Doubly Stochastic Poisson Processes PDF Download

The optimal adaptive estimator structures for a class of doubly stochastic Poisson processes (DSPP) are presented. The structure is used along with a moment assumption to obtain implementable estimators. The class of DSPP considered is that of a linear Markov diffusion process modulating a linear intensity rate. The uncertainty for which the adaptation process is developed includes both structure uncertainty in the Markov diffusion process, and parameter uncertainty in the Markov diffusion process and the intensity rate process. Results are given on the problem of adaptation of which of a finite number of Markov realizations is modulating the intensity process. The nonlinear adaptive estimator structures are obtained by use of a particular theorem that yields an optimal structure for the adaptive estimator. The structure is used to obtain a quasi-optimal adaptive estimator for the problem by use of a zero third central moment assumption. The estimator structure consists of a nonlinear, nonadaptive part, and a nonlinear, adaptive part which contains the parameter structure adaptations.