Spectral Estimation of Time Delay for Dispersive and Non‐Dispersive Systems

SUMMARY The problem considered is that of measuring the delay between the receipt of a signal at two sites where noise, incoherent between the two sites and with the signal, is also received at each site. In the case where the signal is dispersive the delay will be a function of frequency. The optimum solution involves a proper weighting of the phase shifts at each frequency, the weighting being dependent only on the coherence. The asymptotic distribution of the estimate is given. The method is worked out in detail for various special cases and is illustrated by an oceanographic example. The case where there are more than two sites is briefly discussed. A discussion is also given of the virtues of the method, of some possible variations to it and of some practical considerations.