WU Kuangchao, SHEN Wenbin, LI Lihong. Advances and Prospects in Gravity Potential Determination Based on the GNSS Frequency Shift Approach[J]. Geomatics and Information Science of Wuhan University, 2024, 49(11): 2037-2050. DOI: 10.13203/j.whugis20240161
Citation: WU Kuangchao, SHEN Wenbin, LI Lihong. Advances and Prospects in Gravity Potential Determination Based on the GNSS Frequency Shift Approach[J]. Geomatics and Information Science of Wuhan University, 2024, 49(11): 2037-2050. DOI: 10.13203/j.whugis20240161

Advances and Prospects in Gravity Potential Determination Based on the GNSS Frequency Shift Approach

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  • Received Date: April 04, 2024
  • Available Online: June 26, 2024
  • The precise determination of the gravity potential (geopotential) field is one of the foundational tasks in geodesy. With the rapid advancements in time and frequency science, a novel relativistic geodetic approach has garnered widespread attention in geodesy and geophysics. This method, grounded in the principles of general relativity, employs high-precision atomic clocks alongside advanced time and frequency transfer techniques to accurately measure both the geopotential difference and the orthometric height (OH) difference between two arbitrary stations on the ground. Notably, the global navigation satellite system (GNSS) time and frequency transfer technique, boasts advantages such as high precision, all-weather capability, flexible networking, and economic feasibility, gradually forming an intriguing research field of geopotential determination by a GNSS frequency shift approach. First, the principle of the relativistic geodetic approach is outlined, and the mathematical model conducive to centimeter-level geopotential difference measurement is analyzed. Second, the essential characteristics of both the cable connection and GNSS frequency shift approaches are summarized. Third, a focused review is conducted on the research progress of the GNSS frequency shift approach. The two typical GNSS time and frequency transfer methods, the common view and the precise point positioning methods, are investigated in detail. Representative experiments associated with these two methods are reviewed and discussed, followed by an analysis and summary of the development of the GNSS frequency shift approach. Afterward, the critical challenges that necessitate urgent resolution within this field are delineated, including but not limited to the modeling of the GNSS receiver clock offset, the error process in GNSS time and frequency transfer, and the data process for the receiver clock offset series. Considering the vital role of high-performance clocks in the GNSS frequency shift approach, a detailed overview of the development of both microwave atomic clocks and optical atomic clocks is presented. Finally, potential applications of the GNSS frequency shift approach are explored, including high-precision geopotential difference or OH difference measurement, the establishment of a unified world height datum with high accuracy, and the simultaneous measurement of three-dimensional geometric position along with their corresponding geopotential values. This paper aims to serve as a reference for further research on geopotential determination through the GNSS frequency shift approach and related studies.

  • [1]
    陈俊勇. 现代大地测量学的进展[J]. 测绘科学, 2003, 28(2): 1-5.

    Chen Junyong. On the Development of Modern Geo⁃desy[J]. Science of Surveying and Mapping, 2003, 28(2): 1-5.
    [2]
    宁津生, 陈俊勇, 李德仁, 等. 测绘学概论[M]. 3版. 武汉: 武汉大学出版社, 2016.

    Ning Jinsheng, Chen Junyong, Li Deren, et al. Introduction to Geomatics[M]. 3rd ed. Wuhan: Wuhan University Press, 2016.
    [3]
    李建成. 我国现代高程测定关键技术若干问题的研究及进展[J]. 武汉大学学报(信息科学版), 2007, 32(11): 980-987.

