Circle fitting using semi-definite programming

The fitting of a collection of noisy data points to a circle is a nonlinear and challenging problem, and it plays an important role in many signal processing applications. This paper proposes a semi-definite programming solution for the circle fitting problem based on the semi-definite relaxation technique. The relaxation of the maximum likelihood estimation converts a nonconvex problem to an approximate but convex one that can be solved by using the semi-definite programming method. The performance of the proposed solution is examined via simulations and compared with the Kasa method.