# Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction
## 3 Results and Analysis
### Analysis of Different ECOM SRP Models for Orbit Prediction  
BDS-3 satellites adopt a different attitude control mode from the BDS-2 satellite. For the BDS-3 MEO/IGSO satellites, the CYS mode is adopted during the eclipse seasons, and the YS mode is adopted out of eclipse seasons. The BeiDou satellite navigation system has three satellite attitude-control modes: YS mode, orbit-normal (ON) mode, and CYS mode. The BDS-2 satellite adopts the YS and ON modes. For the YS mode, the satellite uses the solar sensor and the Earth sensor to detect the position of the sun and the Earth; thus, this mode satisfies that requirement in which the satellite antenna points to the center of the earth and the solar panel is always perpendicular to the direction of the sun's illumination. After the BDS-2 IGSO/MEO satellites move into the eclipse season and the \(\beta\) angle (defined by the angle of the sun above the orbit plane) is between \(-4^{\circ}\) and \(+4^{\circ}\), the attitude control mode of the BDS-2 IGSO/MEO satellites changes from the YS mode to the ON mode [34]. As for the ON mode, the yaw angle \(\varphi\) (defined by the angle between the instantaneous velocity and the body-fixed x-axis) is always zero. However, studies have shown that when BDS-2 IGSO/MEO satellites move into the eclipse season, the satellites adopting the ON mode will cause a significant decrease in the accuracy of the satellite's orbit determination [35]. Therefore, the CYS mode is adopted in the BDS-3 MEO/IGSO satellites. When the BDS-3 MEO/IGSO satellites move in the eclipse season, the satellite adopts the YS and CYS modes. During most of the eclipse season, the BDS-3 MEO/IGSO satellites use the YS mode. The CYS mode includes two periods of midnight-turn maneuver and noon-turn maneuver. Midnight-turn maneuver and noon-turn maneuver are activated when the \(\beta\) angle is between \(-3^{\circ}\) and \(+3^{\circ}\), and the sun's azimuth angle \(\mid\alpha\mid\) (defined by the angle between Earth-satellite vector and Earth-\"noon\" vector on the orbit plane) is \(\leq\)10\({}^{\circ}\) or \(\mid\alpha\)\(\pm\) 180\({}^{\circ}\)\(\mid\)\(\leq\) 10\({}^{\circ}\) [20]. As for the CYS mode, the solar sensor can no longer control the yaw's attitude, and the BDS-3 MEO/IGSO satellites start to yaw with estimated hardware yaw rates in order to make the yaw angle transform 180\({}^{\circ}\). Yaw attitude departs from the nominal values and it can take up to 30 min to 1 h to correct [36]. Compared with the YS mode, the CYS mode adopts the method of starting the maneuver in advance and ending  
Figure 6: The URE of BDS-3 predicted orbits in and out of eclipse season with prediction intervals of 6 h (**top**) and 24 h (**bottom**). the maneuver with a delay; thereby, the CYS mode avoids rapid yaw slews near collinear sun-spacecraft-Earth geometries. The satellite attitude control mode will affect the solar radiation pressure related to the irradiated surface, which will further affect the accuracy of the satellite's precise orbit predictions [37]. Therefore, it is necessary to study the BDS-3 satellite's orbit prediction accuracy for different ECOM SRP models in and out of the eclipse seasons. Similarly to Section 3.3, eight BDS-3 satellites (C19, C20, C21, C22, C32, C33, C41, and C42) were selected to study the orbital prediction accuracy of the ECOM5, ECOM7, and ECOM9 SRP models when moving in and out of the eclipse seasons. As shown in Figure 7, the orbit prediction accuracy of the ECOM5, ECOM7, and ECOM9 SRP models is similar in and out of eclipse seasons. The orbital UREs using the ECOM5, ECOM7, and ECOM9 SRP models are 0.035 m, 0.031 m, and 0.030 m outside eclipse seasons, respectively. However, the orbital UREs using the ECOM5, ECOM7, and ECOM9 SRP models are 0.048 m, 0.037 m, and 0.036 m during the eclipse seasons, respectively. The results show that the orbital URE of the ECOM9 model is 19% lower than that of using the ECOM5 SRP model.