This paper describes the implementation of a simple, robust and cost-effective sensorless control technique for PMSM machines. The method uses stator current derivative measurements made in response to certain PWM vectors. In this work the derivatives are created from measurements made with standard hall-effect sensors (at the start and end of switching vectors), meaning that specialist transducers, such as Rogowski Coils, are not required. However, under narrow PWM vectors high frequency (HF) oscillations can disrupt the current and current derivative responses. In previous work, the time that PWM vectors were applied to the machine for was extended to a threshold known as the minimum pulse width (tmin) in order to allow the HF oscillations to decay and a derivative measurement to be obtained. This introduces additional distortion to the motor current. It is shown here that an artificial neural network can be used to estimate derivatives using measurements from a standard current sensor before the HF oscillations have fully decayed, thus permitting a reduction of the minimum pulse width (and associated distortion).