Cauchy kernel-based maximum correntropy Kalman filter

Non-Gaussian noise processing is a difficult and hot spot in the study of filters. A currently effective method to deal with non-Gaussian noise is replacing the minimum mean square error criterion with the maximum correntropy criterion. Based on the maximum correntropy criterion, maximum correntropy Kalman filter, which usually uses the Gaussian kernel function to define the distance between vectors, is developed. However, when the non-Gaussian noise is multi-dimensional, maximum correntropy Kalman filter tends to break down due to the appearance of singular matrices. To overcome the drawback, a novel filter named Cauchy kernel-based maximum correntropy Kalman filter is proposed, which utilises the Cauchy kernel function to define the distance between vectors. Due to the insensitive feature to the kernel bandwidth and thick-tailed characteristic of the Cauchy kernel function, Cauchy kernel-based maximum correntropy Kalman filter can effectively avoid filter faults and has a better stability. Simulation results demonstrate the excellent performance of the proposed algorithm by comparing it with other conventional methods, such as Kalman filter, ideal Kalman filter, Huber-based filter, Gaussian sum filter and maximum correntropy Kalman filter.