# Sound Localization Framework for Construction Site Monitoring
## 5 Experiments
### Microphone Array Shape for 3D Localization  
At least four microphones were needed to localize sound sources in a 3D space. The triangular microphone array for the pilot localization test in 2D was used in two forms for 3D localization tests: a right-angled pyramidal array and a tetrahedral array [39]. The right-angled pyramidal array is the most common array configuration for localizing 3D sound sources (Figure 7) [40]. However, considering that the distance between the microphones is not uniform, the points are mainly in the space inside the pyramid, while errors occur in the space outside the array [40]. A tetrahedral array refers to a pyramidal volume surrounded by four triangular faces, where each triangular face of the tetrahedron is the same (Figure 8). The tetrahedral array overcomes the monitoring directionality shortcomings of the right-angled pyramidal array, as all directions can be monitored from the center point of the base triangle. In the right-angled pyramidal array tests, microphone 1 was used as the relative origin point, whereas microphones 2, 3, and 4 were placed at positions (0.00, 0.00, 0.00), (6.3, 0.00, 0.00), (0.00, 11.25, 0.00), and (\(-\)0.60, 0.00, 4.00), respectively (Table 3). Then, certain recorded sounds were played at (4.05, 7.65, 1.15). In the tetrahedral array tests, microphone 1 was used as the relative origin point (0.00, 0.00, 0.00), owing to the limited height of the laboratory, and microphones 2, 3, and 4 were placed at positions (5.40, 6.30, 0.00), (5.40, 6.30, 0.00), and (5.40, 3.125, 3.00), respectively (Table 4). Figure 7: Preliminary tests with a right-angled pyramidal array. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **x (m)** & **y (m)** & **z (m)** & **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& \\ \hline Source & 2.25 & 4.50 & 1.40 & & & & & & & & & \\
1 & 2.58 & 4.48 & 1.20 & 0.33 & 0.02 & 0.20 & 0.09 & 2 & 2.70 & 4.40 & 1.34 & 0.40 \\
2 & 2.70 & 4.40 & 1.34 & 0.45 & 0.10 & 0.06 & 0.09 & 2.70 & 4.40 & 1.34 & 0.40 \\
3 & 2.34 & 4.22 & 1.93 & 0.09 & 0.28 & 0.53 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\
4 & 2.80 & 4.35 & 1.02 & 0.55 & 0.15 & 0.38 & 0.05 & 0.03 & 0.03 & 0.03 & 0.03 \\
5 & 2.47 & 4.01 & 0.76 & 0.22 & 0.49 & 0.64 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\
6 & 2.21 & 5.13 & 1.69 & 0.04 & 0.63 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\
7 & 3.12 & 4.47 & 1.20 & 0.87 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\
8 & 2.57 & 4.36 & 1.05 & 0.32 & 0.14 & 0.35 & 0.03 & 0.03 & 0.03 \\
9 & 2.09 & 4.15 & 1.27 & 0.16 & 0.35 & 0.13 & 0.03 & 0.03 & 0.03 \\
10 & 2.05 & 4.06 & 1.56 & 0.20 & 0.44 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\  & \multicolumn{3}{c}{Average} & & 0.32 & 0.26 & 0.29 & 0.03 & 0.03 & 0.03 & 0.03 \\ \hline \end{tabular}
\end{table} 
Table 4: Preliminary test results with the tetrahedral arrangement. Figure 8: Preliminary tests with tetrahedral arrangements. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **x (m)** & **y (m)** & **z (m)** & **\& **\& **\& **\& **\& **\& **\& **\& **\& **\& \\ \hline Source & 4.05 & 7.65 & 1.15 & & & & & & \\
1 & 3.39 & 8.33 & 1.64 & 0.66 & 0.68 & 0.49 & 0.41 & 0.41 \\
2 & 3.66 & 8.42 & 0.24 & 0.39 & 0.77 & 0.91 & 0.45 & 0.03 & 0.03 \\
3 & 3.67 & 8.36 & 0.00 & 0.38 & 0.71 & 0.15 & 0.03 & 0.03 & 0.03 \\
4 & 4.15 & 7.96 & 1.59 & 0.10 & 0.31 & 0.03 & 0.03 & 0.03 & 0.03 \\
5 & 3.94 & 7.89 & 1.32 & 0.11 & 0.24 & 0.17 & 0.03 & 0.03 & 0.03 \\
6 & 3.66 & 7.90 & 1.64 & 0.39 & 0.25 & 0.15 & 0.03 & 0.03 & 0.03 \\
7 & 4.21 & 8.10 & 1.25 & 0.16 & 0.45 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\
8 & 3.85 & 7.92 & 1.09 & 0.20 & 0.27 & 0.03 & 0.03 & 0.03 & 0.03 \\
9 & 4.07 & 8.15 & 1.17 & 0.02 & 0.50 & 0.03 & 0.03 & 0.03 & 0.03 \\
10 & 3.55 & 6.76 & 2.29 & 0.50 & 0.89 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\  & \multicolumn{3}{c}{Average} & & 0.32 & 0.26 & 0.29 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\ \hline \end{tabular}
\end{table} 
Table 3: Preliminary test results with the right-angled pyramidal arrangement.