wirel. Commun. 21(2), 976–990 (2021) 7. Cao, J., Song, X., Xu, S., et al.: Energy-efficient resource allocation for heterogeneous network with grouping D2D. China Commun. 18(3), 132–141 (2021) 8. Liu, M., Zhang, L., You, Y.: Joint power and channel allocation for underlay D2D communications with proportional fairness. In: 2019 15th International Wireless Communications & Mobile Computing Conference (IWCMC), pp. 1333–1338. IEEE, Tangier (2019) 9. Xianbin, L., Jian, W., Xiaoqian, C. et al.: Power allocation method for integration signals of ranging communication between stars of a constellation of navigation satellites. Beijing: CN110708754B, 2020/9/4 10. Yin, L., Cao, J., Lin, K., et al.: A novel positioning-communication integration signal in wireless communication systems. IEEE Wirel. Commun. Lett. 8(5), 1353–1356 (2019) 11. Yin, L., Cao, J., Ni, Q., et al.: Design and performance analysis of multi-scale NOMA for future communication-positioning integration system. IEEE J. Sel. Areas Commun. 40(4), 1333–1345 (2022) 12. Yin, L., Jiang, T., Deng, Z., et al.: Joint uplink power allocation method in wireless communication and positioning integration system. IEEE Access 9, 53669–53678 (2021) 13. Betz, J.W., Kolodziejski, K.R.: Generalized theory of code tracking with an early-late discriminator part II: noncoherent processing and numerical results. IEEE Trans. Aerosp. Electron. Syst. 45(4), 1557–1564 (2009) 14. Jirong, Z., Fanke, M., Shenghuan, W.: D2D power allocation based on improved particle swarm optimization algorithm. J. Xi’an Univ. Posts Telecommun. 26(2), 8–14 (2021)

Space Observation Data Processing of XPNAV-01 Linli Yan1,2

, Qingyong Zhou3,4(B) , Shaojuan Fan1,2 , Xiaolong Hao5 , Kun Jiang5 , and Xiwei Chong6

1 School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China 2 Key Laboratory of Architectural Acoustics Environment of Anhui High Education Institutes,

Hefei, Anhui 230601, People’s Republic of China 3 State Key Laboratory of Geographic Information Engineering, Xi’an 710054, China

[email protected]

4 Xi’an Institute of Surveying and Mapping, Xi’an 710054, China 5 Beijing Institute of Communication and Tracking Technology, Beijing 100090, China 6 Space Engineering University, Beijing 101416, China

Abstract. The pulsar navigation test satellite 01 (XPNAV-01) is the first space test platform dedicated to exploring the verification of X-ray pulsar navigation technology in China. It has collected a large amount of scientific observation data in orbit, which can be used for scientific research and timing navigation analysis. In this work, more than three years of observations of the Crab pulsar of XPNAV01 are analyzed, and the pulse profiles of the Crab pulsar each orbit, day and year are obtained. The experimental goal of the satellite being able to accurately “see” the pulsar was achieved. The pulse profiles of four energy bands based on the observation data of XPNAV-01 are reported for the first time in China, and their variation trends with energy are in good agreement with the observation results abroad. A variety of parameters are used to comprehensively evaluate the change of the Crab pulsar’s pulse profile shape over time. It is found that the distribution of each parameter is relatively uniform, and the standard deviation of each parameter is small. The estimated single pulse arrival time accuracy is about 83 μs. All these results indicate that the X-ray detector independently developed in China has a good in-orbit operation status in its first four years. Keywords: X-ray · Pulsar navigation · Pulse profile

1 Introduction Pulsars are a kind of high-speed rotating neutron stars which can radiate pulse signals stably, and their positions can be accurately measured, so they can provide autonomous navigation services for spacecraft [1]. X-ray pulsar navigation is a new type of astronomical autonomous navigation technology, which has the common characteristics of traditional astronomical navigation systems: strong autonomy, high security, and no accumulation of navigation errors [2, 3]. Pulsars with uniform spatial distribution can be used to build constellations similar to navigation satellites, enhance the autonomous © Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 541–550, 2024. https://doi.org/10.1007/978-981-99-6928-9_47

