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.