两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

基于SLR精密轨道的天文定位精度分析

利用全球卫星激光测距服务系统(ILRS,International Laser Ranging Service)标准点资料对Ajisai卫星进行精密定轨,残差均方根(RMS)优于3 cm,得到该星的精密轨道.进而对长春站40 cm空间碎片光电望远镜获得的Ajisai卫星的天文定位资料进行精度分析,外符合精度约3″左右.单独利用天文定位数据进行轨道改进,内符合精度优于3″.改进轨道的x、y、z坐标3分量在观测数据覆盖范围内的精度在100 m之内.同样地对Jason-1卫星作数据分析,结果和Ajisai卫星精度相当.分析各个弧段的精度变化,发现定标星个数减少,会导致天文定位精度下降.据此提出可以把最少定标星比例作为评定数据质量的参考指标之一.     

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.     

Orbit Determination Using Satellite—to—Satellite Tracking Data

1 INTRODUCTIONThe tracking arc-length should be increased in order to approve the accuracy in orbitdetermination of LEO (Low Earth Orbit) satellites. The local ground-based tracking networkdoes not provide sufficient orbit coverage for the user satellites. The most promising methodis to use high orbiting satellites, such as GPS and TDRS, as trackers to observe the usersatellites. For examPle, tWO geosynclironous satellites could cover more than 85% of the orbitof any given user sate…     

Estimation of Distribution Algorithm for Initial Orbit Determination of Too-short-arc Based on Kernel Density Estimation

A new approach of the initial orbit determination for too-short-arc with angular measurements is implemented by building the probabilistic model in the solution space with the estimation of distribution algorithm. Without any assumption about distribution, the non-parametric kernel density estimation is employed in the model building. The method, unlike other evolutionary algorithms, such as the genetic algorithm and particle swarm optimization, considers the fitness as well as the characteristics of the solution space. Numerical experiments with real observations indicate that without any constraints, the proposed technique has a good performance for the observations of usual accuracy.     

Kinematic Precise Orbit Determination for LEO Satellites Using Space-borne Dual-frequency GPS Measurements

As a special approach to orbit determination for satellites with spaceborne GPS receivers, the kinematic Precise Orbit Determination (POD) is independent of any mechanical model (e.g., the Earth gravity ?eld, atmospheric drag, solar radiation pressure, etc.), and thus especially suitable for the orbit determination of Low Earth Orbiting (LEO)satellites perturbed strongly bythe atmosphere. In this paper, based on the space-borne dual-frequency GPS data, we study the kinematic POD, discuss the pre-processing of the data, and construct an algorithm of zero-difference kinematic POD. Using the observational data from GRACE (Gravity Recovery And Climate Experiment) satellites covering the whole month of February 2008, we verify the effectiveness and reliability of this algorithm. The results show that the kinematic POD may attain an accuracy of about 5 cm (with respect to satellite laser ranging data), which is at the same level as the dynamic and reduced-dynamic PODs     

同步卫星短弧定轨

同步卫星受到摄动力的影响,它的实际轨道有一点漂移．卫星需要不断的调轨调姿,以保证其正常运行．为了研究卫星在几小时,甚至更短的时间内的轨迹情况,采用短弧段定轨法．用动力学方法进行短弧定轨,分别研究1小时和15分钟定轨并进行比较,目的是为了在同步轨道卫星变轨后,能尽快地为卫星提供精密的预报轨道．此外,在系列短弧定轨后,得到精密轨道系列,为研究轨道变化的力学因素及研究短弧中卫星转发器时延变化规律等提供依据．     

加速仪数据在CHAMP卫星精密定轨中的贡献

通过用几个实例计算，评估了CHAMP卫星加速仪数据对SLR数据定轨精度的贡献．结果显示用加速仪数据代替非保守力对CHAMP卫星进行精密定轨时，其SLR的残差从原来的16．5cm减少到2．7cm，与精密轨道相比，卫星位置误差由18．9cm减少到6．2cm(一天资料)．     

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.     

一种初轨计算的稳健方法

光学测角资料的初轨计算在空间目标搜索发现中具有重要作用,当观测资料存在野值时,基于最小二乘的经典初轨计算方法不够稳健.采用最小一乘方法建立了一种初轨计算的稳健方法,方法将初轨计算问题转换为线性规划问题求解,并通过bootstrap方法给出估计精度.数值计算结果表明方法稳健有效,并具有较高的崩溃点.     

