The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler et al. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CMA.     

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.     

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.     

Improved antenna phase center models for GLONASS

Thanks to the increasing number of active GLONASS satellites and the increasing number of multi-GNSS tracking stations in the network of the International GNSS Service (IGS), the quality of the GLONASS orbits has become significantly better over the last few years. By the end of 2008, the orbit RMS error had reached a level of 3–4 cm. Nevertheless, the strategy to process GLONASS observations still has deficiencies: one simplification, as applied within the IGS today, is the use of phase center models for receiver antennas for the GLONASS observations, which were derived from GPS measurements only, by ignoring the different frequency range. Geo++ GmbH calibrates GNSS receiver antennas using a robot in the field. This procedure yields now separate corrections for the receiver antenna phase centers for each navigation satellite system, provided its constellation is sufficiently populated. With a limited set of GLONASS calibrations, it is possible to assess the impact of GNSS-specific receiver antenna corrections that are ignored within the IGS so far. The antenna phase center model for the GLONASS satellites was derived in early 2006, when the multi-GNSS tracking network of the IGS was much sparser than it is today. Furthermore, many satellites of the constellation at that time have in the meantime been replaced by the latest generation of GLONASS-M satellites. For that reason, this paper also provides an update and extension of the presently used correction tables for the GLONASS satellite antenna phase centers for the current constellation of GLONASS satellites. The updated GLONASS antenna phase center model helps to improve the orbit quality.     

高轨卫星天基定轨原理演示系统的设计与实现

以高轨卫星天基定轨原理作为理论基础,设计了一种在MATLAB仿真软件环境下运行的高轨卫星天基定轨原理演示系统。该系统实现了高轨及低轨用户星轨道仿真、全球导航卫星系统（GPS、GLONASS、Galileo和Compass）星座卫星仿真、高轨卫星及地面用户星对全球导航卫星系统的可见性仿真和高轨卫星天基定轨仿真。仿真结果表明：该系统具有效能高、清晰直观等优点,也具有较强的理论和现实意义。     

北斗混合星座分层约束下的精密定轨方法

针对北斗导航卫星系统首创的GEO+IGSO+MEO混合星座设计,本文研究了根据不同星座,采取不同约束条件和数据处理策略的北斗卫星精密定轨方法,提出了一种针对北斗系统混合星座的分层约束精密定轨方案.该方案首先将北斗卫星分为非GEO(IGSO/MEO)和GEO两部分进行解算,利用GPS解算的公共参数对北斗IGSO/MEO精...     

小型化LEO星座与BDS-3全星座联合定轨仿真

受限于区域监测站及地球静止轨道(geosynchronous earth orbit, GEO)卫星的静地特性,北斗卫星导航系统(BeiDou satellite navigation system,BDS)定轨精度较差,加入低轨卫星(low earth orbit,LEO)星载数据可显著提升定轨精度。使用一种由24颗LEO卫星组成的小型低轨卫星星座,在BDS-3全星座情况下,仿真分析了导航卫星与低轨卫星联合定轨对北斗卫星轨道的提升程度。分别进行仅地面测站定轨、地面测站与LEO联合定轨试验,包含全球均匀、亚太区域、亚海分布3类测站布局。结果表明:(1)仅地面测站定轨时,GEO卫星轨道三维精度在分米量级,加入LEO观测数据后,定轨精度在厘米量级,提升程度达80%以上;(2)区域地面测站时,导航卫星轨道三维精度在分米量级,加入LEO卫星后,所有类型导航卫星定轨精度均提升至数个厘米,提升效果显著;(3)全球均匀测站时,LEO的加入仍然可提升倾斜地球同步轨道/中高轨道卫星定轨精度,提升效果在毫米至厘米量级。     

Characterization of Compass M-1 signals

An analysis of observations from China’s first medium earth orbit satellite Compass M-1 is presented, with main focus on the first orbit and clock solution for this satellite. The orbit is computed from laser ranging measurements. Based on this orbit solution, the apparent clock offset is estimated using measurements from two GNSS receivers, which allow Compass tracking. The analysis of the clock solutions reveals unexpectedly high dynamics in the pseudorange and carrier-phase observations. Furthermore, carrier-to-noise density ratio, pseudorange noise, and multipath are analyzed and compared to GPS and GIOVE. The results of the clock analysis motivate further research on the signals of the geostationary satellites of the Compass constellation.     

持续性全球多重覆盖的圆轨道导航星座的设计

首先描述卫星覆盖的理论以及卫星星下点在地面上的轨迹规律,然后根据导航星座的特点,通过对星座基本参数特点的讨论,并在参考GPS和GLONASS星座的基础上,确定了导航星座的构成。最后,在理论上证明了最小覆盖性的条件,随着模拟实际数据进行了验证。     

GNSS卫星精密定轨综述:现状、挑战与机遇

GNSS卫星精密轨道是高精度GNSS应用的基础与前提,GNSS卫星精密定轨技术也一直都是卫星导航领域的研究重点与热点。本文首先介绍了GNSS星座与跟踪数据概况,梳理了精密定轨函数模型、动力学模型及随机模型构建过程中的关键问题,归纳了低轨星载观测和星间链路观测等多源数据增强GNSS精密定轨的研究进展;然后,从应用的角度总结了当前GNSS精密轨道产品的基本状态,并进行了精度评估;最后,讨论了GNSS精密定轨在大网快速解算、多层次观测数据融合、太阳光压模型精化及高精度实时定轨等方面所面临的挑战,并展望了低轨星座、光钟、激光链路等新技术给GNSS精密定轨带来的机遇。     

顾及星座稳定性及综合成本的低轨导航星座优化设计方法

利用低轨道地球卫星(LEO)进行导航增强首先需要设计低轨星座,在进行星座构型设计时,星座的稳定性及综合成本是需要考虑的两个重要因素,本文提出了顾及星座稳定性及综合成本进行低轨导航星座优化设计的方法.首先,利用遗传算法对铱星星座进行了优化,优化后的铱星星座与未优化前星座相比较,全球可见卫星数均值由2.3颗增至2.9颗,可见卫星数标准差由2.3降至0.7,综合成本因子由5.3降至4.5,证明了本方法的有效性.然后以Walker星座作为基本构型,在保证低轨混合星座稳定性的基础上,顾及导航性能和综合成本,利用遗传算法进行了混合星座的优化.将优化后的低轨混合星座与北斗星座进行了组合,组合后的星座与北斗星座相比较,全球可见卫星数均值由6.9颗增至9.3颗,可见卫星数标准差由1.1降至0.4.     

Precise orbit determination of BeiDou constellation: method comparison

Chinese BeiDou navigation satellite system is in official service as a regional constellation with five geostationary earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium earth orbit (MEO) satellites. There are mainly two methods for precise orbit determination of the BeiDou constellation found in the current literatures. One is the independent single-system method, where only BeiDou observations are used without help from other GNSS systems. The other is the two-step GPS-assisted method where in the first step, GPS data are used to resolve some common parameters, such as station coordinates, receiver clocks and zenith tropospheric delay parameters, which are then introduced as known quantities in BeiDou processing in the second step. We conduct a thorough performance comparison between the two methods. Observations from the BeiDou experimental tracking stations and the IGS Multi-GNSS Experiment network from January 1 to March 31, 2013, are processed with the Positioning and Navigation Data Analyst (PANDA) software. The results show that for BeiDou IGSO and MEO satellites, the two-step GPS-assisted method outperforms the independent single-system method in both internal orbit overlap precision and external satellite laser ranging validation. For BeiDou GEO satellites, the two methods show close performances. Zenith tropospheric delays estimated from the first method are very close to those estimated from GPS precise point positioning in the second method, with differences of several millimeters. Satellite clock estimates from the two methods show similar performances when assessing the stability of the BeiDou on board clocks.     

