## 3 Results
### Control Network Impact Analysis  
An important issue related to the processing of GNSS-derived railway track coordinates is relating the satellite measurements with a railway surveying control network. Obtained spatial data, after proper harmonization [52], are stored in numerical maps for further use, e.g., in the maintenance of the track. The quality of the control network along the railway track is not constant and includes points of various network orders. In this study, one POLREF point and two adjacent lower-order points were used. Coordinates of receivers in the planar PL-2000 coordinate system were determined using the total station and compared with coordinates from post-processing and LS adjustments (Table 2). Three LS-adjustment methods used coordinates from post-processing calculation. Hence, the shifts of positions of receivers related to the reference coordinates were similar, which was represented by mean values. The factor that was changing was the standard deviation indicating the degree of distribution of points. Standard deviations of differences of coordinates exceeded the 1 mm threshold in the initial (unadjusted) and RLS datasets, with the greatest values in the north-south direction of the \(X\)-axis. At this stage, the OLS-, and CLS-adjustments results show similar quality reducing the precision of receivers \(x\)- and \(y\)-coordinates to 0.6 mm and 0.8 mm, and 0.5 mm and 0.6 mm, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{**Init**} & \multicolumn{2}{c}{**OLS**} & \multicolumn{2}{c}{**RLS**} & \multicolumn{2}{c}{**CLS**} \\ \cline{2-10}  & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** \\ \hline LF & \(-12.0\) & \(-19.8\) & \(-12.6\) & \(-21.5\) & \(-13.4\) & \(-21.9\) & \(-12.7\) & \(-21.6\) \\ \hline CF & \(-19.8\) & \(-20.0\) & \(-11.9\) & \(-20.0\) & \(-14.2\) & \(-19.1\) & \(-12.2\) & \(-20.8\) \\ \hline RF & \(-9.5\) & \(-22.3\) & \(-11.9\) & \(-20.9\) & \(-11.3\) & \(-22.4\) & \(-11.7\) & \(-20.1\) \\ \hline LB & \(-3.2\) & \(-18.6\) & \(-13.2\) & \(-19.7\) & \(-9.1\) & \(-20.2\) & \(-13.0\) & \(-19.9\) \\ \hline CB & \(-12.5\) & \(-19.5\) & \(-12.4\) & \(-19.2\) & \(-11.9\) & \(-20.0\) & \(-12.5\) & \(-20.1\) \\ \hline RB & \(-14.4\) & \(-16.9\) & \(-13.5\) & \(-21.2\) & \(-14.0\) & \(-19.4\) & \(-13.0\) & \(-20.4\) \\ \hline
**Mean** & \(-11.9\) & \(-19.5\) & \(-12.6\) & \(-20.4\) & \(-12.3\) & \(-20.5\) & \(-12.5\) & \(-20.5\) \\ \hline
**StDev** & **5.0** & **1.6** & **0.6** & **0.8** & **1.8** & **1.2** & **0.5** & **0.6** \\ \hline \end{tabular}
\end{table} 
Table 2: Differences in the initial and LS-adjusted receiver coordinates in relation to the reference. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{**Init**} & \multicolumn{2}{c}{**OLS**} & \multicolumn{2}{c}{**RLS**} & \multicolumn{2}{c}{**CLS**} \\ \cline{2-10}  & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** & **dx [mm]** & **dy [mm]** \\ \hline LF & \(-12.0\) & \(-19.8\) & \(-12.6\) & \(-21.5\) & \(-13.4\) & \(-21.9\) & \(-12.7\) & \(-21.6  
Differences for six receivers of approximately \(-1.2\) cm (the \(x\)-coordinate) and \(-2.0\) cm (the \(y\)-coordinate) indicate the presence of a systematic error related to the control network. Significantly smaller standard deviations show high repeatability of measurements. The tachymetric method ensures local station-related accuracies of single millimeters. However, the quality of the control network determines the final accuracy in the used reference frame. The control network point coordinates were not determined in the study but were provided by the local administration cadastre and land surveying department. A potential cause of obtained differences according to the reference coordinates can be the different implementation of ETRF (ITRF) in control networks of different orders.