## 2 Constellation Design and Data Simulation
### Simulation of Observations  
Two types of observations, namely ground-tracking and spaceborne BDS data, were simulated. Considering the BDS monitoring stations are primarily located in China, six ground stations located in China, namely GUA1, CHU1, XIA1, SHA1, LHA1, and KUN1, chosen from the International GNSS Monitoring and Assessment System (iGMAS) network were used for the observation simulation. The time span was from day 001 to day 003 in 2019 and the sampling interval was 10 s. The station distribution is shown in Figure 2.  
Different from the ground receivers, the receivers in space are cycling at a speed of several kilometers per second. Therefore, we need to clarify some special characteristics of the GNSS receivers mounted on the LEO satellites to ensure that GNSS signals can be tracked reliably and continuously. First, the strength of the satellite signal received by the spaceborne receiver changes rapidly. Sometimes, the signal is very weak, only a few dB. It is required that the spaceborne receiver should have a very sensitive signal-receiving system to receive very weak satellite signals. Then, the onboard receiver should have the ability of resisting harsh environmental interference, i.e., the strong solar ultraviolet radiation and charged particles ejected by a solar storm. Finally, the receivers should be equipped with multiple pairs of GPS signal antennas pointing to different directions to satisfy various applications. Simulations of ground or spaceborne observations is in fact the reverse process of positioning. B1c (1575.42 MHz) and B2a (1176.45 MHz) were set for the carrier-phase frequency for all BDS-3 satellites. For the sake of simplicity and convenience, the GPS L1 (1575.42 MHz) and L2 (1227.60 MHz) carrier frequencies were adopted for all LEO satellites. The accurate coordinates were fixed to the International GNSS Service (IGS) weekly solution. The algorithms of the observation simulation have already been described in peer-reviewed publications, i.e., in [PERSON] et al. (2018) and [PERSON] et al. (2019). Most of the observational errors need to be carefully considered so as to make the simulated data as close to the actual-observed data as possible. The satellite-receiver geometric distance was computed using the center-of-mass positions of the satellite and the receiver, which was corrected using the phase center offsets (PCO) and variations (PCV) of the satellite antennas. For the geometry observation model of the ground observations, the relativistic effect, phase wind-up corrections, tidal  
Figure 2: The distribution of ground tracking stations. displacements, dry tropospheric delay, and hardware delays were all considered [25; 26]. The igs14 antenna information ([[https://files.igs.org/pub/station/general/igs14_2148.atx](https://files.igs.org/pub/station/general/igs14_2148.atx)]([https://files.igs.org/pub/station/general/igs14_2148.atx](https://files.igs.org/pub/station/general/igs14_2148.atx)) accessed on 20 June 2021) was applied for the BDS-3 satellites; meanwhile, this information was set to zero for the LEO satellites. Regarding the simulation of the ground observations, the receiver-independent error sources including the receiver clock offsets, the zenith wet delay, and the inter-system bias (ISB) between the LEO and BDS satellites were obtained by processing actual static multi-GNSS data. The ISB parameter is usually referred to as the difference in the code hardware delay between two GNSS; here, the standard deviation of the hardware delay was set to 0.1 m [27]. The dry component of the slant tropospheric delay was computed using the Saastamoinen model [28] together with the global mapping function (GMF) [29]. Meanwhile, the ionospheric delay errors were not considered because ionosphere-free (IF) combined observations were used for the POD.