Acoustic smart sensor networks can provide valuable actionable intelligence to authorities for managing safety in the urban environment. A spatial filter (beamformer) for localization and separation of acoustic sources is a key component of such a network. However, classical methods such as delay-and-sum beamforming fail, because sources are located at varying distances from the sensor array. This causes a regularization problem where either far-away sources are wrongly attenuated, or noise is wrongly amplified.
We solve this by considering source strength and location as random variables. The posterior distributions are approximated using Gibbs sampling. Each marginal is computed by combining importance sampling and inverse transform sampling using Chebyshev polynomial approximation. This leads to an iterative algorithm with similarities to deconvolution beamforming.Our method is robust against deviations in manifold model, can deal with sources at different distances and power levels, and does not require an a priori known number of sources.