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navigation capability of aircraft far away from ground measurement and control stations, and reduce the burden on ground deep space networks. Although the accuracy of X-ray pulsar navigation in near-Earth space cannot be compared with ground-based navigation technology [4], it has more broad application prospects in deep space field than the traditional astronomical navigation and ground-based navigation technology. Compared with satellite navigation system, the pulsar time-space reference frame is larger [5], which can realize seamless navigation in near-Earth, deep space and interstellar range, and the navigation error does not increase sharply with the distance. It is currently the only ultra-long-distance autonomous navigation means. In 2018, NASA successfully implemented the “The Station X-ray Timing and Navigation Technology” (SEXTANT) project. Using SEXTANT to obtain the timing data of four millisecond pulsars to achieve the convergence of the position accuracy of the International Space Station to 16km, preferably up to 5 km [4]. At the same time, pulsar autonomous navigation technology also occupies an important position in the demonstration and construction of the navigation positioning and time service system in China [6]. Pulsar navigation technology is the main means to provide benchmark information for deep space users, and it forms an important complementary role with ground-based deep space networks [7, 8]. XPNAV-01 is the first experimental satellite dedicated to verifying pulsar navigation technology in China, which was developed by China Academy of Space Technology [9, 10]. Since the normal operation of XPNAV-01, a large amount of observation data has been collected. Chinese scholars have carried out pulsar signal processing and timing analysis [11, 12], which confirmed that XPNAV-01 has successfully detected the signals of the Crab pulsars and carried out preliminary pulsar navigation experiments [13]. Dr. Zhang Dapeng analyzed the satellite observation performance from three aspects: the statistics of observation data, photon energy response and timing performance [12]. Dr. Huang Liangwei and researcher Shuai Ping used the 85-day observation data of XPNAV-01 to carry out the ground pulsar navigation calculation experiment. They used the Crab pulsar timing observation as the control point to suppress the satellite orbit propagation error. The average navigation error at the control point is 38.4 km [13]. In addition, Chinese scholars have also explored the pulsar navigation technology by using other X-ray astronomical satellites. Dr. Zheng Shijie proposed a method to achieve spacecraft orbit determination by using the significance of pulsar pulse profile. Using the observation data for the Crab pulsar from the gamma burst polarization detector on Tiangong 2 and Insight-HXMT to achieve spacecraft accuracy better than 30 km and 10 km, respectively [14]. XPNAV-01 has a design life of one year and has been in orbit for six years, providing a large amount of observation data for scientific research and time-based navigation. Due to the small effective area of the focused X-ray detector on XPNAV-01 and the strong fluidity of the photon signal emitted by the Crab pulsar, this work mainly analyzes the observation data for about its first four years. The second section introduces XPNAV-01 and its observations, the third section presents the data processing methods, and the fourth section analyzes the data processing results. Compared with the previous works, this paper has processed the Crab pulsar data for a longer period, and the characteristic parameters of the pulse profile are more accurate.

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2 Basic Information of XPNAV-01 and Its Observations XPNAV-01 is the first satellite dedicated to the pulsar navigation space test in China, which was successfully launched at Jiuquan Satellite Launch Center on November 10, 2016. It adopts the zero-momentum three-axis stable attitude control mode of the whole satellite, and operates in a sun-synchronous orbit. The semi-major axis of the orbit is 6878.137 km, the inclination is 97.4°, and its whole weight is about 243 kg. XPNAV-01 adopts an integrated electronic design, integrating satellite services, control calculations, measurement and control, GNSS navigation, and power control into integrated electronic components [9], as shown in Fig. 1. The XPNAV-01 scientific tasks include: firstly, verifying the performance of X-ray detectors in orbit, solving the problem of visibility of X-ray detectors in orbit, and providing basis for subsequent detector selection and improvement; the second is to obtain the space observation data for more than one Xray pulsar and provide data supports for the study of pulsar physical properties and the exploration of navigation systems. The main payload of the satellite is the grazing incidence Wolter-I focused X-ray detector, which is the first equipment of this type working in orbit in China. The focused X-ray detector adopts four-layer nested Wolter-I focusing optical lens, which can collect parallel X-ray photons onto a small area of SDD. When X-ray photons act on the SDD detector, a pair of electron-hole will be generated, the hole pair will be absorbed by the nearby cathode electrode, and the electrons will drift towards the anode of the detector under the electric field drive. The anode collects these electrons and converts them into electrical signals. The energy of electrons is read out based on the amplitude of the electrical signal. When the rising edge exceeds a certain threshold, a time will be triggered. The time will be marked by an on-board rubidium clock, which is recorded as the photon arrival time. XPNAV-01 is equipped with micro sensors in the form of 3 × 3, which can realize rough search and precise positioning on orbit [11], and the pointing control accuracy is better than 2 .

