# Hierarchical Model Updating Method for Vector Electric-Propulsion Satellites
## 4 Results and Discussion
### The Result of Hierarchical Model Updating
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Real**} & \multicolumn{3}{c}{**The First Loop**} & \multicolumn{3}{c}{**The Second Loop**} \\ \cline{3-8}  & & **Estimated** & **Error** & **Relative Error** & **Estimated** & **Error** & **Relative Error** \\ \hline \(\varphi_{0,\,\,}^{\circ}\) & 1 & 0.94 & 0.06 & 0.64\% & 0.99 & 0.01 & 0.11\% \\ \(\theta_{0,\,\,}^{\circ}\) & 2 & 2.09 & 0.09 & 0.89\% & 2.02 & 0.02 & 0.16\% \\ \(\psi_{0,\,\,}^{\circ}\) & 3 & 2.90 & 0.10 & 1.00\% & 2.98 & 0.02 & 0.19\% \\ \(\omega_{x0,\,\,}^{\circ}\)/s & 0.2 & 0.20 & 0.00 & 0.01\% & 0.20 & 0.00 & 0.00\% \\ \(\omega_{y0,\,\,}^{\circ}\)/s & 0.1 & 0.10 & 0.00 & 0.01\% & 0.10 & 0.00 & 0.00\% \\ \(\omega_{z0,\,\,}^{\circ}\)/s & \(-0.1\) & \(-0.10\) & 0.00 & 0.01\% & \(-0.10\) & 0.00 & 0.00\% \\ \(\mu_{Gyro,\,\,}^{\circ}\)/h & 0.003 & 0.00 & 0.00 & 1.35\% & 0.00 & 0.00 & 0.14\% \\ \(\epsilon_{Gyro,\,\,}^{\circ}\)/h & 0.05 & 0.28 & 0.23 & 452.54\% & 0.08 & 0.03 & 56.27\% \\ \(\sigma_{Gyro,\,}^{\circ}\)/h & 0.04 & 0.07 & 0.03 & 73.58\% & 0.05 & 0.01 & 27.73\% \\ \(\mu_{StarSensor}\)\(\,\,^{\circ}\) & 0.002 & 0.09 & 0.08 & 2083.63\% & 0.02 & 0.02 & 380.04\% \\ \(\sigma_{StarSensor}\)\(\,\,^{\circ}\) & 0.002 & 0.00 & 0.00 & 9.79\% & 0.00 & 0.00 & 0.50\% \\ \hline RMSE & & & 0.09366\% & & & 0.020678\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The estimation of attitude state variables. Variable modification of the propulsion subsystem is shown in Tables 9 and 10. The results of electric propulsion state variables also show that some errors decrease and some increase, but the total RMSE of telemetry variables decreases. The updating result of the thruster force and moment is shown in Table 11.  
To illustrate the effect of the hierarchical method, an experiment of model updating without the hierarchical method, that is, all variables were updated at the same time, was taken as a comparison. As is shown in Figure 4, most of the estimation errors grew rapidly and showed no downward trend. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**RMSE**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Uncorrected**} & \multicolumn{2}{c}{**The First Loop**} & \multicolumn{2}{c}{**The Second Loop**} \\ \hline \(\varphi_{m}\) & 0.0988\% & 0.0522\% & 0.0237\% \\ \(\theta_{m}\) & 0.0705\% & 0.0665\% & 0.0564\% \\ \(\psi_{m}\) & 0.0944\% & 0.0807\% & 0.0548\% \\ \(\omega_{XcGyro}\) & 0.0661\% & 0.0493\% & 0.0129\% \\ \(\omega_{yGyro}\) & 0.0547\% & 0.0531\% & 0.00952\% \\ \(\omega_{ZcGyro}\) & 0.0651\% & 0.0753\% & 0.0238\% \\ \(P_{Xe,m}\) & 2.686\% & 0\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The RMSE of propulsion telemetry variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**RMSE**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Uncorrected**} & \multicolumn{2}{c}{**The First Loop**} & \multicolumn{2}{c}{**The Second Loop**} \\ \hline \(Q_{Loop}\) & 11.39\% & 6.46\(\times 10^{-9}\)\% & 0.00\% \\ \(U_{Loop}\) & 24.39\% & 0.05\% & 0.02\% \\ \(I_{Loop}\) & 8.72\% & 0.26\% & 0.07\% \\ \(P_{Loop}\) & 0.28\% & 0.27\% & 0.08\% \\ \(\theta_{1,SunSensor}\) & 9.84\% & 0.09\% & 0.10\% \\ \(P_{Wing1}\) & 34.27\% & 0.01\% & 0.01\% \\ \(\theta_{2,SunSensor}\) & 9.84\% & 0.09\% & 0.10\% \\ \(P_{Wing2}\) & 34.27\% & 0.01\% & 0.01\% \\ \(I_{Battery}\) & 41.53\% & 1.02 \(\times\)\(10^{-8}\)\% & 0.00\% \\ \(Q_{Battery}\) & 11.39\% & 6.46 \(\times\)\(10^{-9}\)\% & 0.00\% \\ \(U_{Battery}\) & 0\% & 0\% & 0.00\% \\ \(P_{Battery}\) & 41.53\% & 1.02 \(\times\)\(10^{-8}\)\% & 0.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The RMSE of power telemetry variables.