Partially error-affected point-wise weighted closed-form solution to the similarity transformation and its variants

The paper presents a closed-form solution to the point-wise weighted similarity transformation and its variants in the least squares framework under two estimation scenarios. In the first scenario a target system is subject to random errors whilst in the second one a source system is considered to b...

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Bibliographic Details
Published inJournal of applied geodesy Vol. 14; no. 2; pp. 231 - 239
Main Author Ligas, Marcin
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.04.2020
Walter de Gruyter GmbH
Subjects
Closed form solutions
Errors
Exact solutions
Genetic transformation
polar decomposition
Procrustes analysis
Random errors
rigid-body transformation
Similarity
similarity transformation
Transformations
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Summary:The paper presents a closed-form solution to the point-wise weighted similarity transformation and its variants in the least squares framework under two estimation scenarios. In the first scenario a target system is subject to random errors whilst in the second one a source system is considered to be erroneous. These transformation models will be named asymmetric in contrast to the symmetrical one solved under the errors-in-variables model where both systems are contaminated by random errors. The entire derivation is based on Procrustes Analysis. The formulas presented herein hold for both 2D and 3D transformations without any modification. The solution uses a polar decomposition to recover the rotation matrix.
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content type line 14
ISSN:1862-9016
1862-9024
DOI:10.1515/jag-2019-0067