Deterministic MeanField 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. 598631] is extended to nonGaussian statespace models. In this paper, a densitybased deterministic approximation of the meanfield 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/nonGaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
 Authors:

 King Abdullah Univeristy of Science and Technology (KAUST) SRIUQ Center, Thuwal (Saudi Arabia); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 King Abdullah Univeristy of Science and Technology (KAUST) SRIUQ Center, Thuwal (Saudi Arabia)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1311261
 Grant/Contract Number:
 AC0500OR22725; 32112580
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; filtering; FokkerPlanck; EnKF
Citation Formats
Law, Kody J. H., Tembine, Hamidou, and Tempone, Raul. Deterministic MeanField Ensemble Kalman Filtering. United States: N. p., 2016.
Web. doi:10.1137/140984415.
Law, Kody J. H., Tembine, Hamidou, & Tempone, Raul. Deterministic MeanField Ensemble Kalman Filtering. United States. doi:10.1137/140984415.
Law, Kody J. H., Tembine, Hamidou, and Tempone, Raul. Tue .
"Deterministic MeanField Ensemble Kalman Filtering". United States. doi:10.1137/140984415. https://www.osti.gov/servlets/purl/1311261.
@article{osti_1311261,
title = {Deterministic MeanField 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. 598631] is extended to nonGaussian statespace models. In this paper, a densitybased deterministic approximation of the meanfield 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/nonGaussianity 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}
}
Web of Science
Works referencing / citing this record:
Ensemble Kalman Methods for HighDimensional Hierarchical Dynamic SpaceTime Models
journal, March 2019
 Katzfuss, Matthias; Stroud, Jonathan R.; Wikle, Christopher K.
 Journal of the American Statistical Association
Ensemble Kalman Methods for HighDimensional Hierarchical Dynamic SpaceTime Models
journal, March 2019
 Katzfuss, Matthias; Stroud, Jonathan R.; Wikle, Christopher K.
 Journal of the American Statistical Association