The impact of orbital errors on the estimation of satellite clock errors and PPP

Precise satellite orbit and clocks are essential for providing high accuracy real-time PPP (Precise Point Positioning) service. However, by treating the predicted orbits as fixed, the orbital errors may be partially assimilated by the estimated satellite clock and hence impact the positioning solutions. This paper presents the impact analysis of errors in radial and tangential orbital components on the estimation of satellite clocks and PPP through theoretical study and experimental evaluation. The relationship between the compensation of the orbital errors by the satellite clocks and the satellite-station geometry is discussed in details. Based on the satellite clocks estimated with regional station networks of different sizes (∼100, ∼300, ∼500 and ∼700 km in radius), results indicated that the orbital errors compensated by the satellite clock estimates reduce as the size of the network increases. An interesting regional PPP mode based on the broadcast ephemeris and the corresponding estimated satellite clocks is proposed and evaluated through the numerical study. The impact of orbital errors in the broadcast ephemeris has shown to be negligible for PPP users in a regional network of a radius of ∼300 km, with positioning RMS of about 1.4, 1.4 and 3.7 cm for east, north and up component in the post-mission kinematic mode, comparable with 1.3, 1.3 and 3.6 cm using the precise orbits and the corresponding estimated clocks. Compared with the DGPS and RTK positioning, only the estimated satellite clocks are needed to be disseminated to PPP users for this approach. It can significantly alleviate the communication burdens and therefore can be beneficial to the real time applications.     

Achievable debris orbit prediction accuracy using laser ranging data from a single station

Earlier studies have shown that an orbit prediction accuracy of 20 arc sec ground station pointing error for 1–2 day predictions was achievable for low Earth orbit (LEO) debris using two passes of debris laser ranging (DLR) data from a single station, separated by about 24 h. The accuracy was determined by comparing the predicted orbits with subsequent tracking data from the same station. This accuracy statement might be over-optimistic for other parts of orbit far away from the station. This paper presents the achievable orbit prediction accuracy using satellite laser ranging (SLR) data of Starlette and Larets under a similar data scenario as that of DLR. The SLR data is corrupted with random errors of 1 m standard deviation so that its accuracy is similar to that of DLR data. The accurate ILRS Consolidated Prediction Format orbits are used as reference to compute the orbit prediction errors. The study demonstrates that accuracy of 20 arc sec for 1–2 day predictions is achievable.     

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.     

High accuracy satellite drag model (HASDM)

The dominant error source in force models used to predict low-perigee satellite trajectories is atmospheric drag. Errors in operational thermospheric density models cause significant errors in predicted satellite positions, since these models do not account for dynamic changes in atmospheric drag for orbit predictions. The Air Force Space Battlelab’s High Accuracy Satellite Drag Model (HASDM) estimates and predicts (out three days) a dynamically varying global density field. HASDM includes the Dynamic Calibration Atmosphere (DCA) algorithm that solves for the phases and amplitudes of the diurnal and semidiurnal variations of thermospheric density near real-time from the observed drag effects on a set of Low Earth Orbit (LEO) calibration satellites. The density correction is expressed as a function of latitude, local solar time and altitude. In HASDM, a time series prediction filter relates the extreme ultraviolet (EUV) energy index E_10.7 and the geomagnetic storm index a_p, to the DCA density correction parameters. The E_10.7 index is generated by the SOLAR2000 model, the first full spectrum model of solar irradiance. The estimated and predicted density fields will be used operationally to significantly improve the accuracy of predicted trajectories for all low-perigee satellites.     

星地激光时间比对在卫星导航系统中的应用

星地精密激光时间比对具有精度高、系统误差少等优点,因此利用星地精密激光时间比对,不但可以对无线电时间比对进行外部精度检验,而且可以检验并分离无线电伪距测量的系统误差,分析检测设备时延的不稳定性和卫星钟的中短期性能指标,提高卫星钟差的预报精度。     

差分技术在双星快速定位通信系统中的应用

卫星定位通信系统是具有10米以内高精度的第二代卫星导航定位系统。达到高精度的关键是应用了伪随机码扩谱及差分定位技术。诸如星历误差、电离层时延变化和地球模型不准等误差,通过应用差分技术可以大部分消除。本文阐述了差分技术的应用和系统精度分析。     

基于星敏感器的卫星角速度估计精度分析

重点研究星敏感器自身特性对角速度估计精度的影响,分析了星敏感器动态情况下恒星矢量测量精度,推导出恒星矢量测量误差与星像目标中心提取误差之间的关系;进而研究了最小二乘角速度估计算法的精度,得出其精度影响因素:星像目标中心提取误差、曝光时间、恒星矢量数目及相互夹角;最后以给定的星敏感器参数和实际恒星分布进行数学仿真,验证了采用星敏感器估计角速度的可行性.     

