China has made continuous efforts to establish its own independent BeiDou Navigation Satellite System (BDS) to provide Positioning, Navigation and Timing services, which rely on the high quality of orbit and clock products.
This article summarizes the achievements in the Precise Orbit Determination of BDS satellites in the past decade with the focus on observation and orbit dynamic models, e.g., phase center corrections, satellite attitude, and solar radiation pressure.
In addition, the urgent requirement for error modeling of the ISL data is emphasized based on the analysis of the observation noises, and the incompatible characteristics of orbit and clock derived with L-band and ISL data are discussed.
The further researches on the improvement of ISL and L-band observation models, dynamic perturbations and the potential contribution of BDS to the estimation of geodetic parameters are identified.
当前，北斗卫星导航系统空间段由北斗二号系统（5颗GEO、7颗IGSO和3颗MEO）、北斗三号实验系统（2颗IGSO和2颗MEO）和北斗三号全球系统（3颗GEO、3颗IGSO和24颗MEO）组成，其详细在轨状态可参见中国卫星导航系统管理办公室测试评估研究中心（http://www.csno-tarc.cn/system/constellation）。包含北斗二号和三号卫星天线相位中心偏差、质量、卫星星体结构和光学属性、姿态控制模式等在内的元数据已于2019年年底公开（CSNO 2019a），以支持北斗卫星高精度数据处理和轨道动力学建模。由中国空间技术研究院（简称五院）制造的北斗三号GEO和IGSO卫星星体呈沿Z轴拉伸的长方体，除太阳帆板以外，GEO卫星在±X面上安装有桁架式天线；除在+X面上安装有桁架式天线外，IGSO卫星在-X面上还安装有两个小型天线（Chen and Wu, 2020）。中国空间技术研究院（简称五院）的北斗三号MEO卫星采用专用平台，其结构呈现由大小两块长方体组成的T型，以适于一箭多星发射、直接入轨，从而满足卫星组批研制、快速组网的任务要求（Zhang et al., 2020）。此外，部分卫星在-X面安装有额外的通讯天线。中国科学院微小卫星创新研究院（简称小卫星）研制的北斗三号MEO卫星星体结构呈沿X轴拉伸的长方体形状。星体拉伸方向的差异将造成五院和小卫星MEO卫星轨道误差具有不同的特性。
公开的北斗卫星元数据中仅包含卫星星体和太阳帆板的吸收参数，缺乏镜面反射和漫反射系数以用于光压力建模。Chen et al. (2019)较为详细的给出了北斗二号IGSO和MEO卫星星体和太阳帆板的材料类型以及相应光学系数。以此为参考，本文得到并给出了北斗二号和三号卫星粗略的光学系数值以用于非保守力建模。
II 北斗卫星跟踪数据
北斗星地L波段跟踪数据主要来自武汉大学北斗实验跟踪网（BETS）、国际卫星导航服务组织（IGS）和全球连续监测和评估系统（iGMAS）。BETS网由武汉大学卫星导航定位技术研究中心于2011年3月起建立，约由15个测站组成（Shi et al., 2011），提供了对于北斗二号卫星信号的最初跟踪数据。iGMAS网由全球连续监测和评估系统项目构建，由31个全球分布的站点组成（Jiao et al., 2011），这些数据可以从相应数据中心下载。随着新兴导航系统的蓬勃发展，IGS统筹成立了多模GNSS工作组（MGEX）并积极推动多模跟踪站建立。截至2021年9月，MGEX网中已有超过250个测站可跟踪北斗信号，其数据可以从 IGS 数据中心下载。图 2 IGS和iGMAS测站对北斗二号和三号卫星的跟踪情况。
III 几何观测模型姿态描述卫星星固系在轨指向，对天线相位中心和相位缠绕等几何误差以及光压力等非保守力建模具有显著影响。北斗二号和三号GEO卫星采用零偏置姿态（偏航角为0°）；北斗二号IGSO和MEO卫星则采用与其他导航卫星相似的动态偏置姿控模式（偏航姿态随卫星位置动态变化），而当太阳相对于卫星轨道面倾角（β角）的绝对值小于4°时则采用零偏姿态。对北斗二号IGSO和MEO卫星姿态转换条件，国内外许多学者开展了大量研究（Guo et al., 2014; Dai et al.,2015; Li et al., 2018）。由于北斗二号IGSO和MEO卫星在零偏期间以及动零姿态模式转换期间轨道精度显著性降低，部分北斗二号和北斗三号IGSO和MEO卫星则采用了连续动偏模式。对于五院卫星，Dilssner (2017)和Wang et al. (2018)则先后构建了相应的姿态控制模型。对于小卫星MEO卫星，Yang et al. (2021)研究表明其偏航姿态基本遵循“北斗/全球卫星导航系统（GNSS）卫星高精度应用参数定义及描述”中所给出模型，也即当β角在(0, 3°]时采用β=3°时偏航姿态，而β角在[-3°, 0]时采用β=3°时偏航姿态。但是，当太阳通过轨道面，也即β角符号变化时，姿态切换存在延迟从而导致在正午或者午夜机动呈现反向调整。 其他几何误差研究主要集中在北斗卫星端随高度角相关的系统性误差、北斗二号和三号卫星间的系统性偏差以及码和相位观测值偏差上。Wanninger and Beer (2015)最先报道北斗二号IGSO和MEO卫星端存在于高度角相关的系统性误差，并且构建了相应模型加以改正，而北斗三号则显著消除了相关误差。近来较多研究揭示北斗二号和三号重叠频点信号间存在偏差（如Mi et al., 2021），其将影响模糊度固定等，因此在数据处理时应将北斗二号和三号卫星视为独立系统。 除上述L波段观测值误差外，北斗星间链路观测值中也存在显著性系统误差。通过将双向星间链路观测值归化为单向与几何无关的观测值以用于钟差估计，并通过将三颗以上卫星与几何无关的观测值求和获得相应闭合差。图4中给出了C20-C21-C41、C28-C30-C44、C21-C28-C29和C20-C25-C45等不同卫星间闭合差变化。从理论上讲，上述几何无关的观测值闭合差在消除轨道误差的基础上，进一步消除了接收机钟差和星间链路收发通道延迟，理应呈现白噪声特性。但是图中除C20-C21-C41以外，其他卫星组闭合差呈现偏差、周期性等系统性误差特性，从而会影响星间链路数据处理。此外，研究发现星间链路观测值残差中存在和链路相关的常量偏差（如图5）（Xieet al., 2019），其可以通过直接估计与连续相关的收发通道延迟加以消除。上述系统性误差来源仍需进一步确认和研究。
图 4 北斗不同卫星组星间链路闭合差误差特性。
图 5 北斗星间链路观测值残差。
IV 轨道动力学模型太阳光压力是影响北斗卫星定轨精度的核心因素。受卫星相对地面站静止，几何观测条件变化较小制约，北斗GEO卫星定轨精度在米级。通过构建先验光压模型以考虑GEO卫星通讯天线影响，Wang et al. (2019)将其径向轨道精度提升至10 cm。对于北斗二号IGSO和MEO卫星，由于缺乏适用于零偏的偏航姿态模型，其零偏期间定轨精度显著性降低。国内外众多研究通过构建适用于零偏模式的分析型模型或者经验性模型，显著提升了北斗IGSO和MEO卫星零偏期间定轨精度（Wang et al., 2013; Guo et al., 2014; Montenbrucket al., 2017b）。对于北斗三号MEO卫星，当直接使用ECOM1光压模型进行精密定轨时，其径向轨道误差呈现与太阳辐角（太阳-地球-卫星间夹角）相关的系统误差（如图6）。由于长方体拉伸方向不同，五院和小卫星轨道误差特性呈现相反变化。通过使用ECOM2或者先验盒翼模型等方法，可以显著减弱或者消除此类误差（Wang et al., 2019; Yan et al., 2019a; Li etal., 2020; Duan et al., 2021）。 图 6 基于星地L波段和ECOM1模型的北斗SLR观测值残差。除光压力外，天线推力、地球反照辐射和热辐射等对北斗卫星轨道产生系统性影响。天线推力是由卫星对外发射信号所产生的反作用力，其大小与信号发射功率和质量有关。Steigenberger et. al. (2018)以及Steigenberger & Thoelert (2020)分别测定了北斗二号和三号卫星信号功率。其使得北斗二号IGSO和MEO以及北斗三号五院和小卫星MEO径向轨道产生约28、5、16和19 mm左右的偏差。相应地，地球反照辐射将引起北斗二号IGSO和MEO以及北斗三号五院和小卫星MEO径向轨道产生约25、20、15和12 mm左右的偏差。 V 基于L波段和星间链路的北斗卫星精密定轨北斗卫星精密轨道确定可以采用L波段或者星间链路观测值。当前，IGS MGEX和iGMAS及其各个分析中心提供基于L波段的北斗高精度轨道和钟差产品以及不同分析中心间产品的比较和综合结果。随着地面观测站数目增多，不同分析中心间产品一致性和精度在逐步提升。当前，不同分析中心北斗GEO卫星轨道一致性在米级，IGSO约为15 cm，MEO则为7 cm左右（Steigenberger and Montenbruck, 2020）。激光测距检核表明北斗二号GEO、IGSO和MEO卫星轨道误差为20、5-7和3.5 cm左右（Sośnica et al., 2020）。北斗三号卫星轨道精度从2019年3-4 cm提甚至2 cm左右（Guo et al., 2021）。 图 7 基于星间链路和ECOM1模型的北斗SLR观测值残差。