Fig. 1. Satellite Structure of XPNAV-01 Satellite [9]

XPNAV-01 has made long-term observations for the Crab pulsar. According to statistics, a total of 1455 times observations of 4.1 million seconds were carried out, and 60.84 million photons were collected in more than three years from November 2016 to December 2019. See Table 1 for observation. The original data is extracted and processed to

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obtain the arrival time (UTC time scale), energy and satellite orbit information of X-ray photons. The photon arrival time is measured with an accuracy of 100 ns. Table 1. Statistical information of the XPNAV-01 observations of the Crab pulsar. Year

Orbits

Exposure (ks)

2016

137

381

2017

553

1530

2018

516

1484

2019

249

705

Total

1455

4101

3 Data Processing and Navigation Solution Method 3.1 Data Preprocessing The data preprocessing follows these steps: select the X-ray photon data that correctly uses the GPS system timing, remove the X-ray photons with incorrect energy information or redundant records, and use dynamics to repair the missing part of the orbital information of the satellite. The observation data during the period when the photon flux exceeds 50 cts/s needs to be deleted to reduce the influence of space background particles noise. 3.2 Barycenter Corrections The signal processing of pulsars is generally carried out in the barycentric reference system of the solar system (BCRS), and it is necessary to convert the arrival time of X-ray photons to the barycentric center of the solar system (SSB). The XPNAV-01 carries a high-precision GPS receiver and uses GPS technology for positioning and timing. The orbit value of the telemetry downlink satellite value is in the WGS-84 geocentric coordinate, and the photon arrival time reference is UTC. The process of barycenter correction is as follows: firstly, according to the Earth’s rotation parameters (precession, nutation, polar motion, EOP), the satellite orbit value is converted to the J2000 geocentric inertial coordinate system, and the satellite orbit at the time of photon arrival is obtained by linear interpolation; secondly, considering that the time scale of the JPL planetary calendar is TDB time, UTC time is converted to TT time, and then to TDB time according to the resolution of the IERS 2010 bulletin; finally, considering the geometric propagation delay and the relativistic effect, the calculation of the position of the large celestial bodies in the solar system is based on the JPL DE405 ephemeris. And the first-order Newtonian gravitational delay of the large celestial bodies is also considered. See the reference [15] for the detailed barycenter correction formula.

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3.3 Pulse Profile Folding The Jodrell Bank Observatory monitors the Crab pulsar daily and provides very accurate radio ephemerides [15]. After the photon arrival time is corrected to the SSB, and the pulse profile can be folded using the precise pulsar ephemeris with radio observations as the phase reference point. The rotation parameters of the Crab pulsar are from the ephemeris of Jodrell Bank Observatory. It should be noted that the valid time period of the pulsar ephemeris overlaps, and the glitch period is not within the valid time of the ephemeris. 3.4 Pulse Profile Shape Fitting The X-ray pulse profile of the Crab pulsar is a double-peak structure. In order to accurately determine the peak phase of the double peaks and quantitatively describe the shape and phase evolution of the pulse profile with time, it is necessary to fit the pulse profile. The fitting function used for pulse profile fitting comes from the empirical formula proposed by Nelson et al. [16]: L(φ − φ0 ) = N

1 + a(φ − φ0 ) + b(φ − φ0 )2 −h(φ−φ0 )2 e +l 1 + c(φ − φ0 ) + d (φ − φ0 )2

(1)

where L is the intensity of the pulse profile, l, φ0 , N, a, b, c, d and h are the fitting parameters of the pulse profile shape respectively. The error of each shape parameter can be estimated by Monte Carlo simulation method, and the specific steps are as follows: 1. Generates a simulated pulse profile. Because the number of photons appearing in a certain phase interval conforms to the Poisson distribution, the total number of photons in each phase interval is Poisson sampled to obtain the simulated pulse profile; 2. Fit the simulated pulse profile to obtain its various shape parameters; 3. Repeat the second step 100 times, and calculate the standard deviation of each shape parameter of 100 groups of simulated pulse profiles as the error of observed pulse profile shape parameters.

