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Volume 10 Issue 5
May  2023

IEEE/CAA Journal of Automatica Sinica

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B. Shen, X. L. Wang, and  L. Zou,  “Maximum correntropy Kalman filtering for non-Gaussian systems with state saturations and stochastic nonlinearities,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1223–1233, May 2023. doi: 10.1109/JAS.2023.123195
Citation: B. Shen, X. L. Wang, and  L. Zou,  “Maximum correntropy Kalman filtering for non-Gaussian systems with state saturations and stochastic nonlinearities,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1223–1233, May 2023. doi: 10.1109/JAS.2023.123195

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

doi: 10.1109/JAS.2023.123195
Funds:  This work was supported in part by the National Natural Science Foundation of China (62273088, 62273087), the Shanghai Pujiang Program of China (22PJ1400400), and the Program of Shanghai Academic/Technology Research Leader (20XD1420100)
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  • 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 state-multiplicative 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.

     

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    Highlights

    • A modified performance index is constructed against the non-Gaussian noises
    • A new Kalman-type filtering algorithm is put forward
    • The influence of kernel parameter selection on the filtering performance is analyzed

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