I. Introduction
The permanent magnet synchronous motors (PMSMs) are used in many different applications ranging from industrial automation to domestic appliances and electric vehicles [1]–[3]. The vector control algorithms of the PMSM drives require rotor position feedback which is obtained by a shaft-mounted optical encoder or a resolver in a conventional drive. The shaft sensor may reduce the overall ruggedness of the drive and increases its cost and size [4]–[6]. To eliminate the electromechanical position sensors, sensorless methods have been introduced, that determine the electrical rotor position usually based on current measurement and an extended machine model. Sensorless methods that are based on the fundamental excitation model are reliable above about 3 % of the nominal speed [6]–[10]. However, to start the PMSM drive without any undesirable vibrations and reverse rotation, the initial rotor position and the polarity of the rotor magnets also have to be detected [11].