## 4 Simulation Analysis
### Experimental Results  
#### 4.3.1 INS+LEO 3-Satellite Alternate Switching Ranging Integrated Navigation Algorithm  
(1) Based on same orbits  
According to the GDOP value, we select the three LEO satellites that are always visible during the aircraft's movement. These three satellites must be in the same orbit. For this experiment, we select three satellites with PRN (pseudorandom noise code) numbers 209, 221 and 245 on the fifth orbit of the SpaceX LEO satellite system and named them PRN1, PRN2 and PRN3, respectively. Finally, the simulation is carried out and the result is shown in Figure 5 (EPE, NPE and UPE represent the position errors of the east, north and up directions, respectively). The meaning of the other parameters, such as EVE and AEE, can be deduced by analogy, so we do not discuss them later. Figure 5: Positioning error curve of INS+LEO3-satellite alternate switching ranging integrated navigation based on the same orbit. (**a**) Position error. (**b**) Velocity error. (**c**) Attitude error. (**d**) 3D trajectory error. In Figure 5, the INS+LEO3-satellite alternate switching ranging integrated navigation algorithm is based on the same orbit. Whether it is a position (Figure 5a), velocity (Figure 5b) or attitude error (Figure 5c), the error can be well restrained compared with INS navigation. The stable values of errors almost all tend to zero. In Figure 5d, the final trajectory curve closely follows the real movement trajectory of the aircraft. As a whole, as the switching time increases, the error increases accordingly. From the effect point of view, we sort the effects in descending order as follows: 5 s > 10 s > 30 s > 60 s; that is, the switching time is the best for 5 s, 10 s and 30 s, but 60 s has the worst effect. However, there are certain fluctuations in the error of the individual switching time, since the IMU is constantly correcting navigation errors. (2) Based on different orbits  
The principle of selecting satellites is the same as in the same orbit. We select three satellites in different orbits that are always visible on the trajectory of the aircraft. In this experiment, three satellites with the fifth orbit plane PRN number 209, the sixth orbit plane PRN number 299 and the eighth orbit plane PRN number 376 satellites were selected for the SpaceX satellite system and they were named PRN1, PRN2 and PRN3. Finally, the simulation is performed and the result is shown in Figure 6.  
Figure 6: Positioning error curve of INS+LEO3 satellite alternate switching ranging integrated navigation based on different orbits, (**a**) Position error. (**b**) Velocity error. (**c**) Attitude error. (**d**) 3D trajectory error. In Figure 6, the INS+LEO3 satellite alternate switching ranging integrated navigation algorithm based on different orbits can also suppress the divergence of position (Figure 6a), velocity (Figure 6b) and attitude error (Figure 6c) in the INS. Furthermore, in Figure 6d, the final trajectory curve is close to the aircraft's real movement trajectory to a greater extent. From an intuitive perspective, the algorithm based on different orbits is obviously better than the algorithm based on the same orbit compared to Figure 5a-d and the error fluctuation is much smaller. This can be observed from each error and the final trajectory error curve. As the switching time increases, the error gradually increases; among them, the error with a switching time of 60 s fluctuates relatively greatly. Nevertheless, it can overcome the divergence in the INS. 3.2 Integrated Navigation Algorithm of INS+2- Satellite Alternate Switching Ranging under LEO 3- Satellite  
(1) Based on same orbits  
The principle of satellite selection is the same as above. In this experiment, the original scenarios selected are the three satellites with PRN numbers 209, 221 and 245 on the fifth orbital plane of the SpaceX satellite system and they are named PRN1, PRN2 and PRN3, respectively.