# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 1 Introduction  
Water vapor is the main driving force for weather and climate change [1]. The capability and feasibility of atmospheric water vapor monitoring, by using a global positioning system (GPS), was first proposed in [2]. Since then, the technique used to obtain atmospheric precipitable water vapor (PWV) has been well studied. However, the obtained PWV only reflects one-dimensional water vapor variation over a GPS ground-based station. To provide the distribution of water vapor at different altitudes, and in the vertical direction, the technology of obtaining the three-dimensional (3D) spatial distribution of water vapor, by using GPS observation data, was first proposed in [3]. This discretizes the study area into finite voxels, and assumes that water vapor density values within voxels are stable at a certain time. Then, the slant wet delay (SWD) that is obtained from the GPS observations can be used to invert the water vapor density values for each voxel. However, constrained by the spatial geometry relationship between global navigation satellite system (GNSS) satellites and ground-based stations, there are still many voxels that cannot be observed, leading to the singular problem in the design matrix [4]. Generally, it can be solved by adding constraint equations [3; 4; 5]. In addition, optimizing the voxel distribution [6], using rays passing from the side [7], and fusing GNSS station observations outside the tomographic region [8], were all proven to be effective in reducing the proportion of empty voxels in a tomographic region. A new algorithm for discrete tomography regions into inverted cones also proved to be very effective [9]. Introducing moderate-resolution imaging spectroradiometer (MODIS) [10], interferometric synthetic aperture radar (InSAR) [11], and ground-based meteorological observation [12] data into the tomographic model, also helps to solve the above problem. Introducing wet refractivity profiles that are derived from radio occultation data can also considerably improve tomographicsolutions [13; 14; 15]. In addition to the effective methods mentioned above, increasing the number of observations is also effective. The multi-GNSS can produce more observations, which can achieve better accuracy and space-time resolution [16; 17]. The potential of multi-GNSS tomography was verified by the triple system tomography experiments of GPS, BDS, and GLONASS [18]. [PERSON] et al. [19] studied the accuracy and stability of GNSS tomography, and noted that the accuracy improvement did not meet the expectations, in addition to the fact that 50% of the voxels were still unobserved under certain conditions. The current rapid development of low Earth orbit (LEO) navigation satellites results in a large number of observations that could reduce the number of empty tomographic voxels. Some companies and institutes, such as OneWeb, SpaceX, and Boeing, have announced ambitions for their own LEO constellations. Once all the constellations are completed, the number of available LEO satellites would be in the tens of thousands [20]. Some of these LEO constellations can provide navigation augmentation services, which can contribute to precision point position (PPP) ambiguity solving, shorten convergence time [21; 22], and improve the accuracy of the ionospheric model [23; 24]. Compared with GNSS, LEO satellites have some of the following characteristics: lower orbits, stronger signals, less interference, longer trajectories across the sky in the same time, and faster geometry changes. These also facilitate the rapid modelling of the atmosphere and the 3D tomography of water vapor. Apart from the aforementioned advantages, LEO satellites require a large number of satellites to cover the entirety of Earth, and have a short lifetime, which are also challenges for the development of LEO satellites. In this paper, a tomographic model was constructed on the basis of the Hong Kong satellite positioning reference station network (SatRef), and two different numbers of LEO constellations were simulated.