Semi-supervised source localization on multiple manifolds with distributed microphones

The problem of single-source localization with ad hoc microphone networks in noisy and reverberant enclosures is addressed in this paper. A training set is formed by prerecorded measurements collected in advance and consists of a limited number of labelled measurements, attached with corresponding positions, and a larger number of unlabelled measurements from unknown locations. Further information about the enclosure characteristics or the microphone positions is not required. We propose a Bayesian inference approach for estimating a function that maps measurement-based features to the corresponding positions. The signals measured by the microphones represent different viewpoints, which are combined in a unified statistical framework. For this purpose, the mapping function is modelled by a Gaussian process with a covariance function that encapsulates both the connections between pairs of microphones and the relations among the samples in the training set. The parameters of the process are estimated by optimizing a maximum likelihood criterion. In addition, a recursive adaptation mechanism is derived, where the new streaming measurements are used to update the model. Performance is demonstrated for both simulated data and real-life recordings in a variety of reverberation and noise levels.