# Monitoring of Structures and Infrastructures by Low-Cost GNSS Receivers
## 3 The Experience
### Results of the Absolute Motion  
The permanent station \(S\) (Figure 9), which is 1.6 km away from the bridge and is framed in the global ITRF system, has been used to compute the absolute displacements.  
The time series of the coordinates of \(S\) with respect to other permanent stations in the area included in the International Terrestrial Reference Frame allows for careful monitoring of the stability of the reference station. In Figures 10-12, we present the time series of the shifts of the three stations, C1, C2, and C3, with respect to the permanent station \(S\). Therefore, we interpret the plots of Figures 10-12 as the motion of the bridge with respect to the surrounding area, say, of some tens of kilometers of diameter.  
The first remark we can make on Figures 10-12 is that the estimates of the longer bases, \(S\)-C3, \(S\)-C1, and \(S\)-C2, are significantly noisier than those of the very short baselines on the bridge, as expected. This is confirmed by numbers in Table 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Baseline** & **Length** & \(\sigma\)**X (Longitudinal)** & \(\sigma\)**Y (Transversal)** & \(\sigma\)**Z (Up)** \\ \hline \(S\)–C1 & horiz.: 2390.5 m, & & & \\  & vertic: \(-\)214.6 m & 0.6 mm & 1.0 mm & 2.7 mm \\ \(S\)–C2 & horiz.: 2390.3 m, & & & \\  & vertic: \(-\)214.2 m & 1.1 mm & 1.0 mm & 2.7 mm \\ \(S\)–C3 & horiz.: 2405.2 m, & & & \\  & vertic: \(-\)214.2 m & 0.6 mm & 1.0 mm & 2.6 mm \\ \hline \hline \end{tabular}
\end{table}
Table 4: Root mean squares (RMSs) of \(XYZ\) with respect to the mean motion (splines every 14 days) for the 3 baselines over the monitoring period.  
Figure 9: Conceptual scheme showing the position of permanent station \(S\) with respect to the monitoring network on the bridge. The aspect ratio is not maintained.  
Next, we can analyze the plot in Figure 10 to study the absolute motion of our local reference C3.  
The series in \(X\) of C3 (Figure 10) shows a non-significant trend of a couple of millimeters over 4 years, while \(Y\) has a more important trend of about 8 mm over 4 years. To better understand this motion, we plotted the shift in the horizontal plane with the \(Y\)-axis along the steepest descent direction of the slope (Figure 13).  
Figure 11: Baseline \(S\)–C1.  
Figure 10: Baseline \(S\)–C3.  
As can be seen, in this system, we find that the motion of C3 is only in the slope direction. More accurate analysis shows that the motion presents mostly in the years 2018-2019, while it slows down in later years. Corresponding to the sliding of C3 towards the valley, we also see motion of C2 in the uphill direction, displaying a possible clockwise rotation of the structure in the horizontal plane.  
The behavior of C3 in the up direction is interesting; in fact, though much noisier, the plot shows a clear subsidence of about 1 cm in 4 years. Even more interesting is that a subsidence almost coinciding with that of C3 is found in the plots of C1 (Figure 11) and C2 (Figure 12). This also demonstrates the importance of framing the local intrinsic network  
Figure 12: Baseline S–C2.  
Figure 13: \(X\) and \(Y\) components on the baseline \(S\)–C3 with the \(X\)-axis oriented along the steepest descent direction of the slope.  
within a larger network of permanent stations so that parallel motion of the structure with respect to the surrounding area can be revealed. Another important remark regards the plot of the \(X\) time series of C2 (Figure 12), where the thermal oscillation is again fairly visible.  
Given that C3 does not move so much in \(X\), it is not surprising that we again find an oscillation of about 1.5 cm, as in Figure 6.