Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles

• Main Authors: LI Bofeng, HUANG Shanqi
• Format: Article
• Language: zho
• Published: Surveying and Mapping Press 2016-03-01
• Series: Acta Geodaetica et Cartographica Sinica
• Subjects: three-dimension datum transformation; big rotation angle; Bursa model; error-in-variables(EIV) model
• Online Access: http://html.rhhz.net/CHXB/html/2016-3-267.htm

The small rotation angles are typically involved in the traditional geodetic datum transformation, for which one can iteratively solve for its linearized model with ignoring its second-smaller terms. However, the big rotation angles are introduced to transform the outcomes from the advanced space surveying techniques. For this transformation model with big rotation angles, all elements of rotation matrix are usually parameterized as unknown parameters and then solved with the constrained adjustment theory by using the orthogonal condition of rotation matrix. With three-dimensional datum transformation with big rotation angles as example, this paper derives the analytical close-form solutions by formularizing the coordinates of multi-points as a matrix and using the orthogonal condition of rotation matrix. Expanding the transformation model with introducing the errors to common points of both datum, we derive out its analytical solutions as well. The results of simulation computations show that the presented three-dimensional datum transformation can realize the comparable transformation result while the new method can outcome the complicated and time-consuming iterations, therefore improving the computation efficiency.