A Gaussian-mixture ensemble transform filter

Reich, S. (2012) A Gaussian-mixture ensemble transform filter. Quarterly Journal of the Royal Meteorological Society, 138 (662). pp. 222-233. ISSN 1477-870X doi: 10.1002/qj.898

Abstract/Summary

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society