Inverse and Compound Datum/Frame Transformations
Publication: Journal of Surveying Engineering
Volume 135, Issue 2
Abstract
Transformations between local datums/frames have provided an indispensable method for expressing coordinates in the same datum. The advent of space-based geodetic techniques propelled the homogenization of national networks through the definition of conventional earth-centered, earth-fixed datums globally accessible through satellite observations. On the other hand, datum transformations enhanced mapping applications by using different realizations of the conventional reference frames. Realization of conventional datums/frames also led to investigations determining the transformation parameters between conventional terrestrial frames, and local datums rather than between local datums themselves. In this context, both inverse and sequential transformations are needed to express the coordinates of one local datum into another. Obtaining the transformation parameters through a “compound transformation” rather than transforming coordinates in a sequential scheme has several advantages. In this study, avenues to rigorously compute compound datum transformation parameters given two independent sets of transformation parameters are examined and compact analytical equations free of any matrix inversion are derived. New linear equations are presented both in compact matrix notation and in its expanded form to facilitate the propagation of errors from individual sets of transformation parameters to those of the compound datum transformation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writer thanks Dr. Mehmet Ali Gürdal, Dr. Ali Kılıçoğlu, Dr. Coşkun Demir, and Dr. Mustafa Ata for helpful comments and suggestions. It is also particularly acknowledged that useful criticism and suggestions provided by the editor and three anonymous reviewers improved the content of this paper. The manuscript solely reflects the personal views of the author and does not necessarily represent the views, positions, strategies or opinions of Turkish Armed Forces.
References
Altamimi, Z., Collilieux, X., Legrand, J., Garayt, B., and Boucher, C. (2007). “ITRF2005: A new release of the international terrestrial reference frame based on time series of station positions and earth orientation parameters.” J. Geophys. Res., 112(B09401), 1–19.
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., 107(B10), 1–19.
Boucher, C., and Altamimi, Z. (1996). “International terrestrial reference frame.” GPS World, 7(9), 71–74.
Boucher, C., and Altamimi, Z. (2001). “Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS campaign.” ⟨http://lareg.ensg.ign.fr/EUREF/memo.pdf⟩ (Oct. 13, 2003).
Boucher, C., and Altamimi, Z. (2007). “Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS campaign.” ⟨http://lareg.ensg.ign.fr/EUREF/memo2007.pdf⟩ (Jan. 27, 2008).
Burša, M. (1966). Fundamentals of the theory of geometric satellite geodesy, Trav. Inst. Géophys. Acad. Tchéc. Sci., Vol. 241, Československá Akademie Věd, Prague, Czechoslovakia.
Environmental Systems Research Institute (ESRI). (2007). “Geographic transformations.” Redlands, Calif., ⟨http://downloads.esri.com/support/whitepapers/ao_/Map_Projection_Tables.pdf⟩ (Oct. 10, 2007).
Featherstone, W. E. (1996). “An updated explanation of the Geocentric Datum of Australia (GDA) and its effects upon future mapping.” Australian Surveyor, 41(2), 121–130.
Han, J. Y., van Gelder, B. H. W., Soler, T., and Snay, R. A. (2008). “Geometric combination of multiple terrestrial network solutions.” J. Surv. Eng., 134(4), 126–131.
IERS. (2008). “Transformation parameters from ITRF 2000 to previous frames.” ⟨ftp://lareg.ensg.ign.fr/pub/itrf/ITRF.TP⟩ (Jan. 3, 2004).
Kaula, W. M. (1966). Theory of satellite geodesy, Blaisdell Publishing Co., Waltham, Mass.
Kouba, J. (2002). “The GPS toolbox ITRF transformations.” GPS Solutions, 5(3), 88–90.
Mueller, I. I. (1969). Spherical and practical astronomy as applied to geodesy, Ungar, New York.
National Geospatial-Intelligence Agency (NGA). (2008). “Nato datum transformation parameters.” ⟨http://earth-info.nga.mil.GandG/coordsys/datum/NATO_DT.pdf⟩ (May 15, 2007).
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. (1976). “On differential transformations between Cartesian and curvilinear (geodetic) coordinates.” Rep. No. 236, Dept. of Geodetic Science, Ohio State Univ., Columbus, Ohio.
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. (2002). “Rigorous transformation of variance-covariance matrices of GPS-derived coordinates and velocities.” GPS Solutions, 6(1–2), 76–90.
Soler, T., and Marshall, J. (2003). “A note on frame transformations with applications to geodetic datum.” GPS Solutions, 7(1), 23–32.
Soler, T., and Snay, R. A. (2004). “Transforming positions and velocities between ITRF00 and NAD83.” J. Struct. Eng., 130(2), 49–55.
Vaníček, P., and Krakiwsky, E. J. (1982). Geodesy: The concepts, North- Holland, Amsterdam, The Netherlands.
Wolf, P. R., and Ghilani, C. D. (1997). Adjustment computations: Statistics and least squares in surveying and GIS, Wiley, New York.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 135 • Issue 2 • May 2009
Pages: 46 - 55
Copyright
© 2009 ASCE.
History
Received: Feb 1, 2008
Accepted: Sep 26, 2008
Published online: May 1, 2009
Published in print: May 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.