A Seamless Multilevel Ensemble Transform Particle Filter
Abstract
This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter. The algorithm uses a combination of optimal coupling transformations between coarse and fine ensembles in difference estimators within a multilevel framework, to minimize estimator variance. It differs from that of Gregory, Cotter, and Reich [SIAM J. Sci. Comput., 38 (2016), pp. A1317--A1338] in that strong coupling between the coarse and fine ensembles is seamlessly maintained during all stages of the assimilation algorithm, instead of using independent transformations to equal weights followed by recoupling with an assignment problem. This modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside evidence of asymptotic consistency, in numerical examples.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A2684 - A2701
DOI: 10.1137/16M1102021
ISSN (online): 1095-7197
Copyright
© 2017, Society for Industrial and Applied Mathematics. This work is licensed under a Creative Commons Attribution 4.0 International License
History
Submitted: 3 November 2016
Accepted: 20 June 2017
Published online: 28 November 2017
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Funding Information
Natural Environment Research Council https://doi.org/10.13039/501100000270
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