Data snooping algorithm for universal 3D similarity transformation based on generalized EIV model

摘要

Three-dimensional (3D) similarity datum transformation is extensively applied in geodetic field and many other areas. In recent years, the total least squares (TLS) solution for universal 3D similarity transformation problem (with arbitrary rotation angles and scale ratio) has become a hot research issue and many algorithms have been proposed. However, the estimated transformation parameters are affected or even severely distorted when the observed coordinates are contaminated by gross errors. In this study, the 3D similarity transformation problem is described as a generalized errors-in-variables (EIV) model, and then the data snooping algorithm for this model is proposed. The weighted total least squares (WTLS) solution to the generalized EIV model is firstly derived through Euler-Lagrange method and then we reformulate it as a classical least squares problem. Two types of test statistics for data snooping are constructed based on the classical least squares theory under the conditions with known and unknown variance component, respectively. The results of the real and simulated experiments indicate that the proposed algorithm can effectively reduce the influence of the gross errors and obtain reliable transformation parameters.