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标題：北鬥衛星精密軌道确定
作者：趙齊樂，郭靖*，王晨，呂逸飛，許小龍，楊超，李俊強
主題詞：北鬥衛星導航系統；軌道和鐘差；太陽光壓力；姿态；相位中心；星間鍊路
（圖檔來自作者）
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檔案下載下傳連結：
https://satellite-navigation.springeropen.com/articles/10.1186/s43020-021-00062-y
-長按識别二維碼檢視/下載下傳全文-
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.
本文亮點
- 本文總結了過去近10年國内外有關北鬥衛星精密定軌的研究，特别是在幾何觀測模型、軌道動力學模型以及定軌政策方面的研究進展。首先給出了北鬥衛星中繼資料，特别是衛星星體和太陽帆闆的幾何和實體屬性參數，并梳理和總結了北鬥衛星地面測站和低軌衛星跟蹤情況。在幾何誤差模型方面，詳細總結了衛星偏航姿态和天線相位中心改正模型的研究現狀。在軌道動力學研究方面，則重點讨論和分析了太陽光壓力、地球反照輻射、天線推力和熱輻射力等非保守力模型的研究進展。
- 本文進一步總結和分析了星間鍊路觀測值特性和對北鬥精密定軌的貢獻。在描述星間鍊路拓撲結構和建鍊方式的基礎上，采用精密定軌殘差和雙向歸化鐘差觀測值閉合差揭示星間鍊路觀測值中存在成因未知的常量、趨勢項和周期項等系統性誤差。進一步表明采用星間鍊路和星地L波段觀測值所确定的兩類衛星徑向軌道誤差特性的不一緻，讨論了觀測值特性對衛星軌道和非保守力估計的影響。
- 本文探讨了北鬥衛星精密定軌的後續研究及展望。具體包括，在完善北鬥衛星中繼資料的基礎上，進一步聯合地面和低軌衛星星載北鬥跟蹤資料，估計和IGS架構一緻的所有衛星天線相位中心偏差和變化；進一步優化太陽光壓力和熱輻射力等非保守力模型，以提高蝕衛星以及零偏期間衛星定軌精度；分析星間鍊路系統誤差來源以及消除方法；研究鐘差模型或星間鍊路所估鐘差限制下的北鬥衛星精密定軌；考察和分析北鬥系統及其星地、星間和星載觀測值對地心、尺度和地球自轉參數等大地測量參數估計的影響和貢獻。
内容簡介
中國從20世紀80年代開始積極探索建立獨立的北鬥衛星導航系統，通過三步走的政策，先後成功建立了由三顆地球靜止軌道（GEO）衛星組成的北鬥一号系統，由 5 顆GEO、5顆傾斜地球同步軌道（IGSO）衛星和4 顆中軌道（MEO）衛星組成的北鬥二号系統，以及由3顆GEO、3顆IGSO和24顆MEO組成的北鬥三号系統。北鬥二号系統從2012年12月底正式提供區域定位、導航和授時（PNT）服務，而北鬥三号自2020年7月31日起正式提供全球PNT服務。
軌道和鐘差是決定北鬥衛星系統服務性能的核心參數，也對地球定向參數（EOP）、地心等大地測量參數的估計和确定有重要影響。本文從衛星系統、跟蹤資料、幾何觀測模型、軌道動力學模型和定軌政策等方面，總結了過去近10年北鬥衛星精密定軌的研究進展。并進一步讨論了北鬥衛星對大地測量參數估計的影響和貢獻，最後探讨了北鬥衛星精密定軌的後續研究内容。
圖文導讀
I 北鬥系統狀态和衛星中繼資料
目前，北鬥衛星導航系統空間段由北鬥二号系統（5顆GEO、7顆IGSO和3顆MEO）、北鬥三号實驗系統（2顆IGSO和2顆MEO）和北鬥三号全球系統（3顆GEO、3顆IGSO和24顆MEO）組成，其詳細在軌狀态可參見中國衛星導航系統管理辦公室測試評估研究中心（http://www.csno-tarc.cn/system/constellation）。
