基于多项式近似的空间碎片群体轨道预报算法

快速准确地分析空间碎片群轨道演化行为对于其他在轨航天器碰撞规避至关重要。在各摄动力的作用下，空间碎片群演化运动呈现出复杂的非线性特征。空间碎片群体个体数量巨大，如果通过对空间碎片群中每个空间碎片进行轨道积分来分析群体预报的方法会导致计算量过大。针对该问题，提出一种基于多项式近似的轨道快速预报分析方法。该方法将空间碎片群分为少量的标称碎片和其他大量关联碎片。针对标称碎片的轨道预报采用数值积分求解保证预报精度；而针对其他大量的关联碎片轨道预报问题，采用多项式泰勒展开半解析方法求解，从而在保证预报精度的前提下有效减少空间碎片群轨道预报的计算量。为了验证方法的有效性，对不同空间碎片群进行了轨道预报仿真。仿真结果表明，当轨道预报精度设定在1m范围内时，多项式近似算法的计算量较蒙特卡洛方法计算效率提高了2.2~17.2倍，验证了所提出方法的有效性。

Orbit prediction algorithm for space debris cluster based on polynomial approximation

It is important to analyze the orbital evolution behavior of space debris cluster quickly and accurately for collision avoidance of spacecraft in orbit.Under the action of each perturbation force，the evolutionary movement of space debris cluster presents complex nonlinear characteristics.The space debris population has a large number of individuals.If the orbital integration of each space debris in the space debris population is used to analyze the population prediction，the amount of calculation will be too large.To solve this problem，a fast orbit prediction method based on polynomial approximation was proposed.This method divided space debris cluster into a small number of nominal fragments and a large number of other associated fragments.For orbit prediction of nominal debris，numerical integration was used to ensure the accuracy of prediction.For a large number of other associated debris orbit prediction problems，polynomial Taylor expansion semi-analytical method was used，so as to effectively reduce the calculation of space debris cluster orbit prediction on the precondition of ensuring the prediction accuracy.Orbit prediction simulations for different space debris cluster were carried out.The simulation results show that when the orbit prediction accuracy is set within 1 meter，the calculation efficiency of polynomial approximation algorithm is 2.2 to 17.2 times higher than that of Monte Carlo method，which verifies the effectiveness of the proposed method.