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

TL;DR

This paper introduces a hybrid particle-ensemble Kalman filter designed for problems with medium non-Gaussianity, combining particle filtering and ensemble Kalman filtering to improve data assimilation in nonlinear systems.

Contribution

A novel hybrid filtering method that splits the likelihood to effectively handle medium non-Gaussian problems, avoiding particle collapse and degeneracy.

Findings

Outperforms pure particle filter in 2D problem

Outperforms pure ensemble Kalman filter in Lorenz-`96 model

Effective in systems with medium nonlinearity and non-Gaussianity

Abstract

A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal 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 pure ensemble Kalman filter, and in the multiscale Lorenz-`96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.