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).
Highlights
State estimation theory has been regarded as an important research area in modern control systems.In the appearance of the Kalman filtering theory in the last century had a profound influence on modern optimal control [1,2,3]
The contribution of this paper is to develop a new filtering strategy for multivariable nonlinear systems with non-Gaussian disturbances by utilizing a novel performance index which contains the entropy of estimation error, square error and constraints on gain matrix of the filter
The purpose of filtering algorithm for nonlinear non-Gaussian systems is to ensure that the estimation errors achieve small dispersion and approach to zero
Summary
State estimation theory has been regarded as an important research area in modern control systems. The contribution of this paper is to develop a new filtering strategy for multivariable nonlinear systems with non-Gaussian disturbances by utilizing a novel performance index which contains the entropy of estimation error, square error and constraints on gain matrix of the filter. The filter gain matrix for nonlinear non-Gaussian systems is designed by minimizing the proposed performance index. This filtering algorithm yields to the estimation errors which have small uncertainty and approach to zero.
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