## 4 Results
### Evaluation of DGNSS and SPP Standard Deviation
Figure 3 shows the behaviour of the standard deviation for \(\Delta\)E, \(\Delta\)N and \(\Delta\)U sub-dataset of Single Point Positioning over the time and reports the R\({}^{2}\) values for the sub-datasets \(\Delta\)E, \(\Delta\)N and \(\Delta\)U. Regarding the SPP, unlike the DGNSS, it is possible to note a linear relationship between the standard deviations and observation times for all three sub-datasets. \(\Delta\)E and \(\Delta\)N have a strong relationship, with R\({}^{2}\) values equal to 0.92, 0.88, and \(\Delta\)U demonstrates a moderate relationship, with an R\({}^{2}\) = 0.68 [30]. The relationships between standard deviations and observation times are shown in Appendix B (Figures A4-A6). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Standard Deviations SPP**} \\ \hline
**Session Length (min)** & \(\Delta\)**E (m)** & \(\Delta\)**N (m)** & \(\Delta\)**U (m)** \\ \hline
5 & 1.67 & 2.16 & 6.02 \\
10 & 1.39 & 1.90 & 4.92 \\
15 & 1.29 & NTNV & 5.39 \\
30 & NTNV & 1.82 & 1.43 \\
60 & 0.79 & 1.55 & 1.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard deviations for SPP sub-datasets: \(\Delta\)E, \(\Delta\)N, \(\Delta\)U.  
Figure 2: Linear regression between DGNSS standard deviation and observation time. From Tables 7-9, we can evaluate the DGNSS mean positioning error. In particular, the minor Easting error (\(\Delta\)E\({}_{\text{Mm}}\) = 1.471 m) was obtained at 15 min for the sub-dataset \(\Delta\)E\({}_{\text{Mm}}\). This result suggests for \(\Delta\)E\({}_{\text{Mm}}\) non-dependency on the duration of observation times with the achievable error; in fact, it is possible to observe an error value of 1.875 m for an acquisition of 60 min.. This result is not consistent with what is expected in the GNSS measurements with topographic receivers. For the Easting coordinate, at 60 min, the greatest error was detected for \(\Delta\)E and \(\Delta\)E\({}_{\text{Mm}}\) and the lowest error was equal to 1.698 m for \(\Delta\)E\({}_{\text{Km}}\). For the North position, the lowest error was reached at 10 min for the subsets \(\Delta\)N and \(\Delta\)N\({}_{\text{Mm}}\) and was equal to 2.016, but also, in this case, for the 60-min acquisition, the error did not decrease (\(\Delta\)N and \(\Delta\)N\({}_{\text{Mm}}\) = 2.489 m). The lowest positioning error in the Up coordinate was obtained for 15 min for \(\Delta\)U\({}_{\text{Mm}}\) and \(\Delta\)U\({}_{\text{Km}}\) and was equal to 3.087 m, while at 60 min, the error was equal to 3.572 m for \(\Delta\)U\({}_{\text{Km}}\). This was also the minor Up error at 60 min between the three sub-datasets, while the greatest error at 60 min in Up was equal to 3.579 m for \(\Delta\)U\({}_{\text{Mm}}\) and \(\Delta\)U. Through the study of linear regressions between the means of all sub-datasets of the DGNSS positioning errors and the observation times, it is possible to note a general weak relationship with values of R\({}^{2}\) < 0.5, for the most part, of the sub-datasets. Only the sub-datasets \(\Delta\)E and \(\Delta\)E\({}_{\text{Km}}\) show a linear relationship between variables, with R\({}^{2}\) values equal to 0.64 (moderate relationship) and 0.85 (strong relationship), respectively (Figure 4).