This report concerns the problem of estimating the time delay between the signals received at spatially separated sensors. Most of the approaches for time delay estimation employ the FFT (fast Fourier transform) averaging method to find the cross-correlation function of the prefiltered signals [1], while the algorithms discussed in this report are adaptive time-domain methods.
The PHAT (phase transform) [1] is implemented in the time domain in this report. The relevant adaptive inpleme- tations include the APHAT-1 (adaptive PHAT-1) and APHAT-2. The first one uses a simple recursive lewpass filter [2], while the second one uses the least-mean-squares (LMS) adaptive filter (3).
The performances of these methods are compared with other existing adaptive algorithms through computer simulations. It is shown that APHAT-1 and APHAT-2 are capable of tracking time-varying delay functions and very effective in reducing the effect of interfering tonals. The constraint on using the adaptive methods and the selection of time constant are also studied.