TY - JOUR

T1 - On linear transformations of spatial data using the structured total least norm principle

AU - Felus, Yaron A.

N1 - Funding Information:
ACKNOWLEDGMENT The author would like to thank Burkhard Schaffrin, Robert Burtch, and Chad M. Schaeding for their suggestions and assistance. The author was supported by the National Geospatial-Intelligence Agency under contract no. HM1582-04-1-2026.

PY - 2006/7

Y1 - 2006/7

N2 - Coordinate transformation is the process of converting spatial data from a source coordinate to a target coordinate system. A set of control points, measured in the two coordinate systems, is used to estimate the transformation parameters. In general, more control points are measured, and the over-determined system is adjusted using the least squares method. However, the standard least squares method assumes that errors exist only in the measurements made at one coordinate system, or at the observation vector (y). This is not the case in many physical systems where errors exist in all the measurements made in both the source coordinate and the target coordinate systems. The Structured Total Least Norm (STLN) method is a relatively new mathematical concept developed to solve estimation problems of so-called Error-In-Variables (EM models. The method is specifically suitable for dealing with transformation problems, since it can handle the special structure of the data matrix (A). The STLN method is uniquely used to compute the parameters of common linear coordinate transformations (affine and similarity). A numerical example is presented to demonstrate the superiority of this technique in terms of accuracy and to compare the standard LS method, the generalized LS algorithm, and the STLN approach.

AB - Coordinate transformation is the process of converting spatial data from a source coordinate to a target coordinate system. A set of control points, measured in the two coordinate systems, is used to estimate the transformation parameters. In general, more control points are measured, and the over-determined system is adjusted using the least squares method. However, the standard least squares method assumes that errors exist only in the measurements made at one coordinate system, or at the observation vector (y). This is not the case in many physical systems where errors exist in all the measurements made in both the source coordinate and the target coordinate systems. The Structured Total Least Norm (STLN) method is a relatively new mathematical concept developed to solve estimation problems of so-called Error-In-Variables (EM models. The method is specifically suitable for dealing with transformation problems, since it can handle the special structure of the data matrix (A). The STLN method is uniquely used to compute the parameters of common linear coordinate transformations (affine and similarity). A numerical example is presented to demonstrate the superiority of this technique in terms of accuracy and to compare the standard LS method, the generalized LS algorithm, and the STLN approach.

KW - Coordinates transformation

KW - Error analysis

KW - Least squares

KW - Structured Total Least-Norm

UR - http://www.scopus.com/inward/record.url?scp=33845972686&partnerID=8YFLogxK

U2 - 10.1559/152304006779077273

DO - 10.1559/152304006779077273

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AN - SCOPUS:33845972686

SN - 1523-0406

VL - 33

SP - 195

EP - 205

JO - Cartography and Geographic Information Science

JF - Cartography and Geographic Information Science

IS - 3

ER -