# Feasibility of Using Low-Cost Dual-Frequency GNSS Receivers for Land Surveying
## 3 Results and Discussion
### Static Positioning  
#### 3.2.1 Session Length  
The ambiguity fixing rate, i.e., the percentage of fixed carrier phase ambiguities in a session, was considered as a first quality indicator of the baseline solution. In the open sky environment (point S1), the average ambiguity fixing rate for the shortest baseline reached almost 80%, even though it varied from 43.3% to 97.9% for sessions of 15 min (Table 2). Therefore, it indicated that ambiguity fixing rate depends on satellite geometry and environmental conditions. The longer sessions were, the smaller the range of fixed ambiguities among sessions was. For the longest baseline, the average ambiguity fixing rate did not exceed 60%, and no ambiguity fixed was recorded during sessions of 15 min. Unresolved ambiguity resolution was mainly caused by atmospheric biases, which start playing a role for baselines exceeding 20 km [30].  
For each session, the last fixed position was used for further accuracy analysis. The extended session length went in line with the increased accuracy of estimated coordinates (Figure 5). For the shortest baseline, the horizontal accuracy was better than 10 mm even during 1-h-long sessions. Yet, also during 15-min-long sessions, horizontal accuracy greater than 20 mm was achieved. Although the precision, i.e., the repeatability of the vertical component (Up), was similar for the horizontal coordinates (East and North), an average bias of +19 mm was recorded with respect to reference coordinates. This offset exceeded  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Session Length**} & \multicolumn{3}{c}{**Reference Station: KALI**} & \multicolumn{3}{c}{**Reference Station: WIEL**} \\ \cline{2-7}  & **min** & **max** & **Average** & **min** & **max** & **Average** \\ \hline
15 min & 43.3 & 97.9 & 78.2 & 0.0 & 94.1 & 41.3 \\
30 min & 61.2 & 95.3 & 79.5 & 10.5 & 85.3 & 53.0 \\
1 h & 71.5 & 88.8 & 79.5 & 35.4 & 86.7 & 55.6 \\
2.5 h & 78.4 & 81.2 & 79.8 & 46.2 & 68.2 & 57.2 \\
5 h & 79.9 & 79.9 & 79.9 & 58.0 & 58.0 & 58.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of fixed ambiguities [%] in the relative mode for point S1.  
Figure 4: Histograms of carrier-to-noise ratio (C/N\({}_{0}\)) for each Global Navigation Satellite Systems (**a**) GPS, (**b**) GLONASS, (**c**) Galileo and (**d**) BeiDou and frequency, computed by using a u-blox receiver. 22 September 2020 (24 h).  
the sub-centimeter antenna PCO/PCV in the vertical plane, declared by the manufacturer. The scatter of coordinates estimated with the longest baselines was higher by a factor of 2 to 3. Even during the 5-h-long session, the horizontal and vertical accuracy exceeded 20 mm. Moreover, an average bias of \(-18\) mm, \(+14\) mm, and \(-20\) mm was recorded for the North, East, and Up components, respectively.  
For absolute positioning, the improvement of accuracy over time was even more evident than in the relative positioning. However, this was expected even for geodetic-grade receivers, because a significant change in satellite geometry was required to effectively de-correlate carrier phase ambiguities in PPP. After processing the 5 h-long sessions, the accuracy of \(-3\) mm, \(+13\) mm, and \(0\) mm was achieved for the North, East, and Up components, respectively.