Feedback particle filter with mean-field coupling

A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory. The optimal control is chosen so that the posterior distribution of a particle matches as closely as possible the posterior distribution of the true state given the observations: This is achieved by introducing a cost function, defined by the Kullback-Leibler (K-L) divergence between the actual posterior, and the posterior of any particle.