基于机动力模型的GEO卫星恢复期间定轨

北斗卫星导航系统(BDS)中GEO卫星频繁的轨道机动对高精度、实时不间断的导 航服务需求提出了更高要求, 如何在短弧跟踪条件下提高GEO卫星轨道快速 恢复能力, 是提升导航系统服务精度的关键因素. 针对该问题, 本文提出了基 于机动力模型的动力学定轨方法, 尝试利用高精度的C波段转发式测距数据, 辅 以机动期间的遥测遥控信息建立机动力模型, 联合轨控前后的观测数据进行动 力学长弧定轨. 利用BDS中GEO卫星实测数据进行了定轨试验与分析, 结果表明, 恢复期间需要采用解算机动推力的定轨方法, 联合机动前、机动期间和机 动后4h数据定轨的轨道位置精度在20m量级, 径向精度优于2.5m. 该方 法克服了短弧跟踪条件下动力学法定轨和单点定位中的诸多问题, 提供了解决 GEO卫星机动后轨道快速恢复问题的技术方法.      

Overview of TDRSS

The National Aeronautics and Space Administration (NASA) has developed the Tracking and Data Relay Satellite (TDRS) System (TDRSS) for operational tracking and communications support of low Earth-orbiting satellites. TDRSS currently consists of five geosynchronous spacecraft and the White Sands Complex (WSC) at White Sands, New Mexico. The Bilateration Ranging Transponder (BRT) System (BRTS) supports range and Doppler measurements for each TDRS using standard user tracking services. These measurements are used to generate well-determined ephemerides for the TDRSs. TDRSS provides S-band and Ku-band services through the single access (SA) antennas and S-band services through the S-band multiple access (SMA) phased array. TDRSS is capable of supporting coherent range and two-way Doppler tracking as well as noncoherent one-way return-link and one-way forward-link Doppler tracking of user spacecraft. Accurate one-way return-link tracking, which can use SMA, the most available TDRSS resource, requires a stable oscillator onboard the user spacecraft as the source of frequency. Two-way and one-way return-link tracking measurements are used for ground orbit determination for navigation and precise positioning; one-way forward-link tracking is used for autonomous onboard navigation with achievable accuracies better than those of the Global Positioning System (GPS) Precise Positioning System (PPS). This overview will discuss the various tracking and navigation capabilities of TDRSS, as well as many of the operational and research applications that have been conducted for missions such as Landsat-4, Ocean Topography Experiment (TOPEX)/Poseidon (T/P), Cosmic Background Explorer (COBE), and Extreme Ultraviolet Explorer (EUVE).     

Autonomous navigation using the TDRSS Onboard Navigation System (TONS)

The National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing a Tracking and Data Relay Satellite (TDRS) System (TDRSS) Onboard Navigation System (TONS) to provide onboard knowledge of highly accurate navigation products autonomously to users of TDRSS. The TONS I operational system processes Doppler data derived from scheduled forward-link S-band services to provide onboard orbit and frequency determination and time maintenance. TONS I is implemented using a stable onboard frequency reference, a Doppler measurement capability in the user transponder, and onboard navigation/signal acquisition software. The success of the TONS experiment (1992/1993), which was implemented on the Explorer Platform/Extreme Ultraviolet Explorer (EP/EUVE) spacecraft, demonstrated the flight readiness of TONS I. TONS II-A provides the user with additional Doppler data derived from an S-band beacon signal, available approximately 80 percent of the time. This paper describes the TONS operational capabilities, configurations, and expected performance.     

北斗卫星导航系统实时定轨与钟差处理策略

目前鲜有对北斗卫星导航系统（BeiDouNavigationSatelliteSystem,BDS）实时精密定轨与钟差确定的研究,文章提出了BDS实时轨道与实时钟差处理策略,包括了观测与动力学模型、实时轨道与实时钟差处理流程与评估方法。尤其对于实时钟差,为了提高计算效率,联合使用两个独立并行的线程估计非差绝对钟差和历元间相对钟差。利用多模全球卫星导航系统试验(MGEX)与全球连续检测评估系统（iGMAS）实测数据进行了北斗实时轨道与钟差解算,BDS实时轨道径向平均精度对于GEO卫星优于20cm,对于IGSO与MEO一般优于10cm;钟差精度对于GEO卫星为0.5~4.5ns,对于IGSO／MEO为0.2~2.0ns。基于目前的轨道与钟差结果,实时精密单点定位（PrecisePointPositioning,PPP）结果可以达到分米量级。     

联合北斗导航与星间链路的大椭圆卫星定轨方法

传统的地面测控和GNSS均无法实现HEO卫星全弧段的跟踪观测.在分析北斗导航信号及其星间链路信号对典型HEO的观测几何及覆盖特性的基础上,利用北斗导航及其星间链路对HEO测控支持形成互补的特点,提出了一种卫星导航与星间链路相结合的自主导航方法.对HEO定轨进行分段划分并基于EKF设计了卫星导航与星间链路数据融合定轨的自主导航算法.分析结果表明,本文提出的方法能够从全弧段上改善HEO的观测几何,定轨精度比仅使用卫星导航提高了2个数量级,并且仅需较少的星间链路资源.      

