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标题：北斗卫星精密轨道确定
作者：赵齐乐，郭靖*，王晨，吕逸飞，许小龙，杨超，李俊强
主题词：北斗卫星导航系统；轨道和钟差；太阳光压力；姿态；相位中心；星间链路
（图片来自作者）
Precise orbit determination for BDS satellites
Qile Zhao, Jing Guo* , Chen Wang, Yifei Lv, Xiaolong Xu, Chao Yang and Junqiang Li
Satellite Navigation (2022) 3: 2
引用文章:
Zhao, Q. L., Guo, J., Wang, C. et al. Precise orbit determination for BDS satellites. Satell Navig3, 2 (2022). https://doi.org/10.1186/s43020-021-00062-y
PDF文件下载链接：
https://satellite-navigation.springeropen.com/articles/10.1186/s43020-021-00062-y
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Editorial Summary
BDS: Precise orbit determination
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.
本文亮点
- 本文总结了过去近10年国内外有关北斗卫星精密定轨的研究，特别是在几何观测模型、轨道动力学模型以及定轨策略方面的研究进展。首先给出了北斗卫星元数据，特别是卫星星体和太阳帆板的几何和物理属性参数，并梳理和总结了北斗卫星地面测站和低轨卫星跟踪情况。在几何误差模型方面，详细总结了卫星偏航姿态和天线相位中心改正模型的研究现状。在轨道动力学研究方面，则重点讨论和分析了太阳光压力、地球反照辐射、天线推力和热辐射力等非保守力模型的研究进展。
- 本文进一步总结和分析了星间链路观测值特性和对北斗精密定轨的贡献。在描述星间链路拓扑结构和建链方式的基础上，采用精密定轨残差和双向归化钟差观测值闭合差揭示星间链路观测值中存在成因未知的常量、趋势项和周期项等系统性误差。进一步表明采用星间链路和星地L波段观测值所确定的两类卫星径向轨道误差特性的不一致，讨论了观测值特性对卫星轨道和非保守力估计的影响。
- 本文探讨了北斗卫星精密定轨的后续研究及展望。具体包括，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；进一步优化太阳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；分析星间链路系统误差来源以及消除方法；研究钟差模型或星间链路所估钟差约束下的北斗卫星精密定轨；考察和分析北斗系统及其星地、星间和星载观测值对地心、尺度和地球自转参数等大地测量参数估计的影响和贡献。
内容简介
中国从20世纪80年代开始积极探索建立独立的北斗卫星导航系统，通过三步走的策略，先后成功建立了由三颗地球静止轨道（GEO）卫星组成的北斗一号系统，由 5 颗GEO、5颗倾斜地球同步轨道（IGSO）卫星和4 颗中轨道（MEO）卫星组成的北斗二号系统，以及由3颗GEO、3颗IGSO和24颗MEO组成的北斗三号系统。北斗二号系统从2012年12月底正式提供区域定位、导航和授时（PNT）服务，而北斗三号自2020年7月31日起正式提供全球PNT服务。
轨道和钟差是决定北斗卫星系统服务性能的核心参数，也对地球定向参数（EOP）、地心等大地测量参数的估计和确定有重要影响。本文从卫星系统、跟踪数据、几何观测模型、轨道动力学模型和定轨策略等方面，总结了过去近10年北斗卫星精密定轨的研究进展。并进一步讨论了北斗卫星对大地测量参数估计的影响和贡献，最后探讨了北斗卫星精密定轨的后续研究内容。
图文导读
I 北斗系统状态和卫星元数据
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。
图 1 北斗三号GEO、IGSO卫星以及五院和小卫星分别制造的MEO卫星（图源：中国卫星导航系统管理办公室测试评估研究中心和中国科学院微小卫星创新研究院）。
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。
图2显示了2014年以来能够跟踪北斗二号和北斗三号的iGMAS和MGEX台站数量变化。从中可见，对于MGEX测站，北斗二号和三号卫星的跟踪能力在逐步改善，特别是在2018年中期提升较大。然而并非所有北斗卫星跟踪站数目相似。基本而言，越早发射的卫星其跟踪测站数目越多（如图3）。而跟踪测站数目的差异将对卫星轨道精度产生系统性影响。
图 3 北斗三号不同卫星地面站跟踪情况。
除地面跟踪站外，还有少数低轨卫星携带星载GNSS接收机以提供星载北斗观测值，如灵巧通讯试验卫星、风云三号C星和D星、珞珈一号 A星和天平一号 B星等。其为改善北斗卫星几何跟踪条件，提高定轨精度以及天线相位中心等几何误差标定提供了重要的数据源。
此外，北斗三号卫星具有Ka波段星间链路功能，可实现星间通讯和测距，并用于精密轨道和钟差估计。北斗星间链路采用时分多址体制进行双向测距，按照地面预先上注给卫星的时隙规划表，每颗卫星轮循与其他可见卫星（或地面锚固站）建链。一对建链卫星在一个时隙内（3s）先后发射测量信号，完成一次星间相互测量，其中前向测量在第一个1.5 s内完成，反向测量在第二个1.5 s内完成。在每个3s的时隙内，会有多对卫星同时建链，使得星间测距能够在较短的时间内覆盖整个星座。此外，时隙规划表也会根据卫星的可见性在一段时间内（如1小时）进行更新，从而形成动态链路（Xie, 2019）。双向单程测距观测值可以归化为单程与距离无关或与钟差无关的观测值以用于精密钟差估计和轨道确定。
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。
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作者简介
赵齐乐 教授
本文第一作者
武汉大学
▍作者简介
赵齐乐，武汉大学教授，目前重点开展卫星精密定轨定位及天地一体化导航增强方面的理论、方法和软件系统的研究。发表了SCI索引论文100余篇，获得国家发明专利7项，软件著作权18项。相关成果获得了国家科学技术进步一等奖、二等奖，及教育部科技进步一等奖等多项奖励。
郭靖 副教授
本文通讯作者
郭靖，武汉大学卫星导航定位技术研究中心，副教授。主要从事北斗/GNSS卫星精密定轨等方面的理论、算法和软件系统研究。已发表论文40余篇，获国家和省部级奖多项。国际卫星导航服务组织（IGS）实时和参考框架工作组成员，负责武汉大学IGS MGEX（WUM产品）和iGMAS分析中心以及IGS第三次GNSS历史数据重处理。
初审：段鹏丽
复审：宋启凡
终审：金 君
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