TY - GEN

T1 - Performing similarity transformations using the error-in-variable model

AU - Felus, Yaron A.

AU - Schaffrin, Burkhard

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84869074611&partnerID=8YFLogxK

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AN - SCOPUS:84869074611

SN - 1570830762

SN - 9781570830761

T3 - American Society for Photogrammetry and Remote Sensing - Annual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet

SP - 220

EP - 227

BT - American Society for Photogrammetry and Remote Sensing - Annual Conference 2005 - Geospatial Goes Global

T2 - Annual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet

Y2 - 7 March 2005 through 11 March 2005

ER -