Efficient Algorithm for Inverse of the Fully Populated Covariance Matrix in Global Positioning System Relative Positioning
Publication: Journal of Surveying Engineering
Volume 130, Issue 1
Abstract
Stochastic modeling of the global positioning system (GPS) residual errors yields a fully populated covariance matrix for the GPS carrier phase double difference observations. Implementing this fully populated covariance matrix into a software package usually slows down the numerical computations. This, however, is not the case if an exponential function can be used to approximate the actual covariance function of the GPS residual errors. Using the exponential function results in a block diagonal weight matrix for the double-difference observations. In this paper, an algorithm for the efficient computation of the inverse of this fully populated covariance matrix is developed. Both the ideal case of tracking the same satellites over time as well as the more realistic case of tracking different satellites over time are considered. The storage requirement for the adjustment process is also discussed.
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References
Beutler, G., Davidson, D., Langley, R., Santerre, R., Vanicek, P., and Wells, D. (1984). “Some theoretical and practical aspects of the geodetic positioning using carrier phase difference observations of GPS satellites.” Technical Rep. 109, Dept. of Surveying Engineering, Univ. of New Brunswick, New Brunswick, Canada.
El-Rabbany, A. (1994). “The effect of physical correlations on the ambiguity resolution and accuracy estimation in GPS differential positioning.” Technical Rep. 170, Dept. of Geodesy and Geomatics Engineering, Univ. of New Brunswick, New Brunswick, Canada.
El-Rabbany, A., and Kleusberg, A.(2003). “Effect of temporal physical correlation on accuracy estimation in GPS relative positioning.” J. Surv. Eng., 129(1), 28–32.
Hofmann-Wellenhof, B., Lichtenegger, H., and Collins, J. (2001). Global positioning system theory and practice, 5th Ed., Springer, New York.
Mikhail, E. (1976). Observations and least squares, University Press, New York.
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Published In
Journal of Surveying Engineering
Volume 130 • Issue 1 • February 2004
Pages: 29 - 35
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Sep 24, 2002
Accepted: Dec 23, 2002
Published online: Jan 16, 2004
Published in print: Feb 2004
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