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 const...