The GPS equations and the Problem of Apollonius

@article{Hoshen1996TheGE,
  title={The GPS equations and the Problem of Apollonius},
  author={Joseph Hoshen},
  journal={IEEE Transactions on Aerospace and Electronic Systems},
  year={1996},
  volume={32},
  pages={1116-1124}
}
  • Joseph Hoshen
  • Published 1996 in
    IEEE Transactions on Aerospace and Electronic…
By relating the Global Positioning System (GPS) problem of location to the ancient Problem of Apollonius, this work presents a closed solution to the pseudorange positioning problem for two and three dimensions The positioning problem, given by a set of nonlinear equations, has been reduced to the solution of a quadratic equation. The resulting expressions yield either two or one physically meaningful solutions for both the two- and three-dimensional problems. Expressions for the boundary… CONTINUE READING
Highly Cited
This paper has 42 citations. REVIEW CITATIONS
21 Citations
12 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 21 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 12 references

67—68 (for English translation see: Sir Isaac Newton’s Mathematical Principle of Natural Philosophy by F. Cajori

  • I. Newton
  • Philosophiae Naturalis Principia Mathematica…
  • 1687
Highly Influential
5 Excerpts

On the exact solution of the pseudorange equations

  • J. Chauffe, J. Abel
  • IEEE Transactions on Aerospace and Electronic…
  • 1994
Highly Influential
4 Excerpts

An alternative closed form solution to the GPS pseudorange equation

  • J. Leva
  • In Proceedings of the Institute of Navigation…
  • 1995
3 Excerpts

Keeping tabs on criminals

  • J. Hoshen, J. D. Sennott, M. Winkler
  • IEEE Spectrum,
  • 1995
1 Excerpt

High performance position tracker for embedded paging cellular telephone, and law enforcement applications

  • J. D. Sennott, R. Matusiak
  • In Proceedings of the 1992 IEEE Position Location…
  • 1992
1 Excerpt

A History of Mathematics

  • C. B. Boyer
  • New York: Wiley,
  • 1989
1 Excerpt

A Survey of Modern Algebra

  • G. Birkhoff, S. MacLane
  • New York: MacMillan,
  • 1977
1 Excerpt

Similar Papers

Loading similar papers…