On the Convergence of a Non-linear Ensemble Kalman Smoother

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^p 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.

References in corpus (3)

• Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
• Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit
• 4DVAR by ensemble Kalman smoother

Cited by in corpus (5)

• Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
• 4DVAR by ensemble Kalman smoother
• A Langevinized Ensemble Kalman Filter for Large-Scale Static and Dynamic Learning
• A strongly convergent numerical scheme from Ensemble Kalman inversion
• Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case