对于北斗三号MEO卫星，基于星间链路观测值可以获得与全球L波段观测值相类似的定轨精度，但是其轨道误差呈现与L波段不一致的特性。图7中给出了基于星间链路观测值和ECOM1模型的北斗C20和C30卫星SLR观测值残差。与图6不同，其径向轨道误差并未显著性呈现与太阳辐角相关的线性变化，其主要原因在于星间链路观测值对光压参数，特别是D0参数具有较高的可估性。 VI 北斗对大地测量参数估计的影响当前，北斗卫星精密定轨研究主要集中于几何和动力学模型精化方面，而缺乏对大地测量参数估计的研究。从理论上来说，上述参数估计理应独立于GNSS系统，然而有研究表明大地测量参数估计序列中所表现出的交点年误差与卫星轨道动力学模型（如光压模型）残余误差以及GNSS卫星星座构成相关（Zajdel et al., 2020, 2021; Scaramuzza et al., 2018）。此外，由于测站坐标、钟差、模糊度等参数间相关性影响，北斗/GNSS难以精确测定地心运动和框架尺度(Rebischung et al., 2014a)。虽然北斗系统天线相位中心地面标定值已经公布，但是Qu et al. (2021)分析表明其与Galileo地面标定值在框架尺度上差异可达+1.854 ppb (part-per-billion)，因此基于北斗或GNSS技术构建独立尺度需要进一步研究。随着众多携带星载北斗/GNSS接收机的低轨卫星数据公开将为构建独立尺度提供可能。此外，北斗星间链路数据用于大地测量参数估计的能力和制约因素仍需进一步分析和研究。 VII 后续研究方向本文认为北斗精密定轨研究可以进一步在如下方向展开。一是，在完善北斗卫星元数据的基础上，进一步联合地面和低轨卫星星载北斗跟踪数据，估计和IGS框架一致的所有卫星天线相位中心偏差和变化；二是，进一步优化光压力和热辐射力等非保守力模型，以提高蚀卫星以及零偏期间卫星定轨精度；三是，分析星间链路系统误差来源以及消除方法，并研究钟差模型或星间链路估计钟差约束下的北斗卫星精密定轨；四是，考察和分析北斗对地心、尺度和地球自转参数等大地测量参数估计的影响和贡献。
参考文献
1 Arnold D, Meindl M, Beutler G, Dach R, Schaer S, Lutz S, Prange L, Sośnica K, Mervart L, Jäggi A (2015). CODE’s new solar radiation pressure model for GNSS orbit determination. Journal of Geodesy 89: 775–791. https://doi.org/10.1007/s00190-015-0814-42 Bar-Sever YE (1996) A new model for GPS yaw attitude. Journal of Geodesy 70(11):714-723. https://doi.org/10.1007/BF008671493 Bar-Sever Y, Kuang D (2004) New empirically derived solar radiation pressure model for global positioning system satellites. The Interplanetary Network Progress Report, pp 42–1594 Bar-Sever Y, Kuang D (2005) New empirically derived solar radiation pressure model for global positioning system satellites during eclipse seasons. The Interplanetary Network Progress Report, pp 42–1605 Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for geodynamics (IGS): theory and initial results. Manuscripta Geodaetica 19(6):367-386.6 Bury G, Sosnica K, Zajdel R (2018) Multi-GNSS orbit determination using satellite laser ranging. Journal of Geodesy 93:2447-2469. https://doi.org/10.1007/s00190-018-1143-17 Cai H, Meng Y, Geng T, Xie X (2020) Initial Results of Precise Orbit Determination Using Satellite-Ground and Inter-Satellite Link Observations for BDS-3 Satellites. Geomatics and Information Science of Wuhan University, 45:1493-1500. https://doi.org/10.13203/j.whugis201804998 Chen Z, Wu X (2020) General design of the third generation BeiDou Navigation Satellite System. Journal of Nanjing University of Aeronautics & Astronautics 52:6. https://10.16356/j.1005-2615.2020.06.0019 CSNO (2019a). Satellite Information of BDS, China Satellite Navigation Office. Available online: http://en.beidou.gov.cn/SYSTEMS/Officialdocument/201912/P020200103556125703019.rar. Accessed on 1 September 202110 CSNO (2019b) Definitions and descriptions of BDS/GNSS satellite parameters for high precision application. http://www.beidou.gov.cn/yw/gfgg/201912/W020200323534413026471.doc. Accessed on 1 September 202111 Chen G, Guo J, Geng T, Zhao Q (2020) Multi-GNSS orbit combination at Wuhan University: strategy and preliminary products. Journal of Geodesy (Under review)12 Chen Q, Yang H, Chen Z, Wang H, Wang C (2019) Solar radiation pressure modeling and application of BDS satellite. Acta Geodaeticaet Cartographica Sinica 48(2):169-175. https://doi.org/10.11947/j.AGCS.2019.2018009713 Chen X, Zhao S, Wang M, Lu M (2016) Space-borne BDS receiver for LING QIAO satellite: design, implementation and preliminary in-orbit experiment