## 4 Discussion  
The method used for precise determination of the position of the primary system designed along the railway was tested on four different railway lines under operating conditions. Satellite instruments with GPS, GLONASS, Galileo and BeiDou signals were used, which improves the availability of a larger number of satellites, even in problematic observation conditions. The achieved accuracy is about 10\(-\)20% better than the pilot measurements with GPS+GLONASS signals published in [12]. The availability of a larger number of satellites even under degraded operational conditions simplifies the planning of observations and enables achieving a higher reliability of results. In the paper [26], the authors concluded that the accuracy of PPP positioning could be improved by using BeiDou data. The time series of position components of selected EUREF Permanent Network (EPN) stations generated from sub-daily (30 min and longer) solutions was analyzed. The obtained results prove that the addition of BeiDou observations, even in the case of using an incomplete constellation, leads to visible improvements, which can be observed both in the reduction of the differences between estimated and true coordinates, as well as in the reduction of the standard deviation (SD). The improvement in accuracy due to  
Figure 6: Overview of analyzed railway lines (sub-lines are distinguished by color) in the territory of the Czech Republic. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Range [mm/km]** & **DL [\%]** & **DQ [\%]** & **DLDQ [\%]** \\ \hline
0–5 & 65 & 70 & 40 \\
5–10 & 26 & 22 & 40 \\
10–20 & 8 & 7 & 18 \\
20–25 & 0.6 & 1 & 2 \\
25–40 & 0.3 & 0.1 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Geometric inhomogeneities of the uniform transformation key (v. 2018). the addition of BeiDou data is particularly noticeable for short observation sessions (in the range of 0.5-2.0 h) and in the case of a joint solution with GLONAS or Galileo observations. The GNSS/IMU/odometer combination [5] is suitable for indicative, rapid detection of the spatial position of the track for diagnosis and design purposes; however, it fails in longer forested sections and is not applicable during the construction or laying of new tracks. In [27], different non-geodetic GNSS sensors were tested, and it was confirmed that the correlations between forest cover variability and horizontal position error were significant; however, the trends were not consistent. The effect of nearby tree size on horizontal position error cannot be generalized; however, it is quite clear that there is a significant effect on horizontal position accuracy due to the presence of nearby trees. In our solution, we use geodetic GNSS sensors and quantify the degree of degradation in horizontal accuracy by comparing the accuracy calculated from the variance of a series of repeated measurements taken using the same procedure at a GNSS calibration base and under field conditions. We find a two-three times degradation in horizontal accuracy under operational railway conditions compared to ideal observation conditions at the GNSS calibration base (Tables 1 and 2). We interpret the degradation in accuracy under operational conditions as an effect due to multipath with respect to horizon obstructions and surrounding vegetation. The multipath effect affects the entire short GNSS observation time. By increasing the number of repetitions of short observations with time intervals for changing conditions (change in satellite configuration, change in multipath effect, change in atmospheric conditions, etc.) it is possible to achieve randomness of the effect of these components in the result. In [12] the principle of repeated measurements under different conditions is used in a similar way. The Trimble R780, for example, has Trimble EVEREST Plus to eliminate multipath, but the difference in quality is not conclusive when compared to the results obtained with the Trimble R2.