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

Marcin Ligas; Piotr Banasik

doi:10.2478/rgg-2014-0009

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

Reports on Geodesy and Geoinformatics

Volume 97 (2014): Issue 1 (December 2014)

By: Marcin Ligas and Piotr Banasik

Open Access

|Feb 2015

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.

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Articles in this issue

DOI: https://doi.org/10.2478/rgg-2014-0009 | Journal eISSN: 2391-8152 | Journal ISSN: 0867-3179

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Language: English

Page range: 23 - 34

Published on: Feb 3, 2015

Published by: Warsaw University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

least squares collocation,

Helmert’s transformation,

covariance function,

post–transformation correction

Related subjects:

Computer sciences,

Computer sciences, other,

Geosciences,

Geodesy,

Cartography and photogrammetry,

Geosciences, other

© 2015 Marcin Ligas, Piotr Banasik, published by Warsaw University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 97 (2014): Issue 1 (December 2014)