## 4 Simulation Analysis
### Experimental Results
#### 4.3.1 INS+LEO 3-Satellite Alternate Switching Ranging Integrated Navigation Algorithm
In the original scenarios, we keep the satellite with a PRN of 209 as a continuous real satellite ranging value and let the two satellites with PRNs of 221 and 245 use virtual ranging values for alternate ranging. By comparing scenario selection, we remove the satellite with PRN number 209, the two satellites with PRN numbers 221 and 245 are named the same as the original scenario, then let the satellites with PRN numbers 221 and 245 alternately switch between the real range value and the virtual range value. The simulation results are shown in Figure 7 (where the OE represents the original scenario experiment, CE represents the comparison scenario experiment, SO represents the same orbit and DO represents different orbits. \(\tau\) s-OE/SO and \(\tau\) s-CE/SO represent the original scenario and the comparison scenario of the alternate switching experiment of the 2-satellite alternate switching ranging under LEO 3-satellite on the same orbit, respectively, and \(\tau\) represents the switching time. \(\tau\) s-OE/DO and \(\tau\) s-CE/DO have the same meaning as \(\tau\) s-OE/SO and \(\tau\) s-CE/SO, so we do not discuss them later.). Figure 7: Positioning error curve of integrated navigation algorithm of INS+2-satellite alternate switching ranging under LEO 3-satellite on the same orbit. (**a**) Position, velocity and attitude errors. (**b**) 3D trajectory error. In Figure 7a,b, we can see that under the same orbit, the original scenario and the comparison scenario can also overcome the problem of INS navigation error divergence to a certain extent. However, in the comparison scenario, the effect is significantly worse due to the satellite's removal for continuous ranging. The effect in the original scenario is intuitively similar to that of the 3-satellite alternate switching ranging algorithm under the same orbit, but it is better than the positioning effect in the comparison scenario. Similarly, as the switching time increases, the error gradually increases. (2) Based on different orbits  
The principle of selecting satellites is the same as above. We select three satellites in different orbits that are always visible on the trajectory of the aircraft. In this experiment, the original scenario selected three satellites in the SpaceX satellite system with the fifth orbit PRN number 209, the sixth orbit PRN number 299 and the eighth orbit PRN number 376 and we named them PRN1, PRN2 and PRN3, respectively. In the original scenarios, we keep the satellite with a PRN of 209 as a continuous real satellite ranging value and let the two satellites with the PRN of 299 and 376 use virtual ranging values for alternate ranging. In comparing scenario selection, we remove the satellite with PRN number 209 and let the two satellites with PRNs numbers 299 and 376 alternately switch between the real range value and the virtual range value. The simulation result is shown in Figure 8.  
In Figure 8a,b, we can see that under different orbits, the original scenario and the comparison scenario can overcome INS navigation error divergence to a large extent. Similarly, since the satellite that is continuously ranging is removed from the comparison scenario, the effect is significantly worse. The effect in the original scenario is intuitively similar to the 3-satellite alternate switching ranging algorithm under different orbits and the effect is better than the positioning effect of the comparison scenario under different orbits. Similarly, as the switching time increases, the error gradually increases. From the above qualitative analysis, we can initially find that algorithms based on different orbits are significantly better than those based on the same orbit, verifying the correctness of judging the pros and cons of positioning accuracy based on the spatial distribution characteristics of satellites proposed in Section 2. Additionally, the original scenario  
Figure 8: Positioning error curve of integrated navigation algorithm of INS+2-satellite alternate switching ranging under LEO 3-satellite on a different orbit.