## 3 Results and Discussion (Numerical Example)  
The proposed method for adjusting an integrated network was verified with a simple practical example (Figure 5b). Calculations were performed for a GNSS vector network (without classical linear-angular observations, Figure 5a) as well, to compare the results. The test calculations involved actual survey results for a section of a control network for monitoring ground displacement in an active mining area. Vectors between vertices of the network were measured with a static GNSS method (two receivers, survey duration 60 min). GNSS vectors were used in both test variants: GNSS network (Figure 5a) and integrated network (Figure 5b). Classical terrestrial measurements (horizontal and vertical angles, horizontal distances) were performed with a precise total station. The surveying instrument and the signal (reflector) were placed on carefully levelled and centred tripods with tribrachs. The height of both the instrument (\(i\)) and the signal (\(s\)) was measured repeatedly with a special device. The classical observations were used in the integrated network (Figure 5b). For calculation purposes, points 2 and 6 were assumed to be fixed (reference points), while the other points (3, 4 and 5) were to be determined--in both cases (Figure 5a,b). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Edge \(j\)-\(k\)** & \(d_{jk}\) [**m**] & \(m_{jk}\)**(\(d\))** [**m**] & **Edge \(L\)-\(R\)** & \(\overline{d}_{LR}\) [**m**] & \(d_{LR}\) [**m**] & \(m_{LR}\)**(\(d\))** [**m**] \\
**From (\(j\))** & **To (\(k\))** & **Equation (\(S\))** & **Equation (\(9\))** & **From (\(L\))** & **To (\(R\))** & **Equation (\(6\))** & **Equation (\(8\))** & **Equation (\(10\))** \\ \hline \(5\) & 6 & 24.6374 & 0.0040 & 6 & 4 & 44.4639 & 44.4663 & 0.0051 \\ \(5\) & 4 & 24.4412 & 0.0040 & 5 & 3 & 48.8329 & 48.8329 & 0.0056 \\ \(4\) & 5 & 24.4444 & 0.0040 & 4 & 2 & 49.7224 & 49.7225 & 0.0056 \\ \(4\) & 3 & 24.8924 & 0.0040 & & & & \\ \(3\) & 4 & 24.8925 & 0.0040 & & & & \\ \(3\) & 2 & 24.9656 & 0.0040 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Linear pseudo-observations of types \(j\)-\(k\) (\(5\)) and \(L\)-\(R\) (\(8\)) and their mean errors (\(9\)) (\(10\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point** & \(X\) **[m]** & \(Y\) **[m]** & \(Z\) **[m]** \\ \hline \(2\) & 3,871,857.1432 & 1,345,974.9571 & 4,870,463.1848 \\ \(3\) *_ & 3,871,866.8786 & 1,345,952.0257 & 4,870,461.5791 \\ \(4\) *_ & 3,871,874.0806 & 1,345,928.2155 & 4,870,462.4879 \\ \(5\) *_ & 3,871,875.6704 & 1,345,904.3918 & 4,870,467.6734 \\ \(6\) & 3,871,861.5368 & 1,345,890.3711 & 4,870,482.1739 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinates of reference points (\(2\) and \(6\)) and approximate coordinates (*) of points to be determined (_3_, \(4\), _5_)—geocentric system ETRF’89. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Station** & **Target** & **Height** & **Height** & **Horizontal Angle** & **Vertical Angle** & **Horizontal** \\
**(\(j\))** & **(\(k\))** & **(\(i\) [**m**] & **\(s\) [**m**] & **\(\beta\) [Grad]** & **\(\alpha\) [Grad]** & \(\overline{d}\) [**m**] \\ \hline \(5\) & 6 & 1.733 & 1.882 & 144.35765 & 100.63750 & 24.6360 \\  & 4 & & 1.858 & 1.858 & 99.48384 & 24.4400 \\ \(4\) & 5 & 1.858 & 1.733 & 181.80672 & 100.51717 & 24.4434 \\  & 3 & & 1.821 & 100.20077 & 24.8923 \\ \(3\) & 4 & 1.821 & 1.858 & 190.63125 & 99.80366 & 24.8924 \\ \(2\) & & & 1.630 & & 100.07838 & 24.9649 \\ A priori mean errors & 0.002 & 0.002 & 0.0030 & 0.0020 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classical measurements (total station) and their mean errors. The final results of the calculations made using Equations (22)-(26) are summarized in Tables 6 and 7 (for the two test variants, respectively). A comparison of results of the adjustment of the GNSS vector network and the integrated network (Table 8) reveals only minor differences in the coordinates \(X\), \(Y\), \(Z\) (up to about 5 mm).