Multiple Sound Source Localization Based on Stochastic Modeling of Spatial Gradient Spectra

We propose source localization methods for multiple sound sources. The proposed method requires only an observation of a sound pressure and its spatial gradient at one fixed point, which can be realized by a small microphone array. The key idea is to utilize the partial differential equation relating the observed signals and the source position, which was originally proposed for the direct method for the single source localization problem. We extend this framework using stochastic modeling and proposed a method for the mutliple source localization in the presence of noises. Two source localization methods are proposed: one is the expectation-minimization algorithm for a given number of sources, and the other is the variational Bayesian inference for an unknown number of sources. By numerical experiments, the localization accuracies of the two proposed methods are compared with the baseline method.