TIME-DELAY ESTIMATION FOR FILTERED POISSON PROCESSES USING AN EM-TYPEALGORITHM

In this paper, we develop a modified EM algorithm to estimate a nonran dom time shift parameter of an intensity associated with an inhomogene ous Poisson process N(t), whose points are only partially observed as a noise-contaminated output X of a linear time-invariant filter excite d by a train of delta functions-A filtered Poisson process. The exact EM algorithm for computing the maximum likelihood time shift estimate generates a sequence of estimates each of which attempt to maximize a measure of similarity between the assumed shifted intensity and the co nditional mean estimate of the Poisson increment dN(t). We modify the EM algorithm by using a linear approximation to this conditional mean estimate. The asymptotic performance of the modified EM algorithm is i nvestigated by an asymptotic estimator consistency analysis. We presen t simulation results that show that the linearized EM algorithm conver ges rapidly and achieves an improvement over conventional time-delay e stimation methods, such as linear matched filtering and leading edge t hresholding. In these simulations our algorithm gives estimates of tim e delay whose mean square error virtually achieves the CR lower bound for high count rates.