Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter

We describe the use of the Kalman filter to find optimal fits to short sections of ellipse data and to predict confidence envelopes in order to facilitate search for further ellipse data. The extended Kalman filter in its usual form is shown not to reduce the well known bias to high curvature involved in least squares ellipse fitting. This problem is overcome by developing a linear bias correction for the extended Kalman filter. The estimate covariance is used to evaluate confidence envelopes for the fitted ellipse. Performance is shown on both real and synthetic data.