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 -