Stepwise Parameter Estimations in a Time-Variant Similarity Transformation
Publication: Journal of Surveying Engineering
Volume 132, Issue 4
Abstract
A classic seven-parameter similarity transformation is typically applied in reference frame transformations. For modern day global applications with a higher accuracy requirement, this model is extended to accommodate time-dependent positional variations. The time-variant transformation, however, also brings a new problem—rank deficiency—while performing parameter estimations. In this paper, a stepwise parameter estimation approach is proposed to overcome this problem and give a reliable solution. It also enables one to investigate different types of transformation parameters independently. To prove its feasibility on present day global datum applications, this approach is applied to the reference frame transformation between ITRF2000 and ITRF97 at epoch 1997.0. In addition, a simulation test is performed to show the advantages of the proposed approach against other parameter estimation approaches currently in use, for its wider range of applications in science and engineering.
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Acknowledgments
Comments by Dr. T. Soler and Dr. R. A. Snay prior to the review process are gratefully acknowledged. The writers appreciate the help of three anonymous reviewers, whose comments significantly improved the manuscript. They also want to express their gratitude to National Geodetic Survey (NOAA), International GNSS Service (IAG), and many other institutions that constantly provide essential data and make precise GPS solutions available to the public.
References
Altamimi, Z., Sillard, P., and Boucher, C. (2002). “ITRF2000: A new release of the international terrestrial reference frame for earth science applications.” J. Geophys. Res., [Solid Earth], 107(10), 1–19.
Burša, M. (1967). “On the possibility of determining the rotation elements of geodetic reference systems on the basis of satellite observations.” Stud. Geophys. Geod., 11(4), 390–396.
Leick, A., and van Gelder, B. H. W. (1975). “On similarity transformations and geodetic network distortions based on doppler satellite observations.” Rep., Dept. of Geodetic Science, No. 235, prepared for the National Aeronautics and Space Administration, The Ohio State Univ. Research Foundation, Columbus, Ohio.
McCarthy, D., and Petit, G. (2004). “Transformation parameters between ITRF solutions.” IERS Conventions (2003), IERS Technical Note No. 32, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, Germany, 30–31.
Mikhail, E. M., and Ackermann, F. (1976). “A united approach to least squares adjustment.” Observations and least squares, IEP-A Dun-Donnelley, New York, 333–359.
Snay, R. A. (1999). “Using the HTDP software to transform spatial coordinates across time and between reference frames.” Surv. Land Inf. Sys., 59(1), 15–25.
Snay, R. A. (2003). “Introducing two spatial reference frames for regions of the Pacific Ocean.” Surv. Land Inf. Sys., 63(1), 5–12.
Soler, T. (1998). “A compendium of transformation formulas useful in GPS work.” J. Geodesy, Berlin, 72(7–8), 482–490.
Soler, T., and Marshall, J. (2003). “A note on frame transformations with applications to geodetic datums.” GPS Solutions, 7(1), 23–32.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 132 • Issue 4 • November 2006
Pages: 141 - 148
Copyright
© 2006 ASCE.
History
Received: Jan 25, 2005
Accepted: Sep 1, 2005
Published online: Nov 1, 2006
Published in print: Nov 2006
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