Saccadic Ratio (SR), a ratio between Peak Saccadic Velocity and the Saccadic Duration, exhibits correlation with human alertness. A simple non-linear model of horizontal saccade with input as the position of pupil center relative to the corners is proposed. The relative position of pupil center is initially determined using recently developed method based on horizontal, and vertical form factors and edge detection method based on local form factor. An Extended Kalman filter based algorithm has been developed to estimate the saccadic velocity and the saccadic ratio from this initial information for eye image video database captured with a speed higher than 60 fps. A Kalman filter based technique is also applied on the same database and the results are compared with that of the proposed method. Correlation of SR with a questionnaire based alertness assessment index is investigated. The experimental results indicate that the estimated SR by the proposed method is highly correlated with state of human alertness.