Algorithm for estimating the absolute total electron content of the ionosphere from dual-frequency phase and range satellite measurements

Objectives. The problem of developing an algorithm for estimating the absolute total electron content of the ionosphere from dual-frequency phase and range satellite measurements for a single receiving station of global navigation satellite systems is being solved.

Methods. To obtain an estimate the phase measurement data are corrected using digital signal processing methods, well known total electron content formulas for phase and range measurements are applied and combined, and also the differential code bias of the receiving station is estimated using the least squares method.

Results. It is shown that the total electron content calculated from phase measurements provides high accuracy, but up to an unknown constant, but the content calculated from range measurements allows one to obtain the absolute value, but with a large noise component and differential code bias of a satellite and receiver equipment. An algorithm for estimating the absolute total electron content of the ionosphere has been developed, its description and diagram are given. The algorithm was used to estimate the total electronic content within six months of observations, and the average error of the resulting estimate was calculated.

Conclusion. The developed algorithm can be used to estimate the absolute total electron content of the ionosphere for a single receiving station of global navigation satellite systems. In contrast to theoretically known formulas for phase and range measurements, this article contains information about adjusting phase measurements and estimating the differential code delay of receiving station. Further research may be related to the adaptive selection of parameters and testing of the algorithm for working with nanosatellites of the CubeSat format.

1. Davies K. Ionospheric Radio Waves. Blaisdell Publishing Company, 1969, 460 р.

2. Ratcliffe J. A. The Magneto-Ionic Theory and its Applications to the Ionosphere. Cambridge, University Press, 1959, 226 p.

3. Afraimovich E. L., Perevalova N. P. GPS-monitoring verhnej atmosfery Zemli. GPS Monitoring of the Earth’s Upper Atmosphere. Irkutsk, Gosudarstvennoe uchrezhdenie "Nauchnyj centr Vostochno-Sibirskogo nauchnogo centra Sibirskogo otdelenija Rossijskoj akademii nauk", 2006, 480 p. (In Russ.).

4. Kunitsyn V. E., Tereshchenko E. D., Andreeva E. S. Radiotomografija ionosfery. Radio Tomography of the Ionosphere. Moscow, Fizmatlit, 2007, 336 p. (In Russ.).

5. Belokonov I. V., Krot А. М., Kozlov S. V., Kapliarchuk Y. А., Savinykh I. E., Shapkin А. S. A method for estimating the total electron content in the ionosphere based on the retransmission of signals from the global navigation satellite system GPS. Informatika [Informatics], 2023, vol. 20, no. 2, pp. 7−27 (In Russ.). https://doi.org/10.37661/1816-0301-2023-20-2-7-27.

6. Hofmann-Wellenhof B., Lichtenegger H., Collins J. Global Positioning System: Theory and Practice. New York, Springer-Verlag Wien, 1992, 327 p.

7. Mylnikova A. A., Yasyukevich Yu. V., Kunitsyn V. E., Padokhin A. M. Variability of GPS/GLONASS differential code biases. Results in Physics, 2015, vol. 5, pp. 9–10.

8. Kunitsyn V. E., Tereshenko E. D. Ionospheric Tomography. Springer, 2003, 272 p.

9. Bernhardt P., Selcher C., Basu S., Bust G., Reising S. Atmospheric studies with the tri-band beacon instrument on the COSMIC constellation. Terrestrial, Atmospheric and Oceanic Sciences, 2001, vol. 11, no. 1, pp. 291–312. https://doi.org/10.3319/TAO.2000.11.1.291(COSMIC)

10. Romanov A. A., Novikov A. V. Measurement of the total electron content of the Earth's ionosphere using a multi-frequency coherent sounding signal. Voprosy jelektromehaniki. Trudy Nauchno-proizvodstvennogo predprijatija Vserossijskogo nauchno-issledovatel'skogo instituta jelektromehaniki [Questions of Electromechanics. Proceedings of the Research and Production Enterprise of the All-Russian Research Institute of Electromechanics], 2009, vol. 111, no. 4, pp. 31–36 (In Russ.).

11. Ferreira V., He X., Tang X. Study on cycle-slip detection and repair methods for a single dual-frequency global positioning system (GPS). Boletim de Ciensicas, 2014, vol. 20, no. 4, pp. 984–1004.

12. Cai C., Liu Z., Xia P. Dai W. Cycle slip detection and repair for undifferenced GPS observation under high ionospheric activity. GPS Solutions, 2012, vol. 17, no. 2, pp. 247–260. https://doi.org/10.1007/s10291-012-0275-7

13. Blewitt G. An automatic editing algorithm for GPS data. Geophysical Research Letters, 1990, vol. 17, no. 3, pp. 199–202.

14. Goad C. Precise positioning with the global positioning system. Proceedings of the Third International Symposium on Inertial Technology for Surveying and Geodesy, Banff, 16–20 September 1985. Banff, 1985, pp. 745–756.

15. Ya’acob N., Abdullah M., Ismail M. Determination of GPS total electron content using single layer model (SLM) ionospheric mapping function. International Journal of Computer Science and Network Security, 2008, vol. 8, no. 9, pp. 154–160.