Communications - Scientific Letters of the University of Zilina 2026, 28(3):A73-A82 | DOI: 10.26552/com.C.2026.043

Circular Analysis of Gnss Positioning Error for Short-Term Rapidly Developing Ionospheric Storm Sub-Classification

Lucija Žužić ORCID...1, 2, *, Ivan Heđi ORCID...3, Jonatan Lerga ORCID...1, 2, Renato Filjar ORCID...1, 2, 4
1 University of Rijeka, Faculty of Engineering, Department of Computer Engineering, Rijeka, Croatia
2 University of Rijeka, Center for Artificial Intelligence and Cybersecurity, Rijeka, Croatia
3 Virovitica University of Applied Sciences, ICT Department, Virovitica, Croatia
4 Hrvatsko Zagorje Krapina University of Applied Sciences, Department of Transport Logistics, Krapina, Croatia

In the development of Global Navigation Satellite System (GNSS) Positioning, Navigation, and Timing (PNT), short-lived, fast-growing ionospheric storms (lasting up to three days) were assumed to constitute a single, uniform class of space weather events. To challenge this premise, here is presented a circular analysis of single-frequency commercial-grade Global Positioning System (GPS) horizontal positioning errors in the mid-latitude region during four observed storms (one in 2015 and three in 2017), revealing significant heterogeneity. Maximum positioning errors reached 7.495 m in March 2015, but peaked at 4.261 m, 4.387 m, and 3.948 m during storms in May, early September, and late September 2017, respectively. By demonstrating that short-duration, fast-growing storms require subclassification, in this study is offered a new perspective on disturbances.

Keywords: GNSS PNT performance, circular analysis, ionospheric correction model, Location-Based Services (LBS)
Grants and funding:

This work was supported by the European Regional Development Fund - grant no. PK.1.1.13.0083 and the EU - NextGenerationEU project - grant no. uniri-mzi-25-1 implemented through the University of Rijeka.

Conflicts of interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Received: April 29, 2026; Accepted: July 8, 2026; Prepublished online: July 20, 2026; Published: July 24, 2026  Show citation

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Žužić, L., Heđi, I., Lerga, J., & Filjar, R. (2026). Circular Analysis of Gnss Positioning Error for Short-Term Rapidly Developing Ionospheric Storm Sub-Classification. Communications - Scientific Letters of the University of Zilina28(3), A73-82. doi: 10.26552/com.C.2026.043
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References

