GPS Solutions: Closed Forms, Critical and Special Configurations of P4P

  title={GPS Solutions: Closed Forms, Critical and Special Configurations of P4P},
  author={E. Grafarend and Jeffrey J. Shan},
  journal={GPS Solutions},
  • E. Grafarend, Jeffrey J. Shan
  • Published 2002
  • Mathematics
  • GPS Solutions
  • P4P is the pseudo-ranging 4-point problem as it appears as the basic configuration of satellite positioning with pseudo-ranges as observables. In order to determine the ground receiver/satellite receiver (LEO networks) position from four positions of satellite transmitters given, a system of four nonlinear (algebraic) equations has to be solved. The solution point is the intersection of four spherical cones if the ground receiver/satellite receiver clock bias is implemented as an unknown. Here… CONTINUE READING
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    An Algebraic Solution of the GPS Equations
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