results. GPS Solutions 20:837-847. https://doi.org/10.1007/s10291-015-0493-x14 Chen K, Xu T, Chen G, Li J, Yu S (2015) The Orbit and Clock Combination of iGMAS Analysis Centers and the Analysis of Their Precision. In: Sun et al. (eds) China Satellite Navigation Conference (CSNC) 2015 Proceedings: Volume II. Lecture Notes in Electrical Engineering, vol 341. Springer, Berlin, Heidelberg. https://doi/org/10.1007/978-3-662-46635-3_3615 Dai X, Ge M, Lou Y, Shi C, Wickert J, Schuh H (2015) Estimating the yaw-attitude of BDS IGSO and MEO satellites, Journal of Geodesy 89(10):1005-1018. https://doi.org/10.1007/s00190-015-0829-x16 Deng Z (2021) WL_UPD, integer clock and OBX from GFZ MGEX RAPID products. IGSMAIL-8068.17 Dilssner F, Springer T, Gienger G, Dow J (2011) The GLONASS-M satellite yaw-attitude model. Advances in Space Research 47(1):160–171. https://doi.org/10.1016/j.asr.2010.09.00718 Dilssner F, Springer T, Schönemann E, Enderle W (2014) Estimation of satellite Antenna Phase Center corrections for BeiDou. In: Proceedings of IGS workshop 2014, 23–27 June 2014, Pasadena, USA19 Dilssner F (2017). A note on the yaw attitude modeling of BeiDou IGSO-6. http://navigation-office.esa.int/attachments_24576369_1_BeiDou_IGSO6_Yaw_Modeling.pdf. Accessed on 21 September 202120 Dilssner F, Springer T, Schönemann, Enderle W (2018) Initial orbit determination of third-generation BeiDou MEO spacecraft. IGS Workshop 2018, 28 Oct -2 Nov 2018, Wuhan, China21 Duan B, Hugentobler U, Selmke I (2019) The adjusted optical properties for Galileo/BeiDou-2/QZS-1 satellites and initial results on BeiDou-3e and QZS-2 satellites. Advances in Space Research 63(5):1803-1812. https://doi.org/10.1016/j.asr.2018.11.00722 Duan B, Hugentobler U, Hofacker M, Selmke I (2020) Improving solar radiant pressure for GLONASS satellites. Journal of Geodesy 94:72. https://doi.org/10.1007/s00190-020-01400-923 Duan B, Hugentobler U, Selmke I, Marz S (2021a) Physical a priori solar radiation pressure models for GNSS satellites with focus on BDS. EGU2021, vPICOonline, 27.Apr, 2021, EGU21-1235824 Duan B, Hugentobler U, Selmke I, Marz S, Killian M, Rott M (2021b) BeiDou satellite radiation force models for precise orbit determination and geodetic applications. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.15111978.v125 Fliegel H, Gallini T (1996) Solar force modeling of block IIR global positioning system satellites. J Spacecraft Rockets 33(6):863–866. https://doi.org/10.2514/3.2685126 Fliegel H, Gallini T, Swift E (1992) Global positioning system radiation force model for geodetic applications. Journal of Geophysical Research 97(B1):559–568. https://doi.org/10.1029/91JB0256427 Glaser S, Michalak G, Männel B, König R, Neumayer K H, Schuh H (2020) Reference system origin and scale realization with the futhre GNSS constellation “Kapler”. Journal of Geodesy 94:117. https://doi.org/10.1007/00190-020-01441-028 Ge M, Zhang HP, Jia XL, Song SL, Wickert L (2012) What is achievable with the current COMPASS Constellations? In: Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, 17–21 Sept 201229 Guo J, Zhao Q, Geng T, Su X, Liu J (2013) Precise orbit determination for COMPASS IGSO satellites during yaw maneuvers. In: Sun J, Jiao W, Wu H, Shi C (Eds.), Proceedings China Satellite Navigation Conference (CSNC) 2013. Vol. III. Springer 245:41–53. https://doi.org/10.1007/978-3-642-37407-4_430 Guo J, Zhao Q (2014a) Analysis of precise orbit determination for Beidou satellites during yaw maneuvers. Presented at China Satellite Navigation Conference (CSNC) 2014, Wuhan, 22 May 2014.31 Guo J (2014b) The Impacts of Attitude, Solar Radiation and Function Model on Precise Orbit Determination for GNSS Satellites. PhD Dissertation, GNSS Research Center, Wuhan University 32 Guo J, Xu X, Zhao Q, Liu J (2016a) Precise orbit determination for quad-constellation satellites at Wuhan University: Strategy, result validation, and comparison. Journal