一种高阶无迹卡尔曼滤波方法

摘要

Currently there is still no specific analytical solution for the high order unscented transform (UT), thus high order UT can not be used to obtain high order unscented Kalman filter (UKF) with higher accuracy. In order to solve this problem, an analytical solution of high order UT is obtained by introducing a free parameterκon the basis of fifth-order cubature transform (CT), and the high order UKF is then obtained. It is illustrated that the existing fifth-order CT and fifth-order UT are two special cases of the high order UT whenκ=2 andκ=6−n, respectively. Furthermore, the optimal choice of parameterκin the high order UKF is analyzed and discussed for different dimensional systems, and the stability of the proposed method is discussed. Simulations based on the bearings-only tracking model and ballistic object reentry model show that the proposed method is correct and it has better performance as compared with the existing methods.%现有的研究中,高阶无迹变换(Unscented transform, UT)还不存在具体的解析解,因此,无法利用高阶无迹变换获得具备更高精度的高阶无迹卡尔曼滤波器(Unscented Kalman filter, UKF)。为了解决这一问题,本文在五阶容积变换(Cubature transform, CT)的基础上,通过引入一个自由参数κ,得到高阶无迹变换的解析解,从而获得了高阶无迹卡尔曼滤波器(Unscented Kalman filter, UKF)。同时验证了现有的五阶容积变换和五阶无迹变换分别是本文所提出的高阶无迹变换在κ=2和κ=6−n 时的两个特例。进而分析和讨论了高阶无迹卡尔曼滤波器在系统不同维数条件下κ值的最优选取,并讨论了其稳定性。纯方位跟踪模型和弹道目标再入模型仿真验证了本文方法的正确性,且与现有方法相比具有更高的精度。