Algorithm for Three-Dimensional Ionospheric Radio Tomography Based on GNSS Data
EDN: VZKGED
Abstract
The paper describes the design of an algorithm for three-dimensional radio tomography of electron concentration in the ionosphere based on the GNSS data. Simulation data are used to describe the algebraic reconstruction techniques underlying the algorithm design; also considered are the methods taking into account a priori information as well as the approaches to optimization of parameters of these algebraic methods. The results of the experimental ionospheric reconstruction obtained with the use of the data obtained from the satellite system of precise positioning of the Republic of Belarus are presented.
About the Authors
V. M. ArtemievBelarus
Minsk
A. O. Naumov
Belarus
Minsk
P. A. Khmarski
Belarus
Minsk
References
1. Куницын В.Е., Терещенко Е.Д., Андреева Е.С. Радиотомография ионосферы. М.: Физматлит, 2007. 693 с.
2. Afraimovich, E.L., Astafyeva, E.I., Demyanov, V.V., Edemskiy, Il.K., Gavrilyuk, N.S., Ishin, A.B., Kosogorov, E.A., Leonovich, L.A., Lesyuta, O.S., Palamartchouk, K.S., Perevalova, N.P., Polyakova, A.S., Smolkov, G.Y., Voeykov, S.V., Yasyukevich, Y.V., Zhivetiev, I.V., A review of GPS/GLONASS studies of the ionospheric response to natural and anthropogenic processes and phenomena, Space Weather Space Clim., 2013, vol. 3, doi: 10.1051/swsc/2013049.
3. Hofmann-Wellenhof, B., Lichtenegger, H., Wasle, E., GNSS – Global Navigation Satellite Systems. GPS, GLONASS, Galileo, and More, Springer, 2008, 516 p.
4. Solonar, A.S., Khmarski, P.A., Tsuprik, S.V., Tracking estimator of the ground target coordinates and motion parameters using onboard optical location system data, Gyroscopy and Navigation, 2023, vol. 14, no. 3, pp. 244–258, doi: 10.1134/S2075108723030082.
5. Solonar, A.S., Khmarski, P.A., Naumov, A.O., Juraev, D.A., Muxammedov, B.M., The use of numerical Monte Carlo integration to verify the physical feasibility of a trajectory based on surveillance radar data, Stochastic Modelling and Computational Sciences, 2023, vol. 3, no. 1, pp. 59–73, doi: 10.61485/smcs.27523829/v3n1p5.
6. Solonar, A.S., Khmarski, P.A., Main problems of trajectory processing and approaches to their solution within the framework of multitarget tracking, J. Phys. Conf. Ser., 2021, vol. 1864, doi: 10.1088/1742-6596/1864/1/012004.
7. Yasyukevich, Y.V., Zhang, B., Devanaboyina, V.R., Advances in GNSS positioning and GNSS remote sensing, Sensors, 2024, vol. 24, no. 4, pp. 1200, doi: 10.3390/s24041200.
8. Astafyeva, E., Yasyukevich, Y., Maksikov, A., Zhivetiev, I., Geomagnetic storms, super-storms, and their impacts on GPS-based navigation systems, Space Weather, 2014, vol. 12, pp. 508–525, doi: 10.1002/2014SW001072.
9. Yasyukevich, Yu.V., Mylnikova, A.A., Polyakova, A.S., Estimating the total electron content absolute value from the GPS/GLONASS data, Results in Physics, 2015, vol. 5, pp. 32–33, doi: 10.1016/j.rinp.2014.12.006.
10. Nesterov, I.A., Kunitsyn, V.E., GNSS radio tomography of the ionosphere: The problem with essentially incomplete data, Advances in Space Research, 2011, vol. 47, issue 10, pp. 1789–1803, doi: 10.1016/j.asr.2010.11.034.
11. Kunitsyn, V.E., Nesterov, I.A., Padokhin, A.M., et al., Ionospheric radio tomography based on the GPS/GLONASS navigation systems, Journal of Communications Technology and Electronics, 2011, vol. 56, pp. 1269–1281, doi: 10.1134/S1064226911100147.
12. Kunitsyn, V.E., Andreeva, E., Nesterov, I.A., Padokhin, A.M., Ionospheric sounding and tomography by GNSS, Geodetic Sciences – Observations, Modeling and Applications, 2013, doi: 10.5772/54589.
13. Naumov, A.O., Khmarskiy, P.A., Byshnev, N.I., Piatrouski, M.A., Determination of total electron content in the ionosphere over the territory of the Republic of Belarus based on global navigation satellite systems data, Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-technichnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2024, vol. 69, no. 1, pp. 53–64, doi: 10.29235/1561-8358-2024-69-1-53-64.
14. Stankov, S.M., Stegen, K., Muhtarov, P., Warnant, R., Local ionospheric electron density profile reconstruction in real time from simultaneous ground-based GNSS and ionosonde measurements, Advances in Space Research, 2011, vol. 47, issue 7, pp. 1172–1180, doi: 10.1016/j.asr.2010.11.039.
15. Naumov, A.O., Khmarski, P.A., Aronov, G.A., Kotov, D.S., Results of studies on processes occurring in the ionosphere and Earth’s magnetic field over the territory of the Republic of Belarus for the year 2023, Nonlinear Phenomena in Complex Systems, 2024, vol. 27, no. 3, pp. 225–233, doi: 10.5281/zenodo.13960570.
