Multilevel Ensemble Kalman Filtering with local-level Kalman Gains

Multilevel Ensemble Kalman Filtering with local-level Kalman Gains

Hoel, Håkon, Gaukhar Shaimerdenova, and Raúl Tempone, "Multilevel Ensemble Kalman Filtering with local-level Kalman Gains", arXiv preprint 2002.00480
Håkon Hoel, Gaukhar Shaimerdenova, Raúl Tempone
Stochastic differential and integral equations, Complexity and performance of numerical algorithms
2020
We introduce a new multilevel ensemble Kalman filtering method (MLEnKF) which consists of a hierarchy of samples of the ensemble Kalman filter method (EnKF) using local-level Kalman gains. This new MLEnKF method is fundamentally different from the preexisting method introduced by Hoel, Law and Tempone in 2016, and it is also 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 asymptotically, in the large-ensemble and small-numerical-resolution limit, for weak approximations of quantities of interest than EnKF. The method is developed for discrete-time filtering problems with a finite-dimensional state space and partial, linear observations polluted by additive Gaussian noise.