On the convergence of a non-linear ensemble Kalman smoother

El Houcine Bergou (1, 2, 3) , Serge Gratton (4, 5) , Jan Mandel (6, 7, 8)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
2 Université Paris Saclay (COmUE)
3 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
4 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
5 ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications
6 University of Colorado [Boulder]
7 Institute of Computer Science
8 IRIT-APO - Algorithmes Parallèles et Optimisation

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.

Mots clés: Levenberg-Marquardt method; Least squares; Kalman filter/smoother; Ensemble Kalman filter/smoother; L-P convergence

Domaines: Mathématiques [math]; Informatique [cs]; Sciences du Vivant [q-bio]

El Houcine Bergou, Serge Gratton, Jan Mandel. On the convergence of a non-linear ensemble Kalman smoother. Applied Numerical Mathematics, 2019, 137, pp.151-168. ⟨10.1016/j.apnum.2018.11.008⟩. ⟨hal-02618742⟩