In this paper, a modified Kalman filter is proposed to estimate speed. At first, the influence of the magnetic saturation is taken into account in the modelling. In the second part, the direct torque control (DTC) is elaborated; the control of the speed loop is ensured by an IP controller, the flux and the torque are estimated from source voltages and measured currents. The last part of this work is devoted to the operating system without mechanical sensor, using a Kalman filter as a speed observer. Simulation results are presented to verify the effectiveness of the proposed approach.