# Hierarchical Model Updating Method for Vector Electric-Propulsion Satellites
## 3 Method  
### The Hierarchical Model Updating Method  
The state variables and telemetry variables are selected, grouped, and sorted before being updated. The rule for determining whether variables need to be modified are as follows: (1) variables that have a significant impact on the system because when their change will significantly affect the other variables; (2) variables that change obviously over time; and (3) variables that are different from those on the ground or difficult to measure accurately on the ground. As for the updating sort, the variables that play a more dominant role in the system are updated earlier, and the less influential variables are updated later. The specific group strategy for the vector electric-propulsion satellite is as follows:* Orbit-related variables The orbit telemetry variables refer to the position vector and velocity vector in the geocentric inertial system measured by GPS. Unless the orbit performs maneuver, orbit variables are less affected by other subsystems. On the other hand, orbit variables play a greater or even more decisive role in other variables. So the updating of orbit variables is given priority. The state variables to be updated are the initial values of orbit position \(\mathbf{r}_{0}\) and velocity \(\mathbf{v}_{0}\). In addition, there are errors during the measurement process of GPS, so the constant errors and random errors of GPS position and velocity measurement should also be considered, that is, \(\mu_{GPS,r},\sigma_{GPS,r},\mu_{GPS,r},\sigma_{GPS,v}\). The telemetry variables are \(\mathbf{r}_{GPS}\) and \(\mathbf{v}_{GPS}\).
* Attitude-related variables Attitude variables also have a great impact on other parts, so they are a second priority. The attitude telemetry variables are the attitude angle calculated by the attitude determination algorithm and the angular velocity measured by the gyroscope. So besides the initial Euler angles \(\varphi_{0},\theta_{0},\psi_{0}\) and the initial angular velocity being updated, the error parameters of the gyro \(\mu_{Gyro,\omega},\sigma_{Gyro,\omega},\epsilon_{Gyro,\omega}\) and the star sensor \(\mu_{StarSensor},\sigma_{StarSensor}\) also require correction, due to their influence. The telemetry variables selected are \(\varphi_{m},\theta_{m},\psi_{m}\) and \(\mathbf{\omega}_{Gyro}\).
* Power subsystem variables The power subsystem includes dynamic state variables of the solar wings, and electrical state variables of the solar arrays, battery, and bus loop. The state variables are the initial angles \(\theta_{wing_{1},0}\) and \(\theta_{wing_{2},0}\), the photoelectric conversion efficiency of the solar array \(\eta_{w}\), and the charging coefficient \(k_{Charge}\) and discharging coefficient \(k_{Discharge}\) of the battery. Telemetry variables include the solar wings variables \(P_{Wing_{1}},P_{Wing_{2}},\theta_{SW1,SunSensor}\), \(\theta_{SW2,SunSensor}\); the battery variables \(I_{Battery}\), \(Q_{Battery}\), \(U_{Battery}\), \(P_{Battery}\); and the bus loop variables \(Q_{Loop}\),\(Q_{Loop}\),\(U_{Loop}\),\(I_{Loop}\), \(P_{Loop}\).
* Propulsion subsystem variables Because the variables of vector electric thruster are difficult to measure accurately on the ground, it needs to be updated on orbit. The thrust variables of the electric thruster have the greatest influence on the attitude variables and the pressure of the xenon gas, so they are put in the same group for updates; they are installation attitude variables \(\varphi_{T_{N1}}^{Install},\theta_{T_{N1}}^{Install}\), \(\psi_{T_{N1}}^{Install}\), installation variables \(X_{T_{N1}}^{Install},Y_{T_{N1}}^{Install},Z_{T_{N1}}^{Install}\), and force \(F_{T_{N1}}\). Triaxial attitude angle, angular velocity, and xenon cylinder pressure are selected as the telemetry parameters. The attitude variables \(\varphi_{m},\theta_{m},\psi_{m},\omega_{xGyro},\omega_{yGyro},\omega_{zGyro}\) and xenon gas pressure \(P_{Xe,m}\) are selected as the telemetry variables.  
The result of grouping and the relationship between them are shown in Figure 1.