## 3 Monitoring Data Collecting for the Forth Bridge
### Availability and PDOP  
In order to reflect the satellite observation condition of the base station, we counted the mean number of visible satellites and the mean value of Position Dilution of Precision (PDOP) under different cutoff angles (ranging from 0\({}^{\circ}\) to 40\({}^{\circ}\)) during the whole day of 2 May. The corresponding curves can be found in Figure 4a,b. According to the theoretical calculations and experience, the minimum number of satellites that can achieve single point or relative positioning is 4, and good satellite-user geometry corresponds to a PDOP of less than 6. Therefore, these two thresholds evaluate the pass rate of visibility and PDOP (P-num and P-PDOP), and the corresponding curves can be seen in Figure 4c,d. The statistical data of Figure 4 is also shown in Table 2. As the cutoff angle becomes larger, the number of visible satellites decreases, the PDOP increases, and thus the reliability of positioning decreases. For a single GPS system, when the cut-off angle is below 25\({}^{\circ}\), the number of visible satellites can be kept at more than four throughout the day; when the cut-off angle is 30\({}^{\circ}\), the number of satellites is not up to the minimum standard in 4.1% time; when the cut-off angle reaches 40\({}^{\circ}\), the number of satellites in more than half time is insufficient to achieve positioning. Galileo not only has the identical frequency bands as GPS, but also consists of MEO satellites, which ensures strong complementarity between Galileo and GPS--the Galileo satellites can be tracked wherever the GPS satellites are available. Accordingly, Galileo augmenting GPS is an effective and necessary approach to supplement satellites. As we can see from Table 2, the integrated GPS/Galileo has approximately five more satellites than a single GPS when the cutoff angle is below 10\({}^{\circ}\), the number gradually decreases to 2.6 and 1.8 as the cutoff angle increases to 30\({}^{\circ}\) and 40\({}^{\circ}\), respectively. The most obvious improvement is the pass rate of  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Location** & **Receiver** & **Sampling (Hz)** & **Frequency Band** & **Baseline** & **Baseline Length (m)** \\ \hline shm1 & & Leica GR10 & 10 & L1, E1 & & \\ shm2 & Middle span & Leica GR10 & 10 & L1, E1 & shm1-shm2 & 1529 \\ shm4 & South tower & Leica GR10 & 10 & L1, E1 & shm1-shm4 & 1033 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The detailed information of the two baselines.  
Figure 3: Sky plots (azimuth vs. elevation) for the various satellites systems at station shm1 on 2 May 2018: (**a**) global positioning system (GPS); (**b**) Galileo; and, (**c**) GPS/Galileo.  
the satellite number--that of GPS/Galileo still keep more than 98.9% under the cutoff angle of 40\({}^{\circ}\) and it is better than the single system under the cutoff angle of 30\({}^{\circ}\). From the perspective of PDOP, the improvement is not obvious below 15\({}^{\circ}\) cutoff angle (about 0.3-0.4) and it increases to 0.861, 1.863, 2.876, 3.714, and 3.86 as the cutoff angle increases to 20\({}^{\circ}\)-40\({}^{\circ}\). At the same time, the PDOP pass rate of GPS/Galileo also improves when compared to that of a single GPS, which is clearly indicated in Figure 4 and Table 2.