飞行器碰撞概率计算的一般方法

研究了飞行器碰撞概率计算的一般方法,这种方法通过飞行器和空间物体各自的状态矢量、位置误差协方差矩阵以及形状尺寸来计算飞行器和空间物体的碰撞概率。从位置误差协方差矩阵的一般形式出发,推导了飞行器的碰撞概率计算公式。在推导过程中,将飞行器的相对运动速度看作是方向不变的矢量,从而可以消去平行于相对速度的一维,将三维的概率计算问题转化为和相对速度垂直的相遇平面内的二维概率问题。针对二维概率问题分别研究了三种碰撞概率的计算方法,并比较了它们各自的优缺点。最后通过数值算例验证了三种方法各自的特点及正确性。

General Method for Calculating Spacecraft Collision Probability

A general method for calculating spacecraft collision probability is developed.In this method the input required to perform a calculation includes the respective state vectors,position error covariance matrices and physical sizes of objects involved.The method is valid for the general case because it only relies on the general form of error covariance matrices.The relative velocity is assumed to be vector having constant direction,and then the collision probability problem can be reduced to two dimensions in encounter plane normal to the relative velocity vector by eliminating the dimension parallel to the relative velocity vector.Three kinds of method resolving the two dimensions problem are developed and compared.Test case results indicate the method is valid and applicable.