## 2 Constellation Design and Data Simulation
### BDS/LEO Combined Constellation Configurations  
According to the nominal parameter configuration of the BDS constellation, the full constellation BDS-3 comprises three GEO, three inclined geosynchronous orbits (IGSO), and 24 medium Earth orbit (MEO) satellites, with the orbital inclinations of the GEO and IGSO satellites being 0\({}^{\circ}\) and 55\({}^{\circ}\), respectively, and all the orbital altitudes being 35,786 km. The three GEO satellites are placed at eastern longitudes of 80\({}^{\circ}\), 110.5\({}^{\circ}\), and 140\({}^{\circ}\), and the three IGSO satellites are at ascending-node geographical longitudes of 0\({}^{\circ}\), 120\({}^{\circ}\), and 240\({}^{\circ}\). The 24 MEO satellites are in a sun-synchronous-orbiting constellation called the Walker 24/3/1 constellation [19], in which the 24 satellites are placed on three planes.  
To assess the impact of the size of the LEO constellation on the BDS POD, five polar circular orbits with different numbers of LEO satellites were designed, namely, the Walker 2/1/0, Walker 6/2/1, Walker 12/3/1, Walker 24/4/2, and Walker 60/6/4 constellations, which are shown in Figure 1b-f, respectively. According to previous studies, up to 60 LEO satellites are sufficient to enhance the BDS orbits to achieve the best accuracy [9; 10]. This set of gradually increasing satellite numbers is used to determine the minimum number of LEO satellites that can fully enhance the BDS POD to achieve the best performance. For each constellation, satellites are placed on a certain number of equally spaced planes with the orbital altitudes of 1200 km and the inclinations of 86.4\({}^{\circ}\) to the equatorial plane for all satellites. The nominal parameter configurations are shown in Table 1. The dynamic models for the constellation configurations are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**System** & \multicolumn{2}{c}{**BDS-3**} & \multicolumn{2}{c}{**LEO**} \\ \hline
**Orbit Type** & **GEO** & **IGSO** & **MEO** & **Polar** \\ \hline Satellite number & 3 & 3 & 24 & 2, 6, 12, 24, and 60, \\  & & & respectively \\ \hline Constellation & Placed at east longitude & Placed at geographical & Walker & 1, 2, 3, 4, and 6 planes, \\  & 80\({}^{\circ}\), 110.5\({}^{\circ}\), and 140\({}^{\circ}\) & longitude 0\({}^{\circ}\), 120\({}^{\circ}\), and 240\({}^{\circ}\) & 24/3/1 & respectively \\ \hline Inclination & 0 & 55\({}^{\circ}\) & 55\({}^{\circ}\) & 86.4\({}^{\circ}\) \\ \hline altitude [km] & 35,786 & 35,786 & 21,528 & 1200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Nominal parameters of the BDS-3/LEO constellation configurations.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dynamic Model** & **BDS** & **LEO** \\ \hline Earth gravity & EIGEN-6C (12 \(\times\) 12) [20] & EIGEN-6C (120 \(\times\) 120) \\ N-body & JPL DE405 & JPL DE405 \\ Solid tide and pole tide & IERS 2010 [21] & IERS 2010 \\ Ocean tide & FES 2004 [22] & FES 2004 \\ Relatively & IERS 2010 & IERS 2010 \\ Solar radiation pressure & ECM2 7-parameter model [3] & Box-Wing model [23] \\ Atmospheric drag & None & DTM94 [24] \\ \hline \hline \end{tabular}
\end{table}
Table 2: The dynamic models applied in the constellation configurations.  
Figure 1: Designed BDS-3/LEO constellation: (**a**) BDS-3, (**b**) Walker 2/1/0, (**c**) Walker 6/2/1, (**d**) Walker 12/3/1, (**e**) Walker 24/4/2, and (**f**) Walker 60/6/4.