Error analysis of the 3D similarity coordinate transformation |
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| Authors: | Guobin Chang Tianhe Xu Qianxin Wang |
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| Institution: | 1.School of Environmental Science and Spatial Informatics,China University of Mining and Technology,Xuzhou,China;2.Institute of Space Science,Shandong University,Weihai,China;3.State Key Laboratory of Geo-information Engineering,Xi’an Research Institute of Surveying and Mapping,Xi’an,China |
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| Abstract: | The 3D similarity coordinate transformation with the Gauss–Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3 × 1 multiplicative error vector is defined to effectively parameterize the rotation matrix estimation error. The propagation of the errors in the coordinate measurements to the errors in the estimated transformation parameters is derived step-by-step, and the formulae for calculating the variance–covariance matrix of the estimated parameters are presented. |
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