This paper investigates the rotor position errors introduced by inductance asymmetry and proposes an error suppression method in high frequency signal injection based sensorless control of permanent magnet synchronous machines. It is shown that a 2nd order harmonic error is introduced in the position estimation and for a given inductance asymmetry, the amplitude of this error is theoretically proved to be the same for square wave, pulsating, and rotating signal injection sensorless control methods. The proposed rotor position error suppression method based on a synchronous reference frame filter can effectively suppress the 2nd order harmonic error in not only square wave, but also pulsating and rotating based high frequency signal injection sensorless control methods. The theoretical analyses and the proposed suppression method are validated by simulation and experiment results.