## 8 SQI and RAIM Interaction
### Simulation Results without Using GDOP Data  
The purpose of the Section 3 simulations is to show the effects of some MP distortions in the GNSS receiver. In order to validate this method we chose scenarios in which the MP phenomenon had longer durations than those ones from Section 3. We show simulation results obtained by processing these new scenarios, with different numbers of satellites in view, and with MP events that affect specific satellites in the time windows indicated in Table 2. The purpose is to analyze the effects of satellite exclusion and P-WLS, without considering GDOP data. For the PVT computation, the WLS solution is used. The RAIM algorithm used in simulation has a false alarm probability \(\alpha=5\times 10^{-5}\) and missed detection probability \(\beta=5\times 10^{-5}\). The two simulation scenarios represent the same static position and they have different durations and are presented in Table 2:  
* Scenario 1 of duration of 50 s
* Scenario 2 of duration of 90 s  
Both scenarios globally have 10 satellites in view. When in the scenarios we consider only 5 chosen satellites in view, obviously FDE cannot be used for exclusion, but the anomalies on PRs can be detected. An example of the position errors in East-North-Up (ENU) coordinates in scenario 1 with 5 satellites, without using RAIM and signal processing assistance, is shown in Figure 11. In Figure 12 the output of the detector, the SQI and the \(C/N_{0}\) trend related to PRN 11 in scenario 1 is shown. The Tables 3 and 4 show the position errors in East-North-Up (ENU) coordinates in scenario 1 and 2 with several values of the penalty weight in the P-WLS method. The performance is also evaluated in terms of MSE over the whole duration of the scenarios. It is possible to observe that especially in scenario 2, where the environment is more degraded than in the scenario 1, the penalty on pseudorange variances can have a strong impact in terms of accuracy expressed in MSE. In scenario 1 the MP affects several PRN in different time windows but with shorter duration, so the penalty weight is between 0 and 1 except for the case with 5 satellites. In fact, in both scenarios another parameter that influences the choice of the penalty weight is the satellites geometry. If most of the satellite signals that we have are not affected by any \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **MP Windows (s)** & **PRN** \\ \hline
1 & 8–16 & 27 \\  & 21–25 & 11, 22 \\  & 30–35 & 16 \\  & 40–45 & 1, 4, 21, 27 \\
2 & 20–80 & 1, 4, 21, 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time windows when MP is present for the scenario 1 and 2.  
impairment and also we have a good geometry, penalising the variances may be useless. Finally, the accuracy takes benefit from the penalty weight in a harsh environments. Figure 11: WLS solution of the scenario 1. In (**a**) the position error is shown. The East-North coordinates (**b**) and the skylpot (**c**). Figure 12: Example related to PRN 11 in scenario 1: the MPDD output (**a**); the SQI (**b**) and the \(C/N_{0}\) trend (**c**). The results summarised in Tables 5 and 6 show the effects of the exclusion performed by applying a threshold on SQI. The results have been obtained with \(\text{SQI}_{\text{thres}}=0.7\). As it can be seen in the first row of Table 5 relative to the case of 5 satellites, if we exclude one satellite with low SQI, we could get a worse solution due to the bad geometry. This is true with a low number of satellites, but the exclusion leads to an improved solution with a high number of satellites. In summary these results prove that the effect of GDOP has to be considered in the set up of the exclusion algorithms, when the number of satellites in view is very low.