## 5 Discussion  
By analyzing Figures 7-10, it can be seen that the far-field solution and the solution proposed in [29] give close results. According to the appropriate microphone aperture and source distance, the angle error value decreases below 0.5\({}^{\circ}\) with our proposed method. In Figure 7c, at 44.1 kHz sampling frequency, 0.5 m distance between microphones, and 100 m the sound source distance, the far-field solution and other methods produce an angular error of up to 3\({}^{\circ}\). In the same case, our proposed method produces an angular error of less than 0.5\({}^{\circ}\). By analyzing the result of Figure 11, while a significant degree measurement error occurs between 0-30 degrees in the far-field approach and proposed [29], our proposed method has the same stability at all angle values.  
When Figures 7b and 8b are analyzed together, it can be seen that for very close and very far source distances, the angle errors increase for both existing methods. In our proposed solution, there is no significant change in the angle errors, which shows that it produces more stable results against source distance variations. Figure 9 shows that the angle error decreases to 0.5\({}^{\circ}\) and below after \(d_{m}>0.2\) m and \(d_{k}>0.3\) m with our proposed solution.  
When Figures 7b and 10 are analyzed together, the angle errors decrease down to 0.1\({}^{\circ}\) with increasing sampling frequency; at low sampling frequencies, the angle errors in the other two methods increase excessively, while our proposed method has a very small increase compared to the others.  
When Figure 11 and Table 1 are analyzed together, our proposed solution for azimuth angle measurement produces more stable results against TDoA measurement errors in the 0\({}^{\circ}\)-90\({}^{\circ}\) angle range than the other two methods. The results are 41% better than the far-field method and 39.8% better than the other proposed method. When Figure 13 and Table 3 are analyzed for the elevation angle, the success of the three methods is close to each other.  
The far-field solution and the other proposed solution require algorithmic inference to determine the quadrant of the DoA. The studies in [21; 22; 23] used the tangent function, but they also used algorithmic inference to determine the quadrant. Our proposed solution  
Figure 17: MAE values of the elevation angle values calculated with experimental results with respect to explosion distance.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Distance** & **50 m** & **100 m** & **150 m** & **200 m** & **250 m** & **300 m** & **350 m** & **400 m** & **450 m** & **500 m** \\ \hline Shot1 & \(-1.92\) & \(-2.1\) & \(-1.26\) & \(-0.34\) & \(-0.14\) & \(-0.24\) & \(0.54\) & \(0.40\) & \(0.14\) & \(0.15\) \\ Shot2 & \(-2.47\) & \(-1.86\) & \(-1.07\) & \(-0.34\) & \(0.19\) & \(-0.34\) & \(0.50\) & \(0.11\) & \(-0.25\) & \(0.39\) \\ Mean & \(-2.19\) & \(-1.98\) & \(-1.17\) & \(-0.34\) & \(0.03\) & \(-0.29\) & \(0.52\) & \(0.25\) & \(-0.05\) & \(0.27\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: MAE values of experimental elevation angle results with respect to explosion distance.  
produces the correct quadrant result along with the angle information. This eliminates the additional computational cost and provides fast and accurate results.  
The field test results support the simulation results. When Tables 4-6 are analyzed, while some TDoA values have errors greater than three samples, the largest azimuth measurement error obtained was less than 3.5\({}^{\circ}\). When analyzing Tables 7 and 8 for the elevation angle, the largest measurement error obtained was 3.26\({}^{\circ}\). These results were within the limits obtained in the simulation studies.