of Geodesy 90:143–159. https://doi.org/10.1007/s00190-015-0862-933 Guo F, Li X, Zhang X, Wang J (2016b) Assessment of precise orbit and clock products for Galileo, BeiDou, and QZSS from IGS Multi-GNSS Experiment (MGEX). GPS Solution 21:279–290. https://doi.org/10.1007/s10291-016-0523-334 Guo J, Chen G, Zhao Q, Liu J, Liu X (2017) Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality. GPS Solutions 21:511-522. https://doi.org/10.1007/s10291-016-0540-235 Guo J, Qu Z, Chao Y, Chen G, Wang C, Zhao Q (2020) The potential contributions and challenges of BDS to establishment of terrestrial reference frame. Presented at China Satellite Navigation Conference (CSNC) 2020, Chengdu, 23 November 2014.36 Guo J, Wang C, Zhao Q (2021) BDS-3 precise orbit and clock solution at Wuhan University: status and improvement. Journal of Geodesy (under review)37 Guo R, Zhou J, Hu X, Liu L, Tang B, Li X, Wu S (2015) Precise orbit determination and rapid orbit recovery supported by time synchronization. Advances in Space Research 55(12):2889–2898. https://doi.org/10.1016/j.asr.2015.03.00138 Hackel S, Steigenberger P, Hugentobler U, Uhlemann M, Montenbruck O (2015) Galileo orbit determination using combined GNSS and SLR observations. GPS Solution 19 (1):15-25. https://doi.org/10.1007/s10291-013-0361-539 Hauschild A, Montenbruck O, Sleewaegen J-M, Huisman L, Teunissen P (2011) Characterization of Compass M-1 signals. GPS Solutions 16:117-126. https://doi.org/10.1007/s10291-011-0210-340 Hauschild A, Montenbruck O, Sleewaegen J-M, Huisman L, Teunissen PG (2012) Characterization of compass M-1 signals. GPS Solutions 16:117–126. https://doi.org/10.1007/s10291-011-0210-3 41 Huang G, Yan X, Zhang Q, Liu C, Wang L Qin Z (2018) Estimation of antenna phase center offset for BDS IGSO and MEO satellites. GPS Solution 22:49. https://doi.org/10.1007/s10291-018-0716-z42 Huang W, Männel B, Brack A, Schuh H (2021) Two methods to determine scale-independent GPS PCOs and GNSS-based terrestrial scale: comparison and cross-check. GPS Solution 25:4. https://doi.org/10.1007/s10291-020-01035-543 Jiao W, Ding Q, Li J, Lu X, Feng L, Ma J, Chen G (2011) Monitoring and assessment of GNSS open services. Journal of Navigation 64(S1):S19–S29. https://doi.org/10.1017/s037346331100038544 Krzan G, Dawidowicz K, Wielgosz P (2020) Antenna phase center correction differences from robot and chamber calibrations: the case study LEIAR25. GPS Solutions 24:747. https://doi.org/10.1007/s10291-020-0957-545 Kröger J, Kersten T, Breva Y, Schön S (2021) Multi-frequency multi-GNSS receiver antenna calibration at IfE: Concept - calibration results - validation. Advances in Space Research. https://doi.org/10.1016/j.asr.2021.01.02946 Li X, Hu X, Guo R, Tang C, Zhou S, Liu S, Chen J (2018) Orbit and positioning accuracy for new generation BeiDou satellites during the earth eclipsing period. The Journal of Navigation 71:1069-1087. https://doi.org/10.1017/S037346331800010347 Li X, Yuan Y, Zhu Y, Huang J, Wu J, Xiong Y, Zhang X, Li X (2019) Precise orbit determination for BDS3 experimental satellites using iGMAS and MGEX tracking networks. Journal of Geodesy 93:103–117. https://doi.org/10.1007/s00190-018-1144-048 Li X, Yuan Y, Zhu Y, Jiao W, Bian L, Li X, Zhang K (2020a) Improving BDS-3 precise orbit determination for medium earth orbit satellites. GPS Solution 24:53. https://doi.org/10.1007/s10291-020-0967-349 Li X, Zhu Y, Zheng K, Yuan Y, Liu G, Xiong Y (2020b) Precise Orbit and Clock Products of Galileo, BDS and QZSS from MGEX Since 2018: Comparison and PPP Validation. Remote Sensing 2020(12):1415. https://doi.org/10.3390/rs1209141550 Li X, Zhang K, Meng X, Zhang Q, Zhang W, Li X, Yuan Y (2020c) LEO-BDS-GPS integrated precise orbit modeling using FengYun-3D, FengYun-3C onboard and ground observations. GPS Solutions 24:48. https://doi.org/10.1007/s10291-020-0962-851 Li X, Zhang K, Meng X, Zhang W, Zhang Q, Zhang X, Li X (2020d) Precise orbit