GPS Solutions

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

Simplified equivalent multiple baseline solutions with elevation-dependent weights

Original Article

Abstract

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.

Keywords

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

Notes

Acknowledgments

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.

References

  1. Leick A (2004) GPS satellite surveying, 3rd edn. Wiley, New YorkGoogle Scholar
  2. Li B, Shen Y, Xu P (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chin Sci Bull 53(20):3219–3225. doi: 10.1007/s11434-008-0293-6
  3. Schaffrin B, Grafarend E (1986) Generating classes of equivalent linear models by nuisance parameter elimination, applications to GPS observations. Manuscr Geod 11:262–271Google Scholar
  4. Shen Y, Xu G (2008) Simplified equivalent representation of GPS observation equations. GPS Solut 12:99–108. doi: 10.1007/s10291-007-0070-z CrossRefGoogle Scholar
  5. Teunissen P (1997) GPS double difference statistics: with and without using satellite geometry. J Geod 71:137–148. doi: 10.1007/s001900050082 CrossRefGoogle Scholar
  6. Wang J, Stewart M, Tsakiri M (1998) Stochastic modelling for GPS static baseline data processing. J Surv Eng 124:171–181. doi: 10.1061/(ASCE)0733-9453(1998)124:4(171) CrossRefGoogle Scholar
  7. Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geod 76(2):95–104. doi: 10.1007/s00190-001-0225-6 CrossRefGoogle Scholar
  8. Xu G (2002) GPS data processing with equivalent observation equations. GPS Solut 6(1–2):28–33. doi: 10.1007/s10291-002-0009-3 CrossRefGoogle Scholar

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

Personalised recommendations