# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 3 Results and Analysis
Given that existing methods generate points on grid nodes, while the method based on sequential estimation defines the model as a mathematical function, the heights of points on the DTM generated using sequential estimation were calculated to correspond to the points at grid nodes of the DTM from the existing method. Following the algorithm presented in Figure 6, the heights of points (node equivalents) were determined for DTM generated using the principles of the new concept. This algorithm can be stored and utilized to determine characteristics at any point within the object. For instance, the algorithm can be read from a file in a Python v. 3.11 program and subsequently invoked to calculate its characteristics or to generate a grid of points using it. Figure 5: ALS point clouds representing the ground after applying the OptD method. The DTMs were generated with a grid size of 5.0 m so that the grid size was smaller than the measuring strip widths when calculating the function parameters for the sequential estimation method. In Figure 7, the generated DTMs are presented. Then, the height differences \(\Delta Z\) between the heights \(Z\) (from the new concept) and \(Z\) (from the nearest neighbors method grid interpolation) were calculated. Table 2 summarizes the calculated absolute values of \(\Delta Z\) (only minimum, maximum, and mean values are given). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Variant**} & \multicolumn{2}{c}{**v.1**} & \multicolumn{2}{c}{**v.2**} \\ \hline \multicolumn{2}{c}{**Percentage of Points**} & \multicolumn{4}{c}{\(\Delta Z\) **[m]**} \\ \cline{2-7}
**in Dataset** & **Min** & **Max** & **Mean** & **Min** & **Max** & **Mean** \\ \hline
100\% & 0.000 & 1.115 & 0.051 & 0.000 & 1.375 & 0.073 \\
50\% & 0.000 & 0.538 & 0.051 & 0.000 & 1.132 & 0.073 \\
30\% & 0.000 & 0.541 & 0.053 & 0.000 & 0.816 & 0.070 \\
10\% & 0.001 & 0.602 & 0.062 & 0.000 & 1.125 & 0.083 \\
2\% & 0.001 & 0.590 & 0.086 & 0.001 & 1.137 & 0.123 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(\Delta Z\) characteristics for differential DTMs. Figure 6: Scheme for generating \(Z\) height values from a characteristics file. Figure 7: DTMs: (**a**) existing method—the nearest neighbor method, (**b**) DTMs based on points calculated using a Python program after applying the new concept—v.1, (**c**) DTMs based on points calculated using a Python program after applying the new concept—v.2. When analyzing the height differences between the nearest neighbors method model and the model created with new concept, higher values were observed for the model in the variant v.2. However, there were also points where the heights were the same (min values). In models generated from all points (100%), the greatest height differences were observed (1.115 m for the variant v.1, 1.375 m for the variant v.2). Focusing on the \(\Delta Z\) values in variant v.1, it is observed that these values are generally smaller compared to those in variant v.2. This indicates that variant v.1 of the generated models exhibits a higher degree of similarity to DTMs produced using the established method. To assess whether the height differences (\(\Delta Z\)) between DTMs generated using sequential estimation and the reference nearest neighbor method are statistically significant, a statistical significance test was performed. A non-parametric Wilcoxon signed-rank test was used [44]. The test results indicate a \(p\)-value of 0.0625, suggesting that the differences are not statistically significant at the conventional \(\alpha=0.05\) level, but they are close to the threshold of significance. Additionally, a 95% confidence interval for the mean difference was calculated, indicating a small but consistent deviation between the two methods. These findings suggest that while differences exist, they may not be substantial enough to significantly impact the overall accuracy of the DTM. In the next stage of results verification, the RMSEs for the DTMs based on the new concept were calculated.