Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 54, Issue 3, Pages 1813-1839Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M100955X
Keywords
Monte Carlo; multilevel; filtering; Kalman filter; ensemble Kalman filter
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Funding
- King Abdullah University of Science and Technology (KAUST)
- ORNL LDRD Strategic Hire grant
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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.
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