Two-dimensional multiple-snapshot grid-free compressive beamforming

Abstract

Abstract Compressive beamforming with planar microphone arrays can effectively achieve the two-dimensional direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. This paper focuses on developing a multiple-snapshot grid-free method and comparing it against the existing grid-based and single-snapshot grid-free ones. The minimization of the atomic norm of multiple-snapshot microphone pressure induced by acoustic sources and the matrix pencil and pairing method are utilized jointly. The former is utilized to denoise the measured pressure and therefore obtain the pressure from acoustic sources. The latter is utilized to estimate DOAs and quantify strengths. Both simulations and experiments demonstrate the advantages of the developed method. For sources that are active across multiple snapshots, it can overcome the basis mismatch conundrum of the grid-based compressive beamforming. When the sources are uncorrelated or partially correlated in both spatial and temporal dimensions, it outperforms the single-snapshot grid-free compressive beamforming in terms of denoising, DOA estimation and strength quantification accuracy and resolution. These advantages stand up whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is utilized.