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Abstract: The minimum mean-square error (MMSE) and minimum error entropy (MEE) are two important criteria in the estimation related problems. The MMSE can be viewed as a robust MEE criterion in the minimax sense, as its minimization is equivalent to minimizing an upper bound (the maximum value) of the error entropy. This note gives a new and more meaningful interpretation on the robustness of MMSE for problems in which there exists uncertainty in the probability model. It is shown that the MMSE estimator imposes an upper bound on error entropy for the true model. The upper bound consists of two terms. The first term quantifies the “MMSE performance” under nominal conditions, and the second term measures the “distance” between the true and nominal models. This robustness property is parallel to that of the risk-sensitive estimation. Illustration examples are included to confirm the robustness of MMSE. [Copyright &y& Elsevier]

Recently, the Kalman filter algorithm based on the minimum error entropy criterion has been presented to outperform the conventional Kalman filter in the case of impulsive noise. In practice, it may be unstable in numerical calculation. This paper proposes a robust algorithm to solve the problem of instability in numerical calculation. The convergence and stability of the algorithm are verified by the performance analysis and simulations. In the mean square behavior analysis, we propose a method to estimate the steady-state errors. Simulations show that the experimental steady-state errors of the algorithms agreed with the theoretical values. [ABSTRACT FROM AUTHOR]

• A variant of the quantized minimum error entropy (QMEE) algorithm is proposed. • The mean square convergence performance analysis for QMEE algorithm is given. • The theoretical values of the steady-state EMSE for QMEE algorithm are validated by simulations. • QMEE algorithm is applied in electroencephalo (EEG) de-noising task. Adaptive filtering algorithms have been widely used in many areas, among which the minimum error entropy (MEE) algorithm is a superior choice, due to its excellent performance in the non-Gaussian noise situations. However, the computational complexity of the MEE algorithm is expensive, which leads to the computational bottlenecks, especially for large-scale datasets. In order to address the problem, we propose an adaptive filtering algorithm based on the quantized minimum error entropy (QMEE) criterion with an online quantization method, named QMEE algorithm. Moreover, we analyze the transient behavior characteristic and derive an approximate analytical expression for the steady-state excess mean square error (EMSE) based on the Taylor expansion. The extensive simulation results in linear modeling and electroencephalogram (EEG) denoising task demonstrate that the proposed method can outperform other robust adaptive filtering algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust target localization in distributed multiple-input multiple-output (MIMO) radar using possibly outlier range measurements. To achieve robustness against outliers, we construct an objective function for MIMO target localization via the maximum correntropy criterion. To deal with such a nonconvex and nonlinear function, we apply a half-quadratic optimization technique to determine the target position and auxiliary variables alternately. Especially, we derive a semidefinite relaxation formulation for the aforementioned position determination step. The robust performance of the developed approach is demonstrated by comparing with several conventional localization methods via computer simulation. [ABSTRACT FROM AUTHOR]