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

Yunlong Teng, Qi Huang, Yongcai Ao, Yun Li

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


With the impact of the Global Navigation Satellite System (GNSS), dual-GNSS constellations are playing an increasingly significant role in positioning, navigation and timing (PNT) applications. Aiming at improving from the existing method, i.e., linearization, of solving the single-point positioning problem under a dual-GNSS, this paper develops a closed-form method for solving PNT problems in the case of six satellites. This method reduces the positioning problem to a simple mathematical problem of finding solutions to a quadratic equation, thereby needing only one receiver clock bias (RCB) as variable. By solving the RCB, the positioning information in three dimensions is obtained by utilizing a linear equation. Compared with the existing method, the closed-form method requires no initial position or iterations. This method thus provides a direct solution to single-point positioning. Further, how to check the uniqueness and the validity of the solutions is also derived. Experimental results verify the validity, applicability and efficiency of the proposed method.

Original languageEnglish
Pages (from-to)2280-2286
Number of pages7
JournalAdvances in Space Research
Issue number11
Early online date27 Jul 2016
Publication statusPublished - 1 Dec 2016


  • Global Navigation Satellite System (GNSS)
  • GPS positioning
  • positioning, navigation and timing (PNT)
  • receiver clock bias (RCB)


Dive into the research topics of 'A closed-form method for single-point positioning with six satellites in dual-GNSS constellations'. Together they form a unique fingerprint.

Cite this