# Ionospheric Error Models for Satellite-Based Navigation--Paving the Road towards LEO-PNT Solutions
## 5 Discussion and Future Works  
The results presented in the previous section showed that our proposed model (IAMM) accurately predicts the ionospheric delay for a given time and location and can even outperform the IRI and Klobuchar models when comparing the positioning errors of GNSS reference stations. However, the Klobuchar model showed the best performance for Android smartphones. As previously discussed, one possible explanation could be that a GNSS station's exact position is calculated thoroughly, with high precision, before it is used as a reference to calculate the positioning error. In contrast, a smartphone's exact position (used as a reference) is based on its NMEA estimates. Although these estimates are close to the actual position, they are still prone to errors. For example, in the data collected while driving on a highway in Poland, shown in Figure 7, the NMEA estimates showed that the phone's position was outside of the road (white line) for a while, and the positioning errors of the WLS estimates made by IAMM were being calculated as a reference to the NMEA estimates. This proves we cannot entirely rely on Android data to validate our model.  
Figure 8: Ionospheric delays for GPS and LEO users at random times and locations. Note that the scale of the y-axis for plot (**a**) is different from that of the other three plots (**b–d**).  
Future research will also focus on acquiring higher-accuracy reference tracks in dynamic conditions, using, for example, differential GNSS with the TAU GNSS roof antenna as a reference and a professional mobile GNSS receiver in a backpack to acquire more accurate reference data.  
The results for LEO simulations showed a significant decrease in ionospheric delay for higher carrier frequencies. Fortunately, such higher frequencies are expected to be more present for LEO satellites, as they are preferred for communication services, which will be the prime usage of LEO satellites in the future. These higher frequencies will reduce the impact of the ionospheric delay (Equation (6)). On the other hand, lower frequencies from the L-bands are used for GNSS systems, resulting in a higher value for the ionospheric delay. Moreover, unlike GNSS, LEO satellites operate within the ionosphere (Figure 1), so their signals are affected only by the bottomside ionosphere, defined as the region below the F2 peak layer (hmF2). We can deduce from this unique distinction that LEO signals are not affected by the ionosphere as much as GNSS signals.  
To enhance the accuracy of the IAMM, future research should focus on including anomalous data, such as ionospheric parameters under extreme space weather scenarios, to improve the robustness and responsiveness of the model. Moreover, to improve the quality of the positioning solution, the user's environment should be considered; for example, one should look at whether the user is in an urban area (or an area with low signal quality) or an area with strong signal quality, and this remains a topic of future investigations. Future research should also work on finding and applying better mapping functions to scale the generated STEC value to suit the orbital height of the desired satellite. The scale factor should depend on the difference between the bottomside and topside ionosphere with respect to the time of day and day of year. The IAMM model can also be improved by applying compression algorithms to reduce the size of the \(Y\) matrix, making it easier to store in the memory of any device. Further improvements will also investigate more accurate modelling of the bottomside ionosphere, which is more relevant in LEO cases than the topside.  
Overall, these steps should enhance the precision of the TEC estimation from an LEO satellite to a ground receiver and provide a more detailed description of the ionospheric behaviour for LEO satellite communications.