# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 3 Results and Analysis
DTMs generated from the measurement dataset and from the reduction datasets were assumed as reference models. The speed of DTM generation was also calculated. Additionally, the speed of DTM generation is given. For processing, a computer with processor: Intel Core i7-11800H, RAM size [GB]: 32, disk: 2000 GB SSD, and graphics card: NVIDIA GeForce RTX 3080 was used. Calculated RMSEs and speeds are presented in Table 3.  
The highest RMSE was recorded for 2%_DTMv.1, and the lowest for 30%_DTMv.1. As is also clear from the considerations presented above, the accuracy of a DTM is always characterized by a single value if it is generated by existing methods or compared with another model. The differences in RMSE between versions v.1 and v.2 can be attributed to several factors. Firstly, the quality and resolution of the data used in each version may impact the accuracy of the results. Version v.1 utilized a higher-resolution DTM, resulting in a lower RMSE. Secondly, the differences in algorithms introduced in v.2 may have improved performance in some cases while degrading it in others. In the case of a DTM using sequential estimation, \(m_{0}\) is given in each sequence. Therefore, based on the characteristics file, it can be concluded that the variability of accuracy characteristics of the DTM is expressed in each fragment of the area with a different value. We believe this is the right approach because in each fragment of the area, a different number of points is used to build the DTM. The processing times for both variants were comparable and, as expected, decreased with smaller datasets. Existing methods for DTM creation generate the coordinates of the grid nodes and then give one value of the accuracy calculated from the average height of the entire terrain. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variant** & \multicolumn{2}{c}{**v.1**} & \multicolumn{2}{c}{**v.2**} \\ \hline
**Reference DTM** & **RMSE [m]** & **Speed [s]** & **RMSE [m]** & **Speed [s]** \\ \hline
100\%\_DTM & 0.104 & 480 & 0.098 & 398 \\
50\%\_DTM & 0.051 & 160 & 0.074 & 154 \\
30\%\_DTM & 0.041 & 135 & 0.043 & 126 \\
10\%\_DTM & 0.052 & 71 & 0.103 & 63 \\
2\%\_DTM & 0.121 & 36 & 0.099 & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSE and speed characteristics. It does not take into account the situation in which the number of points is very small in some places. An example situation is presented in Figure 8. There are only six points in area A and 350 points in area B. The generated DTMs in these areas cannot be described with the same value of the accuracy parameter. A much more accurate model will be generated for area B than for area A. In order to verify and compare the results, the following additional study was performed:  
1. One hundred points were selected from the original ALS dataset and datasets after applying the OptD method;
2. The measuring strips in which individual points are located were determined;
3. The parameters \(a_{0}\), \(a_{1}\), \(a_{2}\) were found (from the characteristics file) for the sequences in which these points were located;
4. The \(Z\) height of each point was calculated and compared with the height in the original ALS point cloud;
5. The height difference was calculated. The calculated differences are summarized in Table 4.  
The highest \(\Delta Z\) was noticed for the 10% point cloud in variant v.2, and the lowest for the 100% and 50% point clouds in the v.1 and v.2 variants, respectively. Thus, all of them are within the limits 0.010-0.825 m. Such results prove that the characteristics file stores the correct parameters in the individual sequences and the heights obtained from the characteristics file meet the assumptions of the method.