An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation

Abstract

This paper presents an improved weighted total least squares (IWTLS) method for the errors-in-variables (EIV) model with applications in linear fitting and coordinate transformation. In addition, an improved constrained weighted TLS (ICWTLS) method is further obtained based on the IWTLS algorithm. Following the weighted TLS solution (WTLSS) method in which the precisions of any two columns of the design matrix differ only by a scalar factor in linear orthogonal regression problems, the IWTLS method is derived for a more generic case in which there is no proportionality assumption for the cofactor matrix of the design matrix in the EIV model. Compared with existing research on the constrained TLS method under the assumption that both the constraining matrix and the right-hand-side (RHS) vector are error-free, or that only the RHS vector contains errors, the ICWTLS method is proposed for resolving the EIV model with constraints by integrating the observation equations and constraint equations under the assu...