## 4 Simulation Experiment
### Experimental Results  
#### 4.2.1 INS + LEO2 + Unbiased Altimeter and No Altimeter Scenario Experiment under the Same Orbit  
According to the parameter settings in Tables 1-3, in the same orbit, the experimental results of the INS + LEO2 switching + unbiased altimeter algorithm are shown in Figure 4. \begin{table}
\begin{tabular}{l l} \hline \hline
**Orbital Parameters** & **Value** \\ \hline Cycle (min) & 120 \\ Height (km) & 1150 \\ Orbit radius (km) & 7521 \\ Inclination (\({}^{\circ}\)) & 53 \\ Track surface number & 32 \\ Number of satellites on a single orbital surface & 50 \\ Total number of satellites & 1600 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the system. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter Type** & **Value** \\ \hline Initialization position error & (0 m, 0 m, 0 m)ENU \\ Initialization velocity error & (0 m/s, 0 m/s, 0 m/s)ENU \\ Initialization attitude error & (0\({}^{\circ}\), 0\({}^{\circ}\), 0\({}^{\circ}\))ENU \\ Initial position & (50.425\({}^{\circ}\) N, \(-\)3.5958\({}^{\circ}\) E, 10,000 m) \\ Initializing velocity & 200 m/s \\ Initial attitude & 0\({}^{\circ}\)/ Roll, 0\({}^{\circ}\)/Pitch, 90\({}^{\circ}\)/Yaw \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial parameter setting of orbit. At the same time, the experiment of the INS + LEO2 switching without an altimeter algorithm under the same orbit is also given. As a comparison, we included the standard INS + LEO2 switching navigation and positioning algorithm and the standard INS + LEO2 switching + altimeter navigation and positioning algorithm. Where, INS means pure INS navigation algorithm; the standard INS + two LEO satellites alternate switching ranging algorithm; we abbreviate it as: Standard INS + LEO2. Similarly, for the standard INS + two LEO satellites alternate switching ranging + altimeter algorithm, we abbreviate it as: Standard INS + LEO2 + altimeter; unbiased altimeter + \(\Delta t\) s switching algorithm of two LEO satellites, we abbreviate it as: unbiased altimeter + \(\Delta t\) s switching, the value of \(\Delta t\) is shown in Table 3; and the alternate switching algorithm of two LEO satellites without the aid of an altimeter is abbreviated as \(\Delta t\) s switching. In addition, the meaning of each \(y\)-axis title is as follows, EPE: east position error; NPE: north position error; UPE: up position error, the meaning of velocity error is similar, while in attitude error, AEE: attitude error of east, other abbreviated meanings by analogy, there is no special description in the following diagrams, and all can be understood according to the above abbreviations. Figure 4: Experimental results of INS + LEO2 + unbiased altimeter and no altimeter scenarios under the same orbit. From Figure 4, we can see that the INS + LEO2 switching + unbiased altimeter navigation and positioning algorithm can also effectively suppress the divergence of INS. Compared to the INS + LEO2 switching algorithm without an altimeter, after combining the altimeter, the algorithm can effectively suppress the divergence of various errors under relatively large switching times (such as 60 and 90 s). In this way, the large switching time divergence can be suppressed without frequent switching of LEO satellites, which can ensure the navigation and positioning functions without affecting the communication services of the LEO satellites. We count the final trajectory errors of the larger switching times of 60 and 90 s, as shown in Figure 5.  
From Figure 5, we can obtain that with the assistance of the altimeter, when the switching time is 60 s, comparing with the INS + LEO2 switching algorithm, the INS + LEO2 switching + unbiased altimeter navigation and positioning algorithm in longitude, latitude and altitude's errors improve by 35.19%, 23.13% and 99.66%, respectively, and the corresponding standard deviation performance improve by 59.27%, 52.91% and 96.89%, respectively.