Discrete time filters for doubly stochastic Poisson processes and other exponential noise models

The well-known Kalman filter is the optimal filter for a linear Gaussian st ate-space model. Furthermore, the Kalman filter is one of the few known fin ite-dimensional filters. In search of other discrete-time finite-dimensiona l filters, this paper derives filters for general linear exponential state- space models, of which the Kalman filter is a special case, One particularl y interesting model for which a finite-dimensional filter is found to exist is a doubly stochastic discrete-time Poisson process whose rate evolves as the square of the state of a linear Gaussian dynamical system. Such a mode l has wide applications in communications systems and queueing theory. Anot her filter, also with applications in communications systems, is derived fo r estimating the arrival times of a Poisson process based on negative expon entially delayed observations. Copyright (C) 1999 John Wiley & Sons, Ltd.