Modified State Coherence Transform to reduce spatial aliasing in TDOA estimation of multiple sound sources

As an approach to multiple sound sources localization, Time Difference Of Arrival (TDOA)-based methods have been widely explored. In the last decade, many algorithms have been studied for the estimation of the TDOA using the formulation of Blind Source Separation (BSS). In this paper, to estimate the TDOAs, we focus on the State Coherence Transform (SCT) that is resulted from BSS analysis. For multiple sound sources localization, maximum likelihood TDOA estimations can be found by searching the peaks of SCT function. We show that the spatial aliasing occurs in high frequency bands may change the correct position of the SCT peaks. In the proposed method, called Modified SCT (MSCT), this problem is solved by considering a maximum for frequency range where spatial aliasing does not occur and neglecting higher frequencies. The MSCT method reduces the amplitude of wrong peaks and increases the accuracy of TDOA estimation. Since the MSCT also reduces the amplitude of true local maxima in the noisy environments, in the next step we propose Weighted SCT (WSCT) by weighting the frequency range that cause spatial aliasing. In this way, the amplitude of wrong local maxima is reduced without noticeable attenuation of correct peaks and loss of useful information from high frequency band. The evaluation results in terms of estimation error demonstrate the effectiveness of the proposed MSCT and WSCT methods.