Rational-quadratic kernel-based maximum correntropy Kalman filter for the non-Gaussian noises

In this paper, a rational-quadratic kernel-based maximum correntropy Kalman filter (RKMCKF) algorithm is proposed to improve the estimation accuracy for non-Gaussian noise interference. Firstly, the RKMCKF algorithm is derived to eliminate the singular matrix produced by multi-dimensional non-Gaussian noise disturbance. Secondly, the upper limit is analyzed to provide a theoretical range for kernel bandwidth, which is beneficial for the selection of proper kernel bandwidths and boosting the precision of state estimation. Furthermore, the boundness of the state estimation error is verified to manifest the RKMCKF algorithm stability. Finally, under different types of non-Gaussian noise, the proposed RKMCKF algorithm is demonstrated to promote the accuracy of state estimation compared with the conventional Kalman filter, Gaussian sum filter, Huber filter, and maximum correntropy Kalman filter through the simulations.