# Hierarchical Model Updating Method for Vector Electric-Propulsion Satellites
## 1 Introduction
Model updating for electric-propulsion satellites implies the multiparametric optimization of a large number of electric, magnetic, thermodynamic, and other processes [11]. From the perspective of the space dimension, the satellite is influenced by forces and moments from the environment. The satellite system itself can be divided into multiple subsystems, including the orbit and attitude control system; power system; thermal control system; propulsion system; and telemetry, telecommand, and control system. Each subsystem is further composed of many components. Additionally, there are coupling relationships between the environment and the subsystems, as well as the various components. As the functions and structures of satellites develop in a more complex and changeable direction, these coupling effects will become increasingly significant, and the physical properties and magnitudes of interactions will be more inconsistent, causing satellite model updating to be more challenging and resource-consuming. Since the amount of satellite parameters that need to be updated is large and the degree of coupling between different parameters is different, if all the parameters are updated simultaneously, there is a high probability that the solution will not converge. Thus, it is imperative to divide them into different hierarchies according to the degree of the sparseness of the interaction between parameters and then perform updating separately. The hierarchical method means to divide the complex engineering system into subsystems; the subsystems are partitioned into components, the components into parts, and so on [12]. [PERSON] et al. proposed the use of a hierarchical model for model validation [13]. First, the characteristics of the corresponding model are confirmed by using the test data of the simple system, and then the whole system model is deduced recursively. The hierarchical idea reduces the complexity of solving the original problem, so it is also used in the model updating problem of multi-coupled complex systems [14]. [PERSON] et al. [15] divided parameters into key parameters and non-key parameters by sensitivity analysis. The key parameters were corrected first, then the non-key parameters, and finally, all parameters at the same time. This method had higher accuracy than directly correcting all parameters. [PERSON] et al. [16] decomposed the landing buffer system into the recovery module and the airbag system, and their finite element (FE) models were respectively established and updated. By considering the measurement uncertainty brought about by the high-temperature environment in the complex aeromechanical system, [PERSON] et al. [17; 18] and [PERSON] et al. [19] identified the thermodynamic parameters and the mechanical structure parameters sequentially. [PERSON] et al. [20] proposed a hierarchical model updating strategy for the FE model of complex structures, which decomposed the assembled structure into a series of substructures. These substructures were accurately modeled and updated. [PERSON] et al. [21] proposed a two-stage hierarchical objective model updating pattern for cable force identification, and the method improved the accuracy and efficiency of FE model updating. Since the thrust generated by electric propulsion is very small, in the order of millinew-tons, the thrusters need to be turned on for a long time when performing an orbit mission. If the thrust direction does not exceed the center of mass of the satellite, an eccentric moment will be generated, and the angular momentum will be increased. In addition, since electric thrusters are also intended to perform attitude control tasks, most electric thrusters are equipped with vector adjustment mechanisms to change the thrust direction of the force. Each vector adjustment mechanism is composed of two rotating shafts so that the thrust direction can be changed in three dimensions, but this is also a reason why its motion parameters are coupled, and many parameters are involved.