Received 22.12.2025
Revised 06.01.2026
Accepted 26.03.2026
Published 07.04.2026
Retrieved from Iss. 119, 2026
Pages 121 -131
Abstract
Global Navigation Satellite Systems (GNSS) are critical for high-precision positioning, navigation, and time synchronization across various domains, including transportation, geodesy, aviation, and scientific research. However, the accuracy of GNSS signals is significantly affected by ionospheric delay, caused by the interaction of radio signals with charged particles in the ionosphere. This delay, influenced by signal frequency, ionospheric conditions, time of day, geographic location, and solar activity, introduces positioning errors that can reach several meters, posing challenges for applications requiring high precision, such as geodesy and autonomous navigation. Existing correction methods, including the widely used Klobuchar model, SBAS augmentation systems, and global ionospheric maps (GIM), have limitations, such as high equipment costs, reliance on external data, or insufficient accuracy in regions with high ionospheric variability. This article reviews current methods for mitigating ionospheric delay, analyzing their features, advantages, and drawbacks, and evaluates their effectiveness in real-time and post-processing coordinate determination tasks. The study highlights that single-frequency GNSS receivers, commonly used in practice, rely on models like Klobuchar, which compensates for approximately 50% of ionospheric errors. More advanced models, such as NTCM and NeQuick, offer improved accuracy, reducing root mean square errors (RMSE) by 0.24–0.45 meters depending on ionospheric conditions. Dual-frequency GNSS receivers, utilizing ionosphere-free linear combinations of L1 and L2 band measurements, provide superior accuracy but require resolving phase ambiguities, which complicates implementation. Regional Total Electron Content (TEC) models outperform global GIMs due to higher spatial-temporal resolution (e.g., 0.5°×0.5° vs. 2.5°×5°), achieving up to 90–95% error reduction in specific cases. Time-series analysis methods, such as ARIMA, SARIMA, and Kalman filtering, enable short-term TEC forecasting, enhancing real-time navigation and geodetic measurements. The article emphasizes the importance of selecting correction methods based on application requirements, receiver type, and regional ionospheric characteristics, advocating for the integration of regional TEC models, dualfrequency measurements, and advanced forecasting techniques to achieve optimal GNSS accuracy
Keywords:
Earth's ionosphere, GNSS technologies, ionospheric delay, global ionospheric map, regional TES model, satellite geodesy, mathematical processing of geodetic data, complex systems1. Yarosh, O., Yankiv-Vitkovska, L. (2024) Modern approaches to the analysis of ionospheric correction in GNSS measurements. Modern achievements in geodetic science and production. Issue II (48). Pp. 29–33. https://ena.lpnu.ua/items/8f8a178c-e6e1-4a4f-8870-b794d54c38dc [in Ukrainian].
2. Yankiv-Vitkovska, L., Dzhumann, B. (2020). Construction of a spatial-temporal model of the ionosphere parameter VTEC. Bulletin of the National Technical University «KPI». Series: Radio Engineering and Radio Apparatus Engineering. № 80. Pp. 21–28. [in Ukrainian].
3. Yankiv-Vitkovska, L. (2013). Methodology for determining ionosphere parameters in the network of satellite stations in western Ukraine. Space Science and Technology. Т. 19. №6. Рр. 47–52. [in Ukrainian].
4. Yarosh, O., Yankiv-Vitkovska, L. (2024) Modern approaches to reducing ionospheric correction in GNSS measurements. Proceedings of the International Scientific and Technical Conference ‘Geforum-2024’, Lviv-Bryukhovychi. Lviv: Lviv Polytechnic Publishing House, pp. 141–142. [in Ukrainian].
5. Yankiv-Vitkovska, L., Savchuk, S., Pauchok, V., Matviichuk, Y., Bodnar, D. (2016) Recovery of the Spatial State of the Ionosphere Using Regular Definitions of the TEC Identifier at the Network of Continuously Operating GNSS Stations of Ukraine. Journal of Geodesy and Geomatics Engineering. Vol. 1(9). P. 37–48. https://doi.org/10.17265/2332-8223/2016.01.005 [in Ukrainian].
6. Bezsonov, E. (2015) Improvement of network methods and algorithms for assessing and accounting for ionospheric and tropospheric signal delays of global navigation satellite systems in precise positioning tasks: abstract of thesis ... Candidate of Technical Sciences: 05.12.17. Kharkiv National University of Radio Electronics. Kharkiv, 23 p. [in Ukrainian].
7. Yankiv-Vitkovska, L., Savchuk, S., Yanchuk, R. (2013) On determining ionosphere parameters at the RVNE GNSS station in real time. Bulletin of the National University of Water and Environmental Management. Series ‘Technical Sciences’. Issue 3(63). P. 308–315. [in Ukrainian].
8. Mohammed Mainul Hoque, Norbert Jakowski and Jens Berdermann (2018) Positioning performance of the NTCM model driven by GPS Klobuchar model parameters. J. Space Weather Space Clim. Volume 8, Article Number 20. P. 10. https://doi.org/10.1051/swsc/2018009
9. Lizunov, G., Korepanov, V., Lukenyuk, A., Pyankova, O., Fedorov, O. (2022) Space project ‘Iono-sat-Micro’: readiness for implementation. Space Science and Technology. № 6 (139). Pp. 3–11. https://doi.org/10.15407/knit2022.06.003 [in Ukrainian].
10. Yankiv-Vitkovska, L. (2012) Use of dual-frequency GNSS observations to determine ionosphere parameters. Geodesy, Cartography and Aerial Photography. №. 76. P. 19–28. https://doi.org/10.23939/istcgcap [in Ukrainian].
11. Bingbing Zhang, Jiqiang Niu, Wang Li, Yi Shen, Tangting Wu, Weifeng Yang, Wenping Deng (2021) A single station ionospheric empirical model using GPS-TEC observations based on nonlinear least square estimation method. Advances in Space Research. Volume 68. Issue 9. P. 3821–3834. https://doi.org/10.1016/j.asr.2021.07.017
12. Mallika, L., Ratnam, D.V., Raman, S., Sivavaraprasad, G. (2020) Machine learning algorithm to forecast ionospheric time delays using global navigation satellite system observations. Acta Astronautica. № 173. P. 221–231.
13. Sandro Radicella, Nava, B. (2009) NeQuick model: Origin and evolution. Annals Of Geophysics. Vol. 52. № ¾. Рр. 417–422. https://doi.org/10.1109/ISAPE.2010.5696491
14. Bilitza, D. (2018) IRI the international standard for the ionosphere. Advances in Radio Science. № 16. P. 1–11.
15. Reznychenko, M., Bogomaz, O., Reznychenko, A., Kotov, D. (2024) Comparison of the IRI-2020 model predictions with the observations in the european-african longitudinal sector during the period of 1-9 february 2022. Information technologies: science, engineering, technology, education, health: abstracts of the 32nd International Scientific and Practical Conference MicroCAD–2024, Kharkiv: NTU ‘KhPI’. P. 1487. https://repository.kpi.kharkov.ua/items/8b1fd9c2-a63c-4b5c-8661-180b9c97be52
16. Yankiv-Vitkovska, L., Dzhuman, B. (2017) Constructing of regional model of ionosphere parameters. Geodesy, Cartography and Aerial photography. Volume 85. № 85. P. 27–35. https://doi.org/10.23939/istcgcap2017.01.027
17. Ren, X., Chen, J., Li, X., Zhang, X., Freeshah, M. (2019) Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centersє GPS Solutions. № 23(4). P. 1–17.