包含北鬥二号和三号衛星天線相位中心偏差、品質、衛星星體結構和光學屬性、姿态控制模式等在内的中繼資料已于2019年年底公開（CSNO 2019a），以支援北鬥衛星高精度資料處理和軌道動力學模組化。由中國空間技術研究院（簡稱五院）制造的北鬥三号GEO和IGSO衛星星體呈沿Z軸拉伸的長方體，除太陽帆闆以外，GEO衛星在±X面上安裝有桁架式天線；除在+X面上安裝有桁架式天線外，IGSO衛星在-X面上還安裝有兩個小型天線（Chen and Wu, 2020）。中國空間技術研究院（簡稱五院）的北鬥三号MEO衛星采用專用平台，其結構呈現由大小兩塊長方體組成的T型，以适于一箭多星發射、直接入軌，進而滿足衛星組批研制、快速組網的任務要求（Zhang et al., 2020）。此外，部分衛星在-X面安裝有額外的通訊天線。中國科學院微小衛星創新研究院（簡稱小衛星）研制的北鬥三号MEO衛星星體結構呈沿X軸拉伸的長方體形狀。星體拉伸方向的差異将造成五院和小衛星MEO衛星軌道誤差具有不同的特性。
圖 1 北鬥三号GEO、IGSO衛星以及五院和小衛星分别制造的MEO衛星（圖源：中國衛星導航系統管理辦公室測試評估研究中心和中國科學院微小衛星創新研究院）。
公開的北鬥衛星中繼資料中僅包含衛星星體和太陽帆闆的吸收參數，缺乏鏡面反射和漫反射系數以用于光壓力模組化。Chen et al. (2019)較為詳細的給出了北鬥二号IGSO和MEO衛星星體和太陽帆闆的材料類型以及相應光學系數。以此為參考，本文得到并給出了北鬥二号和三号衛星粗略的光學系數值以用于非保守力模組化。
II北鬥衛星跟蹤資料
北鬥星地L波段跟蹤資料主要來自武漢大學北鬥實驗跟蹤網（BETS）、國際衛星導航服務組織（IGS）和全球連續監測和評估系統（iGMAS）。BETS網由武漢大學衛星導航定位技術研究中心于2011年3月起建立，約由15個測站組成（Shi et al., 2011），提供了對于北鬥二号衛星信号的最初跟蹤資料。iGMAS網由全球連續監測和評估系統項目建構，由31個全球分布的站點組成（Jiao et al., 2011），這些資料可以從相應資料中心下載下傳。随着新興導航系統的蓬勃發展，IGS統籌成立了多模GNSS工作組（MGEX）并積極推動多模跟蹤站建立。截至2021年9月，MGEX網中已有超過250個測站可跟蹤北鬥信号，其資料可以從 IGS 資料中心下載下傳。
圖 2 IGS和iGMAS測站對北鬥二号和三号衛星的跟蹤情況。
圖2顯示了2014年以來能夠跟蹤北鬥二号和北鬥三号的iGMAS和MGEX台站數量變化。從中可見，對于MGEX測站，北鬥二号和三号衛星的跟蹤能力在逐漸改善，特别是在2018年中期提升較大。然而并非所有北鬥衛星跟蹤站數目相似。基本而言，越早發射的衛星其跟蹤測站數目越多（如圖3）。而跟蹤測站數目的差異将對衛星軌道精度産生系統性影響。
圖 3 北鬥三号不同衛星地面站跟蹤情況。
除地面跟蹤站外，還有少數低軌衛星攜帶星載GNSS接收機以提供星載北鬥觀測值，如靈巧通訊試驗衛星、風雲三号C星和D星、珞珈一号 A星和天平一号 B星等。其為改善北鬥衛星幾何跟蹤條件，提高定軌精度以及天線相位中心等幾何誤差标定提供了重要的資料源。
此外，北鬥三号衛星具有Ka波段星間鍊路功能，可實作星間通訊和測距，并用于精密軌道和鐘差估計。北鬥星間鍊路采用時分多址體制進行雙向測距，按照地面預先上注給衛星的時隙規劃表，每顆衛星輪循與其他可見衛星（或地面錨固站）建鍊。一對建鍊衛星在一個時隙内（3s）先後發射測量信号，完成一次星間互相測量，其中前向測量在第一個1.5 s内完成，反向測量在第二個1.5 s内完成。在每個3s的時隙内，會有多對衛星同時建鍊，使得星間測距能夠在較短的時間内覆寫整個星座。此外，時隙規劃表也會根據衛星的可見性在一段時間内（如1小時）進行更新，進而形成動态鍊路（Xie, 2019）。雙向單程測距觀測值可以歸化為單程與距離無關或與鐘差無關的觀測值以用于精密鐘差估計和軌道确定。
III幾何觀測模型
姿态描述衛星星固系在軌指向，對天線相位中心和相位纏繞等幾何誤差以及光壓力等非保守力模組化具有顯著影響。北鬥二号和三号GEO衛星采用零偏置姿态（偏航角為0°）；北鬥二号IGSO和MEO衛星則采用與其他導航衛星相似的動态偏置姿控模式（偏航姿态随衛星位置動态變化），而當太陽相對于衛星軌道面傾角（β角）的絕對值小于4°時則采用零偏姿态。對北鬥二号IGSO和MEO衛星姿态轉換條件，國内外許多學者開展了大量研究（Guo et al., 2014; Dai et al.,2015; Li et al., 2018）。由于北鬥二号IGSO和MEO衛星在零偏期間以及動零姿态模式轉換期間軌道精度顯著性降低，部分北鬥二号和北鬥三号IGSO和MEO衛星則采用了連續動偏模式。對于五院衛星，Dilssner (2017)和Wang et al. (2018)則先後建構了相應的姿态控制模型。對于小衛星MEO衛星，Yang et al. (2021)研究表明其偏航姿态基本遵循“北鬥/全球衛星導航系統（GNSS）衛星高精度應用參數定義及描述”中所給出模型，也即當β角在(0, 3°]時采用β=3°時偏航姿态，而β角在[-3°, 0]時采用β=3°時偏航姿态。但是，當太陽通過軌道面，也即β角符号變化時，姿态切換存在延遲進而導緻在正午或者午夜機動呈現反向調整。
其他幾何誤差研究主要集中在北鬥衛星端随高度角相關的系統性誤差、北鬥二号和三号衛星間的系統性偏差以及碼和相位觀測值偏差上。Wanninger and Beer (2015)最先報道北鬥二号IGSO和MEO衛星端存在于高度角相關的系統性誤差，并且建構了相應模型加以改正，而北鬥三号則顯著消除了相關誤差。近來較多研究揭示北鬥二号和三号重疊頻點信号間存在偏差（如Mi et al., 2021），其将影響模糊度固定等，是以在資料處理時應将北鬥二号和三号衛星視為獨立系統。
除上述L波段觀測值誤差外，北鬥星間鍊路觀測值中也存在顯著性系統誤差。通過将雙向星間鍊路觀測值歸化為單向與幾何無關的觀測值以用于鐘差估計，并通過将三顆以上衛星與幾何無關的觀測值求和獲得相應閉合差。圖4中給出了C20-C21-C41、C28-C30-C44、C21-C28-C29和C20-C25-C45等不同衛星間閉合差變化。從理論上講，上述幾何無關的觀測值閉合差在消除軌道誤差的基礎上，進一步消除了接收機鐘差和星間鍊路收發通道延遲，理應呈現白噪聲特性。但是圖中除C20-C21-C41以外，其他衛星組閉合差呈現偏差、周期性等系統性誤差特性，進而會影響星間鍊路資料處理。此外，研究發現星間鍊路觀測值殘差中存在和鍊路相關的常量偏差（如圖5）（Xieet al., 2019），其可以通過直接估計與連續相關的收發通道延遲加以消除。上述系統性誤差來源仍需進一步确認和研究。
圖 4 北鬥不同衛星組星間鍊路閉合差誤差特性。
圖 5 北鬥星間鍊路觀測值殘差。
IV軌道動力學模型
太陽光壓力是影響北鬥衛星定軌精度的核心因素。受衛星相對地面站靜止，幾何觀測條件變化較小制約，北鬥GEO衛星定軌精度在米級。通過建構先驗光壓模型以考慮GEO衛星通訊天線影響，Wang et al. (2019)将其徑向軌道精度提升至10 cm。對于北鬥二号IGSO和MEO衛星，由于缺乏适用于零偏的偏航姿态模型，其零偏期間定軌精度顯著性降低。國内外衆多研究通過建構适用于零偏模式的分析型模型或者經驗性模型，顯著提升了北鬥IGSO和MEO衛星零偏期間定軌精度（Wang et al., 2013; Guo et al., 2014; Montenbrucket al., 2017b）。對于北鬥三号MEO衛星，當直接使用ECOM1光壓模型進行精密定軌時，其徑向軌道誤差呈現與太陽輻角（太陽-地球-衛星間夾角）相關的系統誤差（如圖6）。由于長方體拉伸方向不同，五院和小衛星軌道誤差特性呈現相反變化。通過使用ECOM2或者先驗盒翼模型等方法，可以顯著減弱或者消除此類誤差（Wang et al., 2019; Yan et al., 2019a; Li etal., 2020; Duan et al., 2021）。
圖 6 基于星地L波段和ECOM1模型的北鬥SLR觀測值殘差。
除光壓力外，天線推力、地球反照輻射和熱輻射等對北鬥衛星軌道産生系統性影響。天線推力是由衛星對外發射信号所産生的反作用力，其大小與信号發射功率和品質有關。Steigenberger et. al. (2018)以及Steigenberger & Thoelert (2020)分别測定了北鬥二号和三号衛星信号功率。其使得北鬥二号IGSO和MEO以及北鬥三号五院和小衛星MEO徑向軌道産生約28、5、16和19 mm左右的偏差。相應地，地球反照輻射将引起北鬥二号IGSO和MEO以及北鬥三号五院和小衛星MEO徑向軌道産生約25、20、15和12 mm左右的偏差。
