Posterior probabilistic modeling for inter-channel phase and time difference estimation in audio signals

Abstract

A method is proposed for the estimation of the time difference of arrival (TDOA) from a sound source to a pair of microphones. Given noisy observations of the source, the magnitude spectrum of the source is first estimated via smoothing across time frames. Then, a probability density function (PDF) for the phase conditioned upon the magnitude is constructed based on the signal-to-noise ratio (SNR) at every frequency. Subsequently, the conditional PDF for the inter-channel phase difference (IPD) is calculated, and the computation can be accelerated via Gaussian curve fitting. Finally, by combining the information from all frequencies, the TDOA can be estimated in the maximum a posteriori (MAP) sense. Results from anechoic simulation showed that, at various SNRs (0 to 40 dB), the proposed method consistently produced more accurate estimation than the well known GCC-PHAT [1] and a recent method that was also based on IPD modeling [2]. Experiments conducted in an office environment are also reported, using speech and footsteps as test materials.