Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions

Uygur S. O., Aydın C., Akyılmaz O.

JOURNAL OF SPATIAL SCIENCE, vol.67, no.2, pp.255-272, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1080/14498596.2020.1776170
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Geobase, INSPEC
  • Page Numbers: pp.255-272
  • Keywords: 3D similarity transformation, quaternion, euler rotation angle, covariance matrix, total least squares, TOTAL LEAST-SQUARES, ERRORS-IN-VARIABLES, PARAMETER-ESTIMATION, ITERATIVE SOLUTION, ADJUSTMENT, VARIANCE, MODEL
  • Yıldız Technical University Affiliated: Yes


Recently, it has been shown how quaternion-based representation of a rotation matrix has advantages over conventional Eulerian representation in 3D similarity transformations. The iterative estimation procedure in similarity transformations based on quaternions results in translations and (scaled) quaternion elements. One needs, therefore, an additional procedure for evaluating the rest of the transformation parameters (translation, scale factor and rotation angles) after this solution.This contribution shows how to evaluate the rotation angles and the full covariance matrix of the transformation parameters from the estimation results in asymmetric and symmetric 3D similarity transformations based on quaternions.