A saliency back-EMF estimator with a proportional-integral-derivative neural network (PIDNN) torque observer is proposed in this study to improve the speed estimating performance of a sensorless interior permanent magnet synchronous motor (IPMSM) drive system for an inverter-fed compressor. The PIDNN torque observer is proposed to replace the conventional proportional-integral-derivative (PID) torque observer in a saliency back-EMF estimator to improve the estimating performance of the rotor flux angle and speed. The proposed sensorless control scheme use square-wave type voltage injection method as the start-up strategy to achieve sinusoidal starting. When the motor speed gradually increases to a preset speed, the sensorless drive will switch to the conventional saliency back-EMF estimator using the PID observer or the proposed saliency back-EMF estimator using the PIDNN observer for medium and high speed control. The theories of the proposed saliency back-EMF rotor flux angle and speed estimation method are introduced in detail. Moreover, the network structure, the online learning algorithms and the convergence analyses of the PIDNN are discussed. Furthermore, a DSP-based control system is developed to implement the sensorless inverter-fed compressor drive system. Finally, some experimental results are given to verify the feasibility of the proposed estimator.Key Words: Sensorless DC inverter-fed compressor, interior permanent magnet synchronous motor, proportional-integralderivative neural network, torque observer, saliency back-EMF, rotor flux angle and speed estimation.