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A hybrid particle ensemble Kalman filter is developed for problems withmedium non-Gaussianity, i.e. problems where the prior is very non-Gaussian butthe posterior is approximately Gaussian. Such situations arise, e.g., whennonlinear dynamics produce a non-Gaussian forecast but a tight Gaussianlikelihood leads to a nearly-Gaussian posterior. The hybrid filter starts byfactoring the likelihood. First the particle filter assimilates theobservations with one factor of the likelihood to produce an intermediate priorthat is close to Gaussian, and then the ensemble Kalman filter completes theassimilation with the remaining factor. How the likelihood gets split betweenthe two stages is determined in such a way to ensure that the particle filteravoids collapse, and particle degeneracy is broken by a mean-preserving randomorthogonal transformation. The hybrid is tested in a simple two-dimensional(2D) problem and a multiscale system of ODEs motivated by the Lorenz-`96 model.In the 2D problem it outperforms both a pure particle filter and a pureensemble Kalman filter, and in the multiscale Lorenz-`96 model it is shown tooutperform a pure ensemble Kalman filter, provided that the ensemble size islarge enough.

A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity