Analysis of the GCC-PHAT technique for multiple sources

Techniques to estimate the time delay of arrival (TDOA) using the measurements of the acoustic signals by microphones have been studied in various fields such as the robot auditory system, teleconference system and speech recognition system. One common method of determining TDOA is to compute the cross correlation function. The Generalized Cross Correlation (GCC) method, which calculates the correlation function by using inverse Fourier transformation of the cross power spectral density function multiplied by the proper weighting function, was proposed by Knapp and Cater in 1976. This method analyzed the weighting functions to estimate the optimal TDOA for a single source. In this paper, we derived the cross correlation function by GCC method with PHAT weighting function for multiple sources and ascertained the relationship between the correlation value and source characteristics. Moreover, we compared the derived GCC function for two sources case with the real GCC function calculated by the actual signals and verified their similarity.