Abstract: When solving the cross-spectral matrix by the matrix completion algorithm based on nuclear norm minimization (NNM) model in the non-synchronous measurements of sound source localization, the singular values are given the same weights, and the prior knowledge of the singular values is ignored. For the deficiency of NNM model, the alternating direction method of multipliers (ADMM) and the accelerated proximal gradient (APG) algorithms based on weighted nuclear norm minimization (WNNM) are proposed to complete the cross-spectral matrix with missing data in non-synchronous measurement of sound source localization, and finally complete the sound source localization. The matrix completion algorithms based on WNNM can better solve the non-convex and non-smooth low rank minimization problem, which assigns weights adaptively on different singular values. The algorithms based on WNNM and NNM are compared under the numerical simulation and experiment of different frequencies and SNRs. The results show that the matrix completion algorithms based on WNNM have higher matrix completion accuracy, and the results of non-synchronous measurement based on WNNM can effectively reduce the main lobe, suppress the sidelobes and improve the spatial resolution of the array under low SNRs.

Key words: non-synchronous measurement, matrix completion, sound source localization, weighted nuclear norm minimization