# Accuracy of Code GNSS Receivers under Various Conditions
## 4 Results
### Surface  
The result of calculating the measurement points from the surveying instrument was loaded into the QGIS 3.16.14 program. As a result of interpreting the accuracy of measurement points, the average value of the circle radius (35.5 m) and the coordinates of the theoretical circle center were calculated based on precise solutions. Considering the conditions and execution of the measurement in motion, a range of \(\pm\)0.5 m was assumed from the determined (based on the calculated radius and coordinates of the center of the circle) line forming the circle, in which the comparison points should be located. The points were selected to represent the accepted geometric figure of the surface measurement (Figure 11). Figure 11: Points from the RTK measurement (**purple**) and the fitted reference circle (**green**). Figure 10: Plot of U-component deviations of linear measurement with code receivers. After exporting the reference points, we proceeded to determine the NEU components analogously to the point measurement. Analysis of Figure 12 shows a plot of NE components deviations for the 5 code receivers in which similar accuracies between the handheld receivers were noted. It was observed that smartphone X_1 lost signal after one minute of measurement and recorded the same last recorded coordinates until the end of the survey. The G_1 receiver using the GPS measurement mode was positioned with an accuracy of 9 m for the N component and 8 m for the E component, while the G_2 receiver equipped with the GPS+GLONASS signal recorded horizontal coordinates with an accuracy of 8 m for the N component and 6 m for the E component. Comparing the graphs of G_1 and G_2, one can see the consistency between the handheld receivers in determining the horizontal coordinates while measuring on the move. Phone X_2 obtained deviation values of the N component not exceeding 15 m and of the E component not exceeding 13 m. Smartphone X_3 recorded data with an accuracy up to 15 m, although values less than 9 m for the N component prevailed, and this phone was within 12 m for the E component. The cell phone plots were not consistent with each other, the points could be described as highly scattered, and the accuracies were variable over a short time interval. When analyzing the U-component deviation plot of the surface measurement (Figure 13), large error values were observed for receiver G_2, which ranged from 25 to 54 m. Receiver G_1 recorded data with an accuracy of 14 m, except for one larger error that reached 25 m. During altitude determination, a better measurement capability was guaranteed by the receiver using GPS (G_1) compared to the receiver using the GPS+GLONASS mode (G_2). This means, as in the measurement across a line (Section 3.2), that in a moving receiver, GLONASS signals underestimated the accuracy, causing artefacts up to even 50 m.  
Figure 12: Plot of NE component deviations of surface measurements with code receivers. Table 2 shows a statistical summary of obtained accuracies and deviations. The bias is a mean of absolute difference between coordinates gathered by the receiver vs. the RTK result at the same point, according to the equation:  
\[b_{c}\ =\ \frac{\sum_{i\ =\ 1}^{n}\lvert r_{i}\ -\ \text{RTK}_{i}\rvert}{n}. \tag{4}\]  
where \(b_{c}\) is the bias, \(c\ =\ N,E,\ \text{or}\ U\) are coordinate components, \(r_{i}\) is the coordinate value gathered by either smartphone or handheld receiver, \(\text{RTK}_{i}\) is the coordinate component gathered from RTK mode, and \(n\) is the number of the coordinates. The deviations were calculated as the mean, absolute value of the deviation from the RTK measurement. \[\sigma_{c}\ =\ \sqrt{\frac{\sum_{i\ =\ 1}^{n}\left(r_{i}\ -\ \text{RTK}_{i} \right)^{2}}{n}}. \tag{5}\]  
where \(\sigma_{c}\) is the standard deviation.