Solnechno-Zemnaya Fizika Solnechno-Zemnaya Fizika Солнечно-земная физика 2712-9640 42231 10.12737/szf-72202104 Обзоры Reviews Обзоры Space weather: risk factors for Global Navigation Satellite Systems Космическая погода: факторы риска для глобальных навигационных спутниковых систем Демьянов Владислав Владимирович Demyanov Vladislav Vladimirovich vv.emyanov@gmail.com Ясюкевич Юрий Владимирович Yasyukevich Yury Vladimirovich yasukevich@iszf.irk.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar-Terrestrial Physics SB RAS Irkutsk Russian Federation Иркутский государственный университет путей сообщения Иркутск Россия Irkutsk state transport university Irkutsk Russian Federation Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar Terrestrial Physics SB RAS Irkutsk Russian Federation Иркутский государственный университет Иркутск Россия Irkutsk State University Irkutsk Russian Federation 7 2 30 52 07 02 2021 31 03 2021 https://naukaru.ru/en/nauka/article/42231/view

Устойчивость и качество работы глобальных навигационных спутниковых систем (ГНСС) второго поколения (GPS, Galileo, BeiDou/Compass, ГЛОНАСС) и их функциональных дополнений зависят от воздействия экстремальных факторов космической погоды. В обзоре представлены сведения о механизмах воздействия геомагнитных бурь, ионосферных неоднородностей и мощных всплесков радиоизлучения Солнца на сегмент пользователей ГНСС. Представленные сведения подкреплены обзором результатов наблюдений последствий воздействия космической погоды на функционирование ГНСС в 2000–2020 гг. Рассматриваются относительная плотность сбоев измерений радионавигационных параметров и снижение точности позиционирования пользователей ГНСС в режиме двухчастотных измерений и в режиме дифференциальной навигации (Real Time Kinematic, RTK), в том числе при решении задач высокоточного позиционирования (Precise Point Positioning, PPP). Рассмотрена частота появления опасных факторов космической погоды и возможности прогнозирования последствий их воздействия на сегмент пользователей ГНСС. В качестве основных выводов обзора можно выделить следующие: 1) при воздействии экстремальных факторов космической погоды погрешность позиционирования пользователей ГНСС в различных режимах навигационно-временных определений может увеличиваться более чем в 10 раз в сравнении с фоновыми условиями; 2) за последнее десятилетие проведена модернизация космического и наземного сегмента ГНСС, позволившая существенно повысить помехоустойчивость системы в условиях воздействия мощных вспышек радиоизлучения Солнца; 3) существует принципиальная возможность дальнейшего увеличения устойчивости и повышения точности измерения радионавигационных параметров в условиях влияния факторов космической погоды за счет внедрения алгоритмов адаптивной настройки измерителей; 4) в настоящее время остаются нерешенными проблемы контроля целостности системы и доступности требуемых навигационных характеристик с учетом воздействия экстремальных факторов космической погоды.

Extreme space weather events affect the stability and quality of the global navigation satellite systems (GNSS) of the second generation (GPS, GLONASS, Galileo, BeiDou/Compass) and GNSS augmentation. We review the theory about mechanisms behind the impact of geomagnetic storms, ionospheric irregularities, and powerful solar radio bursts on the GNSS user segment. We also summarize experimental observations of the space weather effects on GNSS performance in 2000–2020 to confirm the theory. We analyze the probability of failures in measurements of radio navigation parameters, decrease in positioning accuracy of GNSS users in dual-frequency mode and differential navigation mode (RTK), and in precise point positioning (PPP). Additionally, the review includes data on the occurrence of dangerous and extreme space weather phenomena and the possibility for predicting their impact on the GNSS user segment. The main conclusions of the review are as follows: 1) the positioning error in GNSS users may increase up to 10 times in various modes during extreme space weather events, as compared to the background level; 2) GNSS space and ground segments have been significantly modernized over the past decade, thus allowing a substantial increase in noise resistance of GNSS under powerful solar radio burst impacts; 3) there is a great possibility for increasing the tracking stability and accuracy of radio navigation parameters by introducing algorithms for adaptive lock loop tuning, taking into account the influence of space weather events; 4) at present, the urgent scientific and technical problem of modernizing GNSS by improving the scientific methodology, hardware and software for monitoring the system integrity and monitoring the availability of required navigation parameters, taking into account the impact of extreme space weather events, is still unresolved.

 космическая погода ГНСС GPS ГЛОНАСС солнечные вспышки магнитные бури мерцания PPP RTK space weather GNSS GPS GLONASS solar flares magnetic storms scintillations PPP RTK Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта № 20-15-50079 The reported study was funded by RFBR, project number 20-15-50079

