This paper focuses on the sensorless control of the bearingless doubly salient permanent motor (BDSPM) with a sinusoidal driver. Conventional sensorless control for interior permanent-magnet motors based on the extended electromotive force (EEMF) is not applicable to BDSPMs since the inductance of two types of motors alternate at different frequencies with the same electrical angular velocity. To solve this problem, we propose performing a Park Transform using a transform angle which is half of the electrical angle. In the new dq coordinate frame, the inductance matrix is derived to be a constant diagonal matrix, which allows a typical extended electromotive force (EEMF) to be feasible. By observing the EEMF derived by the proposed Park Transform, we effectively estimate the rotor angle with a sliding mode observer (SMO). The instructions on parameter selection of the SMO are presented, which guarantees the asymptotic convergence of the EEMF. We experimented with the proposed method with a BDSPM prototype, and the result shows that the sensorless observer can accurately track the angle from medium to high speeds.