## 4 Experimental Results of Applying Robust-EKF
### Experimental Results  
To demonstrate the above algorithm, this study uses the GPS, Galileo and GLONASS data from ABMF station (RINEX version 2.11 (GPS and GLONASS) and version 3.02 (Galileo) format). This reference station is located in Guadeloupe. RINEX data and broadcast ephemeris data used for calculation were downloaded from RGP network and CDDIS for day of 1 January 2019. In order to assess the algorithm performance, five scenarios are investigated under MATLAB environment:  
* Scenario #1: Navigation solution based on GPS data,
* Scenario #2: Navigation solution based on Galileo data,
* Scenario #3: Navigation solution based on GLONASS data,
* Scenario #4: Navigation solution based on GPS/Galileo/GLONASS data,
* Scenario #5: Navigation solution based on robust-EKF GPS/Galileo/GLONASS data. Figure 2 illustrates the number visible satellites of GPS (red curve), Galileo (black curve), GLONASS (cyan curve), and combined GPS/Galileo/GLONASS (blue curve) systems over an elevation mask of 10\({}^{\circ}\). It demonstrates that the number Galileo and GLONASS satellites is zero during some epochs. The average number of visible satellites is about 20 satellites when GPS, Galileo, and GLONASS are combined for positioning, which presents an advantage since they bring more signals to the receiver. However, it also presents a disadvantage since they may bring fault signals which can penalize the position estimation accuracy. The results are given Figure 3 which represents the position errors of the five scenarios with respect to time. dE, dN, dU are the errors in the East, North and Vertical components of the user's position estimates. In Figure 3, the red curve pertains to scenario #1 with GPS data only. The black curve represents scenario #2 with Galileo data only. The cyan curve is related to scenario #3 with GLONASS data only. It can be seen that the position errors of GPS and Galileo data are small and stable whereas those from GLONASS data are large and unstable. The blue curve represents for scenario #4 with combination of GPS, Galileo, and GLONASS data. The position accuracy from the combination improves compared to the use of GLONASS data only. However, the errors still remain unsteady and large in the East axis. In particular, the positions are not determined around the times 22 h, 23 h, and 24 h, because of the large HPL (in Figure 4). Consequently, the robust-EKF method is applied to enhance the accuracy of user position in scenario #5 and the obtained position errors are represented in the green curve. They are more stable and more accurate than the other scenarios. Figure 4 represents the HPLs of combined GPS, Galileo and GLONASS data as a function of time. HPL is represented to check an assured zone of the estimated position. If the HPL is bigger than the HAL, the failure signals are detected and affect the position accuracy. After applying robust-EKF method, HPLs of robust GPS, Galileo and GLONASS data are recalculated in Figure 5 and the large HPLs are reduced. For more insights about the position accuracy obtained for the five scenarios, Table 2 presents a comparison of the corresponding position errors. Figure 4: HPLs of combined GPS, Galileo and GLONASS data at station ABMF. Figure 5: HPLs of robust GPS/GAL/GLO data at station ABMF. Figure 3: Position errors of the five scenarios at station ABMF. According to the RMS (Root Mean Square) error values listed in Table 2, the robust combination of GPS, Galileo, and GLONASS data improves the position accuracy by about 53 %, 41%, and 95% compared to the use of GPS data only, Galileo data only, and GLONASS data only, respectively. It is also improved by about 84% compared to the non-robust combination of GPS, Galileo, and GLONASS data. In the introduction section, it has been stated that the robust-EKF can be better than the Weighted Least-Squares Estimation (WLSE) to improve the position accuracy.