The Kalman-Bucy filter revisited: Mean-field equations & duality
Kalman and Bucy derived their famous filtering equations for time-continuous linear systems from the perspective of optimal estimation. Their approach has now been largely superseded by the Bayesian perspective and the Kushner-Stratonovitch equation in particular. In this talk, I will report on two recent developments: (i) Mean field SDE formulations for the Kushner-Stratonovitch equations which maintain the important gain times innovation structure of the Kalman-Bucy filter even under nonlinear filtering problems. (ii) Return of the dual estimation perspective in the form of an optimal control problem over a set of forward-backward SDEs.