Introduction of the Runge-Kutta method in GPS orbit computation

Yıl 2024, , 256 - 263, 28.07.2024

Sid Ahmed Medjahed

https://doi.org/10.26833/ijeg.1403435

Öz

In all Global Navigation Satellite Systems (GNSS) applications, the determination of the satellite orbits is an important task. In this study, we present the equations given in the Interface Specification Document of GPS and the Runge-Kutta method in the computation of the position P, velocity V, and acceleration A of the GPS satellites using the broadcast ephemeris. The definition of the differential equation describing the GPS satellite's motion has enabled us to introduce the Runge-Kutta method in the GPS orbit computation; this method uses the initial conditions determined in this study from the Keplerian elements provided in the broadcast ephemeris files. The Lagrange interpolation method is used for comparison of the results, where the vectors P, V, and A are estimated using the precise ephemeris. The difference not exceeding 2.4 m was obtained in the X, Y, and Z axes during seven days on the position of the GPS satellite number 9 tested in this study. In velocity and acceleration, the difference is about a few mm/s and mm/s2, respectively.

Anahtar Kelimeler

Broadcast ephemeris, IS-GPS algorithm, Runge-Kutta method, Precise ephemeris, Lagrange interpolation

Kaynakça

• Hofmann-Wellenhof, B., Lichtenegger, H., & Wasle, E. (2007). GNSS–global navigation satellite systems: GPS, GLONASS, Galileo, and more. Springer Science & Business Media.
• IS-GPS (2022). Interface specification document: Navstar GPS Space Segment/Navigation User Segment Interfaces.
• Medjahed, S. A., Niati, A., Kheloufi, N., & Taibi, H. (2021). Implementation of the variation of the luni-solar acceleration into GLONASS orbit calculus. Geodetski Vestnik, 65(3), 459-471. https://doi.org/10.15292/geodetski-vestnik.2021.03.459-471
• ICD-GLONASS. (2016). Interface control document: General Description of Code, Interface Control Document. Edition 1.0. Moscow.
• El-naggar, A. M. (2012). New method of GPS orbit determination from GCPS network for the purpose of DOP calculations. Alexandria Engineering Journal, 51(2), 129-136. https://doi.org/10.1016/j.aej.2012.06.002
• Ferrão, P. F. F. N. (2013). Positioning with combined GPS and glonass observations. [Master’s Thesis., Técnico Lisboa].
• Roßbach, U. (2001). Positioning and navigation using the Russian satellite system GLONASS. Universitat der Bundeswehr München, Studiengang Geodäsie und Geoinformationen.
• GPS.gov. (2023). Interface Control Documents. https://www.gps.gov/technical/icwg
• Remondi, B. W. (2004). Computing satellite velocity using the broadcast ephemeris. GPS solutions, 8(3), 181-183. https://doi.org/10.1007/s10291-004-0094-6
• Thompson, B. F., Lewis, S. W., Brown, S. A., & Scott, T. M. (2019). Computing GPS satellite velocity and acceleration from the broadcast navigation message. Navigation, 66(4), 769-779. https://doi.org/10.1002/navi.342
• Gurtner, W. (2013). The Receiver Independent Exchange Format RINEX, Version 3.02. International GNSS Service (IGS), RINEX Working Group and Radio Technical Commission for Maritime Services. Special Committee 104 (RTCM-SC104)
• Teunissen, P. J., & Montenbruck, O. (2017). Springer handbook of global navigation satellite systems. https://doi.org/10.1007/978-3-319-42928-1
• Subirana, J. S., Hernandez-Pajares, M., & Zornoza, J. M. J. (2013). GNSS Data Processing: Vol. I [Fundamentals and Algorithms]. ESA Communications.
• Tusat, E., & Ozyuksel, F. (2018). Comparison of GPS satellite coordinates computed from broadcast and IGS final ephemerides. International Journal of Engineering and Geosciences, 3(1), 12-19. https://doi.org/10.26833/ijeg.337806
• Ogaja, C. A. (2013). Appendix 3: Calculation of Satellite Position from Ephemeris Data. Applied GPS for Engineers and Project Managers. American Society of Civil Engineers, ASCE Library. https://ascelibrary.org/doi/book/10.1061/9780784411506#
• Montenbruck, O., & Gill, E. K. A. (2014). Models, Methods, and Applications. Satellite Orbits, 293-318. Springer.
• Vallado, D. A., & MacClain, W. D. (2013). Fundamentals of Astrodynamics and Applications. Space Technology Library, Microcosm Press.
• Lin, Y., Guo, H., & Yu, M. (2009). A Comparison for GLONASS Satellite Coordinate Calculation. 2009 International Conference on Information Engineering and Computer Science, 1-4. https://doi.org/10.1109/ICIECS.2009.5365110
• IGS. (2023). International GNSS Service. https://www.gps.gov/technical/icwg
• Hilla, S. (2016). The Extended Standard Product 3 Orbit Format (SP3-c). National Geodetic Survey, National Ocean Service, NOAA, Silver Spring, MD 20910-6233, USA.
• Wang, J., Li, Y., Zhu, H., & Ma, T. (2018). Interpolation method research and precision analysis of GPS satellite position. Journal of Systems Science and Information, 6(3), 277-288. https://doi.org/10.21078/JSSI-2018-277-12