已知e的先验值的初轨寻优算法

本文讨论由短弧测角资料,已知偏心率e的先验值时,初轨的寻优算法。把偏心率的先验值看作是对e的约束条件,再固定观测弧段两端点的观测量与作为约束条件,本文导出了一维(对M_0)非线性寻优算法;针对观测资料中可能存在异常值的情形,本文提出了一种初轨的稳健寻优算法。仿真结果表明,当e的先验值有足够高的精度时,能明显提高周期P的估计精度;稳健算法还可用作剔除观测资料的异常值。     

野值预剔除方法的改进

在初轨有较大误差时，传统的光学资料野值预剔除方法——截断最小二乘L估计法不能有效地剔除野值．从门限和模型两方面改进野值预处理方法，即改用统计中误差定门限．将残差的线性模型改为2次曲线模型，结果为：对于模拟产生的所有卫星弧段，在初轨有10^-4（半长轴α为其5％，以下不再说明）误差情况下，野值比例都能降低到10％以下．     

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.     

已知e或a的先验值的初轨迭代算法

本文讨论由短弧测角资料,已知偏心率ｅ 或半长轴ａ 的先验值时,初轨的迭代算法。某根数的先验值可看作是对该根数的具有一定精度的观测量,在加权残差平方和达到极小意义下,本文导出了最小二乘估计的迭代算法。仿真结果显示,周期的估计精度主要取决于偏心率先验值的精度;当ｅ 足够小时,可用园轨道计算的ａ′作为ａ 的先验值,定出的初轨有较高精度。     

人卫光学观测中大异常值的剔除方法

本文详细讨论了人造卫星学观测中大异常值的剔除问题，我们首先将复杂的非线性问题，利用初始轨道，将它转化为便于数学处理的线性模型，用时间差△Ｔ，以及轨道面法向差△θ两个量来分析判别，并提出了一种采用截断最小二乘的Ｌ－估计目标函数进行大异常值剔除的方法，方法的崩溃点为５０％，同时给出了算例，并对初轨精度和剔除门限进行了讨论。     

初轨计算的参考矢量法

本文从最优估计角度研究短弧资料定初轨问题，提出一种最小二乘估计算法，同时提出一种符合实用的参考矢量法．仿真结果显示，参考矢量法克服了现有初轨算法所承受病态影响，把定轨精度提高到接近最佳水平．     

基于自适应稳健最小p范数估计的轨道确定方法研究

当测轨数据误差不服从正态分布时,传统的最小二乘(LSE)轨道确定方法将不是最优的.为了获得高精度的定轨结果,一种可行的策略是采用基于最小p范数(Lp)的轨道确定方法.通过分析Lp估计的相关性质,得出普通Lp估计不具有良好的抗差性的结论.为抑制模型误差和异常值的影响,提出了基于数据深度加权的稳健最小p范数估计方法,并证明了相关性质,得出了其崩溃点可以达到1/2的结论.最后,通过残差分析和矩估计法自适应估计相关参数,使得估计达到最大效率.以天基空间目标监视系统为背景进行了仿真试验.结果表明,当观测数据存在系统误差或异常值时,或者当目标动力学模型存在误差或者天基观测平台存在系统误差时,即使观测数据服从正态分布,LSE也不是最优的,在这种意义下自适应稳健Lp估计轨道确定方法比传统轨道确定方法更加稳健,定轨精度也更高.     

LP估计在星载GPS运动学定轨中的应用及精度分析

为得到高精度的星载GPS运动学定轨,必须利用观测精度高的相位观测值,但是相位观测值预处理后,仍然存在残余小周跳．在残差服从正态分布情况下LS法是最佳参数解算方法,但该方法不能解决资料的系统误差消除问题,LP估计是处理资料残差分布含有系统误差的有效方法之一．基于LS、LP方法的有效条件和GPS数据预处理的特性,将LP估计方法引入星载GPS运动学定轨数据处理中,以CHAMP卫星资料为例,研究了LP估计在星载GPS运动学定轨中的应用及其精度分析．实践表明:在处理含有残余小周跳的相位观测值时,LP估计比LS更有效,提高了星载GPS运动学定轨精度,但随着残余周跳的进一步修复,LP估计相对于LS估计的优越性越来越弱,在资料完全没有系统误差,残差服从正态分布的情况下,LP估计不能很好地体现其优越性,精度反而低于LS估计．     

初轨计算精度的bootstrap估计

从非参数统计角度,在仅有观测资料而没有其它信息的情况下,分别给出了初轨计算的精度和置信区间的估计方法.该方法基于bootstrap方法,仅依赖于观测资料,不需要精密定轨结果作为参考,也无需假设观测资料误差呈正态分布,并且对各种初轨计算方法均适用.数值计算结果表明该方法应用简便,可作为初轨的评估和后续应用的重要参考.     

