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Robust weighted fusion Kalman estimators for multisensor systems with multiplicative noises and uncertain‐covariances linearly correlated white noises
Author(s) -
Liu WenQiang,
Wang XueMei,
Deng ZiLi
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3649
Subject(s) - estimator , kalman filter , covariance intersection , control theory (sociology) , robustness (evolution) , mathematics , multiplicative noise , multiplicative function , covariance , computer science , extended kalman filter , statistics , artificial intelligence , mathematical analysis , biochemistry , chemistry , control (management) , signal transfer function , digital signal processing , computer hardware , analog signal , gene
Summary This paper addresses the design of robust weighted fusion Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include the same multiplicative noises perturbations both on the systems state and measurement output and the uncertain noise variances. The measurement noises and process noise are linearly correlated. By introducing two fictitious noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case systems with the conservative upper bounds of the noise variances, the four robust weighted fusion time‐varying Kalman estimators are presented in a unified framework, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, scalar weights, and a modified robust covariance intersection fusion estimator. The robustness of the designed fusion estimators is proved by using the Lyapunov equation approach such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. The corresponding robust local and fused steady‐state Kalman estimators are also presented, a simulation example with application to signal processing to show the effectiveness and correctness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.