Minimax filtering problems for observed poisson processes with uncertain rate functions

This paper treats the following decision problems for continuous-time systems with discontinuous observations (i.e., for systems observed through point processes): I. Robust matched filtering. II. Robust Wiener filtering III. Minimax state estimation for systems with noise uncertainty. In each case there is assumed to be some degree of uncertainty in the rate function of an observed Poisson process, and a corresponding minimax design philosophy is adopted. In Problem I we assume that the rate of the observation process is a deterministic function of time, and in Problems II and III we assume that these rates are wide-sense-stationary stochastic processes. General solutions to the three problems are considered in terms of least-favorable rate functions or processes, and several useful models of uncertainty are discussed in this context.