## 3 Results and Discussion
### Comparison of Positioning Deviations according to the Current State of the System  
The graphs (Figure 7) below show the distribution of the positioning deviations during the individual states of the RTK receiver system in the form of boxplots. The values of the median deviations of the positioning can also be found in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline
**RTK Receiver** & \(n_{d}\) & \(min(t_{d})\) & \(max(t_{d})\) & \(\mu(t_{d})\) & \(Me(t_{d})\) \\ \hline Receiver A & 70 & 1 s & 186 s & 5.04 s & 1 s \\ Receiver B & 54 & 0.3 s & 228.3 s & 11.42 s & 3.4 s \\ Receiver C & 32 & 0.05 s & 753.15 s & 60.98 s & 10.6 s \\ Receiver D & 56 & 5.8 s & 472 s & 48.85 s & 21.4 s \\ \hline \end{tabular}
\end{table} 
Table 4: Number of outages and recovery time of the “FIX” state after its loss: \(n_{o}\) number of detected outages from the “FIX” state (-), \(min(t_{o})\) the shortest duration of the outage (s), \(max(t_{o})\) the longest duration of the outage (s), \(\mu(t_{o})\) the mean duration of the outage (s) and \(Me(t_{o})\) the median duration of the outage (s). It was possibly assumed that the RTK receivers with an INS unit (Receiver A and Receiver B) were able to return to the “FIX” state earlier than the receivers without an INS unit (Receiver C and Receiver D). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Whole Measurement**} & \multicolumn{4}{c}{**“FIX” State Epoch**} \\ \cline{2-9}
**RTK Receiver** & \(r_{dr}\) & \(r_{da}\) & \(r_{sv}\) & \(r_{sa}\) & \(r_{sd}\) & \(r_{dr}\) & \(r_{da}\) \\ \hline Receiver A & 0.150 & 0.071 & 0.020 & 0.005 & \(-\)0.358 & 0.190 & 0.079 \\ Receiver B & 0.120 & 0.021 & \(-\)0.072 & \(-\)0.014 & \(-\)0.372 & 0.045 & 0.042 \\ Receiver C & 0.310 & 0.060 & \(-\)0.586 & \(-\)0.121 & \(-\)0.435 & 0.082 & 0.041 \\ Receiver D & 0.360 & 0.005 & \(-\)0.138 & \(-\)0.026 & \(-\)0.178 & 0.26 & \(-\)0.032 \\ \hline \end{tabular}
\end{table} 
Table 5: Linear dependences of the positioning deviations with instantaneous speed, positioning deviations with instantaneous contact acceleration, current system state of a RTK receiver with instantaneous speed, current system state of a RTK receiver with instantaneous acceleration and current system state of a RTK receiver with a positioning deviation expressed by a Pearson correlation coefficient (\(\alpha\) = 0.05). The current state of the RTK receivers was evaluated by three states on a linear scale with specific values: “FIX” = 2, “FLOAT” = 1 and “GNSS” = 0. All the detected dependences cannot be considered statistically significant. Figure 7: The distribution of the deviations during current states of the four RTK receivers from the whole measurement period (a–d). The boxplots display plots for each condition in a rectangular area \(\pm\)25% of the values occurring around the median, as shown by the red line. The extreme red lines show the boundaries dividing the contents of the external observations from the outlier area. The outsiders are shown with a black dot with a set transparency of 20%. A logarithm of base 10 was used to display the deviation axis. For all RTK receivers, the current state of the system had a significant effect on their positioning deviations. The first graph (Figure 7a) clearly indicates that only Receiver A reached the states \"FIX\" and \"GNSS\" during the whole measurement period. The value of its median from the \"FIX\" period _Me(FIX)_ was the largest value of all of the four RTK receivers. Receiver B and Receiver D had the smallest median errors. Receiver B had the smallest value of _Me(FLOAT)_, and Receiver C had a much higher value. In the \"GNSS\" period, Receiver A had the lowest _Me(GNSS)_ value, and Receiver D had more than 101 times the _Me(GNSS)_ value. It is evident that, for all the four RTK receivers, the deviations calculated from the median increased if the RTK receiver was in different states of the system in the following order of states: \"FIX\", \"FLOAT\" and \"GNSS\".