## 1 Introduction  
Currently, the precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is not comparable to that of the Global Positioning System (GPS) or Global Navigation Satellite System (GLONASS), which is a disadvantage of the BDS in providing high precision service to global users. In addition to the inaccurate solar radiation pressure model and the special attitude control mode of the BDS [1, 2, 3], one other reason for this lies in the few and unevenly distributed global BDS monitoring stations. Furthermore, the generally static characteristics of the BDS' geostationary orbit (GEO) satellite to the ground stations leads to a poor orbit determination accuracy, even if the ground tracking stations were to be globally distributed. Currently, the 3D orbital accuracy of BDS GEO satellites is at the meter level using the current BDS ground monitoring stations [4; 5]. Fortunately, weaknesses in the observability and tracking geometry can be overcome by introducing low Earth orbit (LEO) satellites as moving stations. LEO satellites have been primarily used for Earth observations, commercial communications, and navigation over the past 20 years, and the Iridium constellation is the world's first LEO satellite constellation used primarily for mobile communication, integrating the functions of communication and navigation [6]. This constellation can provide navigation services or augment GNSS for positioning. Simulations of BDS POD enhancement with large LEO constellations have been conducted by many researchers [7; 8; 9; 10]. It has been found that, compared with a ground-based POD, a remarkable accuracy improvement of over 70% can be observed for all GNSS satellites when a large LEO constellation with 60 satellites is introduced, with the orbital accuracy of BDS GEO satellites reaching the centimeter level. In particular, [PERSON] et al. [8] simulated 66 satellites of the Iridium satellite constellation and found that the \"one-step\" method, in which the GNSS and LEO orbits and the satellite clock offsets are estimated simultaneously, generates the best orbit and clock accuracy. However, the problem of time consumption needs to be taken into consideration because dozens of hours of computation are not beneficial for real-time services; accordingly, it has been concluded that introducing part of an LEO constellation could be an effective way to balance the conflict between the orbital accuracy and the computational efficiency. [PERSON] et al. [10] studied the effect of satellite numbers, orbital types, and altitudes, as well as global and regional ground networks on the LEO-constellation-augmented GNSS POD performance. Their results indicate that a sun-synchronous-orbiting LEO constellation could yield a better tracking geometry for GNSS satellites and a stronger augmentation than a polar-orbiting constellation. Furthermore, the GNSS orbit accuracy is less dependent on ground stations when incorporating a large number of LEO satellites. One common problem in the above studies is that the simulations are overly ideal. In typical cases, spacetime observational errors are generally ignored. In various simulations, the measurement noise of onboard receivers had been treated as being the same as that of ground geodetic receivers, i.e., the pseudo-range noise is set to 1 m and the carrier-phase measurement noise is set to 0.005 m [8]. For a large LEO constellation, the performances of the GNSS receivers onboard the LEO satellites are usually different from those of the geodetic receivers [6; 11] and, therefore, the noise level needs to be analyzed with actual observations and then carefully calibrated for the simulation. Otherwise, the simulated LEO-constellation-augmented GNSS POD will not accurately reflect the actual situation. In addition, the outer space environment is much more complicated than the ground environment and solar particles emitted from a solar storm may damage the hardware of a spacecraft or a satellite.