## 3 Results  
Data associated with the Mi8 smartphone were recalculated in GPS/EGNOS mode according to [30], with the following variations: smoothing window--10 s, smoothing window--20 s, smoothing window--30 s, no smoothing. Each of these options has sub-options: excluding satellites before reaching a steady state at 1 s, excluding satellites before reaching a steady state at 60 s, excluding satellites before reaching a steady state at 180 s, and excluding satellites before reaching steady state at 360 s.  
Figures 2 and 3 show the results of the smoothing window and steady-state analysis of GPS/EGNOS positioning using an Mi8 smartphone compared to GPS/EGNOS positioning using a Sepetratio AsteRx2 receiver. The horizontal positioning error (HPE) and vertical positioning error (VPE) values were calculated. Different colours indicate the number of individual solutions with similar values, so one can deduce which error values occurred most often in the calculations. Already, using the results presented in Figure 2, we can deduce that for the Mi8 smartphone, the best accuracy obtained both horizontally and vertically is characterised by a steady state of 60 s and a smoothing window of 20 s. The numerical values of the accuracy analysis presented in Table 1 show that indeed, for both horizontal and vertical analysis, the best results of the mean positioning errors, their standard deviation, as well as the VPE\({}_{\text{max}}\) were obtained for a steady state of 60 s and a smoothing window of 20 (HPE\({}_{\text{mean}}\) = 2.24 m, HPE\({}_{\text{std}}\) = 1.95 m, VPE\({}_{\text{mean}}\) = 3.27 m, VPE\({}_{\text{std}}\) = 2.78 m, VPE\({}_{\text{max}}\) = 24.48). However, the best results of maximum horizontal error values were obtained for a steady state of 1 s and a smoothing window of 30 s, where HPE\({}_{\text{max}}\) = 26.03 m. In further analyses, a steady state of 60 s and a smoothing window of 20 s were assumed to be the best pairing among the analysed variants and were included in further analyses as a positioning variant using the Xiaomi Mi8 GPS/EGNOS smartphone. In the case of the results obtained for the Sepetratio AsteRx2 receiver presented in Figure 3, the differences obtained between the variants are not so noticeable, but the analysis of the numerical results obtained also identifies a steady state of 60 s and a smoothing window of 20 s as being optimal (HPE\({}_{\text{mean}}\) = 0.38 m, HPE\({}_{\text{std}}\) = 0.17 m, HPE\({}_{\text{max}}\) = 1.48 m, VPE\({}_{\text{mean}}\) = 0.50 m, VPE\({}_{\text{std}}\) = 0.43 m, VPE\({}_{\text{max}}\) = 2.19 m). Compared to the results obtained for the smartphone, this variant performs much better, which is understandable due to the different GNSS chipsets and antennas used in these two measuring devices. Figure 2: HPE and VPE values for Xiaomi Mi8 GPS/EGNOS steady-state smartphone positioning from top to bottom: 1 s, 60 s, 180 s, 360 s.  
Figure 3: HPE and VPE values for Septentrio AsteRx2 GPS/EGNOS steady-state receiver positioning from top to bottom: 1 s, 60 s, 180 s, 360 s.  
Figure 4 compares the best GPS/EGNOS positioning result with smoothing (steady state of 60 s and a smoothing window of 20 s) with the solution without smoothing code observations. It can be seen that the vertical and horizontal accuracy results are significantly better for the solution based on smoothing (according to Table 1: for the no-smoothing variant, \(\text{HPE}_{\text{mean}}=4.47\) m, \(\text{HPE}_{\text{std}}=3.01\) m, \(\text{HPE}_{\text{max}}=43.03\) m, \(\text{VPE}_{\text{mean}}=6.38\) m, \(\text{VPE}_{\text{std}}=5.32\) m, \(\text{VPE}_{\text{max}}=64.95\) m). Also noticeable in Figure 4 is the significant improvement in vertical positioning accuracy when using carrier-phase smoothed code observation.