    Li Jiancheng. Study and Progress in Theories and Crucial Techniques of Modern Height Measurement in China[J]. Geomatics and Information Science of Wuhan University, 2007, 32(11): 980-987.
    [4]
    Bjerhammar A. On a Relativistic Geodesy[J]. Bulletin Géodésique, 1985, 59(3): 207-220.
    [5]
    Shen W, Chao D, Jin B. On Relativistic Geoid[J]. Bollettino di Geodesia et Scienze Affini, 1993, 52(3):207–216.
    [6]
    Shen Z Y, Shen W B, Zhang S X. Determination of Gravitational Potential at Ground Using Optical-Atomic Clocks on Board Satellites and on Ground Stations and Relevant Simulation Experiments[J]. Surveys in Geophysics, 2017, 38(4): 757-780.
    [7]
    Mcgrew W F, Zhang X, Fasano R J, et al. Atomic Clock Performance Enabling Geodesy Below the Centimetre Level[J]. Nature, 2018, 564(7734): 87-90.
    [8]
    Philipp D, Hackmann E, Lämmerzahl C, et al. Re⁃lativistic Geoid: Gravity Potential and Relativistic Effects[J]. Physical Review D, 2020, 101(6): 064032.
    [9]
    Brewer S M, Chen J S, Hankin A M, et al. An 27Al+ Quantum-Logic Clock with a Systematic Uncertainty Below 10-18[J]. Physical Review Letters, 2019, 123(3): 033201.
    [10]
    Wu Y W, Burau J J, Mehling K, et al. High Phase-Space Density of Laser-Cooled Molecules in an Optical Lattice[J]. Physical Review Letters, 2021, 127(26): 263201.
    [11]
    Bothwell T, Kennedy C J, Aeppli A, et al. Resol⁃ving the Gravitational Redshift Across a Millimetre-Scale Atomic Sample[J]. Nature, 2022, 602(7897): 420-424.
    [12]
    申文斌, 宁津生, 晁定波. 相对论与相对论重力测量[M]. 武汉: 武汉大学出版社, 2008.

    Shen Wenbin, Ning Jinsheng, Chao Dingbo. Relativity and Relativistic Gravity Measurement[M]. Wuhan: Wuhan University Press, 2008.
    [13]
    Time Mai E., Clocks Atomic, and Geodesy Relativistic[M]. München, Germany: Deutsche Geodätische Kommission, 2013.
    [14]
    Puetzfeld D, Lämmerzahl C. Relativistic Geodesy[M]. Cham, Switzerland: Springer International Publishing, 2019.
    [15]
    Mehlstäubler T E, Grosche G, Lisdat C, et al. Atomic Clocks for Geodesy[J]. Reports on Progress in Physics, 2018, 81(6):64401.
    [16]
    Tanaka Y, Katori H. Exploring Potential Applications of Optical Lattice Clocks in a Plate Subduction Zone[J]. Journal of Geodesy, 2021, 95(8): 93.
    [17]
    Zheng X, Dolde J, Cambria M C, et al. A Lab-Based Test of the Gravitational Redshift with a Mi⁃niature Clock Network[J]. Nature Communications, 2023, 14(1): 4886.
    [18]
    孙和平, 杨元喜, 叶朝辉, 等. 精密(量子)测量时代下时空基准研究中的关键科学问题和核心技术[J]. 中国科学基金, 2024, 38(1): 172-181.

    Sun Heping, Yang Yuanxi, Ye Zhaohui, et al. Key Scientific Frontiers and Core Technologies in Space-Time Reference Research in the Era of Precision (Quantum) Measurement[J]. Bulletin of National Natural Science Foundation of China, 2024, 38(1): 172-181.
    [19]
    Lion G, Panet I, Wolf P, et al. Determination of a High Spatial Resolution Geopotential Model Using Atomic Clock Comparisons[J]. Journal of Geodesy, 2017, 91(6): 597-611.
    [20]
    Shen Z Y, Shen W B, Xu X Y, et al. A Method for Measuring Gravitational Potential of Satellite’s Orbit Using Frequency Signal Transfer Technique Between Satellites[J]. Remote Sensing, 2023, 15(14): 3514.
    [21]
    申子宇. 时频信号传递测定重力位的研究[D]. 武汉: 武汉大学, 2017.