determination for the FY-3C satellite using onboard BDS and GPS observations from 2013, 2015, and 2017. Engineering 6(8):904-913. https://doi.org/10.1016/j.eng.2019.09.00152 Li J, Yuan Y, Huang S, Liu C, Lou J, Li X (2021a) Examination and enhancement of solar radiation pressure model for BDS-3 satellites. EGU2021, vPICOonline, 27.Apr, 2021, EGU21-1235817163553 Li R, Wang N, Li Z, Shang Y, Wang Z, Ma H (2021b) Precise orbit determination of BDS-3 satellites using B1C and B2a dual-frequency measurements. GPS Solutions 25:95. https://doi.org/10.1007/s10291-021-01126-x54 Liu J, Gu D, Ju B, Shen Z, Lai Y, Yi D (2016) A new empirical solar radiation pressure model for BeiDou GEO satellites. Advances in Space Research 57(1):234–244. https://doi.org/10.1016/j.asr.2015.10.04355 Liu C, Gao W, Pan J, Tang C, Hu X, Wang W, Chen Y, Lu Y, Su C (2020) Inter-satellite clock offsets adjustment based on closed-loop residual detection of BDS inter-satellite link. Acta Geodaetica et Cartographica Sinica 49(9):1149-1157. https://doi.org/10.11947/j.AGCS.2020.2020031956 Loyer S, Perosanz F, Versini L, Katsigianni G, Mercier F, Mezerette (2018) CNES/CLS IGS Analysis center: recent activities. IGS Workshop 2018, 29 October to 2 November, Wuhan, China57 Lv Y, Geng T, Zhao Q, Xie X, Zhang F, Wang X (2020) Evaluation of BDS-3 orbit determination strategies using ground-tracking and inter-satellite link observation. Remote Sensing 12(16):2647. http://dx.doi.org/10.3390/rs1216264758 Mi X, Sheng C, EI-Mowafy A, Zhang B (2021) Characteristics of receiver‑related biases between BDS‑3 and BDS‑2 for five frequencies including inter‑system biases, differential code biases, and differential phase biases. GPS Solutions 25:113. http://dx.doi.org/10.1007/s10291-021-01151-w59 Montenbruck O, Hauschild A, Hessels U (2011) Characterization of GPS/GIOVE sensor stations in the CONGO network. GPS Solution 15 (3):193–205. http://dx.doi.org/10.1007/s10291-010-0182-860 Montenbruck O, Steigenberger P, Hugentobler U (2015a) Enhanced solar radiation pressure modeling for Galileo satellites. Journal of Geodesy 89 (3):283-297, 10.1007/s00190-014-0774-061 Montenbruck O, Schmid R, Mercier F, Steigenberger P, Noll C, Fatkulin R, Kogure S, Ganeshan AS (2015b) GNSS satellite geometry and attitude models. Advances in Space Research 56(6):1015–1029. https://doi.org/10.1016/j.asr.2015.06.01962 Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Romero I, Noll C, Stürze A, Weber G, Schmid R, MacLeod K, Schaer S (2017a) The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) – Achievements, prospects and challenges. Advances in Space Research 59:1671-1697. http://dx.doi.org/10.1016/j.asr.2017.01.01163 Montenbruck O, Steigenberger P, Darugna F (2017b) Semi-analytical solar radiation pressure modeling for QZS-1 orbit-normal and yaw-steering attitude. Advances in Space Research 59(8):2088-2100. http://dx.doi.org/10.1016/j.asr.2017.01.03664 Pan J, Hu X, Zhou S, Tang C, Guo R, Zhu L, Tang G, Hu G (2018) Time synchronization of new-generation BDS satellites using inter-satellite link measurements. Advances in Space Research 61(1):145–153. https://doi.org/10.1016/j.asr.2017.10.00465 Pan J, Hu X, Zhou S, Tang C, Wang D, Yang Y, Dong W (2021) Full-ISL clock offset estimation and prediction algorithm for BDS3. GPS Solutions 25:140. http://dx.doi.org/10.1007/s10291-021-01177-066 Pearlman MR, Degnan JJ, Bosworth JM (2002) The International Laser Ranging Service. Advances in Space Research 30:135–143. http://dx.doi.org/10.1016/S0273-1177(02)00277-667 Rebischung P, Altamimi Z, Springer T (2014) A collinearity diagnosis of the GNSS geocenter determination. Journal of Geodesy 88:65–85. https://doi.org/10.1007/s00190-013-0669-568 Rebischung P (2014) Can GNSS contribute to improving the ITRF definition? PhD Thesis, Ecole Doctorale Astronomie et Astrophysique d’Ile-de-France69 Rodríguez-Solano C (2009) Impact of albedo modeling on GPS orbits. Master