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Entropy 2013, 15(7), 2510-2523; doi:10.3390/e15072510
Article

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

1
, 2,* , 1
, 1
 and 3
1 School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China 2 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China 3 The Beijing Key Laboratory of New and Renewable Energy, North China Electric Power University, Beijing 102206, China
* Author to whom correspondence should be addressed.
Received: 26 April 2013 / Revised: 31 May 2013 / Accepted: 19 June 2013 / Published: 25 June 2013
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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).
Keywords: non-Gaussian systems; stochastic filtering; generalized density evolution equation; exponentially mean-square boundedness non-Gaussian systems; stochastic filtering; generalized density evolution equation; exponentially mean-square boundedness
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ren, M.; Zhang, J.; Fang, F.; Hou, G.; Xu, J. Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation. Entropy 2013, 15, 2510-2523.

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