A Novel Robust Quaternions-Based Algorithm for 3-D Symmetric Similarity Datum Transformation

Recently, the total least squares (TLS) method has gained significant attention for solving the challenge in 3-D symmetric similarity datum transformation. The conventional approaches of using Euler angles to represent rotation matrices are time-consuming and yield unstable results. Moreover, the estimated transformation parameters become distorted when the spatial dataset is polluted by outliers. In our study, we address this issue by introducing a generalized errors-in-variables (EIV) model for 3-D symmetric similarity transformation and employ quaternions to describe the 3-D rotation parameters. The proposed algorithm utilizes a robust estimation scheme based on an equivalent weight to perform 3-D symmetric similarity datum transformation. Unlike earlier studies, our algorithm improves computational efficiency by using quaternions that do not require suitable initial parameter values at the beginning of the iteration. Furthermore, our algorithm is capable of identifying outliers of various magnitudes and resisting their detrimental impacts. Based on simulations and real-world examples, it can prove that our method is more efficient and accurate than classical algorithms.