    Shen Ziyu. Study of Determining the Geopotential Using the Time and Frequency Transfer Approach[D]. Wuhan: Wuhan University, 2017.
    [22]
    Hafele J C, Keating R E. Around-the-World Ato⁃mic Clocks: Predicted Relativistic Time Gains[J]. Science, 1972, 177(4044): 166-168.
    [23]
    Briatore L, Leschiutta S. Evidence for the Earth Gravitational Shift by Direct Atomic-Time-Scale Comparison[J]. Il Nuovo Cimento B (1971—1996), 1977, 37(2): 219-231.
    [24]
    Chou C W, Hume D B, Rosenband T, et al. Optical Clocks and Relativity[J]. Science, 2010, 329(5999): 1630-1633.
    [25]
    Shen W B, Ning J S. The Application of GPS Technique in Determining the Earth’s Potential Field[J]. Journal of Global Positioning Systems, 2005, 4(1&2): 268-276.
    [26]
    Takano T, Takamoto M, Ushijima I, et al. Geopotential Measurements with Synchronously Linked Optical Lattice Clocks[J]. Nature Photonics, 2016, 10: 662-666.
    [27]
    Grotti J, Koller S, Vogt S, et al. Geodesy and Metrology with a Transportable Optical Clock[J]. Nature Physics, 2018, 14: 437-441.
    [28]
    Takamoto M, Ushijima I, Ohmae N, et al. Test of General Relativity by a Pair of Transportable Optical Lattice Clocks[J]. Nature Photonics, 2020, 14(7): 411-415.
    [29]
    Huang Y, Zhang H, Zhang B, et al. Geopotential Measurement with a Robust, Transportable Ca+ Optical Clock[J]. Physical Review A, 2020, 102(5):50802.
    [30]
    Shen Z Y, Shen W B, Zhang S X. Formulation of Geopotential Difference Determination Using Optical-Atomic Clocks Onboard Satellites and on Ground Based on Doppler Cancellation System[J]. Geophysical Journal International, 2016, 206(2): 1162-1168.
    [31]
    Katori H. Optical Lattice Clocks and Quantum Metrology[J]. Nature Photonics, 2011, 5: 203-210.
    [32]
    Shen Q, Guan J Y, Ren J G, et al. Free-Space Dissemination of Time and Frequency with 10-19 Instability over 113 km[J]. Nature, 2022, 610(7933): 661-666.
    [33]
    Bagherbandi M, Shirazian M, Amin H D, et al. Time Transfer and Significance of Vertical Land Motion in Relativistic Geodesy Applications: A Review Paper[J]. Frontiers in Earth Science, 2023, 11: 1139211.
    [34]
    Shen W B, Ning J S, Liu J N, et al. Determination of the Geopotential and Orthometric Height Based on Frequency Shift Equation[J]. Natural Science, 2011, 3(5): 388-396.
    [35]
    Kopeikin S M, Kanushin V F, Karpik A P, et al. Chronometric Measurement of Orthometric Height Differences by Means of Atomic Clocks[J]. Gravitation and Cosmology, 2016, 22(3): 234-244.
    [36]
    Wu K C, Shen W B, Sun X, et al. Measuring the Gravity Potential Between Two Remote Sites with CVSTT Technique Using Two Hydrogen Clocks[J]. Geo⁃Spatial Information Science, 2023,DOI: 10.1080/10095020.2023.2231515.
    [37]
    Kim K, Aeppli A, Bothwell T, et al. Evaluation of Lattice Light Shift at Low 10-19 Uncertainty for a Shallow Lattice Sr Optical Clock[J]. Physical Review Letters, 2023, 130(11): 113203.
    [38]
    Wu H, Müller J, Lämmerzahl C. Clock Networks for Height System Unification: A Simulation Study[J]. Geophysical Journal International, 2019, 216(3): 1594-1607.
    [39]
    姚宜斌, 杨元喜, 孙和平, 等. 大地测量学科发展现状与趋势[J]. 测绘学报, 2020, 49(10): 1243-1251.

    Yao Yibin, Yang Yuanxi, Sun Heping, et al. Geo⁃desy Discipline: Progress and Perspective[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(10): 1243-1251.
    [40]
    党亚民, 蒋涛, 陈俊勇. 全球高程基准研究进展[J]. 武汉大学学报(信息科学版), 2022, 47(10):1576–1586.

    Dang Yamin, Jiang Tao, Chen Junyong. Review on Research Progress of the Global Height Datum[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10):1576-1586.
    [41]
    Shen Z Y, Shen W B, Zhang S X, et al. Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links[J]. Remote Sensing, 2023, 15(12):3020.
    [42]
    Weinberg S, Dicke R H. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity[M]. New York, Chichester: John Wiley & Sons, 1972.
    [43]
    Damour T, Soffel M, Xu C M. General-Relativistic Celestial Mechanics. I. Method and Definition of Reference Systems[J]. Physical Review D, 1991, 43(10): 3273-3307.
    [44]
    Kopeikin S, Vlasov I, Han W B. Normal Gravity Field in Relativistic Geodesy[J]. Physical Review , 2018, 97(4): 045020.
    [45]
    Savalle E, Guerlin C, Delva P, et al. Gravitational Redshift Test with the Future ACES Mission[J]. Classical and Quantum Gravity, 2019, 36(24): 245004.
    [46]
    韩文标, 陶金河, 马维. 相对论天文参考系的回顾与展望[J]. 天文学进展, 2014, 32(1): 95-117.

