We present a new method to correct eye movement artifacts in electroencephalogram (EEG) data. By using an eye tracker, whose data cannot be corrupted by any electrophysiological signals, an accurate method for correction is developed. The eye-tracker data is used in a Kalman filter to estimate which part of the EEG is of ocular origin. The main assumptions for optimal correction are summed and their validity is proven. The eye-tracker-based correction method is objectively evaluated on simulated data of four different types of eye movements and visually evaluated on experimental data. Results are compared to three established correction methods: Regression, Principal Component Analysis, and Second-Order Blind Identification. A comparison of signal to noise ratio after correction by these methods is given in Table II and shows that our method is consistently superior to the other three methods, often by a large margin. The use of a reference signal without electrophysiological influences, as provided by an eye tracker, is essential to achieve optimal eye movement artifact removal.