This paper develops a position self-sensing approach for a motion actuator based on a dielectric elastomer membrane. The proposed method uses voltage and current measurements to estimate the electrical resistance and capacitance online by means of a high-frequency low-amplitude voltage component injected in the actuation signal. The actual deformation is subsequently reconstructed using a model-based estimate of the electrical parameters implemented on a field programmable gate array platform (FPGA) with a sampling frequency of 20 kHz. The main peculiarity of the approach is the use of recursive identification and filtering algorithms that avoid the need of charge measurements. The self-sensing algorithm is extensively validated on a precision linear-motion actuator, which uses a nonlinear biasing system to obtain large actuation strokes.