On the convergence of a non-linear ensemble Kalman smoother

0498774 - ÚI 2020 RIV NL eng J - Journal Article
Bergou, E. - Gratton, S. - Mandel, Jan
On the convergence of a non-linear ensemble Kalman smoother.
Applied Numerical Mathematics. Roč. 137, March (2019), s. 151-168. ISSN 0168-9274. E-ISSN 1873-5460
R&D Projects: GA ČR GA13-34856S
Institutional support: RVO:67985807
Keywords : Ensemble Kalman filter/smoother * Kalman filter/smoother * Lp convergence * Least squares * Levenberg–Marquardt method
OECD category: Statistics and probability
Impact factor: 1.979, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.apnum.2018.11.008

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.
Permanent Link: http://hdl.handle.net/11104/0291049