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 τ of the intensity λ(t-τ) of an inhomogeneous Poisson process N_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_t, given X and τ. 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