# GNSS-Assisted Low-Cost Vision-Based Observation System for Deformation Monitoring
## 3 Results
### Preliminary Analysis of the VOS Accuracy for the Test Structure  
The results obtained in the previous subsection permit determining the VOS operation's accuracy for a typical building. Insofar as this is a step in the preliminary accuracy estimation, it is possible to simulate the VOS operation for a building with simple geometry. It is supposed that the sensors are placed 30 m apart from each other. The simulation was performed for two buildings with different heights, which were 90 m and 420 m. The first building is presented in Figure 22. The VOS scheme was implemented according to Figure 5a. As the test building height was insignificant, it was decided not to use GNSS measurements for this test analysis.  
In Figure 22, the blue points are the places of sensor installation. The arrows indicate the measurement directions. Points 10, 11, 12, and 13 are the targets on the surrounding objects that determine the external coordinate system. These points are accepted as errorless, but the accuracy of their determination was also estimated. The root mean square errors from Table 7 were used as descriptive statistics for the statistical simulation of measurement errors. The simulation was performed by the Monte-Carlo method for normal (Gaussian) distribution. The measurement errors were considered random  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & \(\mathcal{S}\) **(m)** & \(\mathbf{m_{a}}\) **(mm)** & \(\mathbf{m_{b}}\) **(mm)** & **Total RMS (mm)** \\ \hline Test 1 & 33 & 4.3 & 3.4 & 5.5 \\ Test 2 & 25 & 6.8 & 1.0 & 6.9 \\ Test 3 & 17 & 7.8 & 1.2 & 7.9 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Accuracy of displacement determination.  
Figure 21: Finding the target center based on the reference and input images: (**a**) image acquisition; (**b**) input image of 100 \(\times\) 100 pixels; (**c**) reference image.  
The numerical results are summarized in Appendix A, Tables A3 and A4. The values in Tables A1-A4 allow assessing the probable accuracy of the monitoring parameter determination in the external and internal coordinate systems.  
The second simulation analysis deals with a tall building (420 m). The simulation parameters were the same as for the previous case. However, this case allows us to check the effectiveness of the combined solution, namely, the integration of the VOS and GNSS. Thus, the GNSS accuracy for the top of the building was integrated with the accuracy of the simulated VOS. The simulation results are presented in Appendix B, Figure A1, where the absolute accuracy is given, and in Figure A2 for the relative observations. The accuracy of the GNSS measurements was assigned using standard values, e.g., \(\pm\)2-3 mm along the horizontal axis and \(\pm\)5 mm for elevation. For the first case (Figure A1a), the GNSS measurements are considered non-fixed. In other words, these measurements are supposed to be included in the adjustment procedure. Two GNSS antennas on the building top are suggested as the most widespread case. The second case (Figure A1b) presents the measurements without GNSS observations. Therefore, the errors of the VOS are not restricted by GNSS measurements and propagate with the building height.  
The numerical results are summarized in Figures 26 and 27 as the preliminary accuracy of the massive number of points is better portrayed in the graphs. Figure 26 describes the RMS errors of coordinate determination along the coordinate axis for the case of absolute measurements accompanied by GNSS, i.e., the measurements referenced to some external coordinate system.  
Figure 27 shows the simulation results for measurements without GNSS support.  
The results outlined in Tables A1-A4 and Figures 2