# Ionospheric Error Models for Satellite-Based Navigation--Paving the Road towards LEO-PNT Solutions
## 1 Introduction and Motivation
### Sources of Errors in Satellite-Based Positioning  
All satellite signals (e.g., from LEO or MEO orbits) encounter various sources of error, leading to decreased precision in the accuracy of their final PNT solution: terrestrial errors, such as multipath delays, receiver clock and hardware errors, and terrestrial interferences; atmospheric errors, such as tropospheric and ionospheric delays; and orbital errors, such as satellite hardware delays and satellite orbital uncertainties.  
Amongst these multiple sources, ionospheric delay, which is the focus of our paper, stands out as the most significant error source [17; 18], at least in all GNSS systems. This delay is induced by the \"ionospheric layer\", or simply \"ionosphere\", which is a part of the Earth's atmosphere, ranging approximately from 50 km to 2000 km in altitude [19; 20]. Figure 1 represents this region according to its layer description in [21] and with respect to LEO and MEO satellites. The figure also shows how atmospheric layers typically delay the signal by making them follow a path (green line) that is longer than the straight path (dotted green line). The ionospheric layer is typically divided into three sub-layers, D, E, and F, as shown in Figure 1. The most critical region for ionospheric activity is the F layer, shown in bright red in, which spreads from around 300 km to around 600 km above the Earth. The ionosphere can induce positioning errors of up to 100 m on passing signals [22]. Therefore, it is crucial to mitigate its impacts by modelling its effects.  
There are several existing models in the literature that aim to mitigate ionospheric delays, such as the NeQuick, Klobuchar, BeiDou Global broadcast Ionospheric delay correction Model (BDGIM), and Quasi-4-Dimension Ionospheric Modeling (Q4 DIM) models [23]. These models measure or predict the error induced by the ionosphere, depending on the user's location, time of day, and day of the year [24; 25]. However, all of these models are tailored for correcting errors for GNSS signals and, therefore, cannot be directly applied to signals from LEO satellites. The primary reason for this is the altitude difference between the orbits of the MEO and LEO.  
As shown in Figure 1, signals from GNSS satellites penetrate the whole ionosphere, whereas signals from LEO satellites travel only through a portion of it. Furthermore, the topside ionosphere has a greater electron concentration than the bottomside ionosphere, which is around 75% and 25% of the total TEC for the topside and bottomside, respectively [20; 26; 27]. This indicates that LEO signals experience less interference than  
Figure 1: Ionosphere layer representation w.r.t. to satellite altitudes.  
GNSS signals. In addition, according to researchers in [28], the topside ionosphere undergoes more significant changes in its electron content than the bottomside ionosphere during solar storms. Hence, the bottomside ionosphere can be considered more stable than the topside ionosphere. This distinction indicates that GNSS signals experience higher ionospheric delay than LEO signals.