    Han Wenbiao, Tao Jinhe, Ma Wei. Review and Prospect of the Relativistic Astronomical Reference System[J]. Progress in Astronomy, 2014, 32(1): 95-117.
    [47]
    Kopeikin S, Han W B, Mazurova E. Post-Newtonian Reference Ellipsoid for Relativistic Geodesy[J]. Physical Review D, 2016, 93(4):044069.
    [48]
    Misner C W, Thorne K S, Wheeler J A. Gravitation[M]. UK: Macmillan, 1973.
    [49]
    Shen W B, Ning J S, Chao D B, et al. A Proposal on the Test of General Relativity by Clock Transportation Experiments[J]. Advances in Space Research, 2009, 43(1): 164-166.
    [50]
    Heiskanen W A, Moritz H. Physical Geodesy[J]. Bulletin Géodésique, 1967, 86(1): 491-492.
    [51]
    Moritz H. Classical Physical Geodesy[M]. Berlin, Heidelberg: Springer, 2013: 1-33.
    [52]
    Hofmann-Wellenhof B, Moritz H. Physical Geodesy[M]. Heidelberg: Springer, 2005.
    [53]
    孙和平, 孙文科, 申文斌, 等. 地球重力场及其地学应用研究进展——2020中国地球科学联合学术年会专题综述[J]. 地球科学进展, 2021, 36(5):445–460.

    Sun Heping, Sun Wenke, Shen Wenbin, et al. Research Progress of Earth's Gravity Field and Its Application in Geosciences—A Summary of Annual Meeting of Chinese Geoscience Union in 2020[J]. Advances in Earth Science, 2021, 36(5):445–460.
    [54]
    Hu Z K, Sun B L, Duan X C, et al. Demonstration of an Ultrahigh-Sensitivity Atom-Interferometry Absolute Gravimeter[J]. Physical Review A, 2013, 88(4): 043610.
    [55]
    Allan D W, Weiss M A. Accurate Time and Frequency Transfer During Common-View of a GPS Satellite[C]//The 34th Annual Symposium on Frequency Control, Philadelphia, USA, 1980.
    [56]
    Allan D W, Thomas C. Technical Directives for Standardization of GPS Time Receiver Software: To Be Implemented for Improving the Accuracy of GPS Common-View Time Transfer[J]. Metrologia, 1994, 31(1): 69-79.
    [57]
    Imae M, Suzuyama T, Hongwei S. Impact of Satellite Position Error on GPS Common-View Time Transfer[J]. Electronics Letters, 2004, 40(11): 709-710.
    [58]
    高玉平, 漆溢, 王正明. 用于JATC远程时间比对的双频GPS接收机[J]. 时间频率学报, 2006, 29(1): 6-12.

    Gao Yuping, Qi Yi, Wang Zhengming. A Dual Frequency GPS Receivers Developed to Compare Time for JATC[J]. Journal of Time and Frequency, 2006, 29(1): 6-12.
    [59]
    Ray J, Senior K. Geodetic Techniques for Time and Frequency Comparisons Using GPS Phase and Code Measurements[J]. Metrologia, 2005, 42(4): 215-232.
    [60]
    Lewandowski W, Thomas C. GPS Time Transfer[J]. Proceedings of the IEEE, 1991, 79(7):991–1000.
    [61]
    李征航, 黄劲松. GPS测量与数据处理[M]. 武汉: 武汉大学出版社, 2005.

    Li Zhenghang, Huang Jinsong. GPS Surveying and Data Processing[M]. Wuhan: Wuhan University Press, 2005.
    [62]
    Larson K M, Levine J. Carrier-Phase Time Transfer[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1999, 46(4): 1001-1012.
    [63]
    聂桂根. 高精度GPS测时与时间传递的误差分析及应用研究[D]. 武汉: 武汉大学, 2002.