4 Data Processing Results and Analysis 4.1 Pulse Profile The pulse profiles of the 1455-orbit observation from XPNAV-01are folded, and these profiles are aligned by using the cross-correlation. The integral pulse profile can also be obtained by adding all the single-orbit pulse profiles. As shown in Fig. 2, significant integrated pulse profiles in four years are folded, and it proves that the observation quality of the Crab pulsar is relatively good. In the X-ray band, the shapes of the two peaks are asymmetric, and the intensity of the main pulse is higher than the secondary pulse. The pulse profiles are basically the same and their similarity is more than 99.9%. The pulse profile in 2016 is with larger fluctuations because of its shorter exposure time. The annual observation parameters of the Crab pulsar from 2016 to 2019 are counted, as shown in Table 2. The count rate of pulsed radiation and the count ratio of background

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to pulsed radiation in four years is equivalent, which shows that the radiation of the Crab pulsar and the X-ray detection performance of the XPNAV-01 are relatively stable. So the domestic focused X-ray detector can accurately “see” the Crab pulsar, and it runs stably in orbit, and has completed the collection of pulsar observation data for more than one year.

Fig. 2. The integrated pulse profile of the Crab pulsar from 2016 to 2019

Table 2. The statistics of four-year observations of the Crab pulsar Year

Photon count (104 )

Exposure (ks)

Count rate (cts/s)

Count rate of background (cts/s)

Count rate of pulsed radiation (cts/s)

Count rate ratio

2016

469

375

12.51

11.82

0.69

17.07

2017

2169

1474

14.71

13.91

0.80

17.43

2018

2111

1457

14.50

13.68

0.81

16.81

2019

951

658

14.45

13.63

0.82

16.60

4.2 Quality Analysis of the Observed Pulse Profiles As X-ray photons with energy above 9 keV are affected by space particle noise and radiation of special elements of the telescope, all photons with energy below 9 keV are selected in this work. The average pulse profile in 0.01–9 keV is shown in Fig. 3. The profile shape in this energy band are similar to that from other X-ray satellites. They all exhibit a double-peak structure with the highest background intensity in the low-energy band. By comparing their normalized profiles, it can be found that as the energy increases, the intensity ratio of the two pulse pulses, the widths of two pulses,

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and the intensity of the bridge pulse all increases. The similarity of pulse profiles from XPNAV-01 and from the PCA of RXTE is 98.6%. The difference of them is mainly due to the different working energy bands of the X-ray detectors on the two satellites. In the same way, we can get the profile of each orbit and every day. As shown in Fig. 4, the shape of pulse profiles of each orbit or day are basically the same. It can be seen that the radiation of the Crab pulsar and the working state of the instrument are relatively stable.

Fig. 3. The multi-band pulse profiles of the Crab pulsar observed by different satellites (the left picture shows the average pulse profiles without removing the background, and the right picture shows the normalized pulse profile with background subtracted.)

Fig. 4. The pulse intensity distribution diagram of the Crab pulsar for each orbit (on the left picture) and every day (on the right picture)

In order to obtain accurate shape parameters and quantitatively analyze the stability of pulse profile, the formula (1) in Sect. 3 is used to fit the double pulses of the pulse profiles of the Crab pulsar. The observation quality is mainly measured by the shape parameters of the average pulse profiles, the ration of the intensity of the main pulse to the background (RI ) and the ratio of the total number of photons in the pulse region to the background (RN ). The shape parameters contain the intensity of the main pulse and second pulse, the phase separation of two pulses, the widths of two pulses, and the background intensity, which are recorded as IMP , ISP , , FWHMMP , FWHMSP , Ibkg . Due to the limitation of the amount of observation, the daily observation profile is divided into 200 bins, and the parameters of average profiles are obtained by eliminating the observations with photon number less than 20000, as shown in Fig. 5. The distribution

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of each parameter is relatively uniform, and the standard deviation of each parameter is small, as shown in Table 3.

