Maximum Correntropy Ensemble Kalman Filter

In this article, a robust ensemble Kalman filter (EnKF) called MC-EnKF is proposed for nonlinear state-space model to deal with filtering problems with non-Gaussian observation noises. Our MC-EnKF is derived based on maximum correntropy criterion (MCC) with some technical approximations. Moreover, we propose an effective adaptive strategy for kernel bandwidth selection.Besides, the relations between the common EnKF and MC-EnKF are given, i.e., MC-EnKF will converge to the common EnKF when the kernel bandwidth tends to infinity. This justification provides a complementary understanding of the kernel bandwidth selection for MC-EnKF. In experiments, non-Gaussian observation noises significantly reduce the performance of the common EnKF for both linear and nonlinear systems, whereas our proposed MC-EnKF with a suitable kernel bandwidth maintains its good performance at only a marginal increase in computing cost, demonstrating its robustness and efficiency to non-Gaussian observation noises.Comment: Accepted by 62nd IEEE Conference on Decision and Control (CDC 2023

State Estimation of Wireless Sensor Networks in the Presence of Data Packet Drops and Non-Gaussian Noise

Distributed Kalman filter approaches based on the maximum correntropy criterion have recently demonstrated superior state estimation performance to that of conventional distributed Kalman filters for wireless sensor networks in the presence of non-Gaussian impulsive noise. However, these algorithms currently fail to take account of data packet drops. The present work addresses this issue by proposing a distributed maximum correntropy Kalman filter that accounts for data packet drops (i.e., the DMCKF-DPD algorithm). The effectiveness and feasibility of the algorithm are verified by simulations conducted in a wireless sensor network with intermittent observations due to data packet drops under a non-Gaussian noise environment. Moreover, the computational complexity of the DMCKF-DPD algorithm is demonstrated to be moderate compared with that of a conventional distributed Kalman filter, and we provide a sufficient condition to ensure the convergence of the proposed algorithm

Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation

Disturbance observers have been attracting continuing research efforts and are widely used in many applications. Among them, the Kalman filter-based disturbance observer is an attractive one since it estimates both the state and the disturbance simultaneously, and is optimal for a linear system with Gaussian noises. Unfortunately, The noise in the disturbance channel typically exhibits a heavy-tailed distribution because the nominal disturbance dynamics usually do not align with the practical ones. To handle this issue, we propose a generalized multi-kernel maximum correntropy Kalman filter for disturbance estimation, which is less conservative by adopting different kernel bandwidths for different channels and exhibits excellent performance both with and without external disturbance. The convergence of the fixed point iteration and the complexity of the proposed algorithm are given. Simulations on a robotic manipulator reveal that the proposed algorithm is very efficient in disturbance estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023