In a sensorless control of PMSM based on Extended Kalman Filter (EKF), the correct selection of system and measurement noise covariance has a great influence on the estimation performances of the filter. In fact, it is extremely difficult to find their optimal values by trial and error method. Therefore, the main contribution of this work is to prove the efficiency of Biogeography-Based-Optimization (BBO) technique to obtain the optimal noise covariance matrices Q and R. The BBO and EKF combination gives a BBO-EKF algorithm, which allows to estimate all the state variables of PMSM drive particularly, the rotor position and speed. In this paper, three evolutionary algorithms namely Particle Swarm Optimization (PSO), genetic algorithms (GAs) and BBO are used to get the best Q and R of EKF. Simulations tests performed in Matlab Simulink environment show excellent performance of BBO-EKF compared to GAs-EKF and PSO-EKF approaches either in resolution or in convergence speed.