单站单圈测距资料初轨计算的单位矢量法

根据单位矢量法测轨原理，在已知轨道面参数i，Ω的前提下，给出了一种适用于单站单圈测距资料的初轨计算方法．计算结果表明，方法是有效的．在没有测角资料或测角资料精度显著低于测距精度的情况下，有应用价值．     

多星混合资料的定轨

在空间目标光学观测资料定轨中常常会遇到多个目标的观测被标记为同一个目标的情况,由于包含了多个目标的数据,定轨过程无法收敛或者完全错误.从极大似然估计角度,采用EM(Expectation Maximum)方法提出一种将轨道改进和识别过程相互融合的处理方法,并在具体实现过程中给出一种稳健估计方法.数值模拟表明方法简便、有效、可行.采用站间差历元差的手段,对当前电离层变化值进行求解与预测,可以将电离层延时误差的变化控制在一定范围,满足频率传递的要求.     

分布逼近的卡尔曼滤波及其在星载GPS卫星定轨中的应用

探讨了利用推广卡尔曼滤波估计非线性系统状态时存在的问题，进而简要介绍了目前自动控制领域广泛使用的分布逼近的卡尔曼滤波UKF(Unscented Kalman Filter)，考虑到卫星定轨中系统的动态方程和量测方程存在严重非线性的情形，提出了将UKF用于星载GPS卫星定轨．实例计算结果表明，UKF的性能要优于推广卡尔曼滤波．     

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．     

移动站的运动对轨道确定影响的分析

介绍了测站移动速度对四元素短弧初轨确定的影响．从测站速度矢量的影响因素着手，简化地对移动站的移动速度与影响因素之间的关系进行了理论推导．以单位矢量方法中的3种方法为例，修改了轨道的条件方程，并做了大量的数据验算，最后给出了两圈外测数据的两种不同情况的单圈定轨结果，就此初步分析了移动站的移动速度对定轨结果的影响及规律．这种在定轨方法中补充考虑移动站的移动速度影响的方法，计算模型简洁，容易理解，便于运用．     

抗差估计在星载GPS卫星非差运动学定轨中的应用

针对星载GPS卫星非差运动学定轨的特点,提出将抗差估计应用于星载GPS卫星运动学定轨,一方面尽量保留来自每颗GPS卫星的观测值,保持较强的卫星几何强度,避免轨道求解出现奇异;另一方面,采用等价权思想,有效地降低质量较差的观测值对定轨结果的影响,保证定轨精度．还采用CHAMP卫星的实测GPS数据验证了新方案的可行性和有效性．     

月球探测器过渡轨道的短弧定轨方法

论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考．     

一种适用于长弧段的初轨计算方法

根据单位矢量法测轨原理，在人造卫星初轨计算的单位矢量法基础上，给出了一种适用于长弧段的初轨计算方法．该方法既适用于长弧段，也适用于短弧段；适用于各种不同类型的观测资料和任意偏心率、任意轨道倾角的人造地球卫星；有利于提高初轨测定精度；并改善整个计算收敛性．特别需要指出的是，该方法与有摄初轨计算的单位矢量法相结合，为单位矢量法从初轨计算推广到轨道改进打下了坚实的基础．     

初轨计算方法中的常数系统差修正

在单位矢量法的基础上给出了一种常数系统误差修正方法．大量的数据验算结果表明,当测量数据中含有显著常数系统误差时,在初轨计算中修正常数系统差是有效的,可以提高测轨精度．     

The Application of GIM in Precise Orbit Determination for LEO Satellites with Single-Frequency GPS Measurements

With the precise GPS ephemeris and clock error available, the iono- spheric delay is left as the dominant error source in the single-frequency GPS data. Thus, the removal of ionospheric effects is a ma jor prerequisite for an improved orbit reconstruction of LEO satellites based on the single-frequency GPS data. In this paper, the use of Global Ionospheric Maps (GIM) in kine- matic and dynamic orbit determinations for LEO satellites with single-frequency GPS pseudorange measurements is discussed first, and then, estimating the iono- spheric scale factor to remove the ionospheric effects from the C/A-code pseu- dorange measurements for both kinematic and dynamic orbit determinations is addressed. As it is known that the ionospheric delay of space-borne GPS sig- nals is strongly dependent on the orbit altitudes of LEO satellites, we select the real C/A-code pseudorange measurement data of the CHAMP, GRACE, TerraSAR-X and SAC-C satellites with altitudes between 300 km and 800 km as sample data in this paper. It is demonstrated that the approach to eliminating ionospheric effects in C/A-code pseudorange measurements by estimating the ionospheric scale factor is highly effective. Employing this approach, the accu- racy of both kinematic and dynamic orbits can be improved notably. Among those five LEO satellites, CHAMP with the lowest orbit altitude has the most remarkable improvements in orbit accuracy, which are 55.6% and 47.6% for kine- matic and dynamic orbits, respectively. SAC-C with the highest orbit altitude has the least improvements in orbit accuracy accordingly, which are 47.8% and 38.2%, respectively.