# GNSS-Based Vertically Monitoring of Super-Tall Buildings
## 4 Simulation  
Before applying the method in this paper to super-tall buildings, a simulation is first conducted to show the efficiency of the method. The goal of this simulation is to analyze the displacements of the stable JG building with a height of 10 m located at the Guangdong University of Technology. This building is held up by a reinforced concrete structure. On its roof, a GNSS station was installed to monitor the building's displacements. In addition, we established a reference network around the JG building consisting of three reference points, D8, LNYX, and LX. We chose these locations based on their suitability as reference stations according to the International GNSS service (IGS) criteria, keeping in mind the difficulty of finding adequate locations in an urban setting. Figure 4 shows the locations of the three points of the reference network and their distances to the JG building. Two points, D8 and LX, were located on low concrete buildings and one, LNYX, on a metal stand at ground level. Dual-frequency Trimble R8 GNSS receivers were employed to collect data for 2 h with a sampling interval of 1 s at all stations. As per the prior information, it is reasonable to assume that the displacement of the JG building is small or even negligible due to its low height and nonexposure to the effects of construction load, sun exposure, etc. The GNSS data of the reference network, consisting of D8, LNYX, and LX, was first processed in the static mode to obtain the baseline vectors amongst the reference stations. Second, the GNSS data of the monitoring station, namely JG, was processed in the post-processed kinematic mode to obtain the baseline vectors from the monitoring station to each reference station, giving a total of 21,789 baseline vectors at 7263 epochs. Finally, the monitoring network was constructed by the reference network and the baseline vectors between the monitoring station and reference stations at each epoch. Table 2 lists the statistics of the GNSS monitoring network's misclosures. The misclosures of the \(X\) direction are all smaller than the tolerance, and the 1.26% and 0.02% misclosures exceed the tolerances in the \(Y\) and \(Z\) direction, respectively, where \(X\), \(Y\), and \(Z\) are geocentric coordinates. \begin{table}
\begin{tabular}{c c c} \hline
**Building Height (m)** & \(\Delta x\) (mm) & \(\Delta y\) (mm) \\ \hline
100 & \(-1.6\) & \(+3.2\) \\
200 & \(-3.2\) & \(+6.4\) \\
300 & \(-4.7\) & \(+9.6\) \\
400 & \(-6.3\) & \(+12.8\) \\ \hline \end{tabular}
\end{table} 
Table 1: Approximations of the systematic bias at different building heights. By checking the misclosure, a total of 420 single-baseline vectors are eliminated as gross errors. After processing, the misclosures of all closed loops are all smaller than tolerance. An amount of 99.89% and 97.81% of the misclosures are within \(\pm\)2.0 cm in both the \(x\) and \(y\) directions, while 96.19% are within \(\pm\)4.0 cm in the \(H\) direction. After the previously described processing, some gross errors of the baseline vectors were eliminated. In order to further detect the potential gross errors of the baseline vectors, we process the GNSS monitoring network at each epoch by using the adjustment method of a free network with corrections of baseline vectors as outputs. Table 3 lists the statistics of the baseline vectors' corrections. The results show that the corrections are all smaller than the tolerance for both the \(X\) and \(Z\) directions and the corrections of 1.71% of the baseline vectors exceed the tolerance for the \(Y\) direction. The gross errors of baseline vectors can be eliminated by the tolerance of corrections, with a total of 360 single-baseline vectors eliminated. After processing, the corrections of all baseline vectors are smaller than the tolerance. Amounts of 99.95%, 93.35%, and 99.96% of corrections are within \(\pm\)2 cm for all of the three directions, respectively.