TY - GEN
T1 - Multivariate total least - squares adjustment for empirical affine transformations
AU - Schaffrin, B.
AU - Felus, Y. A.
PY - 2008
Y1 - 2008
N2 - In Geodetic Science it occurs frequently that, for a given set of points, their coordinates have been measured in two (or more) different systems, and empirical transformation parameters need to be determined by some sort of adjustment for a defined class of transformations. In the linear case, these parameters appear in a matrix that relates one set of coordinates with the other, after correcting them for random errors and centering them around their mid-points (to avoid shift parameters). In the standard approach, a structured version of the Errors-in-Variables (EIV) model would be obtained which would require elaborate modifications of the regular Total Least-Squares Solution (TLSS). In this contribution, a multivariate (but unstructured) EIV model is proposed for which an algorithm has been developed using the nonlinear Euler-Lagrange conditions. The new algorithm is used to estimate the TLSS of the affine transformation parameters. Other types of linear transformations (such as the similarity transformation, e.g.) may require additional constraints.
AB - In Geodetic Science it occurs frequently that, for a given set of points, their coordinates have been measured in two (or more) different systems, and empirical transformation parameters need to be determined by some sort of adjustment for a defined class of transformations. In the linear case, these parameters appear in a matrix that relates one set of coordinates with the other, after correcting them for random errors and centering them around their mid-points (to avoid shift parameters). In the standard approach, a structured version of the Errors-in-Variables (EIV) model would be obtained which would require elaborate modifications of the regular Total Least-Squares Solution (TLSS). In this contribution, a multivariate (but unstructured) EIV model is proposed for which an algorithm has been developed using the nonlinear Euler-Lagrange conditions. The new algorithm is used to estimate the TLSS of the affine transformation parameters. Other types of linear transformations (such as the similarity transformation, e.g.) may require additional constraints.
KW - Errors-in-Variables modeling
KW - Multivariate Total Least-Squares Solution (MTLSS)
KW - empirical coordinate transformation
UR - http://www.scopus.com/inward/record.url?scp=79957654967&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-74584-6_38
DO - 10.1007/978-3-540-74584-6_38
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AN - SCOPUS:79957654967
SN - 9783540745839
T3 - International Association of Geodesy Symposia
SP - 238
EP - 242
BT - VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy - IAG Symposium
T2 - IAG Symposium - 6th Hotine-Marussi Symposium on Theoretical and Computational Geodesy
Y2 - 29 May 2006 through 2 June 2006
ER -