# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 2 Materials and Methods  
### LEO Constellation Simulation  
In navigation, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites, but with much faster geometric change to enhance GNSS capability; this is called LEO constellation- augmented GNSS [25]. Figure 1 shows the comparison of the trajectory of GPS and LEO satellites across the sky within 10 min. It can be seen that LEO has a longer trajectory in the same amount of time.  
Figure 1: GPS and LEO trajectories across the sky in 10 min.  
The ability of LEO satellites to broadcast navigation signals brought about the possibility of 3D water vapor tomography. Figure 2 shows that LEO satellites can receive GNSS navigation signals, broadcast GNSS navigation-augmentation signals, and broadcast navigation signals, similarly to GNSS satellites. In addition, LEO satellites orbit at a higher altitude than that of the tropospheric region, so the signal can cross the troposphere.  
LEO satellite's orbit and clock error accuracy are the key factors to determine the accuracy of LEO water vapor inversion. For orbit accuracy, GNSS-based orbits of satellites in LEO have reached generally very high qualities due to advances in dynamical modeling and carrier phase ambiguity fixing. At present, satellite laser ranging (SLR) verification shows that the orbit determination accuracy of LEO satellites is even better than that of GNSS orbit determination [26; 27]. Moreover, the function of inter-satellite link between LEO satellites will also help to improve satellite orbit accuracy [28]. [PERSON] et al. [29] also proposed a method to obtain high medium-long stability LEO clock. Besides, the real observation results from the Luoja-1A satellite also show that the accuracy of the pseudorange and carrier phase measurement at high elevation angles is better than 1.5 m and 1.7 mm, respectively [30]. With the support of these studies, we believe that LEO satellites are expected to be introduced into water vapor tomography in the future.  
Precise satellite orbit information is the basis for the tomographic experiment. In this study, the real orbit of GNSS satellites was applied, while the orbit of LEO satellites was generated by Satellite Tool Kit (STK) software [31] since most of the LEO constellation is still under construction. For the number of LEO satellites, 60 and 288 satellites were selected for analysis. The 60-satellite scheme ensured that at least 1 satellite was visible from any location on the globe, while the 288-satellite scheme ensured that at least 4 satellites were globally visible. Their planes were 6 and 12 equidistant orbital planes, respectively, and the orbit inclination was set as 90\({}^{\circ}\). Orbit altitudes were set as 1000 km, and orbit types were set as polar orbit. In this way, LEO satellite constellation could travel north-south at both poles of Earth, which can cover all of Earth's surface. The specific track design scheme is shown in Table 1. More details of the LEO orbit simulation can be found in [32].  
Figure 2: Schematic of LEO-enhanced GNSS system.