Maximum likelihood time-of-arrival estimation of optical pulses via photon-counting photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. In systems utilizing photon-counting photodetectors, which are finding increased use, the detected process is well modeled as a Poisson point process. In this paper, we analyze the performance of maximum likelihood (ML) estimators of the arrival time of an optical pulse, based on observations of a Poisson process. We develop an analytic model for the mean-square error of the ML estimator, illustrating two phenomena that cause deviations from the Cramer-Rao bound at low signal photon flux. The model accurately predicts the ML performance over all regimes considered. We also derive an approximation to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time.