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Fitting Noisy Data to a Circle: A Simple Iterative Maximum Likelihood Approach

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Executive Summary

Fitting noisy measurements to a circle is a classic statistical estimation problem. In this paper, the authors make two contributions to the study of this problem. First, they propose a novel formulation of the Maximum Likelihood (ML) estimator for identifying the center and radius of the circle from noisy measurements. This new estimator uses the unknown true values of the measurement points as the nuisance parameter to obtain an exact ML formulation. Second, from the insights gained in deriving the optimum solution, a computationally simple circle fitting algorithm based on greedy search is proposed.

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