## 2 Materials and Methods  
Position And Navigation Data Analyst (PANDA) software [25] is used in this study for the computation of the BeiDou precise orbit. PANDA is a multifunctional software developed by Wuhan University that is capable of conducting multi-system precise orbit determination, positioning, and atmospheric studies. Generally, the BeiDou POD method mainly includes BDS single-system and BDS/GPS joint orbit determination. The BDS single-system orbit determination solely uses the BeiDou observation data to solve the BeiDou satellite orbit, satellite clock, tropospheric delay, receiver clock error, and other parameters. The joint orbit determination method utilizes both GPS and BeiDou observation data of the ground stations to solve the GPS and BeiDou satellite orbit, satellite clock error, tropospheric delay, receiver clock error, and inter-system biases in a combination fashion. The method for satellite orbit determination mainly includes the choice of observation model parameters, the error correction model, and the satellite dynamic model. Important options of the considered processing methods for the observation model and for the forces model [11] are listed in Tables 1 and 2. The POD of navigation satellites mainly includes the acquisition of satellite orbit initial conditions, the orbit integration, the reduction and linearization of observation data, and the formation and solution of the normal equation. Firstly, the observation data of ground tracking stations are preprocessed. After the outliers' detection and removal, in addition to the cycle slips' marking, the LC and PC observations are combined. Orbit integration of the broadcast ephemeris is performed to obtain the initial orbit solution of the satellite. Then, the parameters are initialized; the observation equation is formed using the satellite initial orbit, the dynamic model, and the observations. The unknown parameters in the least square estimation are the initial satellite position and velocity, solar radiation parameters, satellite clock errors, zenith tropospheric delay corrections, receiver clock errors, inter-system biases, and ambiguities. Finally, the least squares estimation is used to obtain corrections of the initial satellite orbit, and the satellite orbit parameters are integrated to obtain the orbit products. This is an iterative process, which means that orbit integration and parameter \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Model** \\ \hline Preprocessing & Automatic edition of single-station data \\ Observation data & Undifferenced iono-free code and phase combination of L1/L2 and B1/B2, \\  & higher-order ionospheric delay not considered \\ Sample rate & 300 s \\ Cutoff elevation angle & 7\({}^{\circ}\) \\ Weight & Priori precision of 0.01 cycle phase and 0.5 m code. When the elevation angle is \textgreater{}30\({}^{\circ}\), \\  & the weight is 1; otherwise 2 \(\times\) sin(E) \\ Phase windup & Considered \\ Inter-system bias & Constant parameters estimated using the zero mean datum constraint conditions \\ Phase center model & jsg08.txt \\ Topospheric delay & GPT model [26], GMF mapping function [27], 2-hourly wet delay estimation \\ Satellite and receiver clock & White noise \\ Station coordinates & Fixed to GPS precise point positioning \\ ERP & Estimate the polar motion x, y components and its rates; fix UT1 and estimate its rate. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Observation model and configuration of parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Model** \\ \hline Earth Gravity & EGM2008 up to 12 \(\times\) 12 \\ N-body gravitation & Sun, moon, and other planets (DE405) \\ Tides & Solid tide, ocean tide, polar tide \\ Solar radiation pressure & ECOM five parameters [28] \\ Relativity effect & IERS Convention 2010 \\ Albedo and antenna thrust model & Considered for GPS only \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Satellite force model.