Relativity of GPS measurement

Physical Review D

Volumn 68, Issue 6, 2003, Pages

  Bahder, Thomas B ^a  

^a U S ARMY RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; ELECTROMAGNETIC FIELD; GEOMETRY; GLOBAL POSITIONING SYSTEM; GRAVITY; MATHEMATICAL ANALYSIS; MEASUREMENT; MODEL; OPTICS; ROTATION; SIGNAL DETECTION; SPACE; TIME; VELOCITY;

EID: 0242384074     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.063005     Document Type: Article

References (36)

1. I. L. Chuang, Phys. Rev. Lett. 85, 2006 (2000); quant-ph/0004105.
2. R. Jozsa, D. S. Abrams, J. P. Dowling, and C. P. Williams, Phys. Rev. Lett. 85, 2006 (2000).
3. J. Preskill, quant-ph/0010098.
4. V. Giovannetti, S. Lloyd, and L. Maccone, Nature (London) 412, 417 (2001).
5. Y. Shih (unpublished).
6. E. A. Burt, C. R. Ekstrom, and T. B. Swanson, Phys. Rev. Lett. 87, 129801 (2001);
7. "A Reply to "Quantum Clock Synchronization," quant-ph/0007030.
8. R. Jozsa, D. S. Abrams, J. P. Dowling, and C. P. Williams, Phys. Rev. Lett. 87, 129802 (2001).
9. U. Yurtsever and J. P. Dowling, Phys. Rev. A 65, 052317 (2002).
10. Global Positioning System: Theory and Applications, Vols. I and II, edited by B. W. Parkinson and J. J. Spilker, Progress in Astronautics and Aeronautics, Vols. 163 and 164 (Amer. Inst. Aero. Astro., Washington, D.C., 1996).
11. E. D. Kaplan, Understanding CPS: Principles and Applications, Mobile Communications Series (Artech House, Boston, 1996).
12. B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, Global Positioning System Theory and Practice (Springer-Verlag, New York, 1993).
13. The Russian satellite system known as GLONASS is similar to GPS.
14. C. Rovelli, Phys. Rev. D 65, 044017 (2002).
15. M. Blagojevi, J. Garecki, F. W. Hehl, and Yu. N. Obukhov, Phys. Rev. D 65, 044018 (2002).
16. A. H. Krall and T. B. Bahder, J. Appl. Phys. 90, 6513 (2001).
17. Actually there are three main relativistic effects that contribute significantly, see Sec. II.
18. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, New York, Fourth Revised English edition, 1975).
19. M. Caputo, The Gravity Field of the Earth (Academic, New York, 1967).
20. N. Ashby and J. J. Spilker, in Global Positioning System: Theory and Applications, Vols. I and II, edited by B. W. Parkinson and J. J. Spilker, Progress in Astronautics and Aeronautics, Vols. 163 and 164 (Amer. Inst. Aero. Astro., Washington, D.C., 1996).
21. R. S. Nerem, F. J. Lerch, J. A. Marshall, E. C. Pavlis, B. H. Putney, B. D. Tapley, R. J. Eanes, J. C. Ries, B. E. Schutz, C. K. Shum, M. M. Watkins, S. M. Klosko, J. C. Chan, S. B. Luthcke, G. B. Patel, N. K. Pavlis, R. G. Williamson, R. H. Rapp, R. Biancale, and F. Nouel, J. Geophys. Res. 99, 24421 (1994b).
22. See J. J. Spilker, in Global Positioning System: Theory and Applications, Vols. I and II [9], Chap. 2.
23. Anonymous, "Navstar GPS Space Segment/Navigation User Interfaces," Revision C, Initial Release, ARINC Research Corporation, 10 October 1993, ICD-GPS-200.
24. J. L. Synge, Relativity: The General Theory (North-Holland, New York, 1960).
25. A. Kheyfets, "Spacetime geodesy," Weapons Laboratory, Air Force Systems Command, Kirtland Air Force Base, New Mexico, Technical Report No. WL-TN-90-13, 1991.
26. This statement neglects the correction needed due to the eccentricity of the satellite orbit, the so-called "e sin E effect."
27. V. Fock, The Theory of Space, Time and Gravitation (Pergamon, Oxford, England, 1964).
28. F. De Felice and C. J. S. Clarke, Relativity on Curved Manifolds, Cambridge Monographs on Mathematical Physics (Cambridge University Press, New York, 1990).
29. T. B. Bahder, Am. J. Phys. 69, 315 (2001).
30. (ab) are invariants under coordinate transformations, but they depend on the observer world line through the definition of the tetrad, see Ref. [23].
31. P. Ward, in E. D. Kaplan, Understanding GPS: Principles and Applications, Mobile Communications Series (Artech House, Boston, 1996), Chap. 5.
32. F. A. E. Pirani, Bull. Acad. Pol. D. Sci. Cl. III V, 143 (1957).
33. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
34. R. Omnes, The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994).
35. See also the discussion in J. Preskill, Lecture Notes for Physics 229: Quantum Information and Computation (California Institute of Technology, Pasadena, CA, 1998), http://www.theory.caltech.edu/people/preskill/ph229/
36. N. Ashby and M. Weiss, Global Positioning System Receivers and Relativity, NIST Technical Note 1385 (U.S. GPO Washington, D.C. 1999).