Advertisement

Positioning by Ranging Methods

  • Joseph L. Awange
  • Béla Paláncz
Chapter

Abstract

Throughout history, position determination has been one of the fundamental task undertaken by man on daily basis. Each day, one has to know where one is, and where one is going. To mountaineers, pilots, sailors etc., the knowledge of position is of great importance. The traditional way of locating one’s position has been the use of maps or campus to determine directions. In modern times, the entry into the game by Global Navigation Satellite Systems GNSS that comprise the Global Positioning System (GPS) , Russian based GLONASS and the proposed European’s GALILEO have revolutionized the art of positioning.

Keywords

Global Position System Global Navigation Satellite System Global Navigation Satellite System Global Position System Receiver Unknown Station 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abel JS, Chaffee JW (1991) Existence and uniqueness of GPS solutions. IEEE Trans Aerosp Electron Syst 27:952–956CrossRefGoogle Scholar
  2. 17.
    Awange JL (2002) Groebner bases, multipolynomial resultants and the Gauss-Jacobi combinatorial algorithms-adjustment of nonlinear GPS/LPS observations. Ph.D. thesis, Department of Geodesy and GeoInformatics, Stuttgart University, Germany. Technical reports, Report Nr. 2002 (1)Google Scholar
  3. 27.
    Awange JL, Grafarend EW (2002) Algebraic solution of GPS pseudo-ranging equations. J GPS Solut 4:20–32CrossRefGoogle Scholar
  4. 28.
    Awange JL, Grafarend EW (2002) Nonlinear adjustment of GPS observations of type pseudo-range. J GPS Solut 4:80–93CrossRefGoogle Scholar
  5. 35.
    Awange JL, Fukuda Y, Takemoto S, Ateya I, Grafarend EW (2003) Ranging algebraically with more observations than unknowns. Earth Planets Space 55:387–394CrossRefGoogle Scholar
  6. 44.
    Awange JL, Grafarend EW (2005) Solving algebraic computational problems in geodesy and geoinformatics. Springer, BerlinGoogle Scholar
  7. 60.
    Bancroft S (1985) An algebraic solution of the GPS equations. IEEE Trans Aerosp Electron Syst AES-21:56–59CrossRefGoogle Scholar
  8. 61.
    Bancroft S (1985) An algebraic solution of the GPS equations. IEEE Trans Aerosp Electron Syst AES-21:56–59CrossRefGoogle Scholar
  9. 116.
    Chaffee JW, Abel JS (1994) On the exact solutions of the pseudorange equations. IEEE Trans Aerosp Electron Syst 30:1021–1030CrossRefGoogle Scholar
  10. 220.
    Grafarend EW, Schaffrin B (1989) The geometry of nonlinear adjustment-the planar trisection problem-. In: Kejlso E, Poder K, Tscherning CC (eds) Festschrift to T. Krarup. Geodaetisk Institut, Copenhagen, 58:149–172Google Scholar
  11. 221.
    Grafarend EW, Schaffrin B (1991) The planar trisection problem and the impact of curvature on non-linear least-squares estimation. Comput Stat Data Anal 12:187–199CrossRefGoogle Scholar
  12. 223.
    Grafarend EW, Shan J (1996) Closed-form solution of the nonlinear pseudo-ranging equations (GPS). Artif Satell Planet Geod 31:133–147Google Scholar
  13. 246.
    Han SC, Kwon JH, Jekeli C (2001) Accurate absolute GPS positioning through satellite clock error estimation. J Geod, Berlin Heidelberg 75:33–43CrossRefGoogle Scholar
  14. 275.
    Hofman-Wellenhof B, Lichtenegger H, Collins J (2001) Global positioning system: theory and practice, 5th edn. Springer, WienCrossRefGoogle Scholar
  15. 296.
    Kahmen H, Faig W (1988) Surveying. Walter de Gruyter, BerlinCrossRefGoogle Scholar
  16. 301.
    Kleusberg A (1994) Die direkte Lösung des räumlichen Hyperbelschnitts. Zeitschrift für Vermessungswesen 119:188–192Google Scholar
  17. 302.
    Kleusberg A (2003) Analytical GPS navigation solution. In: Grafarend EW, Krumm FW, Schwarze VS (eds) Geodesy – the challenge of the 3rd millennium. Springer, Heidelberg, pp 93–96CrossRefGoogle Scholar
  18. 312.
    Krause LO (1987) A direct solution of GPS-type navigation equations. IEEE Trans Aerosp Electron Syst 23:225–232CrossRefGoogle Scholar
  19. 338.
    Lichtenegger H (1995) Eine direkte Lösung des räumlichen Bogenschnitts. Österreichische Zeitschrift für Vermessung und Geoinformation 83:224–226Google Scholar
  20. 395.
    Paláncz B, Awange JL, Grafarend EW (2007) Computer algebra solution of the GPS N-points problem. GPS Solut 11(4):1080. Springer, Heidelberg. http://www.springerlink.com/content/75rk6171520gxq72/. Accessed 1 Dec 2008
  21. 397.
    Paláncz B (2008) Introduction to linear homotopy, Wolfram Library Archive, MathSource. http://library.wolfram.com/infocenter/MathSource/7119/. Accessed 27 Aug 2008
  22. 430.
    Rinner K (1962) Über die Genauigkeit des räumlichen Bogenschnittes. Zeitschrift für Vermessungswesen 87:361–374Google Scholar
  23. 466.
    Singer P, Ströbel D, Hördt R, Bahndorf J, Linkwitz K (1993) Direkte Lösung des räümlichen Bogenschnitts. Zeitschrift für Vermessungswesen 118:20–24Google Scholar
  24. 475.
    Strang G, Borre K (1997) Linear algebra, geodesy and GPS. Wellesley Cambridge Press, WellesleyGoogle Scholar
  25. 478.
    Sturmfels B (1998) Introduction to resultants. Proc Symp Appl Math 53:25–39CrossRefGoogle Scholar
  26. 535.
    Xu P (2002) A hybrid global optimization method: the one-dimensional case. J Comput Appl Math 147:301–314CrossRefGoogle Scholar
  27. 536.
    Xu P (2003) A hybrid global optimization method: the multi-dimensional case. J Comput Appl Math 155:423–446CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Joseph L. Awange
    • 1
  • Béla Paláncz
    • 2
  1. 1.Curtin UniversityPerthAustralia
  2. 2.Budapest University of Technology and EconomicsBudapestHungary

Personalised recommendations