This two-part study proposes a new sensorless control strategy for non-sinusoidal multiphase permanent magnet synchronous machines (PMSMs), especially integrated motor drives (IMDs). Based on the Sliding Mode Observer (SMO), the proposed sensorless control strategy uses the signals (currents and voltages) of all fictitious machines of the multiphase PMSMs. It can estimate the high-accuracy rotor positions that are required in vector control. This proposed strategy is compared to the conventional sensorless control strategy that applies only current and voltage signals of the main fictitious machine, including the fundamental component of back electromotive force (back EMF) of non-sinusoidal multiphase PMSMs. Therefore, in order to choose an appropriate sensorless control strategy for the non-sinusoidal multiphase PMSMs, these two sensorless control strategies will be highlighted in terms of precision with respect to rotor position and speed estimation. Simulations and the experimental results obtained with a non-sinusoidal seven-phase PMSM will be shown to verify and compare the two sensorless control strategies. In this part of the study (part I), only sensorless control in the medium and high-speed range is considered. Sensorless control at the zero and low-speed range will be treated in the second part of this study (part II).