## 5 Simulation Analysis
### Simulation Results
#### 5.2.1 Without Altimeter Scenario
From the above analysis, we can conclude that, in most cases, whether we consider the mean or STD, the navigation and positioning error of the LEO 1 satellite + INS algorithm is better than the navigation and positioning error of INS, satisfying the navigation and positioning needs of the position accuracy within 100 m and velocity error within 2.5 m/s. However, the LEO 1 satellite + INS algorithm cannot overcome the divergence of INS. In challenging environments that require a high accuracy, such as indoor and urban environments, this positioning result is difficult for people to accept. From Tables 2-4, compared with INS navigation, we find the following:  
1. In terms of the position error, the position error accuracy of the INS + LEO 1 satellite in the north direction is increased by 31.40%, and the STD is increased by 59.76%; the position error and STD accuracy in the east direction are increased by 37.99% and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Error** & **Algorithm** & **Mean** & **STD** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Lon (\({}^{\circ}\)) \\ \end{tabular} } & INS & \(3.2788\times 10^{-4}\) & \(3.1049\times 10^{-4}\) \\  & LEO 3 satellites & \(2.1020\times 10^{-9}\) & \(2.1205\times 10^{-8}\) \\  & INS+LEO 1 satellite & \(-2.9315\times 10^{-4}\) & \(1.9212\times 10^{-4}\) \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Lat (\({}^{\circ}\)) \\ \end{tabular} } & INS & \(4.6735\times 10^{-5}\) & \(4.4677\times 10^{-5}\) \\  & LEO 3 satellites & \(6.7541\times 10^{-9}\) & \(2.6435\times 10^{-8}\) \\  & INS+LEO 1 satellite & \(-5.8839\times 10^{-4}\) & \(6.5044\times 10^{-4}\) \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Alt (m) \\ \end{tabular} } & INS & \(104.1891\) & \(93.3793\) \\  & LEO 3 satellites & \(-0.0021\) & \(0.1105\) \\ \cline{1-1}  & INS+LEO 1 satellite & \(70.4270\) & \(79.3741\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Trajectory error statistics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Error** & **Algorithm** & **Mean** & **STD** \\ \hline \multirow{3}{*}{\begin{tabular}{c} NVE (m/s) \\ \end{tabular} } & INS & \(0.4449\) & \(0.3872\) \\  & LEO 3 satellites & \(-0.0027\) & \(0.0023\) \\  & INS+LEO 1 satellite & \(-0.1898\) & \(0.1139\) \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} EVE (m/s) \\ \end{tabular} } & INS & \(0.8386\) & \(0.9838\) \\  & LEO 3 satellites & \(4.3448\times 10^{-4}\) & \(0.0023\) \\  & INS+LEO 1 satellite & \(-0.6012\) & \(0.6136\) \\ \hline \multirow{3}{*}{
\begin{tabular}{c} DVE (m/s) \\ \end{tabular} } & INS & \(-0.7583\) & \(0.4507\) \\  & LEO 3 satellites & \(-0.0037\) & \(0.0023\) \\ \cline{1-1}  & INS+LEO 1 satellite & \(-0.5068\) & \(0.5080\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Velocity error statistics. 50.19%, respectively; and the position error accuracy and STD of the down direction are improved by 32.40% and 15.00%, respectively;
2. The accuracy of the INS + LEO 1 satellite in the north direction is improved by 57.34%, and the STD is increased by 70.58%; the velocity error and STD accuracy in the east direction are increased by 28.31% and 37.63%, respectively; and the velocity error accuracy in the earth direction is increased by 33.17%, while the STD is reduced by 12.71%;
3. In the final trajectory error, the mean error accuracy of the longitude error is improved by 10.59% and the STD is increased by 38.12%. Since IMU is constantly correcting the navigation error, there are some fluctuations in the latitude error. This result can be seen in Figure 6c. Therefore, the mean and STD of the latitude decrease significantly, but the average accuracy of the altitude error is improved by 32.40% and the STD is increased by 15.00%. From the above analysis, we can conclude that, in most cases, whether we consider the mean or STD, the navigation and positioning error of the LEO 1 satellite + INS algorithm is better than the navigation and positioning error of INS, satisfying the navigation and positioning needs of the position accuracy within 100 m and velocity error within 2.5 m/s.