Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32731
Appraisal of Relativistic Effects on GNSS Receiver Positioning

Authors: I. Yakubu, Y. Y. Ziggah, E. A. Gyamera

Abstract:

The Global Navigation Satellite System (GNSS) started with the launch of the United State Department of Defense Global Positioning System (GPS). GNSS systems has grown over the years to include: GLONASS (Russia); Galileo (European Union); BeiDou (China). Any GNSS architecture consists of three major segments: Space, Control and User Segments. Errors such as; multipath, ionospheric and tropospheric effects, satellite clocks, receiver noise and orbit errors (relativity effect) have significant effects on GNSS positioning. To obtain centimeter level accuracy, the impacts of the relative motion of the satellites and earth need to be taken into account. This paper discusses the relevance of the theory of relativity as a source of error for GNSS receivers for position fix based on available relevant literature. Review of relevant literature reveals that due to relativity; Time dilation, Gravitational frequency shift and Sagnac effect cause significant influence on the use of GNSS receivers for positioning by an error range of ± 2.5 m based on pseudo-range computation.

Keywords: GNSS, relativistic effects, pseudo-range, accuracy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 266

References:


[1] Aboelmagd N, Karmat T, and Georgy J. (2013), “Satellite-Based Positioning and their Integration”, Fundamentals of Inertial Navigation, 1st Edition. New York: Springer-Verlag Berlin Heidelberg.
[2] Ashby, N., (2014), Relativity in GNSS, Springer, Berlin Heidelberg, pp. 509-525.
[3] Askne, J. and Nordius, H., (1987), “Estimation of tropospheric delay for microwaves from surface weather data” Radio science, Vol. 22, No. 3, pp. 379 - 386.
[4] Badder, T. B. (2001), “Navigation in curved space-time”, Am. J. Phys, Vol. 69, pp 315 - 321.
[5] Beitler, A., Tollkühn, A., Giustiniano, D. and Plattner, B., (2015}, CMCD: Multipath detection for mobile GNSS receivers. In Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, pp. 455-464.
[6] Bialyk, I., Byalyk, M. and Chernyaha, P. (2002), “Influence of relativistic distortion of space-time on preciseness of GPS-measurements” Modern achievements of geodesic science and industry, Vol.1, No. 7, pp. 85 - 88.
[7] Bialyk, I., Stepanchenko, O. and Wójcik, W., (2018). “Mathematical model of calculating metric tensor and GNSS-observations errors taking into account relativistic effects”, International Journal of Electronics and Telecommunications, Vol. 64, No. 3, pp. 379 - 384.
[8] Bijjahalli, S., Ramasamy, S. and Sabatini, R., (2016), “A GNSS Integrity Augmentation System for Sustainable Autonomous Airside Operations” In 2nd International Symposium on Sustainable Aviation, Istanbul, Turkey.
[9] Bohinec, J. (2014), “Relativistic Global Navigation Satellite Systems”, Seminar 1 – 1st year, Physics 2nd stage, Ljubljana, 11pp.
[10] Braasch, M. S. (2001), “Performance comparison of multipath mitigation receiver architecture”, In IEEE Aerospace Conference, Vol. 3, pp. 1309 – 1315.
[11] Čadež, A., Kostić, U., Delva, P., Carloni, S. and Čadež, A. (2011), “Mapping the Spacetime Metric with a Global Navigation Satellite System–extension of study: Recovering of orbital constants using inter-satellites links”, Ariadna Final Report ID, Vol. 9, 1301 pp.
[12] Calero, D., Fernandez, E. and Pares, M.E. (2016), “Positioning performance of chip-scale atomic clock GNSS augmentation systems” In 2016 8th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC), pp. 1-7.
[13] De Lacy, M. C., Gil, A. J., Rodriguez-Caderot, G. and Moreno, B. (2008), “A method to estimate the ionospheric bias by using the new GNSS frequencies: an analysis of its theoretical accuracy in a PPP context”, Fisica de la Tierra, Vol. 20, pp. 133-150.
[14] Einstein, A. (1922), “The general theory of relativity”, In The Meaning of Relativity, pp. 54-75.
