Maximum Correntropy Kalman Filtering for Non-Gaussian Systems With State Saturations and Stochastic Nonlinearities

作     者：Bo Shen Xuelin Wang Lei Zou Bo Shen;Xuelin Wang;Lei Zou

作者机构：the College of Information Science and TechnologyDonghua UniversityShanghai 201620 the Engineering Research Center of Digitalized Textile and Fashion TechnologyMinistry of EducationShanghai 201620China 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报（英文版）)

年 卷 期：2023年第10卷第5期

页      面：1223-1233页

核心收录：

学科分类：0711[理学-系统科学] 080902[工学-电路与系统] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported in part by the National Natural Science Foundation of China (62273088, 62273087) the Shanghai Pujiang Program of China (22PJ1400400) the Program of Shanghai Academic/Technology Research Leader (20XD1420100) 

主　　题：Fixed-point theorem maximum correntropy criterion non-Gaussian noises state saturations stochastic nonlinearities 

摘      要：This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.