Residual Ionospheric Errors of the NeQuick-G Model for LEO PNT

As interest grows in leveraging Low Earth Orbit (LEO) satellites in positioning, navigation, and timing (PNT), characterizing ranging errors for LEO satellite signals has become essential for the system design. The ionospheric group delay affecting PNT signals, which causes significant positioning errors, is proportional to the total electron content (TEC) along the signal path. Existing Global Navigation Satellite System (GNSS) ionospheric models (e.g., Klobuchar, NeQuick) provide ionospheric corrections by using broadcast model parameters, enabling real-time estimation of slant TEC (STEC). However, conventional GNSS ionospheric models were primarily developed and validated for the full slant path to GNSS satellites. Thus, they are not directly appliable to LEO satellites, which operate at much lower altitudes than GNSS constellations.  

Accurate TEC estimation for LEO PNT requires precise vertical electron density profiles to account specifically for the ionosphere below the LEO satellite. The NeQuick-G model, developed for Galileo single-frequency users, provides a three-dimensional electron density distribution based on ionospheric parameters of CCIR (International Radio Consultative Committee) numerical map and broadcast effective ionization level (Az) parameters. Several studies have investigated the validity of the NeQuick-G model in estimating partial TEC above LEO satellites (topside ionosphere) for spaceborne applications. Montenbruck & Rodriguez (2020) evaluated its performance for LEO satellite onboard orbit determination using GNSS measurements from Swarm LEO satellites orbiting at mean altitudes of 480 km and 520 km. Oezmaden et al. (2025) extended this analysis to multiple LEO constellations across different altitudes and developed a residual error model for the NeQuick-G model in the topside ionosphere. However, for LEO PNT applications, the NeQuick-G model should be validated for the bottomside ionosphere below the LEO satellite. This study analyzes the residual error of the NeQuick-G model for bottomside STEC by differencing STEC observations from ground receivers and LEO satellite onboard receivers. The bottomside STEC can be estimated by differencing these observations when the ground receiver, LEO satellite, and GNSS satellite are geometrically aligned. Using position data from IGS stations, GNSS, and Swarm satellites, we searched for alignment events for 2019 and 2024 and derived the bottomside STEC. These bottomside STECs are then compared with NeQuick-G model estimates using Az parameters broadcast in Galileo navigation messages.

Residual errors are analyzed under different ionospheric conditions such as solar activity, geomagnetic latitude, and local time. The standard deviations of the residual errors are 10.62 TECU during the solar maximum (2024) and 4.47 TECU during the solar minimum (2019), satisfying Galileo target specification for residual STEC errors (68% probability within 20 TECU or 30% of STEC). The variability of residual error is consistently higher in low latitude regions than at mid or high latitudes, indicating increased model uncertainty associated with equatorial ionospheric dynamics. These findings provide empirical validation of the NeQuick-G model for bottomside ionospheric correction in emerging LEO PNT applications.

References

Montenbruck,O., González Rodríguez,B.(2020).NeQuick-G performance assessment for space applications. GPS Solut 24, 13 https://doi.org/10.1007/s10291-019-0931-2

C.Oezmaden, S.Pelzer, O.G.Crespillo, M.Brachvogel, M.Niestroj and M.Meurer.(2025).Residual GNSS Ionospheric Error Analysis in Future Low Earth Orbit Applications. 2025 IEEE/ION Position, Location and Navigation Symposium(PLANS), doi:10.1109/PLANS61210.2025.11028459.