## 4 Practical Applications of GNSS in Railway Surveys and Alignment Results  
On 16-17 July 2019, on a route between Tczew-Chojnice-Brusy-Chojnice-Tczew, located in northern Poland, a study was conducted using six Leica GS-18 GNSS receivers (Figure 2). On the day preceding the proper measurements, surveying devices and instruments were mounted on a railway car (Figure 3). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \multirow{3}{*}{**Signals Tracked**} & GPS (L1, L2, L2C, L5), Glonass (L1, L2, L2C, L32), \\  & BeiDou (B1, B2, B32), Galileo (E1, E5a, E5b, Alt-BOC, E62), \\  & QZSS (L1, L2C, L5, L62), NavIc L53, SBAS (WAAS, GENOS, MSAS, GAGAN), Band L \\ \hline \multirow{3}{*}{**Initialisation Time**} & Normally 4 s \\ \cline{2-3}  & A single baseline: Hz 8 mm + 1 ppm/V 15 mm + 1 ppm \\ \cline{2-3}  & Network RTK: Hz 8 mm + 0.5 ppm/V 15 mm + 0.5 ppm \\ \hline \multirow{3}{*}{**Postprocessing Accuracy**} & Static mode (phase), long-term observations: Hz 3 mm + 0.1 ppm/V 3.5 mm + 0.4 ppm, \\  & Static and fast static mode (phase): Hz 3 mm + 0.5 ppm/V 5 mm + 0.5 ppm \\ \hline \multirow{2}{*}{**Weight**} & 1.20 kg/3.50 kg—a standard configuration of an RTK receiver on a pole \\ \hline
**Dimensions** & 173 mm \(\times\) 173 mm \(\times\) 108 mm \\ \hline
**Position Measurement** & 5 Hz/20 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected parameters of a LEICA GS 18T receiver. Figure 2: A LEICA GS-18 receiver used during the surveys. To precisely determine the distance between the receiver antennas axes, tacheometric surveys were then conducted using a LEICA TS 1103 total station. The measured distances are provided in Figure 4.  
Six GNSS receivers were used in the study. Furthermore, 507,251 coordinate surveys were obtained for each receiver from the conducted observations, after rejecting incomplete observations. The data obtained were aligned using the Method of Least Squares with conditional equations. The observation results were aligned in the flat rectangular coordinate system PL-2000. The system was developed based on the mathematically unique alignment of points on the reference spheroid GRS80 with the corresponding points on the plane, in accordance with the Gauss-Kruger projection theory, and is valid in the territory of the Republic of Poland [48]. Because of the large number of data, the alignment results for only one measurement epoch (marked as 20190717_104340150), conducted in postprocessing, are presented below. The following input data were obtained from satellite observations (Table 2):  
* coordinates of GNSS antennas on the MSP,
* errors in determining the GNSS antenna position coordinates. Figure 4: Determined distances between antennas on the surveying platform. Figure 3: Global Navigation Satellite System (GNSS) receivers by Leica mounted on the mobile surveying platform. The position of antennas on the surveying platform is shown in the Figure 5.  
Moreover, for further calculations, the measured distances between antennas (Figure 4) as well as errors of their determination: \(m_{1-3}=0.0031\), \(m_{1-4}=0.0033\), \(m_{2-5}=0.0034\), \(m_{3-6}=0.0035\), \(m_{4-6}=0.0030\), resulting from the total station instrumental errors, were used. In the calculations, the measured distances to three reference stations being part of the SmartNet network [49] were used. The coordinates of the station exposures are provided in the Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**GNSS Receiver** & \(x\) & \(y\) & \(m\) \\ \hline GNSS \#1 & 5967572.5583 & 6505456.2272 & 0.0669 \\ GNSS \#2 & 5967571.9058 & 6505456.6093 & 0.2609 \\ GNSS \#3 & 5967571.2635 & 6505456.9836 & 0.0966 \\ GNSS \#4 & 5967576.0405 & 6505462.2802 & 0.0046 \\ GNSS \#5 & 5967575.3857 & 6505462.6552 & 0.0285 \\ GNSS \#6 & 5967574.7377 & 6505463.0309 & 0.0404 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinates of GNSS receiver antennas along with the errors of their determination, obtained from satellite observations.