非线性相对运动的飞行器碰撞概率研究

发展了一种非线性相对运动情况下的飞行器碰撞概率描述和计算方法。采用拟最大瞬时碰撞概率和总碰撞概率两个主要指标来定量描述飞行器碰撞的危险性，并针对这两个指标发展了相应的计算方法。对于拟最大瞬时碰撞概率的计算，首先需要在相对轨迹上寻找最小相对距离或最大概率密度的点，然后在这个点上计算拟最大瞬时碰撞概率。对于总碰撞概率的计算，由于总碰撞概率的增量可以表示成一个时间的函数，因此总碰撞概率的计算就是一个在时间域上的积分。所建立的这种描述和计算方法适用于相对速度和误差协方差矩阵随时间任意变化的情况。数值算例表明所提出的指标比单纯采用总碰撞概率能够更好的描述飞行器的碰撞危险性，并且碰撞概率的计算方法和线性相对运动情况下的计算方法是兼容的。

Space Vehicle Collision Probability for Nonlinear Relative Motion

A method for describing and calculating the collision probability between two space vehicles when the relative motion is nonlinear is developed. The method involves quantitatively analyzing the collision probability using quasi maximum instantaneous collision probability and total collision probability. The method calculating the two indexes is developed. The process calculating quasi maximum instantaneous collision is divided into two steps. Firstly the position having minimum relative distance or maximum probability density on the relative trajectory is found, then quasi maximum instantaneous collision probability can be calculated in this position. The calculation of total collision probability increment can be treated as a function of time throughout the encounter. Thus, total collision probability is integration throughout encounter time. This method established is applicable to collision probability problem involving relative velocity and error covariance changing with time. Test case results prove the indexes presented can describe the collision risk better, and the method calculating the index is compatible with the method calculating linear relative motion developed before.