The generalized correlation method for estimation of time delay

TLDR

Prefilters accentuate high‑S/N frequencies and suppress noise, a function also achieved by the generalized Eckart filter that maximizes the correlator’s S/N ratio. The authors develop a maximum‑likelihood estimator to determine time delay between signals received at two spatially separated sensors amid uncorrelated noise. The estimator is implemented as two receiver prefilters feeding a cross correlator and is benchmarked against other similar processors. The delay estimate is the correlator’s peak time, and the estimator matches Hannan–Thomson and MacDonald–Schultheiss models under certain conditions and reduces to Eckart prefiltering at low S/N.

Abstract

A maximum likelihood (ML) estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise. This ML estimator can be realized as a pair of receiver prefilters followed by a cross correlator. The time argument at which the correlator achieves a maximum is the delay estimate. The ML estimator is compared with several other proposed processors of similar form. Under certain conditions the ML estimator is shown to be identical to one proposed by Hannan and Thomson [10] and MacDonald and Schultheiss [21]. Qualitatively, the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and, simultaneously, to suppress the noise power. The same type of prefiltering is provided by the generalized Eckart filter, which maximizes the S/N ratio of the correlator output. For low S/N ratio, the ML estimator is shown to be equivalent to Eckart prefiltering.