Starshades are a leading technology to enable the direct detection and spectroscopic characterization of Earth-like exoplanets. To maintain high contrast during observations, the starshade and telescope must keep within 1 m of relative alignment over large separations (>20,000 km). This formation flying is made possible with precise spacecraft position information obtained through accurate sensing of the occulted star’s diffraction peak (referred to as the spot of Arago) incident on the telescope aperture. We present a lightweight image processing method based on a convolutional neural network paired with a simulation-based inference technique to estimate the position of the spot of Arago and its uncertainty. On simulated images, the method achieves an accuracy of a few centimeters across the entire telescope aperture. By deploying our method at the Princeton Starshade Testbed, we demonstrate that the neural network can be trained on simulated images and used on real images and that it can successfully be integrated in the control system for closed-loop formation flying.