# GNSS-Assisted Low-Cost Vision-Based Observation System for Deformation Monitoring
## 3 Results  
### In-Field Experimental Study of the Displacement Measurements for a Single Chain  
It was decided to prepare and perform experimental measurements for a single chain of the VOS sensors to verify the above theoretical considerations. As a sensor of the VOS, a General Electric G100 digital camera was used. The images were collected under the conditions in Section 2.1 but with an f-number of 3.9. To simulate the target movements, the QR target was on a solid plate and a test bench, which allowed moving the target in a horizontal plane by small given values \((\delta a_{i},\delta b_{i})\), which were manufactured and applied. The operation of the VOS sensor chain in a horizontal plane was simulated for different distances between the target and the camera (Figure 18). The test bench (Figure 19a) was developed at Kyiv National University of Construction and Architecture, Department of Applied Geodesy. The test bench generally allows the precise movement of any attached device (QR target) in space with accuracy of \(\pm\)0.1 mm. Initially, this device was deployed for precise alignment measurements and setting-out but was revamped for our study purpose. The simulation of the single chain was performed at the Department of Applied Geodesy (Figure 19b). Figure 19: The equipment for the single-chain simulation: (**a**) mechanical equipment on a tripod for the precise displacement of QR target; (**b**) place for the test bench setup and single-chain test; (**c**) the sampling images from the testing site (**left** image: ISO-800, **right** image: ISO-100). Since the primary element of the VOS is a camera, it must be calibrated before usage. The calibration was accomplished with Photomodeler software. However, the various software that calculates the necessary parameters can be used for the calibration procedure. The calibration quality is presented in Figure 19. The calibration parameters were: focal length: \(-\)68.02 mm, image format size: 6.39 mm \(\times\) 4.79 mm, principal point coordinates: 3.83 mm \(\times\) 2.39 mm, and lens distortion coefficients K1 = 0.000152, K2 = 4.18 \(\times\) 10\({}^{-7}\). The overall calibration accuracy is equal to 0.28 px, with maximum residual of 1.38 px. The calibration error distribution for different photos is presented in Figure 20.  
Three simulation tests were performed for different distances of the camera (sensor)-target. The camera was focused to infinity, and the standard parameters for daylight conditions image capturing were set up. No additional light sources were necessary. Image processing was performed using the phase correlation algorithm. The processing was carried out using MatLab software. The image resolution parameter for each distance was determined according to the previous propositions (Table 2). In the first step, the stability of the camera position during the experiment was determined. The results showed that the camera was stable during the image capturing. This result is due to setting the camera in the automatic mode for images captured during the surveying time. The images were taken automatically with a time interval of 30 s. The ISO speed values were changed from ISO-100 to ISO-800. The results are similar between the series, and the data are given in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Test** & \(S\) **(m)** & \(a\) **(m)** & \(b\) **(m)** & \(m\) **(px)** & \(n\) **(px)** & \(c\) **(mm/px)** \\ \hline Test 1 & 33 & 2.83 & 2.08 & 4320 & 3240 & 1.92 & 1.92 \\ Test 2 & 25 & 2.14 & 1.58 & 4320 & 3240 & 1.45 & 1.45 \\ Test 3 & 17 & 1.46 & 1.07 & 4320 & 3240 & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resolution values for different distances. Figure 20: Calibration errors for different photos. In the course of the displacement study, the images were taken in automatic mode. The interval between consequent images was set up to 60 s. Every minute, the QR target displacement was changed manually to the values presented in Tables 4-6.