# Analysis of Precise Orbit Determination for the HY2D Satellite Using Onboard GPS/BDS Observations
## 3 POD Method and Strategies
### Dynamic Model  
The equation of motion of a single LEO satellite in the inertial frame can be expressed as follows [25]:  
\[\overset{\rightharpoonup}{r}=-\frac{GM}{\left|\overset{\rightharpoonup}{r} \right|^{3}}\overset{\rightharpoonup}{r}+a_{r}+a_{rtn} \tag{2}\]  
where, \(GM\) stands for geocentric gravitational constant, \(\overset{\rightharpoonup}{r}\) and \(\overset{\rightharpoonup}{r}\) are the position and acceleration of the satellite in the inertial coordinate system, respectively; \(a_{r}\) refers to main perturbation acceleration excluded Earth center gravity, that includes the Sun and Moon perturbation, atmosphere drag, solar radiation pressure, Earth radiation pressure, solid Earth tide, ocean tide and so on. \(a_{rtn}\) refers to the periodic radial, tangential, and normal (RTN) perturbation, which can make up for these unmodeled perturbation acceleration errors [26; 27; 28]. In this study, the tangential and normal perturbation parameters are estimated for the POD processing.  
In order not to affect the calculation efficiency and accuracy of orbit determination, the process of choosing the dynamic and observation model is important. For this purpose, the used dynamic model and measurement model are designed in the POD processing for the HY2D satellite refers to the above descriptions. Furthermore, this study also shows the used model information of the SLR validation for the calculated HY2D orbit. The details are given in Table 4. We adopted the 24 h arc solution based on the dynamical method orbit determination, the atmospheric drag coefficient, the solar radiation pressure coefficient, and RTN perturbation parameters are estimated per 6 h, 24 h, and 24 h, respectively. Moreover, the receiver clock parameter for HY2D is estimated with the gaussian white noise model, and the float solutions of ambiguities are also estimated.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Project** & **Selection/Description** \\ \hline \multicolumn{2}{c}{Dynamic model} \\ \hline Gravity model & EIGEN-GRGS.RL04. MEAN-FIELD 120 \(\times\) 120 [29] \\ Atmosphere drag & MSIS00 density model [30] \\ Solar radiation pressure & Box-Wing model [31] \\ Sun and moon ephemeris & JPL DE405 [32] \\ Earth radiation pressure & Knocke-Ries-Tapley model [33] \\ Empirical force model & RTN perturbation \\ Ocean tide [34] & FES2004 [35] \\ Solid Earth tide [34] & TIDE2000 [34] \\ Earth orientation parameter & IERS EOP 14 C04 [36], IAU2000A model \\ \hline \multicolumn{2}{c}{Observation model} \\ \hline Data type & Code and phase observation of ionosphere-free combination \\ Data interval & 30 s \\ Elevation cutoff & 7\({}^{\circ}\) \\ HY2D satellite attitude & Quaternion data \\ GPS and BDS phase model & IGS14.atx \\ Orbit determination arc length and & 24 h arc dynamic solution, 30 s integral step \\ integration step & CODE precise products \\ GPS and BDS satellite ephemeris and clock & Cd/6 h \\ Atmospheric drag coefficient estimation & Cr/24 h \\ Solar radiation pressure coefficient & Tangential and normal/24 h \\ estimation & Gaussian white noise \\ RTN perturbation estimation & Float solutions of ionosphere-free combination \\ Receiver clock error estimation & \\ Ambiguities & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dynamical and observation model employed in the POD for HY2D.