An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation   in nonlinear dynamical systems
  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. 
Mamatha Venugopal, Ram Mohan Vasu and Debasish Roy
stat.ME