  An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change
in the state, followed by a Particle Filer (PF, the corrector) which assigns
importance weights to describe non-Gaussian distribution. The weights are
obtained by nonparametric density estimation. It is demonstrated on several
numerical examples that the new predictor-corrector filter combines the
advantages of the EnKF and the PF and that it is suitable for high dimensional
states which are discretizations of solutions of partial differential
equations.