Акасофу С.И., Чепмен С. Солнечно-земная физика. М.: Мир, 1975. Т. 2. 512 с. Aa E., Huang W., Liu S., Ridley A., Zou S., Shi L., Chen Y., Shen H., Yuan T., Li J., Wang T. Midlatitude plasma bubbles over China and adjacent areas during a magnetic storm on 8 September 2017. Space Weather. 2018, vol. 16, pp. 321-331. DOI: 10.1002/2017SW001776. Афраймович Э.Л., Перевалова Н.П. GPS-мониторинг верхней атмосферы Земли. Иркутск: Изд-во ГУ НЦ РВХ ВСНЦ СО РАМН, 2006. 479 с. Aarons J. Global morphology of ionospheric scintillations. Proc. of the IEEE. 1982, vol. 70, no. 4, pp. 360-378. DOI: 10.1109/PROC.1982.12314. Афраймович Э.Л., Лесюта О.С., Ушаков И.И. Геомагнитные возмущения и функционирование навигационной системы GPS. Геомагнетизм и аэрономия. 2002. Т. 42, № 2. С. 220-227. Afraimovich E.L., Perevalova N.P. GPS-monitoring verkhnei atmosfery Zemli [GPS monitoring of the Earth’s upper atmosphere]. Irkutsk, 2006, 480 p. (In Russian). Афраймович Э.Л., Гаврилюк Н.С., Демьянов В.В. и др. Cбои функционирования спутниковых навигационных систем GPS-ГЛОНАСС, обусловленные мощным радиоизлучением солнца во время солнечных вспышек 6, 13 декабря 2006 г. и 28 октября 2003 г. Космические исследования. 2009. Т. 47, № 2. С. 146-157. Afraimovich E.L., Lesyuta O.S., Ushakov I.I. Voeykov S.V. Geomagnetic storms and the occurrence of phase slips in the reception of GPS signals. Ann. Geophys. 2002, vol. 45, no. 1, pp. 55-71. DOI: 10.4401/ag-3494. Базаржапов А.Д., Матвеев М.И., Мишин В.М. Геомагнитные вариации и бури. Новосибирск: Наука, 1979. 287 c. Afraimovich E.L., Demyanov V.V., Ishin A.B. Smolkov G.Ya. Powerful solar radio bursts as a global and free tool for testing satellite broadband radio systems, including GPS-GLONASS-GALILEO. J. Atmos. Solar-Terr. Phys. 2008, vol. 70, no 15, pp. 1985-1994. DOI: 10.1016/j.jastp.2008.09.008. Барабанова Л.П. К минимизации геометрических факторов GNSS. Известия РАН. Теория и системы управления. 2010. № 2. С. 145-152. Afraimovich E.L., Astafyeva E.I., Demyanov V.V. Gamayunov I.F. Mid-latitude amplitude scintillation of GPS signals and GPS performance slips. Adv. Space Res. 2009, vol. 43, iss. 6, pp. 964-972. DOI: 10.1016/j.asr.2008.09.015. Бруцек А., Дюран Ш. Солнечно-земная физика. Иллюстрированный словарь терминов. М.: Мир, 1980. 256 с. Afraimovich E.L., Demyanov V.V., Gavrilyuk N.S., Ishin A.B., Smolkov G.Ya. Malfunction of satellite navigation systems GPS and GLONASS caused by powerful radio emission of the Sun during solar flares on December 6 and 13, 2006, and October 28, 2003. Cosmic Res. 2009, vol. 47, pp. 126-137. DOI: 10.1134/S001095250902004X. Вдовин В.С., Дворкин В.В., Карпик А.П. и др. Проблемы и перспективы развития активных спутниковых геодезических сетей в России и их интеграции в ITRF. Вестник СГУГиТ (Сибирского государственного университета геосистем и технологий). 2018. Т. 23, № 1. С. 6-27. Akasofu S.I., Chapman S. Solar-Terrestrial Physics. Chapter 2. Oxford University Press, 1972, 901. p. Демьянов В.В., Ясюкевич Ю.В. Механизмы воздействия нерегулярных геофизических факторов на функционирования спутниковых радионавигационных систем: монография. Иркутск: Изд-во ИГУ, 2014. 349 с. Anderson P.C., Straus P.R. Magnetic field orientation control of GPS occultation observations of equatorial scintillation. Geophys. Res. Lett. 2005, vol. 32, L21107. DOI: 10.1029/ 2005GL023781. Жеребцов Г.А. Комплекс гелиогеофизических инструментов нового поколения. Солнечно-земная физика. 2020. Т. 6, № 2. С. 6-18. DOI: 10.12737/szf-62202001. 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, no. 7, pp. 508-525. DOI: 10.1002/2014SW001072. Затолокин Д.А. Программа решения навигационной задачи ГНСС «Navi»: свидетельство о государственной регистрации программы ЭВМ № 2020612010. 2020. Barabanova L.P. Minimization of GNSS geometric factors. J. Comput. Syst. Sci. Int. 2010, vol. 49, pp. 310-317. DOI: 10.1134/S1064230710020164. Захаров В.И., Чернышов А.А., Милох В. Джин Я. Влияние ионосферы на параметры навигационных сигналов GPS во время геомагнитной суббури. Геомагнетизм и аэрономия. 2020. Т. 60, № 6. С. 769-782. DOI: 10.31857/S0016794020060152. Bartels J., Heck N.H., Johnston H.F. The three-hour-range index measuring geomagnetic activity. Terrestrial Magnetism and Atmospheric Electricity. 1939, vol. 44, no. 4, pp. 411-454. DOI: 10.1029/ TE044i004p00411. ИКД СДКМ. Система дифференциальной коррекции и мониторинга (редакция 1). 2012. 133 с. Bazarzhapov A.D., Matveev M.I., Mishin V.M. Geomagnitnye variacii i buri [Geomagnetic variations and storms]. Novosibirsk, Nauka Publ., 1979, 287 p. (In Russian). Кравцов А.Ю. Прохождение радиоволн через ионосферу Земли. М.: Радио и связь, 1983. 224 с. BDS-SIS-ICD. BeiDou Navigation Satellite System Signal In Space Interface Control Document: Open Service Signal B1I (Version 3.0). 2019. BDS-SIS-ICD-B1I-3.0. 2019-02. Пашинцев В.П., Гамов М.В. Влияние дисперсионной ионосферы на измерениe псевдодальности в спутниковых радионавигационных системах. Изв. вузов. Радиоэлектроника. 2002. № 12. С. 3-13. Berdermann J., Kriegel M., Banyś D., Heymann F., Hoque M.M., Wilken V., Borries C., Heßelbarth A., Jakowski N. Ionospheric response to the X9.3 Flare on 6 September 2017 and its implication for navigation services over Europe. Space Weather. 2018, vol. 16, iss. 10, pp. 1604-1615. DOI: 10.1029/2018SW001933. Пашинцев В.П., Ахмадеев Р.Р. Прогнозирование помехоустойчивости спутниковых радиосистем по данным GPS-мониторинга ионосферы. Электросвязь. 2015. № 11. С. 58-65. Berghmans D., Van der Linden R.A.M., Vanlommel P., Warnant R., Zhukov A., Robbrecht E., et al. Solar activity: nowcasting and forecasting at the SIDC. Ann. Geophys. 2005, vol. 23, no. 6, pp. 3115-3128. DOI: 10.5194/angeo-23-3115-2005. Харгривс Дж.К. Верхняя атмосфера и солнечно-земные связи. Л.: Гидрометеоиздат, 1982. 351 с. Bhattacharrya A., Yen K.C., Franke S.J. Deducing turbulence parameters from transionospheric scintillation measurements. Space Sci. Rew. 1992, vol. 61, pp. 335-386. DOI: 10.1007/BF00222311. Яковлев О.И. Космическая радиофизика. Воронеж: Научная книга, 1998. 432 с. Bruyninx C., Habrich H., Söhne W., Kenyeres A., Stangl G., Völksen C. Enhancement of the EUREF Permanent Network Services and Products. Geodesy for Planet Earth. IAG Symposia Series. 2012, vol. 136, pp. 27-35. DOI: 10.1007/978-3-642-20338-1_4. Aa E., Huang W., Liu S., et al. Midlatitude plasma bubbles over China and adjacent areas during a magnetic storm on 8 September 2017. Space Weather. 