This paper aims to improve the full speed sensorless drive for permanent-magnet (PM) synchronous machines on the region of initial zero speed and the region of medium speed. At zero and low speed, the saliency-based drive using the square-wave voltage injection has demonstrated the comparable performance to the sensor-based drive using the encoder with hundreds of pulses per revolution. For PM machines at initial state, the magnet polarity is typically identified based on the injection of voltage pulses before the saliency-based drive. Instead of pulses injection, this paper directly adds the polarity detection capability in the saliency-based drive by superimposing the same square-wave voltage. A fast detection period and negligible current spikes are benefits for the drive using the same square-wave injection voltage for both the polarity detection and position estimation. At medium speed, electromotive force voltage can be estimated to replace the saliency for the sensorless drive. To achieve a smooth operation between two estimation methods, a transition algorithm is also proposed based on a single-phase-lock loop by blending two feedback position signals. According to the experimental evaluation, the reduced power consumption as well as the smooth switch between two different drives is achieved. All the sensorless methods are verified by an interior PM machine with a saliency ratio of 1.37 (L_q/L_d = 1.37).