Time delay estimation in the presence of source or receiver motion

Abstract

Generalized cross-correlation of the outputs of two spatially-separated sensors provides an estimate of the time delay (or differential time of arrival) of a broadband acoustic signal at the pair of sensors. The time lag at which the cross-correlation function attains its maximum value corresponds to the time delay. However, if relative motion between the source and the sensors leads to the time scales of the received signals being mismatched, then the time delay will be in error. This mismatch in the time scales is also referred to as the differential Doppler effect. Two practical examples are presented that demonstrate this effect, which is observed when a jet aircraft transits over and along the axis of two widely-spaced microphones or a scuba diver travels past two spatially separated hydrophones. It is shown that the correct time delay and relative time scale can be obtained by implementing wideband cross-correlation with differential Doppler compensation using the continuous wavelet transform. The continuous wavelet transform has the same functional form as the more familiar wideband cross-ambiguity function.