# GNSS-Assisted Low-Cost Vision-Based Observation System for Deformation Monitoring
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Building Height (m)**} \\ \cline{2-10}
**Sensor-to-Target** & 50 & 100 & 150 & 200 & 250 & 300 & 350 & 400 & 450 \\ \cline{2-10}
**Distance (m)** & \multicolumn{10}{c}{**Displacement Accuracy \(M\) (mm)**} \\ \hline
**17** & 13.5 & 19.2 & 23.5 & 27.1 & 30.3 & 33.2 & 35.8 & 38.3 & 40.6 \\
**25** & 9.8 & 13.8 & 16.9 & 19.5 & 21.8 & 23.9 & 25.8 & 27.6 & 29.3 \\
**33** & 7.3 & 10.3 & 12.6 & 14.5 & 16.2 & 17.8 & 19.2 & 20.5 & 21.8 \\
**Allowable value** & 3.3 & 6.7 & 10.0 & 13.4 & 16.7 & 20.0 & 23.4 & 26.7 & 30.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Accuracy dependency between the chain’s length and building height. Figure 28: VOS accuracy propagation. As seen in Figure 29, the simulation results provide a more lifelike picture of the VOS accuracy. The final accuracy has improved thanks to accounting for the measurement redundancy. Therefore, the VOS provides a reliable determination of monitoring parameters starting from the height of 90 m for absolute measurements. That is obvious; the installation of the VOS for such a small building is useless, and the conventional geodetic methods provide the necessary accuracy and are well studied. Things get much more complicated for the higher buildings. To estimate the efficiency of the VOS for tall structures, with the inclusion of the GNSS measurements, the simulation was performed for the building's 420 m height. Let us analyze the results in Figures 26 and 27. Again, the analysis is better presented graphically. To do so, the RMS errors over each floor were averaged and compared in Figure 30.  
The results of the GNSS-assisted VOS simulation look different from the VOS-only simulation. One may infer a couple of interesting findings. At first, thanks to the GNSS observations, the accuracy of the VOS is saved almost at the same level for the whole structure. This effect grows with the structure height as far as the GNSS restricts the error propagation in the VOS. Secondly, as was expected, the GNSS-assisted VOS may ensure the  
Figure 30: Simulation results comparison for GNSS-accompanied case. Figure 29: Simulation results comparison. necessary accuracy starting from 60 m. We obtained a weighted accuracy value for the high structures thanks to combined adjustment. Therefore, the simulation results proved the high capability of the developed GNSS-assisted low-cost vision-based observation system for deformation monitoring. The specific structure of the VOS puts forward some restrictions on the application of this system. These restrictions are defined by the geometry and construction technology of the monitoring objects. Considering the geometry, one needs to pay attention to the VOS scheme. It is clear that for chains we need straight lines between the sensors. Curvilinear structures require modification of single-chain construction. Moreover, the measurement processing is not straightforward. As an example, let us consider the simplest case, namely, the VOS for horizontal monitoring of a curvilinear structure (e.g., dams, tunnels, shells, etc.) between two reference points (Figure 31). The QR targets are placed perpendicularly to the sensors but with angles (\(\alpha\), \(\varphi\)) between each other. The measured displacements must be converted regarding coordinate axes. The manufacturing and installation of the system gets complicated. Therefore, the idea of VOS has to be developed and studied in the future for the case of curvilinear structures. So far, the considered and examined scheme applies to high-rise buildings. The second condition is the material of the monitoring structure that was built. This condition especially makes sense when we deal with temperature deformation. The temperature influence leads to structure bending. In the Introduction, it was pointed out that bending is one of the primary issues of monitoring, and the VOS is the solution to this problem. The bending values will be different for different heights (Figure 32).