Low-Frequency Sound Source Localization Algorithm for Small-Aperture AVSA Under Nonuniform Noise Scenarios

For low-frequency source localization with small aperture acoustic array, we propose a high-resolution localization algorithm based on complex Wishart prior. The algorithm, named Wishart-CSM-SBL, employs vectorized cross-spectral matrix (CSM) preprocessing and performs parameter updating within the sparse Bayesian learning (SBL) framework. Existing SBL algorithms struggle to capture the complex correlations between non-adjacent columns of the dictionary set in small aperture, low-frequency scenarios, often resulting in failed signal recovery. To solve this problem, the Wishart-CSM-SBL algorithm introduces the complex Wishart distribution and develops novel priors for sparse signal and noise. Specifically, the sparse signal is characterized by a two-layer prior model comprising complex Gaussian and complex Wishart distributions. By capturing the intricate correlations among the columns of the dictionary set, this modeling approach significantly improves the accuracy and robustness of sparse recovery. The complex Wishart distribution is employed to represent the noise with unknown structure, addressing the performance degradation in existing algorithms that assume noise with uniform variance. This is achieved by accounting for noise in-homogeneity and correlation. In addition, a two-dimensional off-grid solution is extended to eliminate localization errors caused by coarse grid division. Finally, simulations verify that the algorithm outperforms existing algorithms for small aperture arrays and low-frequency sources scenarios.