Fig. 5. Shape parameters of the Crab pulsar’s daily profiles Table 3. The average values and standard deviations of the pulse shape parameters IMP

ISP

FWHMMP

FWHMSP



Ibkg

Average

1.44

1.18

0.04

0.08

0.40

0.94

Std. Deviation

2%

2%

5%

12%

1%

1%

For the daily observed pulse profile, as shown in Fig. 6, the average value of RI and RN is 1.80 and 0.06 respectively, and the RI of each profile is greater than 1.53, so the observation quality is good. It can be seen from the distribution of RN that the pulse radiation accounts for a small part of the total radiation, it is about 5.7%. The ratio of the number of photons between pulse part and background fluctuates, which may be caused by the changes in instrument background or/and the nebula background. In addition, the pulse signal-to-noise ratio (SNR) and the pulse arrival time precision (σTOA ) are also used to characterize the profile quality. Their calculation formulas are: Npulsed SNR = √ (2) Ntotal FWHMMP σTOA = (3) SNR where Npulsed is the number of photons in the pulse part, Ntotal is the total number of photons, and FWHMMP is the half width of the main pulse. As shown in Fig. 7. The

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Fig. 6. Distribution of intensity ratio and photon number ratio of pulse to background contour observed every day (RI on the left and RN on the right)

average SNR is about 17, and its significance is relatively high. The average value of σTOA is about 83 μs, which is only about 3/1000 of the period of the Crab pulsar.

Fig. 7. The distribution of signal-to-noise ratio and TOA error of each pulse profile

5 Conclusion More than three-year observations from XPNAV-01 for the Crab pulsar is completed in this work, including data preprocessing, barycenter correction, pulse profile folding and profile feature analysis. The pulse profiles of the Crab pulsars in different time ranges and different energy bands. It is found that the pulse profiles in four years are basically the same, and their similarities are more than 99.9%. A variety of parameters are used to comprehensively evaluate the changes of the Crab pulsar’s pulse profile over time. It is found that the distribution of each parameter in four years is relatively uniform, and the standard deviation of each parameter is small. The SNR of each observed pulse profile is about 17, and the average value of σTOA is about 83 μs. It has achieved the goal that the domestic focused X-ray detector could accurately “see” the Crab pulsar, and XNPAV-01 works stable in its first four years. Foundation Item: National Natural Science Foundation of China (Grant No.: 42004004, 42074006, 11903001), National Key Basic Research Development Plan (Grant No.: 2020YFB0505801), the Doctor Foundation of Anhui Jianzhu University 2019 (2019QDZ14, 2019QDZ31).

