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Journal of Geodetic Science

Editor-in-Chief: Eshagh, Mehdi

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2081-9943
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The Case of the Homogeneous Errors-In-Variables Model

B. Schaffrin
  • Corresponding author
  • Geodetic Science Program, School of Earth Sciences, The Ohio State University, Columbus, Ohio, USA
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ K. Snow
  • Corresponding author
  • Geodetic Science Program, School of Earth Sciences, The Ohio State University, Columbus, Ohio, USA
  • Topcon Positioning Systems, Inc., Columbus, Ohio, USA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-12-10 | DOI: https://doi.org/10.2478/jogs-2014-0017

Abstract

Recently, it has been claimed that the Homogeneous Errors-In-Variables (HEIV) Model, where the lefthand side (LHS) vector is allowed to be multiplied with an unknown scale factor, would represent a generalization of the regular EIV-Model for which a number of efficient algorithms already exist. Unfortunately, due to the forced rank deficiency in the case of the HEIV-Model, an additional constraint needs to be introduced to guarantee uniqueness of the TLS solution (“datum constraint”). If this constraint is linear, a simple manipulation will reduce the HEIV-Model with one constraint to the regular EIV-Model. But also in the case of a non-linear datum constraint, by introducing parameter ratios as unknowns, an EIV-Model may result that can be treated by standard TLS adjustment, followed by a solution of the datum constraint for the additional LHS scale parameter. This approach will be applied to an example where the datum constraint is chosen to be quadratic.

Keywords: Errors-In-Variables Model: Homogeneous vs. regular; Total Least-Squares adjustment: With and without datum constraint; model equivalency

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About the article

Received: 2014-10-10

Accepted: 2014-11-24

Published Online: 2014-12-10


Citation Information: Journal of Geodetic Science, Volume 4, Issue 1, ISSN (Online) 2081-9943, DOI: https://doi.org/10.2478/jogs-2014-0017.

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©2014 B. Schaffrin, K. Snow. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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