Search

The multivariate autoregressive (MVAR) model is widely used in describing the dynamics of nonlinear systems, in which the estimates of model parameters and underlying states can be achieved by dual extended Kalman filter (DEKF). However, when the measurements are corrupted by complicated non-Gaussian noises, the DEKF based on the minimum mean-square error (MMSE) criterion may provide biased estimates. In the present article, we develop a novel dual Kalman-type filter, referred to as DEKF under minimum error entropy (MEE) with fiducial points (MEEFs-DEKF) to deal with the non-Gaussian noises. First, the equivalent state-space model and parameter-space model are presented based on the MVAR model. Then, an optimality criterion based on MEE with fiducial points (MEEFs) is applied in the batch-mode regression equation to improve the robustness. Finally, a fixed-point iteration algorithm gives the posterior estimates of state and parameter. Simulation results confirm that the proposed MEEF-DEKF can achieve excellent performance in various noises with different distributions, especially in heavy-tailed and multimodal noises. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The minimum error entropy (MEE) criterion has been receiving increasing attention due to its promising perspectives for applications in signal processing and machine learning. In the context of Bayesian estimation, the MEE criterion is concerned with the estimation of a certain random variable based on another random variable, so that the error's entropy is minimized. Several theoretical results on this topic have been reported. In this work, we present some further results on the MEE estimation. The contributions are twofold: (1) we extend a recent result on the minimum entropy of a mixture of unimodal and symmetric distributions to a more general case, and prove that if the conditional distributions are generalized uniformly dominated (GUD), the dominant alignment will be the MEE estimator; (2) we show by examples that the MEE estimator (not limited to singular cases) may be non-unique even if the error distribution is restricted to zero-mean (unbiased). [ABSTRACT FROM AUTHOR]