Asynchronous measurement sound source localization method based on truncated nuclear norm joint Lp norm minimization under low signal-to-noise ratio

• This paper proposes an innovative improved truncated nuclear norm joint Lp norm minimization model. • An asynchronous measurement sound source localization is proposed based on truncated nuclear norm and Lp norm minimization. • This paper integrates Lp norm into truncated nuclear norm minimization and uses ADMM to solve the objective function. • For the non-convex sub-problem, a weighted L2 norm approximation is incorporated into the ADMM iteration process. In the context of asynchronous measurement for sound source localization, the completion method relying on the truncated nuclear norm minimization framework faces certain limitations when it comes to processing low SNR signals. Noise can disrupt the algorithm’s accurate estimation of small singular values, leading to the formation of sidelobes. To address this challenge, this paper puts forward an asynchronous measurement sound source localization method that combines truncated nuclear norm and Lp norm minimization. This approach integrates the Lp norm into the existing truncated nuclear norm minimization strategy and uses the Alternating Direction Method of Multipliers (ADMM) algorithm to solve the objective function. For the non-convex sub-problem that contains the Lp norm, a weighted L2 norm approximation technique is introduced and incorporated into the ADMM iteration process. After completing the cross-spectral matrix using this matrix completion technique, the traditional beamforming method is employed to achieve asynchronous measurement sound source localization. To verify the superiority and effectiveness of this method, simulations and experiments of sound source localization are performed under different SNR and frequency conditions. The imaging performances of multiple algorithms are compared. The findings show that the asynchronous measurement approach for locating sound sources, which is based on the combination of truncated nuclear norm and Lp norm minimization, performs better than other models in low-SNR scenarios. This method is capable of significantly shrinking the main lobe, curbing the sidelobes, and boosting the spatial resolution.