An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

Abstract

The Gauss-Markov (GM) model and the Errors-in-Variables (EIV) model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares (WTLS) technique has been introduced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance-Covariance Matrix (VCM) of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a nonlinear problem, the WTLS is no longer suitable in this case. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints (NWTLS-EC) for 3D datum transformation with large rotation angle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality (LSE) constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

Keywords

• nonlinear weighted total least squares
• equality constraints
• 3D datum transformation
• heteroscedastic and correlated
• orthogonal transformation