Robust Estimation Model for 3D Coordinate Transformations based on Differential Total Least Squares Algorithm

Abstract

Existing Gauss-Newton methods for solving the problem of 3D similarity transformation are all based on the method of numerical partial derivatives, which can linearize the 3D similarity transformation model by using Taylor expansion for approximated variables to the first order derivative. And by using the linearized 3D transformation model, all of the unknown variables can be obtained by an iterative process. In existing models, the model considering random errors of design matrix is called errors-in-variables (EIV) model. In contrast to the Gauss-Newton methods, a Gauss-quasi-Newton method for solving the problem of 3D similarity transformation is proposed in this paper. In the Gauss-quasi-Newton method, 3D similarity transformation model is linearized by a differential method, and based on the differential linearization model, an iterative robust estimation can be carried out by considering both random errors and gross errors in 3D coordinates of common points. The new method proposed in this paper can be applied to 3D similarity transformation of arbitrary rotational angles. Finally, the new method is validated by three cases, and results showed that the new method is effective and feasible.