A random error estimation method for satellites being launched into orbit based on ellipsoid theory

基于椭球理论的卫星入轨位置随机误差估计方法

¹ School of Computer Science, China University of Geosciences(Wuhan), Wuhan 430074, China
² Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences(Wuhan), Wuhan 430074, China

Received: 16 September 2022

Abstract

Accurate and fast random error estimation is essential to improve satellite control. In this paper, the random error of the satellite being launched into orbit is explored. According to the uncertainty matrix of six satellite orbit parameters associated with the project, the uncertainty of the orbit position in the three axes of the geocentric inertial frame of reference is calculated via the propagation rate of the covariance matrix. Then, the random error probability density of the satellite position is constructed for normal distribution. The surface of the error with the same probability density is approximated as an ellipsoid, the size is deduced along with the ellipsoid's shape and direction, and the satellite's spatial position probability is obtained. Monte Carlo method and STK software were employed to simulate low-earth orbit micro-nano satellite launching into the same orbital position. It is confirmed that the results obtained via the theoretical model are in line with practice. Therefore, the ellipsoid theory proposed in this paper can be used to describe the satellite random position error.

摘要

准确快捷地估计卫星位置随机误差有利于更好地控制卫星。针对卫星入轨位置的随机误差, 分析了入轨位置随机误差的概率密度函数, 根据卫星入轨六根数不确定性矩阵, 利用协方差阵传播率确定地心惯性坐标系下入轨位置在3个坐标轴方向的不确定性, 把入轨位置等概率密度曲面近似为椭球, 推导出椭球的形状、大小和方向, 进而计算卫星入轨在一定空间范围内的概率。利用蒙特卡罗方法, 借助STK软件模拟低轨微纳卫星在随机因素影响下发射入轨, 仿真实际入轨位置分布, 并对比椭球理论模型下入轨位置的概率分布。仿真结果表明椭球理论误差模型分析结果与模拟实验结果基本一致, 说明该椭球理论模型可以用来估计卫星随机位置误差。