Nonlinear analysis of the three-dimensional datum transformation [conformal group ℂ7(3)]

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On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model (2015, background): “Note that the rotation parameters can be represented in different forms, e.g., Euler angles (Fang 2014b; Yang 1999), direction cosine matrix (Grafarend and Awange 2003; Teunissen 1984a), normalized quaternion (Sanso 1973; Shen et al. 2006), etc.”
A total least squares solution for geodetic datum transformations (2014, methodology): “Two fundamental algorithms for adjusting the GMM are the Procrustes analysis (e.g., Grafarend and Awange 2003; Grafarend 2006; Awange et al. 2010; Grafarend and Awange 2012) and the unit quaternion-based approach (e.g., Shen et al. 2006).”
A Quaternion-based Geodetic Datum Transformation Algorithm (2006, methodology): “these coordinates, we compute the transformation parameters from a local geodetic system (system A) to WGS84 (system B) and list the results in Table 2 and give the corresponding quaternion and rotation matrix in Table 3. The transformation parameters and transformed coordinates are exactly equal to”