优化卡尔曼滤波算法中的目标函数选择

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (1): 200-203.

优化卡尔曼滤波算法中的目标函数选择

王建文¹, 税海涛¹, 马宏绪¹, 李迅¹, 刘述田²

1. 国防科技大学机电工程与自动化学院, 湖南, 长沙, 410073;
2. 91065部队教研部, 辽宁, 葫芦岛, 125001

收稿日期:2007-06-22 修回日期:2008-07-09 出版日期:2009-01-20 发布日期:2010-01-03
作者简介:王建文(1979- ),男,博士研究生,主要研究方向为信号处理,无人直升机系统.E-mail:wangjianwen7921@sina.com

Choice of cost functions in optimized Kalman filters

WANG Jian-wen¹, SHUI Hai-tao¹, MA Hong-xu¹, LI Xun¹, LIU Shu-tian²

1. Dept. of Automatic Control, National Univ. of Defense Technology, Changsha 410073, China;
2. Dept. of Teaching and Research, 91065 Unit, the PLA, Huludao 125001, China

Received:2007-06-22 Revised:2008-07-09 Online:2009-01-20 Published:2010-01-03

摘要/Abstract

摘要： 针对优化卡尔曼滤波算法(optimized Kalman filter,OKF)中的目标函数选择问题,设计了两种适用于OKF算法优化的目标函数,证明了这两种目标函数是最优的,即当目标函数取最小值时,OKF算法中的滤波估计值H_kx_k|k-1^⌒*是(或概率意义下)系统真实状态H_kx_k的最优估计。把上述目标函数应用于多模型卡尔曼滤波算法(multiple model adaptive Kalman filter,MM-AKF)中,设计了一种优化多模型卡尔曼滤波算法(optimizedmultiple model adaptive Kalman filter,OMM-AKF),OMM-AKF算法能够根据目标函数优化子滤波器的滤波估计值权值,从而能够得到系统真实状态的较优估计值。最后,通过仿真验证了上述理论的正确性和方法的有效性。

Abstract: The choice of cost functions in optimized Kalman filters(OKF) is thoroughly analyzed.Two cost functions suitable to OKFs are designed.It is proved that these cost functions are optimal,that is,when the cost function is minimal,the estimated state H_kx_k|k-1^⌒* is(or in probability) an optimal estimator for H_kx_k in OKFs.Then,these cost functions are applied in a multiple model adaptive Kalman filter(MM-AKF),thus an optimized multiple model adaptive Kalman filter(OMM-AKF) is designed.The OMM-AKF can optimize the weights of state estimations,thus a superior state estimation can be obtained.Finally,the findings in this paper are verified by some simulations.

中图分类号:

TP274

王建文, 税海涛, 马宏绪, 李迅, 刘述田. 优化卡尔曼滤波算法中的目标函数选择[J]. Journal of Systems Engineering and Electronics, 2009, 31(1): 200-203.

WANG Jian-wen, SHUI Hai-tao, MA Hong-xu, LI Xun, LIU Shu-tian. Choice of cost functions in optimized Kalman filters[J]. Journal of Systems Engineering and Electronics, 2009, 31(1): 200-203.

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