Risk sensitive filtering with Poisson process observations

In this paper we consider risk sensitive filtering for Poisson process obse rvations. Risk sensitive filtering is a type of robust filtering which offe rs performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dyna mics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral eq uations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter.