This paper focuses on the improvement of an air-gap-power-vector-based observer for sensorless doubly fed induction generators. After showing how a mismatch in the machine inductances can worsen the performance of the basic observer scheme, an adaptive tuning of the stator inductance is proposed. The adaptation is achieved by minimizing the error between the squared modulus of two suitable air-gap complex power space vectors. A criterion to settle the dynamics of the adaptation mechanism is provided, and a sensitivity analysis in the steady-state operation is performed. Some experimental results are reported and discussed in order to validate the soundness of the proposed adaptive tuning algorithm.