Performance enhanced Kalman filter design for non-Gaussian stochastic systems with data-based minimum entropy optimisation

Almost all of the complex dynamic processes are subjected to non-Gaussian random noises which leads to the performance deterioration of Kalman filter and Extended Kalman filter (EKF). To enhance the filtering performance, this paper presents an EKF-based filtering algorithm using minimum entropy criterion for a class of stochastic non-linear systems subjected to non-Gaussian noises. For practical implementations, the Kalman filters are widely used and the structure will not be changed due to the system integration, therefore, it is important to enhance the performance without changing the existing system design. In particular, a compensative framework has been developed where the EKF design meets the basic filtering requirements and the polynomial-based non-linear compensation has been used to adjusted the basic estimation from EKF with the entropy criterion. Since the entropy of the system output estimation error can be approximated using the measured data by kernel density estimation (KDE). A data-based framework can be obtained to enhance the performance. In addition, the presented algorithm is analysed from the view of the estimation convergence and a numerical example has been given to demonstrate the effectiveness.