Multichannel source separation and tracking with phase differences by random sample consensus

Blind audio source separation (BASS) is a fascinating problem that has been tackled from many different angles. The use case of interest in this thesis is that of multiple moving and simultaneously-active speakers in a reverberant room. This is a common situation, for example, in social gatherings. We human beings have the remarkable ability to focus attention on a particular speaker while effectively ignoring the rest. This is referred to as the ``cocktail party effect'' and has been the holy grail of source separation for many decades. Replicating this feat in real-time with a machine is the goal of BASS. Single-channel methods attempt to identify the individual speakers from a single recording. However, with the advent of hand-held consumer electronics, techniques based on microphone array processing are becoming increasingly popular. Multichannel methods record a sound field from various locations to incorporate spatial information. If the speakers move over time, we need an algorithm capable of tracking their positions in the room. For compact arrays with 1-10 cm of separation between the microphones, this can be accomplished by applying a temporal filter on estimates of the directions-of-arrival (DOA) of the speakers. In this thesis, we review recent work on BSS with inter-channel phase difference (IPD) features and provide extensions to the case of moving speakers. It is shown that IPD features compose a noisy circular-linear dataset. This data is clustered with the RANdom SAmple Consensus (RANSAC) algorithm in the presence of strong reverberation to simultaneously localize and separate speakers. The remarkable performance of RANSAC is due to its natural tendency to reject outliers. To handle the case of non-stationary speakers, a factorial wrapped Kalman filter (FWKF) and a factorial von Mises-Fisher particle filter (FvMFPF) are proposed that track source DOAs directly on the unit circle and unit sphere, respectively. These algorithms combine directional statistics, Bayesian filtering theory, and probabilistic data association techniques to track the speakers with mixtures of directional distributions