Aim. In order to improve the definition of GNSS-stations coordinate changes, it is important to find out how the processes that occur in the near-Earth space influence the significance of these changes. To describe such processes we can use the seismic activity index, the infrasound rate, and the number of daily flashes in the Sun. In this regard the purpose of this work is to study the influence of the above processes on small changes in the coordinates of GNSS-stations. Method. To solve this problem we have selected the coordinates of permanent GNSS-station, seismic activity indicators, infrasound indicators and the number of daily flares in the Sun for the same 295 day epoch. For modeling the influence of processes in the near-Earth space on the definition of coordinate changes the method of constructing a macromodel is developed based on averaged data with the use of a regularization method and with help of the reduction of the approximation basis of many arguments of polynomials. The arguments of the polynomials in the modelling are chosen to reflect the influence of external factors on the coordinates. Parameters and their corresponding multidies of polynomials are found from the identification tasks recorded by the Tikhonov regularization functions. Results. We constructed a macromodel that includes parameters of seismic processes, the Sun, the Moon, and the coordinates of the GNSS-station. We have found derivatives and different characteristics of the obtained model. Correlation analysis we used to clarify the assumptions. Scientific novelty. For the first time a macromodel was obtained which allows to calculate the influence of the index of seismic activity, infrasound and solar activity on small changes in the coordinates of GNSS-stations. Practical significance. After studying this model we obtained results that can be used to increase the accuracy of coordinates obtained using GNSS observations.
1. Akasofu, S. I., & Chapman, S. (1972). Solar-terrestrial physics. Oxford (International Series of Monographs on Physics) (Clarendon Press)
2. Hardreaves, J. K. (1992). The solar-terrestrial environment. Cambridge: Univ. press.
https://doi.org/10.1017/CBO9780511628924
3. Hayakawa, M. (2015). Earthquake Prediction with Radio Techniques, Wiley & Sons, Singapore.
https://doi.org/10.1002/9781118770368
4. Kremenetskyi, I. A., & Cheremnykh, O. K. (2009). Space weather: Mechanisms and manifestations. Kyiv: Naukova dumka.
5. Kurhanevych, A. P., & Matviichuk, Ya. M. (2000). Regularization of the problem of identification of macromodels of nonlinear dynamical systems by the method of reduction of the approximation basis. Theoretical electrical engineering, 55, 31–36.
6. Matviichuk, Ya. M., (2000) Mathematical macromodeling of dynamic systems: theory and practice. Lviv Polytechnic Publishing House.
7. Matviichuk, Ya. M., & Pauchok V. (2006). The statement of the problem of macromodeling of geo-heliogenic quantities. Visnyk of Lviv Polytechnic National University: Telecommunications and radio electronics. 557, 171–173.
8. Parnowski, A. S., Yermolayev, Yu. I., & Zhuk, I. T. (2010). Space weather: the history of research and forecasting. Space science and technology. 16, 1, 90–99.
https://doi.org/10.15407/knit2010.01.090
9. Parrot, M., Hayosh, M., & Soroka, S. (2007). Acoustic experiments in the ionosphere with the DEMETER satellite, EGU General Assembly, Vienna, 15–20 April 2007, 1607-7962/gra/EGU2007- A-04428.
10. Pauchok, V. K. (2010). Regularized identification of mathematical macromodels of processes and systems of various nature. Manuscript. Dissertation for the degree of a candidate of technical sciences in specialty 01.05.02 – mathematical modeling and computational methods. Lviv Polytechnic National University. Ministry of Education and Science of Ukraine
11. Tikhonov, A. N., Honcharovskyi, A. V., Stepanov, V. V., & Yahola, A. H. (1990). Numerical methods for solving ill-posed problems. Мoscow: Science.
12. Frydman, A. M., Poliachenko, E. V., & Nasyrkanov N. R. (2010). On some correlations in seismodynamics of the Earth's activity. UFN. 3, 303–312. https://doi.org/10.3367/UFNr.0180.201003f.0303
13. Yankiv-Vitkovska, L., & Pauchok, V. (2012). About macromodels of changes in geodetic coordinates and geoseismic processes. Modern achievements in geodetic science and industry, II (24), 188–191.
14. Yankiv-Vitkovska, L. M., Savchuk, S. H., & Pauchok V. K. (2007). To the analysis of regular stolen coordinates of permanent GPS stations SULP. Kyiv. Bulletin of Geodesy and Cartography, 5, 9–13.
15. Yankiv-Vitkovska, L. M., Savchuk, S. H., & Pauchok V. K. (2008). Investigation of the dynamics of coordinate changes of permanent GPS stations. Kyiv. Bulletin of Geodesy and Cartography, 1, 7–12.
16. Yankiv-Vitkovska, L. M., Matviichuk, Ya. M, Savchuk, S. H., & Pauchok V. K. (2012). Investigation of coordinate changes of GNSS-stations by the method of macromodeling. Kyiv. Visnyk of Geodesy and Cartography, 3, 9–17.