    Nie Guigen. Error Analysis and Application Investigation of Precise Timing and Time Transfer by GPS[D]. Wuhan: Wuhan University, 2002.
    [64]
    张小红, 程世来, 李星星, 等. 单站GPS载波平滑伪距精密授时研究[J]. 武汉大学学报(信息科学版), 2009, 34(4): 463-465.

    Zhang Xiaohong, Cheng Shilai, Li Xingxing, et al. Precise Timing Using Carrier Phase Smoothed Pseudorange from Single Receiver[J]. Geomatics and Information Science of Wuhan University, 2009, 34(4): 463-465.
    [65]
    Ge Y L, Zhou F, Dai P P, et al. Precise Point Positioning Time Transfer with Multi-GNSS Single-Frequency Observations[J]. Measurement, 2019, 146: 628-642.
    [66]
    Petit G, Meynadier F, Harmegnies A, et al. Continuous IPPP Links for UTC[J]. Metrologia, 2022, 59(4):45007.
    [67]
    Teunissen P J G, Montenbruck O. Handbook of Global Navigation Satellite Systems[M]. Cham: Springer International Publishing, 2017
    [68]
    Brumberg V A, Groten E. On Determination of Heights by Using Terrestrial Clocks and GPS Signals[J]. Journal of Geodesy, 2002, 76(1): 49-54.
    [69]
    刘杨, 申文斌, 夏敏, 等. 利用GPS共视法确定重力位差及海拔高差的实验研究[J]. 武汉大学学报(信息科学版), 2011, 36(6): 640-643.

    Liu Yang, Shen Wenbin, Xia Min, et al. Determination of Geopotential Difference and Orthometric Height Difference Using GPS Common View[J]. Geomatics and Information Science of Wuhan University, 2011, 36(6): 640-643.
    [70]
    李纯. 多系统GNSS精密单点定位时间传递与高程差估计[D]. 湘潭: 湘潭大学, 2020.

    Li Chun. Time-Frequency Transfer and Elevation Difference from Multi-GNSS Precise Point Positio⁃ning[D]. Xiangtan: Xiangtan University, 2020.
    [71]
    金双根, 汪奇生, 史奇奇. 单频到五频多系统GNSS精密单点定位参数估计与应用[J]. 测绘学报, 2022, 51(7): 1239-1248.

    Jin Shuanggen, Wang Qisheng, Shi Qiqi. Parameters Estimation and Applications from Single to Five-Frequency Multi-GNSS Precise Point Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(7): 1239-1248.
    [72]
    徐炜. 多频多模GNSS载波相位时频信号测定重力位的研究[D]. 武汉大学, 2022.

    Xu Wei. Research on the Determination of Geopotential by Multi-frequency and Multi-mode GNSS Carrier Phase Time and Frequency signal[D]. Wuhan:Wuhan University, 2022.
    [73]
    Cai C H, Shen W B, Shen Z Y, et al. Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation[J]. IEEE Access, 2020, 8: 204283-204294.
    [74]
    吴富梅, 魏子卿. 利用GNSS和EGM2008模型进行跨海高程传递[J]. 武汉大学学报(信息科学版), 2016, 41(5): 698-703.

    Wu Fumei, Wei Ziqing. Height Transfer from Land to Island Based on GNSS and EGM2008 Model[J]. Geomatics and Information Science of Wuhan University, 2016, 41(5): 698-703.
    [75]
    魏子卿. 高程现代化问题[J]. 武汉大学学报(信息科学版), 2001, 26(5): 377-380.

    Wei Ziqing. Height Modernization Issue[J]. Geomatics and Information Science of Wuhan University, 2001, 26(5): 377-380.
    [76]
    赫林, 李建成, 褚永海. 1985国家高程基准与全球高程基准之间的垂直偏差[J]. 测绘学报, 2016, 45(7): 768-774.

    He Lin, Li Jiancheng, Chu Yonghai. The Vertical Shift Between 1985 National Height Datum and Global Vertical Datum[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(7): 768-774.
    [77]
    Jaduszliwer B, Past Camparo J., Present and Future of Atomic Clocks for GNSS[J]. GPS Solutions, 2021, 25(1): 27.
    [78]
    张小红, 陈兴汉, 郭斐. 高性能原子钟钟差建模及其在精密单点定位中的应用[J]. 测绘学报, 2015, 44(4): 392-398.

