Maximum Correntropy Criterion Kalman Filter with Adaptive Kernel Size

Kernel size plays a significant role in the performance of the maximum correntropy Kalman filter (MCC-KF). Kernel size is usually chosen by trail and error. If the kernel size is large, the MCC-KF reduces to the Kalman filter (KF). However, if the kernel size is small, the MCC-KF may diverge, or converge slowly. We propose a novel method for adaptive kernel size selection. We calculate kernel size as a weighted sum of the innovation term and the covariance of the filter-indicated estimation error at each time step. We call this filter the "MCC with adaptive kernel size filter" (MCC-AKF). We analytically prove that the true mean square error (TMSE) of the MCC-AKF is less than or equal to that of the MCC-KF under certain conditions. A simulation example is provided to illustrate the analytical results.