Sound-source position tracking from direction-of-arrival measurements: Application to distributed first-order spherical microphone arrays

Rendering 6-degrees-of-freedom (6DoF) spatial audio requires sound-source position tracking. Without further assumptions, directional receivers, such as a spherical microphone array (SMA), can estimate the direction of arrival (DoA), but not reliably estimate sound-source distance. By utilizing multiple, distributed SMAs, further methods are available that directly infer the position in 3-D space. Typically used DoA intersection by triangulation delivers problematically noisy estimates, therefore, statistical filters are better suited. In this study, we compare the performance of different DoA to position tracking strategies. DoA angles suffer from the well-known angle wrapping problem, which is especially problematic in Gaussian filters. However, these filters are attractive due to their low computational complexity. Using circular and spherical statistics, the non-linear extensions of the Kalman filter can be formulated to explicitly treat the discontinuity of DoA angles. Furthermore, we introduce a time adaptive regularization of the filter update by the instantaneous sound-field diffuseness estimate. An experiment with three first-order SMAs in a reverberant room shows an improved distance error compared to the mean DoA intersection baseline. The results highlight the importance of treating the angle wrapping and the stabilization when incorporating the sound-field diffuseness estimate.