Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Hakon Hoel (RWTH Aachen)
The ensemble Kalman filter (EnKF) is a Monte-Carlo-based sequential filtering method that is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of ensemble members/particles is high. I will present recent results [1, 2, 3] on marrying the multilevel Monte Carlo method with EnKF to obtain the multilevel ensemble Kalman filter (MLEnKF). The new method can be applied in the following filtering settings:
(I) finite-dimensional state space and discrete-time observations,
(II) infinite-dimensional state space and discrete-time, finite-dimensional observations.
Theoretical results and numerical evidence of the performance gain of MLEnKF over EnKF will be presented.
 H. Hoel, K. Law, and R. Tempone, Multilevel ensemble Kalman filtering, SIAM J. Numer. Anal. 54(3), 18131839, 2016.
 A. Chernov, H. Hoel, K. Law, F. Nobile, and R. Tempone, Multilevel ensemble Kalman filtering for spatio-temporal processes, arXiv:1710.07282, 2017.
 H. Hoel, G. Shaimerdenova, and R. Tempone, Multilevel Ensemble Kalman Filtering with local-level Kalman gains, arXiv:2002.00480, 2020.