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 state-space model. Furthermore, the Kalman filter is one of the few known finite-dimensional filters. In search of other discrete-time finite-dimensional filters, this paper derives filters for general linear exponential state-space models, of which the Kalman filter is a special case. One particularly 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 model has wide applications in communications systems and queueing theory. Another filter, also with applications in communications systems, is derived for estimating the arrival times of a Poisson process based on negative exponentially delayed observations. Copyright © 1999 John Wiley & Sons, Ltd.

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