In recent years, the diffraction barrier in fluorescence imaging has been broken and optical nanoscopes now routinely image with resolutions of down to 20 nm, an improvement of more than 10 fold. Because this allows imaging much smaller features and because all super-resolution approaches trade off speed for spatial resolution, mechanical instabilities of the microscopes become a limiting factor. Here, we propose a fully data-driven statistical registration method for drift detection and drift correction for single marker switching (SMS) imaging schemes, including a guideline for parameter choice and quality checks of the drift analysis. The necessary assumptions about the drift are minimal, allowing a model-free approach, but more specific models can easily be integrated. We determine the resulting performance on standard SMS measurements and show that the drift determination can be routinely brought to the range of precision achievable by fiducial marker-tracking methods.