星载GPS卡尔曼滤波定轨算法

利用卡尔曼滤波定轨算法，处理神舟4号星载GPS伪距实测资料，重点在于研究卡尔曼滤波中模型误差方差矩阵的选取准则，GPS信号中断或连续野值对递推滤波的影响，如何自主监控滤波的运行状态，即是正常还是趋于发散，目的在于评价该算法用于星上自主定轨长期平稳运行的可靠性．     

基于双频星载GPS数据的LEO卫星运动学定轨研究

运动学定轨是星载GPS特有的定轨方法,该方法不依赖于任何力学模型(地球重力场、大气阻力及太阳辐射压等),尤其适用于受大气阻力影响严重的低轨卫星定轨.基于双频星载GPS数据,研究了运动学定轨原理,讨论了数据预处理方法,建立了一套非差运动学定轨算法.并以GRACE (Gravity Recovery And Climate Experiment)-A、B卫星2008年2月实测数据作为试算验证了本研究方法的有效性和可靠性.GRACE 卫星实测数据计算结果表明:运动学定轨能达到5 cm精度(相对于SLR (Satellite Laser Ranging)),与动力学和简化动力学定轨精度相当.     

星载GPS相位观测值非差运动学定轨探讨

在几何法、动力学法和减缩动力学法定轨基础上，探讨了星载GPS相位观测值非差运动学定轨方法及其实现程序。该方法无需复杂的力学模型和地面资料，只需LEO(Low Earth Orbit)卫星上的GPS数据和IGS的GPS精密星历产品，它计算简单、方便，能快速、高精度地确定轨道，同时，还能确定一些动力学参数，但没有轨道预报功能；针对法方程系数矩阵比较庞大，提出了矩阵分块、上三角化的参数解算方法，并用CHAMP卫星资料分析了上述方法的定轨精度。     

利用低轨卫星激光资料检验地球引力场模型的精度

地球引力场模型是人造卫星轨道计算中最重要的动力学模型之一.近年来国际上空间重力卫星计划取得了极大成功,相继推出了一系列新的引力场模型.从近地卫星轨道计算的角度检验了2种传统引力场模型(JGM3,EGM96)和4种新引力场模型(EIGENCHAMP05S,GGM03S,GOCE02S,EGM2008)的精度,利用4颗近地卫星的激光测距资料进行精密定轨预报,统计比较了不同模型的定轨残差和预报误差.结果表明:(1)4种新引力场模型精度基本在同一水平,对于近地卫星定轨精度普遍优于9 cm,最高达到5cm,相对于JGM3和EGM96模型有明显改善;(2)以JGM3模型为基准,EGM96模型的精度有所提高,2000年以后的4种新模型的精度则普遍提高了12%～47%(定轨)和63%(预报).70阶之前定轨精度随着模型阶次增大而提高,70阶以后定轨精度基本保持稳定,这表明对于近地卫星轨道计算而言,70阶的引力场已经能够满足厘米级的精度需求.     

利用VLBI数据确定"探测一号"卫星的轨道

双星计划的“探测一号”是中国首颗真正严格意义上的科学实验卫星,其运行轨道为中国迄今所发射的卫星中距地球最远,远地点地心距达7．8万公里．采用射电天文的VLBI技术可以对“探测一号”以及更远的深空目标,如探月飞行器实现跟踪．为了验证VLBI技术在我国探月计划中的作用,上海天文台组织了国内目前仅有的上海、乌鲁木齐和昆明3个台站对“探测一号”进行试跟踪,利用对“探测一号”约两天的VLBI观测数据,确定“探测一号”卫星的轨道,对VLBI的定轨能力做初步的探讨．按照测控部门提供的初轨 (其精度仅保证跟踪)推算的轨道与VLBI时延的拟合误差平均约2 km,时延率的拟合误差平均约15 cm／s．而利用VLBI数据定轨后的拟合程度相对于初轨有了很大的改善,结果表明,单独利用VLBI时延定轨,时延的拟合精度约5．5 m,作为外部检核的VLBI时延率的拟合精度在2 cm／s左右．单独利用VLBI时延率定轨,时延率的拟合精度约为1．3 cm／s,作为外部检核的VLBI时延的拟合精度约为29 m．而若将时延和时延率数据联合定轨,采用其内符精度加权,VLBI时延和时延率的残差分别为5．5 m和 2 cm／s．为了合理地评估VLBI定轨的真实精度,利用模拟数据进行误差协方差分析,结果表明VLBI定轨精度受动力学模型误差的影响较大,由于"探测一号”卫星的动力学模型难以精确确定,所以利用两天弧段的VLBI数据确定“探测一号”卫星轨道的位置误差为km量级,而速度误差可达cm／s量级．模拟计算还表明, VLBI和USB数据联合定轨可以大大提高定轨精度．     

SGP4/SDP4模型精度分析

本文基于最新发布的SGP4/SDP4(Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)模型设计了一套定轨方案,从空间目标库中挑选出不同类型和轨道参数的1120个目标进行计算,定量给出了SGP4/SDP4模型处理不同类型空间目标的定轨预报精度.结果表明:近地目标定轨精度为百米量级;半同步和同步轨道定轨精度平均为0.7和1.9km.椭圆轨道目标的定轨精度与偏心率有关,除少数e>0.8的椭圆轨道目标,绝大多数椭圆轨道目标定轨误差均小于10km.用SGP4/SDP4模型对近地目标预报3天,半同步轨道预报30天,同步轨道预报15天,椭圆轨道预报1天,预报误差一般不超过40km.     