[15] Farrell, J. L. (2008), “Robust Design for GNSS Integration”, Proceedings of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 1596-1599.
[16] Fernandes, M.J., Lázaro, C., Nunes, A.L., Pires, N., Bastos, L. and Mendes, V. B. (2010), “GNSS-derived path delay: An approach to compute the wet tropospheric correction for coastal altimetry”, IEEE Geoscience and Remote Sensing Letters, Vol. 7, No. 3, pp. 596 - 600.
[17] G. Seeber. (2003), Satellite Geodesy. Walter de Gruyter - Berlin - New York.
[18] Galperin, E. A. (2009), “Information transmittal, time uncertainty and special relativity”, Computers and Mathematics with Applications, Vol. 57, pp. 1554 - 1573.
[19] Gjevestad, J.G. and Grøn, Ø. (2013), “On the Global Navigation Satellite Systems and Relativity”, pp. 32-39.
[20] Gualdino, C., M., R. (2011), “Relativity in Engineering – Characteristics and Performance of Global Positioning Systems”, Published project work, Technical University of Lisbon, 10pp.
[21] Håkansson, M., Jensen, A.B., Horemuz, M. and Hedling, G. (2017), “Review of code and phase biases in multi-GNSS positioning”, GPS Solutions, Vol. 21, No. 3, pp. 849 - 860.
[22] Hećimović, Z. (2013), “Relativistic Effects on Satellite Navigation”, Technical Gazette, Vol. 20, No. 1, pp. 195 - 205.
[23] Hofmann-Wellenhof, B., Lichtenegger, H. and Wasle, E. (2008), GNSS Global Navigation Satellite Systems. Springer Wien New York.
[24] Huang, Z. and Yuan, H. (2014), “Ionospheric single-station TEC short-term forecast using RBF neural network” Radio Science, Vol. 49, No. 4, pp. 283 - 292.
[25] Humphreys, T. (2017), “Interference”, Springer Handbook of Global Navigation Satellite Systems, pp. 469 - 503.
[26] Irsigler, M. and Eissfeller, B. (2003), “Comparison of multipath mitigation techniques with consideration of future signal structures”, Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp 2584 - 2592.
[27] Jacobsen, K.S. and Dähnn, M. (2014), “Statistics of ionospheric disturbances and their correlation with GNSS positioning errors at high latitudes”, Journal of Space Weather and Space Climate, Vol. 4, 27pp.
[28] Januszewski, J. (2005), “GPS Vertical Accuracy for Different Constellations”, Scientific Journals of the Maritime University of Szczecin, Vol. 6, No. 78. pp. 181-190.
[29] Januszewski, J. (2010), Systemy satelitarne GPS, Galileoi inne. Warszawa: Wydawnictwo Naukowe PWN.
[30] Jin S. (2012), “Global Navigation Satellite Systems Signal” In Tech Theory and Applications Croatia.
[31] Jo, B. C. and Kim, S. (2010), “Multipath interference cancellation technique for high precision tracking in GNSS receiver”, IEICE transactions on communications, Vol. 93, No. 7, pp.1961-1964.
[32] Kaplan E., Hegarty C. (2006), Understanding GPS Principles and Applications. Norwood, MA, USA: ARTECH HOUSE, Inc.
[33] Karaim, M., Elsheikh, M., Noureldin, A. and Rustamov, R. B. (2018), “GNSS error sources”, Multifunctional Operation and Application of GPS, pp. 69 - 85.
[34] Kim H., and Lee H. (2009), “Compensation of time alignment error in heterogeneous GPS receivers”, Proceedings of the 13th IAIN World Congress, pp. 27-30
[35] Kulbiej, E. (2016), “Relevance of Relativistic Effects in Satellite Navigation”, Scientific Journals of the Maritime University of Szczecin, Vol. 47, No. 119, pp 85 -90.
[36] Leick, A. (2004), GPS Satellite Surveying. John Wiley & Sons, Inc.
[37] Lesouple, J., Robert, T., Sahmoudi, M., Tourneret, J. Y. and Vigneau, W. (2018), “Multipath mitigation for GNSS positioning in an urban environment using sparse estimation”, IEEE Transactions on Intelligent Transportation Systems, Vol. 20, No. 4, pp.1316 -1328.
[38] Li, G., Wu, J., Zhao, C. and Tian, Y. (2017), “Double differencing within GNSS constellations”, GPS Solutions, Vol. 21, No. 3, pp.1161-1177.
[39] MacGougan, G., Lachapelle, G., Nayak, R. and Wang, A. (2001), “Overview of GNSS signal degradation phenomena”, In Proceedings of the International Symposium Kinematic Systems and Geodesy, Geomatics and Navigation.