    Zhang Xiaohong, Chen Xinghan, Guo Fei. High-Performance Atomic Clock Modeling and Its Application in Precise Point Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(4): 392-398.
    [79]
    Li X X, Ge M R, Dai X L, et al. Accuracy and Reliability of Multi-GNSS Real-Time Precise Positio⁃ning: GPS, GLONASS, BeiDou, and Galileo[J]. Journal of Geodesy, 2015, 89(6): 607-635.
    [80]
    Wang K, Rothacher M. Stochastic Modeling of High-Stability Ground Clocks in GPS Analysis[J]. Journal of Geodesy, 2013, 87(5): 427-437.
    [81]
    于合理, 郝金明, 刘伟平, 等. 附加原子钟物理模型的PPP时间传递算法[J]. 测绘学报, 2016, 45(11): 1285-1292.

    Yu Heli, Hao Jinming, Liu Weiping, et al. A Time Transfer Algorithm of Precise Point Positioning with Additional Atomic Clock Physical Model[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(11): 1285-1292.
    [82]
    Ge Y L, Zhou F, Liu T J, et al. Enhancing Real-Time Precise Point Positioning Time and Frequency Transfer with Receiver Clock Modeling[J]. GPS Solutions, 2018, 23(1): 20.
    [83]
    Zhang X B, Guo J, Hu Y H, et al. Influence of Precise Products on the Day-Boundary Discontinuities in GNSS Carrier Phase Time Transfer[J]. Sensors, 2021, 21(4): 1156.
    [84]
    黄观文. GNSS星载原子钟质量评价及精密钟差算法研究[D]. 西安: 长安大学, 2012.

    Huang Guanwen. Research on Quality Evaluation and Precision Clock Error Algorithm of GNSS Satellite Atomic Clock[D]. Xi’an: Chang’an University, 2012.
    [85]
    张鹏飞. GNSS载波相位时间传递关键技术与方法研究[D]. 北京: 中国科学院大学, 2019.

    Zhang Pengfei. The Research of Key Technology and Approach for Time and Frequency Transfer Based on GNSS Carrier Phase Observation[D]. Beijing: University of Chinese Academy of Sciences, 2019.
    [86]
    Lyu D Q, Zeng F L, Ouyang X F, et al. Enhancing Multi-GNSS Time and Frequency Transfer Using a Refined Stochastic Model of a Receiver Clock[J]. Measurement Science and Technology, 2019, 30(12): 125016.
    [87]
    Zhang P F, Tu R, Gao Y P, et al. Improving Gali⁃leo’s Carrier-Phase Time Transfer Based on Prior Constraint Information[J]. Journal of Navigation, 2019, 72(1): 121-139.
    [88]
    张小红, 柳根, 郭斐, 等. 北斗三频精密单点定位模型比较及定位性能分析[J]. 武汉大学学报 ( 信息科学版), 2018, 43(12): 2124-2130.

    Zhang Xiaohong, Liu Gen, Guo Fei, et al. Model Comparison and Performance Analysis of Triple-Frequency BDS Precise Point Positioning[J]. Geomatics and Information Science of Wuhan University, 2018, 43(12): 2124-2130..
    [89]
    张宝成. GNSS非差非组合精密单点定位的理论方法与应用研究[D]. 武汉:中国科学院测量与地球物理研究所, 2013.

