Iteratively weighted least squares solution for universal 3D similarity transformation

Abstract

The 3D similarity coordinate transformation is widely used to estimate the transformation parameters for measurement datum transformation. Accurate and reliable transformation parameters are crucial for accurate and reliable data integration. However, the accuracy of the transformation parameters can be significantly affected or even severely distorted when the observed coordinates are contaminated by gross errors. To address this problem, an advanced iteratively weighted least squares (IWLS) solution based on the weighted least squares (WLS) is proposed. This solution utilizes the singular value decomposition (SVD) method to obtain the rotation matrix and introduces a novel weight estimation approach based on Gaussian function. This approach enables the weight to be normalized and optimized iteratively. To verify the accuracy and reliability of the proposed algorithm, the root mean square errors (RMSEs) from both true and pseudo-observed values are analyzed by simulation experiments. Furthermore, the results of simulated and empirical experiments show that the proposed algorithm can effectively reduce the influence of gross errors to obtain reliable measurement datum transformation parameters. It should be noted that the new algorithm can easily be extended to the 2D/3D affine and rigid transformation cases, such as image matching, point cloud registration, and absolute orientation of photogrammetry.

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