## 1 Introduction  
The Solar X-ray and Extreme Ultraviolet Imager (X-EUVI) is a payload of the Sun synchronous orbit (twilight) FY-3E satellite, which has an orbital altitude of 836 km and an orbital period of 102 min. This is the first space-based solar X-ray and extreme ultraviolet (EUV) imager for space weather and space physics in China [1]. FY-3E is a three-axis stabilized spacecraft with respect to the Earth and changes in the position of the Sun the X-EUVI coordinate system in real time. Therefore, the two-dimensional turntable system was developed to track the Sun [1]. It is shown in Figure 1.  
When X-EUVI works in orbit, the two-dimensional turntable system first roughly points to the Sun according to the sun vector from the satellite. Then, X-EUVI precisely points to the Sun using a turntable lock-in control system based on Trace Guide Telescope (TGT) solar position data [1]. The two-dimensional turntable includes the pitch axis and the azimuth axis. The control system of the two-dimensional turntable realizes the accurate direction of the target by controlling the position, speed, and torque of the two brushless motors, namely the position axis and the pitch axis [2]. This paper takes the pitch axis trajectory as the research object. The two-dimensional turntable controls the trajectory depending on the sun vector data and the solar position data combined with the satellite attitude and other factors. When the turntable controls the optical axis to point to the sun, the image obtained by the XEUV is in the center of the field of view as shown in Figure 2.  
The main factors affecting the normal running of the turntable include the turntable motor current, motor voltage, target solar position, and solar position error signal. The prediction of the two-dimensional turntable trajectory can show the operation status of the turntable. It is not only important to understand the operation of the turntable itself but also that it has an important impact on the evaluation of the operation status of the satellite platform. The same applies to the trajectory prediction of the spaceborne integrated platform or intelligent load. The existing models of trajectory prediction involve different algorithms in different fields, but research on trajectory predictions of a two-dimensional turntable in space is still lacking. By establishing the traditional motion model, the running track of the turntable can be predicted. However, due to many unknown and variable factors in the model, the error is difficult to measure, so the accuracy of the motion model is difficult to guarantee [3]. There are many different methods for trajectory prediction. They include the hidden Markov model (HMM), based on mathematical statistical methods [4], the Kalman filter [5], or neural networks and deep learning in machine learning methods [6; 7; 8; 9; 10]. The advantage of the hidden Markov model is that it has a relatively good prediction effect for tracks with variable states, and the disadvantage is that because of its memoryless nature, it cannot use the preorder information of track sequence. The hidden Markov model is often used for long-sequence prediction [11]. It is often used for pedestrian trajectory prediction. A Kalman filter relies on the information of the previous sequence point and the current position information to predict the next moment. The advantage is that the state estimation process is very stable, and because its calculation process is a continuous prediction and  
Figure 1: Schematic diagram of the position of the sun, satellite, and turntable. (**a**) Schematic diagram of satellite orbit, and sun is in \(-\mathrm{Y}\) direction. (**b**) Turntable optical axis coordinate system. Figure 2: Solar images obtained by X-EUVI when the optical axis points to the sun (from the National Meteorological Satellite Center of China). correction process, it is suitable for trajectory-prediction scenarios requiring strong real-time performance.