# Testing Multi-Frequency Low-Cost GNSS Receivers for Geodetic Monitoring Purposes
## 3 Results and Discussions
### Displacement Detection Results  
Within this section, the results of displacement detections are represented. Statistical tests were performed to detect displacements in height component (1D tests), where the results are shown in Table 8, in horizontal plane (2D tests), where the results are represented in Table 9 and for spatial displacements (3D tests), where the results are represented in Table 10.  
Because the imposed displacements were in the horizontal plane only, we should fail to reject the null hypothesis in all cases of statistical tests for 1D displacement detection. The results from Table 8 show that this is true in 98% cases for the G-baseline but only in 77% cases for the L-baseline. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Position** & **1D** & **2D** & **3D** \\ \hline Differences [mm] & 10.4 & 2.6 & 10.7 \\ Differences precision & 4.6 & 2.5 & 5.2 \\
[mm] & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Differences of 1D, 2D, and 3D positions from G-baseline and L-baseline. \begin{table}
\begin{tabular}{c c c} \hline \hline
**ANOVA** & **Y** & **X** & **h** \\ \hline F & 5.27 & 17.61 & 110.69 \\ F\({}_{\text{critical}}\) & 4.02 & 4.02 & 4.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of low-cost and geodetic GNSS antennas with ANOVA statistical test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**G-Baseline**} & \multicolumn{2}{c}{**L-Baseline**} \\ \hline Displacement & 10 mm & 15 mm & 20 mm & 10 mm & 15 mm & 20 mm \\ Size & 100\% & 100\% & 100\% & 100\% & 100\% \\ Detected & 100\% & 100\% & 100\% & 97\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Detection of displacement in 1D (height component). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**G-Baseline**} & \multicolumn{2}{c}{**L-Baseline**} \\ \hline Displacement & 10 mm & 15 mm & 20 mm & 10 mm & 15 mm & 20 mm \\ Size & 100\% & 100\% & 100\% & 97\% & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Detection of 3D displacements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**G-Baseline**} & \multicolumn{2}{c}{**L-Baseline**} \\ \hline Displacement & 10 mm & 15 mm & 20 mm & 10 mm & 15 mm & 20 mm \\ Size & 100\% & 100\% & 100\% & 97\% & 100\% & 100\% \\ Detected & 100\% & 100\% & 100\% & 97\% & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Detection of 2D displacements. This result is interesting; it shows that the height component is determined with higher accuracy in the case of the G-baseline compared to the L-baseline when the true value of zero displacement is considered. In the precision determination, the RMSE of the L-baseline was shown to be smaller than the G-baseline (see previous Section 3.1), while in detecting 1D displacements the height component obtained from G-baseline was more accurate, as shown in Table 8. The reason for these results may be found in missing antenna calibration parameters for low-cost antennae, but the performance of low-cost receivers and antennae may also account for that. In the case of horizontal displacements, Table 9 presents the number of successfully determined displacements of size 10, 15, and 20 mm. The results for 5 mm displacements are not shown, since none of the two tested baselines were able to reliably detect 5 mm displacement in a high percentage (less than 90%). On the other hand, displacements greater than 20 mm are not presented, because all of them were reliably detected. Results from Table 9 are based on 270 statistical tests that were done for all possible differences between sessions where displacement was imposed. We may see that displacements of 10 mm and onward are all successfully detected on a basis of 30-min sessions and in favorable conditions. In real situations, we may experience a decrease in the rate of successfully detected displacements due to the impact of obstacles, multipath, bad weather conditions, etc. [11; 12].