# Testing Multi-Frequency Low-Cost GNSS Receivers for Geodetic Monitoring Purposes
## 3 Results and Discussions
### Positional Quality Assessment  
Some elementary statistics for baseline residuals are presented in Table 2 (G-baseline) and Table 3 (L-baseline). The RMSE values for both baselines, the G- and L-baseline, are comparable and are on a level of 2 mm or better for both horizontal components. However, for the vertical component, the RMSE value is slightly higher, especially for the G-baseline. Results show that in the case of L-baseline, the height component is determined with higher precision, as in the case of G-baseline. The reason may be found in unknown antenna phase center offset and variation in the low-cost GNSS antenna. Since the L-baseline has low-cost GNSS antennae for the base as well as for the rover, the bias of the missing antenna calibration is eliminated with single differences. On the other hand, for the G-baseline, which has a geodetic GNSS antenna, with known antenna calibration parameters, the missing calibration parameters affect the final results, especially the height component [12; 20]. Figure 6 represents results from Tables 2 and 3 in graphical form. Graphs in Figure 6 depicts baseline residuals for all coordinate components (Y, X, and h) and, for both baselines, the left graphs are for G-baseline, whereas the right graphs are for L-baseline. All residuals were classified into five groups according to their absolute values, where the results are represented in Table 4 for G-baseline and in Table 5 for L-baseline. In the case of G-baseline, the residuals for both horizontal components are within 4 mm; only 3% of X residuals are in the third group. For the height component, 86% of them are within 6 mm, while the rest are equally represented in the 4 th and 5 th group. On the other hand, the results for the L-baseline are slightly worse, 3% of Y residuals and 6% of X residuals are in the third group. However, for the height component, the results are slightly better; all residuals are within 8 mm. This may again be due to the unknown antenna offset and phase variation bias in the case of low-cost antennae. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistics** & **Y (mm)** & **X (mm)** & **h (mm)** \\ \hline Min. & \(-\)3.6 & \(-\)3.2 & \(-\)9.1 \\ Max. & 2.8 & 4.4 & 8.2 \\ RMSE & 1.5 & 2.0 & 4.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Elementary residual statistics for G-baseline. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistics** & **Y (mm)** & **X (mm)** & **h (mm)** \\ \hline Min. & \(-\)2.8 & \(-\)3.5 & \(-\)7.7 \\ Max. & 4.1 & 4.3 & 5.2 \\ RMSE & 1.6 & 2.0 & 2.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Elementary residual statistics for L-baseline. Differences in determined FGG1 coordinates from both tested baselines, namely, the G-baseline and L-baseline, are shown in Table 6. Differences in position arise mostly from the height component of the baseline. \begin{table}
\begin{tabular}{c c c c} \hline
**Range** & **Y** & **X** & **h** \\ \hline
0–2 mm & 86\% & 54\% & 32\% \\
2–4 mm & 14\% & 43\% & 29\% \\
4–6 mm & 0\% & 3\% & 25\% \\
6–8 mm & 0\% & 0\% & 7\% \\
8–10 mm & 0\% & 0\% & 7\% \\ \hline \end{tabular}
\end{table} 
Table 4: Residual classification for G-baseline. Figure 6: Baseline residuals for all coordinate components and both baselines: (**a**) \(Y\) component, G-baseline (**b**) \(Y\) component, L-baseline (**c**) \(X\) component, G-baseline (**d**) \(X\) component, L-baseline (**e**) height, G-baseline (**f**) height, L-baseline. \begin{table}
\begin{tabular}{c c c c} \hline
**Range** & **Y** & **X** & **h** \\ \hline
0–2 mm & 81\% & 68\% & 46\% \\
2–4 mm & 16\% & 26\% & 36\% \\
4–6 mm & 3\% & 6\% & 14\% \\
6–8 mm & 0\% & 0\% & 4\% \\
8–10 mm & 0\% & 0\% & 0\% \\ \hline \end{tabular}
\end{table} 
Table 5: Residual classification for L-baseline. (10.4 mm), whereas the horizontal difference in position is only 2.6 mm. The difference in 3D position has been estimated with lower precision (5.2 mm), followed by 1D position (4.6 mm) while the difference in 2D position was estimated with higher precision (2.5 mm).