Abstract: The parameter estimation will be adversely affected when the observation coordinates are polluted by gross errors. In this study, the 3D coordinate transformation problem is described as a generalized errors-in-variables (EIV) model, and the data snooping algorithm for this model is proposed. Firstly, the generalized total least squares (GTLS) solution of the nonlinear EIV model is derived by using the Euler Lagrange method, and then it is transformed into the 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 experimental results show that the proposed data detection algorithm can effectively reduce the influence of gross errors and obtain reliable conversion parameters.

Key words: 3D coordinate transformation, total least squares, outlier detection, generalized EIV model