Multilevel Ensemble Kalman filtering for spatially extended models

Multilevel Ensemble Kalman filtering for spatially extended models

​Chernov, Alexey, Haakon Hoel, Kody Law, Fabio Nobile, and Raúl Tempone, "Multilevel Ensemble Kalman filtering for spatially extended models", arXiv preprint 1608.08558. To appear in Numerische Mathematik, 2020
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Alexey Chernov, Haakon Hoel, Kody Law, Fabio Nobile, Raúl Tempone
Monte Carlo, multilevel, filtering, Kalman filter, ensemble Kalman filter
2020
This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF), thereby yielding a multilevel ensemble Kalman filter (MLEnKF) which has provably superior asymptotic cost to a given accuracy level. The development of MLEnKF for finite-dimensional state-spaces in the work [20] is here extended to models with infinite-dimensional state- spaces in the form of spatial fields. A concrete example is given to illustrate the results.