脉冲星方位误差估计的两步卡尔曼滤波算法

为了克服钟差和卫星位置误差对脉冲星方位误差估计的影响,设计了两步卡尔曼滤波（TSKF）算法。首先,介绍了脉冲星方位误差估计的传统模型,并通过分析和仿真验证了钟差、卫星位置误差以及2种误差同时存在时会使脉冲星方位误差估计结果产生较大偏差。其次,在传统的估计模型中加入了钟差和卫星位置误差,并将钟差和钟差变化率增广为新的状态量,从而推导出包含2种误差的新模型,并证明了该模型的完全可观测性;根据该模型并按照两步卡尔曼滤波原理,得到了TSKF算法的步骤。最后,通过仿真表明:在钟差和卫星位置误差同时影响下,传统脉冲星方位误差估计算法偏差较大且发散;TSKF算法则能够有效隔离2种误差的影响,使赤经和赤纬误差估计达到0.2 mas之内的精度。      

GPS多径信号建模及接收机测试评估

多径信号误差是GPS(Global Positioning System)及其它卫星导航系统的重要误差源之一,有关多径建模与多径消除技术一直是卫星导航领域的研究热点.根据多径信号特性,推导了对GPS定位精度影响最大的镜面反射多径信号模型.基于这一多径模型,利用GPS软件接收机测试了多径对接收机伪距测量精度的影响.测试结果验证了所建立的多径模型的有效性,所获得的多径误差曲线为窄相关多径抑制技术提供了实验支持.     

卫星与测站钟差支持条件下的GEO卫星精密定轨

在基于伪距的GEO卫星精密定轨中, GEO卫星的静地特性导致定轨解算无法对星地组合钟差进行有效估计, 需要独立的时间同步支持. 本文讨论了卫星和测站钟差支持条件下的GEO卫星定轨原理, 利用仿真数据系统地分析了中国区域网跟踪条件下GEO卫星的定轨精度, 从定性和定量角度分析了钟差二次项、星地时间同步精度、站间时间同步精度及系统差等因素对定轨精度的影响.      

一种用于同步静止卫星监测的微型VLBI网

针对地球静止轨道（GEO）卫星全天时全天候高精度的监测需求，考虑传统甚长基线干涉（VLBI）测站高成本、高投入和GEO卫星专用观测时段有限等制约条件，研发了简易型VLBI观测系统，并组建了包括上海、都匀和乌鲁木齐三站的微型VLBI网（micro VLBI network，MVN），开展了并置站测试以及对GEO卫星亚太6C的连续监测，并评估了当前MVN的观测能力。结果表明MVN扣除系统差后的单站接收精度为2ns，各基线观测时延拟后残差约几纳秒，GEO目标实测位置精度为百米级（内外符精度分别约100m和400m）。不同于传统VLBI和其他GEO监测手段，MVN还具备全天时、全天候、低造价、易布设及易推广等特点，充分表明了其在GEO卫星监测领域的应用价值。     

Evaluation of geomagnetic field models using magnetometer measurements for satellite attitude determination system at low earth orbits: Case studies

In this study, different geomagnetic field models are compared in order to study the errors resulting from the representation of magnetic fields that affect the satellite attitude system. For this purpose, we used magnetometer data from two Low Earth Orbit (LEO) spacecraft and the geomagnetic models IGRF-12 (Thébault et al., 2015) and T89 (Tsyganenko, 1989) models to study the differences between the magnetic field components, strength and the angle between the predicted and observed vector magnetic fields. The comparisons were made during geomagnetically active and quiet days to see the effects of the geomagnetic storms and sub-storms on the predicted and observed magnetic fields and angles. The angles, in turn, are used to estimate the spacecraft attitude and hence, the differences between model and observations as well as between two models become important to determine and reduce the errors associated with the models under different space environment conditions. We show that the models differ from the observations even during the geomagnetically quiet times but the associated errors during the geomagnetically active times increase. We find that the T89 model gives closer predictions to the observations, especially during active times and the errors are smaller compared to the IGRF-12 model. The magnitude of the error in the angle under both environmental conditions was found to be less than 1°. For the first time, the geomagnetic models were used to address the effects of the near Earth space environment on the satellite attitude.     

基于会切场推力器无拖曳系统建模及参数优化

随着卫星重力测量技术的突破性进展,对航天器试验环境要求也在不断提高,航天器受到的残余扰动必须尽可能减小。作为中国将来重力场测量卫星备选主推力器的会切场推力器,其推力器的控制精度直接决定了测量的准确性。文章首先通过PID方法设计了位移模式下的无拖曳控制器,该控制器在预估阻力系数、参考质量与卫星本体的位移差、速度差等性能方面有良好的表现,在应对卫星运行时的突发情况时表现出很强的稳定性。但PID参数没有达到最优解,在此基础上对于该模型的控制精度进行优化,用遗传算法对PID控制的参数进行筛选。结果分析表明,会切场推力器的控制精度有所改善,NTW方向上的速度和位移误差均减小;推力阻力和显著减少;控制精度提高,更好地满足使用需求。     