2018. Vol. 16. P. 321-331. DOI: 10.1002/2017SW001776. Bruzek A., Durrant C.J. Illustrated Glossary for Solar and Solar-Terrestrial Physics. 1977, 207 p. DOI: 10.1007/978-94-010-1245-4. Aarons J. Global morphology of ionospheric scintillations. Proc. of the IEEE. 1982. Vol. 70, iss. 4. P. 360-378. DOI: 10.1109/PROC.1982.12314. Carrano C.S., Groves K.M., Bridgwood C.T. Effects of the December 2006 Solar Radio Bursts on the GPS Receivers of the AFRL-SCINDA Network // Proceedings of the International Beacon Satellite Symposium, Boston College. June 11-15, 2007. Afraimovich E.L., Demyanov V.V., Ishin A.B. Smolkov G.Ya. Powerful solar radio bursts as a global and free tool for testing satellite broadband radio systems, including GPS-GLONASS-GALILEO. J. Atmos. Solar-Terr. Phys. 2008. Vol. 70, iss. 15. P. 1985-1994. DOI: 10.1016/j.jastp.2008.09.008. Carrano C.S., Bridgwood C.T., Groves K.M. Impacts of the December 2006 solar radio bursts on the performance of GPS. Radio Sci. 2009, vol. 44, RS0A25. DOI: 10.1029/2008RS004071. Afraimovich E.L., Astafyeva E.I., Demyanov V.V. Gamayunov I.F. Mid-latitude amplitude scintillation of GPS signals and GPS performance slips. Adv. Space Res. 2009. Vol. 43, iss. 6. P. 964-972. DOI: 10.1016/j.asr.2008.09.015. Cerruti A.P., Kintner P.M., Gary D.E., Lanzerotti L.J., de Paula E.R., Vo H.B. Observed Solar Radio Burst Effects on GPS/WAAS Carrier-to-Noise Ratio. Space Weather. 2006, vol. 4, S10006. DOI: 10.1029/2006SW000254. Anderson P.C., Straus P.R. Magnetic field orientation control of GPS occultation observations of equatorial scintillation. Geophys. Res. Lett. 2005. Vol. 32, L21107. DOI: 10.1029/ 2005GL023781. Cerruti A.P., Kintner P.M., Gary D.E. Effect of intense December 2006 solar radio bursts on GPS receivers. Space Weather. 2008, vol. 6, S10D07. DOI: 10.1029/2007SW000375. 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, no. 7. P. 508-525. DOI: 10.1002/2014SW001072. Chen Z., Gao Y., Liu Z. Evaluation of solar radio bursts' effect on GPS receiver signal tracking within International GPS Service network. Radio Sci. 2005, vol. 40, RS3012. DOI: 10.1029/2004RS003066. Bartels J., Heck N.H., Johnston H.F. The three-hour-range index measuring geomagnetic activity. Terrestrial Magnetism and Atmospheric Electricity. 1939. Vol. 44, no. 4. P. 411-454. DOI: 10.1029/TE044i004p00411. Cherniak I., Zakharenkova I. First observations of super plasma bubbles in Europe. Geophys. Res. Lett. 2016, vol. 43, no. 21, pp. 11137-11145. DOI: 10.1002/2016GL071421. BDS-SIS-ICD. BeiDou Navigation Satellite System Signal In Space Interface Control Document: Open Service Signal B1I (Version 3.0). 2019. BDS-SIS-ICD-B1I-3.0. 2019-02. Conker R.S., El-Arini M.B., Hegarty C.J., Hsiao T. Modeling the effects of ionospheric scintillation on GPS/Satellite-Based Augmentation System availability. Radio Sci. vol. 38, no. 1, 1001. DOI: 10.1029/2000RS002604. Berdermann J., Kriegel M., Banyś D., et al. Ionospheric response to the X9.3 Flare on 6 September 2017 and its implication for navigation services over Europe. Space Weather. 2018. Vol. 16, iss. 10. P. 1604-1615. DOI: 10.1029/2018SW001933. Coster A.J., Foster J.C., Erickson P.J., Rich F.J. Regional GPS mapping of storm enhanced density during the July 15-16 2000 geomagnetic storm. Proceedings of International Beaco Satellite Symposium, June 4-6, 2001. Boston College; Institute for Scientific Research. USA: Chestnut Hill, MA. 2001, pp. 176-180. Berghmans D., Van der Linden R.A.M., Vanlommel P., Warnant R., et al. Solar activity: nowcasting and forecasting at the SIDC. Ann. Geophys. 2005. Vol. 23, no. 6. P. 3115-3128. DOI: 10.5194/angeo-23-3115-2005. Dabove P., Linty N., Dovis F. Analysis of multi-constellation GNSS PPP solutions under phase scintillations at high latitudes. Appl. Geomatics. 2020, vol. 12, pp. 45-52. DOI: 10.1007/s12518-019-00269-4. Bhattacharrya A., Yen K.C., Franke S.J. Deducing turbulence parameters from transionospheric scintillation measurements. Space Sci. Rew. 1992. Vol. 61. P. 335-386. DOI: 10.1007/BF00222311. Demyanov V.V., Yasyukevich Yu.V. Mekhanizmy vozdeistviya neregulyarnykh geofizicheskikh faktorov na funktsionirovanie sputnikovykh radionavigatsionnykh system [Mechanisms of impact of irregular geophysical factors on operation of radio positioning satellite systems], Irkutsk, Irkutsk State University Publ., 2014, 349 p. (In Russian). Bruyninx C., Habrich H., Söhne W., et al. Enhancement of the EUREF Permanent Network Services and Products. Geodesy for Planet Earth. IAG Symposia Series. 2012. Vol. 136. P. 27-35. DOI: 10.1007/978-3-642-20338-1_4. Demyanov V.V., Afraimovich E.L., Jin S. An evaluation of potential solar radio emission power threat on GPS and GLONASS performance. GPS Solutions. 2012a, vol. 16, pp. 411-424. DOI: 10.1007/s10291-011-0241-9. Carrano C.S., Groves K.M., Bridgwood C.T. Effects of the December 2006 Solar Radio Bursts on the GPS Receivers of the AFRL-SCINDA Network. Proceedings of the International Beacon Satellite Symposium, Boston College. June 11-15, 2007. Demyanov V.V., Yasyukevich Y.V., Ishin A.B., Astafyeva E.I. Ionospheric super-bubble effects on the GPS positioning relative to the orientation of signal path and geomagnetic field direction. GPS Solutions. 2012b, vol. 16, pp. 181-189. DOI: 10.1007/s10291-011-0217-9. Carrano C.S., Bridgwood C.T., Groves K.M. Impacts of the December 2006 solar radio bursts on the performance of GPS. Radio Sci. 2009. Vol. 44, RS0A25. DOI: 10.1029/2008 RS004071. Demyanov V.V., Zhang X., Lu X. Moderate geomagnetic storm condition, WAAS Alerts and real GPS positioning quality. J. Atmos. Sci. Res. 2019, vol. 2, no. 1, pp. 10-23. DOI: 10.30564/jasr.v2i1.343. Cerruti A.P., Kintner P.M., Gary D.E., et al. Observed Solar Radio Burst Effects on GPS/WAAS Carrier-to-Noise Ratio. Space Weather. 