## 2 Materials and Methods
### Positioning Deviations of and Their Error Indicators for the Whole Measurement Period  
To determine the results, the deviation of the location determination was determined as the hypotenuse of a right-angle triangle, with perpendicular-based distance between the reference and measurement points in two mutually perpendicular directions (north and east):  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Label** & **Receiver A** & **Receiver B** & **Receiver C** & **Receiver D** \\ \hline Manufacturer & Novatel & Tersus & Ashtech & u-blox \\ Model & PwrPak7. & BX305 & MB800 & C94-M8P \\ Dynamic mode & “LAND” & default & “Automobile” & “Automotive” \\ Firmware & VER 7.07.01 & V2.1-20180725 & 2.06.8580 Kn27 & FW3.01 HPG1.40 \\ \hline INS & Epson G320N IMU & 6 DOF IMU & - & - \\ \hline GNSS antenna quantity & 2 & 1 & 1 & 1 \\ \hline Signal tracking: & & & & \\ GPS & L1 C/A, L1C, L2C, L2P, L5 & L1, L2 & L1 C/A, L1P, L2P, L2C, L5 & L1 C/A \\ GLONASS & L1 C/A, L2C, L2P, L3, L5 & L1 & L1 C/A, L2 C/A & L1 OF \\ BDS (unused) & B1, B2, B3 & B1, B3 & - & B1 \\ \hline Manufacturer \(RMS_{err}\): & & & & \\ GNSS & 1.2 m & 1.5 m & - & 2.5 m \\ RTK & 0.01 m + 1 ppm & 0.01 m + 1 ppm & 0.01 m + 1 ppm & 0.025 m + 1 ppm \\ \hline \end{tabular}
\end{table}
Table 1: Essential properties of the four RTK receivers selected for evaluation. Receiver A allowed for the application of two antenna solutions to determine the absolute orientation, which was not, however, evaluated in this study. Receiver A and Receiver B contained INS. All RTK receivers were multi-GNSS types. Receiver A, Receiver B and Receiver C were multifrequency types and Receiver D a single-frequency type. The precision of the location determination in the GNSS status presented using \(RMS_{err}\) was not indicated by the manufacturer of Receiver C. The manufacturer of Receiver D stated a higher error rate of \(RMS_{err}\) than the other RTK receivers.  
Deviation (\(d_{i}\))--Euclidean distance between the reference and measured points (hypotenuse) on the horizontal plane (m):  
\[d_{i}=\sqrt{\left(x_{ref}-x_{rtk}\right)^{2}+\left(y_{ref}-y_{rtk}\right)^{2}}, \tag{2}\]  
where \(x_{ref}\)--x-axis (east) coordinate of the reference point (m), \(y_{ref}\)--y-axis (north) coordinate of the reference point (m), \(x_{rtk}\)--x-axis (east) coordinate of the measured point (m) and \(y_{rtk}\)--y-axis (North) coordinate of the measured point (m).  
For the obtained range of deviations of the location determination, the error precision indicators were set using the following calculations:  
Accuracy (\(\mu_{err}\))--sample mean of deviations from the reference point (offset of error) (m):  
\[u_{err}=\frac{1}{n}\sum_{i=1}^{n}d_{i}, \tag{3}\]  
where \(n\)--dataset size of the measured samples (-) and \(d_{i}\)--deviation from the reference point at the \(i\) index of a dataset (m).  
Precision (\(s_{err}\))--sample standard deviation (stability of the positioning) (m):  
\[s_{err}=\sqrt{\frac{\sum_{i=1}^{n}\left(d_{i-}u_{err}\right)^{2}}{n-1}}, \tag{4}\]  
where \(n\)--dataset size of the measured samples (-), \(d_{i}\)--deviation from the reference point at the \(i\) index of a dataset (m) and \(\mu_{err}\)--sample mean of deviations from the reference point (accuracy) (m).  
RMS error (\(RMS_{err}\))--value specified by the manufacturer (metric emphasising large errors) (m):  
\[RMS_{err}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}{d_{i}}^{2}}, \tag{5}\]  
where \(n\)--dataset size of the measured samples (-) and \(d_{i}\)--deviation from the reference point at the \(i\) index of a dataset (m).  
To determine the indicators describing the properties of all the four RTK receivers (\(\mu_{err}\), \(s_{err}\) and \(RMS_{err}\)), no method was used to remove the deviation outliers.