Entropy optimization based filtering for non-Gaussian stochastic systems  

作　　者：Bo TIAN Yan WANG Lei GUO 

机构地区：[1]School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China [2]National Key Laboratory on Aircraft Control Technology, Beihang University, Beijing 100191, China

出　　处：《Science China(Information Sciences)》2017年第12期29-39,共11页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61320106010,61573019,61627810)

摘　　要：This paper is concerned with the entropy optimization based filter design for a class of multivariate dynamic stochastic systems with simultaneous presence of non-Gaussian process noise and measurement noise.The filter consists of time update and measurement update two steps, where the selection of the filter gain in the measurement update equation is a key issue to be addressed. Different from the classic Kalman filter theory, entropy rather than variance is employed as the filtering performance criterion due to the non-Gaussian characteristic of the estimation error. Following the establishment of the relationship between the probability density functions of random noises and estimation error, two kinds of entropy based performance indices are provided. On this basis, the corresponding optimal filter gains are obtained respectively by using the gradient optimization technique. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed filtering algorithms.This paper is concerned with the entropy optimization based filter design for a class of multivariate dynamic stochastic systems with simultaneous presence of non-Gaussian process noise and measurement noise.The filter consists of time update and measurement update two steps, where the selection of the filter gain in the measurement update equation is a key issue to be addressed. Different from the classic Kalman filter theory, entropy rather than variance is employed as the filtering performance criterion due to the non-Gaussian characteristic of the estimation error. Following the establishment of the relationship between the probability density functions of random noises and estimation error, two kinds of entropy based performance indices are provided. On this basis, the corresponding optimal filter gains are obtained respectively by using the gradient optimization technique. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed filtering algorithms.

关 键 词：non-Gaussian systems joint probability density function（JPDF） quadratic information potential relative entropy optimal filtering 

分 类 号：TN713[电子电信—电路与系统]