## 5 Simulation Analysis
### Simulation Results
#### 5.2.2 Altimeter Scene  
To overcome the problem of the low positioning accuracy in the LEO 1 satellite + INS algorithm, we introduced an altimeter on the basis of the algorithm. In the altimeter scene, according to the altimeter deviation, we divided the altimeter scene into three types: The altimeter no deviation scene; the fixed deviation 30, 15, and 5 m scenes; and the fixed deviation \(-\)30, \(-\)15, and \(-\)5 m scenarios for comparative analysis. The simulation results are shown in Figure 7.  
Figure 7 shows that the LEO 1 satellite + INS + altimeter algorithm can significantly improve the navigation and positioning accuracy and solve the problem of INS divergence. Similarly, in the altimeter scene, we calculated and counted the mean and variance of navigation and positioning results, and the results are shown in Tables 5-7. Without losing generality, we only counted the altimeter without deviation scene, fixed deviation 30 m scene, and fixed deviation \(-\)30 m scene, and when the altimeter deviation was \(\pm\)15 and \(\pm\)5 m, the same conclusion could be obtained. \begin{table}
\begin{tabular}{c c c c} \hline
**Error** & **Scene** & **Mean** & **STD** \\ \hline \multirow{3}{*}{NVE (m/s)} & altimeter without deviation & \(-\)0.1385 & 0.1543 \\  & fixed deviation 30 m & \(-\)0.1281 & 0.2549 \\ \cline{1-1}  & fixed deviation \(-\)30 m & \(-\)0.1481 & 0.2549 \\ \hline \end{tabular}
\end{table} 
Table 6: Velocity error statistics. \begin{table}
\begin{tabular}{c c c c} \hline
**Error** & **Scene** & **Mean** & **STD** \\ \hline \multirow{3}{*}{NPE (m)} & altimeter without deviation & \(-\)6.6661 & 7.8891 \\  & fixed deviation 30 m & \(-\)8.2601 & 11.8440 \\  & fixed deviation \(-\)30 m & \(-\)4.9182 & 11.8440 \\ \hline \multirow{3}{*}{EPE (m)} & altimeter without deviation & \(-\)9.5780 & 17.4749 \\  & fixed deviation 30 m & 9.5512 & 25.7566 \\ \cline{1-1}  & fixed deviation \(-\)30 m & \(-\)28.3873 & 25.7566 \\ \hline \multirow{3}{*}{DPE (m)} & altimeter without deviation & \(-\)8.1980 \(\times\)10\({}^{-4}\) & 0.0182 \\ \cline{1-1}  & fixed deviation 30 m & 9.5512 & 0.2763 \\ \cline{1-1}  & fixed deviation \(-\)30 m & \(-\)28.3873 & 0.2763 \\ \hline \end{tabular}
\end{table} 
Table 5: Position error statistics. Figure 7: _Cont._  
According to Tables 5-7, we can observe that the positioning error of the LEO 1 satellite + INS algorithm was significantly reduced due to the addition of altimeters. In the case of no deviation altitude, relative to INS navigation error,  
1. The average position error of the north direction is increased from 31.40% to 86.00%, the accuracy of STD is improved from 59.76% to 85.17%, the average position error of the east direction is increased from 37.99% to 85.86%, the accuracy of STD is improved from 50.19% to 81.25%, the mean value of the down position error is increased from 32.40% to almost 100% (indicating that the error is almost reduced to 0), and the accuracy of STD is increased from 15.00% to 99.98%;
2. The mean value of the north velocity accuracy is increased from 57.34% to 68.87%. However, due to the continuous correction of inertial navigation, the STD accuracy drops from 70.58% to 60.15%, but the mean value of the east velocity error increases from 28.31% to 37.24%, and the accuracy of STD increases from 37.63% to 71.67%, and the mean value of down velocity error is increased from 33.17% to 99.94%. Obviously, the accuracy of STD is improved from 12.71% lower than INS navigation to 98.78%;