Abstract: A conventional Kalman filter is suitable for integerorder systems. In order to apply the Kalman filter to fractionalorder systems， a statespace expression defined by discrete fractionalorder calculus is introduced into the conventional Kalman filter， thus a fractionalorder Kalman filter algorithm is proposed. A simulation experiment is carried out， with two state variables and one output signal as research objects. The fractionalorder Kalman filter module is designed in MATLAB. The states of the system are estimated by the input variables and the output variable with noise， showing that the fractionalorder Kalman filter algorithm proposed has satisfactory filtering and stateestimating capacity.

Key words: fractionalorder system, Kalman filter, state estimation, simulation, MATLAB