## 3 Simulation Configuration
### The Simulation Software  
Until now, there is no GNSS-like observation data from LEO satellites to ground tracking stations available. In this study, simulation software is developed to simulate the GNSS and LEO observations for ground stations. We include the Iridium satellite constellation into our LeGNSS and assume that the frequencies of LEO constellation are the same as of GPS for the sake of convenience to simulate the observations. Thus, most of the correction models of GPS can be directly used for the LEO constellation. All the relevant data are simulated strictly according to the observation model to make the simulation data as close as possible to reality. The simulation configuration is introduced as follows. The observation equations for the undifferenced (UD) code \(P\) and phase \(L\) read:  
\[P^{s}_{r,j_{k},k}=\rho^{s}_{r,k}+\Delta t_{r,k}-\Delta t^{s}_{k}+T^{s}_{r,k}+T^ {s}_{r,j_{k},k}+b_{r,j_{k}}-b^{s}_{j_{k}}+\varepsilon_{r^{s}_{r,j_{k},k}} \tag{1}\]  
Figure 1: LeGNSS constellation used in this study. \[L^{s}_{r,j,k}=\rho^{s}_{r,k}+\Delta t_{r,k}-\Delta t^{s}_{k}+T^{s}_{r,k}-I^{s}_{r, j,k}+\lambda_{j_{s}}N^{s}_{r,j_{s}}+\delta_{r,j_{s}}-\delta^{s}_{j_{s}}+\varepsilon_{L^{s}_{r, j,k}} \tag{2}\]  
where the super- and subscripts \(s,r,j_{s}\), and \(k\) denote the satellite, receiver, carrier frequency, and epoch, respectively. \(\rho^{s}_{r,k}\) denotes the geometric distance between the phase centers of satellite and receiver antenna at the signal transmitting and receiving time. \(\Delta t_{r,k}\) and \(\Delta t^{s}_{k}\) are the clock biases of receiver and satellite; \(T^{s}_{r,k}\) is the tropospheric delay; \(I^{s}_{r,j_{s},k}\) is the ionospheric delay at frequency \(j_{s}\); \(b_{r,j_{s}}\) and \(b^{s}_{j_{s}}\) are code biases of receiver and satellite, respectively; \(\delta_{r,j_{s}}\) and \(\delta^{s}_{j_{s}}\) are the receiver- and satellite-dependent uncalibrated phase delay (UPD) [5]; \(N^{s}_{r,j_{s}}\) is the integer ambiguity with the wavelength \(\lambda_{j_{s}}\); and \(\varepsilon_{r,j_{s},k}\) and \(\varepsilon_{L^{s}_{r,j,k}}\) denote the measurement noises of code and phase. The primary task of the simulator is to calculate all the components on the right side of observation equations. Some important issues should be clarified here. The satellite-to-receiver distance is computed with the receiver positions and precise satellite orbits. Especially, this distance is associated with the center of mass of the satellite and the receiver, which should be corrected by the phase center offset (PCO) and phase center variation (PCV) of the receiver and the satellite. For the PCO and PCV corrections of GNSS satellites, jigs08.4 tx is used, while for those of LEO satellites, we set the PCO and PCV values to zero. For BDS and LEO satellites, the PCO and PCV corrections of tracking stations are assumed to be the same as the corrections of GPS frequencies. The receiver and satellite clocks can be simulated as white noise. The satellites clock biases can also be extracted from the precise clock file, except for the LEO satellites. Regarding the tropospheric delay, we use the Saastamoinen model [26] together with the Global Mapping Function (GMF) [27] for the ground tracking stations. We do not simulate the ionospheric delay since the ionospheric-free (IF) combination will be used in the PPP model and higher-order ionospheric delays will be neglected in this study. Moreover, the relativistic correction, phase wind-up correction, and tidal displacements are all taken into consideration in the simulation, though they are not included in the equations. The observation noises are simulated as a zero-mean normal distribution with a standard deviation of 1.0 m and 5 mm for code and phase observations, respectively. In summary, the simulation configurations are listed in Table 1.