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This paper considers the problem of removing unwanted noise from a gaze tracking signal real-time. The proposed remedy is a linear dynamic model for the gaze and a Kalman filter for estimating its optimal solution in closed form. The location and velocity of gaze are treated as independent parameters of the model. Two alternative methods for estimating the velocity are presented; the first is based on the difference in the subsequent eye images and the second on the PCA model and an affine mapping from the principal component space to the gaze space. The covariance matrix of the measurement noise distribution is modified real-time based on the estimated velocity. The presented filtering algorithm can be utilized with any eye camera based gaze tracker. Here, its ability to decrease noise of two published gaze tracking methods is demonstrated.