Deterministic mean-field ensemble Kalman filtering

Kody J.H. Law, Hamidou Tembine, Raul Tempone

Research output: Contribution to journalArticle

Abstract

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598-631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

Original languageEnglish (US)
Pages (from-to)A1251-A1279
JournalSIAM Journal on Scientific Computing
Volume38
Issue number3
DOIs
StatePublished - 2016

Keywords

  • EnKF
  • Filtering
  • Fokker-planck

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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