# A Combined Method for Localizing Two Overlapping Acoustic Sources Based on Deep Learning
## 4 Results and Discussion
The simulation results presented in Table 2 show that for certain samples (e.g., samples 2, 11, 13, and 15), the model predicted the same direction for both sources. In these cases, the predicted direction matched that of one of the actual sources, resulting in a correct prediction for one source and an incorrect one for the other. This type of error can be attributed to the relatively small size of the microphone array, which limits the discernible differences in amplitude and time delay between signals from different sources. As a result, applying the separation model to mixed source signals can impair the model's sensitivity to distinguishing between features associated with each individual source. The geometry of the microphone array plays a crucial role in resolving phase differences. Different configurations influence the array's ability to differentiate between signals arriving at various angles or with distinct phase shifts. While larger arrays and more \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample No.** & \(\theta_{1}\) & \(\hat{\theta_{1}}\) & \(\theta_{2}\) & \(\hat{\theta_{2}}\) & **SSR (dB)** & **PA (\%)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 2: Values of metric PA for each test sample containing source signals with different SSR values. complex geometries combined with beamforming preprocessing can lead to improved signal characterization and separation accuracy, our research was constrained by limitations in adapting large-scale microphone arrays to work in conjunction with the single-source localization model. In [26], it was shown that the size of the array has a similar effect on all the localization methods used, including the proposed method based on using the features of SI as input data, so that the localization performance deteriorates when the array size is either too small or too large. One reason is that the SI features are based on the finite difference of the acoustic pressure signals to approximate the particle velocity using an orthogonal microphone array. As a result, as the size of the array increases, the approximation error will increase accordingly, thus leading to poor SI estimation. On the other hand, if the array size is too small, the microphone array will exhibit poor noise sensitivity, especially at low frequencies [27]. It was also shown that the optimal range of array sizes for the proposed method is 2-5.5 cm. The GCC-PHAT-CNN approach, which utilizes GCC-PHAT features as input, showed significantly worse performance than comparable methods when using small arrays, but outperformed them with larger array sizes (approximately 40 cm). To maintain consistency with our method's requirements while ensuring good localization accuracy, we selected an intermediate array size of 20 cm for the final implementation. The features were extracted using STFT, which divides the audio signal into fixed-length time windows, treating each segment as a time-invariant signal. Due to its computational efficiency and straightforward implementation, STFT is widely adopted in audio signal processing. However, a key limitation is its fixed window size, which cannot optimally resolve all frequency components simultaneously. In contrast, the wavelet transform addresses this issue by employing variable time scales--inversely proportional to frequency--to better analyze different spectral components. While this adaptability improves frequency resolution, it comes at the cost of higher computational complexity. The integration of wavelet transform-based feature extraction with time-frequency masking targets (e.g., ideal ratio mask (IRM)) could improve the performance of the proposed approach. The source separation model was trained on 500 ms short-term signals to align with the raw audio length used in the single SSL model. In real-time scenarios where sources may move within the room, applying the localization model to short audio segments ensures timely updates to source directions, maintaining accuracy as positions change.