Measurement of the relative delay between signals propagating in a multipath environment

The problem of measuring the relative delay from a composite signal in additive noise is considered. The performance of standard autocovariance, nonlinear spectral analysis (cepstrum), and the delay-locked loop is analyzed and compared to the results of maximum a posteriori estimation. Comparison is based on: ability to detect a multipath situation, accuracy of the delay measurement, and resolution. Under conditions typically encountered in practice, cepstrum is shown to provide near optimum estimates. The relative ability of cepstrum and standard autocovariance to extract delay measurements is demonstrated by the results of an underwater experiment performed under conditions where the acoustic signal propagates along a direct and reflected path.