Multiple Speaker Tracking Using Coupled HMM in the STFT Domain

We present a multi-microphone multi-speaker direction of arrival (DOA) tracking algorithm. In the proposed algorithm, the DOA values are discretized to a set of candidate DOAs. Accordingly, and following the W-disjoint orthogonality (WDO) property of the speech signal, each time-frequency (TF) bin in the short-time Fourier transform (STFT) domain is associated with a single DOA candidate. The conditional probability of each TF observation given its corresponding DOA association, is modeled as a multivariate complex-Gaussian distribution, with the power spectral density (PSD) of each source an unknown parameter. By applying the Fisher-Neyman factorization, it can be shown that this conditional probability is proportional to the signal-to-noise ratio (SNR) at the outputs of minimum variance distortionless response (MVDR)-beamformers (BFs), directed towards all candidate DOAs. We model these observations as either a frequency-wise parallel Hidden Markov Model (HMM) or as a coupled HMM with coupling between adjacent frequency bins. The posterior probability of these associations is inferred by applying an extended FB (FB) algorithm, and the actual DOAs can be inferred from this posterior. An experimental study demonstrates the benefits of the proposed algorithm using both a simulated dataset and real recordings drawn from the acoustic source localization and tracking (LOCATA) dataset.