# Low-Cost Dual-Frequency GNSS Receivers and Antennas for Surveying in Urban Areas
## 3 Results and Discussion
### Relative Positioning Performance  
The positioning performance of low-cost GNSS receivers in combination with Survey calibrated antenna (LC\(-\)1) was tested in urban areas, considering sessions of 60, 30, 20, and 15 min. Three of the stations were located in areas with obstacles in the vicinity (ST 2, ST 3, and ST 4), while one of them (ST 1) was in the open sky to highlight the differences. For each of the stations, the differences in the obtained coordinates (easting, northing, and ellipsoid height) from the true coordinates are estimated for sessions of 15-60 min. The horizontal (d\({}_{\text{2D}}\)) and spatial differences (d\({}_{\text{3D}}\)) between the estimated and true coordinates are also presented for each station. Figure 9: Positioning solutions in open sky and urban conditions: (**a**) LC\(-\)1 on ST 1 (open sky); (**b**) LC\(-\)2 on ST 1 (open sky); (**c**) LC\(-\)1 on ST 1A (urban areas); and (**d**) LC\(-\)2 on ST 1A (urban areas). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenarios** & **Solution** & **LC\(-\)1** & **LC\(-\)2** \\ \hline Open sky & Fixed & 96.8\% & 98.3\% \\  & Float & 3.2 \% & 1.7\% \\ Urban area & Fixed & 75.0\% & 93.4\% \\  & Float & 25.0\% & 6.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ambiguity resolution ratio for LC\(-\)1 and LC\(-\)2. The results for ST 1 are shown in Table 4. Based on the obtained results, it can be concluded that low-cost GNSS receivers perform well in the open sky. The horizontal, vertical, and spatial position differences are less than 5 mm, and these results are valid even for short sessions lasting 15 min. The ambiguity fix ratio for the main session is 99.5%, and LC\(-1\) can provide fix solutions in all the sessions considered. ST 2 was located in an urban area with obstacles/buildings nearby where higher influence of multipath was expected than in ST 1. For the horizontal positions, the differences are less than 10 mm in 80% of the sessions, while the differences in spatial positions are between 5-30 mm (Table 5). For the 60 min session, the ambiguity rate of the fixed solutions is 64.8% under these conditions, even though a short baseline is considered. Compared to ST 1, the positioning performance in ST 2 is worse, especially for the spatial component. This was due to the accuracy obtained for the ellipsoid height, which was determined with lower accuracy compared to the horizontal components. ST 3 has fewer obstacles from the south side than ST 2 and obtained results are shown in Table 6. The horizontal position differences do not exceed 10 mm even in the short sessions, while the differences in the spatial and vertical positions remain below 15 mm. In comparison to the previous station, better accuracy is achieved for the vertical component, while the ambiguity fix ratio is 90.3%, which is 25.5% higher than for ST 2 (64.8%). ST 4 is surrounded by tall trees (10 m) on the south side, therefore, poorer results are obtained, which are listed in Table 7. The sub-sessions of 40-60 min, as well as sub-sessions 45-60 min, do not provide fix solutions. In these two sessions, the accuracy exceeds 10 cm, therefore, these values are not shown. Nevertheless, for sessions with fix solutions, the horizontal and spatial differences are below 15 and 25 mm, respectively, while the vertical position differences are less than 20 mm. For this station with more obstacles for satellite signals, the percentage of ambiguity fix ratio is 51.6%, which is the lowest value for all stations.