The estimation of subsample time delay of arrival in the discrete-time measurement of phase delay

Abstract

Time delay estimation (TDE) techniques based upon the identification of the extremum of the cross-correlation function, or some other statistic of two signals, typically use some form of interpolation between points to obtain a resolution finer than the sample period. Often these techniques introduce some bias because of mismatch between the interpolating function and the actual discrete-time correlation function. We present a discrete-time TDE suitable for measuring the delay between two periodic signals with a resolution of a fraction of the sampling period. The technique is based upon a separate reference, external to the two measured signals, which is allowed to vary with subsample increments of delay. Simulations show that the incremental reference technique does not exhibit any significant bias and is superior to parabolic interpolation at both high and low SNR. The technique is suited to the measurement of group-delay or range of an object.