Abstract
We introduce a new multilevel ensemble Kalman filter method (MLEnKF) which consists of a hierarchy of independent samples of ensemble Kalman filters (EnKF). This new MLEnKF method is fundamentally different from the preexisting method introduced by Hoel, Law and Tempone in 2016, and it is suitable for extensions towards multi-index Monte Carlo based filtering methods. Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity than plain vanilla EnKF in the large-ensemble and fine-resolution limits, for weak approximations of quantities of interest. The method is developed for discrete-time filtering problems with finite-dimensional state space and linear observations polluted by additive Gaussian noise.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 351-390 |
| Number of pages | 40 |
| Journal | Foundations of Data Science |
| Volume | 2 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2020 |
Bibliographical note
KAUST Repository Item: Exported on 2021-01-28Acknowledged KAUST grant number(s): URF/1/2584-01-01
Acknowledgements: This work was funded by the KAUST Office of Sponsored Research (OSR) under Award No. URF/1/2584-01-01; the Alexander von Humboldt Foundation; the Federal Ministry of Education and Research (BMBF) and the Ministry of Culture and Science of the German State of North Rhine-Westphalia (MKW) under the Excellence Strategy of the Federal Government and the Länder. G.Shaimerdenova and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.