## 2 Materials
### Study of the GNSS Receiver Convergence Time for a Specified Accuracy of the RTK Solution
Accuracy of Geodetic, Precise Positioning with the Use of RTK Method Based on Observations of Galileo Satellites  
The main purpose of this work is to present real capabilities and performance of precise, geodetic GNSS real time measurements, using signals from Galileo satellites only and corrections from ground reference stations. The constellation of 14 fully operational Galileo satellites now enables RTK (Real Time Kinematic) measurements. However, it is possible only in certain time spans during a day and in specific areas of the globe. These capabilities were used to analyze the availability of Galileo satellites, first in general for the territory of Poland, and then for the selected site (Krakow \(\phi\) = 50.0207, \(\lambda\) = 20.0221). Measurements were made within six days to cover a sufficiently long period of time and thus give reliable results. The period 362-365 DOY 2017 (GPS WEEK 1981) and 001-002 DOY 2018 (GPS WEEK 1982) was selected. On the basis of detailed assessments of availability and continuity of positioning carried out for the Galileo system (Tables 1-7) and pre-identified 62 time intervals in which five or more satellites were available, 36 time windows were selected with a duration of 30 min to 1 h.  
In the measurements the Trimble R10 company kit with the TSC3 controller were used (Figure 2). The Trimble R10, is a new generation, 440 channel integrated with the R10 Internal antenna, multi-system satellite receiver. It can simultaneously track up to 18 observation codes. It is adapted for tracking all currently available positioning and navigation systems: GPS (L1-C/A, L2E, L2C, L5), GLONASS (L1-C/A, L1P, L2C/A, L3), Galileo (E1, E5-A, E5-B, E5 AltBOC), BeiDou (B1, B2), QZSS (L1-C/A, L1-SAIF, L1C, L2C, L5), SBAS (L1-C/A, L5), MSS (Service: RTX/xFill) (Trimble AccessTM software 2015). RTK corrections were provided by the KRUR scientific reference station, (Figure 3) working permanently since 1 November 2009 at the University of Agriculture in Krakow. The GNSS receiving antenna is located on a special observation pillar built for this purpose integrated into the building of the Faculty of Environmental Engineering and Geodesy at Balice 253C Street in Krakow. The observation pillar is independent of the entire building. Its upper part reaches about 1.5 m above the roof of the building (Figure 3), so that the satellite antenna installed on the pillar has a fully open observation horizon. The reference station KRUR works on the basis of the Trimble NetR9 measurement set (Serial Number: 5025K68510) and antenna GNSS Choke w/SCIS Dome (Serial Number: 5511356093) with the individual calibration. This station observes and provides differential corrections to all currently available navigation systems (Figure 3b: GPS, GLONASS, Galileo, BeiDou QZSS). For the purpose of research carried out as a part of this work, multiple RTK measurements were made using the KRUR station as a single reference station. During experimental measurements, the KRUR station provided corrections to the observed satellites of the Galileo system via a mobile internet connection. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**Value of PDOP**} & \multicolumn{2}{c}{**Number of Observed Satellites**} \\ \cline{3-6}
**No.** & **Convergence** & & & **After Reaching the** & **After Reaching the** & **After Reaching the** & **Assumed Accuracy** \\ \cline{3-6}
21 & 00:02:30 & 6.01 & 2.74 & 5 & 6 \\
22 & 00:02:50 & 3.12 & 3.13 & 5 & 5 \\
23 & 00:03:40 & 5.84 & 3.04 & 6 & 7 \\
24 & 00:04:00 & 3.68 & 2.08 & 5 & 6 \\
25 & 00:05:20 & 6.21 & 3.52 & 5 & 5 \\
26 & 00:05:50 & 3.61 & 3.59 & 5 & 5 \\
27 & 00:06:02 & 2.82 & 2.52 & 5 & 5 \\
28 & 00:08:40 & 2.99 & 2.85 & 5 & 5 \\
29 & 00:09:20 & 3.99 & 3.74 & 6 & 6 \\
30 & 00:10:10 & 3.96 & 3.91 & 5 & 6 \\ \hline \end{tabular} Source: Own elaboration based on performed experimental tests.  
\end{table} 
Table 8: _Cont._The KRUR reference station determines satellite corrections based on the internal Trimble NetR9 receiver software--Active Firmware Version 5.30.