Gridless covariance matrix fitting methods for three dimensional acoustical source localization

Abstract

In this article, we consider gridless source localization based on the spatial covariance matrix of acoustical data collected by an array of microphones. Covariance matrix fitting problems are formulated in infinite-dimensional settings, and solved by the Sliding Frank–Wolfe algorithm. The proposed method does not impose any constraint on the geometry of the array, the propagation model or the domain of interest, and does not necessitate a training phase. It is tested on simulated and experimental measurements for the localization of sources in a three-dimensional domain. Performances are compared to the state of the art, showing in particular a better resolution than MUSIC (MUltiple SIgnal Classification) at low SNR.