基于ORBCOMM卫星机会信号的定位技术

为摆脱对全球导航卫星系统（GNSS）的依赖，克服其有意或无意干扰情况下无法工作等问题，可采用机会信号（SOP）实现定位，低轨卫星机会信号具备信号功率高、覆盖性广及无需增建基础设施等优点。提出了利用轨道通信卫星（ORBCOMM）系统实现天基机会信号定位。通过对ORBCOMM卫星机会信号的通信体制进行深入研究，实现了利用ORBCOMM卫星机会信号获取多普勒测量信息，建立了瞬时多普勒定位及其几何精度因子的数学模型，并采用卫星TLE数据结合轨道预测模型获得的卫星轨道信息实现ORBCOMM卫星机会信号定位。实测结果表明:利用ORBCOMM卫星机会信号可实现精度优于140 m的定位。研究成果对基于天基机会信号定位技术的理论研究及应用具有重要意义。      

Accuracy assessment of TDRSS-based TOPEX/Poseidon orbit determination

Orbit determination results are obtained for the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using a batch-least-squares estimator available in the Goddard Trajector Determination System (GTDS) to process Tracking and Data Relay Satellite (TDRS) System (TDRSS) measurements. The GTDS orbit solutions are compared with the definitive Precision Orbit Determination (POD) orbit solutions. The root-mean-square (RMS) solution difference in the radial component is 28 centimeters.     

Precision orbit determination performance for CryoSat-2

In this paper we discuss our efforts to perform precision orbit determination (POD) of CryoSat-2 which depends on Doppler and satellite laser ranging tracking data. A dynamic orbit model is set-up and the residuals between the model and the tracking data is evaluated. The average r.m.s. of the 10?s averaged Doppler tracking pass residuals is approximately 0.39?mm/s; and the average of the laser tracking pass residuals becomes 1.42?cm. There are a number of other tests to verify the quality of the orbit solution, we compare our computed orbits against three independent external trajectories provided by the CNES. The CNES products are part of the CryoSat-2 products distributed by ESA. The radial differences of our solution relative to the CNES precision orbits shows an average r.m.s. of 1.25?cm between Jun-2010 and Apr-2017. The SIRAL altimeter crossover difference statistics demonstrate that the quality of our orbit solution is comparable to that of the POE solution computed by the CNES. In this paper we will discuss three important changes in our POD activities that have brought the orbit performance to this level. The improvements concern the way we implement temporal gravity accelerations observed by GRACE; the implementation of ITRF2014 coordinates and velocities for the DORIS beacons and the SLR tracking sites. We also discuss an adjustment of the SLR retroreflector position within the satellite reference frame. An unexpected result is that we find a systematic difference between the median of the 10 s Doppler tracking residuals which displays a statistically significant pattern in the South Atlantic Anomaly (SSA) area where the median of the velocity residuals varies in the range of ?0.15 to +0.15?mm/s.     

天地基联合多星定轨及精度分析

数据中继卫星和双星定位系统通常由2或3颗地球同步卫星和数颗近地卫星组成,这些系统所提供的“星-星”测量数据提出了多星同时定轨的需求。文章介绍了已知天基星星历定轨和未知天基星星历定轨的主要差别,建立了距离和观测量的测量模型,描述了多星同时定轨的技术难点,分析了整个系统的定轨精度。     

静止卫星轨道的高精度确定

基于单站或三站跟踪测轨数据,对静止卫星轨道进行精确确定,提出一种新的有效的轨道确定的算法,星下点位置精度优于30m。     

Landsat-4 orbit determination using TDRSS

This paper presents the results of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite (TDRS) System (TDRSS)-user spacecraft, Landsat-4, obtained using a Prototype Filter Smoother (PFS), with the accuracy of an established batch-least-squares system, the Goddard Trajectory Determination System (GTDS). The results of Landsat-4 orbit determination provide useful experience for the Earth Observing System (EOS) series of satellites. The filtered and smoothed PFS orbit solutions were compared with the definitive GTDS orbit solutions for Landsat-4; the root-mean-square (RMS) solution difference was 6.6 meters.     

