  Despite the numerous applications that may be expeditiously modelled by
counting processes, stochastic filtering strategies involving Poisson-type
observations still remain somewhat poorly developed. In this work, we propose a
Monte Carlo stochastic filter for recursive estimation in the context of
linear/nonlinear dynamical systems with Poisson-type measurements. A key aspect
of the present development is the filter-update scheme, derived from an
ensemble approximation of the time-discretized nonlinear filtering equation,
modified to account for Poisson-type measurements. Specifically, the additive
update through a gain-like correction term, empirically approximated from the
innovation integral in the filtering equation, eliminates the problem of
particle collapse encountered in many conventional particle filters. Through a
few numerical demonstrations, the versatility of the proposed filter is brought
forth, first with application to filtering problems with diffusive or
Poisson-type measurements and then to an automatic control problem wherein the
extremization of the associated cost functional is achieved simply by an
appropriate redefinition of the innovation process.
