基于T-H方程的椭圆轨道初始误差传播

Initial Error Propagation of Elliptical Orbit Based on T-H Equation

针对椭圆轨道误差传播问题,提出了一种基于T-H方程状态转移矩阵的初始误差传播特性分析方法。首先将空间目标真实状态和预报状态对应于一"实"一"虚"两个近距离空间目标,把预报误差看作"虚"目标相对"实"目标的相对运动,利用空间目标近距离相对运动理论来研究预报误差的特性。然后引入T-H方程状态转移矩阵分析初始误差的传播,得到了各个方向误差传播的规律。最后进行仿真验证,分别使用蒙特卡洛法和文中方法计算了典型椭圆轨道的误差传播,并与STK高精度轨道预报模型(HPOP)进行对比,得到结果的相对误差大都在2%以内,并与理论分析结果的趋势一致,证实了该方法的正确性。

To study the initial error propagation of elliptical orbit , a new method was developed based on the state transition matrix of T-H equation . Firstly , the true state and predict state of one space object can be considered as two objects ：a real one and a virtual one . Considering predict error as relative motion between these two objects , the relative motion theory was used to study the characteristic of error propagation . Secondly , the state transition matrix of T-H equation was introduced to analyze the propagation of initial error , with which the trend of error propagation in each direction was obtained . Finally ,a simulation case was designed to validate the correctness of the new method ,and the Monte-Carlo method and the new method were used to calculate error propagation of typical elliptical orbit . The results were compared with the HPOP′s results . Most of the relative error is less than 2% , and is consistent with the trend of the theoretical analysis results .