This paper suggests a novel methodology for the estimation of motor speed in the low speed range, in the presence of random disturbances. The angular velocity is estimated from the position data using a single rotary encoder. A typical model-based Kalman filter has limitations when applied to robotics; hence, a filter is designed based on the relations between the kinematic parameters. We have investigated the position and angular velocity tracking performance of a standard kinematic Kalman filter (KKF), and suggested a modified Kalman filter that overcomes the defects of the standard KKF. The performances of the two filters were compared with respect to the estimation of the position and angular velocity in the presence of random disturbances.