## 2 Materials
### Study of the GNSS Receiver Convergence Time for a Specified Accuracy of the RTK Solution  
The study involved the determination of the convergence time of the Trimble R10 receiver, in RTK measurements, for a single baseline \(<\)14 km, for the accuracy of horizontal and vertical measurements  
\begin{table} \begin{tabular}{c c c c c} \hline \hline  & **Local Time: 2018-01-02 00:00:00–2018-01-03 00:00-00 (UTC + 2) Cutoff 10\({}^{\circ}\)** & \\ \hline \hline
**Initial Time** & **End Time** & **Number of Satellites** & **Visible Satellites** & **Period of Time** \\ \hline
00:00:00 & 02:00:00 & 2–4 & E \(<\) 5 & 02:00:00 \\
02:00:00 & 02:10:00 & 5 & E01, E08, E12, E24, E26 & 00:10:00 \\
02:10:00 & 02:30:00  
\(\leq\)0.05 m using only Galileo satellites [15]. The convergence time included the RTK measurement initialization time, which was counted from the moment the mobile receiver \"rover\" was connected to the assistance system (correction from KRUR--single reference station) until the assumed accuracy of the solution was achieved (\(\leq\)0.05 m). Convergence time varies depending on the state of Galileo constellation, the level of multithreading, the proximity of obstacles such as high trees and buildings, and the calculation algorithms used by the receiver. The software used for experimental measurements of the Trimble R10 receiver, includes the new processing algorithm--Trimble HD-GNSS. It can use all GNSS constellations and implements a new approach in determination of the phase uncertainty. The applied solution determines the total number of phase cycles in a continuous manner based on data from subsequent measurement epochs [16]. It omits the traditional, two-stage method of initiating RTK measurements with taking into account the transition from the \"float\" solution to the \"fixed\" one.  
Table 8 summarizes the detailed results of the obtained convergence times. During the tests, they ranged from 10 s to 10 min and 10 s. The shortest convergence times \(\leq\)10 s occurred in 14 cases, with the most advantageous satellites positions at the observation site, when PDOP (Position Dilution of Precision) <3.0. The initialization time from the interval (20 s-59 s) occurred in 5 cases when the PDOP values were within the range (3.26-4.81). Convergence times (1 min 20 s-4 min 00 s) occurred in 5 cases when the PDOP values were within the range (3.04-6.01). The longest convergence times in the interval (5 min 20 s-10 min 10 s) occurred in the remaining 6 cases when the PDOP values were within the range (2.82-6.21). In general, it can be concluded that the initial value of the PDOP parameter determines the duration of the convergence strict (in the case under study accuracy \(\leq\)0.05 m was arbitrarily assumed). However, this is not a strict rule. As can be seen from Table 8, in some cases lower values (theoretically more favorable) of the PDOP yielded longer initialization times. This confirms the well-known principle that the PDOP is only one of several parameters which is correlated with the duration of the initialization time. The results obtained indicate that it is also important which satellites are observed at a given moment. Each navigation satellite is characterized by its unique observational parameters, which in general can be described as non-system equipment noise of satellites. Unfortunately Trimble R10 GNSS receiver software (Trimble Access TM), used to manage measurements in real time, does not allow to obtain detailed information about satellites participating in a given solution. However, there is no information about the names of satellites. Therefore, a detailed analysis of the data in this respect is hindered.  
\begin{table}
\begin{tabular}{c} **After Reaching the** \\ **Assumed Accuracy** \\ \end{tabular} \\ \hline  
\hline \hline \end{tabular} 
\end{table}
Table 8: The list of obtained convergence times.