a method for determining a position of a rotor of a synchronous alternating - current permanent - magnet machine includes injecting a high - frequency voltage superimposed on a voltage delivered by a machine control system ; measuring a current of the motor and extracting a current corresponding to the injected voltage ; and obtaining , from the injected voltage and from the corresponding current , an electrical angle θ suitable to identify the position of the rotor by using a sine and cosine of twice the electrical angle θ of the machine .