## 3 Results and Discussion (Numerical Example)
The difference in the point location is illustrated by the resultant linear discrepancy (\(\delta_{XYZ}\)), which assumes values from about 3 mm to about 5 mm. The values demonstrate the impact of the classical measurements on the adjustment of the GNSS vector network (this order of differences in coordinates can be significant when the absolute ground displacements are measured, for example). Note also the mean errors of the coordinates (\(m_{X}\), \(m_{Y}\), \(m_{Z}\)) and the error of position (\(m_{P}\)). They are almost identical for both variants. This might be indicative of the correctness of equations of the pseudo-observation mean errors (9) and (10), always assuming that both the procedures employed similar observation weighting principles. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multicolumn{4}{c}{**Coordinates of Points to Be Determined**} & \multicolumn{2}{c}{**Mean Error of Coordinates**} & \multicolumn{2}{c}{**Error of Position**} \\  & \multicolumn{2}{c}{**[m]**} & & & \multicolumn{2}{c}{**[m]**} & & \multicolumn{2}{c}{**[m]**} \\ \cline{2-10}  & \(X\) & \(Y\) & \(Z\) & \(m_{X}\) & \(m_{Y}\) & \(m_{Z}\) & \(m_{P}\) \\ \hline
3 & 3,871,866.8806 & 1,345,952.0287 & 4,870,461.5783 & 0.0017 & 0.0014 & 0.0015 & 0.0026 \\
4 & 3,871,874.0824 & 1,345,928.2179 & 4,870,462.4867 & 0.0016 & 0.0013 & 0.0015 & 0.0026 \\
5 & 3,871,875.6742 & 1,345,904.3947 & 4,870,467.6723 & 0.0027 & 0.0022 & 0.0024 & 0.0042 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Adjusted coordinates and mean errors (GNSS vector network). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Pseudo-Observation**} & \multicolumn{2}{c}{**Edge**} & \multicolumn{2}{c}{**Point No. 3**} & \multicolumn{2}{c}{**Point No. 4**} & \multicolumn{2}{c}{**Point No. 5**} & \multicolumn{2}{c}{**Absolute Term**} \\  & **From** & **To** & \(X\) & \(Y\) & \(Z\) & \(X\) & \(Y\) & \(Z\) & \(X\) & \(Y\) & \(Z\) & \(l\)**[m]** \\ \hline \multirow{4}{*}{_j-\(k\)_} & 5 & 6 & 0 & 0 & 0 & 0 & 0 & 0.574 & 0.569 & \(-0.589\) & \(-0.0081\) \\  & 5 & 4 & 0 & 0 & 0 & \(-0.065\) & 0.975 & \(-0.212\) & 0.065 & \(-0.975\) & 0.212 & \(-0.0080\) \\ \cline{2-10}  & 4 & 5 & 0 & 0 & 0 & \(-0.065\) & 0.975 & \(-0.212\) & 0.065 & \(-0.975\) & 0.212 & \(-0.0080\) \\ \cline{2-10}  & 4 & 3 & \(-0.289\) & 0.957 & \(-0.037\) & 0.289 & \(-0.957\) & 0.037 & 0 & 0 & 0 & \(-0.0002\) \\ \cline{2-10}  & 3 & 4 & \(-0.289\) & 0.957 & \(-0.037\) & 0.289 & \(-0.957\) & 0.037 & 0 & 0 & 0 & \(-0.0004\) \\  & 3 & 2 & 0.390 & \(-0.919\) & \(-0.064\) & 0 & 0 & 0 & 0 & 0 & \(0\) & \(-0.0015\) \\ \hline \multirow{4}{*}{_L-R_} & 6 & 4 & 0 & 0 & 0 & 0.282 & 0.851 & \(-0.443\) & 0 & 0 & 0 & \(-0.0019\) \\  & 5 & 3 & \(-0.180\) & 0.976 & \(-0.125\) & 0 & 0 & 0 & 0.180 & \(-0.976\) & 0.125 & \(-0.0126\) \\ \cline{1-1}  & 4 & 2 & 0 & 0 & 0 & 0.341 & \(-0.940\) & \(-0.014\) & 0 & 0 & 0 & \(-0.0019\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Coefficients at the unknowns (partial derivatives) and the absolute terms (13), (16) in the equations of corrections for the pseudo-observations (12), (15). For ground displacement monitoring, the relative positions of points (so-called relative displacement) are measured as well. Therefore, the adjusted coordinates (Tables 6 and 7) were used to calculate spatial distances between the points (Table 9). Despite differences of several millimetres in point coordinates (Table 8), the computed values are practically identical for both variants (the differences are below 1 mm in most cases). This fact may indicate cumulative GNSS survey errors (caused by antenna phase centre variations, for example). The calculated distances (Table 9) were juxtaposed with reference distances (\(d_{CL}\)), which were obtained from the additional precise (repeated several times) classical surveys: the horizontal distances were measured with a precise total station, and the height differences were measured using the precise geometric levelling method.