Parameter variations strongly affect the application of indirect field-oriented control (FOC) of the induction motor. To estimate those parameters which cannot be obtained by means of a direct measure, an augmented state observer can be constructed; in particular, the presence of noise introduced by the inverter and sensors suggests the use of an extended Kalman filter (EKF). In this paper, by analysing the indirect FOC technique via a two-time-scale approach, we formally justify its effectiveness and propose a reduced-order EKF which is used to construct an adaptive version of the FOC method. The practical drawback of reduced-order EKFs, i.e. the necessity to differentiate measured quantities, is avoided by exploiting some peculiarities of the field-oriented controller.