Machine Learning Modelling of Geostationary SBAS Satellite Orbit Errors Observed from an Equatorial West African Station

Geostationary satellites used by satellite-based augmentation systems are continuously visible from equatorial Africa, but their raw broadcast ephemeris accuracy has received limited assessment in West Africa. This study measured and modelled the broadcast orbit errors of three SBAS GEO satellites, comprising EGNOS S23 and S36 and GAGAN S27, observed with a u-blox ZED-F9P receiver at Ogbomoso, Nigeria, from January to March 2026. Broadcast positions were propagated using a second-order Taylor model and compared with interpolated IGS Final precise orbits. Atmospheric drag and piecewise polynomial models were used as mathematical baselines before comparison with Random Forest, XGBoost, support vector regression and long short-term memory models. S23 and S36 maintained stable mean 3D errors near 1.27 m, with standard deviations of approximately 0.55 m. S27 recorded mean errors near 2.6 m in January and February and an isolated March maximum of 97.250 m. The atmospheric drag and polynomial baselines produced RMSE values of 1.329 and 1.293 m, respectively. LSTM achieved 1.282 m, while XGBoost, Random Forest and support vector regression reduced RMSE to 0.272, 0.250 and 0.171 m. The staged residual scheme achieved the lowest RMSE of 0.164 m, representing a 92.8% reduction from the uncorrected value of approximately 2.278 m, and produced a 2DRMS of 1.144 m. The results show that GEO broadcast orbit errors contain nonlinear, satellite-specific patterns that data-driven models can correct effectively, provided anomalous satellites are identified before use.

geostationary orbit; SBAS; EGNOS; GAGAN; broadcast ephemeris; orbit error; machine learning; support vector regression; low latitude; Nigeria

1. Adewumi, A.S., Àlàgbé, G.A., Azeez, I.A., Ayantunji, G.B., Ogobor, E.A., Oyelowo, O., Fajobi, I. and Eleyele, D.E. (2025). PPP potential of a compact, low-cost GNSS receiver's module in a low latitude region: A case study at the LAUTECH GNSS Laboratory, Nigeria. In Adimula, I. et al. (eds.) Proceedings of the 8th URSI-NG Annual Conference (URSI-NG 2024), pp. 175-180. Atlantis Press. [Google Scholar] [Crossref]

2. Hohensinn R, Stauffer R, Glaner MF, Herrera Pinzón ID, Vuadens E, Rossi Y, Clinton J, Rothacher M (2022). Low-cost GNSS and real-time PPP, assessing the precision of the u-blox ZED-F9P for kinematic monitoring applications. Remote Sensing 14, 5100. [Google Scholar] [Crossref]

3. Mohanty A, Gao G (2024). A survey of machine learning techniques for improving Global Navigation Satellite Systems. EURASIP Journal on Advances in Signal Processing 2024, 73. [Google Scholar] [Crossref]

4. Nie Z, Zhou P, Liu F, Wang Z, Gao Y (2019). Evaluation of orbit, clock and ionospheric corrections from five currently available SBAS L1 services, methodology and analysis. Remote Sensing 11, 411. [Google Scholar] [Crossref]

5. Prange L, Beutler G, Dach R, Arnold D, Schaer S, Jäggi A (2020). An empirical solar radiation pressure model for satellites moving in the orbit-normal mode. Advances in Space Research 65, 235–250. [Google Scholar] [Crossref]

6. Pratiwi N, Herdiwijaya D, Ahmad N, Hidayat T, Ikhsan MI (2025). Effect of solar radiation pressure on a geostationary satellite, comparison with spherical and flat models. Journal of Multidisciplinary Applied Natural Science 5, 1088–1108. [Google Scholar] [Crossref]

7. Robustelli U, Cutugno M, Pugliano G (2023). Low-cost GNSS and PPP-RTK, investigating the capabilities of the u-blox ZED-F9P module. Sensors 23, 6074. [Google Scholar] [Crossref]

8. Song J, Liu T, Chen X, Wu Z (2024). Satellite navigation message authentication in GNSS, research on message scheduler for SBAS L1. Sensors 24, 360. [Google Scholar] [Crossref]

9. Soop EM (1994). Handbook of Geostationary Orbits. Springer Science and Business Media, Dordrecht. [Google Scholar] [Crossref]

10. Yang C (2021). Innovation and development of BeiDou Navigation Satellite System (BDS) project management mode. Frontiers of Engineering Management 8, 312–320. [Google Scholar] [Crossref]

• Classifying News Articles on Nigerian Newspapers Using Machine Learning
• Approaching Early Dyslexia Prediction with Ensemble Machine Learning: A Secondary Empirical Analysis of the Rello Et Al. Public Behavioural Dataset