A generalized weighted total least squares-based, iterative solution to the estimation of 3D similarity transformation parameters

Abstract

The essence of point cloud registration is to estimate the seven similarity transformation parameters of the Bursa-Wolf model which describes the relative position of the two neighboring LiDAR stations. So far, Gauss–Markov (GM) model has been widely used in point cloud registration, however, only the random errors contained in one LiDAR station are considered, which is seriously inconsistent with the reality. To simultaneously take the random errors contained in both of the two neighboring LiDAR stations into account in registration, the EIV model is constructed based on the introduction of unit quaternions to describe the spatial rotation in 3D similarity transformation, and an iterative solution to the estimation of the transformation parameters is systematically discussed. Detailed derivation of the formulas for the estimation of the seven transformation parameters are displayed step by step. Finally, three experiments are designed to verify the correctness and effectiveness of the solution.