A robust circle fitting method for component fiducialization

Abstract

The fiducialization for the round component is an indispensable step in the alignment. The traditional geometric and algebraic fitting algorithms are prone to be contaminated by outliers and the accuracy of existing robust algorithms can be further improved. In this study, we present a robust weighted Hyper method that combines the strengths of both the M-estimator and the Hyper method. Through Black-Rangarajan duality, outliers are assigned minimal or even zero weights, effectively enhancing robustness. We tested the proposed algorithm with several benchmarking algorithms using Monte Carlo data. In the presence of outliers, our method demonstrates the lowest root mean squared errors (RMSE). Specifically, when fitting points observed by the laser tracker in Dalian Advanced Light Source (DALS), our method outperforms existing algorithms in terms of repeat accuracy, yielding standard errors (STD) of 11.7μm and 14.31μm for the center and radius respectively. The robust weighted Hyper algorithm enhances fiducialization precision without requiring additional instruments and provides valuable guidance in the alignment.