# Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval
## 4 Experiment and Analysis
### Evaluation of PHMI for Solution Separation Araim
It can be seen that the absence of one satellite during the interval significantly impacts the integrity performance of navigation applications. Compared to situation 1, the region where the actual ARAIM achieves a 95% availability is reduced by 57.87%. In contrast, the ARAIM determined by the traditional method is only reduced by 6.79%. This indicates that the traditional method is overly optimistic in evaluating the integrity risk based only on the current epoch. In particular, when \(\beta\) equals 100, the ARAIM's availability decreases more obviously. According to the global simulation results, the average availability loss significantly increased to 6.94%, and the coverage meeting 95% availability was reduced by 53.70%. As far as we know, ARAIM currently  
Figure 8: Availability map of the ARAIM under the nominal situation. The subfigure (**a,b**) represents the availability of ARAIM based on the traditional method and the proposed method, respectively. utilizes carrier smoothing code (CSC) to mitigate high-frequency code noise, and the time constant of the CSC is also set at 100. Therefore, satellite geometry variations must be taken into account for integrity risk evaluation, particularly in situations involving aircraft banking and ionospheric scintillation. One potential approach to rigorously evaluate the integrity risk is to utilize multiple-epoch information through batch processing or filtering methods [18]. This will be discussed further in our future work. Finally, we analyzed the availability of H-ARAIM in the RNP 0.1 phase. According to Figure 10, it can be seen that the availability loss of traditional ARAIM during this phase is small. This is because the HAL during the RNP 0.1 phase is very loose, resulting in significantly lower integrity risks than the \(P_{\text{HMI,REQ}}\). According to Table 2, the maximum loss of average availability based on NES-based ARAIM evaluation is only 0.17%. Based on the above analysis, this study demonstrates the impact of satellite geometry variation on the integrity performance of NES-based ARAIM. Firstly, the previously geometry constant assumption for the ARAIM integrity risk evaluation does not appear to be overly optimistic under nominal conditions for LPV-200 and RNP 0.1 phases. However, when the navigation applications encounter situations involving aircraft banking and ionospheric scintillation, the traditional method of integrity risk evaluation could become overly optimistic. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{\(\beta\) = 10} & \multicolumn{2}{c}{\(\beta\) = 100} & \multicolumn{2}{c}{\(\beta\) = 1000} \\ \cline{3-8}  & & **Average** & **Coverage** & **Average** & **Coverage** & **Average** & **Coverage** \\ \hline \multirow{3}{*}{LPV-200 nominal} & Traditional & 98.41\% & 93.67\% & 98.41\% & 93.67\% & 98.41\% & 93.67\% \\ \cline{2-8}  & Actual & 98.17\% & 92.44\% & 97.59\% & 91.05\% & 97.71\% & 90.74\% \\ \cline{2-8}  & Loss & 0.24\% & 1.23\% & 0.82\% & 2.62\% & 0.70\% & 2.93\% \\ \hline \multirow{3}{*}{LPV-200 one-satellite outage} & Traditional & 97.91\% & 86.88\% & 97.91\% & 86.88\% & 97.91\% & 86.88\% \\ \cline{2-8}  & Actual & 94.51\% & 58.02\% & 91.69\% & 33.18\% & 90.97\% & 26.39\% \\ \cline{2-8}  & Loss & 3.40\% & 28.86\% & 6.22\% & 53.70\% & 6.94\% & 60.49\% \\ \hline \multirow{3}{*}{RNP 0.1} & Traditional & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\ \cline{2-8}  & Actual & 99.86\% & 100.00\% & 99.86\% & 100.00\% & 99.83\% & 100.00\% \\ \cline{2-8}  & Loss & 0.14\% & 0.00\% & 0.14\% & 0.00\% & 0.17\% & 0.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average availability results and coverage (95%) of the ARAIM. Figure 9: Availability map of the ARAIM with one-satellite outages. The subfigure (**a**,**b**) represents the availability of ARAIM based on the traditional method and the proposed method, respectively.