## 3 Simulation and Analysis
### Result Comparison  
To compare the results from the proposed method and existing methods, we first need to clarify the calculation principle of the existing methods. Existing methods predominantly utilize the 2D contour data of MGFs and are limited to sea-skimming aircraft. These methods do not account for potential errors and merely provide a binary result of \"identified\" or \"unidentified\" rather than a probability of identification. The relevant calculation is based  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point Name** & **Aircraft State** & \
\begin{tabular}{c} \(P_{ident}\) at \(T_{a}\) with the Interference of \\ **Narrow-Shaped Island** \\ \end{tabular} &
\begin{tabular}{c} \(P_{ident}\) at \(T_{b}\) with the Interference of \\ **Triangular-Shaped Island** \\ \end{tabular} \\ \hline \(S_{1}\) & Sea-skimming & 0.9564 & 0.0505 \\ \(S_{2}\) & High-altitude & 0.9990 & 0.3833 \\ \(S_{5}\) & Sea-skimming & 0.0877 & 0.9625 \\ \(S_{6}\) & High-altitude & 0.5887 & 0.9997 \\ \hline \hline \end{tabular}
\end{table}
Table 6: \(P_{ident}\) of \(T_{a}\) and \(T_{b}\) under different radar position points.  
on the 2D contour data of MGFs, using the LOS condition and Equations (1) and (2), while neglecting the impact of radar elevation angle resolution (Equation (3)). As these methods do not incorporate error considerations, there is no requirement for Monte Carlo simulation.  
To further illustrate the differences between the proposed method and existing methods, we selected radar position points \(S_{1}\), \(S_{3}\), and \(S_{5}\) as examples (sea-skimming aircraft), and calculated and visualized the binary result surrounding the narrow-shaped island. The comparison of these results with those obtained from the proposed method is shown in Figure 7.  
Figure 7: Comparison of results from two methods. (**a**) Probability result of proposed method (When regarding \(S_{1}\) as radar position); (**b**) Binary result of existing method (When regarding \(S_{1}\) as radar position); (**c**) Probability result of proposed method (When regarding \(S_{3}\) as radar position); (**d**) Binary result of existing method (When regarding \(S_{3}\) as radar position); (**e**) Probability result of proposed method (When regarding \(S_{5}\) as radar position); (**f**) Binary result of existing method (When regarding \(S_{5}\) as radar position).  
From Figure 7, it can be seen that the shape and area of the \"unidentified\" region from existing methods is similar to those of the sum of Level I and Level II regions from the proposed method, which validates the effectiveness of the proposed method from a different angle.  
Besides that, the proposed method not only can be applied to aircraft at any altitude, but it can also take more errors into consideration, and the probability result rather than the binary result provides more precise and intuitive decision-making support for aircraft mission planners.  
The detailed comparison between the proposed method and the existing methods in terms of RTA determination conditions, MGF data utilization, and other factors is shown in Table 7.  
In summary, the proposed method, which incorporates radar elevation angle resolution and the MGF 3D model, is applicable to aircraft at any altitude in 3D space. It can quantitatively calculate the probability of radar correctly identifying a target at a specific marine location, providing more precise and intuitive decision-making support for aircraft mission planners. Compared with existing methods, it better aligns with the current performance and requirements of aircraft.