Abstract
The GPS observables are subject to several errors. Among them, the systematic ones have great impact, because they degrade the accuracy of the accomplished positioning. These errors are those related, mainly, to GPS satellites orbits, multipath and atmospheric effects. Lately, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique (PLS). In this method, the errors are modeled as functions varying smoothly in time. It is like to change the stochastic model, in which the errors functions are incorporated, the results obtained are similar to those in which the functional model is changed. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method (CLS). In general, the solution requires a shorter data interval, minimizing costs.
The method performance was analyzed in two experiments, using data from single frequency receivers. The first one was accomplished with a short baseline, where the main error was the multipath. In the second experiment, a baseline of 102 km was used. In this case, the predominant errors were due to the ionosphere and troposphere refraction. In the first experiment, using 5 minutes of data collection, the largest coordinates discrepancies in relation to the ground truth reached 1.6 cm and 3.3 cm in h coordinate for PLS and the CLS, respectively. In the second one, also using 5 minutes of data, the discrepancies were 27 cm in h for the PLS and 175 cm in h for the CLS. In these tests, it was also possible to verify a considerable improvement in the ambiguities resolution using the PLS in relation to the CLS, with a reduced data collection time interval.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alves, D. B. M. (2004a). Método dos Mínimos Quadrados com Penalidades: Aplicação no posicionamento relativo GPS. 133f. Dissertação (Mestrado em Ciências Cartográficas)-Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista, Presidente Pradente.
Alves, D. B. M. (2004b). Using Cubic Splines to Mitigate Systematic Errors in GPS Relative Positioning. In: Proc. of ION GNSS 2004, Long Beach, California.
Blewitt, G. (1998). GPS Data Processing Metodology. In: Teunissen, P. J. G.; Kleusberg, A. GPS for Geodesy. Berlin: Springer Verlage, pp.231–270.
Braasch, M. S. (1991). A Signal Model for GPS, Navigation. vol. 37, no. 4, pp. 363–377.
Fessler, J. A. (1999). Nonparatnetric Fixed-Interval Smoothing With Vector Splines. In: Proc. IEEE Transactions on Signal Processin, pp. 852–859.
Fortes, L. P. S. (1997). Operacionalização da Rede Brasileira de Monitoramento Contínuo do Sistema GPS (RBMC). 152f. Disscrtação (Mestrado em Ciências cm Sistcmas e Computação) — Institute Militar de Engenharia (IME), Rio de Janeiro.
Fortes, L. P. S. (2002). Optimising the Use of GPS Multi-Reference Stations for Kinematic Positioning. 2002. 355f. Thesis (PhD) — University of Calgary, Calgary.
Green, P. J. and B. W. Silverman (1994). Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. 1.ed. London: Chapman & Hall.
Hofmann-Wellenhof, B. et al. (1997). GPS Theory and Practice. Wien: Spring-Verlage. 326p.
Jia, M. (2000). Mitigation of Systematic Errors of GPS Positioning Using Vector Semiparametric Models. In: Proc. of ION GPS 2000, Salt Lake City, pp. 1938–1947.
Jia et al. (2001). Mitigation of Ionospheric Errors by Penalised Least Squares Technique for High Precision Medium Distance GPS Positioning. In: Proc. of KIS 2001, Banff, Canada.
Klobuchar, J. (1996). A. Ionospheric Effects on GPS. In: Parkinson, B. W. and J. J. Spilker. Global Positioning System: Theory and Applications. Cambridge: American Institute of Aeronautics and Astronautics, pp.485–515.
Machado, W. C. and J. F. G. Monico (2002). Utilização do software GPSeq na solução rápida das ambigüidades GPS no posicionamento relativo cinemático de bases curtas. In: Pesquisa em Geociências, Porto Alegre, pp.89–99.
Seeber, G. (2003). Satellite Geodesy: Foundations, Methods, and Applications. Berlin, New York: Walter de Gruyter.
Souza, E. M. and J. F. G. Monico (2004). Wavelet Shirinkage: High frequency multipath reduction from GPS relative positioning. GPS Solutions, vol. 8, no. 3, pp. 152–159.
Teunissen, P. J. G. (1998a). GPS Carrier Phase Ambiguity Fixing Concepts. In: Teunissen, P. J. G.; Kleusberg, A. GPS for Geodesy. Berlin: Springer Verlage, pp.271–318.
Teunissen, P. J. G. (1998b). Quality Control and GPS. In: Teunissen, P. J. G.; Kleusberg, A. GPS for Geodesy. Berlin: Springer Verlage, 1998b, pp.271–318.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Alves, D.B.M., Monico, J.F.G. (2007). Modifying the Stochastic Model to Mitigate GPS Systematic Errors in Relative Positioning. In: Tregoning, P., Rizos, C. (eds) Dynamic Planet. International Association of Geodesy Symposia, vol 130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49350-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-49350-1_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49349-5
Online ISBN: 978-3-540-49350-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)