## 3 Results and Discussion
### Positioning Deviations of and Their Error Indicators for the Whole Measurement Period  
The graph (Figure 3) plots histograms of the density of the horizontal deviations from the MRA reference trajectory in latitude and longitude (north and east). The occurrence density of the deviations \(d_{i}\) is further shown in Figure 4, together with the calculated error indicators (\(\mu_{err},s_{err}\) and \(RMS_{err}\)). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**RTK Receiver**} & \multicolumn{6}{c}{**Whole Measurement**} & \multicolumn{6}{c}{**“FIX” State Epoch**} \\ \cline{2-10}  & \(n_{w}\) & \(n_{f}\) & \(SSR\) & \(\mu_{err}\) & \(s_{err}\) & \(RMS_{err}\) & \(\mu_{err}\) & \(s_{err}\) & \(RMS_{err}\) \\ \hline Receiver A & 106 347 & 103 091 & 96.94\% & 0.047 m & 0.194 m & 0.06 m & 0.045 m & 0.182 m & 0.056 m \\ Receiver B & 106 347 & 97 075 & 91.28\% & 0.167 m & 0.893 m & 0.816 m & 0.055 m & 0.576 m & 0.336 m \\ Receiver C & 104 939 & 66 841 & 63.7\% & 0.589 m & 1.418 m & 2.097 m & 0.029 m & 0.172 m & 0.041 m \\ Receiver D & 26 150 & 3 600 & 13.77\% & 1.722 m & 2.314 m & 5.628 m & 0.036 m & 0.17 m & 0.046 m \\ \hline \end{tabular}
\end{table} 
Table 2: Error indicators during the dynamic measurements: the number of samples \(n_{w}\) for each RTK receiver from the whole measurement period to which a valid MRA reference coordinate could be assigned (-); the number of samples \(n_{f}\) marked as “FIX” in the NMEA message (-); \(SSR\) indicator indicating the RTK receiver’s ability to solve the ambiguity of the integer carrier phase during the whole measurement period (%) and the error indicators \(\mu_{err},\sigma_{err}\) and \(RMS_{err}\) separately from the whole measurement period and separately from the “FIX” period (m). In the whole measurement period, based on the submitted error indicators \(\mu_{err}\), \(s_{err}\) and \(RMS_{err}\), RTK Receiver A was undoubtedly evaluated as the best. The plotted density of the occurrence values of the positioning deviations (Figure 4a) showed that Receiver A did not show larger deviations greater than 0.5 m at all, while this maximum positioning deviation manifested itself only during one short section of the measurements (approximately 0.02% of the total measurement time). Apart from this nuance, Receiver A had the worst positioning deviation of 0.31 m. Receiver B displayed slightly worse accuracy indicators (Figure 4b). The largest error was reflected in the \(RMS_{err}\) indicators, where this error was mainly influenced by remote values of the deviations (the maximum deviation was detected to be 6.9 m). The occurrence density and deviation distance were even more pronounced in the \(RMS_{err}\) error of Receiver C (Figure 4c). The accuracy \(\mu_{err}\) and precision \(s_{err}\) indicators for this receiver were already very large compared to the previous ones. The  
Figure 4: The density of the deviations in the graphs of all the RTK receivers (**a–d**), together with the calculated error indicators \(\mu_{err}\), \(\sigma_{err}\) and \(RMS_{err}\) from the whole measurement period. The histogram uses a scale of logarithm base 10 to plot both axes. The density of occurrence of the deviation values was calculated identically for all the four receivers from the range (0–40 m) in the number of 2000 bins (resolution 20 mm). Figure 3: The density of occurrence of the horizontal deviations from the reference trajectory of the MRA in the latitude and longitude of four RTK receivers (**a–d**) from the whole measurement period. The horizontal distribution of the deviations was plotted in the graph of each RTK receiver in the large square area at the bottom-left. The percentage ratio of the occurrence density of the deviation in the area was plotted using a colour scale in a linear normalised distribution (where: black = 0%, red = 50% and white = 100%). The narrow bar histograms on the right and top show the density of the occurrence of the deviation in latitude and longitude in units of the obtained samples.