# BeiDou Augmented Navigation from Low Earth Orbit Satellites
## 3 Strategy for Data Simulation and Procession  
In order to assess the independent and integrated navigation performance of LEO constellation, the ground observations for BeiDou global (BeiDou-3) constellation and a LEO constellation were simulated. According to the Interface Control Document [24], the BeiDou-3 constellation will consist of three GEO, three IGSO, and 24 MEO satellites. The three GEO satellites will operate in the orbit at an altitude of 35,786 km, and are located at 80\({}^{\circ}\)E, 110.5\({}^{\circ}\)E, and 140\({}^{\circ}\)E, respectively. The IGSO satellites with same altitude as GEO have an inclination of the orbital planes of 55 degrees. The MEO satellites will operate in orbit with altitude of 21,528 km and inclination of 55 degrees [24]. The simulated LEO navigation system consists of a constellation of 120 satellites in 10 orbit planes with inclination of 55 degree in a nearly circular orbit (eccentricity about 0.00001) at an approximate altitude of 975 km. As the main aim of the proposed LEO constellation is to argument the BeiDou-3 system, in particularly providing the high accuracy positioning in China. With the initial orbit elements, the 24 h orbits for these BeiDou-3 and LEO satellites can be generated with numerical integration based on the force models summarized on Table 3. Figure 1 shows the distributions of BeiDou-3 and LEO constellation in the space. Three ground stations (CENT located in Wuhan, latitude 30.52779, longitude 114.35686; POTS located in Potsdam, latitude 52.37929, longitude 13.06609; NTUS located in Singapore, latitude 1.34580, longitude 103.67995) are selected for simulating the ground tracking data to demonstrate the positioning performance of the BeiDou-3 and LEO constellation in different regions. Figure 2 shows the distribution. The observations are simulated based on the following observation equations of code and phase:  
\[\rho_{r,i}^{s}=R_{r}^{s}+cdt_{r}-cdt^{s}+m_{r}^{s}T_{r}+\frac{f_{ 1}^{2}}{f_{1}^{2}}I_{r}^{s}+b_{r,i}-b_{i}^{S}+\delta_{PCOj}+\delta_{PCVj}+ \delta_{rel}+\delta_{mul,\rho_{r,i}^{s}}+\varepsilon_{\rho_{r,i}^{s}}\] \[\phi_{r,i}^{s}=R_{r}^{s}+cdt_{r}-cdt^{s}+m_{r}^{s}T_{r}-\frac{f_{ 1}^{2}}{f_{1}^{2}}I_{r}^{s}+\lambda_{i}N_{r}^{s}+B_{r,i}-B_{i}^{S}+\delta_{PCOj }+\delta_{PCVj}+\delta_{rel}+\delta_{mul,\rho_{r,i}^{s}}+\delta_{mul-up}+ \varepsilon_{\varphi_{r,i}^{s}}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Geophysical Models**} & \multicolumn{2}{c}{**Description**} \\ \cline{2-3}  & \multicolumn{2}{c}{**BeiDou-3**} & LEO \\ \hline Static & EGM2008 up to degree and order 12 & Static part of EIGEN-6C up to degree and order 150 \\ \hline Temporal & None & Temporal part of EIGEN-6C up to degree and order 50 \\ \hline Secular rates for low degree coefficients & IERS Conventions 2010 [25] & IERS Conventions 2010 [25] \\ \hline n-body & Moon, Sun, Mercury, Venus, Mars, & Moon, Sun, Mercury, Venus, Mars, \\ Jupiter, Saturn, Uranus, Neptune, Pluto & Jupiter, Saturn, Uranus, Neptune, Pluto \\ JPL DE405 & JPL DE405 \\ \hline Solid Earth Tides & IERS Conventions 2010 [25] & IERS Conventions 2010 [25] \\ \hline Ocean Tides & None & FES2004 \\ \hline Ocean pole tides & None & Desai [26] \\ \hline Relativistic effects & IERS Conventions 2010 [25] & IERS Conventions 2010 [25] \\ \hline \multicolumn{3}{c}{**Satellite surface models and Attitude**} \\ \hline Atmospheric drag & None & DTM94 with Box-wing model \\ \hline Solar Radiation Pressure & 5-parameter ECOM model & Box-wing \\ \hline Attitude & Nominal yaw-steering model & consistent with local orbital reference \\ \hline \multicolumn{3}{c}{**Reference frame**} \\ \hline Inertial frame & [2000.0 & J2000.0 \\ \hline Earth tide and Ocean loading & IERS Conventions 2010 [25] & IERS Conventions 2010 [25] \\ \hline Precession/Nutation & IAU 2000A & IAU 2000A \\ \hline EOP & IERS EOP 08 C04 (IAU2000A) & IERS EOP 08 C04 (IAU2000A) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dynamic models used for generating the 24 h orbits for BeiDou-3 and LEO constellation.