初轨计算中的病态分析

本文对现有初轨计算方法进行病态性分析与误差分析；研究结果表明：病态对现有初轨算法的影响，主要来源于法方程系数中包含观测误差．系数行列式愈大，定轨精度的损失愈多，当■被随机误差项△μ淹盖时，现有初轨算法将失效．此外，仿真结果还显示：■与△μ的大小还极大地依赖观测弧段的空间位置，当观测弧段包含近站点作为中点时，■最大，而■小，此时定轨精度较高；当观测弧段位于近站点的某一侧时，■小，而■大，此时定轨精度较低，观测弧段愈偏离近站点，病态影响愈大；因而在观测时，应尽量使观测弧段与近站点对称（此时μ值较大），这是提高短弧定轨的一种有效途径．     

北斗系统测站钟差短期预报模型比较及其在单星定轨中的应用

北斗卫星导航系统(BDS)地面跟踪站都配置有高精度的氢原子钟,并基于精密定轨数据处理与主站的时间基准进行同步.在卫星轨道机动以及机动恢复期间,通常采用几何法定轨以及单星定轨确定卫星的轨道.而在这两种定轨模式中,需要提供精确的测站钟差作为输入.为提高定轨的实时性,需要对测站钟差进行预报处理.分析了2次多项式模型、附加周期项模型、灰色模型3种模型对北斗地面跟踪站钟差短期拟合和预报的性能,并将钟差预报结果应用于单星定轨,同时还分析了不同预报钟差用于定轨的精度.试验发现,以上3种模型对6个测站钟差的平均拟合精度分别为0.14 ns、0.05 ns、0.27 ns,预报1 h的平均精度分别为1.17 ns、0.88 ns、1.28 ns,预报2 h的平均精度分别为2.72 ns、2.09 ns、2.53 ns.采用3种模型对测站钟差进行预报并用于单星定轨,采用附加周期项的钟差预报模型轨道3维误差最小,不同模型轨道径向精度差异在3 cm以内.以上结果表明,附加周期项的站钟拟合及预报模型在北斗系统机动期间的轨道恢复数据处理具有最好的效果.     

计算多普勒频偏的新算法

利用多普勒资料进行轨道改进,将遇到卫星信标机和测站接收机的频偏带来的系统差,如何估计各站圈的频偏,是决定定轨精度的一个关键问题．文[1]中提出的Guier导航计算频偏的方法,实践表明是行之有效的．但是,Guier导航计算较复杂,在用数值积分计算星历表的软件中,使用这一算法比较困难．提出一种基于法方程系数矩阵分块求逆的新算法,只需求6×6或7×7矩阵的逆,计算频偏十分简单．仿真表明,新算法的定轨精度近似达到C．R．下界一理论最佳精度,比Guier导航算法的精度高15％左右．     

地球定向参数预报误差及其对北斗三号卫星定轨精度的影响

地球定向参数(Earth orientation parameters, EOP)是地球参考系到地心天球参考系之间转换的桥梁,是卫星精密定轨过程中不可缺少的重要参数。以国际地球自转服务(International Earth Rotation Service, IERS)和中国科学院上海天文台(Shanghai Astronomical Observatory,SHAO)提供的EOP参数为例,分析了北斗三号仅区域网观测模式和星地星间联合观测模式下的定轨精度与EOP预报误差间的关系。研究表明,对于IERS提供的产品,其预报误差对仅区域站定轨模式的定轨精度影响较小,但是其10 d内的预报误差对星地星间联合定轨模式定轨精度的影响可达到分米级。对于SHAO提供的产品,两种定轨模式的定轨精度均随着EOP预报天数的增大而逐渐衰减。除此之外,不同产品的星地星间联合定轨模式下定轨精度均小于仅区域网监测下的定轨模式下的定轨精度,表明星间链路的加入可以降低卫星定轨对EOP预报误差的依赖。该研究对区域观测条件下的卫星精密定轨工程实现具有重要意义。     

利用正交变换方法计算协方差分析的统计量

证明用Givens—Gentleman正交变换给出的加仅最小二乘解与统计定轨理论求得的解一致．采用正交变换方法计算其它的一些重要的统计量,如考察协方差矩阵、摄动矩阵等,并计算这些量随时间的传播．这种算法的优点是通过降低法方程的条件数提高计算的稳定性,同时可以方便地对不同的参数组合情况求解而不需多次解算法方程．     

Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

The traditional least square estimation (LSE) method for orbit determination will not be optimal if the error of observational data does not obey the Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method is presented in this paper to deal with the non-Gaussian distribution cases. We show that a suitable selection of parameter p may guarantee a reasonable orbit determination result. The character of Lp estimation is analyzed. It is shown that the traditional Lp estimation method is not a robust method. And a stable Lp estimating based on data depth weighting is put forward to deal with the model error and outlier. In the orbit determination process, the outlier of observational data and coarse model error can be quantitatively described by their weights. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the traditional Lp estimation and the breakdown point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is enhanced. Finally, by taking the Space-based Space Surveillance System as an example and performing simulation experiments, we show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space-based observation platform, LSE will not be optimal even though the observational data obeys the Gaussian distribution, and the orbit determination precision by the self-adaptive robust Lp estimation method is much better than that by the traditional LSE method.     

