Abstract
The 3D similarity transformation models, e.g. Bursa model is usually applied in geodesy and photogrammetry. In general, they are suitable in small angle 3D transformation. However, a lot of large 3D transformations need to be performed. This contribution describes a 3D similarity transformation model suitable for any angle rotation, where the nine elements in the rotation matrix are used to replace the three rotation angles as unknown parameters. In the coordinate transformation model, the Errors-In-Variables (EIV) model will be adjusted according to the theory of Least Squares (LS) method within the nonlinear Gauss–Helmert (GH) model. At the end of the contribution, case studies are investigated to demonstrate the coordinate transformation method proposed in this paper. The results show that using the linearized iterative GH model the correct solution can be obtained and this mixed model can be applied no matter whether the variance covariance matrices are full or diagonal.
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