The GPS equations and the Problem of Apollonius

  title={The GPS equations and the Problem of Apollonius},
  author={Joseph Hoshen},
  journal={IEEE Transactions on Aerospace and Electronic Systems},
  • J. Hoshen
  • Published 1 July 1996
  • Mathematics
  • IEEE Transactions on Aerospace and Electronic Systems
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… 

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