# GNSS-Assisted Low-Cost Vision-Based Observation System for Deformation Monitoring
## 4 Discussion  
The data were analyzed using two approaches: experimental studies analysis and simulation analysis. So far, the obtained results have just demonstrated the opportunities of the VOS. However, what about the acquired accuracy? Is it enough to monitor various engineering structures, especially high-rise buildings? First, let us analyze the results of the experimental studies accomplished in Section 3.1. To do that, it is necessary to propagate the accuracy for one chain in the case of a multi-chain. This question is essential for the case of strict requirements on the accuracy of monitoring parameter determination. Whereas the requirements for the accuracy of vertical displacement determination are not so severe, the demands for roll or bending measurements are pretty tight. The most widespread condition for the roll and bending determination is based on the requirements for ensuring an allowable deviation \(\delta\) from the building's vertical axis during construction. The expression defines this requirement as:  
\[\delta=0,167\cdot H, \tag{20}\]  
where \(H\) is a building height in meters, and \(\delta\) will be millimeters. The allowable deviation \(\delta\) is turned into monitoring accuracy using the expression:  
\[m=\frac{\delta}{t}, \tag{21}\]  
where \(t\) is the Laplace coefficient that depends on the probability level. Typically, \(t\) equals 2 or 2.5, corresponding to 95% and 99% probability values. However, sometimes, in monitoring practice, it is suggested to use \(t\) equals 5 to increase the reliability of the measurement results. Let us suppose that the accuracy along the \(x\) and \(y\) axis is equal to \(m\). The resulting accuracy will depend on the number of chains \(k\) used for measurements. Under this premise, the final accuracy \(M\) can be determined as:  
\[m_{x}=m\sqrt{k};\ m_{y}=m\sqrt{k},\ \ M=\sqrt{m_{x}^{2}+m_{y}^{2}} \tag{22}\]  
The expressions (22) permit us to compute the accuracy for multi-chain VOS and compare these values with the allowable values from (20). The following calculations for  
Figure 27: Accuracy of absolute coordinate determination without additional GNSS observations. the various heights have been performed (Table 8), taking the figures from Table 7. The accuracy calculations have been carried out based on the VOS installation scheme along the entire height of the structure with a step of 17, 25, and 33 m.  
Figure 28 is a graphic summary of the results from Table 8. The horizontal axis describes a building's height, while the vertical axis highlights the accuracy propagation. The experimental results and further calculations yielded some interesting findings. The calculations by (22) prove the impossibility of leveraging the suggested VOS for monitoring alone. The general picture emerging from the results is that the multi-chain VOS can probably ensure the necessary accuracy for monitoring buildings higher than 500 m. The principal stress should be pointed out on the rising efficiency of the VOS with a building height. The inclusion of GNSS measurements changes the final distribution of the RMS errors. However, our findings are not generalizable beyond the subset examined because the calculation approach suggested above does not account for the effect of the interrelated measurements, as seen in Figure 22.  
Thus, it is essential to simulate the VOS measurements to account for the redundancy of measurements. Therefore, the second step is the analysis of the simulation results in Section 3.2. Let us summarize the results presented in Tables A1-A4. The accuracy at each block was averaged, and the mean accuracy value was accepted as final for analysis. These values were compared with allowable values (20). Moreover, the simulation results allow one to estimate two measurement modes: relative and absolute.