Maximum correntropy cubature Kalman filter and smoother for continuous-discrete nonlinear systems with non-Gaussian noises

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To estimate the continuous-discrete nonlinear dynamic systems with non-Gaussian non-zero mean noises, a square-root maximum correntropy cubature Kalman filter with adaptive kernel width and its corresponding smoother are proposed in this paper. Based on the statistical linear regression (SLR) technique, the maximum correntropy criterion (MCC) instead of minimum mean square error (MMSE) is applied to our previously derived continuous-discrete Gaussian estimation method. Compared with MMSE, MCC can not only capture the second-order statistical information of non-Gaussian error, but also utilize its higher-order information. In addition, in order to ensure that MCC can work with an appropriate kernel width, an adaptive kernel width adjustment strategy is given by using the sliding window methodology. Further, for a reliable implementation of the proposed continuous-discrete MCC-based algorithms, they are structurally modified into the square root form. The newly proposed approaches are tested and compared with conventional estimation methods in three commonly used numerical applications. Experimental results show that the proposed algorithms are not only accurate and robust, but also have low computational complexities.