Maximum Correntropy Ensemble Kalman Filter

TL;DR

This paper introduces a robust ensemble Kalman filter based on maximum correntropy criterion (MC-EnKF) that effectively handles non-Gaussian observation noises in nonlinear state-space models, improving filtering performance.

Contribution

The paper proposes MC-EnKF, a novel robust filtering method using MCC, with an adaptive kernel bandwidth strategy, and provides theoretical insights into its relation to the standard EnKF.

Findings

MC-EnKF maintains performance under non-Gaussian noise

It converges to standard EnKF as kernel bandwidth increases

Demonstrates robustness and efficiency in experiments

Abstract

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.