# Galileo: The Added Value for Integrity in
## 5 Experimental Results
### Positioning Results  
In this section, the results obtained in the position domain are presented. Two of the outputs of the RAIM algorithm are the horizontal protection limit (HPL) and vertical protection limit (VPL) defined in [1]. In order to demonstrate the benefits of Galileo inclusion, HPL and VPL are plotted as a function of time in the upper and lower boxes of Figure 3. The improvements due to the Galileo inclusion clearly emerge from Figure 3: both HPL and VPL are lower than in the GPS-only case. In Figure 4, the WARP values are plotted as a function of time and with respect to the threshold, \(T_{G}\). The benefits of the introduction of the Galileo observables are evident as for the HPL and VPL cases. Figure 3: Horizontal protection limit (HPL) and vertical protection limit (VPL) as a function of time. Benefits of the inclusion of Galileo measurements in terms of HPL and VPL. The introduction of the Galileo measurements provides an enhancement of the redundancy of the system; this is a key enabler for the improvements of the performance of the RAIM algorithm. The enhanced redundancy allows the rejection of a higher number of measurements affected by gross errors. The number of pseudoranges excluded epoch by epoch is shown in Figure 5: in the multi-constellation, case a higher number of outliers can be identified and rejected. The SA for the data collection in the case of GPS alone assumes a high value, about 95%. The inclusion of the Galileo measurements enhances the SA, and almost no outages are present in the multi-constellation solution. The application of the RAIM algorithm reduces the availability of the solution, specifically the RA, that in the GPS-only case is more than halved with respect to the SA. When the RAIM algorithm is applied, the benefit of the inclusion of the Galileo measurements is more evident; the RA in the case of the multi-constellation solution is almost twice that of the single system case and passes from 43% to 78%. The results related to the SA and RA of the position solution are detailed in Table 2.  
Figure 4: Weighted approximate radial-error protected (WARP) as a function of time. Benefits of the inclusion of Galileo measurements. Figure 5: Number of pseudoranges excluded epoch by epoch. More exclusions can be performed when the multi-constellation approach is adopted. The integrity algorithm output is a flag indicating the status of the solution; specifically, if the solution is declared reliable, the flag is set to one. If there is no redundancy to apply the RAIM algorithm or if the geometry conditions are not satisfied, the flag is set to zero. Finally, if the solution is declared unreliable, the flag is set to two. The flag values are plotted as a function of time in Figure 6. Only during a short period of time, the solution is not available for the GPS-only case. In Figure 7, a short time interval of the data collection is considered, and the values of the flag are plotted as a function of time. The benefits of the multi-constellation approach clearly emerge from the \begin{table}
\begin{tabular}{l c c} \hline \hline
**Configuration** & **SA (\%)** & **RA (\%)** \\ \hline GPS noRAIM & 95 & N.A. \\ GG noRAIM & 100 & N.A. \\ GPS RAIM & 95 & 43 \\ GG RAIM & 100 & 78 \\ \hline \end{tabular}
\end{table} 
Table 2: Solution availability (SA) and reliable availability (RA) of the different solutions. GG, GPS and Galileo. Figure 6: Integrity flag as a function of time. The flag is set to zero when it is not possible to test the reliability of the solution, and one implies a reliable solution, while two indicates an unreliable solution. Figure 7: Integrity flag as a function of time. A short interval of the data is considered to better analyze the benefits of the multi-constellation. figure: in the grey box on the left, the solution passes from unreliable, for the GPS only case, to reliable for the multi-constellation case. In the box on the right, the solution passes from unavailable to reliable.