2006. Vol. 4, S10006. DOI: 10.1029/2006 SW000254. Dow J.M., Neilan R.E., Rizos C. The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J. Geodesy. 2009, vol. 83, pp. 191-198. DOI: 10.1007/s0019000803003. Cerruti A.P., Kintner P.M., Gary D.E. Effect of intense December 2006 solar radio bursts on GPS receivers. Space Weather. 2008. Vol. 6. S10D07. DOI: 10.1029/2007SW000375. Dulk A.G. Radio emission from the Sun and stars. Ann. Rev. Astron. Astrophys. 1985. vol. 23, pp. 169-224. DOI: 10.1146/ annurev.aa.23.090185.001125. Chen Z., Gao Y., Liu Z. Evaluation of solar radio bursts’ effect on GPS receiver signal tracking within International GPS Service network. Radio Sci. 2005. Vol. 40, RS3012. DOI: 10.1029/2004RS003066. Falcone M., Lucas R., Burger T., Hein G.W. The European Galileo programme. The European EGNOS project. ESA Publications Division, Noordwijk, The Netherlands, SP-1303. 2006, pp. 435-455. Cherniak I., Zakharenkova I. First observations of super plasma bubbles in Europe. Geophys. Res. Lett. 2016. Vol. 43, no. 21. P. 11137-11145. DOI: 10.1002/2016GL071421. Freymueller J.T. AEIC (Kodiak) 2014. GPS/GNSS Observations Dataset. The GAGE Facility operated by UNAVCO, Inc., 2017. Conker R.S., El-Arini M.B., Hegarty C.J., Hsiao T. Modeling the effects of ionospheric scintillation on GPS/Satellite-Based Augmentation System availability. Radio Sci. 2003. Vol. 38, no. 1, 1001. DOI: 10.1029/2000RS002604. Galileo-SIS-ICD. European GNSS (Galileo) open service. Signal-in-space interface control document. Issue 2.0, January 2021. Coster A.J., Foster J.C., Erickson P.J., Rich F.J. Regional GPS mapping of storm enhanced density during the July 15-16 2000 geomagnetic storm. Proceedings of International Beaco Satellite Symposium, June 4-6, 2001 / Boston College; Institute for Scientific Research. USA: Chestnut Hill, MA. 2001. P. 176-180. Giersch O.D., Kennewell J., Lynch M. Solar radio burst statistics and implications for space weather effects. Space Weather. 2017, vol. 15, pp. 1511-1522. DOI: 10.1002/2017SW001658. Dabove P., Linty N., Dovis F. Analysis of multi-constellation GNSS PPP solutions under phase scintillations at high latitudes. Appl. Geomatics. 2020. Vol. 12. P. 45-52. DOI: 10.1007/s12518-019-00269-4. GPS-WAAS-PS. Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard. 2008-10. Demyanov V.V., Afraimovich E.L., Jin S. An evaluation of potential solar radio emission power threat on GPS and GLONASS performance. GPS Solutions. 2012a. Vol. 16. P. 411-424. DOI: 10.1007/s10291-011-0241-9. Gulyaeva T.L., Gulyaev R.A. Chain of responses of geomagnetic and ionospheric storms to a bunch of central coronal hole and high speed stream of solar wind. J. Atmos. Solar-Terr. Phys. 2020, vol. 208, 105380. DOI: 10.1016/j.jastp.2020.105380. Demyanov V.V., Yasyukevich Y.V., Ishin A.B., et al. Ionospheric super-bubble effects on the GPS positioning relative to the orientation of signal path and geomagnetic field direction. GPS Solutions. 2012b. Vol. 16. P. 181-189. DOI: 10.1007/s10291-011-0217-9. Hargreaves J.K. The Upper Atmosphere and Solar-Terrestrial Relations. New York, Van Nostrand Reinhold Co. 1979, 312 p. Demyanov V.V., Zhang X., Lu X. Moderate geomagnetic storm condition, WAAS Alerts and real GPS positioning quality. J. Atmos. Sci. Res. 2019. Vol. 2, no. 1. P. 10-23. DOI: 10.30564/jasr.v2i1.343. Hernandez-Pajares M., Juan J.M., Sanz J., Orus R., Garcia-Rigo A., Feltens J., Komjathy A., Schaer S.C., Krankowski A. The IGS VTEC maps: a reliable source of ionospheric information since 1998. J. Geodesy. 2009, vol. 83, no 3, pp. 263-275. DOI: 10.1007/s00190-008-0266-1. Dow J.M., Neilan R.E., Rizos C. The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J. Geodesy. 2009. Vol. 83. P. 191-198. DOI: 10.1007/s0019000803003. Hofmann-Wellenhof B., Lichtenegger H., Collins J. Global Positioning System: Theory and Practice. 5th edition. New York, Springer-Verlag, 2001. 406 p. DOI: 10.1007/987-3-7091-6199-9. Dulk A.G. Radio emission from the Sun and stars. Ann. Rev. Astron. Astrophys. 1985. Vol. 23. P. 169-224. DOI: 10.1146/ annurev.aa.23.090185.001125. Huang C.-S., de La Beaujardiere O., Roddy P.A., Hunton D.E., Pfaff R.F., Valladares C.E., Ballenthin J.O. Evolution of equatorial ionospheric plasma bubbles and formation of broad plasma depletions measured by the C/NOFS satellite during deep solar minimum. J. Geophys. Res.: Space Phys. 2011, vol. 116, no. A3, A03309. DOI: 10.1029/2010JA015982. Falcone M., Lucas R., Burger T., Hein G.W. The European Galileo programme. The European EGNOS project. ESA Publications Division, Noordwijk, The Netherlands, SP-1303. 2006. P. 435-455. Huang W., Aa E., Shen H., Liu S. Statistical study of GNSS L-band solar radio bursts. GPS Solutions. 2018, vol. 22, 114. DOI: 10.1007/s10291-018-0780-4. Freymueller J.T. AEIC (Kodiak) 2014. GPS/GNSS Observations Dataset. The GAGE Facility operated by UNAVCO, Inc., 2017. IKD SDKM. Sistema differencial’noj korrekcii i monitoringa [System for differential correction and monitoring]: 1st edition. 2012. (In Russian). 133 r. GPS-WAAS-PS. Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard. 2008-10. Jacobsen K.S., Schäfer S. Observed effects of a geomagnetic storm on an RTK positioning network at high latitudes. J. Space Weather Space Clim. 2012, vol. 2, A13. DOI: 10.1051/swsc/2012013. Giersch O.D., Kennewell J., Lynch M. Solar radio burst statistics and implications for space weather effects. Space Weather. 2017. Vol. 15. P. 1511-1522. DOI: 10.1002/2017SW001658. Jacobsen K.S., Andalsvik Y.L. Overview of the 2015 St. Patrick’s day storm and its consequences for RTK and PPP positioning in Norway. J. Space Weather Space Clim. 2016, vol. 6, A9. DOI: 10.1051/swsc/2016004. GPS-WAAS-PS. Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard. 2008. GPS WAAS PS. 2008-10. Jayachandran P.T., Langley R.B., MacDougall J.W., Mushini S.C., Pokhotelov D., Hamza A.M., Mann I.R., Milling D.K., Kale Z.C., Chadwick R., Kelly T., Danskin D.W., Carrano C.S. Canadian High Arctic Ionospheric Network (CHAIN). Radio Sci. 2009, vol. 44, no. 1, RS0A03. DOI: 10.1029/ 2008RS004046. Gulyaeva T.L., Gulyaev R.A. Chain of responses of geomagnetic and ionospheric storms to a bunch of central coronal hole and high speed stream of solar wind. J. Atmos. Solar-Terr. Phys. 2020. Vol. 208, 105380. DOI: 10.1016/j.jastp.2020.105380. Jin S., Cardellach E., Xie F. GNSS Remote Sensing: Theory, Methods and Applications, Remote Sensing and Digital Image Processing. 2014, vol. 19, 276 p. DOI: 10.1007/978-94-007-7482-7. Hernandez-Pajares M., Juan J.M., Sanz J., et al. The IGS VTEC maps: a reliable source of ionospheric information since 1998. J. Geodesy. 2009. Vol. 83, no. 3. P. 263-275. DOI: 10.1007/s00190-008-0266-1. Kaplan E.D. Understanding GPS: principles and applications. 1996, 556 p. Hofmann-Wellenhof B., Lichtenegger H., Collins J. Global Positioning System: Theory and Practice. 5th edition. New York: Springer-Verlag, 2001. 406 p. DOI: 10.1007/987-3-7091-6199-9. King J.H., Papitashvili N.E. Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res.: Space Phys. 2005, vol. 110, no. A2, A02104. DOI: 10.1029/2004JA010649. Huang C.-S., de La Beaujardiere O., Roddy P.A., et al. Evolution of equatorial ionospheric plasma bubbles and formation of broad plasma depletions measured by the C/NOFS satellite during deep solar minimum. J. Geophys. Res.: Space Phys. 2011. Vol. 116. A03309. DOI: 10.1029/2010JA015982. Klobuchar J.A., Kunches J.M., Van Dierendonck A.J. Eye on the ionosphere: Potential solar radio burst effects on GPS signal to noise. GPS Solutions. 1999, vol. 3, no. 2, pp. 69-71. DOI: 10.1007/PL00012794. Huang W., Aa E., Shen H., Liu S. Statistical study of GNSS L-band solar radio bursts. GPS Solutions. 2018. Vol. 22, 114. DOI: 10.1007/s10291-018-0780-4. Kolesnik S.N., Tinin M.V., Afanasiev N.T. Statistical characteristics of a wave propagating through a layer with random irregularities. Waves in Random Media. 2002, vol. 12, pp. 417-431. DOI: 10.1088/0959-7174/12/4/302. Jacobsen K.S., Schäfer S. Observed effects of a geomagnetic storm on an RTK positioning network at high latitudes. J. Space Weather Space Climate. 2012. Vol. 2, A13. DOI: 10.1051/swsc/2012013. Kozyreva O.V., Pilipenko V.A., Zakharov V.I., Engebretson M.J. GPS-TEC response to the substorm onset during April 5, 2010, magnetic storm. GPS Solutions. 2017, vol. 21, no. 3, pp. 927-936. DOI: 10.1007/s10291-016-0581-6. Jacobsen K.S., Andalsvik Y.L. Overview of the 2015 St. Patrick’s day storm and its consequences for RTK and PPP positioning in Norway. J. Space Weather and Space Climate. 2016. Vol. 6, A9. DOI: 10.1051/swsc/2016004. Kravtsov A.Y. Prohozhdenie radiovoln cherez ionosferu Zemli [Propagation of radio waves in the Earth ionosphere]. Moscow, Radio i svyaz’ Publ., 1983, 224 p. (In Russian). Jayachandran P.T., Langley R.B., MacDougall J.W., et al. Canadian High Arctic Ionospheric Network (CHAIN). Radio Sci. 2009. Vol. 44, no. 1, RS0A03. DOI: 10.1029/2008RS004046. Lakhina G., Alex S., Tsurutani B., Gonzalez W. Research on Historical Records of Geomagnetic Storms. Proceedings of the International Astronomical Union, 2004(IAUS226). 2004, pp. 3-15. DOI: 10.1017/S1743921305000074. Jin S., Cardellach E., Xie F. GNSS Remote Sensing: Theory, Methods and Applications. Remote Sensing and Digital Image Processing. 2014. Vol. 19. 276 p. DOI: 10.1007/978-94-007-7482-7. Lekshmi V.D., Balan N., Tulasi S.R., Liu J.-Y. Statistics of geomagnetic storms and ionospheric storms at low and mid latitudes in two solar cycles. J. Geophys. Res.: Space Phys. 2011, vol. 116, A11328. DOI: 10.1029/2011JA017042. Kaplan E.D. Understanding GPS: principles and applications. 1996. 556 p. Li Z., Wang N., Hernández-Pajares M., Yuan Y., Krankowski A., Liu A., Zha J., et al. IGS real-time service for global ionospheric total electron content modeling. J. Geodesy. 2020, vol. 94, 32. DOI: 10.1007/s00190-020-01360-0. King J.H., Papitashvili N.E. Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res.: Space Phys. 2005. Vol. 110, no. A2, A02104. DOI: 10.1029/2004JA010649. Linty N. Codeless tracking algorithms for GNSS software receivers: Tesi di Laurea Magistrale. Torino. 2010, 126 p. Klobuchar J.A., Kunches J.M., Van Dierendonck A.J. Eye on the ionosphere: Potential solar radio burst effects on GPS signal to noise. GPS Solutions. 1999. Vol. 3, no. 2. P. 69-71. DOI: 10.1007/PL00012794. Linty N., Minetto A., Dovis F., Spogli L. Effects of phase scintillation on the GNSS positioning error during the September 2017 storm at Svalbard. Space Weather. 2018, vol. 16, pp. 1317-1329. DOI: 10.1029/2018SW001940. Kolesnik S.N., Tinin M.V., Afanasiev N.T. Statistical characteristics of a wave propagating through a layer with random irregularities. Waves in Random Media. 2002. Vol. 12. P. 417-431. DOI: 10.1088/0959-7174/12/4/302. Loewe C.A., Prölss G.W. Classification and mean behavior of magnetic storms. J. Geophys. Res. 1997, vol. 102, no. A7, pp. 14209-14213. DOI: 10.1029/96JA04020. Kozyreva O.V., Pilipenko V.A., Zakharov V.I., Engebretson M.J. GPS-TEC response to the substorm onset during April 5, 2010, magnetic storm. GPS Solutions. 2017. Vol. 21, no. 3. P. 927-936. DOI: 10.1007/s10291-016-0581-6. Love J.J., Hayakawa H., Cliver E.W. Intensity and impact of the New York Railroad superstorm of May 1921. Space Weather. 