## 4 Results and Analysis
### Construction and Verification of Accuracy for the Dynamic Subsidence Basin  
The dynamic subsidence basin was constructed using DoD analysis, as shown in Figure 5a-e is the DOM for each period, Figure 5f-i is the time series subsidence map obtained by subtracting the DEM of two adjacent periods, Figure 5j-m is the cumulative time-series subsidence map obtained by subtracting 07.20, 09.07, 11.15, and 07.31, respectively, from 06.14; the outliers are shown in the white grids. In the cumulative time series subsidence map, as the working face advanced, the range of influence of the surface expanded accordingly, the maximum subsidence value increased gradually, and the range of the subsidence basin became closer to the center of the goat.  
Based on the total measured data for the station, the accuracy for the subsidence basin was verified by comparing the difference in elevation between the measured data on the monitoring point with the difference in elevation extracted from the UAV subsidence DEM.  
Figure 4: Histogram of the M3C2 distance: **(a)** LiDAR01.16\(-\)UAV06.14; **(b)** LiDAR01.16\(-\)UAV07.20; **(c)** LiDAR01.16\(-\)UAV09.07; **(d)** LiDAR01.16\(-\)UAV11.15; and **(e)** LiDAR01.16\(-\)UAV07.31.  
The mean error (ME), the mean absolute error (MAE), and the root mean square error (RMSE) may be calculated as follows:  
\[ME=\frac{1}{n}{\sum_{i=1}^{n}}(H-h) \tag{1}\]  
\[MAE=\frac{1}{n}{\sum_{i=1}^{n}}(|H-h|) \tag{2}\]  
\[RMSE=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}(H-h)^{2}} \tag{3}\]  
where \(H\) and \(h\) refer to the measured elevation difference and the elevation difference extracted from the subsidence DEM, respectively.  
The calculated results are presented in Table 4, and where the average error was small, being in the range \(\pm\)0.2 m. The RMSE was greatly affected by the abnormal value, and was generally greater than the average error and the average absolute error, most of which being between 0.2 m and 0.3 m. The minimum error was 0.17 m. Under the influence of time decoherence, the RMSE of the data with the larger time interval of 06.14 is larger, and the results of line A and line B for 07.31\(-\)06.14 are more than 0.3 m.  
Taking the intersection of line A and line B as the origin, the measured subsidence was compared with the subsidence for the monitoring points in the DEM, as shown in Figure 6. The subsidence curve extracted by the subsidence DEM was close to the measured subsidence curve, and the deviation was small near the maximum subsidence value. However, many jump points in the elevation may be observed in the subsidence value extracted by the subsidence DEM.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Data Set**} & \multicolumn{2}{c}{**Average Error (m)**} & \multicolumn{2}{c}{**Average Absolute Error (m)**} & \multicolumn{2}{c}{**Root Mean Square Error (m)**} \\ \cline{2-7}  & **Line A** & **Line B** & **Line A** & **Line B** & **Line A** & **Line B** \\ \hline (07.20\(-\)06.14 & \(-\)0.16 & \(-\)0.11 & \(-\)0.20 & 0.14 & 0.24 & 0.17 \\ 09.07\(-\)06.14 & \(-\)0.06 & \(-\)0.14 & 0.25 & 0.20 & 0.27 & 0.23 \\ 11.15\(-\)06.14 & 0.13 & \(-\)0.10 & 0.26 & 0.22 & 0.30 & 0.27 \\ 07.31\(-\)06.14 & 0.06 & \(-\)0.28 & 0.31 & 0.29 & 0.34 & 0.32 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of subsidence value error calculation between measured points and UAV extraction.  
Figure 6: Comparison of subsidence values about the monitoring points: (**a**) line A 07.20\(-\)06.14; (**b**) line A 09.07\(-\)06.14; (**c**) line A 11.15\(-\)06.14; (**d**) line A 07.31\(-\)06.14; (**e**) line B 07.20\(-\)06.14; (**f**) line B 09.07\(-\)06.14; (**g**) line B 11.15\(-\)06.14; and (**h**) line B 07.31\(-\)06.14.