Extended Kalman filter under maximum correntropy criterion

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.