Structured illumination microscopy (SIM) uses a set of images captured with different patterned illumination to computationally reconstruct resolution beyond the diffraction limit. Here, we propose an alternative approach using a static speckle illumination pattern and relying on inherent sample motion to encode the super-resolved information in multiple raw images, for the case of fluorescence microscopy. From a set of sequentially captured raw images, we jointly estimate the sample motion and the super-resolved image. We demonstrate the feasibility of the proposed method both in simulation and in experiment.