考虑J_2摄动的弹道导弹高精度弹道预报和误差传播分析

Analysis on High Precision Trajectory Prediction and Error Propagation of Ballistic Missile Considering J2Perturbation

为进行高精度的弹道导弹弹道预报和误差传播分析,分析了平根数法解摄动方程的解形式,提出了一种考虑J_2摄动并包含短周期项的解析法,并将其用于弹道预报,结合无迹变换构造了弹道预报的误差传播分析方法,解决了解析法中开普勒根数求解过程不可微、偏导数矩阵难以计算的问题。仿真结果表明,将解析法用于弹道预报时,J_2摄动短周期项导致的误差达3个数量级,不可忽略;该算法预报的相对误差只有不到5%,精度与高精度数值法相当,远高于传统解析法,但运算速度是后者的7倍,具有更好的效费比。

To carry out high-precision trajectory prediction and error propagation analysis of ballistic missile,the solution form of mean element algorithms for perturbation equation was analyzed , and an analytical algorithm considering J2 perturbation and containing the short period term was proposed for trajectory prediction .By constructing the error propagation analysis method of trajectory prediction based on unscented transform , the problem that the Kepler elements is not differentiable and the partial derivative matrix is difficult to calculate was solved .The simulation results show that the error caused by the J2 perturbation short period term , which can not be ignored , reaches 3 orders of magnitude when analytical algorithm is applied in the trajectory prediction .The relative error predicted by the proposed al-gorithm is only less than 5%,and the precision is far higher than the precision of traditional analytical al-gorithm,which is comparable with the precision of high-precision numerical algorithm ,but the operation speed is 7 times of the latter ,and the algorithm has a better effectiveness-cost ratio .