2019, vol. 17, pp. 1281-1292. DOI: 10.1029/2019SW002250. Lakhina G., Alex S., Tsurutani B., Gonzalez W. Research on Historical Records of Geomagnetic Storms. Proceedings of the International Astronomical Union (IAUS226). 2004. P. 3-15. DOI: 10.1017/S1743921305000074. Luo M., Pullen S., Ene A., Qiu D., Walter T., Enge P. Ionosphere threat to LAAS: updated model, user impact, and mitigations. 17th International Technical Meeting of the Satellite Division (ION GNSS 2004). Long Beach, 2004, pp. 2771-2785. Lekshmi V.D., Balan N., Tulasi S.R., Liu J.-Y. Statistics of geomagnetic storms and ionospheric storms at low and mid latitudes in two solar cycles. J. Geophys. Res.: Space Phys. 2011. Vol. 116, A11328. DOI: 10.1029/2011JA017042. Luo X., Gu S., Lou Y., Xiong C., Chen B., Jin X. Assessing the performance of GPS precise point positioning under different geomagnetic storm conditions during solar cycle 24. Sensors. 2018, vol. 18, no. 6, 1784. DOI: 10.3390/s18061784. Li Z., Wang N., Hernández-Pajares M., et al. IGS real-time service for global ionospheric total electron content modeling. J. Geodesy. 2020. Vol. 94, 32. DOI: 10.1007/s00190-020-01360-0. Luo X., Gu S., Lou Y., Song W. Better thresholds and weights to improve GNSS PPP under ionospheric scintillation activity at low latitudes. GPS Solutions. 2020, vol. 24, 17. DOI: 10.1007/s10291-019-0924-1. Linty N. Codeless tracking algorithms for GNSS software receivers: Tesi di Laurea Magistrale. Torino, 2010. 126 p. Ma G., Maruyama T. A super bubble detected by dense GPS network at East Asian longitudes. Geophys. Res. Lett. 2006, vol. 33, no. 21, L21103. DOI: 10.1029/2006GL027512. Linty N., Minetto A., Dovis F., Spogli L. Effects of phase scintillation on the GNSS positioning error during the September 2017 storm at Svalbard. Space Weather. 2018. Vol. 16. P. 1317-1329. DOI: 10.1029/2018SW001940. McCaffrey A.M., Jayachandran P.T. Spectral characteristics of auroral region scintillation using 100 Hz sampling. GPS Solutions. 2017, vol. 21, pp. 1883-1894. DOI: 10.1007/s10291-017-0664-z. Loewe C.A., Prölss G.W. Classification and mean behavior of magnetic storms. J. Geophys. Res. 1997. Vol. 102, A7. P. 14209-14213. DOI: 10.1029/96JA04020. Michalek G., Puchowska K., Rams A. Statistical analysis of decimetric radio bursts, flares and coronal mass ejections. Solar Phys. 2009, vol. 257, pp. 113-124. DOI: 10.1007/s11207-009-9343-8. Love J.J., Hayakawa H., Cliver E.W. Intensity and impact of the New York Railroad superstorm of May 1921. Space Weather. 2019. Vol. 17. P. 1281-1292. DOI: 10.1029/2019SW002250. Moreno B., Radicella S., de Lacy M.C., Herraiz M., Rodriguez-Caderot G. On the effects of the ionospheric disturbances on precise point positioning at equatorial latitudes. GPS Solutions. 2011, vol. 15, N 4, pp. 381-390. DOI: 10.1007/s10291-010-0197-1. Luo M., Pullen S., Ene A., et al. Ionosphere threat to LAAS: updated model, user impact, and mitigations. 17th International Technical Meeting of the Satellite Division (ION-GNSS 2004). Long Beach, CA, 2004. P. 2771-2785. Pashintsev V.P., Akhmadeev R.R., Prediction noise immunity of satellite communications system and navigation according to GPS-monitoring ionosphere. Elektrosvyaz, 2015, no. 11, pp. 32-38. (In Russian). Luo X., Gu S., Lou Y., et al. Assessing the performance of GPS precise point positioning under different geomagnetic storm conditions during solar cycle 24. Sensors. 2018. Vol. 18, no. 6, 1784. DOI: 10.3390/s18061784. Pashintsev V.P., Gamov M.V. Influence of dispersion ionosphere on pseudo range measurements in satellite radio navigation systems. Radioelectron. Commun. Syst. 2002, vol. 45, no. 12, pp. 3-13. Luo X., Gu S., Lou Y., Song W. Better thresholds and weights to improve GNSS PPP under ionospheric scintillation activity at low latitudes. GPS Solutions. 2020. Vol. 24, 17. DOI: 10.1007/s10291-019-0924-1. Psiaki M.L. Block acquisition of weak GPS signals in a software receiver. Proc. ION GPS 2001, Salt Lake City, UT, September 11-14, 2001, pp. 2838-2850. Ma G., Maruyama T. A super bubble detected by dense GPS network at East Asian longitudes. Geophys. Res. Lett. 2006. Vol. 33, no. 21, L21103 DOI: 10.1029/2006GL027512. Riley P. On the probability of occurrence of extreme space weather events. Space Weather. 2012, vol. 10, S02012. DOI: 10.1029/2011SW000734. McCaffrey A.M., Jayachandran P.T. Spectral characteristics of auroral region scintillation using 100 Hz sampling. GPS Solutions. 2017. Vol. 21. P. 1883-1894. DOI: 10.1007/s10291-017-0664-z. Rino C.L. The Theory of Scintillation with Applications in Remote Sensing, Hoboken, NJ, John Wiley & Sons, Inc., 2011, 230 p. DOI: 10.1002/9781118010211. Michalek G., Puchowska K., Rams A. Statistical analysis of decimetric radio bursts, flares and coronal mass ejections. Solar Phys. 2009. Vol. 257. P. 113-124. DOI: 10.1007/s11207-009-9343-8. Rodríguez-Bilbao I., Radicella S.M., Rodríguez-Caderot G., Herraiz M. Precise point positioning performance in the presence of the 28 October 2003 sudden increase in total electron content. Space Weather. 2015, vol. 13, pp. 698-708. DOI: 10.1002/2015SW001201. Moreno B., Radicella S., de Lacy M.C., et al. On the effects of the ionospheric disturbances on precise point positioning at equatorial latitudes. GPS Solutions. 2011. Vol. 15, no. 4. P. 381-390. DOI: 10.1007/s10291-010-0197-1. Saito S., Yoshihara T. Evaluation of extreme ionospheric total electron content gradient associated with plasma bubbles for GNSS Ground-Based Augmentation System // Radio Sci. 2017, vol. 52, pp. 951-962. DOI: 10.1002/2017RS006291. Psiaki M.L. Block acquisition of weak GPS signals in a software receiver. Proc. ION GPS 2001. Salt Lake City, UT, September 11-14, 2001. P. 2838-2850. Shi C., Liu J. GNSS status and developments in China. Presentation at the Civil Global Positioning System Service Interface Committee, 46th meeting, Fort Worth, Texas, September 26. 