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This work presents a method using carrier-frequency injection to estimate the initial rotor position and magnetic polarity for an interior permanent-magnet synchronous machine. A nonsaturating inductance model of the machine provides no information about the polarity of the rotor magnet because the position observer based on this model is locally stable at both poles. To distinguish the polarity of the rotor magnet, the magnetic saturation effect can be used. The Taylor series can be used to describe the nonlinear magnetic saturation relationship between the current and the flux linkage in the d-axis rotor reference frame. The second-order term produces the second harmonic component of the carrier frequency, and the sign of its coefficient identifies the polarity of the rotor magnet being tracked. Both simulation and experimental results show good response of the position observer at several rotor electrical positions using either a rotating vector in the stationary reference frame or a oscillating vector in the estimated rotor reference frame.