Abstract
The single and double-differencing operation of GPS observations is effectively used to eliminate nuisance parameters of receiver- and satellite-specific biases. According to the theorem of equivalent representation, we develop the simplified equations that equivalently represent the single and double-differenced observation equations using corresponding pseudo-observations in single or multi-baseline solutions. The transformation of the covariance matrix of original observables is no longer necessary. Therefore, the algorithms are very convenient for programming and efficient in computation. The unbiased estimate of the variance of unit weight is also derived from equivalent observation equations. The simplified equations are verified by numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baksalary JK (1984) A study of the equivalence between a Gauss-Markoff model and its augmentation by nuisance parameters. Math Operationsforsch Statist Ser Statist 15:3-15
Cui X, Yu Z, Tao B, Liu D (2001) Generalized surveying adjustment (in Chinese). Wuhan Technique University of Surveying and Mapping, Wuhan
Hofmann-Wellenhof B, Lichtenegger H, Collins J (2001) GPS theory and practice, 5th edn. Springer, Wien
Leick A (2004) GPS satellite surveying, 3th edn. Wiley, New York
Lindlohr W, Wells D (1985) GPS design using undifferenced carrier beat phase observations. Manuscr Geod 10:255-295
Schaffrin B, Grafarend E (1986) Generating classes of equivalent linear models by nuisance parameter elimination, applications to GPS observations. Manuscr Geod 11:262–271
Shen Y, Liu D (2002) Unbiased estimation formula of unit weight mean square in regularization solution. Geomat Inf Sci Wuhan Univ 27(6):604-606
Teunissen PJG (1997) GPS double difference statistics: with and without using satellite geometry. J Geod 71:137-148
Xu G (2002) GPS data processing with equivalent observation equations. GPS Solut 6(1–2):28-33
Xu G (2003) GPS, theory, algorithms and applications. Springer, Heidelberg
Yang Y (1994) Robust estimation for dependent observations. Manuscr Geod 19:10–17
Yang Y, Song L, Xu T (2002) Robust estimator for correlated observations based on bifactor equivalent weights. J Geodesy 76:353-358
Zhou J (1985) On the Jie factor (in Chinese). Acta Geod Geophys Sin 14(5)
Acknowledgements
This research is sponsored by the National Natural Science Foundation of China (project number: 40674003) and DFG (Deutsche ForschungsGemeinschaft). The first author sincerely thanks Prof. Rothacher for his support and valuable suggestions and Prof. Yuanxi Yang for polishing the English. Bofeng Li, the doctor student of Tongji University, is acknowledged for calculating the numerical examples and checking the formulae of the paper. Last but not least, the anonymous reviewers are highly appreciated for their constructive comments and helpful suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shen, Y., Xu, G. Simplified equivalent representation of GPS observation equations. GPS Solut 12, 99–108 (2008). https://doi.org/10.1007/s10291-007-0070-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10291-007-0070-z