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Phase-Domain Statistical Analysis for Audio Source Localization

We consider the problem of estimating the time-difference-of-arrival (TDOA) for audio source localization in noisy environments, defining a framework for statistical analysis in the phase domain which enables more reliable estimates. This is motivated by the fact that with complex sources, noise, and interfering signals, different frequency bands have significantly different signal-to-noise ratios, creating non-uniform distributions of errors in the phase measurements. Through a new method for analysis of the variations of the phase in frequency windows, we first estimate the signal-to-noise ratio for frequency, and then use it in a maximum-likelihood estimation of the time difference of arrival. We show that this corresponds to a generalization of the Phase Transform method (PHAT), and provides a theoretical justification of why it works so well. Numerical results show how the proposed technique compares favorably with PHAT.