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

Abstract

The use of the Kaiman filter to find optimal fits to short sections of ellipse data, and to predict confidence envelopes to facilitate search for further ellipse data, is described. The extended Kaiman 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 Kaiman filter. The estimate covariance is used to evaluate confidence envelopes for the fitted ellipse. Performance is shown on both real and synthetic data.