Learning techniques for feedback particle filter design

The feedback particle filter (FPF) is an approach to estimating the posterior distribution of the states in a process-observation model. As in other versions of the particle filter, Monte Carlo methods are used to generate and propagate a set of particles, based on the underlying model. The system is designed so that the empirical distribution of the particles approximates the posterior distribution. In contrast to other approaches, particles are propagated as a controlled system using a gain function that is similar in nature to the Kalman gain for linear Gaussian systems. The FPF gain is obtained as a solution to a version of Poisson's equation. Approximation techniques are required, since the FPF gain has no closed-form solution.