## 4 Results
### Evaluation of DGNSS and SPP Standard Deviation  
In this section, the standard deviations of the sub-dataset \(\Delta\)E, \(\Delta\)N, \(\Delta\)U are collected for the various observation times and evaluated through tables and, subsequently, by the application of the linear regression. In this way, it is possible to evaluate functional relationships between standard deviations and length of observation sessions. Table 5 summarises the standard deviations in relation to DGNSS session length positioning of the several sub-datasets. Figure 2 shows the behaviour of the standard deviation for \(\Delta\)E, \(\Delta\)N and \(\Delta\)U sub-dataset of DGNSS positioning over time and the R\({}^{2}\) values for the related sub-datasets. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**SPP Sub-Dataset Normality Test, Threshold Value: 0.05**} \\ \hline
**Normality Test** & \(\Delta\)**E** & \(\Delta\)**N** & \(\Delta\)**U** & \(\Delta\)**E\({}_{\text{Mm}}\)** & \(\Delta\)**N\({}_{\text{Mm}}\)** & \(\Delta\)**U\({}_{\text{Mm}}\)** & \(\Delta\)**E\({}_{\text{Km}}\)** & \(\Delta\)**N\({}_{\text{Km}}\)** & \(\Delta\)**U\({}_{\text{Km}}\)** \\ \hline \multirow{2}{*}{\(p\)-value 5 min} & 0.06 & 0.35 & 0.66 & 0.06 & 0.56 & 0.66 & 0.03 & 0.42 & 0.21 \\  & YES & YES & YES & YES & YES & YES & NO & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 10 min} & 0.05 & 0.34 & 0.32 & 0.05 & 0.34 & 0.78 & 0.07 & 0.02 & 0.02 \\  & YES & YES & YES & YES & YES & YES & YES & NO & NO \\ \hline \multirow{2}{*}{\(p\)-value 15 min} & 0.25 & 0.01 & 0.13 & 0.77 & 0.47 & 0.45 & 0.54 & 0.001 & 0.01 \\  & YES & NO & YES & YES & YES & YES & YES & NO & NO \\ \hline \multirow{2}{*}{\(p\)-value 30 min} & 0.02 & 0.36 & 0.39 & 0.21 & 0.90 & 0.39 & 0.11 & 0.09 & 0.11 \\  & NO & YES & YES & YES & YES & YES & YES & YES & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 60 min} & 0.06 & 0.13 & 0.51 & 0.19 & 0.74 & 0.24 & 0.05 & 0.74 & 0.24 \\  & YES & YES & YES & YES & YES & YES & YES & YES & YES & YES \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Normality test for Single Point Positioning error. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**DGNSS Sub-Dataset Normality Test, Threshold Value: 0.05**} \\ \hline
**Normality Test** & \(\Delta\)**E** & \(\Delta\)**N** & \(\Delta\)**U** & \(\Delta\)**E\({}_{\text{Mm}}\)** & \(\Delta\)**N\({}_{\text{Mm}}\)** & \(\Delta\)**U\({}_{\text{Mm}}\)** & \(\Delta\)**E\({}_{\text{Km}}\)** & \(\Delta\)**N\({}_{\text{Km}}\)** & \(\Delta\)**U\({}_{\text{Km}}\)** \\ \hline \multirow{2}{*}{\(p\)-value 5 min} & 0.03 & 0.16 & 0.42 & 0.03 & 0.16 & 0.30 & 0.03 & 0.14 & 0.14 \\  & NO & YES & YES & NO & YES & YES & NO & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 10 min} & 0.37 & 0.44 & 0.96 & 0.56 & 0.44 & 0.96 & 0.16 & 0.12 & 0.53 \\  & YES & YES & YES & YES & YES & YES & YES & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 15 min} & 0.04 & 0.59 & 0.01 & 0.08 & 0.59 & 0.82 & 0.03 & 0.61 & 0.82 \\  & NO & YES & NO & YES & YES & YES & NO & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 30 min} & 0.14 & 0.35 & 0.24 & 0.14 & 0.35 & 0.24 & 0.06 & 0.27 & 0.05 \\  & YES & YES & YES & YES & YES & YES & YES & YES & YES \\ \hline \multirow{2}{*}{\(p\)-value 60 min} & 0.31 & 0.35 & 0.18 & 0.31 & 0.35 & 0.18 & 0.09 & 0.26 & 0.15 \\  & YES & YES & YES & YES & YES & YES & YES & YES & YES \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Normality test for DGNSS positioning error. Observing Table 5 and Figure 2, it can be seen that there is a strong linear relationship between standard deviation DGNSS and observation time only for \(\Delta\)E (R\({}^{2}\) = 0.71) [30]. In Appendix A (Figures A1-A3), through the normal distributions, it is possible to evaluate the relationships between standard deviation and observation times. Table 6 summarises the standard deviations for all observations in SPP.