[40] Martinez, F.G. and Waller, P. (2009), “GNSS clock prediction and integrity”, In 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum, pp. 1137-1142.
[41] Matolcsi, T.; Matolcsi, M. (2008) “Coordinate time and proper time in the GPS”, Eur. J. Phys, Vol. 29, pp. 1147 - 1151.
[42] Misra, P. and Enge, P. (2005), Global position systems: Signals, measurements and performance, Ganga-Jamuna Press.
[43] Moreno Monge, B. (2012), Development of algorithms for the GNSS data processing: their application to the modernized GPS and Galileo scenarios.
[44] Moreno, B., Radicella, S., de Lacy, M. C., Herraiz, M. and Rodriguez-Caderot, G. (2011), “On the effects of the ionospheric disturbances on precise point positioning at equatorial latitudes”, GPS Solutions, Vol. 15, No. 4, pp. 381- 390.
[45] Munekane, H. (2005), “A semi-analytical estimation of the effect of second-order ionospheric correction on the GPS positioning Geophysical”, Journal International, Vol.163, No. 1, pp. 10 - 17.
[46] Murphy, T. A. (1998) Local-area Augmentation System for satellite navigation precision approach system. U.S. Patent 5,786,773.
[47] Narkiewicz, J. (1999), Fundamentals of navigation systems. Warsaw: Communication and Communication Publishing.
[48] Narkiewicz, J. (2007), GPS and other satellite reference systems. Warsaw: Publications and Communications Publishing.
[49] Novatel, (2023), “An Introduction to GNSS”, https://novatel.com/an-introduction-to-gnss/chapter-4-gnsserror-sources.
[50] Oethler, V. Krueger, J. M. Beck, T. Kirchner, M. Trautenberg, H. L. Hahn, J. and Blonski, D. (2009), “Galileo System Performance Status Report”, In ION GNSS, Vol. 14, pp. 547 - 568.
[51] Parkinson, B.W., Enge, P., Axelrad, P. and Spilker Jr, J.J. (1998), “Global positioning system: Theory and applications”, American Institute of Aeronautics and Astronautics, Vol. 2.
[52] Pascual‐Sánchez, J. F. (2007), “Introducing relativity in global navigation satellite systems” Annalen der Physik, Vol. 519, No. 4, pp. 258 - 273.
[53] Peres, T. R. (2008), “Multipath mitigation techniques suitable for low cost GNSS receivers”, Instituto Superior Técnico, pp. 20 - 56.
[54] Rizos, C., van Cranenbroeck, J. and Lui, V. (2010), “Advances in GNSS-RTK for structural deformation monitoring in regions of high ionospheric activity”, FIG Congress.
[55] Roguirie, S., Carrié, G., Vincent, F., Ries, L. and Monnerat, M. (2012), “A new multipath mitigation method for GNSS receivers based on an antenna array”, International Journal of Navigation and Observation.
[56] Rovira-Garcia, A., Ibáñez-Segura, D., Orús-Perez, R., Juan, J. M., Sanz, J. and González-Casado, G. (2020), “Assessing the quality of ionospheric models through GNSS positioning error methodology and results”, Gps solutions, Vol. 24, No. 1, 4pp.
[57] Skog, I., (2007), “GNSS-aided INS for land vehicle positioning and navigation”, Doctoral dissertation, KTH.
[58] Su, C. C. (2001), “On the Sagnac effect in wave propagation”, Journal of electromagnetic waves and applications, Vol. 15, No. 7, pp. 945 - 955.
[59] Walter, T. and Blanch, J. (2015), “Characterization of GNSS clock and ephemeris errors to support ARAIM”, In Proceedings of the ION 2015 Pacific PNT Meeting, pp. 920-931.
[60] Wung, N., Yuan, Y., Li, Z. and Huo, X. (2013), “Impact of ionospheric correction on single-frequency GNSS positioning”, In China Satellite Navigation Conference (CSNC) 2013 Proceedings, pp. 471- 486.
[61] Gao, Y., Liu, Z. and Liu, Z. Z. (2012), “Internet Based Real-Time Kinematic Positioning”, GPS Solutions, Vol. 5, No. 3, pp. 61 - 69.
[62] Zaidman, S. (2008), “Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard”, Department of Transportation USA, Federal Aviation Administration.
[63] Zhong, J., Lei, J., Yue, X. and Dou, X. (2016), “Determination of differential code bias of GNSS receiver onboard low Earth orbit satellite”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No., pp. 4896 - 4905.
[64] Zhu, S. Y. and Groten, E. (1988), “Relativistic effects in GPS”. Lecture notes in Earth Sciences, pp 41- 46.