Abstract In this contribution, the symmetrical total least squares adjustment for 3D datum transformations is classified as quasi indirect errors adjustment (QIEA). QIEA is a traditional geodetic adjustment category invented by Wolf (Ausgleichungsrechnung nach der Methode der kleinsten Quadrate, 1968), which is specifically used for quasi nonlinear models. The form of the QIEA objective function contains the information of the functional model, and presents an unconstrained minimization problem referring simply to the transformation parameters. Based on QIEA, a solution is presented through a quasi-Newton approach, specially, the Broyden–Fletcher–Goldfarb–Shanno method. In order to justify the solutions of the QIEA, three validation conditions are proposed to check the correctness of the symmetrical treatment by comparison between the transformation and its reverse transformation. Finally, the applicability of the proposed algorithm was tested in a deformation monitoring task.
"Acta Geodaetica et Geophysica" – Springer Journals
Published: Jun 1, 2014