Minimum Error Entropy Kalman Filter

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 9; pp. 5819 - 5829
• Main Authors: Chen, Badong, Dang, Lujuan, Gu, Yuantao, Zheng, Nanning, Principe, Jose C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Covariance matrices; Covariance matrix; Criteria; Entropy; Errors; Estimates; Estimation; Kalman filtering; Kalman filters; Measurement uncertainty; minimum error entropy (MEE); non-Gaussian noises; Probability density function; Recursive functions; robust estimation; Robustness
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2957269

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 this article, we develop a new Kalman-type filter, called minimum error entropy KF (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 the 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 MEE extended KF (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.