The Data Depth-weight-kernel Estimation of the Model Error of Satellite Orbit Determination

It is an objective fact that there exists error in the satellite dynamic model and it will be transferred to satellite orbit determination algorithm, forming a part of the connotative model error. Mixed with the systematic error and random error of the measurements, they form the unitive model error and badly restrict the precision of the orbit determination. We deduce in detail the equations of orbit improvement for a system with dynamic model error, construct the parametric model for the explicit part of the model and nonparametric model for the error that can not be explicitly described. We also construct the partially linear orbit determination model, estimate and fit the model error using a two-stage estimation and a kernel function estimation, and finally make the corresponding compensation in the orbit determination. Beginning from the data depth theory, a data depth weight kernel estimator for model error is proposed for the sake of promoting the steadiness of model error estimation. Simulation experiments of SBSS are performed. The results show clearly that the model error is one of the most important effects that will influence the precision of the orbit determination. The kernel function method can effectively estimate the model error, with the window width as a major restrict parameter. A data depth-weight-kernel estimation, however, can improve largely the robustness of the kernel function and therefore improve the precision of orbit determination.     

环月飞行器精密定轨的模拟仿真

以中国正在实施的探月计划“嫦娥1号”工程为背景，分析了在中国联合S波段(USB)测控网和甚长基线射电干涉(VLBI)跟踪网的现有空间分布、观测精度水平下的环月飞行器精密定轨．采用的方法是模拟仿真计算，即首先模拟观测数据，然后在计入各误差源的影响后进行求解，并对解算结果进行比较．模拟仿真的工具是美国宇航局哥达德飞行中心的空间数据分析软件系统GEODYN．环月飞行的主要误差源是月球重力场，为此首先讨论了目前精度最高的月球重力场模型JGL165P1的(形式)误差．在模拟了测距、测速以及VLBI的时延、时延率数据后，计入月球重力场的误差进行精密轨道确定．定轨时采用了减缩动力学(reduced dynamic)方法，即选用合适的经验加速度参数吸收重力场误差对定轨的影响．结果表明对于一个不将月球重力场作为主要科学目标的探月计划(如“嫦娥1号”)，减缩动力学方法是一个简单、有效地提高环月飞行器定轨精度的方法．     

Orbit covariance propagation via quadratic-order state transition matrix in curvilinear coordinates

In this paper, an analytical second-order state transition matrix (STM) for relative motion in curvilinear coordinates is presented and applied to the problem of orbit uncertainty propagation in nearly circular orbits (eccentricity smaller than 0.1). The matrix is obtained by linearization around a second-order analytical approximation of the relative motion recently proposed by one of the authors and can be seen as a second-order extension of the curvilinear Clohessy–Wiltshire (C–W) solution. The accuracy of the uncertainty propagation is assessed by comparison with numerical results based on Monte Carlo propagation of a high-fidelity model including geopotential and third-body perturbations. Results show that the proposed STM can greatly improve the accuracy of the predicted relative state: the average error is found to be at least one order of magnitude smaller compared to the curvilinear C–W solution. In addition, the effect of environmental perturbations on the uncertainty propagation is shown to be negligible up to several revolutions in the geostationary region and for a few revolutions in low Earth orbit in the worst case.     

A method of astronomical autonomous orbit and attitude determinations for satellites

A method of realtime autonomous orbit determination for earth satellites using the extended Kalman filtering is proposed. The observed quantities are: the satellite-sun direction vector measured by a sun sensor, the satellite-earth and satellite-moon direction vectors measured by an ultraviolet sensor, and the geocentric distance measured by a radar altimeter. At the same time the satellite attitude to the earth is also determined. Results of our simulation of the autonomous orbit determination show that the precision of the orbit determinations is better than 200 m. The effects of the sampling period, orbital inclination, orbital eccentricity and orbital altitude on the precision of orbit determination are analyzed and compared, and certain principles helpful for improving the precision of orbit determination are suggested.     

An orbit determination algorithm by means of the satellite-borne GPS data and Kalman filter

Using the Kalman filter algorithm, we have processed on-board GPS data of Shenzhou 4. The research focuses on three problems, namely, the selection criteria for the model error variance matrix of the Kalman filter, the effects of GPS signal interruption or runs of outliers on the recursive filtering, and the method to monitor the filter running status (normal or divergent). The aim is to evaluate the reliability of long-time stationary running of this algorithm used for on-board autonomous orbit determination