A New Way for Cartesian Coordinate Transformation and Its Precision Evaluation

Abstract

High-precision coordinate transformation is vital for high-quality data fusion involving different coordinate systems. The transformation precision is mainly evaluated by the transformation parameters’ estimation precision, the root mean square error (RMSE) of the conversion of common points, or the RMSE of the conversion of check points. However, there are a number of issues associated with the rotation parameters’ precision estimated by the existing transformation methods. First, the estimated precision is related to the rotation matrix, so it is not suitable for scenarios where different rotation matrices are used. Second, the RMSE of the conversion of check points may not be consistent with the RMSE of the conversion of common points, so that the RMSE of the conversion of common points should not be used as a transformation precision index. In addition, some engineering applications do not have check points, and many applications need to know which range of points can meet our requirements. To deal with these limitations, this paper proposes a new way to calculate the translation parameters and evaluate the transformation precision. A lot of experimental data was used to verify the effectiveness and applicability of the proposed transformation model.

Keywords

• coordinate transformation
• seven-parameter transformation model
• precision evaluation
• arbitrary rotation angle