University of Colorado at Denver and Health Sciences Center Predictor-Corrector Ensemble Filters for the Assimilation of Sparse Data into High Dimensional Nonlinear Systems

An ensemble particle filter is proposed which is suitable for very large systems with smooth state, such as arizing from discretization of partial differential equations. The proposal ensemble comes from an arbitrary unknown distribution, and it is selected to have a good coverage of the support of the posterior. Proposal ensembles from the ensemble Kalman filter and from deterministic nudging to randomly perturbed observation data are considered. The ratio of the the prior and the proposal densities for calculating the importance weights is obtained by density estimation in Sobolev spaces, which are infinitely dimensional, and so the density estimate does not deteriorate in high dimension. Numerical experiments show that the new filter combines the advantages of ensemble Kalman filters and particle filters.