## 3 Results
### Detailed Analysis for MAS100 ESP Station
Also, the GE (red line), where the precision of observations was the same for both systems, showed more improvement than for the GE1 (green line), where for Galileo observations worse precision than GPS observations were accepted. In the next step, we compared the estimated tropospheric delays with the IGS solutions. The results are presented in Figure 6. The worst results were obtained for the E for Function_6, where the average difference was \(-\)16.2 mm. The best solution for the E was obtained for Function_1, where the difference was \(-\)4.0 mm. Similar results were obtained for the G, where for Function_1 the best agreement with IGS solutions of 4.7 mm was also obtained. The worst, G, is based on Function_5, where a difference of 12.4 mm was obtained. In the other cases, the average difference did not exceed 10.0 mm. A systematic difference can be seen between the E and G, where it ranged from 8.7 mm for Function_7 to 24.3 mm for Function_6. Additionally, for the E, the results always showed negative values and positive values for the G.  
GPS+Galileo solutions show much better compatibility with IGS solutions. It confirms the conclusion presented in [74] that using both systems together leads to better accuracy of ZPD. For both the GE and GE1, the mean differences did not exceed 6.5 mm, with the exception of the solutions based on Function_5 (for the GE and GE1) and Function_1 (for GE1), which all gave larger ZPD values than IGS. The highest consistency of the GE was obtained for Function_2, with a score of 0.4 mm, whereas for the GE1, Function_1 and Function_5 had a score of \(-\)1.0 mm. The worst results were obtained for Function_8, with 6.3 mm and 6.5 mm for the GE and GE1, respectively. Figure 4: Time series of U component, 2D and 3D errors for the first four hours for the weighting functions. Functions 1–4 for the MAS100 ESP station for the 39 DoY for all solutions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution. According to [75,76], the ISB parameter must be estimated for multi-GNSS positioning. ISB can be estimated as a constant value or as a time-varying value [67] and should have the same value regardless of the weighting functions. In our analysis, we estimated ISB as a random walk process. Figure 7 shows the estimated ISB for the analyzed GPS+Galileo solutions, where one can see the differences depending on the solution and the function used. For Function_1, for the GE, a big jump of around 14 h:30 min was observed. The difference for ISB was from \(-\)5.2 ns to \(-\)4.8 ns (about 11 cm), which did not occur for the GE1. For Function_6 (yellow) and Function_8 (gray) in the GE solution, a much worse consistency with the other weight functions was obtained after 19 h. The systematic difference was about 0.2 ns (6 cm). Changing the weights for the Galileo observations in the GE1 solution helped to remove this difference for Function_8, but, unfortunately, a  
Figure 5: Time series of U component, 2D and 3D errors for the first four hours for the weighting functions. Functions 5–8 for the MAS100 ESP station for the 39 DoY for all solutions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution. Figure 6: Time series of ZPD differences between the estimated value from PPP and calculated by the IGS for the MAS100 ESP station for the 39 DoY for all solutions and weighting functions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution. discrepancy appeared between 15 h and 18 h. The other functions show a generally high consistency, in the range of 0.1 ns, which corresponds to less than 3 cm.