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

@article{Grafarend2002GPSSC, title={GPS Solutions: Closed Forms, Critical and Special Configurations of P4P}, author={E. Grafarend and Jeffrey J. Shan}, journal={GPS Solutions}, year={2002}, volume={5}, pages={29-41} }

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

#### Figures from this paper

#### Figures

35 Citations

A closed-form method for single-point positioning with six satellites in dual-GNSS constellations

- Computer Science
- 2016

2

Efficient Ambiguity Resolution in Wireless Localization Systems

- Mathematics, Computer Science
- IEEE Transactions on Industrial Informatics
- 2017

9

A comprehensive analysis of the geometry of TDOA maps in localisation problems

- Mathematics, Computer Science
- ArXiv
- 2014

24- PDF

TDOA-based Localization in Two Dimensions: the Bifurcation Curve

- Mathematics, Computer Science
- Fundam. Informaticae
- 2014

11- PDF

A closed-form of Newton method for solving over-determined pseudo-distance equations

- Mathematics
- Journal of Geodesy
- 2014

17

A novel divide and conquer approach for resolving ambiguities in wireless localization

- Mathematics, Computer Science
- 2016 IEEE World Conference on Factory Communication Systems (WFCS)
- 2016

1

Performance Comparison of Positioning Algorithms for Complex GPS Systems

- Computer Science
- 2012 32nd International Conference on Distributed Computing Systems Workshops
- 2012

5- PDF

#### References

SHOWING 1-10 OF 21 REFERENCES

An Algebraic Solution of the GPS Equations

- Mathematics
- IEEE Transactions on Aerospace and Electronic Systems
- 1985

262

Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

- Mathematics
- 1997

28

Closed form solution to the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates

- Mathematics
- 1997

20- PDF

Critical configurations (determinantal loci) for range and range difference satellite networks

- Geography
- 1973

14

Classroom Note: The Global Positioning System and the Implicit Function Theorem

- Mathematics, Computer Science
- SIAM Rev.
- 1998

7

A closed-form solution of the nonlinear pseudo-ranging equations (GPS)

- Artificial Satellites (Polish Academy of Sciences, Space Research Centre),
- 1996