This article proposes a variational Bayesian (VB) inference based on the nonsynchronous array measurement (NAM) (VB-NAM) method in order to obtain the fast and robust localization of low-frequency acoustic sources. To enlarge the aperture size compared with the prototype array, the NAM is performed to measure the acoustic pressures with low-frequency based on the forward power propagation model. The implementation of the NAM can be reformulated into a cross-spectral matrix (CSM) completion problem. Then, to solve the inverse problem of the NAM power propagation model, the VB inference based on the Student-t priors and Kullback–Leibler (KL) divergence optimization is proposed. The advantages of the proposed VB-NAM benefit from the optimization of matrix inversion and adaptive estimation of regularization parameters. The contribution of the adaptive parameter evaluation is to reduce the impact of multiple interferences (such as additive noise and the matrix completion error) in NAM. Finally, both simulations at 800 Hz and experimental results at 1000 Hz are presented to show the validation of the proposed VB-NAM method, even under the anisotropic Gaussian noise conditions. Algorithm performance and iteration process are analyzed to demonstrate the efficiency and robustness.

中文翻译：

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一种快速稳健的低频声源定位方法：基于非同步阵列测量的变分贝叶斯推理

本文提出了一种基于非同步阵列测量 (NAM) (VB-NAM) 方法的变分贝叶斯 (VB) 推理，以获得快速、稳健的低频声源定位。与原型阵列相比，为了扩大孔径尺寸，基于前向功率传播模型，执行NAM以测量低频声压。NAM 的实现可以重新表述为交叉谱矩阵 (CSM) 完成问题。然后，为了解决NAM功率传播模型的逆问题，提出了基于Student-t先验和Kullback-Leibler（KL）散度优化的VB推理。所提出的 VB-NAM 的优点得益于矩阵求逆的优化和正则化参数的自适应估计。自适应参数评估的贡献是减少 NAM 中多重干扰（如加性噪声和矩阵完成误差）的影响。最后，800 Hz 的模拟和 1000 Hz 的实验结果都显示了所提出的 VB-NAM 方法的验证，即使在各向异性高斯噪声条件下也是如此。对算法性能和迭代过程进行了分析，以证明其效率和鲁棒性。