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We introduce a new multilevel ensemble Kalman filter method (MLEnKF) whichconsists of a hierarchy of independent samples of ensemble Kalman filters(EnKF). This new MLEnKF method is fundamentally different from the preexistingmethod introduced by Hoel, Law and Tempone in 2016, and it is suitable forextensions towards multi-index Monte Carlo based filtering methods. Robusttheoretical analysis and supporting numerical examples show that underappropriate regularity assumptions, the MLEnKF method has better complexitythan plain vanilla EnKF in the large-ensemble and fine-resolution limits, forweak approximations of quantities of interest. The method is developed fordiscrete-time filtering problems with finite-dimensional state space and linearobservations polluted by additive Gaussian noise.

Multilevel Ensemble Kalman Filtering based on a sample average of independent EnKF estimators