空间飞行器轨道确定的B样条逼近方法  

Spacecraft Orbit Determination with B Spline Approximation Method

作　　者：宋叶志[1] 黄勇[1] 胡小工[1] 李培佳[1] 曹建峰[1,2] 

机构地区：[1]中国科学院上海天文台,上海200030 [2]北京航天飞行控制中心,北京100094

出　　处：《天文学报》2013年第4期370-381,共12页Acta Astronomica Sinica

基　　金：国家自然科学基金项目(11073047;11173049);863项目(2012AA121603);上海市导航实验室开放课题(Y224353002);上海市科学技术委员会(06DZ22101);中国科学院行星科学重点实验室资助

摘　　要：动力学定轨是空间飞行器精密轨道确定的基本方法.然而,有些情况下,对飞行器进行精确的力学建模是困难的.基于函数逼近理论,给出了B样条逼近空间飞行器统计意义下的轨道确定方法.为了验证方法的有效性,分别对LEO(Low Earth Orbit)、MEO(Medium Earth Orbit)和HEO(Highly Eccentric Orbit)卫星进行了轨道确定数值试验,计算结果证实方法精度可靠、解算稳定.B样条逼近轨道确定方法与坐标系的选择无关,既可以在协议天球坐标系下解算,又可以在协议地球坐标系下解算.B样条逼近可以直接计算飞行器位置和速度,不需要对动力学状态方程进行积分,也不需要计算状态转移矩阵,使得定轨计算量相对于动力学定轨大幅减少.方法既有一定的理论意义,又可以作为工程应用中空间飞行器轨道确定的一个常规算法.It is known that the dynamical orbit determination is the most common way to get the precise orbit of spacecraft. However, it is hard to describe the precise orbit of space- craft sometimes. In order to solve this problem, the technique of the orbit determination with the B spline approximation method based on the theory of function approximation is presented in this article. Several simulation cases of the orbit determination including LEO （Low Earth Orbit）, MEO （Medium Earth Orbit）, and HEO （Highly Eccentric Orbit） satellites are performed stable. The approach can and it is shown that the accuracy of this method is reliable and be performed in the conventional celestial coordinate system and conventional terrestrial coordinate system. The spacecraft＇s position and velocity can be calculated directly with the B spline approximation method, which means that it is unnecessary to integrate the dynamics equations and variational equations. In that case, it makes the calculation amount of orbit determination reduce substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can be as a conventional algorithm in the spacecraft orbit determination.

关 键 词：航天器 天体力学 轨道计算和定轨 方法 数值 

分 类 号：P136[天文地球—天体力学]