Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A total least squares solution for geodetic datum transformations

A total least squares solution for geodetic datum transformations Abstract In this contribution, the symmetrical total least squares adjustment for 3D datum transformations is classified as quasi indirect errors adjustment (QIEA). QIEA is a traditional geodetic adjustment category invented by Wolf (Ausgleichungsrechnung nach der Methode der kleinsten Quadrate, 1968), which is specifically used for quasi nonlinear models. The form of the QIEA objective function contains the information of the functional model, and presents an unconstrained minimization problem referring simply to the transformation parameters. Based on QIEA, a solution is presented through a quasi-Newton approach, specially, the Broyden–Fletcher–Goldfarb–Shanno method. In order to justify the solutions of the QIEA, three validation conditions are proposed to check the correctness of the symmetrical treatment by comparison between the transformation and its reverse transformation. Finally, the applicability of the proposed algorithm was tested in a deformation monitoring task. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Geodaetica et Geophysica" Springer Journals

A total least squares solution for geodetic datum transformations

"Acta Geodaetica et Geophysica" , Volume 49 (2): 19 – Jun 1, 2014

Loading next page...
 
/lp/springer-journals/a-total-least-squares-solution-for-geodetic-datum-transformations-4inUQ0UFvb
Publisher
Springer Journals
Copyright
2014 Akadémiai Kiadó, Budapest, Hungary
ISSN
2213-5812
eISSN
2213-5820
DOI
10.1007/s40328-014-0046-8
Publisher site
See Article on Publisher Site

Abstract

Abstract In this contribution, the symmetrical total least squares adjustment for 3D datum transformations is classified as quasi indirect errors adjustment (QIEA). QIEA is a traditional geodetic adjustment category invented by Wolf (Ausgleichungsrechnung nach der Methode der kleinsten Quadrate, 1968), which is specifically used for quasi nonlinear models. The form of the QIEA objective function contains the information of the functional model, and presents an unconstrained minimization problem referring simply to the transformation parameters. Based on QIEA, a solution is presented through a quasi-Newton approach, specially, the Broyden–Fletcher–Goldfarb–Shanno method. In order to justify the solutions of the QIEA, three validation conditions are proposed to check the correctness of the symmetrical treatment by comparison between the transformation and its reverse transformation. Finally, the applicability of the proposed algorithm was tested in a deformation monitoring task.

Journal

"Acta Geodaetica et Geophysica"Springer Journals

Published: Jun 1, 2014

References