# A Sun-Tracking Algorithm for Satellite-Borne Spectrometers Based on the Orbital Motion Model
## 1 Introduction  
A satellite-based spectrometer is on board all satellite platforms in a solar synchronous orbit. The solar spectral irradiance can be acquired by monitoring the influence of solar activity variation on the solar spectral radiation, providing data support for the field of meteorology [1]. To obtain effective spectral data, it is important that the spectrometer is able to track the sun for long time periods with a high accuracy. Because the incident angle of sunlight in orbit is greater than the effective field of the spectrometer, the spectrometer is mounted on a two-dimensional turntable to compensate for satellite orbital motion, allowing the mission requirements of the spectrometer to be achieved. Furthermore, an optical tracking sensor is mounted on the turntable, whose field of view is parallel to that of the spectrometer, and is employed to measure the deviation angle of the sun in the center of the field of view. The pointing and tracking of the sun by the spectrometer with high precision is achieved by combining data from the optical tracking sensor and the turntable position sensor. When the tracking sensor processes and calculates the solar deviation angle, certain procedures take place, including image signal processing, target position extraction, and data transmission. Therefore, a time lag exists for the deviation angle, which leads to anovershoot when the spectrometer locks the sun in the center of the field of view and an impact on the bandwidth and phase margin of the control system during tracking [2; 3]. In recent years, an on-axis tracking strategy has been widely used in photoelectric tracking systems by taking advantage of the fast computing ability of the controller to compensate for the time lag of the sensor, among which the predictive filtering algorithm and target motion model are two key elements that influence the control performance [4; 5]. In terms of the predictive filtering algorithm, predictive control is combined with proportional-integral-derivative (PID) control, and the dual control strategy of the dynamic matrix control - PID (DMC-PID) cascade is adopted in reference [6] to improve the tracking accuracy and robustness of the system. The angle relationship between the position sensor and tracking sensor is employed in reference [7], taking the measurement data of both into consideration to design a time-lag compensator and improve the tracking performance of the system. However, the aforementioned algorithms cannot filter measurement noise. The current statistical model, based on the Ho robust filtering algorithm, is established in reference [8], which first uses prediction and then fusion to solve the problems of miss distance lag and signal noise of the tracking sensor, where the filtering algorithm is relatively complex. The target state-space description method is adopted in the Kalman filter algorithm, and the process noise and measurement noise are introduced into the state model to describe the uncertainty of the tracking model, which can achieve the optimal estimation of the system state under white noise. Owing to its simple structure, low requirements for controller calculation, and energy storage capacity, this algorithm can be widely used in control systems under different working conditions [9; 10; 11; 12]. In terms of the target model, the constant velocity (CV) model and constant acceleration (CA) model can be used when the system tracks non-maneuverable objects [13]. For maneuverable objects, the randomness of object tracking is estimated through different techniques, one of which is the Singer model, which hypothesizes that the target acceleration is an exponentially correlated stochastic process whose mean value is zero [14]. The acceleration value of the target is taken as the center in the current statistical model (CSM). The modified Rayleigh distribution function is employed to describe the probability distribution of acceleration, which can predict the position and speed of the maneuverable target, along with certain other parameters.