<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper presents a least squares collocation - based alternative to Helmert’s transformation with Hausbrandt’s post – transformation correction. The least squares collocation is used as an exact predictor i.e. it honors the data, thus the problem of zero residuals on transformation control points is overcome and zero residuals are assured by the method applied. Despite the fact that the procedure is presented for Helmert’s transformation it may easily be copied to any other form of coordinate transformation. A numerical example is provided within the content of the paper.</p></abstract>

The paper presents a least squares collocation - based alternative to Helmert’s transformation with Hausbrandt’s post – transformation correction. The least squares collocation is used as an exact predictor i.e. it honors the data, thus the problem of zero residuals on transformation control points is overcome and zero residuals are assured by the method applied. Despite the fact that the procedure is presented for Helmert’s transformation it may easily be copied to any other form of coordinate transformation. A numerical example is provided within the content of the paper.

Least Squares Collocation Alternative to Helmert’s Transformation with Hausbrandt’s Post – Transformation Correction

AGH University of Science and Technology Faculty of Mining Surveying and Environmental Engineering Department of Geomatics, Krakow, Poland

Reports on Geodesy and Geoinformatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper presents a least squares collocation - based alternative to Helmert’s transformation with Hausbrandt’s post – transformation correction. The least...

Least Squares Collocation Alternative to Helmert’s Transformation with Hausbrandt’s Post – Transformation Correction

Published Online: Feb 03, 2015

Page range: 23 - 34

DOI: https://doi.org/10.2478/rgg-2014-0009

Keywords
least squares collocation, Helmert’s transformation, covariance function, post–transformation correction

© 2014 Marcin Ligas and Piotr Banasik

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Least Squares Collocation Alternative to Helmert’s Transformation with Hausbrandt’s Post – Transformation Correction

Published Online: Feb 03, 2015

Page range: 23 - 34

DOI: https://doi.org/10.2478/rgg-2014-0009

Keywordsleast squares collocation, Helmert’s transformation, covariance function, post–transformation correction

© 2014 Marcin Ligas and Piotr Banasik

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
least squares collocation, Helmert’s transformation, covariance function, post–transformation correction