Performance of GCC- and AMDF-based time-delay estimation in practical reverberant environments

Recently, there has been an increased interest in the use of the time-delay estimation (TDE) technique to locate and track acoustic sources in a reverberant environment. Typically, the delay estimate is obtained through identifying the extremum of the generalized cross-correlation (GCC) function or the average magnitude difference function (AMDF). These estimators are well studied and their statistical performance is well understood for single-path propagation situations. However, fewer efforts have been reported to show their performance behavior in real reverberation conditions. This paper reexamines the GCC- and AMDF-based TDE techniques in real room reverberant and noisy environments. Our contribution is threefold. First, we propose a weighted cross-correlation (WCC) estimator in which the GCC function is weighted by the reciprocal of AMDF. This new method can sharpen the peak of the GCC function, which corresponds to the true time delay and thus leads to a better estimation performance as compared to the conventional GCC estimator. Second, we propose a modified version of the AMDF (MAMDF) estimator in which the delay is determined by jointly considering the AMDF and the average magnitude sum function (AMSF). Third, we compare the performance of the GCC, AMDF, WCC, and MAMDF estimators in real reverberant and noisy environments. It is shown that the AMDF estimator can yield better performance in favorable noise conditions and is slightly more resilient to reverberation than the GCC method. The GCC approach, however, is found to outperform the AMDF method in strong noisy environments. Weighting the correlation function by the reciprocal of AMDF can improve the performance of the GCC estimator in reverberation conditions, yet its improvement in noisy environments is limited, The MAMDF algorithm can enhance the AMDF estimator in both reverberant and noisy environments.