This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
|Original language||English (US)|
|Number of pages||27|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Jun 14 2016|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research was supported by King Abdullah
University of Science and Technology (KAUST). The authors were members of the SRI Center for
Uncertainty Quantification at KAUST for much of the research reported.