Weighting function modification used for phase transform-based time delay estimation

Generalized cross-correlation is considered as the most straightforward time delay estimation algorithm. Depending on various weighting function, different methods were derived and a straightforward method, named phase transform (PHAT) has been widely used. PHAT is well-known for its robustness to reverberation and its sensitivity to noise, which is partly due to the fact that PHAT distributes same weights to the frequencies dominated by signal or noise. To alleviate this problem, two weighting functions are proposed in this paper. By taking a posteriori signal-to-noise ratio (SNR) into account to classify reliable and unreliable frequencies, different weights could be assigned. The first proposed weighting function borrows the idea of binary mask and distributes same weights to frequencies in same set, whereas, the second one assigns weights based on coherence function. Experiments showed the robustness of proposed methods to reverberation and noise for improving the performance of time delay estimation through various criteria.