2006. Riley P. On the probability of occurrence of extreme space weather events. Space Weather. 2012. Vol. 10, S02012. DOI: 10.1029/2011SW000734. Siscoe G., Crooker N.U., Clauer C. Dst of the Carrington storm of 1859. Adv. Space Res. 2006, vol. 38, iss. 2, pp. 173-179. DOI: 10.1016/j.asr.2005.02.102. Rino C.L. The Theory of Scintillation with Applications in Remote Sensing. Hoboken, NJ, John Wiley & Sons, Inc., 2011. 230 p. DOI: 10.1002/9781118010211. Skone S., Shrestha S.M. Limitations in DGPS positioning accuracies at low latitudes during solar maximum. Geophys. Res. Lett. 2002, vol. 29, no. 10, p. 81-1-81-4. DOI: 10.1029/ 2001GL013854. Rodríguez-Bilbao I., Radicella S.M., Rodríguez-Caderot G., Herraiz M. Precise point positioning performance in the presence of the 28 October 2003 sudden increase in total electron content. Space Weather. 2015. Vol. 13. P. 698-708. DOI: 10.1002/2015SW001201. Smith J., Heelis R.A. Equatorial plasma bubbles: Variations of occurrence and spatial scale in local time, longitude, season, and solar activity. J. Geophys. Res.: Space Phys. 2017, vol. 122, pp. 5743-5755. DOI: 10.1002/2017JA024128. Saito S., Yoshihara T. Evaluation of extreme ionospheric total electron content gradient associated with plasma bubbles for GNSS Ground-Based Augmentation System. Radio Sci. 2017. Vol. 52. P. 951-962. DOI: 10.1002/2017RS006291. Sreeja V., Aquino M., Jong K. Impact of the 24 September 2011 solar radio burst on the performance of GNSS receivers. Space Weather. 2013, vol. 11, pp. 306-312. DOI: 10.1002/ swe.20057. Shi C., Liu J. GNSS status and developments in China. Civil Global Positioning System Service Interface Committee, 46th meeting. Fort Worth, Texas, September 26. 2006. Vadakke S.V., Aquino M., Marques H.A., Moraes A. Mitigation of ionospheric scintillation effects on GNSS precise point positioning (PPP) at low latitudes. J. Geodesy. 2020, vol. 94, 15. DOI: 10.1007/s00190-020-01345-z. Siscoe G., Crooker N.U., Clauer C. Dst of the Carrington storm of 1859. Adv. Space Res. 2006. Vol. 38, no. 2. P. 173-179. DOI: 10.1016/j.asr.2005.02.102. Vani B.C., Forte B., Monico J.F.G., Skone S., Shimabukuro M.H., Moraes A., Portellla I.P., Marques H.A. A Novel Approach to Improve GNSS Precise Point Positioning During Strong Ionospheric Scintillation: Theory and Demonstration. IEEE Transactions on Vehicular Technology. 2019, vol. 68, no 5, pp. 4391-4403. DOI: 10.1109/TVT.2019.2903988. Skone S., Shrestha S.M. Limitations in DGPS positioning accuracies at low latitudes during solar maximum. Geophys. Res. Lett. 2002. Vol. 29, no. 10. P. 81-1-81-4. DOI: 10.1029/ 2001GL013854. Vdovin V.S., Dvorkin V.V., Karpik A.P., Lipatnikov L.A., Sorokin S.D., Steblov G.M. Current state and future development of active satellite geodetic networks in Russia and their integration into ITRF. Vestnik SGUGiT [Vestnik (Bulletin) of the Siberian State University of Geosystems and Technologies (SSUGT)]. 2018, vol. 23, no. 1, pp. 6-27. (In Russian). Smith J., Heelis R.A. Equatorial plasma bubbles: Variations of occurrence and spatial scale in local time, longitude, season, and solar activity. J. Geophys. Res.: Space Phys. 2017. Vol. 122. P. 5743-5755. DOI: 10.1002/2017JA024128. Warnant R., Lejeune S., Bavier M. Space weather influence on satellite-based navigation and precise positioning. Space Weather. 2007, vol. 344, pp. 129-146. DOI: 10.1007/1-4020-5446-7_14. Sreeja V., Aquino M., Jong K. Impact of the 24 September 2011 solar radio burst on the performance of GNSS receivers. Space Weather. 2013. Vol. 11. P. 306-312. DOI: 10.1002/ swe.20057. Yakovlev O.I. Kosmicheskaya radiofizika [Space radio physics]. Voronezh, Nauchnaya kniga Publ., 1998, 432 p. (In Russian). Vadakke S.V., Aquino M., Marques H.A., et al. Mitigation of ionospheric scintillation effects on GNSS precise point positioning (PPP) at low latitudes. J. Geodesy. 2020. Vol. 94, 15. DOI: 10.1007/s00190-020-01345-z. Yasyukevich Y., Astafyeva E., Padokhin A., Ivanova V., Syrovatskii S., Podlesnyi A. The 6 September 2017 X-class solar flares and their impacts on the ionosphere, GNSS, and HF radio wave propagation. Space Weather. 2018, vol. 16, pp. 1013-1027. DOI: 10.1029/2018SW001932. Vani B.C., Forte B., Monico J.F.G., et al. A Novel Approach to Improve GNSS Precise Point Positioning During Strong Ionospheric Scintillation: Theory and Demonstration. IEEE Transactions on Vehicular Technology. 2019. Vol. 68, no. 5. P. 4391-4403. DOI: 10.1109/TVT.2019.2903988. Yasyukevich Yu.V., Kiselev A.V., Zhivetiev I.V., Edemskiy I.K., Syrovatskii S.V., Maletckii B.M., Vesnin A.M. SIMuRG: System for Ionosphere Monitoring and Research from GNSS. GPS Solutions. 2020a, vol. 24, 69. DOI: 10.1007/s10291-020-00983-2. Warnant R., Lejeune S., Bavier M. Space weather influence on satellite-based navigation and precise positioning. Space Weather. 2007. Vol. 344. P. 129-146. DOI: 10.1007/1-4020-5446-7_14. Yasyukevich Y., Vasilyev R., Ratovsky K. Small-scale ionospheric irregularities of auroral origin at mid-latitudes during the 22 June 2015 magnetic storm and their effect on GPS positioning. Remote Sensing. 2020b, vol. 12, no 10, 1579. DOI: 10.3390/rs12101579. Yasyukevich Y., Astafyeva E., Padokhin A., et al. The 6 September 2017 X-class solar flares and their impacts on the ionosphere, GNSS, and HF radio wave propagation. Space Weather. 2018. Vol. 16. P. 1013-1027. DOI: 10.1029/2018S W001932. Yasyukevich Yu.V., Syrovatskiy S.V., Padokhin A.M., Frolov V.L., Vesnin A.M., Zatolokin D.A., Kurbatov G.A., Zagretdinov R.V., Pershin A.V., Yasyukevich A.S. GPS positioning accuracy in different modes with active forcing on the ionosphere from the SURA high-power HF radiation. Radiophysics and Quantum Electronics. 