16. Chen, C., Pavlov, I., Padokhin, A., Yasyukevich, Y., Demyanov, V., Danilchuk, E., Vesnin, A., Galileo and BeiDou AltBOC Signals and Their Perspectives for Ionospheric TEC Studies, Sensors, 2024, vol. 24, no. 6472, doi: 10.3390/s24196472.
17. Artemiev, V.M., Naumov, A.O., Stepanov, V.L., Murashko, N.I., Method and results of real time modeling of ionosphere radiotomography on the basis of the Kalman filter theory, Journal of Automation and Information Sciences, 2008, vol. 40, no. 2, pp. 52–62.
18. Herman, G.T., Fundamentals of Computerized Tomography, Image Reconstruction from Projections, Springer, New York, 2009, 297 p.
19. Zolotarev, S.A., Ahmed Talat Taufik Taruat, Bilenko, E.G., Taking into account a priori information in the iterative reconstruction of images of foundry products, Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-technichnykhnavuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2023, vol. 68, no. 3, pp. 242–251, doi: 10.29 235/1561-8358-2023-68-3-242-251.
20. Zolotarev, S.A., Vengrinovich, V.L., Smagin, S.I., Iterative tomography of pipes during operation, Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-technichnykh navuk, 2021, vol. 66, no. 4, pp. 505–512, doi: 10.29235/1561-8358-2021-66-4-505-512.
21. Bust, G.S., Garner, T.W., Gaussiran, T.L., II Ionospheric Data Assimilation Three-Dimensional (IDA3D): A global, multisensor, electron density specification algorithm, Journal of Geophysical Research, 2004, vol. 109, A11, doi: 10.1029/2003JA010234.
22. Bruno, J., Mitchell, C.N., Bolmgren, K.H.A., Witvliet, B.A., A realistic simulation framework to evaluate ionospheric tomography, Advances in Space Research, 2020, vol. 65, issue 3, pp. 891–901, doi: 10.1016/j.asr.2019.11.015.
23. Bust, G.S., Mitchell, C.N., History, current state, and future directions of ionospheric imaging, Reviews of Geophysics, 2008, vol. 46, RG1003, doi: 10.1029/2006RG000212.
24. Mitchell, C.N., Cannon, P.S., Multi-Instrument Data Analysis System (MIDAS) Imaging of the Ionosphere, Advances in Space Research, 2002, pp. 147–152.
25. Hobiger, T., Kondo, T., Koyama, Y., Constrained simultaneous algebraic reconstruction technique (C-SART) – a new and simple algorithm applied to ionospheric tomography, Earth Planet., 2008, vol. 60, pp. 727–735, doi: 10.1186/BF03352821.
26. Wen, D., Liu, S., Tang, P., Tomographic reconstruction of ionospheric electron density based on constrained algebraic reconstruction technique, GPS Solution, 2010, vol. 14, pp. 375–380, doi:10.1007/s10291-010-0161-0.
27. Khmarski, P.A., Naumov, A.О., Algorithms for three-dimensional reconstruction of electron concentration fields in the ionosphere using data from the global navigation satellite system, Proceedings 31st Saint Petersburg International Conference, Saint-Petersburg, 2024, pp. 185–188.
28. Lu, W., Ma, G., Wan, Q., A review of voxel-based computerized ionospheric tomography with GNSS ground receivers, Remote Sensing, 2021, vol. 13, no. 3432, doi: 10.3390/rs13173432.
29. Sutton, E., Na, H., Comparison of geometries for ionospheric tomography, Radio Sci., 1995, vol. 30, pp. 115–125.
30. Semeter, J., Kamalabadi, F., A natural pixel decomposition for tomographic imaging of the ionosphere, In Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, Seattle, 1998, vol. 5, pp. 2913–2916.
31. Yasyukevich, Y.V., Zatolokin, D., Padokhin, A., Wang, N., Nava, B., Li, Z., Yuan, Y., Yasyukevich, A., Chen, C., Vesnin, A., Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC ionospheric models: A comparison in total electron content and positioning domains, Sensors, 2023, vol. 23, no. 10, p. 4773, doi: 10.3390/s23104773
32. International Reference Ionosphere. URL: https://ccmc.gsfc.nasa.gov/modelweb/models/iri2016_vitmo.php (дата обращения: 07.06.2023).
33. Иванов В.Б., Затолокин Д.А., Горбачёв О.А. Сравнение моделей полного электронного содержания ионосферы для системы ГЛОНАСС // Гироскопия и навигация. 2017. No. 2 (97). С. 89–96.
34. Dehghan, M., Mohebbi, A., High-order compact boundary value method for the solution of unsteady convection-diffusion problems, Mathematics and Computers in Simulation, 2008, vol. 79, pp. 683–699.
35. Spotz, W.F., High-order compact finite difference schemes for computational mechanics, Ph. D. Thesis, University of Texas at Austin, 1995, 324 p.
36. Jia R., Yu X., Xing J., Ning Y., Sun H., An improved method using adaptive smoothing for GNSS tomographic imaging of ionosphere, PLoS ONE, 2021, vol. 16, no. 5, e0250613, doi: 10.1371/journal.pone.0250613.
Review
For citations:
Artemiev V.M., Naumov A.O., Khmarski P.A. Algorithm for Three-Dimensional Ionospheric Radio Tomography Based on GNSS Data. Gyroscopy and Navigation. 2025;33(2):103-121. (In Russ.) EDN: VZKGED