This paper proposes a permanent-magnet (PM) machine position-sensorless drive for high speed (> 10-kr/min) applications. A discrete-time back electromotive force (EMF) voltage estimation method is developed to overcome several high-speed position sensing issues, including the voltage error due to the digital-to-analog conversion, inductive cross-coupling, and deviation between the estimated EMF and actual EMF resulting from the digital implementation. To overcome these problems, an observer-based EMF estimation is proposed with three implementation considerations. They are 1) a discrete-time dq current observer to remove the inductive cross-coupling effect for the EMF estimation, 2) a delay model to compensate the voltage error, and 3) a discretized model to estimate the sampled EMF in the discrete-time. A high-speed PM machine is experimentally evaluated to verify all proposed sensorless drive methods.