## 4 Simulation Analysis
### Scenario Description  
The object of our experimental research is an aerial aircraft. We adopt the SpaceX LEO satellite system combined with an INS and the integrated navigation and positioning of the aircraft are realized by alternately switching between three satellites. According to the description in Section 2, we divide the research scenarios into different satellite orbital planes and phases:  
1. INS+LEO3-satellite alternate switching ranging integrated navigation and positioning on the same orbital plane.
2. INS+LEO3-satellite alternate switching ranging integrated navigation and positioning on different orbital planes;
3. INS+2-satellite alternate switch ranging under LEO3- satellite on the same orbit integrated navigation and positioning;
4. INS+2-satellite alternate switch ranging under LEO3- satellite on different orbital integrated navigation and positioning.  
At the same time, in scenarios (3) and (4), we divide the research scenarios into original scenarios and comparison scenarios:  
1. The original scenario is INS+ 2-satellite alternate switching ranging under LEO3-satellite integrated navigation and positioning; among them, there is a continuous ranging satellite;
2. The comparison scenario removes the satellite that is continuously ranging and uses the INS+LEO2- satellite to alternate switching ranging integrated navigation and positioning.  
Furthermore, the satellite elevation angle was set to 10\({}^{\circ}\). In the above scenarios, we set the alternate switching time to 5 s, 10 s, 30 s and 60 s according to the different alternate interval times for navigation and positioning research and, finally, the positioning effect is  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter Type** & **Accelerometer** & **Gyro** \\ \hline Quantization level & 20 (micro-g) & 41 (deg/hour) \\ Noise root PSD & 2 (micro-g/\(\sqrt{\text{Hz}}\)) & 0.002 ((deg/hour)0.5) \\ Scale Factor & 100–1000 (\(\times 10^{-6}\) ppm) & 100–1000 (\(\times 10^{-6}\) ppm) \\ Cross-coupling error & 100–1000 (\(\times 10^{-6}\) ppm) & 100–1000 (\(\times 10^{-6}\) ppm) \\ Bias & [30 \(\pm\) 52] (micro-g) & [0.09 \(\pm\) 0.013 (deg/hour) \\ Bias uncertainty per instrument & 30 (micro-g) & 0.001 (deg/hour) \\ \hline \multirow{2}{*}{
\begin{tabular}{l} Initial uncertainty \\ per axis \\ \end{tabular} } & Attitude & 0.01 (deg) \\  & Velocity & 0.01 (m/s) & 0.01 (m/s) \\  & Position & 1 (m) & 1 (m) \\ \hline \hline \end{tabular}
\end{table}
Table 4: IMU main parameters [47].  
\begin{table}
\begin{tabular}{l l} \hline \hline
**UKF Parameter Type** & **Value** \\ \hline Initialization position error (m) & 0 \\ Initialization velocity error (m/s) & 0 \\ Initialized attitude error (\({}^{\circ}\)) & 0 \\ The sampling interval is (s) & 0.01 \\ Initial position & (50.425\({}^{\circ}\) N, \(-\)3.5958\({}^{\circ}\) E) \\ Initialising velocity (m/s) & 200m/s \\ Initial attitude (\({}^{\circ}\)) & 0- Roll, 0- Pitch, 90- Yaw \\ Initial altitude (m) & 10,000 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Main parameters of UKF and aircraft.  
analyzed. We do not consider the influence of multipath, NLOS and LOS interference for the time being and the noise is modeled as single-modal Gaussian noise.