Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters

Understand

In this article we consider the development of an unbiased estimator for the ensemble Kalman--Bucy filter (EnKBF).

• The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter.
• Our unbiased estimators will be motivated from recent work [Rhee \& Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators.
• The randomization enters through both the level of discretization, and through the number of samples at each level.