## 4 Simulation Result Analysis and Discussion  
A simulation analysis was conducted to assess the proposed algorithm's effectiveness in enhancing localization accuracy in satellite occlusion environments, using data from 12,000 satellite observation scenarios. In the simulation, the elevation angle of user-observed satellites is limited to 60\({}^{\circ}\) in urban environments, using a \(100\times 100\) antenna array to receive NLOS signals. NLOS virtual satellite inversions are simulated by adding random azimuth variations between 0\({}^{\circ}\) and 60\({}^{\circ}\) to the retained satellites, modeling reflection-induced azimuth changes. The simulations compare the performance of the quasi-optimal algorithm with the GDOP method. This setup evaluates the algorithm's performance in complex occlusion environments to validate its effectiveness in enhancing localization accuracy under NLOS conditions. The detailed configuration of simulated LEO constellations is shown in Table 9.  
As shown in Figures 7 and 8, in terms of visible satellites, the recovery of NLOS satellites greatly enhanced system performance. Without NLOS satellite recovery, the average number of visible satellites was 7, fluctuating between 6 and 10. In a simulation system with a constellation of 12,000 satellites, such a limited number of visible satellites could potentially drop below 4, rendering positioning impossible. Moreover, without virtual satellite generation, the GDOP remains consistently above 10 throughout the day, with extended periods exceeding 50, resulting in positioning errors of hundreds of meters. With half of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Orbit Height & 550 km \\ Orbit Type & Circular \\ Inclination Angle & 53\({}^{\circ}\) \\ Right Ascension of the Ascending Node & 160\({}^{\circ}\) \\ (RAAN) & 0\({}^{\circ}\) \\ Eccentricity & 0\({}^{\circ}\) \\ Number of Orbits & 24 \\ Number of Satellites per Orbit & 500 \\ Total Number of Satellites & 12,000 \\ Minimum User LOS Elevation & 60\({}^{\circ}\) \\ \(M\) & 100 \\ \(N\) & 100 \\ Signal Frequency & 35 GHz \\ Element Spacing & \(\lambda/2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The detailed configuration of simulated LEO constellations. NLOS satellites recovered, the average number of visible satellites surged to 229, and with a quarter recovered, it increased to 118. These results suggest that even partial recovery of NLOS satellites can greatly expand the number of satellites available for positioning, significantly improving both accuracy and reliability. These findings demonstrate the substantial potential of NLOS satellite recovery strategies in complex environments. The fast satellite selection algorithm for positioning in LEO constellations, as proposed by [31], is used to efficiently select satellites. When employing the proposed virtual satellite creation method and performing inversion on half and one-quarter of the visible satellites, the GDOP conditions for selecting 10 and 20 satellites are as illustrated in Figures 9 and 10. Figure 8: Number of observable satellites under different virtual satellite settings below 60\({}^{\circ}\) NLOS condition: no virtual satellites, half of the satellites are set as virtual, one-quarter of the satellites are set as virtual. Figure 7: GDOP scatter plot at different times under the condition of no virtual satellites below 60\({}^{\circ}\) NLOS. Simulation results indicate that GDOP values generally range between 1 and 2, suggesting improved positioning accuracy. Based on [32], the URE is set to 7.7 m for LEO satellites, which is higher than the typical GNSS URE of 6.1m reported in [33]. Selecting 20 satellites typically yields better results than selecting 10, consistent with the principle that increasing the number of satellites enhances positioning accuracy and stability.