On the convergence of a non-linear ensemble Kalman smoother

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...

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Bibliographic Details
Published inApplied numerical mathematics Vol. 137; pp. 151 - 168
Main Authors Bergou, El Houcine, Gratton, Serge, Mandel, Jan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2019
Elsevier
Subjects
[formula omitted] convergence
Computer Science
Ensemble Kalman filter/smoother
Kalman filter/smoother
Least squares
Levenberg–Marquardt method
Life Sciences
Mathematics
Levenberg–Marquardt method
Lp convergence
Kalman filter/smoother
Least squares
Ensemble Kalman filter/smoother
L-P convergence
Levenberg-Marquardt method
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Summary: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 Lp 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.
ISSN:0168-9274
1873-5460
0168-9274
DOI:10.1016/j.apnum.2018.11.008