Improved penalized beamforming using Hilbert curves for sound source identification with a microphone array

Abstract Conventional beamforming (CBF) algorithm for sound source identification based on microphone arrays have defects such as wide main lobe and numerous high side lobes. To improve the sound source identification performance and computational efficiency, this paper proposes an improved penalty beamforming algorithm based on the Hilbert curves (H-PBF) for microphone arrays. The proposed algorithm utilizes the peak value of the CBF output, normalizes the beam output to construct a penalty matrix, computes the Hadamard product of the penalty matrix and the weighted matrix, adjusts the steering vector weight, and then calculates the output. Moreover, the proposed algorithm uses the Hilbert curve traversal of the focus plane, which optimizes the grid point search strategy to increase the computational efficiency. Additionally, the locality and fixed-point properties of the Hilbert curve enable it to reduce the errors between the steering vectors. The simulations and experimental results show that the proposed algorithm has a narrow main lobe and low side lobes, which significantly improves the spatial resolution and dynamic performance of the CBF algorithm. Compared with the CBF, the proposed algorithm increases the computational efficiency by approximately 3.5 times while effectively increasing the localization accuracy and the accuracy of identifying the sound pressure level of the estimated sound source. In an experiment on identifying the sound source of a compressed gas leak, the proposed algorithm produced clear imaging results and accurately located the leakage source, indicating its promising engineering application prospects as a high-performance sound source identification technology based on microphone arrays.