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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 unscented Kalman filter (UKF) provides a powerful tool for power system forecasting-aided state estimation (FASE). However, when the power systems are affected by the abnormal operating situations, i.e., the non-Gaussian communication noises, sudden loads or state changes, and instrument failures, the original UKF based on the minimum mean square error (MMSE) criterion may suffer from performance degradation. In contrast to the MMSE criterion, the minimum error entropy (MEE) exhibits the robustness with respect to complex non-Gaussian disturbances. In this article, we develop a new unscented Kalman-type filter based on the MEE criterion, termed MEE-UKF. To derive the MEE-UKF, a statistical linearization approach is adopted in the augmented model such that the state and measurement errors are combined in the MEE cost function simultaneously. Then, a fixed-point iteration algorithm is used to recursively update the posterior estimates and covariance matrix. Apart from the impulsive noises, the MEE-UKF can deal with complex multimodal distribution noises in both process and measurement. The high accuracy and strong robustness of MEE-UKF are confirmed by the simulation results on IEEE 14, 30, and 57 bus test systems under different non-Gaussian disturbances. [ABSTRACT FROM AUTHOR]

Common spatial pattern (CSP) is a classic method commonly used in multichannel electroencephalogram (EEG) signal processing, which aims to extract effective features for binary classification by solving spatial filters that maximize the ratio of filtered dispersion between two classes. The aim of this paper is to improve the performance of the conventional CSP method, which will be badly influenced by noises. The recently proposed quantized minimum error entropy (QMEE) criterion is applied to structure a new objective function instead of the ${L} _{2}$ -norm in the conventional CSP. Quantization is utilized to reduce the computational complexity. The new objective function is optimized by a gradient-based iterative algorithm. The desirable performance of the QMEE-based CSP method, namely CSP-QMEE, is demonstrated with a toy example and two real EEG datasets, including Dataset IIb of the brain–computer interfaces (BCIs) Competition IV (three channels) and Dataset IIIa of the BCI Competition III (60 channels). The new method can achieve satisfactory performance compared to existing methods on all datasets. The promising results in this paper suggest that the CSP-QMEE may become a powerful tool for BCIs. [ABSTRACT FROM AUTHOR]