## 3 Results and Discussion  
Firstly, the differences in UZEL site daily coordinates obtained from data collected for 24 h using the dual-frequency U-Blox Zed-F9P GNSS system were divided into different durations and compared with the displacement values generated using the Zeiss BRT 006 basis-reduktionstachymeter. The error is defined by the difference between the observed displacements and the actual displacements. In this study, observed displacement refers to the displacement value obtained by processing and analyzing the GNSS observations while actual displacement refers to the displacement artificially generated using the Zeiss BRT 006 basis-redu-tionstachymeter. Figure 6 illustrates the errors for the 3, 6, 8, and 12 h observation analysis results calculated by Equation (3) for each displacement value. When examining Figure 6, it is seen that displacement values of up to 20 mm cannot be accurately determined within the 3 h measurement period. For example, it is observed that when attempting to determine a displacement of 2 mm with 3 h measurements, a 12 mm error is obtained. Similarly, an attempt to ascertain a displacement of 4 mm through 3 h measurements results in a 15 mm error, and despite aiming to determine a displacement of 10 mm a discrepancy of 18 mm error is observed with the 3 h measurements. Based on similar results obtained for displacements up to 20 mm, it is apparent that 3 h measurements are insufficient for accurately determining displacement values of such magnitudes even with the relative positioning. Figure 6 also shows that a duration time of more than 3 h gives less errors. It makes sense for longer duration measurements to be closer to the true values. Moreover, especially with measurements lasting 6 h or longer, significant results are obtained for all displacement values, and the error values significantly decrease. Furthermore, in Figure 6, it can be observed that as the displacement increases, the error amounts decrease. Figure 6: Error values for 3, 6, 8, and 12 h.  
Table 5 displays the Root Mean Square Error (RMSE) values, calculated with Equation (4), for the 3, 6, 8, and 12 h observation periods. Table 5 indicates that there is an improvement in RMSE values after the 6 h observation period for all displacements. It is observed that the RMSE values obtained with a 12 h observation period are the smallest. When examining the RMSE values for the 3 h measurements, it is observed that insignificant results are obtained for displacement values smaller than 20 mm. For instance, it is observed that for 3 h measurements, a 2 mm displacement can be determined with a 5.9 mm RMSE, a 4 mm displacement with a 7.4 mm RMSE, and an 8 mm displacement with a 9.7 mm RMSE. Similarly, for the 6 h measurements, it is observed that results are insignificant for displacement values smaller than 4 mm. For instance, for 6 h measurements, a 2 mm displacement can be determined with a 2.1 mm RMSE. After 8 h, it is seen that the results are significant for all displacement values. This indicates that at least an 8 h measurement period is necessary to achieve significant results in displacement determination studies using low-cost GNSS systems with relative positioning. To determine the minimum detectable displacement value based on the observation period, mean RMSE values of estimated displacements were calculated for datasets of the same length. The results are given in Table 6.  
The 3-sigma method was employed to determine the minimum detectable displacement value using the RMSE values from Table 6. As shown in Table 6, the minimum detectable displacement values are 22.8 mm, 11.7 mm, 8.7 mm, and 4.8 mm for observation periods of 3 h, 6 h, 8 h, and 12 h, respectively. Ref. [18] reported minimum detectable displacements for relative positioning as 23.4 mm, 13.5 mm, 9.0 mm, and 8.4 mm for observation periods of 3 h, 6 h, 12 h, and 24 h, respectively, using geodetic-grade GNSS equipment. Ref.