# Analysis of Precise Orbit Determination for the HY2D Satellite Using Onboard GPS/BDS Observations
## 2 Materials  
### HY2D Spacecraft  
On 19 May 2021, the HY2D satellite was launched at the Jiuquan satellite launch center successfully. The HY2D satellite adopts a non-sun-synchronous orbit with the inclination of 66\({}^{\circ}\), and the orbit altitude of about 960 km. The primary sensors comprise radar altimeter, microwave scatterometer, calibration radiometer, data collection system and ship automatic identification system [24]. Figure 1 shows the HY2D spacecraft and its payloads. It should be pointed out that the GNSS antennas consists of GPS and BDS antennas but cannot receive GPS/BDS signals simultaneously. Thus, the GPS and BDS receivers would switch to each other as needed. The X, Y and Z are the three axes of the satellite flight reference frame (SFF) in the figure, and the +X and +Z axes point toward the direction of flight and nadir, respectively. The +Y axis completes the right-hand orthogonal reference. When the satellite is at zero attitude, the SFF coincides with the satellite body reference frame (SBF), while the SFF is different from the SBF in a non-zero attitude. Table 1 lists the coordinates of the GPS and BDS antenna phase center, laser retro-array (LRA) spherical center, and center of mass in the SBF. With the help of these coordinates, we can perform phase center correction of receivers for HY2D in POD processing. Figure 1: HY2D satellite and its payloads. When the satellite is flying, surface forces acting on HY2D are mainly from atmospheric drag, earth radiation pressure and solar radiation pressure [10]. In order to model the forces precisely, having a well knowledge of the characteristics for the HY2D satellite surfaces and radiators is very necessary. Table 2 gives the parameters information of spacecraft surfaces and radiators, including the optical characteristics and projected areas. With help of the information, the solar radiation pressure of HY2D can be described with the Box-Wing model. Table 2 shows that the +X and +Z axes point to the directions of flight and nadir, respectively, and -Y axis points to the direction of Sun. As the HY2D satellite belongs to a non-sun-synchronous orbit satellite, the solar arrays are always directed to the sun. Moreover, the HY2D satellite is in a non-zero attitude during the flight, and the SBF has to rotate according to the attitude following the order of yaw-roll-pitch to obtain the SFF. So, it is essential to adopt satellite attitude data to calculate the solar radiation pressure and phase center offset accurately. Table 3 shows a part of attitude data of HY2D satellite, which is provided by National Satellite Ocean Application Service (NSOAS) at present. As can be shown from Table 3, the attitude data consist of date, time, roll angle, pitch angle, and yaw angle. In addition, the change in yaw angle works well with the increase in time, so, this study needs to use the attitude data of HY2D to correct the phase center offset and solar radiation pressure. \begin{table}
\begin{tabular}{c c c c} \hline  & **X (mm)** & **Y (mm)** & **Z (mm)** \\ \hline Center of mass & \(1319.4\) & \(-4.7\) & \(5.7\) \\ GPS phase center (L1) & \(347.2\) & \(-181.9\) & \(-1377.5\) \\ GPS phase center (L2) & \(347.4\) & \(-181.0\) & \(-1396.1\) \\ BDS phase center (B1) & \(427.4\) & \(177.7\) & \(-1378.5\) \\ BDS phase center (B2) & \(427.7\) & \(177.9\) & \(-1397.3\) \\ LRA spherical center & \(311.7\) & \(-215.5\) & \(1060.8\) \\ \hline \end{tabular}
\end{table} 
Table 1: Coordinates of the center of mass, GPS and BDS antenna phase centers and LRA spherical center in the SBF.