A sensorless vector control strategy for induction machine (IM) operating in variable speed systems is presented. The sensorless control is based on a reduced-order linear observer based on terminal voltage and current as input signals. An estimation algorithm based on this observer is proposed to compute speed. It is shown that the proposed sensorless control is more sensitive to the stator resistance than to the rotor resistance. In order to tune the observer and to compensate for the parameter variations and the uncertainties, a separate estimation of the stator resistance is introduced. The equations to estimate the stator resistance are derived from the machine differential equations. For certain operating regions of the machine, it is verified that the stator resistance can be accurately estimated regardless of wide stator resistance variation. It is shown that design and hardware implementation of this method is simpler than the previous works. The simulation and experimental results demonstrate the good performance of the proposed observer and estimation algorithm and of the overall indirect-field-oriented-controlled system.