<p>Bearing fault diagnosis for permanent magnet synchronous motors (PMSMs) under variable-speed conditions has always been a challenge. This paper proposes an observer-based tacholess order analysis method to diagnose motor bearing faults, where the frequency ambiguity caused by speed variation is well treated. First, a sliding mode observer is constructed based on the current state equation of the PMSM to estimate the extended electromotive force (EEMF). Second, the rotor speed is extracted from the EEMF by the phase locked loop. Then, synchronized sampling of the motor vibration signal is conducted according to the estimated rotor speed. Finally, the fault features of the reconstructed signal are attracted by linear predictive filtering and order analysis. Experimental validations for the bearing outer-ring crack demonstrate that the proposed method is effective even in scenarios where an encoder is not available, which shows promising prospects for the safety monitoring of PMSMs.</p>