Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
SRI Uncertainty Quantification Center
Date
2016-05-03Online Publication Date
2016-05-03Print Publication Date
2016-01Permanent link to this record
http://hdl.handle.net/10754/608649
Metadata
Show full item recordAbstract
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 k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. 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.Citation
Deterministic Mean-Field Ensemble Kalman Filtering 2016, 38 (3):A1251 SIAM Journal on Scientific ComputingSponsors
This work was supported by the King Abdullah University of Science and Technology (KAUST) SRI-UQ Center.arXiv
1409.0628Additional Links
http://epubs.siam.org/doi/10.1137/140984415ae974a485f413a2113503eed53cd6c53
10.1137/140984415