In this study, three sensorless estimation algorithms are investigated for the position sensorless technology in the high-speed operation mode in permanent magnet synchronous motors, including the sliding-mode observer, the Luenberger observer, and the model-referenced adaptive system. The sliding mode observer algorithm has good stability, but due to the existence of the discontinuous switching value of the system, it is not conducive to extracting the effective back EMF. By adding a filter, the back EMF can be effectively extracted. Luenberger algorithm is simple, but back EMF coupling can lead to some interfering signals. For engineering purposes, a phase-locked loops needs to be added to make the estimation more accurate. The model reference adaptive system is relatively complicated, so the feedback adaptive law is designed based on Popov stability theory. Simulation analysis of three sensorless observer algorithms show that the sliding-mode observer algorithm has the best robustness. Compared with the Luenberger algorithm, it has fewer parameter and is conducive to engineering realization. The adaptive law design of MRAS is complicated by the fact that two sets of models are required for calculation. Therefore, the performance requirements of the controller are relatively high, which is not conducive to engineering implementation.