  1. TEUNISSEN, P. J. G., MONTENBRUCK, O. (Eds.). Springer handbook of global navigation satellite systems [online] [accessed 2026-07-03]. Chamonix, Switzerland: Springer International Publishing, 2017. ISBN 9783319429281. Available from: https://doi.org/10.1007/978-3-319-42928-1 Go to original source...
  2. OXLEY, A. (Ed.). Uncertainties in GPS positioning: a mathematical discourse [online] [accessed 2026-07-03]. Amsterdam, Netherlands: Elsevier, 2017. ISBN 9780128095942. Available from: https://doi.org/10.1016/b978-0-12-809594-2.09984-6 Go to original source...
  3. DAVIES, K. Ionospheric radio [online] [accessed 2026-07-03]. London, UK: IET, 1990. ISBN 9781849193870. Available from: https://doi.org/10.1049/pbew031e Go to original source...
  4. GUSTAFSSON, F. Statistical sensor fusion. 3rd ed. Linkoepping, Sweden: Studentlitteratur AB, 2018. ISBN 9789144127248.
  5. SCHAER, S. Mapping and predicting the earth's ionosphere using the global positioning system. Vol. 59 [online] [accessed 2026-07-03]. Zurich, Switzerland: Institute of Geodesy and Photogrammetry, Swiss Federal Institute of Technology, 1999. ISBN 9783908440017. Available from: https://www.sgc.ethz.ch/sgc-volumes/sgk-59.pdf
  6. User needs and requirements - EUSPA [online] [accessed 2026-07-03]. 2024. Available from: https://www.euspa.europa.eu/publications-multimedia/publications/user-needs-and-requirements
  7. KLOBUCHAR, J. Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Transactions on Aerospace and Electronic Systems [online]. 1987, AES-23(3), p. 325-331 [accessed 2026-07-03]. ISSN 0018-9251. Available from: https://doi.org/10.1109/taes.1987.310829 Go to original source...
  8. SANZ SUBIRANA, J., JUAN ZORNOZA, J. M., HERNANDEZ-PAJARES, M. GNSS data processing, Vol. I: fundamentals and algorithms [online] [accessed 2026-07-03]. Paris, France: ESA Communications, 2013. ISBN 9789292218867. Available from: https://gssc.esa.int/navipedia/GNSS_Book/ESA_GNSS-Book_TM-23_Vol_I.pdf
  9. LENAC, K., FILJAR, R. Recurrence plot analysis of GPS ionospheric delay time series in extreme ionospheric conditions. Computers and Geosciences [online]. 2021, 147, 104613 [accessed 2026-07-03]. ISSN 0098-3004. Available from: https://doi.org/10.1016/j.cageo.2020.104613 Go to original source...
  10. PARKINSON, B. W., SPILKER JR., J. J., AXELRAD, P., ENGE, P. (Eds.). Global positioning system: theory and applications, 2-volume set [online] [accessed 2026-07-03]. Washington, DC, USA: AIAA, 1996. ISBN 9781563472497. Available from: https://doi.org/10.2514/4.472497 Go to original source...
  11. ENGE, P. K. The global positioning system: signals, measurements, and performance. International Journal of Wireless Information Networks [online]. 1994, 1(2), p. 83-105 [accessed 2026-07-03]. ISSN 1572-8129. Available from: https://doi.org/10.1007/bf02106512 Go to original source...
  12. FILIC, M., FILJAR, R. Modelling the connection between GNSS positioning performance degradation, and space weather and ionospheric conditions using RReliefF features selection. In: 31st International Technical Meeting of the Satellite Division of The Institute of Navigation ION GNSS+ 2018: proceedings [online]. 2018. p. 1999-2006 [accessed 2026-07-03]. Available from: https://doi.org/10.33012/2018.16016 Go to original source...
  13. FILJAR, R. An application-centred resilient GNSS position estimation algorithm based on positioning environment conditions awareness. In: 2022 International Technical Meeting of The Institute of Navigation: proceedings [online]. 2022. p. 1123-1136 [accessed 2026-07-03]. Available from: https://doi.org/10.33012/2022.18247 Go to original source...
  14. CIECKO, A. Analysis of the EGNOS quality parameters during high ionosphere activity. IET Radar, Sonar and Navigation [online]. 2019, 13(7), p. 1131-1139 [accessed 2026-07-03]. ISSN 1751-8792. Available from: https://doi.org/10.1049/iet-rsn.2018.5571 Go to original source...
  15. ASTAFYEVA, E., ZAKHARENKOVA, I., FORSTER, M. Ionospheric response to the 2015 St. Patrick's Day storm: a global multi-instrumental overview. Journal of Geophysical Research: Space Physics [online]. 2015, 120(10), p. 9023-9037 [accessed 2026-07-03]. ISSN 2169-9402. Available from: https://doi.org/10.1002/2015JA021629 Go to original source...
  16. BENIGUEL, Y., CHERNIAK, I., GARCIA-RIGO, A., HAMEL, P., HERNANDEZ-PAJARES, M., KAMENI, R., KASHCHEYEV, A., KRANKOWSKI, A., MONNERAT, M., NAVA, B., NGAYA, H., ORUS-PEREZ, R., SECRETAN, H., SERANT, D., SCHLUTER, S., WILKEN, V. MONITOR Ionospheric network: two case studies on scintillation and electron content variability. Annales Geophysicae [online]. 2017, 35(3), p. 377-391 [accessed 2026-07-03]. ISSN 1432-0576. Available from: https://doi.org/10.5194/angeo-35-377-2017 Go to original source...
