Recent developments in the realm of state estimation of stochastic dynamicsystems in the presence of non-Gaussian noise have induced a new methodologycalled the maximum correntropy filtering. The filters designed under themaximum correntropy criterion (MCC) utilize a similarity measure (orcorrentropy) between two random variables as a cost function. They are shown toimprove the estimators' robustness against outliers or impulsive noises. Inthis paper we explore the numerical stability of linear filtering techniqueproposed recently under the MCC approach. The resulted estimator is called themaximum correntropy criterion Kalman filter (MCC-KF). The purpose of this studyis two-fold. First, the previously derived MCC-KF equations are revise and therelated Kalman-like equality conditions are proved. Based on this theoreticalfinding, we improve the MCC-KF technique in the sense that the new methodpossesses a better estimation quality with the reduced computational costcompared with the previously proposed MCC-KF variant. Second, we devise somesquare-root implementations for the newly-designed improved estimator. Thesquare-root algorithms are well known to be inherently more stable than theconventional Kalman-like implementations, which process the full errorcovariance matrix in each iteration step of the filter. Additionally, followingthe latest achievements in the KF community, all square-root algorithms areformulated here in the so-called array form. All the MCC-KF variants developedin this paper are demonstrated to outperform the previously proposed MCC-KFversion in two numerical examples.
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