GPS Solutions

, Volume 13, Issue 3, pp 165–171 | Cite as

Simplified equivalent multiple baseline solutions with elevation-dependent weights

  • Yunzhong ShenEmail author
  • Bofeng Li
  • Guochang Xu
Original Article


Since the assumption of all stations tracking the same satellites with identical weights was previously employed by Shen and Xu (GPS Solut 12:99–108, 2008) to derive the simplified GNSS single- and double-differenced equivalent equations, this supplementary paper expands these simplified equations in the case of each station tracking different satellites with elevation-dependent weights. Numerical experiments are performed to demonstrate the computational efficiency of the simplified equivalent algorithm relative to the traditional method in various scenarios of multi-baseline solutions with tracking different satellites. The fast computational speed of the simplified equivalent algorithm will potentially benefit the local, regional and even global GNSS multi-baseline solutions as well as the combined GNSS application.


GNSS data processing Multi-baseline solutions Equivalent representation Combined GNSS application 



This research is sponsored by the National Natural Science Foundations of China (Grant No. 40674003; 40874016). The authors are very grateful to the anonymous reviewers for their valuable comments and suggestions. The editor-in-chief, Professor Alfred Leick is sincerely appreciated for his constructive comments and polishing the manuscript.


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Surveying and Geo-informatics EngineeringTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Key Laboratory of Advanced Surveying Engineering of State Bureau of Surveying and MappingShanghaiPeople’s Republic of China
  3. 3.GeoForschungsZentrum Potsdam (GFZ)PotsdamGermany

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