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.

MSC codes

  1. multilevel Monte Carlo
  2. optimal transport
  3. particle filters

MSC codes

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

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A2684 - A2701
ISSN (online): 1095-7197


Submitted: 3 November 2016
Accepted: 20 June 2017
Published online: 28 November 2017

MSC codes

  1. multilevel Monte Carlo
  2. optimal transport
  3. particle filters

MSC codes

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



Funding Information

Natural Environment Research Council https://doi.org/10.13039/501100000270

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