After a technical review on the stator resistance and rotor resistance identification methods for speed sensorless induction motor drives, this paper presents a different solution with a new representation of induction motor dynamics. By virtue of this representation, an adaptive observer is designed. The key step is to introduce the corrective terms and the filtered regressors, which forces the error dynamics of the observer to approach the ones in a form to which the Kalman-Yakubovich lemma can be applied. Only stator currents are required in the parameter adaptation rules. Particularly, the biased sinusoidal flux modulus command assures the convergence of parameters, and the consequent speed ripple problem is discussed. However, the aforementioned design has an imperfection and is found to be insufficient to assure stable operation in low-speed regeneration. Thus, further stability analysis based on the steady-state linearized model and remedies for stabilization are given. Effective experiment and simulation results are included.