Thesis. Technische Universität München70 Rodríguez-Solano C, Hugentobler U, Steigenberger P (2012a) Adjustable box-wing model for solar radiation pressure impacting GPS satellites. Advances in Space Research 49:1113–1128. http://dx.doi.org/10.1016/j.asr.2012.01.01671 Rodriguez-Solano C, Hugentobler U, Steigenberger P, Lutz S (2012b). Impact of earth radiation pressure on GPS position estimates. J Geod 86(5):309–317. doi:10.1007/s00190-011-0517-472 Prange L, Villiger A, Sidorov D, Schaer S, Beutler G, Dach R, Jäggi A (2020a) Overview of CODE’s MGEX solution with the focus on Galileo. Advances in Space Research 66(12):2786-2798. https://doi.org/10.1016/j.asr.2020.04.03873 Prange L, Beutler G, Dach R, Arnold D, Schaer S, Jäggi A (2020b) An empirical solar radiation pressure model for satellites moving in the orbit-normal mode. Advances in Space Research 65(1):235-250. http://dx.doi.org/10.1016/j.asr.2019.07.03174 Ruan R, Jia X, Feng L, Zhu J, Huyan Z, Li J, Wei Z (2020) Orbit determination and time synchronization for BDS-3 satellites with raw inter-satellite link ranging observations. Satellite Navigation 1:8. https://doi.org/10.1186/s43020-020-0008-y75 Qing Y, Lou Y, Dai X, Liu Y (2017) Benefits of satellite clock modeling in BDS and Galileo orbit determination. Advances in Space Research 60(12):2550-2560. https://doi.org/10.1016/j.asr.2017.03.04076 Qu Z, Guo J, Zhao Q (2021a) Phase center corrections for BDS IGSO and MEO satellites in IGb14 and IGSR3 frame. Remote Sensing 13(4):745. http://dx.doi.org/10.3390/rs1304074577 Qu Z (2021b) Phase center corrections for BDS satellites with ground and LEO onboard data. Master Dissertation, Wuhan University.78 Selmke I, Duan B, Hugentobler U (2018) Status of the TUM MGEX orbit and clock products. IGS Workshop 2018, 29 October to 2 November, Wuhan, China79 Scaramuzza S, Dach R, Beutler G, Arnold D, Sušnik A, Jäggi A (2018) Dependency of geodynamic parameters on the GNSS constellation. Journal of Geodesy 92(1):93–104. https://doi.org/10.1007/s0019 0-017-1047-580 Shi C, Zhao Q, Li M, Tang W, Hu Z, Lou Y, Zhang H, Niu X, Liu J (2012) Precise orbit determination of BeiDou Satellites with precise positioning. Science China Earth Sciences 55:1079-1086. http://dx.doi.org/10.1007/s11430-012-4446-881 Sidorov D, Dach R, Polle B, Prange L, Jaggi A (2020) Adopting the empirical CODE orbit model to Galileo satellites. Advances in Space Research 66(12):15. http://dx.doi.org/10.1016/j.asr.2020.05.02882 Sośnica K, Zajdel R, Bury G, Bosy J, Moore M, Masoumi S (2020) Quality assessment of experimental IGS multi-GNSS combined orbits. GPS Solutions 24:54. https://doi.org/10.1007/s10291-020-0965-583 Springer T, Beutler G, Rothacher M (1999) A new solar radiation pressure model for GPS satellites. GPS Solution 2(3):50–62. https://doi.org/10.1007/PL00012757 84 Springer T, Agrotis L, Dilssner F, Feltens J, Van Kints M, Mayer V, Romero I, Enderle W, Schoenemann E, Zandbergen R (2020) The ESA/ESOC IGS Analysis Centre Technical Report 2019. ftp://ftp.aiub.unibe.ch/users/villiger/2019_techreport.pdf. Accessed on 30 August 202185 Steigenberger P, Hugentobler U, Hauschild A, Montenbruck O (2013) Orbit and clock analysis of Compass GEO and IGSO satellites. Journal of Geodesy 87(6):515–525. https://doi.org/10.1007/s00190-013-0625-486 Steigenberger P, Thoelert S, Montenbruck O (2018) GNSS satellite transmit power and its impact on orbit determination. Journal of Geodesy 92:609-624. DOI: 10.1007/s00190-017-1082-287 Steigenberger P, Thoelert S (2020) Initial BDS-3 transmit power analysis (with BDS-2 gain pattern)88 Steigenberger P, Mentenbruck O (2020) Consistency of MGEX orbit and clock products. Engineering 6(8):898-903. DOI: 10.1016/j.eng.2019.12.00589 Su M, Zhao Q, Guo J, Su X, Hu Z, Guo H (2018) Phase Center Calibration for Receiver Antenna and Its Impact on Precise Orbit Determination of BDS Satellites. Acta Geodaetica et Cartographica Sinica 