One of the main difficulties faced in commissioning a sensorless AC motor drive based on an Extended Kalman Filter (EKF) still remains the fine tuning of the noise covariance matrices of the model used for the state estimation. An inadequate choice penalizes the overall system performance, and is the most common cause of the filter divergence. Several manual or automated tuning methods exist in literature, but they often involve time consuming procedures, and are ineffective in dealing with variations of the system dynamics. Aimed to overcome these limitations, in this paper we investigate on the advantages of using an Adaptive Extended Kalman Filter (AEKF) algorithm based on Maximum Likelihood Estimation (MLE) for the simultaneous estimation of the system state and the unknown noise covariance matrices. By continuously adjusting the filter parameters to the actual operating conditions, the proposed system demonstrates greater robustness and outperforms conventional solutions relying on manually tuned EKFs.