The least squares estimation of time delay and its use in signal detection

This paper examines the use of two spatially separated receivers to determine the presence of a distant signal source and its relative bearing. Ideally, the phase shift between the receivers´ output is proportional to the frequency with the time delay between outputs equal to the proportionality constant. Because of noise, the plot of phase against frequency is scattered along a straight line whose slope is the time delay. A least squares estimator of the slope turns out to be equivalent to the maximum likelihood estimator developed by Hamon and Hannan [1]. Since the goodness of fit of the least squares line is a function of the coherence between the receivers´ output, the sum of the squared errors is used as a test statistic in detection. The proposed detector has a detection threshold that depends only on the probability of false alarm and not on the ambient noise level. It can also be simply extended to an array of receivers.