On the convergence of a non-linear ensemble Kalman smoother

El Houcine Bergou, Serge Gratton, Jan Mandel

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume137
DOIs
StatePublished - Nov 29 2018

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