  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.
