Analytical solution of uncertainty with the GUM method for a dynamic stereo vision measurement system

Directed at the strong correlation among the input parameters and long measurement chain, which are difficult for uncertainty analysis with the guide of the expression of uncertainty in the measurement (GUM) method, a novel dynamic stereo vision measurement system based on the quaternion theory is presented to reduce the orthogonality restrictions of shafting manufacturing and application. According to the quaternion theory in the kinematic model of the cameras and the analytical solution of uncertainty with the GUM method, the complete, detailed, and continuous uncertainty results of the full-scale measurement space can be obtained. Firstly, one-dimensional turntables and rigid connections are utilized to form the motion cores and the automatic control carriers in the system. Secondly, the novel measurement model is used in the measurement process to shorten the calibration and measurement chains. Once the system based on the novel measurement model is set up, the analytical solution of uncertainty is utilized in the accuracy process. During the analysis process, the strong correlation among the extrinsic parameters is decoupled by introducing virtual circles and the measurement strategy with the GUM method. Through analyzing the relationship among the attitude angles, the major factors which influence the uncertainties in each axis and the final uncertainty are clarified. Moreover, the analytical continuous uncertainty maps for the uncertainties along each axis, combined standard uncertainty, and the expanded uncertainty are illustrated and the uncertainty variation tendency is declared. Finally, the analytical solution of uncertainty with the GUM method proposed in this paper predicts the uncertainty in the full-scale space and provides a new idea of the uncertainty analysis for the complicated combined measurement system.