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Title: Deterministic Mean-Field Ensemble Kalman Filtering

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. In this paper, 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. Lastly, 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.
Authors:
 [1] ;  [2] ;  [2]
  1. King Abdullah Univeristy of Science and Technology (KAUST) SRI-UQ Center, Thuwal (Saudi Arabia); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. King Abdullah Univeristy of Science and Technology (KAUST) SRI-UQ Center, Thuwal (Saudi Arabia)
Publication Date:
Grant/Contract Number:
AC05-00OR22725; 32112580
Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; filtering; Fokker-Planck; EnKF
OSTI Identifier:
1311261

Law, Kody J. H., Tembine, Hamidou, and Tempone, Raul. Deterministic Mean-Field Ensemble Kalman Filtering. United States: N. p., Web. doi:10.1137/140984415.
Law, Kody J. H., Tembine, Hamidou, & Tempone, Raul. Deterministic Mean-Field Ensemble Kalman Filtering. United States. doi:10.1137/140984415.
Law, Kody J. H., Tembine, Hamidou, and Tempone, Raul. 2016. "Deterministic Mean-Field Ensemble Kalman Filtering". United States. doi:10.1137/140984415. https://www.osti.gov/servlets/purl/1311261.
@article{osti_1311261,
title = {Deterministic Mean-Field Ensemble Kalman Filtering},
author = {Law, Kody J. H. and Tembine, Hamidou and Tempone, Raul},
abstractNote = {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. In this paper, 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. Lastly, 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.},
doi = {10.1137/140984415},
journal = {SIAM Journal on Scientific Computing},
number = 3,
volume = 38,
place = {United States},
year = {2016},
month = {5}
}