星载加速度计增强北斗自主定轨性能

卫星自主定轨是提高全球卫星导航系统(GNSS)可靠性、稳健性、完整性和生存能力的重要保证。新一代的北斗卫星已可以进行星间链路测距,从而达到提高卫星全球跟踪能力以及实现整个卫星导航系统的自主定轨。然而由于卫星运行会受到多种摄动力的影响,如果不能对这些摄动力进行精密的改正,在没有地面或其他天体提供绝对约束的条件下,导航系统会随着自主定轨时间的延长出现星座整体旋转。卫星所受摄动力分为保守力和非保守力两部分:对于保守力,如地球非球形摄动、潮汐摄动、太阳月球和其他三体引力,现在已有的力学模型可以很精确地进行改正;而非保守力(如太阳光压摄动),则难以用精确的模型进行改正,因此成为影响卫星定轨精度的主要因素。星载加速度计可以高精度地测量非保守力,并已成功应用于重力卫星(CHAMP、GRACE、GOCE)的重力场反演与大气研究中。本文研究主要探讨采用星上加速度计提高北斗卫星自主定轨精度和延长自主定轨时长的可行性。利用模拟的卫星轨道和星间链路数据,以及现有的星载加速度计误差模型,对北斗卫星系统分别使用星间链路数据和星间链路与加速度计组合数据,进行自主定轨与精度评定。计算结果表明,使用星间链路与星载加速度计数据进行自主定轨,较单纯使用星间链路数据精度具有明显改进。在模拟的星间测距观测数据具有0.33m随机噪声以及分米级系统误差,自主定轨两个月的情况下,联合使用加速度计数据的自主定轨IGSO和MEO卫星精度为分米级,而仅使用星间链路数据的定轨精度约为3~6m,比使用加速度计精度低一个量级。     

GNSS技术在GEO、IGSO航天器中的导航精度与适用性分析

现阶段高轨道航天器导航主要依靠地基测控系统,为了研究全球卫星导航系统(GNSS)技术用于高轨道航天器导航的可行性,对GNSS技术在地球静止轨道(GEO)卫星、倾斜地球同步轨道(IGSO)卫星航天器中的导航精度及适用性展开了分析研究. 采用2021年11月9日的两行轨道数据(TLE)仿真GNSS星座,以不同星下点的GEO卫星和不同倾角的IGSO卫星作为目标星展开导航仿真试验. 实验结果表明:为了满足GNSS解算所需的卫星数量,须通过接收旁瓣信号来增加可见卫星数目. 对GEO目标星而言,当接收机灵敏度高于?169 dB时,导航精度可达30 m;利用GPS对7个不同的GEO或IGSO轨道目标星进行导航实验表明,GPS对目标星导航的位置误差约为35 m;北斗三号(BDS-3)、GPS、GLONASS、Galileo的导航位置误差均值分别为28.03 m、21.16 m、37.15 m、25.09 m,具有良好的内符合精度,其中GPS精度最高,GLONASS精度最低,但大部分时段也在45 m内.      

地球重力场模型对低轨卫星轨道积分的影响

介绍3种不同的地球重力场模型及其(约化)动力学定轨中所涉及的动力学模型,并基于Collocation轨道积分方法对CHAMP卫星进行数值积分,然后将轨道积分结果与JPL快速精密星历相比较。实验结果表明,由CHAMP卫星SST数据反演生成的EIGEN-2模型引力位系数具有较高的精度,能够满足低轨卫星精密定轨的需要。     