    Zhang Baocheng. Study on the Theoretical Metho⁃dology and Applications of Precise Point Positioning Using Undifferenced and Uncombined GNSS Data[D]. Wuhan: Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 2013.
    [90]
    Odijk D, Zhang B C, Khodabandeh A, et al. On the Estimability of Parameters in Undifferenced, Uncombined GNSS Network and PPP-RTK User Models by Means of S-System Theory[J]. Journal of Geodesy, 2016, 90(1): 15-44.
    [91]
    Chen J, Jiang Y S, Fan Y, et al. Comprehensive Analysis of the Global Zenith Tropospheric Delay Real-Time Correction Model Based GPT3[J]. Atmosphere, 2023, 14(6): 946.
    [92]
    Li X, Li X X, Jiang Z H, et al. A Unified Model of GNSS Phase/Code Bias Calibration for PPP Ambiguity Resolution with GPS, BDS, Galileo and GLONASS Multi-frequency Observations[J]. GPS Solutions, 2022, 26(3): 84.
    [93]
    Petit G. Sub-10-16 Accuracy GNSS Frequency Transfer with IPPP[J]. GPS Solutions, 2021, 25(1): 22.
    [94]
    Wu Y F, Shen W B. Simulation Experiments on High-Precision VGOS Time Transfer for Future Geopotential Difference Determination[J]. Advan⁃ces in Space Research, 2021, 68(6): 2453-2469.
    [95]
    Shen W B, Zhang P F, Shen Z Y, et al. Testing Gravitational Redshift Based on Microwave Frequency Links Onboard the China Space Station[J]. Phy⁃sical Review D, 2023, 108(6): 064031.
    [96]
    Wu K C, Shen Z Y, Shen W B, et al. A Preliminary Experiment of Determining the Geopotential Difference Using Two Hydrogen Atomic Clocks and TWSTFT Technique[J]. Geodesy and Geodyna⁃mics, 2020, 11(4): 229-241.
    [97]
    Cheng P, Shen W B, Sun X, et al. Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer[J]. Remote Sensing, 2022, 14(3): 451.
    [98]
    Shen W B, Sun X, Cai C H, et al. Geopotential Determination Based on a Direct Clock Comparison Using Two-Way Satellite Time and Frequency Transfer[J]. Terrestrial, Atmospheric and Oceanic Sciences, 2019, 30(1): 21-31.
    [99]
    Ramsey N F. History of Early Atomic Clocks[J]. Metrologia, 2005, 42(3): S1-S3.
    [100]
    Diddams S A, Bergquist J C, Jefferts S R, et al. Standards of Time and Frequency at the Outset of the 21st Century[J]. Science, 2004, 306(5700): 1318-1324.
    [101]
    Audoin C, Guinot B. The Measurement of Time: Time, Frequency, and the Atomic Clock[M]. New York: Cambridge University Press, 2001.
    [102]
    Leschiutta S. The Definition of the ‘Atomic’ Se⁃cond[J]. Metrologia, 2005, 42(3): S10-S19.
    [103]
    Arditi M, Carver T R. Pressure, Light, and Temperature Shifts in Optical Detection of 0-0 Hyperfine Resonance of Alkali Metals[J]. Physical Review, 1961, 124(3): 800-809.
    [104]
    Kleppner D, Berg H C, Crampton S B, et al. Hydrogen-Maser Principles and Techniques[J]. Physical Review, 1965, 138(4A): A972-A983.
    [105]
    Bize S, Laurent P, Abgrall M, et al. Cold Atom Clocks and Applications[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2005, 38(9): S449-S468.
    [106]
    Clairon A, Laurent P, Santarelli G, et al. A Cesium Fountain Frequency Standard: Preliminary Results[J]. IEEE Transactions on Instrumentation and Measurement, 1995, 44(2): 128-131.
    [107]
    Guéna J, Abgrall M, Rovera D, et al. Progress in Atomic Fountains at LNE-SYRTE[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2012, 59(3): 391-410.
    [108]
    Oelker E, Hutson R B, Kennedy C J, et al. De⁃monstration of 4.8×10-17 Stability at 1 s for Two Independent Optical Clocks[J]. Nature Photonics, 2019, 13(10): 714-719.
    [109]
    Denker H, Timmen L, Voigt C, et al. Geodetic Methods to Determine the Relativistic Redshift at the Level of 10-18 in the Context of International Time⁃scales: A Review and Practical Results[J]. Journal of Geodesy, 2018, 92(5): 487-516.
    [110]
    Riehle F, Gill P, Arias F, et al. The CIPM List of Recommended Frequency Standard Values: Guidelines and Procedures[J]. Metrologia, 2018, 55(2): 188-200.
    [111]
    Riehle F. Optical Clock Networks[J]. Nature Photonics, 2017, 11(1): 25-31.
    [112]
    Poli N, Schioppo M, Vogt S, et al. A Transpor⁃table Strontium Optical Lattice Clock[J]. Applied Physics B, 2014, 117(4): 1107-1116.
    [113]
    Koller S B, Grotti J, Vogt S, et al. Transportable Optical Lattice Clock with 7×10-17 Uncertainty[J]. Physical Review Letters, 2017, 118(7): 073601.
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