Entropy-based Extended Kalman Filtering for Stochastic Non-linear Systems with Polynomial Compensation

Abstract

This paper presents a novel filtering algorithm to enhance the estimation accuracy for the extended Kalman filter (EKF). For stochastic non-linear systems, the EKF is widely used in practice however this filtering design is not optimal on any aspects and it focuses on the systems which are subjected to Gaussian noises. Moreover, for practical systems, the EKF parameters will be fixed after the design progression. To overcome these problems, an entropy-based optimal filtering design has been developed with a polynomial-based non-linear compensation where another enhancement loop will be designed without changing the existing EKF. In particular, the non-linear compensation term can be re-expressed by polynomial with parameters and these parameters can be further optimised to minimise the entropy-based cost function where the entropy of the system output estimation error can be estimated by kernel density estimation (KDE) and the collected data. In addition, the convergence analysis is obtained in theory sense and the effectiveness of the presented filtering algorithm has been validated using a numerical example.