# A Comprehensive Analysis of Smartphone GNSS Range Errors in Realistic Environments
## 4 Results
### Range Errors Correlation with Elevation Angle and SNR  
Two common weighting schemes are applied to smartphone and geodetic receiver observations, namely SNR-based and elevation angle-based weighting, respectively. These two weighting schemes indicate that measurement quality is highly related to the SNR and elevation angles. Therefore, in this subsection, the relationship between range errors, elevation angle, as well as SNR values, is assessed. Figure 6 depicts the temporal characteristics of range errors and the corresponding relationship with SNR and elevation angles, and  
Figure 4: Distribution of range errors on P1 and P5 for different sensors. (**a**) distribution of range errors on smartphones; (**b**) distribution of range errors on MGEX stations.  
Figure 5: Distribution of range errors of different constellations for (**a**) smartphone and (**b**) ZIM2.  
different colors represent different satellites. It can be noted again that the range errors on the first frequency are larger than those on the third frequency from the left panel which shows the time series of the range errors. In addition, there is a significant decreasing trend when the SNR increases for smartphone data both for P1 and P5, and a similar situation can be observed when comparing the relationship between range errors and elevation angles for geodetic receivers. Due to the short observation time for the smartphone data (only 30 min), elevation angles are not fully distributed from 0-90 degrees. However, it can also be concluded that, when the satellite tracked by a smartphone is newly rising or falling, the range errors will increase slightly, and therefore the elevation cut-off angle should be set reasonably. For the test ZIM3 observation, no correlation between range errors and SNRs can be found; this may be the reason that the geodetic receiver is under an optimal observation environment, and the SNR values are at a high level, which less affects the range errors.  
To further investigate range error correlations, error bars are plotted in Figure 7 to show the mean values and STDs of absolute range errors at different SNR values and elevation angles. The dots and lines denote the mean values and STDs of absolute range errors, respectively. As shown in Figure 7, it can be clearly observed that there is a significant correlation between smartphone range errors and SNR values, especially on the first frequency. Concurrently, a small correlation on the P1 range errors for geodetic receivers can be observed, which is similar to the results in [44]. The small STD for geodetic receivers at low SNR values (around 25) is due mainly to the limited observations with low SNRs. On the other hand, there is a decreasing STD trend on P1 for the geodetic receiver when  
Figure 6: Temporal characteristics of range errors (left) and the relationship with SNR (middle) and elevation angles (right) for smartphone (**a**) and ZIM2 (**b**).  
the elevation angles are increasing, while the mean values and STDs seem to be stable for P5, which have not been mentioned in the previous research.  
In view of the existing literature, the SNR cut-off strategy is widely adopted to screen out satellites that are supposed to contain noisy measurements [49]. However, in this work, it is interesting to identify that sometimes these measurements with lower SNR values are even less noisy and may be beneficial for positioning. Furthermore, range error trends vary with different signal frequencies, indicating that weighting schemes need to be tuned and adjusted when applied to different signals. Meanwhile, the elevation angle-based weighting scheme is usually used for geodetic data processing, which might be well suited to the first frequency. However, there is also a potential weighting scheme that can be proposed in future research, to consider both elevation angle and SNR values or to apply different weighting schemes for different frequencies.