A new short-arc fitting method with high precision using Adam optimization algorithm

The high-precision short-arc measurement is a huge challenge in scientific research and engineering practice. The popular traditional least square fitting (TLSF) however fails to achieve the precise fitting parameters when the arc gets shorter. In this work, an inequation constrained fitting (ICF) method based on four-parameter circle equation is presented. Lagrangian multiplier and Karush-Kuhn-Tucker criteria are used to redefine the objective function. After that, Adam algorithm is utilized to solve the objective function in iterative way. Adam algorithm has a strong ability to resist noise pollution by virtue of modifying continually the first-order momentum and second-order momentum with average of gradients during the course of iteration. Finally, simulation and experimental results show that our ICF method is more robust and high-precision than TLSF and Hyper method, so it is very competent to measure short arcs with noise even their central angles are close to 5°.