一种改进的空间目标接近分析快速算法

An Improved Efficient Algorithm for Close Approach Determination of Space Objects

Alfano-Negron(1993)提出的空间目标接近分析算法将最小相对距离及其对应时刻和进出误差椭球时刻的求解问题均转化为插值多项式求根问题。A-N算法在判断三次多项式根的存在性、筛选合理实根时存在缺陷,可能导致多余计算。由A-N算法提出的准则不能直接计算插值时间步长并可能导致丢根,对此根据多项式插值误差理论提出了一种自适应的插值时间步长选取方法。相比原始A-N算法,完善后的A-N算法计算结果更加可靠。与精确的逐秒比较结果相比,改善后的A-N算法计算速度远高于逐秒比较,具有较高精度,更适合于有实时计算要求的任务。

An algorithm for close approach determination was developed by Alfano and Negron （1993） based on polynomial splining techniques. The local minimum relative distances and the corresponding times, as well as the time when one space object enters and exits in the ellipsoidal region of another one are determined by solving the roots of the polynomials. However, in A-N algorithm there are limitations in the criteria used to check root existence and the process of filtrating rational real roots. Furthermore, the criteria proposed in A-N algorithm for determination of the time step of splining are not appropriate for direct calculation and may lead to root loss. All of these insufficiencies are pointed out and corrected in this paper. A self-adaptive method based on polynomial splining error theory for choosing interpolation step is presented. Comparison shows that the result of the improved A-N algorithm is more reliable than the original one. Finally, compared with the accurate step-by-step method, the improved algorithm is much faster and relatively accurate.