Arrival Time Estimation by Adaptive Thresholding

Arrival time estimation by adaptive thresholding is described. The probability density of arrival time is derived for differentiable Markov processes. The special case of additive, stationary noise is given particular attention. A direct derivation of the probability density of arrival time for pulses with sharply rising edges is given for arbitrary noise. The results are applied to the Gaussian and Rice distributions. Comparison with the Cramer-Rao bound of estimation theory indicates the asymptotic optimality of adaptive thresholding in the latter two cases.