Deterministic mean-field ensemble Kalman filtering

Kody J.H. Law, Tembine Hamidou, 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 - Jan 1 2016

    Fingerprint

    Ensemble Kalman Filter
    Kalman Filtering
    Kalman filters
    Mean Field
    Ensemble
    Approximation
    Mean-field Limit
    Nonlinear filtering
    Random Measure
    Nonlinear Filtering
    Quadrature Rules
    Order of Convergence
    State-space Model
    Total Variation
    Fidelity
    Nonlinearity
    Filter
    Metric
    Numerical Results
    Term

    Keywords

    • EnKF
    • Filtering
    • Fokker-planck

    ASJC Scopus subject areas

    • Computational Mathematics
    • Applied Mathematics

    Cite this

    Deterministic mean-field ensemble Kalman filtering. / Law, Kody J.H.; Hamidou, Tembine; Tempone, Raul.

    In: SIAM Journal on Scientific Computing, Vol. 38, No. 3, 01.01.2016, p. A1251-A1279.

    Research output: Contribution to journalArticle

    Law, Kody J.H. ; Hamidou, Tembine ; Tempone, Raul. / Deterministic mean-field ensemble Kalman filtering. In: SIAM Journal on Scientific Computing. 2016 ; Vol. 38, No. 3. pp. A1251-A1279.
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