论初轨计算的最佳精度及二重解

从最优估计的角度,研究短弧测角资料初轨计算的最佳精度及准最佳精度算法．按照统计理论,对一般的参数估计问题,其估计误差的方差存在Cram’e4-Rao下界,这就是初轨理论的最佳精度;通过大量的模拟计算表明,文［1］中提出参考矢量法,其精度已充分接近C·R下界,且模拟计算轨道统计精度与观测误差成正比,可以认为是一种初轨计算的准最佳精度算法;对于小偏心率情况,发现一个重要的事实：初轨计算有二重解,更准确地说,在M0的左右两个半平面内有真假两个解,偏心率愈小,平近点角M0愈接近±π／2,给出的假解的概率愈大．针对这一情况,提出一种算法,可以给出2个解,其中必定有一个是真解,它有较高的精度.     

Improvement in the method of data processing

When the errors in the initial orbit are comparatively great, the usual truncated least square L estimation can not effectively delete the outliers in the set of optical observations. This method has been modified in both the threshold and the approximation model: the threshold is now determined by the statistics on the rms, and the linear model of fitting the residuals is replaced with a quadratic model. With these modifications, the results show that when the initial orbit has an error of 10[su−4] (the error in the semi-major axis is about 5%), the proportion of outliers is reduced to below 10% for all the simulated satellite passes.     

A Robust Method of Preliminary Orbit Determination

The preliminary orbit determination with optical angular measure- ments plays an important role in the survey of space objects. The classical method of orbit computation based on the least square error estimation is not robust while outliers occur in the observation. A robust method is proposed by employing the least absolute deviation estimation. The method reduces the problem of orbit determination to a linear programming problem, and gives the variance of the estimation with the bootstrap method. Numerical check shows that the method is effective and robust, and has a high breakdown point.     

单频GPS周跳检测与估计算法

提出一种单频GSP载波相位中的野值，周跳俭测与模糊度估计算法，采用三阶多项式的卡尔曼滤波检测野值与周跳，而用一种最佳小波估计模糊度，该算法适用于采样间隔为1秒的载波相位测量，用1995．6．22Topex星载GPS数据计算的结果表明，它有限高的效率，可以准确估计信号中断几秒内的模糊度。     

An algorithm for detecting and estimating cycle slips in single-frequency GPS

An algorithm for detecting outliers and cycle slips in single-frequency GPS using a 3rd order polynomial model of the Kalman filter and for estimating the ambiguity by using optimal wavelet is presented in this paper. It is applicable to the carrier phase measurement with sample rate of one per second. The results of calculation with the GPS data aboard satellite Topex on 1995 June 22 show that the algorithm is so efficient that it can accurately estimate the ambiguity even for signals interrupted by a few seconds.     

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     

Space Event and Outlier Detection Based on Expectation Maximization Algorithm

The United States provide Element Sets (ELSET) database in Two-Line Element (TLE) format for public use, which plays an important role in the inversion of atmospheric density in the thermosphere, ballistic coefficient estimation, early-warning and so on. Due to large uncertainties existing in the TLE generation process, space environment changes, and space events, ELSET database contains a large number of abnormal TLE data to be filtered, such as corrected TLE, orbital element outlier, and Bstar outlier. The existing methods to filter out the outliers lack general applicability and are very complicated, which are only applicable to a few space targets in certain orbit regions. To overcome the shortcomings of the existing methods, a filtering method is proposed based on Expectation Maximization (EM) algorithm employing a sliding window and polynomial fitting method, which can detect outliers for different orbital elements and space events. The research shows that the algorithm can effectively single out the outliers in TLE sequences and is suitable for all orbital debris.     

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．     

GaussFit—A system for least squares and robust estimation

GaussFit is a new computer program for solving least squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.Invited Talk at the 18th meeting of the Division on Dynamical Astronomy of the American Astronomical Society held in Braintree, Massachussetts, May 7–9, 1987.