V基于L波段和星間鍊路的北鬥衛星精密定軌
北鬥衛星精密軌道确定可以采用L波段或者星間鍊路觀測值。目前，IGS MGEX和iGMAS及其各個分析中心提供基于L波段的北鬥高精度軌道和鐘差産品以及不同分析中心間産品的比較和綜合結果。随着地面觀測站數目增多，不同分析中心間産品一緻性和精度在逐漸提升。目前，不同分析中心北鬥GEO衛星軌道一緻性在米級，IGSO約為15 cm，MEO則為7 cm左右（Steigenberger and Montenbruck, 2020）。雷射測距檢核表明北鬥二号GEO、IGSO和MEO衛星軌道誤差為20、5-7和3.5 cm左右（Sośnica et al., 2020）。北鬥三号衛星軌道精度從2019年3-4 cm提甚至2 cm左右（Guo et al., 2021）。
圖 7 基于星間鍊路和ECOM1模型的北鬥SLR觀測值殘差。
對于北鬥三号MEO衛星，基于星間鍊路觀測值可以獲得與全球L波段觀測值相類似的定軌精度，但是其軌道誤差呈現與L波段不一緻的特性。圖7中給出了基于星間鍊路觀測值和ECOM1模型的北鬥C20和C30衛星SLR觀測值殘差。與圖6不同，其徑向軌道誤差并未顯著性呈現與太陽輻角相關的線性變化，其主要原因在于星間鍊路觀測值對光壓參數，特别是D0參數具有較高的可估性。
VI北鬥對大地測量參數估計的影響
目前，北鬥衛星精密定軌研究主要集中于幾何和動力學模型精化方面，而缺乏對大地測量參數估計的研究。從理論上來說，上述參數估計理應獨立于GNSS系統，然而有研究表明大地測量參數估計序列中所表現出的交點年誤差與衛星軌道動力學模型（如光壓模型）殘餘誤差以及GNSS衛星星座構成相關（Zajdel et al., 2020, 2021; Scaramuzza et al., 2018）。此外，由于測站坐标、鐘差、模糊度等參數間相關性影響，北鬥/GNSS難以精确測定地心運動和架構尺度(Rebischung et al., 2014a)。雖然北鬥系統天線相位中心地面标定值已經公布，但是Qu et al. (2021)分析表明其與Galileo地面标定值在架構尺度上差異可達+1.854 ppb (part-per-billion)，是以基于北鬥或GNSS技術建構獨立尺度需要進一步研究。随着衆多攜帶星載北鬥/GNSS接收機的低軌衛星資料公開将為建構獨立尺度提供可能。此外，北鬥星間鍊路資料用于大地測量參數估計的能力和制約因素仍需進一步分析和研究。
VII後續研究方向
本文認為北鬥精密定軌研究可以進一步在如下方向展開。一是，在完善北鬥衛星中繼資料的基礎上，進一步聯合地面和低軌衛星星載北鬥跟蹤資料，估計和IGS架構一緻的所有衛星天線相位中心偏差和變化；二是，進一步優化光壓力和熱輻射力等非保守力模型，以提高蝕衛星以及零偏期間衛星定軌精度；三是，分析星間鍊路系統誤差來源以及消除方法，并研究鐘差模型或星間鍊路估計鐘差限制下的北鬥衛星精密定軌；四是，考察和分析北鬥對地心、尺度和地球自轉參數等大地測量參數估計的影響和貢獻。
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作者簡介
趙齊樂 教授
本文第一作者
武漢大學
▍作者簡介
趙齊樂，武漢大學教授，目前重點開展衛星精密定軌定位及天地一體化導航增強方面的理論、方法和軟體系統的研究。發表了SCI索引論文100餘篇，獲得國家發明專利7項，軟體著作權18項。相關成果獲得了國家科學技術進步一等獎、二等獎，及教育部科技進步一等獎等多項獎勵。
郭靖 副教授
本文通訊作者
郭靖，武漢大學衛星導航定位技術研究中心，副教授。主要從事北鬥/GNSS衛星精密定軌等方面的理論、算法和軟體系統研究。已發表論文40餘篇，獲國家和省部級獎多項。國際衛星導航服務組織（IGS）實時和參考架構工作組成員，負責武漢大學IGS MGEX（WUM産品）和iGMAS分析中心以及IGS第三次GNSS曆史資料重處理。
初審：段鵬麗
複審：宋啟凡
終審：金 君
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