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References 1. Sheikh, S.I.: The Use of Variable Celestial X-ray Sources for Spacecraft Navigation. Department of Aerospace Engineering, University of Maryland, Maryland (2005) 2. Zheng, W., Wang, Y.D., Tang, G.J., et al.: X-ray pulsar-based navigation. Theory and Applications, pp. 1–28. Science Press, Beijing (2015) 3. Zhou, Q.Y.: Research on Theory and Methods of Pulsar Timing Data, pp. 120–146. PLA Strategic Support Force Information Engineering University,Zhengzhou (2020) 4. Mitchell, J.W., Winternitz, L.B., Hassouneh, M.A., et al.: SEXTANT X-ray pulsar navigation demonstration: initial on-orbit results. In: 41st Annual Guidance and Control Conference of American Astronautical Society vol. 18, no. 155, pp.1–12 (2018) 5. Huang, L.W.: Theory and Algorithm Study in X-ray Pulsar Autonomous Navigation Based on Pulsar Timing Model, pp.1–14. Tsinghua University, Beijing (2013) 6. Zhou, Q.Y., Wei, Z.Q., Yan, L.L., et al.: Space/ground based pulsar timescale for comprehensive PNT system. Acta Physica Sinica 70(13), 139701(2021) 7. Yang, Y.X., Yang, C., Ren, X.: PNT intelligent services. Acta Geodaetica et Cartographica Sinica 50(8), 1006–1012 (2021) 8. Xie, J., Liu, Q.J., Bian, L.: Development idea of national integrated positioning and navigation time service (PNT) system based on Beidou system. Space Electron. Technol. 5, 1–6 (2017) 9. Huang, L.W., Shuai, P., Zhang, X.Y., et al.: XPNAV-01 Satellite timing data analysis and pulse profile recovery. Chinese Space Sci. Technol. 37(3), 1–9 (2017) 10. Li, L.S., Mei, Z.W., Lv, Z.X., et al.: Grazing incidence focused x-ray pulsar telescope and on orbit data analysis. J. Ordnance Equ. Eng. 38(12), 175–179 (2017) 11. Shuai, P., Zang, X.Y., Huang, L.W., et al.: X-ray pulsar navigation test satellite science data analysis. Aerospace Control Appl. 43(3), 1–6 (2017) 12. Zhang, D.P., Wang, Y.D., Jiang, K., et al.: Processing and analysis of measured data of XPNAV-01 satellite. Acta Astronaut. 39(04), 411–417 (2018) 13. Huang, L.W., Shuai, P., Zang, X.Y., et al.: Pulsar-based navigation results: data processing of the x-ray pulsar navigation-I telescope. J. Astron. Telesc. Instrum. Syst 5(1), 018003(2019) 14. Zheng, S.J., Zhang, S.N., Lu, F.J., et al.: In-orbit demonstration of x-ray pulsar navigation with the insight-hxmt satellite. ApJ Suppl. Series 244(1), 1–8 (2019) 15. Jordell, B.: Observation crab monthly ephemerisis, http://www.jb.man.ac.uk/pulsar/crab/all. gro/, 2018/11/15 16. Nelson, J., Hills, R., Cudaback, D., Wampler, J.: Optical timing of the pulsar NP 0532 in the crab nebula. Astrophys. J. 161, L235 (1970)

Author Index

A An, Zhiyuan

Feng, Yuxuan

75

107

B Bai, Lu 488 Bao, Lin 51 Bi, Jiahe 132 C Cao, Chong 242 Cao, Xinyun 252 Chai, Hongzhou 107 Chai, Qiang 509 Chang, Jiansong 519 Chen, Guangyan 39 Chen, Lingqiu 107 Chen, Maolin 346 Chen, Peng 107 Chen, Xiao 438 Chen, Yuanjun 60 Chen, Zhanglei 438 Chong, Xiwei 541 Cui, Linlin 3 D Dai, Shisheng 530 Dai, Xiaoji 305, 331 Dempster, Andrew G. 488 Deng, Zhongliang 295, 358, 380, 401 Ding, Kaihua 216 Ding, Qin 39 Djuric, Nikola 530 Duan, Chufeng 201 F Fan, Shaojuan 541 Feng, Ran 144, 155, 165 Feng, Wenquan 488 Feng, Yanming 231

G Gao, Fan 94, 331 Gao, Weiguang 509 Gao, Wenzong 231 Ge, Wenxiao 530 Ge, Yulong 252 Guan, Zhongpei 252 Guo, Hang 273 Guo, Jianxin 519 Guo, Qinyu 51, 75 Guo, Shuren 509 Guo, Xia 497 H Han, Teng 264 Hao, Xiaolong 541 He, Donghan 475 He, Yunqiao 94 Hu, Cheng 85 Hu, Fangxin 176 Hu, Shengwei 51, 75 Hu, Tong 3 Huang, Chengyang 380 Huang, Lu 427 J Ji, Zhengyu 346 Jiang, Caiyun 39 Jiang, Dongfang 475 Jiang, Kun 497, 541 Jiang, Min 497 Jiang, Tianyou 305, 331 Jiang, Yuchen 295 Jiao, Yingxiang 14 Jin, Wenrui 449 Jing, Lili 94

© Aerospace Information Research Institute 2024 C. Yang and J. Xie (Eds.): CSNC 2024, LNEE 1092, pp. 551–553, 2024. https://doi.org/10.1007/978-981-99-6928-9

