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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]

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]

In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example. [ABSTRACT FROM AUTHOR]

The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example. [ABSTRACT FROM AUTHOR]

Robust sparse signal recovery against impulsive noise is a core issue in many applications. Numerous methods have been proposed to recover the sparse signal from measurements corrupted by various impulsive noises, but most of them either lack theoretical guarantee for robust sparse recovery or are not efficient enough for large-scale problems. To this end, a general optimization problem for robust sparse signal recovery, which includes many existing works as concrete instances, is analyzed by a freshly defined Double Null Space Property (DNSP), and its solution is proved to be able to robustly reconstruct the sparse signal under mild conditions. Moreover, for computational tractability, weakly convex sparsity-inducing penalties are applied to the general problem, and properties of the solution to the resultant non-convex problem are further studied. Based on these properties, an algorithm named Robust Projected Generalized Gradient (RPGG) is devised to solve the weakly convex problem. Theoretical results prove that the sparse signal can be precisely reconstructed by RPGG from compressive measurements with sparse noise or robustly recovered from those with impulsive noise. Meanwhile, simulations demonstrate that RPGG with tuned parameters outperforms other robust sparse recovery algorithms. [ABSTRACT FROM AUTHOR]

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully constrained unmixing, with both the nonnegativity and sum-to-one constraints, while the second one deals with the nonnegativity and the sparsity promoting of the abundances. The corresponding optimization problems are solved using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing with ADMM is particularly robust against highly noisy outlier bands. [ABSTRACT FROM PUBLISHER]