A fast local maximum likelihood estimator for time delay estimation

A fast algorithm for the local Maximum Likelihood determination of the difference of arrival time of a common signal at two spatially separated sensors with uncorrelated noise is given. The fast algorithm consists of locally maximizing the crosscorrelation function from the two wideband signals by using Newton´s method for finding the root of an equation. The probability density function of one iteration of Newtons method is explicitly computed in terms of exponential and error functions. Using a theorem by S.O Rice on the probability density of local maxima of Gaussian processes, the probability density of the local maxima of the crosscorrelator is obtained.