## 2 Materials and Methods  
### The Principle of the Real-Time GNSS Measurement Procedure in Railway Operating Conditions  
The technology is intended for the construction and maintenance of the primary railway geodetic point field (RGPF) or the primary system of railway structures using the technologies of Global Navigation Satellite Systems (GNSS) in real time with metrological connection to the geodetic point fields of the Czech Republic [20]. The technology can be used to solve the restoration of the equivalent of the measurement network, often many years apart, in the preparation, design and implementation phases of construction,including solving the problem of ageing or destruction of the measurement network or its part, construction, maintenance or restoration of the primary system during construction. Conversion from the European Terrestrial Reference System (ETRS) to the national S-JTSK system and vice versa is ensured by a single global transformation key defined by the Research Institute of Geodesy, Topography and Cartography (VUGTK) Zdiby, Czech Republic, v.v.i. The measurement procedure is based on a methodology [20] that has been progressively incorporated into the M20/MP007 regulation [19]:  
* Connectivity to permanent station networks CZEPOS or Trimble VRS Now or TOPNet or GEOORBIT, which are part of the independent monitoring VUGTK, v.v.i. ;
* Preference of using the VRS network measurement method;
* The GNSS signal used must be at least GPS + GLONASS;
* Elevation mask from 10\({}^{\circ}\) to 13\({}^{\circ}\);
* Number of observed satellites at least 10, GDOP \(\leq\) 2;
* Time of measurement at least 5 min with fixed solution (start of measurement at least 30 s after fixation to stabilize the solution);
* Number of measurement repetitions at least 3 times with a time interval of 3 to 4 h;
* Antenna centering above the measurement mark better than 1 mm. An open horizon is a prerequisite for good observation; if there are multiple obstacles and horizon occlusions, it is necessary to use observation planning tools with horizon obstacle modelling. The innovation of the used procedure is in its simplification, thus increasing the efficiency of measurements with the availability of GPS, GLONASS, Galileo and BeiDou satellites, and in reducing the effect of multipath on noise by repeating the measurement procedure. The reliability of horizontal position determination when following the procedure is 10 mm (\(p\) = 0.95, \(\alpha\) = 5%). Regulation M20/MP007 [19] is the technical standard of the Railway Administration, State Organization for the Railway Geodetic Point Field. The above-mentioned method of measurement has been used to determine the points of the primary system on the following four railway lines (RL) (Figures 1 and 2):  
* RL 1371 Velka Kras--Vidnava--length of 4.5 km
* RL 2302 Bojkovice--Hostetin--length of 9.5 km
* RL 1363 Jesenik--Mikulovice--length of 16.5 km
* RL 2302 Bzenec railway station--length of 5.5 km  
A geodetic Trimble R2 GNSS instrument (accuracy specified by the manufacturer for the network solution in the horizontal plane 10 mm + 0.5 ppm RMS) was used to measure the first three railway lines. The measurements were carried out between May and July 2023, during the vegetation period. A geodetic Trimble R780 GNSS instrument (accuracy specified by the manufacturer for the network solution in the horizontal plane 8 mm + 0.5 ppm RMS) was used to measure the fourth section. This measurement took place in February 2024, outside the vegetation period. The signals used in the Trimble R2 and Trimble R780 instruments were GPS, GLONASS, Galileo and BeiDou, with tilt compensation disabled in the Trimble R780. The GNSS instruments were centered and levelled on a tripod with an accuracy of better than 1 mm. Figure 1: Localization of the discussed railway lines in the Czech Republic. Numbers correspond to order of appearance in text above.