Multiple speaker tracking with the Factorial von Mises-Fisher Filter

Multiple-target tracking with a microphone array is often addressed via the Bayesian filtering framework. For compact arrays, each source is represented by its direction-of-arrival (DOA), which evolves on the unit sphere. The unique topology of this space leads to analytical intractabilities that are often resolved via costly particle-based methods. In this paper, we derive a novel, deterministic inference algorithm called the von Mises-Fisher Filter (vMFF) for a dynamical system model defined on the sphere, and extend it to the multi-source scenario in the Factorial vMFF (FvMFF). We apply sensor fusion and probabilistic data association techniques to handle clutter and data association ambiguities in the observation set. We show that the vMFF combines the computational efficiency of a Kalman filter with the tracking accuracy of a particle filter to perform well across all noise levels. Finally, we apply the FvMFF to track multiple speakers in a reverberant environment.