On the convergence of a non-linear ensemble Kalman smoother

El Houcine Bergou, Serge Gratton, Jan Mandel

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Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.
Original languageEnglish (US)
Pages (from-to)151-168
Number of pages18
JournalApplied Numerical Mathematics
StatePublished - Nov 29 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Partially supported by the U.S. National Science Foundation under the grant DMS-1216481, the Czech Science Foundation under the grant 13-34856S and the Fondation STAE project ADTAO.


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