## 5 Conclusions  
The aim of this paper is to present a conceivable approach for real-time, multiple sound source, synchronistical localization, separation, and reconstruction. Its performance regarding the processing of speech signals from the ST-CMDS dataset was investigated through simulations and experiments. The major conclusions of this study are as follows.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Sound Source** & **Error (m)** \\ \hline \(s_{1}\) & 0.14 \\ \(s_{2}\) & 0.11 \\ \(s_{3}\) & 0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Localization error of the experimental study performed with BW-MUSIC and DNNs.  
Figure 14: Localization results of the experimental study performed with BW-MUSIC and DNNs: (a) \(s_{1}\), (b) \(s_{2}\), and (c) \(s_{3}\).  
Figure 15: Original signals (a) and the reconstructed signals (b) in the experimental study: (1) \(s_{1}\), (2) \(s_{2}\), and (3) \(s_{3}\).  
1. By adopting the beamforming technique and denoising DNNs by numerical simulations and experimental studies, it is feasible to localize and separate the mixed multiple sound sources of speech signals in the time domain. The sound map of a DAS beamformer is formed by the superposition of the contributions of all sources in the sound field. Sources with lower SWLs may be masked by other sound sources with higher SWLs. Accordingly, compared with the traditional beamforming methods for multiple sound source localization, the proposed approach is quite suitable for a sound field containing a dominant sound source with masked weak sound sources, owing to the signal removal and virtual sound field reconstruction iteration. A decay rate higher than 60% could be an effective SNR range for the proposed method.  
2. The time-domain signals were estimated and denoised using the DAS beamformer with DNNs. However, in reality, the computational cost of the time-domain DAS beamformer is unsuitable for potential applications. Thus, the localization procedure in the proposed approach is improved by the BW-MUSIC method, which is more flexible for broadband speech signals with an adjustable operational speed in the frequency domain. In particular, the accuracy and resolution of the sound source locations are enhanced by the BW-MUSIC method. The sound sources are localized accurately with a location error less than 0.001 m in the numerical simulations, and 0.15 m in the experimental study. The temporal characteristics of the source signals are well-extracted from the measurement signals during simulations, yet the signal reconstruction performance in the experiments is worse because of the ground reflection of sound waves and background noise.  
3. The proposed approach could provide a potential criterion for determining whether a small hotspot in a beamforming map is the main lobe of a weaker source or the side lobe of a stronger source at another place, as each main sound source could be plotted on the beamforming map separately by iterations. This can be regarded as an alternative approach for source number estimation in a given sound field.  
L.C.: methodology, software, validation, formal analysis, data curation, and writing--original draft. G.C.: investigation, data curation, formal analysis, and writing--original draft. W.S.: supervision, conceptualization, and writing--review and editing. L.H.: funding acquisition, resources, and writing--review and editing. Y.-S.C.: writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This work was supported, in part, by the National Natural Science Foundation of China (NSFC) under Grants 62101335, U1713217, and 61925108; in part by the Natural Science Foundation of Guangdong under Grant 2021A1515011706, and in part by the Foundation of Shenzhen under Grant JCYJ20190808122005605.  
Not applicable.  
The authors would like to acknowledge the experimental support from [PERSON] and [PERSON] of SJTU.  
The authors declare no conflict of interest.