This paper presents an effective implementation of an extended Kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor. An algorithm proposed by Hsieh and Chen in [Hsieh, C.S., & Chen, F.C. (1999). Optimal solution of the two-stage Kalman estimator. IEEE Transactions on automatic control, 44(l), 194-199] for linear parameter estimation is extended to non-linear estimation, where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space. Compared to a straightforward implementation of an extended Kalman filter, our modified optimal two-stage Kalman estimator reduces the number of arithmetic operations by 25%. allowing higher sampling rate or the use of a cheaper microcontroller. (C) 2009 Elsevier Ltd. All rights reserved.