  17. MINH, L. H., LAN, T. T., FLEURY, R., AMORY MAZAUDIER, C., THANH, L. T., THANG, N. C., THANH, N. H. TEC variations and ionospheric disturbances during the magnetic storm in March 2015 observed from continuous GPS data in the Southeast Asia region. Vietnam Journal of Earth Sciences [online]. 2016, 38(3), p. 287-305 [accessed 2026-07-03]. ISSN 0866-7187. Available from: https://doi.org/10.15625/0866-7187/38/3/8714 Go to original source...
  18. SCOLINI, C., MESSEROTTI, M., POEDTS, S., RODRIGUEZ, L. Halo coronal mass ejections during Solar Cycle 24: reconstruction of the global scenario and geoeffectiveness. Journal of Space Weather and Space Climate [online]. 2018, 8, A09 [accessed 2026-07-03]. ISSN 2115-7251. Available from: https://doi.org/10.1051/swsc/2017046 Go to original source...
  19. REDDYBATTULA, K. D., PANDA, S. K., SHARMA, S. K., SINGH, A. K., KURNALA, K., HARITHA, C. S., WUYYURU, S. Anomaly effects of 6-10 September 2017 solar flares on ionospheric total electron content over Saudi Arabian low latitudes. Acta Astronautica [online]. 2020, 177, p. 332-340 [accessed 2026-07-03]. ISSN 0094-5765. Available from: https://doi.org/10.1016/j.actaastro.2020.07.045 Go to original source...
  20. ATABATI, A., JAZIREEYAN, I., ALIZADEH, M., PIROOZNIA, M., FLURY, J., SCHUH, H., SOJA, B. Analyzing the ionospheric irregularities caused by the September 2017 geomagnetic storm using ground-based GNSS, swarm, and FORMOSAT-3/COSMIC data near the equatorial ionization anomaly in East Africa. Remote Sensing [online]. 2023, 15(24), 5762 [accessed 2026-07-03]. ISSN 2072-4292. Available from: https://doi.org/10.3390/rs15245762 Go to original source...
  21. CIECKO, A., GRUNWALD, G. Klobuchar, NeQuick G, and EGNOS ionospheric models for GPS/EGNOS single-frequency positioning under 6-12 September 2017 space weather events. Applied Sciences [online]. 2020, 10(5), 1553 [accessed 2026-07-03]. ISSN 2076-3417. Available from: https://doi.org/10.3390/app10051553 Go to original source...
  22. VANKADARA, R. K., PANDA, S. K., AMORY-MAZAUDIER, C., FLEURY, R., DEVANABOYINA, V. R., PANT, T. K., JAMJAREEGULGARN, P., HAQ, M. A., OKOH, D., SEEMALA, G. K. Signatures of equatorial plasma bubbles and ionospheric scintillations from magnetometer and GNSS observations in the Indian longitudes during the space weather events of early September 2017. Remote Sensing [online]. 2022, 14(3), 652 [accessed 2026-07-03]. ISSN 2072-4292. Available from: https://doi.org/10.3390/rs14030652 Go to original source...
  23. POZOGA, M., MATYJASIAK, B., GRZESIAK, M., ROTHKAEHL, H., PRZEPIORKA, D., WRONOWSKI, R. Observations of the geomagnetic storm 27-28.05.2017 with LOFAR PL610. In: XXXVIII Polish Astronomical Society Meeting: proceedings [online]. Vol 7. 2017. p. 91-93 [accessed 2026-07-03]. Available from: https://w.pta.edu.pl/proc/v7p91
  24. CWIKLAK, J., GRZEGORZEWSKI, M., KRASUSKI, K. Influence of the ionospheric delay on designation of an aircraft position. Communications - Scientific Letters of the University of Zilina [online]. 2020, 22(3), p. 3-10 [accessed 2026-07-03]. ISSN 1335-4205, eISSN 2585-7878. Available from: https://doi.org/10.26552/com.C.2020.3.3-10 Go to original source...
  25. PEWSEY, A., NEUHAUSER, M., RUXTON, G. D. Circular statistics in R. Oxford, UK: Oxford University Press, 2013. ISBN 9780199671137.
  26. NASA EarthData CDDIS NASA's archive of space geodesy data, open access upon the free registration - NASA [online] [accessed 2026-07-03]. 2026. Available from: https://cddis.nasa.gov/archive/gnss/data/daily
  27. FABIAN, A., BRUYNINX, C., MIGLIO, A., LEGRAND, J. M3G - metadata management and distribution system for multiple GNSS networks [online] [accessed 2026-07-03]. 2021. Available from: https://doi.org/10.24414/ROB-GNSS-M3G Go to original source...
  28. ZUZIC, L., FILJAR, R. Circular analysis of long-term GNSS horizontal positioning error time series observed in the sub-equatorial region. In: 2025 33rd Telecommunications Forum TELFOR: proceedings [online] [accessed 2026-07-03]. 2025. p. 1-4. Available from: https://doi.org/10.1109/telfor67910.2025.11314378 Go to original source...
  29. R: A language and environment for statistical computing - R Core Team [online] [accessed 2026-07-03]. 2026. Available from: https://www.r-project.org
  30. TAKASU, T. RTKLIB: an open source program package for GNSS positioning, ver. demo5 b34k [online] [accessed 2026-07-03]. 2024. Available from: https://github.com/rtklibexplorer/RTKLIB/releases
  31. KARNEY, C. F. F. Algorithms for geodesics. Journal of Geodesy [online]. 2013, 87(1), p. 43-55 [accessed 2026-07-03]. ISSN 1432-1394. Available from: https://doi.org/10.1007/s00190-012-0578-z Go to original source...

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