## 4 Conclusions  
This study investigated the performance of low-cost GNSS equipment in determining horizontal displacements through the relative positioning method. Errors and RMSE values were assessed based on tests with varying observation times and displacement values. Analysis of RMSE values revealed significant improvements in accuracy, particularly after  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **3 h** & **6 h** & **8 h** & **12 h** \\ \hline RMSE (mm) & 7.6 & 3.9 & 2.9 & 1.6 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mean RMSE values for 3 h, 6 h, 8 h, and 12 h observation periods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Displacement** & \multicolumn{4}{c}{**RMSE (mm)**} \\
**(mm)** & **3 h** & **6 h** & **8 h** & **12 h** \\ \hline
2 & 5.9 & 2.1 & 1.4 & 0.9 \\
4 & 7.4 & 2.0 & 1.8 & 1.8 \\
6 & 3.0 & 2.0 & 2.2 & 1.3 \\
8 & 9.7 & 4.4 & 3.2 & 1.0 \\
10 & 9.1 & 3.9 & 1.9 & 1.5 \\
20 & 7.3 & 6.2 & 4.8 & 2.3 \\
30 & 10.0 & 7.0 & 4.4 & 2.0 \\
40 & 7.6 & 4.6 & 3.6 & 1.6 \\
50 & 8.1 & 2.8 & 3.2 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: RMSE values for 3 h, 6 h, 8 h, and 12 h observation periods.  
the 8 h observation period. This suggests that an observation period of at least 8 h is necessary to accurately determine displacement values with low-cost GNSS equipment through relative positioning. It can be said that an 8 h measurement period is necessary to attain high-precision results with low-cost GNSS systems, akin to high-cost geodetic GNSS systems, particularly in studies such as monitoring tectonic movements and landslides, where high accuracy is imperative.  
However, this study identified the smallest displacement values that can be reliably determined with low-cost GNSS equipment as 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. These values closely align with a study conducted by [18] using geodetic GNSS equipment and [27] using PPP method and low-cost GNSS equipment. The consistency of the results suggests that low-cost GNSS equipment can achieve displacement values with a level of accuracy similar to that of geodetic instruments. These results indicate that low-cost GNSS systems can be used as alternatives to geodetic GNSS systems after 8 h of observation, particularly in engineering measurements where determining horizontal displacements is crucial, such as monitoring landslides, tectonic movements, and deformations in structures. The lower cost of these systems opens the possibility of monitoring larger areas with more GNSS equipment, indirectly enhancing the security of these regions. Thanks to their low costs, these systems can be set up as permanent and continuous GNSS stations, enabling the continuous monitoring of tectonic movements, landslides, and engineering structures. This, in turn, facilitates the timely detection of potential deformations.  
It should be noted that these results are conducted in this study for displacement values. No velocity estimation has been performed in this study. The determination of annual velocity is crucial for tectonic studies, and future research may explore the possibility of velocity calculation for tectonic purposes using low-cost systems. Additionally, this study can be conducted using different GNSS processing software other than GAMIT/GLOBK. However, since the focus of this study was on displacement determination accuracy rather than positioning accuracy, it is believed that the results would not significantly change.  
Methodology, B.A.; Formal analysis, S.O.; Data curation, B.A.; Writing--original draft, B.A.; Writing--review & editing, S.O.; Visualization, S.O. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors. The authors declare no conflicts of interest.