Total Least-Squares Estimation for 2D Affine Coordinate Transformation with Constraints on Physical Parameters

Abstract

The error-in-variable (EIV) model takes the error of all variables into account and has been widely applied to many practical problems arising in environmental study, geology, geographic information science (GIS), and geodesy. Coordinate transformations are among the most frequently encountered problems in spatial data processing, and the EIV model can be built based on two sets of coordinates. In some applications, physical parameters—such as the shift, rotation angle, and scale factor—have constraints. Current implementations of the constrained EIV (CEIV) model do not consider physical constraints explicitly. The purpose of this paper is to convert physical constraints into mathematical forms and to use constrained total least squares (CTLS) to solve the CEIV problem of two-dimensional (2D) affine transformation. The effectiveness of this method is illustrated through a numerical example.