混合星座导航系统的加权几何精度因子分析

不同类型卫星构成的混合星座导航系统或兼容系统中,考虑到广播星历精度不等导致的测距误差不等,用加权几何精度因子(WGDOP)代替几何精度因子(GDOP)作为最佳星座选择、定位精度评估和完好性监测的依据。对静止轨道卫星(GEO)/中高轨道卫星(MEO)构成的混合星座中不同卫星组合的WGDOP和GDOP进行了比较,实验结果表明WGDOP能更准确地反映星座性能和评估定位精度。在对定位精度或完好性监测的可靠性要求较高等场景,要用加权几何精度因子进行分析。     

一种基于连续星图观测的自旋姿态估计方法

传统的利用地球敏感器和太阳敏感器作为测量仪器的自旋卫星姿态确定方法存在系统误差和安装误差等,从而导致自旋姿态确定误差较大的问题,文章提出了一种利用星敏感器获取的连续星图估计卫星自旋姿态参数的新方法。该方法以卫星的自旋轴和旋转角速度作为状态变量,通过星敏感器连续跟踪拍摄的恒星的成像位置作为观测量,利用无迹卡尔曼滤波估计出卫星的自旋姿态参数。仿真结果表明,在星敏感器的精度为3″时,该方法的自旋轴估计精度为0.3448″,自旋角速度估计精度为10^-4(°)/s数量级。     

Utilization of modified spherical coordinates for satellite to satellite bearings-only tracking

A new satellite to satellite passive tracking method using Bearings-Only measurements in Modified Spherical Coordinates (MSC) is proposed. The system dynamics and measurement process are presented in three-dimensional MSC, and then the tracking method is deduced in details based on the Cartesian method. Performance of the new method is validated through computer simulations, which proved that the proposed method is effective in terms of the estimation accuracy and convergence time compared with the Cartesian method no matter the Initial State Errors (ISE) and measurement errors are large or small.      

粗差拟准检定法在星载GPS低轨卫星定轨中的应用

利用自适应卡尔曼滤波进行星载GPS低轨卫星定轨时,必须解决量测方程中经常存在的粗差问题．在分析以往方法的优缺点后,用拟准检定法来探测和修正量测方程中存在的粗差．该法的优点是辨识粗差准确率高,能同时定位多个粗差．另外,为了克服星载GPS低轨卫星定轨的滤波器可能出现的数值不稳定性及发散现象,还采用了UD分解算法及Sage自适应滤波器．最后用一个CHAMP卫星的模拟算例验证本方法的可行性和有效性．     

Orbit determination and prediction of GEO satellite of BeiDou during repositioning maneuver

In order to establish a continuous GEO satellite orbit during repositioning maneuvers, a suitable maneuver force model has been established associated with an optimal orbit determination method and strategy. A continuous increasing acceleration is established by constructing a constant force that is equivalent to the pulse force, with the mass of the satellite decreasing throughout maneuver. This acceleration can be added to other accelerations, such as solar radiation, to obtain the continuous acceleration of the satellite. The orbit determination method and strategy are illuminated, with subsequent assessment of the orbit being determined and predicted accordingly. The orbit of the GEO satellite during repositioning maneuver can be determined and predicted by using C-Band pseudo-range observations of the BeiDou GEO satellite with COSPAR ID 2010-001A in 2011 and 2012. The results indicate that observations before maneuver do affect orbit determination and prediction, and should therefore be selected appropriately. A more precise orbit and prediction can be obtained compared to common short arc methods when observations starting 1 day prior the maneuver and 2 h after the maneuver are adopted in POD (Precise Orbit Determination). The achieved URE (User Range Error) under non-consideration of satellite clock errors is better than 2 m within the first 2 h after maneuver, and less than 3 m for further 2 h of orbit prediction.     

混合星座导航卫星广播星历相关问题研究

GPS卫星广播星历参数具有参数少、物理意义明确以及精度高等特点,可以考虑将它应用于包含MEO、IGSO和GEO卫星的混合星座卫星导航系统。分析了采用GPs卫星广播星历参数时MEO、IGSO和GEO卫星的广播星历拟合精度,并且比较分析了在一个卫星的轨道周期内,广播星历参数拟合结果的变化规律。仿真结果表明,MEO、IGSO和GEO卫星的广播星历拟合误差最大在分米量级;MEO和IGSO卫星在一个轨道周期内星历参数拟合结果的变化规律相近,但是与GEO卫星的差异较大。     

Central difference predictive filter for attitude determination with low precision sensors and model errors

Attitude determination is one of the key technologies for Attitude Determination and Control System (ADCS) of a satellite. However, serious model errors may exist which will affect the estimation accuracy of ACDS, especially for a small satellite with low precision sensors. In this paper, a central difference predictive filter (CDPF) is proposed for attitude determination of small satellites with model errors and low precision sensors. The new filter is proposed by introducing the Stirling’s polynomial interpolation formula to extend the traditional predictive filter (PF). It is shown that the proposed filter has higher accuracy for the estimation of system states than the traditional PF. It is known that the unscented Kalman filter (UKF) has also been used in the ADCS of small satellites with low precision sensors. In order to evaluate the performance of the proposed filter, the UKF is also employed to compare it with the CDPF. Numerical simulations show that the proposed CDPF is more effective and robust in dealing with model errors and low precision sensors compared with the UKF or traditional PF.