Swarm卫星星载GPS精密定轨方法及精度分析

Swarm星座是ESA的首个用于测量来自地球核心、地幔、地壳、海洋、电离层等区域磁场信息的对地观测卫星星座。而高精度的轨道信息正是其有效利用卫星载荷完成上述任务的前提条件。目前国内关于Swarm卫星精密定轨的研究较少,为此建立并推导了Swarm卫星精密定轨的动力学模型、观测模型以及它们之间的数学关系,详细给出了Swarm卫星精密定轨模型与实现过程。针对Swarm卫星精密定轨中姿态数据的处理问题提出了相应的解决方案。利用Swarm卫星星载GPS实测数据,采用约化动力学定轨方法进行Swarm卫星精密定轨实验。通过轨道衔接点位置差异、与外部精密轨道比较以及SLR验证等精度评定方法分析表明:基于星载GPS的Swarm卫星约化动力学定轨各方向的精度都优于3 cm。     

BDS/GPS联合定轨的贡献分析

北斗卫星导航系统（BeiDou satellite navigation system,BDS）目前暂未具有全球导航定位能力,卫星轨道的全程跟踪与测站的几何结构还不完善,影响了卫星轨道的测定精度。针对上述问题,根据动力学定轨的原理与方法,推导了多个全球导航卫星系统（global navigation satellite system,GNSS）联合定轨对参数求解精度的解析贡献量,并利用实测数据分析了BDS/GPS联合定轨对轨道和钟差求解精度的统计贡献量。结果表明,联合定轨对系统间公共参数求解精度的贡献显著,除地球静止轨道（geostationary orbit,GEO）卫星外,其余轨道和钟差求解精度均有显著提高。BDS/GPS联合定轨对BDS卫星轨道、卫星钟差均方根误差（root mean square,RMS）以及接收机钟差RMS的统计贡献量分别为36.21%、26.88%和20.88%,其中对可视卫星数较少的区域接收机钟差求解精度的贡献尤为显著,贡献量为45.95%。     

Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission using GPS

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.     

Swarm系列卫星非差运动学厘米级精密定轨

采用2015年5月24日—30日的Swarm星载GPS双频观测数据,基于Melbourne-Wübbena(MW)和消电离层线性组合,在精密单点定位技术的基础上,采用批处理最小二乘估计法对不同轨道高度的Swarm系列卫星进行非差运动学精密定轨。利用星载GPS相位观测值残差、与欧空局发布的简化动力学轨道对比,以及SLR检核3种方法对Swarm系列卫星非差运动学定轨结果进行精度评估。结果表明:①Swarm系列卫星星载GPS相位观测值残差RMS为6~7 mm;②与欧空局发布的简化动力学轨道进行求差,径向、切向及法向轨道差值RMS为2~4 cm;③与欧空局发布的运动学轨道进行求差,径向、切向及法向轨道差值RMS为1~2 cm;④SLR检核结果表明Swarm-A/B/C卫星轨道精度为3~4 cm。因此,采用非差运动学定轨方法与本文提供的定轨策略进行Swarm系列卫星精密定轨是切实可行的,定轨精度为厘米级。     

基于北斗星间链路的卫星自主导航可行性分析

北斗三号卫星导航系统(BeiDou-3 navigation satellite system, BDS-3)在BDS-2基础上,设计实现了高速宽带星间链路网络,以期实现导航和通信的一体化建设,并为卫星自主定轨(autonomous orbit determination,AOD)技术的实现积累宝贵的实测数据。首先,利用星间链路数据建立分布式AOD模型;然后,利用实测的BDS-3星间链路数据,分析了18颗中圆轨道(medium Earth orbit, MEO)卫星间的建链有效率、星座构型及星间测量噪声,并讨论了轨道初值、滤波处理间隔等因素对AOD精度的影响;最后,给出了基于北斗三号系统18颗MEO卫星星间测距数据的AOD结果,用事后精密轨道产品对其进行了评估分析。结果表明:(1)BDS-3星间链路运行稳定,每颗卫星基本可维持9条左右的星间双向测距链路,星间有效链路数和星座布局已能够支撑实现分布式导航星座的AOD;(2)轨道初始精度、滤波处理间隔等都会影响状态估计精度和收敛速度;(3)轨道初值位置精度为0.1 m、滤波处理间隔为60 s的条件下,AOD连续运行30天的用户测距误差(us...