Precision Motion Measurement for Linear Motor Based on FNCC and Phase Difference M-Estimator Robust Regression in a VLSM System

This paper investigates a low-cost vision-based line-scan measurement (VLSM) system to achieve the high-precision positioning of linear motors. And an improved two-step phase difference method is performed for detecting subpixel translation of 1-D multi-frame images. In the first step of the algorithm, a fast normalized cross-correlation (FNCC) is adopted for coarse estimation to extract the overlapping portions of the two frames. In the second step, M-Estimator robust regression method is used to estimate the displacement parameters of the phase difference matrix of the overlap further accurately. The simulation cases indicate that the proposed approach outperforms the other existing methods in accuracy and robustness. In addition, the system and proposed algorithm are effectively validated in experiments and achieve a displacement detection of 0.01 mm grade of the mover.