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Deterministic Mean-Field Ensemble Kalman Filtering

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/140984415· OSTI ID:1311261
 [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)
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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.
Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
ORNL LDRD Director's R&D; USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1311261
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 38; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (5)

Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation journal September 2019
Gaussian approximations of small noise diffusions in Kullback–Leibler divergence journal January 2017
Performance Analysis of Local Ensemble Kalman Filter journal March 2018
Ensemble Kalman Methods for High-Dimensional Hierarchical Dynamic Space-Time Models journal March 2019
Well posedness and convergence analysis of the ensemble Kalman inversion journal July 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
EnKF
Fokker-Planck
filtering