A model-based Bayesian framework for sound source enumeration and direction of arrival estimation using a coprime microphone array

Coprime microphone arrays use sparse sensing to achieve greater degrees of freedom, while the coprimality of the microphone subarrays help resolve grating lobe ambiguities. The result is a narrow beam at frequencies higher than the spatial Nyquist limit allows, with residual side lobes arising from aliasing. These side lobes can be mitigated when observing broadband sources, as shown by Bush and Xiang [J. Acoust. Soc. Am. 138, 447-456 (2015)]. Peak positions may indicate directions of arrival in this case; however, one must first ask how many sources are present. In answering this question, this work employs a model describing scenes with potentially multiple concurrent sound sources. Bayesian inference is used to first select which model the data prefer from competing models before estimating model parameters, including the particular source locations. The model is a linear combination of Laplace distribution functions (one per sound source). The likelihood function is explored by a Markov Chain Monte Carlo method called nested sampling in order to evaluate Bayesian evidence for each model. These values increase monotonically with model complexity; however, diminished returns are penalized via an implementation of Occam's razor.