Set-valued nonlinear estimation using the Galerkin approximation

A set-valued state estimator for nonlinear dynamic systems is presented. The estimator uses the Galerkin approximation to solve Kolmogorov's equation for the diffusion of a continuous-time, continuous-state nonlinear system, as well as for implementing discrete time updates of noisy measurements. This filtering of the state is accomplished for a convex set of distributions simultaneously, and a functional representation of the set of resulting means is provided at any desired time instance.