基于自适应稳健最小p范数估计的轨道确定方法研究  

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

作　　者：潘晓刚[1,2] 李强[1] 周海银[1] 

机构地区：[1]国防科学技术大学九院,长沙410073 [2]北京航天飞行控制中心载人航天与深空探测飞行力学实验室,北京100094

出　　处：《天文学报》2010年第3期285-298,共14页Acta Astronomica Sinica

基　　金：国家自然科学基金(60974124);载人航天与深空探测飞行力学实验室开放基金资助项目

摘　　要：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.The traditional LSE （least square estimation） method for orbit determination will not be optimal if the error of observational data of orbit determination does not obey Gaussian distribution. In order to solve this problem, the least p-norm （Lp） estimation method for orbit determination is presented to deal with the non-Gaussian distribution cases because of the adaptability of p-norm distribution. Through estimating the parameter p, the results can be more reasonable. The corresponding character of Lp estimation is analyzed. It is proved that the traditional Lp estimation method is not a robust method. So a stable Lp estimation based on data depth weighting is put forward to deal with the model error and outlier. In orbit determination process, the outlier of observational data and coarse model error can be quantitatively described. 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 common Lp estimation and the break down 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 more perfect. Finally, taking the Space Based Space Surveillance System as an example to make simulation experiments, the results 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 Gaussian distribution and the orbit determination precision by the self-adaptive stable Lp estimation method is much higher than that by the common LSE method.

关 键 词：天体力学 轨道计算和定轨 方法 数值 

分 类 号：P135[天文地球—天体力学]