# Hierarchical Model Updating Method for Vector Electric-Propulsion Satellites
## 4 Results and Discussion
### The Result of Hierarchical Model Updating  
The above state variables were corrected according to the updating method described in Section 3. A total of two loops of updating were carried out to compare the deviation between the state variables and the true value of each group after each updating loop, as well as the deviation of each telemetry variable RMSE. The variation in orbit state variables is shown in Figure 3. The iteration from zero to three is the first loop of updating, and four to seven is the second loop. The state variables converge rapidly within three iterations, but the relative error is still large. After other groups were updated and the second loop was executed, the state variables could be further updated. The updating results of orbit state variables are shown in Tables 3 and 4. Table 3 is the comparison between the state variables estimated and the true value, as well as the total residual error of telemetry variables, and Table 4 is the calculation of each telemetry variable RMSE separately. As can be seen from Table 3, although the RMSE of telemetry variables in the first loop converges to a very small value, and most of the state variables are also updated to very small errors, the relative errors of some state variables are still large, which also indicates that the coupling effect of other variables that are not updated cannot be ignored. Through the second loop of updating, the relative errors of these state variables are further significantly reduced. The boost is one to two orders of magnitude. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Min** & **Max** & **Variable** & **Min** & **Max** \\ \hline \(r_{\text{xGPS}}\), m & 6,570,369.34 & 7,098,007.66 & \(Q_{\text{Lapap}}\), mAh & 8,623,152.00 & 8,766,671.98 \\ \(r_{\text{yGPS}}\), m & 60,712.16 & 2,301,754.64 & \(U_{\text{Lapap}}\), V & 28.01 & 83.52 \\ \(r_{\text{zGPS}}\), m & 525.25 & 20,090.67 & \(U_{\text{Lapap}}\), A & 1.79 & 22.92 \\ \(v_{\text{xGPS}}\), m/s & \(-\)2495.26 & \(-\)64.65 & \(P_{\text{Lapap}}\), W & 110.94 & 641.99 \\ \(v_{\text{yGPS}}\), m/s & 7041.83 & 7606.04 & \(\theta_{\text{1,SumSumSum}}\), \({}^{\circ}\) & 66.28 & 89.97 \\ \(v_{\text{zGPS}}\), m/s & 60.89 & 67.07 & \(P_{\text{Wing}}\), W & 2342.28 & 4873.79 \\ \(\theta_{m^{\circ}}\) & \(-\)21.69 & 21.44 & \(\theta_{\text{2,SumSumSum}}\), \({}^{\circ}\) & 67.31 & 89.99 \\ \(\theta_{m^{\circ}}\) & \(-\)7.05 & 7.21 & \(P_{\text{Wing}}\), W & 2320.98 & 4873.40 \\ \(\psi_{m^{\circ}}\) & \(-\)22.38 & 21.65 & \(I_{\text{Battery}}\), A & 20.00 & 20.00 \\ \(\omega_{\text{xGPS}}\), \({}^{\circ}\)/s & \(-\)1.00 & 1.00 & \(Q_{\text{Sattery}}\), mAh & 100,005.56 & 101,666.67 \\ \(\omega_{\text{yGyGyro}}\) & \(-\)1.00 & 1.00 & \(U_{\text{Battery}}\), V & 42.00 & 42.00 \\ \(\omega_{\text{zGyGyro}}\) & \(-\)1.00 & 1.00 & \(P_{\text{Battery}}\), W & 840.00 & 840.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The feasible range of telemetry variables. Figure 2: (a) The minimum in x position; (b) the maximum in x position. The same is true for each telemetry variable. After multiple loops of updating, the residual error is further reduced, and the accuracy can be improved by about one order of magnitude. The updating results of attitude variables are shown in Tables 5 and 6. It can be seen that the state variables and telemetry variables are further improved by multiple loops of updating, and the improvement effect is one to two orders of magnitude.