# Ionospheric Error Models for Satellite-Based Navigation--Paving the Road towards LEO-PNT Solutions
## 1 Introduction and Motivation  
### LEO-PNT versus GNSS  
There are currently two main types of commercial satellite constellations in the sky with potential for global navigation in LEO orbits and in Medium Earth Orbit (MEO) orbits. On one hand, there has been a surge in the deployment of LEO satellites by various companies in order to meet the increasing demand for broadband connectivity in recent years [1]. This surge has been favoured by the decreasing costs of launching and designing satellites, making them easier to maintain and replace. LEO satellites orbits spread from 200 km to 2000 km above the Earth's surface, making them the closest satellites to Earth among all commercial satellites currently in the sky. This proximity allows LEO satellites to provide stronger signals than satellites in MEO or Geo-stationary Orbit (GEO). It also results in higher orbital speeds for LEO satellites, giving them favourable geometry and high availability [2, 3], which are highly important for navigation purposes. However,this close orbital distance creates the need for \"mega-constellations\" (i.e., constellations with hundreds or even thousands of satellites) to provide global coverage. Consequently, the interest in using these satellites for Position, Navigation, and Timing (PNT) and broadband connectivity has risen over the past few years. LEO-PNT can be either used as a replacement for current satellite-based positioning systems, such as GNSS (e.g., in cases where GNSS service is not available, due, for example, to high levels of interference) or, more often, as a complement to GNSS navigation in challenging environments, such as indoors or in urban canyons [2; 4; 5]. On the other hand, GNSS satellites in MEO orbits have been there for decades, and two of these systems, the European Galileo system and the Chinese Beidou system, are still under development. GNSS, as its name points out, is a collection of satellite constellations designed to provide global navigation services. It is utilized by multiple applications, including transport, land surveying, and agriculture [6]. Currently, four major systems inside GNSS provide PNT solutions: Global Positioning System (GPS) provided by the United States, Galileo provided by the European Union, BeiDou provided by China, and GLONASS provided by Russia [7]. Together, they offer extensive coverage for both professional GNSS receivers and mass-market GNSS receivers found in devices such as smartphones. Currently, most satellites in the GNSS system occupy MEO orbits, which lie between 2000 km and 35,786 km above the Earth's surface. Such altitudes lead to weak signals received on Earth due to their long transmission distance, atmospheric attenuation, and the possibly challenging environments around the user's receiver. As previously mentioned, one of the current research trends is to resolve the challenges in GNSS, such as heavy multipath effects in dense urban and indoor environments, and combat the increasing amount of spoofing and jamming in GNSS bands [8] using LEO satellites as complementary or alternative solutions to GNSS. The main potential advantages of LEO-based PNT solutions are the lower path losses (at comparative carrier frequencies) compared to MEO satellites due to their closer proximity to Earth, the lower costs of launching and maintaining LEO satellites compared to MEO satellites, the faster Doppler shifts that make them more suitable for lower-cost Doppler-based positioning in contrast with the code- and carrier-phase positioning used in GNSS, and the wide availability of LEO satellites in the sky (currently there are a few thousand in various constellations, such as Starlink, OneWeb, Iridium, etc., and this number is forecast to reach a few tens of thousands within the next five years) [4]. A complementary solution based on LEO could be, for example, to have GNSS receivers on board LEO satellites and to enable LEO to rebroadcast GNSS-like signals on other frequency bands [9].