# Integrated Precise Orbit Determination of Multi-Gnss and Large LEO Constellations
## 2 Constellations and Observation Simulation
### Observations Simulation Configuration  
At present, no onboard multi-GNSS observations from large LEO constellations are available, because all the LEO constellations providing augmented navigation services are still under construction. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Schemes** & **60 LEO-P** & **60 LEO-P** & **60 LEO-P** & **66 LEO-P** & **60 LEO-S** & **96 LEO-P** \\ \hline
**Satellite number** & 60 & 60 & 60 & 66 & 60 & 96 \\ \hline
**Plane number** & 10 & 10 & 10 & 6 & 10 & 12 \\ \hline
**Altitude** & 600 km & 1000 km & 1400 km & 1000 km & 1000 km & 1000 km \\ \hline
**Inclination** & 84.6\({}^{\circ}\) & 84.6\({}^{\circ}\) & 84.6\({}^{\circ}\) & 84.6\({}^{\circ}\) & 99.4843\({}^{\circ}\) & 84.6\({}^{\circ}\) \\ \hline
**Orbit type** & \begin{tabular}{c} Nearly-polar \\ circular orbits \\ \end{tabular} & \begin{tabular}{c} Nearly-polar \\ circular orbits \\ \end{tabular} & \begin{tabular}{c} Nearly-polar \\ circular orbits \\ \end{tabular} & \begin{tabular}{c} Nearly-polar \\ circular orbits \\ \end{tabular} & \
\begin{tabular}{c} sun-synchronous \\ circular orbits \\ \end{tabular} &
\begin{tabular}{c} Nearly-polar \\ circular orbits \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed information of the designed LEO constellations. Figure 1: LEO constellations designed for augmented GNSS POD. (**a**) 60 LEO, nearly-polar orbits, 600 km, 1000 km, and 1400 km; (**b**) 66 LEO (Iridium satellite constellation), nearly-polar orbits, 1000 km; (**c**) 60 LEO, sun-synchronous orbits, 1000 km; (**d**) 96 LEO, nearly polar, 1000 km. Hence, in order to achieve an augmented four-system POD, all kinds of data should be simulated. Since we mainly focus on the contribution of onboard multi-GNSS observations to the GNSS POD, only ground and onboard multi-GNSS measurements are taken into consideration in the data simulation. In this study, we adopt the same simulation method described in [PERSON] et al. [9]. To make the simulated data as close as possible to the real observations, all errors related to the satellite, receiver, and signal path, as well as observation noise, should be considered and calculated in the process of data simulation. The undifferentiated code and carrier phase observations for ground stations and LEO satellites can be expressed as follows:  
\[\left\{ \begin{array}{c}P_{g,j}^{s}=\rho_{g,j}^{s}+c\Big{(}\delta t_{g}-\delta t ^{s}\Big{)}+I_{g,j}^{s}+T_{g}^{s}+(b_{g,j}-b_{j}^{s})+\varepsilon_{g,j}^{s}\\ P_{leo,j}^{s}=\rho_{leo,j}^{s}+c(\delta t_{leo}-\delta t^{s})+I_{leo,j}^{s}+(b_ {leo,j}-b_{j}^{s})+\varepsilon_{leo,j}^{s}\\ L_{g,j}^{s}=\rho_{g,j}^{s}+c\Big{(}\delta t_{g}-\delta t^{s}\Big{)}-I_{g,j}^{s }+T_{g}^{s}+\lambda_{j}N_{g,j}^{s}+\lambda_{j}(B_{g,j}-B_{j}^{s})+\omega_{g,j}^ {s}\\ L_{leo,j}^{s}=\rho_{leo,j}^{s}+c(\delta t_{leo}-\delta t^{s})-I_{leo,j}^{s}+ \lambda_{j}N_{leo,j}^{s}+\lambda_{j}(B_{leo,j}-B_{j}^{s})+\omega_{leo,j}^{s} \end{array} \right. \tag{1}\]  
where \(s,g,leo\), and \(j\) represent GNSS satellites, ground stations, LEO satellites and signal frequency respectively. \(P\) and \(L\) denote pseudorange and carrier phase observations respectively. \(\rho_{g}^{s}\) is the distance between the mass center of satellites and ground receiver, while \(\rho_{leo}^{s}\) is the distance between the mass center of both GNSS satellites and LEO satellites. \(c\) is the speed of light in a vacuum. \(\delta t_{g}\), \(\delta t_{leo}\), and \(\delta t^{s}\) represent the clock offsets for the ground receiver, onboard receiver, and satellite respectively. \(I_{g,j}^{s}\) and \(I_{leo,j}^{s}\) are the ionospheric delays at frequency \(j\). \(T_{g}^{s}\) is the tropospheric delay of ground station. \(\lambda_{j}^{s}\) is the wavelength at the frequency \(j\). \(N_{g,j}^{s}\) and \(N_{leo,j}^{s}\) refers to the integer ambiguities for ground and onboard receiver respectively.