Multipole orthogonal beamforming combined with an inverse method for coexisting multipoles with various radiation patterns

Identification of sources with non-uniform radiation patterns is attracting considerable attention these years. A multipole beamforming algorithm combined with an inverse method, is proposed to detect coexisting multipoles with various radiation patterns. Positions and strengths of sources are estimated first. The sound field of each source is represented by the eigenvector of the cross-spectral matrix of microphone array signals. Source directivity is removed by the normalization and square operations on elements of the eigenvector. Each source is represented by spherical harmonics after source localization. Types and orientations of sources can be inferred from their reconstructed radiation patterns. The proposed algorithm is verified by numerical simulations and experiments using a loudspeaker and vortex shedding from a cylinder. Compared to existing multipole beamforming algorithms, it reduces the condition number of the transfer matrix and removes the spurious sources on source maps. Positions, types and orientations of sources are estimated more accurately. The resolution of source maps is comparable to that of CLEAN-SC.