FDOA Determination of Velocities and Emission Frequencies of Passive Radiotransmitters in Space

  • Jose M. Gambi
  • Michael M. Tung
  • Maria L. García del Pino
  • Javier Clares
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

Two systems of FDOA equations are introduced to determine in real time the velocities of passive, i.e. non-cooperative, radiotransmitters at the emission instants of the signals, together with the frequencies of emission. The systems correspond to the Newtonian and post-Newtonian frameworks of the Earth surrounding space. The transmitters may be located on the Earth surface or in space. Each system yields accurate unique solutions at the corresponding level of approximation, provided that the locations are determined by appropriated TDOA measurements. The systems are derived by means of Synge’s world functions for the vicinity of the Earth, since it allows to clearly identify the post-Newtonian corrections due to the Earth tidal potential and to the gravitational signals’ time delays.

References

  1. 1.
    Bahder, T.B.: Navigation in curved space-time. Am. J. Phys. 69, 315–321 (2001)Google Scholar
  2. 2.
    Clarke, C.J.S.: Synge world function. In: Encyclopedia of Mathematics. Springer, Berlin (2011). http://www.encyclopediaofmath.org/index.php?title=Synge_world_function&oldid=18235
  3. 3.
    Gambi, J.M., Rodriguez-Teijeiro, M.C., García del Pino, M.L., Salas, M.: Shapiro time-delay within the geolocation problem by TDOA. IEEE Trans. Aerosp. Electron. Syst. 47(3), 1948–1962 (2011)Google Scholar
  4. 4.
    Gambi, J.M., Rodriguez-Teijeiro, M.C., García del Pino, M.L.: The post-Newtonian geolocation problem by TDOA. In: M. Günter, A. Bartel, M. Brunk, S. Schöps, M. Striebel (eds.) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry, vol. 17, pp. 489–495. Springer, Berlin (2012)CrossRefGoogle Scholar
  5. 5.
    Gambi, J.M., Clares, J., García del Pino, M.L.: FDOA post-Newtonian equations for the location of passive emitters placed in the vicinity of the earth. Aerosp. Sci. Technol. 46, 137–145 (2015)Google Scholar
  6. 6.
    Gambi, J.M., Rodriguez-Teijeiro, M.C., García del Pino, M.L.: Newtonian and post-Newtonian passive geolocation by TDOA. Aerosp. Sci. Technol. 51, 18–25 (2016)Google Scholar
  7. 7.
    Gambi, J.M., Clares, J., Rodriguez-Teijeiro, M.C.: Post-Newtonian geolocation of passive radio transmitters by TDOA and FDOA. In: G.R. Russo, V. Capasso, G. Nicosia, V. Romano (eds.) Progress in Industrial Mathematics at ECMI 2014. Mathematics in Industry, vol. 21. Springer, Berlin (2016)Google Scholar
  8. 8.
    Hazewinkel, M.: Synge world function. In: Hazewinkel, M. (ed.) Encyclopaedia of Mathematics: Supplement, vol. 1, pp. 464–465. Kluwer Academic Pub., Dordrecht (2012)Google Scholar
  9. 9.
    Synge, J.L.: Relativity: The General Theory, chap. 2. North-Holland, Amsterdam (1960)Google Scholar
  10. 10.
    Teyssandier, P., Le Poncin-Lafitte, C., Linet, B.: A universal tool for determining the time delay and the frequency shift of light: Synge’s world function. In: H. Dittus, C. Lämmerzahl, S.G. Turyshev (eds.) Lasers, Clocks and Drag-Free Control, pp. 153–180. Springer, Berlin (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Jose M. Gambi
    • 1
  • Michael M. Tung
    • 2
  • Maria L. García del Pino
    • 3
  • Javier Clares
    • 4
  1. 1.Gregorio Millán InstituteUniv. Carlos III de MadridMadridSpain
  2. 2.Instituto de Matemática MultidisciplinarUniv. Politècnica de ValènciaValenciaSpain
  3. 3.Department of Mathematics, I.E.S. AlpajesAranjuez, MadridSpain
  4. 4.Department of PhysicsUniv. Carlos III de MadridMadridSpain

Personalised recommendations