## 3 Results
In the case of positioning using SBAS systems, according to [30], the calculation associated with the \(\sigma\) takes the following form:  
\[\sigma_{i}^{2}=\sigma_{i,fit}^{2}+\sigma_{i,\;UIRE}^{2}+\sigma_{i,air}^{2}+ \sigma_{i,\;tropo}^{2} \tag{17}\]  
where  
\(\sigma_{i,\;tropo}^{2}\) is the variance of pseudorange measurement;  
\(\sigma_{i,\;tfl}^{2}\) is the variance of rapid and long-term adjustments;  
\(\sigma_{i,\;tllre}^{2}\) is the ionospheric delay variance;  
\(\sigma_{i,air}^{2}\) is the variance associated with the operation of the GNSS receiver;  
\(\sigma_{i,\;tropo}^{2}\) is the tropospheric delay variance. Figure 4: HPE and VPE values for GPS/EGNOS positioning with a steady state of 60 s and a smoothing window of 20s versus GPS/EGNOS with no smoothing (upper figures—Xiaomi Mi8, lower figures—Septentrio AsteRx2). Figure 5 shows the SNR (signal-to-noise ratio) and elevation values of sample satellites associated with observations acquired with a Xiaomi Mi8 smartphone and a Sepentrio AsteRx2 receiver. For the Mi8 smartphone, it can be seen that there is no correlation between satellite elevation and SNR, which cannot be inferred for the data presented for the AsteRx2 receiver. The impact of SNR on smartphone positioning is considered in further analyses related to autonomous positioning and GPS/EGNOS. Figure 6 shows the results of autonomous positioning smoothed by phase observations in post-processing mode using a Xiaomi Mi8 smartphone and a Sepentrio AsteRx2 receiver and considering different variants of observation weighting (i.e., weight equal to 1, weight dependent on satellite elevation, and weight dependent on SNR). For the Mi8 smartphone and the variant weighting equal to 1, the results were \(\text{HPE}_{\text{mean}}=3.22\) m, \(\text{HPE}_{\text{std}}=2.66\) m, \(\text{HPE}_{\text{max}}=55.08\) m, \(\text{VPE}_{\text{mean}}=4.39\) m, \(\text{VPE}_{\text{std}}=4.29\) m, and \(\text{VPE}_{\text{max}}=123.29\) m. The variant taking the weighting of observations according to SNR for the Mi8 smartphone presents the best results in this analysis: \(\text{HPE}_{\text{mean}}=2.72\) m, \(\text{HPE}_{\text{std}}=2.18\) m, \(\text{HPE}_{\text{max}}=53.56\) m, \(\text{VPE}_{\text{mean}}=3.90\) m, \(\text{VPE}_{\text{std}}=3.82\) m, and \(\text{VPE}_{\text{max}}=88.14\) m. In contrast, in the case of the Mi8 smartphone, the variant for the observation weight depending on the satellite elevation gave worse results: \(\text{HPE}_{\text{mean}}=4.70\) m, \(\text{HPE}_{\text{std}}=3.72\) m, \(\text{HPE}_{\text{max}}=69.07\) m, \(\text{VPE}_{\text{mean}}=6.58\) m, \(\text{VPE}_{\text{std}}=5.63\) m, and \(\text{VPE}_{\text{max}}=96.68\) m. For the Sepentrio AsteRx2 receiver, the results of various variants are not as significantly different. The smallest maximum error of horizontal and vertical positioning was obtained for the variant based on the weight depending on the elevation of the satellite (\(\text{HPE}_{\text{max}}=2.44\) m, \(\text{VPE}_{\text{max}}=4.35\) m). On the other hand, variants based on weighting equal to 1 and dependent on SNR obtained the best results for \(\text{HPE}_{\text{mean}}\), \(\text{VPE}_{\text{mean}}\), \(\text{HPE}_{\text{std}}\), and \(\text{VPE}_{\text{std}}\) (see Table 2). Figure 5: SNR and elevation of example satellites observed during measurements with a Xiaomi Mi8 and Sepentrio AsteRx2.