Minimum Error Entropy Kalman Filter

TL;DR

This paper introduces the minimum error entropy Kalman filter (MEE-KF) and its extended version (MEE-EKF), which improve robustness and accuracy in state estimation under complex non-Gaussian noise conditions by using the minimum error entropy criterion.

Contribution

It develops a new Kalman-type filter based on the minimum error entropy criterion, enhancing robustness against non-Gaussian noises beyond existing MCC-based methods.

Findings

MEE-KF and MEE-EKF demonstrate high accuracy in experiments.

The proposed filters show strong robustness to complex non-Gaussian noises.

Experimental results confirm the effectiveness of the new approach.

Abstract

To date most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in the present paper we develop a new Kalman-type filter, called minimum error entropy Kalman filter (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC based KFs, the proposed filter is also an online algorithm with recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the minimum error entropy extended Kalman filter (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.