An impartial trimming algorithm for robust circle fitting

Accurate circle fitting can be seriously compromised by the occurrence of even few anomalous points. Then, it is proposed to resort to a robust fitting strategy based on the idea of impartial trimming. Malicious data are supposed to be deleted, whereas estimation only relies on a set of genuine observations. The procedure is impartial in that trimmed points are not decided in advance but they are detected simultaneously to parameters estimation, according to an iterative algorithm: in each step a fixed proportion of the data is trimmed after sorting their geometric distances from the current fitted circle in non decreasing order. A reweighting step is also considered to improve the quality of the fit and make it less dependent on the selected trimming level. The global robustness properties of the method are established. The finite sample behavior of the proposed estimator has been investigated according to some numerical studies and real data examples.