## 3 Results
### Comparisons Results  
A total of 24 couples of vectors were compared, when possible, for each t-th epoch (48 vectors produced for each epoch). The comparisons were executed in terms of \(\Delta_{\text{D}}\) and \(\Delta_{\text{H}}\), thus in terms of discrepancy with respect to the MMS reference trajectory. The evaluations were performed for the four couple of vectors mentioned in point (d) of Section 2.3.3 for each t-th epoch. Particularly, considering the comparison strategy described in Section 2.3.3, for a considered epoch (t) and on equal footage, the comparisons were executed only if it was possible to calculate at least one value for the considered parameter (\(\Delta_{\text{D}}\) or \(\Delta_{\text{H}}\)), for the Galileo t-th epoch and at least one value for the GPS (or GLONASS) t-th epoch. For this reason, the second column in Table 3 (n. of combinations) also provides the potential maximum lengths of the compared vectors: e.g., considering the comparison between the \(\Delta_{\text{D}}\) computed with fixed solutions for all the combinations of four satellites, the maximum length for a vector associated to a t-th epoch was 13 for Galileo and 77 for GPS. Moreover, considering the number of solutions for one selected epoch, the presence of both fixed and float solutions was highly probable and, again, the second column in Table 3 gives the potential maximum lengths of the compared vectors. The tests involved a huge amount of generated data produced in order to consider and compare the average behavior of all possible operative conditions in a real case study, thus simulating all the real working conditions with a virtual reduced operativeness. The results for the 24 couples of comparisons are summarized in Table 4, and, in the Appendix A section, only four images (enclosed in Figure 1) related to the grey rows in Table 4 are provided. For clarity and to avoid a bulky manuscript, the remaining 20 images (related to the remaining 20 rows) are provided as Supplementary Material (Figures S1-S20). Table 4 shows, for each comparison, the global results of the comparisons performed epoch by epoch and the global results of the statistical tests:  
* Each entry in the \"comparison\" column in Table 4 shows the object of the comparison: \"\(\Delta_{\text{D},1}\) gal_vs_gps_4\" and \"\(\Delta_{\text{D},2}\) gal_vs_gps_4\" are, respectively, the comparisons between the \(\Delta_{\text{D}}\) parameter for fixed (\(\Delta_{\text{D},1}\)) and float (\(\Delta_{\text{D},2}\)) solutions for the combination of four satellites of the Galileo and GPS systems;
* The average values comparison (Avg. values comp.) columns report:
* the number of epochs for which it was possible to execute the simple comparisons between the average values of the two vectors;
* the number of times (gal score), expressed in percentage, in which the considered Galileo average planimetric or altimetric deviations performed better (thus was closer to the reference MMS trajectory for the t-th epoch). * The columns related to the \(t\)-test summary report:
* the number of epochs in which it was possible to execute the one-sample \(t\)-test (point f) Section 2.3.3);
the average \(p\)-value, introduced to provide a global vision of statistical significance of the tested differences; \(\odot\) the number of epochs, expressed in percentage, in which the \(p\)-value was less than 0.5. * Lastly, the Appendix A/Supp. Material columns provide the references to the Appendix A/Support Material figures. The reader should bear in mind that the presented figures and results derive from trajectories computed in post-processing with different accuracies (see Section 2.3.2). Table 4 shows, for the performed kinematic test, an evidence of the better planimetric performance of the Galileo system (the first 12 rows of Table 4). This experimental evidence becomes even stronger with the increasing number of satellites, regardless of the considered constellation. In the Galileo-GPS and Galileo-GLONASS comparisons, the GPS performed slightly better than the GLONASS system.