GPS-Network Analysis with BLIMPBE: An Alternative to Least-Squares Adjustment for Better Bias Control
Publication: Journal of Surveying Engineering
Volume 133, Issue 3
Abstract
Geodetic networks, when derived solely from observed GPS baseline vectors, have an inherent datum deficiency of dimension three due to the respective unknown translation parameters. Thus, estimated coordinates from a (weighted) least-squares adjustment will not be unique, although the adjusted baseline vectors are. Uniqueness, without affecting the adjustment as such, can be achieved by introducing a minimum number of constraints for the coordinates, or by applying an objective function on the set of least-squares solutions (LESS) that fulfill the so-called normal equations. In both alternatives, bias control for some (or all) coordinate estimates has so far been treated only as a secondary issue. Here it is shown that the recently introduced estimator of type BLIMPBE—although generally not a LESS—can indeed be expected to be superior to all other linear estimators that minimize the bias for certain coordinates. This performance is demonstrated in a GPS network that includes GPS receivers at several continuously operating reference stations.
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Acknowledgments
The writers would like to thank C. K. Shum for providing the data set used herein.
References
Caspary, W. F. (1987). Concepts of network and deformation analysis, Monograph 11, School of Surveying, Univ. of New South Wales, Kensington, N.S.W., Australia.
Chaubey, Y. P. (1982). “Best minimum bias linear estimates in Gauss-Markov model.” Commun. Stat: Theory Meth., A-11(17), 1959–1963.
Grafarend, E., and Schaffrin, B. (1993). Adjustment computations in linear models, Bibliographical Inst., Manheim, Germany (in German).
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, 2nd Ed., Springer, Berlin.
Kuang, S. L. (1996). Geodetic network analysis and optimal design, Sam’s Publ., Sterling, Ill.
Rao, C. R., and Toutenburg, H. (1999). Linear models: Least-squares and alternatives, 2nd Ed., Springer, New York.
Schaffrin, B., and Cothren, J. (1998). “Towards optimizing hierarchical data revisions.” GIS—Between visions and applications, Proc., ISPRS Commission IV Symp., D. Fritsch, M. Englich, and M. Sester, eds., Univ. of Stuttgart, Germany, 515–521.
Schaffrin, B., and Iz, H. B. (2002). “BLIMPBE and its geodetic applications.” Vistas for geodesy in the new millennium, J. Ádám and K. Schwarz, eds., Springer, Berlin, 377–381.
Snow, K. (2002). “Applications of parameter estimation and hypothesis testing to GPS network adjustments.” Rep. 465, Dept. of Civil and Environmental Engineering and Geodetic Science, Ohio State Univ., Columbus, Ohio.
Snow, K., and Schaffrin, B. (2003). “Three-dimensional outlier detection for GPS networks and their densification via the BLIMPBE approach.” GPS Solutions, 7(2), 130–139.
Strang, G., and Borre, K. (1997). Linear algebra, geodesy, and GPS, Wellesley-Cambridge Press, Wellesley, Mass.
Zlobec, S. (1970). “An explicit form of the Moore-Penrose inverse of an arbitrary complex matrix.” SIAM Rev., 12(1), 132–134.
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© 2007 ASCE.
History
Received: Jan 23, 2006
Accepted: Nov 30, 2006
Published online: Aug 1, 2007
Published in print: Aug 2007
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