An Approximate Maximum Likelihood Linear Estimator of Circle Parameters

The problem of estimating the center and radius of a circle from a given set of noisy coordinate measurements has many applications. Even though the estimation process is inherently nonlinear, it is possible to obtain linear estimators, which are attractive because of their simplicity. This paper presents an approximate maximum likelihood estimator of circle parameters. It is linear. Simulation results showed that under conditions of small arc length and high noise, which occur often in practice, the new estimator outperforms the linear estimator of S. Thomas and Y. T. Chan (Comput. Vision Graph. Image Process.45 (1989), 362–370).