An optimal control approach to particle filtering

Abstract

We present a novel particle filtering framework for the continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows for reformulating the estimation problem over a fixed time window into an optimal control problem. The resulting optimal control problem has a cost function that depends on the measurements, and the closed-loop dynamics under optimal control coincides with the posterior distribution over the trajectories for the corresponding estimation problem. By recursively solving these optimal control problems approximately as new measurements become available, we obtain an optimal control based particle filtering algorithm. Our algorithm uses path integrals to compute the weights of the particles and is thus termed the path integrals particle filter (PIPF). A distinguishing feature of the proposed method is that it uses the measurements over a finite-length time window instead of a single measurement for the estimation at each time step, resembling the batch methods of filtering, and improving fault tolerance. The efficacy of our algorithm is illustrated with several numerical examples.