## 8 SQI and RAIM Interaction
### GDOP Control  
The simulation results just presented motivate the adoption of an exclusion method able to implement a trade-off between the weights of errors removed by signal quality index and weights of the potential errors introduced by the geometry. A possible approach is to calibrate the dictionary on specific error cases, in order to detect and remove satellites affected by these specific problems. A second approach is to consider that, in a future with a high number of satellites, the risk to degrade the DOP will be lower, but in any case, an additional block of DOP control is convenient for these kinds of algorithms. We propose here a control, based on a GDOP budget, which tries to remove satellites starting from the ones with lowest SQI and SQI \(<\) SQI\({}_{\text{thres}}\) in order to eliminate the distorted signals which could not be detected by the RAIM. Then a GDOP test can be performed, for example by observing if the GDOP after removal exceeds \(k\) times the GDOP with all the tracked channels. The idea is to combine several effects: calibration of the dictionary depending on the considered environment, and choice of the parameter \(k\). In this heuristic way, we can have a kind of control even on the geometry effects, avoiding to introduce wide errors due to the weak geometry. For example, we set \(k=0.1\), so it means that the new GDOP after a possible exclusion cannot exceed 10% of the previous GDOP. By taking in consideration the situation in Table 6 with 6 or 7 satellites, with GDOP control we do not perform an erroneous exclusion and we will get in this way the same results as in not assisted RAIM case (as reported in Table 7). Conversely, with 10 satellites, GDOP control simply permits the additional exclusion performed by SQI. Another possible approach to avoid problems in case of a poor geometry is to leave the decision on the exclusion to RAIM algorithms but using SQI to identify unreliable navigation solutions. It is \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Number of Satellites** & **E (m)** & **N (m)** & **U (m)** & **MSE (m)** & **PRN Tracked** & **RAIM** & **SQI Exclusion** \\ \hline \multirow{3}{*}{5} & 44.6886 & 90.4397 & 146.9450 & 150.3777 & 1, 4, 21, 27, 19 & NO & NO \\  & 30.9765 & 65.6038 & 109.0453 & 110.9221 & & YES & NO \\  & 30.9765 & 65.6038 & 109.0453 & 110.9221 & & YES & YES \\ \hline \multirow{3}{*}{7} & 1.51801 & 14.7719 & 8.40841 & 15.7991 & 6, 19, 27, 16, 18, 4, 11 & NO & NO \\  & 1.51801 & 14.7719 & 8.40841 & 15.7991 & & YES & NO \\  & 4.04489 & 24.2859 & 12.5928 & 21.7989 & YES & YES \\ \hline \multirow{3}{*}{10} & 6.9590 & 13.8449 & 36.6576 & 34.9215 & 6, 19, 27, 16, 18, 4, 11, 22, 21, 1 & NO & NO \\  & 2.4263 & 6.2989 & 26.6406 & 24.4607 & & YES & NO \\ \cline{1-1}  & 2.6643 & 10.0206 & 8.5329 & 11.8656 & & YES & YES \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results for the scenario 2 with \(SQl_{thres}=0.7\), no penalty weight and GDOP control enabled with \(k=0.1\) in case of 6 and 7 satellites in view. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Number of Satellites** & **E (m)** & **N (m)** & **U (m)** & **MSE (m)** & **PRN Tracked** & **RAIM** & **SQI Exclusion** \\ \hline \multirow{3}{*}{6} & 44.6886 & 90.4397 & 146.9450 & 150.3777 & 1, 4, 21, 27, 19 & NO & NO \\  & 30.9765 & 65.6038 & 109.0453 & 110.9221 & & YES & NO \\  & 30.9765 & 65.6038 & 109.0453 & 110.9221 & & YES & YES \\ \hline \multirow{3}{*}{7} & 1.51801 & 14.7719 & 8.40841 & 15.7991 & 6, 19, 27, 16, 18, 4, 11 & NO & NO \\  & 1.51801 & 14.7719 & 8.40841 & 15.7991 & & YES & NO \\  & 1.51801 & 14.7719 & 8.40841 & 15.7991 & & YES & YES \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for the scenario 2 with \(SQl_{thres}=0.7\) and no penalty weight. possible to declare a navigation solution unreliable when the global test fails but the local test is passed for all the normalised PR residuals (see Figure 10).