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Methods and Algorithms for Scientific Computing

Multilevel Ensemble Transform Particle Filtering

Abstract

This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.

Keywords

  1. multilevel Monte Carlo
  2. sequential data assimilation
  3. optimal transport

MSC codes

  1. 65C05
  2. 62M20
  3. 93E11
  4. 93B40
  5. 90C05

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A1317 - A1338
ISSN (online): 1095-7197

History

Submitted: 3 September 2015
Accepted: 22 February 2016
Published online: 3 May 2016

Keywords

  1. multilevel Monte Carlo
  2. sequential data assimilation
  3. optimal transport

MSC codes

  1. 65C05
  2. 62M20
  3. 93E11
  4. 93B40
  5. 90C05

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