## 4 Simulation
### Influence of SNR  
The performance of different methods under noise interference was further studied to explore whether the methods have practical application value. The RMSEL and RMSEM of the sound source identification results of the methods under different SNRs are shown in Figure 6, and the average errors are shown in Table 2.  
Figure 6: Identification error statistics of the methods at different SNRs for the frequency of 500 Hz. (**a**) RMSEL. (**b**) RMSEM. Under the influence of noise, the identification errors of the FISTA and off-grid-\(\text{GL}_{1}\) methods increase significantly due to the difficulty in reasonably selecting regularization parameters. OMP selects the basis with the highest correlation with the residuals in each iteration and updates it into the support matrix. If two sources are closely correlated, OMP will select one source and overestimate its strength. This also causes OMP to easily select the wrong basis vector under intense noise, leading to higher source identification errors. SBL and RPCA-SBL perform the best in comparison, and VG-SBL performs better than OMP. VG-SBL can obtain the most accurate sound source localization and strength estimation results in the whole SNR range, and its sensitivity to noise is significantly lower than traditional methods. When the SNR is 10 dB and above, RMSEL and RMSEM can be maintained within 0.1 m and 3.5 dB, respectively. On the one hand, during the iterative process, the initial grid points dynamically approximate the real sound source location under the constraints of the sparse Bayesian learning framework. On the other hand, the low-rank Gaussian mixture model effectively removes the influence of noise. The Impact of Microphone Arrays  
In practical applications, it is sometimes difficult to arrange a large microphone array for measurement. Therefore, the impact of the number of microphones and array aperture on the identification performance of the method is further studied to explore whether the method has practical application value. On the basis of the original array, the outermost rings are removed in turn to reduce the number of microphones and reduce the array aperture. The compared array is shown in Figure 7, which contains five arrays. The number of microphones is reduced from 193 to 45, and the aperture is reduced from 4 m to 1.2 m. The RMSEL and RMSEM of the sound source identification results of each method under different microphone arrays are shown in Figure 8.  
As shown in Figure 8, when the number of microphones decreases and the aperture of the microphone array decreases, the sound source identification errors of different methods all have an obvious upward trend. The reason for this phenomenon is that when the array aperture decreases, the resolution performance will be significantly reduced. Resolution refers to the ability of the algorithm to distinguish the minimum distance between sound sources that are close to each other. According to the Rayleigh criterion, the minimum resolvable source distance can be given by the following formula [60]:  
\[Resolution=\alpha\frac{z\lambda}{D} \tag{30}\]  
where \(\alpha\) is a constant, which is 1.44 for the circular array, \(z\) is the measurement distance, \(\lambda\) is the wavelength of the sound signal, and \(D\) is the aperture of the microphone array. It can be seen that for the problem of far-field, low-frequency sound source identification, due to the large values of \(z\) and \(\lambda\), \(Resolution\) increases, while increasing the array aperture helps enhance the resolution performance of low-frequency sound sources. In addition, the spatial aliasing effect must also be considered. Spatial aliasing occurs when the signal is not fully sampled in space. One way to reduce spatial aliasing is to perform spatial sampling at intervals not exceeding half a wavelength. Therefore, the number of microphones should not be too small.