An Ensemble Kalman-Bucy filter for correlated observation noise

Abstract

In this talk we aim to derive an Ensemble Kalman–Bucy filter (EnKBF) for continuous time filtering problems, where the signal and the observation noise are correlated.  

To achieve this goal we first characterize a large class of mean-field diffusion processes, that give a consistent representation of the desired posterior distribution.  A kinetic interpretation of these processes is discussed.  Next we use this representation to derive an EnKBF for the correlated noise framework.

We then discuss bounds for the (empirical) covariance matrix of both the EnKBF and its mean-field limit, that can be used to establish the well-posedness of these equations.  

Finally we discuss the convergence of the EnKBF to its mean-field limit.