2020s, vol. 62, pp. 807-819. DOI: 10.1007/s11141-020-10026-y. Yasyukevich Yu.V., Kiselev A.V., Zhivetiev I.V., et al. SIMuRG: System for Ionosphere Monitoring and Research from GNSS. GPS Solutions. 2020a. Vol. 24, 69. DOI: 10.1007/s10291-020-00983-2. Yasyukevich Yu.V., Yasyukevich A.S., Astafyeva E.I. How modernized and strengthened GPS signals enhance the system performance during solar radio bursts. GPS Solutions. 2021, vol. 25, 46. DOI: 10.1007/s10291-021-01091-5. Yasyukevich Y., Vasilyev R., Ratovsky K. Small-scale ionospheric irregularities of auroral origin at mid-latitudes during the 22 June 2015 magnetic storm and their effect on GPS positioning. Remote Sensing. 2020b. Vol. 12, no. 10. P. 1579. DOI: 10.3390/rs12101579. Yermolaev Y.I., Lodkina I.G., Nikolaeva N.S., Yermolaev M.Y. Occurrence rate of extreme magnetic storms. J. Geophys. Res.: Space Phys. 2013, vol. 118, pp. 4760-4765. DOI: 10.1002/jgra.50467. Yasyukevich Yu.V., Syrovatskiy S.V., Padokhin A.M., et al. GPS positioning accuracy in different modes with active forcing on the ionosphere from the SURA high-power HF radiation. Radiophysics and Quantum Electronics. 2020с. Vol. 62. P. 807-819. DOI: 10.1007/s11141-020-10026-y. Zakharov V.I., Chernyshov A.A., Miloch W., Jin Y. Influence of the ionosphere on the parameters of the GPS navigation signals during a geomagnetic substorm. Geomagnetism and Aeronomy. 2020, vol. 60, pp. 754-767. DOI: 10.1134/S00 16793220060158. Yasyukevich Yu.V., Yasyukevich A.S., Astafyeva E.I. How modernized and strengthened GPS signals enhance the system performance during solar radio bursts. GPS Solutions. 2021. Vol. 25, 46. DOI: 10.1007/s10291-021-01091-5. Zatolokin D.A. Programma resheniya navigatsionnoi zadachi GNSS «Navi»: Svidetel’stvo o gosudarstvennoi registratsii programmy EVM № 2020612010 [Program Navi for GNSS positioning. Certificate of State Registration No. 2020612010]. 2020. (In Russian). Yermolaev Y.I., Lodkina I.G., Nikolaeva N.S., Yermolaev M.Y. Occurrence rate of extreme magnetic storms. J. Geophys. Res.: Space Phys. 2013. Vol. 118. P. 4760-4765. DOI: 10.1002/jgra.50467. Zherebtsov G.A. Complex of heliogeophysical instruments of new generation. Solar-Terr. Phys. 2020, vol. 6, no. 2, pp. 3-13. DOI: 10.12737/stp-62202001. Zhang X., Guo F., Zhou P. Improved precise point positioning in the presence of ionospheric scintillation. GPS Solutions. 2014. Vol. 18. P. 51-60. DOI: 10.1007/s10291-012-0309-1. Zhang X., Guo F., Zhou P. Improved precise point positioning in the presence of ionospheric scintillation. GPS Solutions. 2014, vol. 18, pp. 51-60. DOI: 10.1007/s10291-012-0309-1. Zhou F., Dong D., Li W., et al. GAMP: An open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations. GPS Solutions. 2018. Vol. 22, 33. DOI: 10.1007/s10291-018-0699-9. Zhou F., Dong D., Li W., Jiang X., Wickert J., Schuh H. GAMP: An open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations. GPS Solutions. 2018, vol. 22, 33. DOI: 10.1007/s10291-018-0699-9. Zumberge J. F., Heflin M.B., Jefferson D.C. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res.: Solid Earth. 1997. Vol. 102, no. B3. P. 5005-5017. DOI: 10.1029/96JB03860. Zumberge J.F., Heflin M.B., Jefferson D.C. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res.: Solid Earth. 1997, vol. 102, no. B3. pp. 5005-5017. DOI: 10.1029/96JB03860. URL: https://qzss.go.jp/en/technical/download/pdf/ps-is-qzss/is-qzss-l6-001.pdf (дата обращения 1 февраля 2021 г.). URL: https://qzss.go.jp/en/technical/download/pdf/ps-is-qzss/is-qzss-l6-001.pdf (accessed February 1, 2021). URL: https://www.isro.gov.in/sites/default/files/irnss_sps_ icd_version1.1-2017.pdf (дата обращения 1 февраля 2021 г.). URL: https://www.isro.gov.in/sites/default/files/irnss_sps_ icd_version1.1-2017.pdf (accessed February 1, 2021). URL: https://www.sonel.org (дата обращения 1 февраля 2021 г.). URL: https://www.sonel.org (accessed February 1, 2021). URL: https://hive.geosystems.aero (дата обращения 1 февраля 2021 г.). URL: https://hive.geosystems.aero (accessed February 1, 2021). URL: https://eft-cors.ru (дата обращения 1 февраля 2021 г.). URL: https://eft-cors.ru (accessed February 1, 2021). URL: https://kb.igs.org/hc/en-us/articles/201096516-IGS-Formats (дата обращения 1 февраля 2021 г.). URL: https://kb.igs.org/hc/en-us/articles/201096516-IGS-Formats (accessed February 1, 2021). URL: http://gps.ece.cornell.edu/briefs.php (дата обращения 25 марта 2021 г.). URL: http://gps.ece.cornell.edu/briefs.php (accessed March 25, 2021). URL: https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/rstn-1-second (дата обращения 25 марта 2021 г.). URL: https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/rstn-1-second (accessed March 25, 2021). URL: https://gps.gov/technical/icwg/IS-GPS-200J.pdf (дата обращения 1 февраля 2021 г.). URL: https://gps.gov/technical/icwg/IS-GPS-200J.pdf (accessed March 25, 2021). URL: https://www.nstb.tc.faa.gov/DisplayArchive.htm (дата обращения 1 февраля 2021 г.). URL: https://www.nstb.tc.faa.gov/DisplayArchive.htm (accessed February 1, 2021). URL: ftp://ftp.ngdc.noaa.gov/STP/swpc_products/daily_reports /solar_event_reports (дата обращения 1 февраля 2021 г.). URL: ftp://ftp.ngdc.noaa.gov/STP/swpc_products/daily_reports /solar_event_reports (accessed February 1, 2021). URL: https://omniweb.sci.gsfc.nasa.gov (дата обращения 25 марта 2021 г.). URL: https://omniweb.sci.gsfc.nasa.gov (accessed March 25, 2021). URL: https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/radio-bursts/reports/fixed-frequency-listings (дата обращения 1 февраля 2021 г.). URL: https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/radio-bursts/reports/fixed-frequency-listings (accessed February 1, 2021).