Distributed minimum error entropy Kalman filter

Abstract

Recently, the distributed Kalman filter (DKF) has been considered a major method for the applications of Wireless sensor networks (WSNs), for instance, the Internet of Things, and Swarm Intelligence, in which non-Gaussian noise influence is an urgent issue. In this paper, taking any sensor of WSNs as a fusion node, a dynamic Gain Matrix is constructed for its neighbors’ information fusion. Then, the Minimum Error Entropy (MEE) is furtherly introduced into the information fusion process, a modified DKF algorithm called the Distributed Fusion MEE Kalman Filter (DF-MEE-KF) is proposed for eliminating the non-Gaussian noise influence, which improved the estimation accuracy well. Moreover, considering many bad communication conditions of WSNs, such as Communication Denial Environments, and Underwater Acoustic Communication Environments, it is required that the higher estimation accuracy the better, and the lower communication cost the better. Therefore, the diffusion rule is applied for the nodes’ information fusion by constructed fusion weights, thereby an extended DF-MEE-KF algorithm, the Diffusion MEE Kalman filter (Diff-MEE-KF), is obtained. Finally, the convergence of the proposed DF-MEE-KF and Diff-MEE-KF algorithms is proved. Numerical simulation examples also demonstrate that the DF-MEE-KF algorithm performs good estimation accuracy, and the Diff-MEE-KF algorithm achieves a lower communication cost under the same estimation accuracy, when in non-Gaussian noise-influenced WSNs’ applications.