The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example.

A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.

As a nonlinear extension of Kalman filter, the extended Kalman filter (EKF) is also based on the minimum mean square error (MMSE) criterion. In general, the EKF performs well in Gaussian noises. But its performance may deteriorate substantially when the system is disturbed by heavy-tailed impulsive noises. In order to improve the robustness of EKF against impulsive noises, a new filter for nonlinear systems is proposed in this paper, namely the maximum correntropy extended Kalman filter (MCEKF), which adopts the maximum correntropy criterion (MCC) as the optimization criterion instead of using the MMSE. In MCEKF, the state mean and covariance matrix propagation equation are used to obtain a prior estimation of the state and covariance matrix, and then a fixed-point algorithm is used to update the posterior estimates. The robustness of the new filter is confirmed by simulation results.