基于GNSS测量的天宫二号质心确定

由于轨道机动燃料消耗，科学载荷加载、分离，以及伴飞小卫星在轨释放等原因引起天宫二号空间站质心(COM)发生位移，从而影响天宫二号的动力学质心定轨精度。针对这一问题，提出了基于全球导航卫星系统(GNSS)测量数据的简化动力学质心估计方法。燃料消耗是引起天宫二号质心发生位移的主要原因，质心在本体坐标系X轴方向位移最为显著。利用GNSS测量数据对天宫二号进行质心估计和精密定轨，在三轴对地稳定姿态下，本体坐标系X轴方向与轨道切向重合，定轨结果对本体坐标系X轴方向的质心位移并不敏感。但在连续偏航模式下，本体坐标系X轴在轨道法向上有较大分量，X轴方向的质心位移对基于GNSS测量计算的精密定轨结果有较大影响。定性和定量分析结果表明:偏航姿态模式下天宫二号本体坐标系X轴方向质心位移估计具有可行性。天宫二号实测数据计算结果表明:与未做质心估计的定轨结果进行对比，质心估计后表征轨道动力学建模误差的经验加速度补偿水平在轨道径向、切向和法向上分别降低62%、50%和65%；载波相位后验残差标准差降低0.04 cm；精密轨道与全球激光测距数据比较精度提高0.86 cm。所提方法可以应用于大型低轨航天器在轨质心估计。      

基于伪距和观测量的地球同步卫星动力学定轨研究

利用伪距和观测量对同步卫星进行了动力学定轨的研究，给出了伪距和观测量的测量方程和修正方法，采用国内4个监测站的模拟数据进行了仿真计算．结果表明，采用7天弧长伪距和数据进行轨道改进及轨道外推的精度，与5天弧长数据的计算结果相当，但远优于3天数据的计算结果．在观测随机误差为3m时，7天弧长数据定轨精度约为5m，预报7天径向精度优于20m．     

Geostationary orbit determination using SATRE

A new strategy of precise orbit determination (POD) for GEO (Geostationary Earth Orbit) satellite using SATRE (SAtellite Time and Ranging Equipment) is presented. Two observation modes are proposed and different channels of the same instruments are used to construct different observation modes, one mode receiving time signals from their own station and the other mode receiving time signals from each other for two stations called pairs of combined observations. Using data from such a tracking network in China, the results for both modes are compared. The precise orbit determination for the Sino-1 satellite using the data from 6 June 2005 to 13 June 2005 has been carried out in this work. The RMS (Root-Mean-Square) of observing residuals for 3-day solutions with the former mode is better than 9.1 cm. The RMS of observing residuals for 3-day solutions with the latter mode is better than 4.8 cm, much better than the former mode. Orbital overlapping (3-day orbit solution with 1-day orbit overlap) tests show that the RMS of the orbit difference for the former mode is 0.16 m in the radial direction, 0.53 m in the along-track direction, 0.97 m in the cross-track direction and 1.12 m in the 3-dimension position and the RMS of the orbit difference for the latter mode is 0.36 m in the radial direction, 0.89 m in the along-track direction, 1.18 m in the cross-track direction and 1.52 m in the 3-dimension position, almost the same as the former mode. All the experiments indicate that a meter-level accuracy of orbit determination for geostationary satellite is achievable.     

SPOT-2 and TOPEX/Poseidon precise orbit determination from DORIS doppler tracking

The French earth observation satellite SPOT-2 has served as a testbed for precise orbit determination from DORIS doppler tracking in anticipation of the TOPEX/Poseidon mission. Using the most up-to-data gravity field model, JGM-2, a radial orbit accuracy of about 2–9 cm was achieved, with an rms of fit of the tracking data of about 0.64 mm/s. Furthermore, it was found that the coordinates of the ground stations can be determined with an accuracy of the order of 2–5 cm after removal of common rotations, and translations.

Using a slightly different model for atmospheric drag, but the same gravity model, precise orbits of TOPEX/Poseidon from DORIS tracking data were determined with a radial orbit accuracy of the order of 4–5 cm, which is far within the 13 cm mission requirement. This conclusion is based on the analysis of 1-day overlap of successive 11-day orbits, and the comparisons with orbits computed from satellite laser tracking (SLR) and from the combination of SLR and DORIS tracking. Results indicate a consistency between the different orbits of 1–4 cm, 4–20 cm, and 6–13 cm in the radial, cross-track, and along-track directions, respectively. The residual rms is about 4–5 cm for SLR data and 0.56 mm/s for DORIS tracking. These numbers are roughly twice as large as the system noise levels, reflecting the fact that there are still some modeling errors left.     

Orbit determination of BDS-3 satellite based on regional ground tracking station and inter-satellite link observations

The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China’s regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China’s regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations.     

