Performing similarity transformations using the error-in-variable model

Yaron A. Felus, Burkhard Schaffrin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

46 Scopus citations

Abstract

Least-Squares (LS) adjustment method aims at estimating a vector of parameters ξ, from a linear model ( y = Aξ, +e) that includes an observation vector y, a vector of normally distributed errors e, and a matrix of variables A. However, in this linear model, also known as the Gauss-Markov model, the matrix of variables A is considered as fixed or error-free. This is not the case in many physical systems where errors exist in both the observation vector y, and the matrix of variables A. The Total Least-Squares (TLS) method uses a relatively new mathematical concept that was developed to solve estimation problems in so-called Error- In-all-Variables models. In this contribution, a novel application of the Total Least-Squares method for the Linear Conformal Coordinate Transformation is described. The unique structure of the data matrix A, where some variables appear twice, is also considered in a newly developed "Structured TLS procedure" for the Similarity Transformation. A practical coordinate transformation problem is presented to demonstrate this new technique, and a comparison is made between the standard (generalized) least squares approach and the TLS approach.

Original languageEnglish
Title of host publicationAmerican Society for Photogrammetry and Remote Sensing - Annual Conference 2005 - Geospatial Goes Global
Subtitle of host publicationFrom Your Neighborhood to the Whole Planet
Pages220-227
Number of pages8
StatePublished - 2005
Externally publishedYes
EventAnnual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet - Baltimore, MD, United States
Duration: 7 Mar 200511 Mar 2005

Publication series

NameAmerican Society for Photogrammetry and Remote Sensing - Annual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet
Volume1

Conference

ConferenceAnnual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet
Country/TerritoryUnited States
CityBaltimore, MD
Period7/03/0511/03/05

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