秩滤波方法

RANK FILTER METHOD

基于秩统计量相关原理提出一种秩采样方法,其采样点分布合理,能够有效地模拟系统状态的概率分布。在此基础上,进一步提出一种非线性秩滤波方法,给出秩滤波的采样策略、时间更新、量测更新公式及其计算步骤。目前常用的非线性滤波方法有无迹Kalman滤波和粒子滤波。无迹Kalman滤波方法只适用于高斯分布的情况;粒子滤波方法虽然可用于非高斯分布的非线性滤波,但却存在粒子退化及重采样引起的粒子贫化问题,且计算复杂、工作量大。而秩滤波方法不仅适用于高斯分布的非线性滤波,也适用于常见的多元t分布、多元极值分布等非高斯分布的非线性滤波,并且计算简单、计算量小,便于工程应用。从仿真算例可以看到,该方法比无迹Kalman滤波方法具有更高的滤波精度。

A rank sampling method based on the principle of rank statistics is presented. Its sampling points have reasonable distribution so that they can efficiently simulate the probability distribution of system state. Furthermore, a nonlinear rank filter （RF） method is proposed. Its filter reeursive process is also given. Unscented Kalman filter （UKF） only for Gaussian distribution and particle filter （PF） for Non-Gaussian distribution are the two common nonlinear filter methods. But PF has the problems of particle degeneracy, particle impoverishment caused by resampling and complicated calculation. Compared with the two methods, the proposed RF is suitable for not only Gaussian distribution but also Non-Gaussian distributions such as multivariate student distributions and extreme value distributions. RF is simple to calculate and easy to apply in engineering. From the simulation comparisons of RF and UKF in the example, RF has higher filtering accuracy than UKF.