Second-order accurate ensemble transform particle filters

Acevedo, W., de Wiljes, J. and Reich, S. (2017) Second-order accurate ensemble transform particle filters. SIAM Journal on Scientific Computing, 39 (5). A1834-A1850. ISSN 1095-7197 doi: 10.1137/16M1095184

Abstract/Summary

Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) (S.~Reich, {\it A non-parametric ensemble transform method for Bayesian inference}, SIAM J.~Sci.~Comput., 35, (2013), pp. A2013--A2014) replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second-order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter (NETF) arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/70180
Identification Number/DOI	10.1137/16M1095184
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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