Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise

State estimation in the presence of non-Gaussian noise is discussed. Since the Kalman filter uses only second-order signal information, it is not optimal in non-Gaussian noise environments. The maximum correntropy criterion (MCC) is a new approach to measure the similarity of two random variables using information from higher-order signal statistics. The correntropy filter (C-Filter) uses the MCC for state estimation. In this paper we first improve the performance of the C-Filter by modifying its derivation to obtain the modified correntropy filter (MC-Filter). Next we use the MCC and weighted least squares (WLS) to propose an MCC filter in Kalman filter form, which we call the MCC-KF. Simulation results show the superiority of the MCC-KF compared with the C-Filter, the MC-Filter, the unscented Kalman filter, the ensemble Kalman filter, and the Gaussian sum filter, in the presence of two different types of non-Gaussian disturbances (shot noise and Gaussian mixture noise).