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.
@article{0a3f7225504c44998c12b28cd89a89b8,
title = "Deterministic mean-field ensemble Kalman filtering",
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.",
keywords = "EnKF, Filtering, Fokker-planck",
author = "Law, {Kody J.H.} and Tembine Hamidou and Raul Tempone",
year = "2016",
month = "1",
day = "1",
doi = "10.1137/140984415",
language = "English (US)",
volume = "38",
pages = "A1251--A1279",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

TY - JOUR

T1 - Deterministic mean-field ensemble Kalman filtering

AU - Law, Kody J.H.

AU - Hamidou, Tembine

AU - Tempone, Raul

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - EnKF

KW - Filtering

KW - Fokker-planck

UR - http://www.scopus.com/inward/record.url?scp=84976902222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976902222&partnerID=8YFLogxK

U2 - 10.1137/140984415

DO - 10.1137/140984415

M3 - Article

AN - SCOPUS:84976902222

VL - 38

SP - A1251-A1279

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -