Abstract: A state observer based on adaptive fixed-lag Kalman smoother for prosthetic hand system with potentiometer as angle sensor is proposed to observe the current position, velocity and acceleration of the fingers. Firstly, the rationality is analyzed which using Kalman filter to filter the thermal noise of the potentiometer and observe the velocity and acceleration, and a discrete state transfer matrix of the system is established. The Kalman smoother has better smoothing effect than the Kalman filter under the same parameters. A state observer based on fixed-lag Kalman smoother is proposed, and a fading factor is introduced to improve the dynamic response. At the same time, an effective way is given to reduce the hysteresis characteristics of the proposed algorithm to one control cycle. Finally, experiments are performed on the HIT-V prosthetic hand experiment platform. The experimental results show that the proposed method significantly reduces the velocity noise by more than 20 times and the acceleration noise by more than 10 000 times comparing with the direct difference of the original data. Compared with the standard Kalman filter and the fixed-lag Kalman smoother, the proposed method has better effect on dynamic response.