We introduce the concept of multi-parameter estimation to enable far-subwavelength imaging with relative motion between a structured field and an object, where either the object or the field moves. Conventional optical imaging techniques are limited to a spatial resolution dictated by the Abbe diffraction limit, around half the optical wavelength depending on constraints and interpretation. Structured illumination microscopy is commonly used to improve this limit by a factor of two. We show that when a field is scanned over an object, multiple far-subwavelength geometric features can be accessed from a far-field measurement with existing lasers and detectors. This work indicates new super-resolution microscopy and other sensing opportunities, with resolution as high as one thousandth of a wavelength.