An apparatus includes an electric motor including a stator and a translator; a three-phase inverter electrically coupled to the electric motor; a power source electrically coupled to the three-phase inverter; and a controller communicatively coupled to the three-phase inverter. The controller is programmed to determine at least three measurements at different times of flux linkage from the electric motor, represent the measurements in Clarke coordinates, determine Clarke coordinates of a center of a circle defined by the Clarke coordinates of the measurements, and determine a position of the translator relative to the stator based on the Clarke coordinates of the center of the circle.