Time delay estimation for filtered Poisson processes using an EM-type algorithm

A modified expectation-maximization (EM) algorithm is used to estimate the time delay tau of the intensity lambda (t- tau ) of an inhomogeneous Poisson process N/sub t/, whose points are only partially observed as a noise contaminated output X(t) of a linear time-invariant filter excited by a train of delta functions: a filtered Poisson process. A modified EM algorithm is implemented by using a linear approximation to the conditional mean estimate of the increment dN/sub t/, given X and tau . Simulation results showing that the EM algorithm converges rapidly, that it achieves an improvement over conventional time delay estimation methods, and that its mean square error virtually achieves the Cramer-Rao (CR) lower bound for high count rates are presented.<
>