552

Author Index

K Kong, Yahui 94 Kuang, Cuilin 201

P Pan, Guofu 60 Pu, Junyu 475

L Lan, Guanghong 216 Lei, Biao 358 Li, Bin 187 Li, Chonghui 475 Li, Chunhua 60 Li, Dengao 144, 155, 165 Li, Jiaxue 449 Li, Kezhao 14 Li, Leyao 519 Li, Min 305 Li, Ping 460 Li, Shinan 380 Li, Siming 39 Li, Xianglu 346 Li, Xing 497 Liang, Yueji 39 Liu, Changjiang 346 Liu, Feifeng 85, 132 Liu, Hairui 242 Liu, Jiaxing 411 Liu, Lixia 107 Liu, Ning 51, 75 Liu, Qi 51, 75 Liu, Wenxiang 509 Liu, Xiaohui 391 Lu, Jun 283, 497, 509 Luo, Jia 176 Lv, Longfei 273 Lv, Shuaikang 14 Lv, Xiang 401 Lv, Xiaoxiao 449

R Ruan, Conghai

M Ma, Zhongmin 51, 75 Meng, Lingguo 242 Meng, Xiangdan 118 Meng, Xinyue 94 N Ni, Ting 273 Nie, Wenfeng 331 Nie, Zhixi 368 Ning, Baojiao 94 Ning, Yafei 242

438

S Sang, Kaiwei 201 Shen, Fei 252 Shen, Yunyan 14 Shi, Danyang 144, 155, 165 Shi, Jian 497 Si, Yibo 25 Su, Jia 427 Su, Mudan 283 Sui, Yeye 283 Sun, Chao 488 Sun, Yimao 346 Sun, Zhen 368 T Tan, Chengyao 3 Tian, Yingguo 475 Tong, Shuai 475 Tu, Xiangzheng 449 W Wan, Tianhe 51 Wan, Zihan 273 Wang, Bin 25 Wang, Charles 231 Wang, Chenghao 85 Wang, Jin 118 Wang, Junjie 3 Wang, Kai 14 Wang, Lifu 51 Wang, Nazi 94 Wang, Ruopu 475 Wang, Shengli 242 Wang, Wei 509 Wang, Xianglei 264 Wang, Yichen 391 Wang, Yidi 320 Wang, Yusong 320 Wang, Zhanze 85, 132 Wang, Zhenjie 368 Wang, Ziyu 460 Wei, Chen 75

Author Index

Wei, Jianhua 187 Wei, Qianru 39 Wen, Chao 391 Wu, Cong 60 Wu, Fanming 144, 155, 165 X Xia, Pengfei 176 Xian, Huiyi 252 Xie, Chao 264 Xie, Jun 411 Xie, Yu 3 Xing, Jianping 242 Xiong, Jian 273 Xu, Beiwen 39 Xu, Jiangning 497 Xu, Kai 509 Xu, Keke 14 Xu, Tianhe 94, 305, 331 Xu, Ying 118 Xu, Zhixiang 85, 132 Xu, Zichen 391 Xue, Linshan 411, 460 Y Yan, Liangquan 144 Yan, Linli 541 Yang, Baocai 201 Yang, Jiahao 358 Yang, Xingmei 242 Yang, Zihan 427

553

Yao, Linghan 305, 331 Ye, Nijun 401 Ye, Shirong 176 Yi, Qingwu 427 Yin, Lu 295, 380, 530 Yue, Zhe 14 Yueyuan, M. A. 497

Z Zang, Zhichao 358 Zhang, Chao 475 Zhang, Gong 509 Zhang, Haonan 201 Zhang, He 475 Zhang, Jingjing 427 Zhang, Shuangcheng 51, 75 Zhang, Shuyao 132 Zhang, Xiangyi 283 Zhang, Xinfang 144, 155, 165 Zhang, Yang 3 Zhang, Zhongkai 438 Zhao, Hebin 51, 75 Zhao, Jinhua 144, 155, 165 Zhao, Jumin 144, 155, 165 Zhao, Panpan 118 Zheng, Naiquan 107 Zheng, Wei 320 Zheng, Yong 438 Zhou, Qingyong 541 Zhou, Xin 51