  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.
