Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

Abstract

This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE) criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF) of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF).

A Novel Perspective of the Kalman Filter from the Rényi Entropy

“…Quadratic Rényi entropy [ 11 ] of innovation has been used as a minimum entropy criterion under a nonlinear and non-Gaussian circumstance [ 12 ] in unscented Kalman filter (UKF) [ 13 ] and finite mixtures [ 14 ]. A generalized density evolution equation [ 15 ] and polynomial-based non-linear compensation [ 16 ] were used to improve the minimum entropy filtering [ 17 ]. Relative entropy has been used to measure the similarity between the probabilistic density functions during the recursive processes of the nonlinear filter [ 18 , 19 ].…”

An Analysis of Information Dynamic Behavior Using Autoregressive Models

“…Main researches in ITL include regression, neural network training, classification and clustering [3][4][5][6][7][8][9][10], parameter estimation, system identification and signal processing [11][12][13][14][15][16][17] areas.…”