Recursive estimation from discrete-time point processes

Abstract

The paper presents models for discrete-time point processes (DTPP) and schemes for recursive estimation of signals randomly influencing their rates. Although the models are similar to the better known models of signals in additive Gaussian noise, DTPP differ from these in that it is possible for DTPP's to find recursive representations for the nonlinear filters. If the signal can be modeled as a finite state Markov process, then these representations reduce to explicit recursive finite-dimensional filters. The derivation of the estimation schemes, as well as the filters themselves, present a surprising similarity to the Kalman filters for signals in Gaussian noise. We present finally an application of the estimation schemes derived in the paper to the estimation of the state of a random time-division multiple access (ALOHA-type) computer network.