The three-dimensional (3-D) symmetric transformation, which simultaneously accounts for measurement errors in both source and target coordinates, has gained significant research attention in measurement science as well as geospatial applications, particularly for geodetic datum transformation and point cloud registration. Current literatures have investigated the solutions to outlier-affected 3-D symmetric transformation problems through two types of approaches: robust estimation and data snooping. However, existing studies still lack a unified, robust, and computationally efficient framework capable of addressing general 3-D symmetric transformations (similarity, affine, and rigid) in the presence of outlier-contaminated measurements. To bridge this gap, we build upon our previous work to provide a unified formulation for these problems using the partial errors-in-variables (PEIV) model with equality constraints. Then, the equality-constrained PEIV model is solved using a constrained total least squares (CTLS) algorithm, and efficient computational formulas are derived. To enhance robustness and mitigate the impact of outliers, a novel data snooping algorithm for CTLS (DS-CTLS) is proposed, incorporating sensitivity analysis-based outlier detection mechanisms. Unlike the existing studies, DS-CTLS enables efficient outlier detection for generic 3-D symmetric transformation problems through a unified formulation framework. Experimental evaluations involving simulated similarity and affine transformations, as well as real-world rigid transformations in the application of point cloud registration, demonstrate that DS-CTLS achieves superior generality and enhanced robustness against outliers compared to existing state-of-the-art methods.
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