## 2 Materials and Methods
### Displacement Analysis: Relative Positioning  
To analyze the sizes of detected movements, static observations were acquired at 1 Hz for four weeks, from 19 October 2020 to 19 November 2020. Three satellite constellations were tracked, namely, GPS, GLONASS, and Galileo. The open-source software RTKLIB (demo5_33b) was used to process the data; the adopted processing parameters are presented in Table 3[31]. The established geodetic network (Figure 1) consisted of four points and six baseline vectors. Each baseline was observed for one hour at 1 Hz, which was found to be an appropriate interval to detect displacements [32]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Antenna** & **Survey Calibrated** & **Survey** & **Tallysman** \\ \hline Weight & 535 g & 535 g & 185 g \\ Frequency & L1/L2 & L1/L2 & L1/L2 \\ Price & 150 EUR & 90 EUR & 300 EUR \\ Calibration & Yes & No & No \\ LNA Gain & 40 db & 40 db & 35 db \\ LNA Noise figure & \(\leq\)1.5 db & \(\leq\)1.5 db & \(\leq\)2.5 db \\ Supply voltage range & 3–12 V DC & 3–5.5 V DC & 2.5–16 V DC \\ Supply current & 50 mA & 45 mA & 24 mA \\ Phase center error & 1 mm & 3 mm & / \\ Ingress protection & IP67 & IP66 & IP67 \\ Mounting method & Screw & Screw & Screw \\ Size & 151.5 mm \(\times\) 61.5 mm & 146.5 mm \(\times\) 62.5 mm & 66.5 mm \(\times\) 48 mm \\ Operating temperature & \(-\)40 \({}^{\circ}\)C to + 85 \({}^{\circ}\)C & \(-\)40 \({}^{\circ}\)C to + 85 \({}^{\circ}\)C & \(-\)40 \({}^{\circ}\)C to + 85 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications for GNSS antennas used. Figure 2: Low-cost GNSS antennas: Survey (**left**), Tallysman TW3882 (**middle**), and Survey Calibrated (**right**). Control movements were imposed in the horizontal and vertical directions using a mechanical device and Vernier scale with high accuracy (0.05 mm) (Figure 3). The moving antenna was set on point FGG1 and was observed in the first position for one hour, after which we moved the antenna to a new position and again observed it for one hour. The procedure was repeated 7 times. The difference between consecutive positions was 2 mm, and in total, 6 movements were observed; starting from the first (session 1) to the seventh position (session 7), the rover was moved 12 mm. The same scenario was then repeated for the vertical direction, but the imposed movements between consecutive positions were 3 mm, and from the first (session 1) to the sixth position (session 6), the rover was moved 15 mm upwards. In total, six movements were imposed in the horizontal plane, and five movements were implemented in the vertical direction. The experiment was repeated for three selected low-cost antennas in the same conditions. The movements were applied to point FGG1 only, and all other points in the GNSS network remained stable. Firstly, horizontal and vertical displacements were estimated from coordinates obtained on the basis of baseline vectors only, which were estimated from points FGG4, FGG3, and FGG2 to point FGG1. Summary statistics, such as minimum, maximum, and Mean Absolute Error (MAE) of the differences between estimated and true displacements were obtained to show the differences from true movements. Computed baseline vectors were used afterward to define a geodetic network (Figure 1). The geodetic network adjustment was carried out for each session to estimate displacements more accurately. In total, the geodetic network was adjusted 39 times, among which 18 adjustments were for vertical and 21 were for horizontal displacements. The points FGG2, FGG3, and FGG4 were used as datum points since we know a priori that they are stable. In the network adjustment, the following conditions were fulfilled [33]:  
\[v_{1}^{T}P_{i}v_{i}=min, \tag{1}\]  
Figure 3: Imposed controlled movements: (**a**) Horizontal movements; (**b**) vertical movements.