基于EM的主动段弹道导弹跟踪算法研究

摘要

为了提高未知弹道参数下主动段目标跟踪的精度,提出基于期望最大化(Expectation Maximization,EM)的联合优化算法框架.首先在E步基于平滑器得到状态和未知参数的后验估计,然后在M步计算初始状态的均值、协方差以及过程噪声协方差等未知统计量,最后推导出基于URTS(Unscented Rauch-Tung-Striebel)的EM算法,并给出未知统计量的最优解析解,避免了非凸优化难以求解的问题.仿真结果表明:在相同量级的计算量下,本文算法的状态估计精度优于迭代UKF(Unscented Kalman Filter)算法.%In this paper,framework of joint optimization algorithm based on EM (Expectation Maximization) is proposed for tracking a boost-phase ballistic target with unknown ballistic parameters.Firstly,the state and unknown parameters are estimated based on smoother in the E step.Then the mean and covariance of initial states,and the noise covariances are calculated in the M step.At last,URTS (Unscented Rauch-Tung-Striebel) based on EM is derived and the analytical forms of unknown statistics parameters are given,which makes the non-convex numerical optimization unnecessary.The result shows that the proposed algorithm is more accurate than iterative UKF (Unscented Kalman Filter) with the same order of magnitude of calculation.