A new family of ensemble filters, called predictor-corrector filters, is introduced. The predictor-corrector filters use a proposal ensemble (obtained by some method, called the predictor) with assignment of importance weights to recover the correct statistic of the posterior (the corrector). The proposal ensemble comes from an arbitrary unknown distribution, and it only needs to have a good coverage of the support of the posterior. The ratio of the prior and the proposal densities for calculating the importance weights is obtained by density estimation. Predictor by the ensemble Kalman formulas and corrector by nonparametric density estimation based on the distance in Sobolev spaces are considered. Numerical experiments show that the new predictor-corrector filters combine the advantages of ensemble Kalman filters and particle filters for highly nonlinear systems, and that they are suitable for high dimensional states which are discretizations of smooth functions.

We also propose another class, called morphing ensemble filters, which combine ensemble Kalman filters with the ideas of morphing and registration from image processing. In the morphing ensemble filters, the ensemble members are represented by the composition of one fixed template function with a morphing function, and by adding a residual function. The ensemble Kalman formulas operate on the transformed state consisting of the morphing function and the residual function. This results in filters suitable for problems with sharp thin moving interfaces, such as in wildfire modeling.

We have demonstrated the potential of predictor-corrector and morphing ensemble filters to perform a successful bayesian update in the presence of non-gaussian distributions, large number of degrees of freedom, large change of the state distribution, and position errors. The work presented here will be useful in wildfire modeling as well as in data assimilation for other problems with strongly non-gaussian distributions and moving sharp interfaces and features, such as hurricanes.