Satellite availability and positioning performance of uncombined precise point positioning using BeiDou-2 and BeiDou-3 multi-frequency signals

To realize the smooth transition from regional BeiDou Navigation Satellite System (BDS-2) to the global one (BDS-3), the integration of BDS-2 and BDS-3 is important for providing continuous, stable and reliable positioning, navigation and timing (PNT) services for global users. This work used 154 globally distributed multi-GNSS (Global Navigation Satellite System) experiment stations spanning 30 days to analyze the satellite availability and positioning performance of uncombined precise point positioning (UC-PPP) under current BDS-2 and BDS-3 constellations. We focused on three issues: the influence of BDS-3 receiver tracking abilities, the positioning performance among different areas, and the benefit of multi-frequency observations. The results show that the elliptical zone caused by poor BDS-2 satellite visibility is disappeared when the evenly distributed BDS-3 medium earth orbit satellites are introduced. When BDS-3 are integrated with BDS-2, the area with the Position Dilution of Precision (PDOP) less than 2 can be expanded to 75° S-75° N and 30° E-150° W. The positioning performance of BDS-3 and BDS-2/BDS-3 UC-PPP are seriously affected by the receiver tracking abilities of BDS-3 signals. When the maximum pseudo-random noise sequences (PRNs) of BDS-3 satellites tracked by stations are within 30 or 37, the positioning accuracy of static UC-PPP can be improved by 22.94% or 8.27% due to the integration of BDS-2 and BDS-3. Besides, the most improvement of BDS-2 and BDS-3 integration is achieved in Asia-Pacific regions, especially for the kinematic UC-PPP or the poor receiver tracking abilities of BDS-3. Similar to the multi-frequency BDS-2 UC-PPP, the benefit of multi-frequency signals for BDS-3 or BDS-2/BDS-3 UC-PPP is also non-vital. The three-dimensional positioning accuracy of BDS-2/BDS-3 multi-frequency UC-PPP in static mode and kinematic mode are 2.24 cm and 5.39 cm, while the corresponding convergence time are 49.62 min and 73.80 min, respectively. Compared with BDS-2, both the positioning accuracy and the convergence time of BDS-2/BDS-3 joint UC-PPP are improved by approximately over 50%, which indicates that BDS-3 has a great potential to provide high-quality PNT services as other global navigation satellite systems.     

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.     

基于GNSS的高轨卫星定位技术研究

利用全球卫星导航系统(GNSS)进行导航定位具有全球、全天候、实时和高精度的优点,应用于高地球轨道(HEO)卫星的定位,能够提供精确的轨道和姿态确定,并且可以克服目前主要利用地面测控系统对HEO卫星进行定位的设备复杂、投资高等缺点,使得自主导航成为可能.本文对利用GNSS的高轨卫星定位相关技术进行了研究,分析了单一GNSS系统和多个GNSS组合系统的卫星可见性、动态性和几何精度因子(GDOP).通过仿真分析表明,利用组合GNSS系统并通过提高GNSS接收机灵敏度的方法,可以解决GNSS进行HEO卫星定位的相关问题,并能保证HEO卫星定位精度的要求.      

Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations

The Global Navigation Satellite System (GNSS) receivers equipped on the Haiyang-2D (HY-2D) satellite is capable of tracking the signals of both the third generation of BeiDou satellite navigation System (BDS-3) and the Global Positioning System (GPS), which make it feasible to assess the performance of real-time orbit determination (RTOD) for the HY-2D using onboard GNSS observations. In this study, the achievable accuracy and convergence time of RTOD for the HY-2D using onboard BDS-3 and GPS observations are analyzed. Benefiting from the binary-offset-carrier (BOC) modulation, the BDS-3 C1X signal includes less noise than the GPS C1C signal, which has the same signal frequency and chipping rate. The root mean squares (RMS) of the noises of C1X and C1C code measurements are 0.579 m and 1.636 m, respectively. Thanks to a ten-times higher chipping rate, the code measurements of BDS-3 C5P, GPS C1W and C2W are less noisy. The RMS of code noises of BDS-3 C5P, GPS C1W, and C2W are 0.044 m, 0.386 m, and 0.272 m, respectively. For the HY-2D orbit, the three-dimensional (3D) and radial accuracies can reach 31.8 cm and 7.5 cm with only BDS-3 observations, around 50 % better than the corresponding accuracies with GPS. Better performance of the BDS-3 in RTOD for the HY-2D is attributed to the high quality of its broadcast ephemeris. When random parameters are used to absorb ephemeris errors, substantial improvement is seen in the accuracy of HY-2D orbit with either BDS-3 or GPS. The 3D RMS of HY-2D orbit errors with BDS-3 and GPS are enhanced to 23.1 cm and 33.6 cm, and the RMS of the radial components are improved to 6.1 cm and 13.3 cm, respectively. The convergence time is 41.6 and 75.5 min for the RTOD with BDS-3 and GPS, while it is reduced to 39.2 and 27.4 min after the broadcast ephemeris errors are absorbed by random parameters. Overall, the achievable accuracy of RTOD with BDS-3 reaches decimeter level, which is even better than that with GPS, making real-time navigation using onboard BDS-3 observations a feasible choice for future remote sensing missions.