# Feasibility of Using Low-Cost Dual-Frequency GNSS Receivers for Land Surveying
## 3 Results and Discussion
### RTK and NRTK  
#### 3.3.1 Baseline Precision  
From the experiment with a spinning mobile receiver, the baseline length, i.e., the horizontal distance between the base station and the mobile receiver, was continuously determined with high precision, i.e., the RMSE of length differences with respect to nominal baseline length was 8.6 mm (Figure 8a). Among 1734 registered epochs (2 Hz registration frequency), 7 epochs (0.7%) with length error exceeding 30 mm and 44 epochs (2.5%) with length error exceeding 20 mm were recorded. The highest positioning error was 52 mm.  
The RMSE for the vertical component was 56.7 mm. For 46% of epochs, the positioning error for the height determination exceeded 5 cm, including 11% of epochs with errors exceeding 10 cm. Moreover, oscillations of the vertical component determination were noticed (Figure 8b). They were recorded during both rotation directions, i.e., clockwise (CW) and counterclockwise (CCW), and were not triggered by the change of rotation direction. All solutions were reported by the receiver as fixed, thus excluding the ambiguity fixing issues as a potential error source.  
Figure 6: Coordinate uncertainty at 95% (2\(\sigma\)) confidence level in: (**a**) relative positioning (the reference station is KALI for S1(K), WIEL for S1(W), WROC for S2 to S5); (**b**) absolute positioning.  
Figure 7: Coordinate differences from 1-h long sessions obtained in: (**a**) relative positioning (the reference station is: KALI for S1(K), WIEL for S1(W), WROC for S2 to S5); (**b**) absolute positioning.  
Solutions were assigned to rotation direction, i.e., CW and CCW. Thus, they were grouped into two disjunctive sets and their concentration was analyzed within a certain range of baseline azimuths (Figure 9). In both sets, small height determination errors were predominant for azimuths from 80 to 240\({}^{\circ}\). Significantly underestimated heights (i.e., with height determination error exceeding 5 cm) were predominant for azimuths from 270 to 50\({}^{\circ}\), while the significantly overestimated heights were recorded only within a limited azimuth range, i.e., between 155 and 231\({}^{\circ}\). Therefore, inaccurate height determination was due to the orientation change of the antenna of the mobile receiver with respect to the antenna of the base station. This implied two possible error sources, i.e., missing PCO/PCV models or improper handling of the wind-up effect. The latter would result in the increase or decrease (depending on the rotation direction) of a measured carrier phase, thus producing accumulated height determination errors, as long as the rotation direction does not change. Since the height determination error did not accumulate (Figure 8b) but oscillated, i.e., they depended on the azimuth (Figure 9b), missing PCO/PCV models was identified as the error source. The opposite orientation of low-cost antennas (which corresponded to the azimuth around 0\({}^{\circ}\)) resulted in accumulated PCO/PCV error, which resulted in inaccurate height determination.  
Figure 8: Positioning error in consecutive epochs: (**a**) for baseline length; (**b**) for the height difference. Dashed black lines indicate changes in the rotation direction (CW—clockwise, CCW—counter-clockwise).