47(S0):78-85. https://doi.org/10.11947/j.AGCS.2018.2018032490 Sun B, Su H, Zhang Z, Kong Y, Yang X (2016) GNSS GEO Satellites Precise Orbit Determination Based on Carrier Phase and SLR Observations. IGS Workshop 2016, Feb 8-12, 2016, Sydney91 Tan B, Yuan Y, Zhang B, Hsu H, Ou J (2016) A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM. Scientific Report 6:32967. https://doi.org/10.1038/srep3296792 Tan B, Yuan Y, Wen M, Ning Y, Liu X (2017) Initial Results of the Precise Orbit Determination for the New-Generation BeiDou Satellites (BeiDou-3) Based on the iGMAS Network. International Journal of Geo-information 5:196. https://doi.org/10.3390/ijgi511019693 Tang C, Hu X, Zhou S, Liu L, Pan J, Chen L (2018) Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements. Journal of Geodesy 92:1155-1169. https://doi.org/10.1007/s00190-018-1113-794 Wang W, Chen G, Guo S, Song X, Zhao Q (2013) A study on the Beidou IGSO/MEO satellite orbit determination and prediction of the different yaw control mode. In: Sun J, Jiao W, Wu H, Shi C (Eds.), Proceedings China Satellite Navigation Conference (CSNC) 2013. Vol. III. Springer, pp 31–40, https://doi.org/10.1007/978-3-642-37407-4_395 Wang C, Guo J, Zhao Q, Liu J (2018) Yaw attitude modeling for BeiDou I06 and BeiDou-3 satellites. GPS Solutions 22:117. https://doi.org/10.1007/s10291-018-0783-196 Wang C, Guo J, Zhao Q, Liu J (2019a) Empirically derived model of solar radiation pressure for BeiDou GEO satellites. Journal of Geodesy 93: 791. https://doi.org/10.1007/s00190-018-1199-y97 Wang C, Zhao Q, Guo J, Liu J, Chen G (2019b) The contribution of intersatellite links to BDS-3 orbit determination: Model refinement and comparisons. Navigation 66 (1):71-82. https://doi.org/10.1002/navi.29598 Wang J, Liu G, Guo A, Xiao G, Wang B, Gao M, Wang S (2020c) BDS receiver antenna phase center calibration．Acta Geodaetica et Cartographica Sinica 49(3):312-321. https://doi.org/10.11947/j.AGCS.2020.2019007299 Wang L, Xu B, Fu F, Chen R, Li T, Han Y, Zhou H (2020d) Centimeter-level precise orbit determination for the Luojia-1A satellite using BeiDou observations. Remote Sensing 12:2063. https://doi.org/10.3390/rs12122063100 Wanninger L, Beer S (2015) BeiDou satellite-induced code pseudorange variations: diagnosis and therapy. GPS Solutions 19:639-648. https://doi.org/10.1007/s10291-014-0423-3101 Willi D, Lutz S, Brockmann E, Rothacher M (2020) Absolute field calibration for multi-GNSS receiver antennas at ETH Zurich. GPS Solutions 24:375. https://doi.org/10.1007/s10291-019-0941-0102 Wübbena G, Schmitz M, Warneke A (2019) Geo++ Absolute Multi Frequency GNSS Antenna Calibration. In Presentation at the EUREF Analysis Center (AC) Workshop, October 16–17, Warsaw, Poland. http://www.geopp.com/pdf/gpp_cal125_euref19_p.pdf . Accessed on 01 September 2021103 Xia F, Ye S, Chen D, Jiang N (2019) Observation of BDS-2 IGSO/MEOs yaw-attitude behavior during eclipse seasons. GPS Solutions 23:71. https://doi.org/10.1007/s10291-019-0857-8 104 Xia F, Ye S, Chen D, Wu J, Wang C, Sun W (2020) Estimation of antenna phase center offsets for BeiDou IGSO and MEO satellites. GPS Solution 24:90. https://doi.org/10.1007/s10291-020-01002-0105 Xie X (2019) Precise Orbit and Clock Determination for BDS-3 Satellites Using Inter-satellite Link Observations. PhD Dissertation, GNSS Research Center, Wuhan University.106 Xie X, Geng T, Zhao Q, Lv Y, Cai H, Liu J (2020). Orbit and clock analysis of BDS-3 satellites using inter-satellite link observations. J Geodesy 94(7):64. https://doi.org/10.1007/s00190-020-01394-4107 Xu T, Yu S, Li J (2014) Earth Rotation Parameters Determination Using BDS and GPS Data Based on MGEX Network. In: Sun J., Jiao W., Wu H., Lu M. (eds) China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume III. Lecture Notes in Electrical Engineering, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54740-9_26 108 Yan X, Huang G, Zhang Q, Wang L, Qin Z, Xie S (2019a) Estimation of the Antenna Phase Center Correction Model for the BeiDou-3 MEO Satellites. Remote Sensing 11:2850. https://doi.org/10.3390/rs11232850109 Yan X, Liu C, Huang G, Zhang Q, Wang L, Qin Z, Xie S (2019b) A Priori Solar Radiation Pressure Model for BeiDou-3 MEO Satellites. Remote Sensing 11:1605. https://doi.org/10.3390/rs11131605110 Yang Y, Tang J, Montenbruck O (2017a) Chinese Navigation Satellite Systems. In: Teunissen PJ, Montenbruck O (eds) Springer Handbook of Global Navigation Satellite Systems. