ACOUSTIC IMAGING VIA EIGENDECOMPOSITION OF CROSS-SPECTRAL MATRIX WITH DIMENSIONALITY REDUCTION

This paper addresses the problem of identifying multiple sound sources using pressure signals measured by a microphone array. The proposed method leverages the eigenvalues and eigenvectors of the cross-spectral matrix (CSM) to match their theoretical model, as a function of source parameters, thereby estimating the locations and powers of multiple sound sources. The key innovation of this approach lies in reducing the parameter searching space to the zeros of only S+1 equations (S is the number of sources). This is made possible through two theoretical findings: (i) we derive an alternative S×S matrix from the M×M CSM (where M is the number of microphones and M≫S), such that it shares identical eigenvalues and equivalent eigenvectors; (ii) we demonstrate that only one eigenvalue and its corresponding eigenvector from this dimension-reduced matrix, rather than the entire set of eigenvalues and eigenvectors, can uniquely determine all sound source parameters. As a result, the proposed method provides an efficient and accurate solution for estimating the parameters of multiple sound sources with super-resolution, without the need for complex optimization procedures. The effectiveness of the approach is validated through both numerical simulations and experimental data.