Positioning configurations with minimum GDOP from orthogonal trigonometric functions

Shuqiang Xue, Yuanxi Yang, Wu Chen, Yamin Dang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


In this paper, single-point-positioning configurations with minimum GDOP employing orthogonal trigonometric functions are presented. The preconditions for minimizing the GDOP are introduced, and the set composed of all configurations with minimal GDOP is defined. Some properties of the minimum GDOP configurations, including the invariance of rotation and superposition, are detailed. For arbitrary given number n of control points, regular polygon solutions are immediately deduced from the orthogonal trigonometric functions. Based on the two dimensional configurations with minimum GDOP, three kinds of three dimensional configurations with minimum GDOP, including the cone configuration with cone angle 108.48°, the Descartes configuration, and the Walker configuration with inclination angle 54.74°, are discussed. The geometrical conditions of these configurations provide us some knowledge for GNSS constellation design.
Original languageEnglish
Pages (from-to)820-825
Number of pages6
JournalWuhan Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University
Issue number7
Publication statusPublished - 1 Jan 2014


  • Cone configuration
  • Descartes configuration
  • GDOP
  • Positioning configuration
  • Trigonometric functions
  • Walker configuration

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Earth-Surface Processes

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