# An Improved RAIM Availability Assessment Method Based on the Characteristic Slope
## 5 Simulation
### Simulation Results Statistical Analysis  
Both the rates of optimistic and conservative assessments for RAIM availability are calculated for each grid point using the classic-PL-based, enhanced-PL-based, ideal-PL-based and slope-based methods. The optimistic assessment rate is indicated by the ratio between the count of epochs in which RAIM is assessed to be available but is actually unavailable and the count of epochs in which RAIM is actually unavailable. The conservative assessment rate is indicated by the ratio between the count of epochs in which RAIM is assessed to be unavailable but is actually available and the count of epochs in which RAIM is actually available. Figure 11: Optimistic assessment rate using the classic-PL-based method. Table 4 records the specific optimistic and conservative assessment data for all 4 kinds of RAIM availability assessment methods. As shown in Table 4, both the rates of optimistic and conservative assessments are 0 for each grid point using the slope-based and ideal-PL-based methods. These prove that both optimistic and conservative assessments can be prevented. The reason for the 0 conservative assessment rate of the slope-based method is that the \(a_{v}\) step size is small enough (0.01) for offline calculation of \(T_{Slope}\), leading to the assigned \(T_{Slope}\) value being nearly equal to its true value. For the classic-PL-based method, there are both grid points with nonzero optimistic assessment rate and grid points with nonzero conservative assessment rate. Figures 11 and 12 present the optimistic and conservative assessment rates for each grid point using the classic-PL-based method, respectively. As shown in Table 4 and Figure 11, there are 2032 grid points with nonzero optimistic assessment rate, 4.65% of the total grid points, and there are 41 grid points with a 100% optimistic assessment rate, meaning that optimistic assessment always happens when RAIM is unavailable at these grid points. As shown in Table 4 and Figure 12, there are 16,678 grid points with nonzero conservative assessment rate, 38.18% of the total grid points, and the maximum conservative assessment rate is 2.59%. Comparing Figure 12 with Figure 11, the coverage area of conservative assessment is much larger than that of optimistic assessment, but the maximum optimistic assessment rate is much higher than the maximum conservative assessment rate for a single grid point using the classic-PL-based method. For the enhanced-PL-based method, there are no grid points with a nonzero optimistic assessment rate. This finding illustrates that the value of \(P_{a}(\text{HMI}|1F)\) is small enough at \(\xi_{b}=\sigma_{m}^{2}\sqrt{\frac{\lambda_{a}}{s_{mm}}}\) for the enhanced PL, which leads to the \(\xi_{b}-lgP_{a}(\text{HMI}|1F)\) curve always \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Grid Points of Optimistic Assessment**} & **Grid Points of Conservative** & **Maximum Optimistic Assessment Rate on Single Grid Point** & **Maximum Conservative Assessment Rate on Single Grid Point** \\ \cline{2-4}  & & **Assessment** & **Rate on Single Grid Point** & **Rate on Single Grid Point** \\ \hline classic-PL-based & 2032 & 16,678 & 100\% & 2.59\% \\ \hline enhanced-PL-based & 0 & 43,038 & 0 & 8.15\% \\ \hline Ideal-PL-based & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison for the four kinds of RAIM availability assessment methods. Figure 12: Conservative assessment rate using the classic-PL-based method. being separated from the \(P_{r}(\text{HMI}|1F)\) line, preventing optimistic assessment. However, there are 43,038 grid points with nonzero conservative assessment rate, as shown in Table 4 and Figure 13, representing 98.53% of the total grid points. The maximum conservative assessment rate is 8.15%.