## 4 Simulation Analysis
### Simulation and Result Analysis
#### 4.2.2 INS+LEO2-Satellite Alternate Switching Ranging Integrated Navigation Algorithm
The data in Table 4 show that as the switching time increases, the corresponding longitude, latitude and altitude errors increase accordingly. Relative to simple INS navigation, when the switching time is 5 s, 10 s, 30 s and 60 s, the mean performances with respect to longitude error increased by 99.27%, 95.93%, 95.78% and 74.46%, respectively, and the corresponding standard deviations increased 96.04%, 93.20%, 90.09% and 62.49%, respectively. The improvement in longitude error is very significant. The mean latitude performance also improved significantly, increasing by 99.53%, 99.30%, 99.09%, and 90.10% relative to the INS error, respectively, and the corresponding standard deviation increased by 94.07%, 92.78%, 91.26% and 78.67%, respectively. In terms of altitude error, the mean error increased by 99.78%, 97.61%, 97.49% and 88.80%, and the corresponding standard deviation increased by 95.90%, 95.34%, 94.33% and 85.34%, respectively, with altitude performance increasing by more than 85% in terms of mean and standard deviation. From the data analysis above, it can be concluded that the INS+LEO2-satellite alternate switching integrated navigation algorithm based on the same orbit surface can effectively overcome the INS divergence problem. Specifically, the improvement in the longitude and altitude error is more prominent, and it is obvious from the figure that as the switching time increases, the corresponding performance shows a downward trend. In general, the INS+LEO2-satellite alternate switching ranging integrated navigation algorithm based on the same orbital surface can meet real-time location service requirements in challenging environments well. Adjacent orbits surface  
Similarly, according to the fundamental principle that the altitude angle of the satellite cannot be less than \(10^{\circ}\), we selected two satellites that are always visible on the aircraft's trajectory, and which are in the adjacent orbital surface and have adjacent phases. In this experiment, the SpaceX satellite system, with 245 orbital surfaces V and 269 orbital surfaces VI, was selected, and assigned the names satellites #1 and #2, respectively, for simulation. The simulation results are shown in Figure 5. \begin{table}
\begin{tabular}{c l c c} \hline \hline
**Error Index** & **Algorithm** & **Mean** & **Std** \\ \hline Longitude (\({}^{\circ}\)) & INS+LEO2 5 s/Same orbits surface & \(-1.1203\times 10^{-5}\) & \(1.7047\times 10^{-4}\) \\  & INS+LEO2 10 s/Same orbits surface & \(6.2366\times 10^{-5}\) & \(2.1058\times 10^{-4}\) \\  & INS+LEO2 30 s/Same orbits surface & \(-6.4679\times 10^{-5}\) & \(2.5468\times 10^{-4}\) \\  & INS+LEO2 60 s/Same orbits surface & \(3.9182\times 10^{-4}\) & \(6.4647\times 10^{-4}\) \\  & INS & \(-1.5333\times 10^{-3}\) & \(1.4192\times 10^{-3}\) \\ \hline Latitude (\({}^{\circ}\)) & INS+LEO2 5 s/Same orbits surface & \(1.1128\times 10^{-5}\) & \(1.3245\times 10^{-4}\) \\  & INS+LEO2 10 s/Same orbits surface & \(-1.6601\times 10^{-5}\) & \(1.6117\times 10^{-4}\) \\  & INS+LEO2 30 s/Same orbits surface & \(-2.1445\times 10^{-5}\) & \(1.9511\times 10^{-4}\) \\  & INS+LEO2 60 s/Same orbits surface & \(-2.3428\times 10^{-4}\) & \(4.7607\times 10^{-4}\) \\  & INS & \(2.3666\times 10^{-3}\) & \(2.2320\times 10^{-3}\) \\ \hline Altitude (m) & INS+LEO2 5 s/Same orbits surface & 0.1765 & 3.0525 \\  & INS+LEO2 10 s/Same orbits surface & 1.8892 & 3.4736 \\  & INS+LEO2 30 s/Same orbits surface & 1.9771 & 4.2247 \\  & INS+LEO2 60 s/Same orbits surface & 8.8348 & 10.9232 \\  & INS & 78.8923 & 74.5186 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The trajectory error statistics. Figure 5: Error curve of the INS+LEO2-alternate switching ranging integrated navigation algorithm based on adjacent orbit surfaces. According to the switching algorithm, on the adjacent orbital surface (Figure 5), where one satellite provides the real ranging value and the other satellite provides the virtual ranging value, INS error is effectively improved, and INS divergence suppressed.