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-42928-1_10111 Yang D, Yang J, Li G, Zhou Y, Tang C (2017b) Globalization highlight: orbit determination using BeiDou inter-satellite ranging measurements. GPS Solutions 21:1395-1404. https://doi.org/10.1007/s10291-017-0626-5112 Yang Y, Yang Y, Hu X, Chen J, Guo R, Tang C, Zhou S, Zhao L, Xu J (2019) Inter-Satellite Link enhanced orbit determination for BeiDou-3. The Journal of Navigation 73:115-130. https://doi.org/10.1017/S0373463319000523113 Yang C, Guo J, Zhao Q (2021) Yaw attitudes for BDS-3 IGSO and MEO satellites: estimation, validation and modeling with inter-satellite link observations. Submitted to Journal of Geodesy114 Zajdel R, Sosnica K, Bury G, Dach R, Prange L (2020) System‑specifc systematic errors in earth rotation parameters derived from GPS, GLONASS, and Galileo. GPS Solutions 24:74. https://doi.org/10.1007/s10291-020-00989-w115 Zajdel R, Sosnica K, Bury G (2021) Geocenter coordinates derived from multi-GNSS: a look into the role of solar radiation pressure modeling. GPS Solutions 25:1. https://doi.org/10.1007/s10291-020-01037-3116 Ziebart M, Dare P (2001) Analytical solar radiation pressure modelling for GLONASS using a pixel array. Journal of Geodesy 75:587–599. https://doi.org/10.1007/s001900000136117 Zhao Q, Guo J, Li M, Qu L, Hu Z, Shi C, Liu J (2013) Initial results of precise orbit and clock determination for COMPASS navigation satellite system. Journal of Geodesy 87:475-486. https://doi.org/10.1007/s00190-013-0622-7118 Zhao Q, Wang C, Guo J, Yang G, Liao M, Ma H, Liu J (2017) Enhanced orbit determination for BeiDou satellites with FengYun-3C onboard GNSS data. GPS Solutions 21:1179-1190. https://doi.org/10.1007/s10291-017-0604-y119 Zhao Q, Wang C, Guo J, Bin W, Liu J (2018) Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis. GPS Solutions 22:4. https://doi.org/10.1007/s10291-017-0673-y120 Zhao X, Zhou S, Ci Y, Hu X, Cao J, Chang Z, Tang C, Guo D, Guo K, Liao M (2020) High-precision orbit determination for a LEO nanosatellite using BDS-3. GPS Solutions 24:102. https://doi.org/10.1007/s10291-020-01015-9121 Zhang X, Zhou Y, Cong F, Ji J, Sun G (2020) Research of the dedicated platform for BeiDou-3 satellite directly into orbit. Astronautical Systems Engineering Technology 4(6):1-8122 Zhang X, Wu M, Liu W, Li X, Yu S, Lu C, Wichert J (2017) Initial assessment of the COMPASS/BeiDou-3: new generation navigation signals. Journal of Geodesy 91:1225-1240. https://doi.org/10.1007/s00190-017-1020-3123 Zhou R, Hu Z, Zhao Q, Li P, Wang W, He C, Cai C, Pan Z (2018) Elevation-dependent pseudorange variation characteristics analysis for the new-generation BeiDou satellite navigation system. GPS Solutions 22:60. https://doi.org/10.1007/s10291-018-0726-x124 Zhou S, Hu X, Wu B, Liu L, Qu W, Guo R, He F, Cao Y, Wu X, Zhu L, Tan H (2011) Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network. Science China Physics, Mechanics and Astronomy 54:1089–1097. https://doi.org/10.1007/s11433-011-4342-9125 Zhou S, Hu X, Liu L, He F, Tang C, Pang J (2020) Status of satellite orbit determination and time synchronization technology for global navigation satellite system. Chinese Astronomy and Astrophysics 44(1):105-118. https://doi.org/10.1016/j.chinastron.2020.04.007126 Zheng J (2020) Inter-satellite link and autonomous navigation of BDS. Presented at China Satellite Navigation Conference (CSNC) 2020, Chengdu, 23 November 2020.