Abstract-Transmission electron microscopes are the tools of choice in materials science, semiconductor, and biological research and it is expected that they will be increasingly used to autonomously perform high-volume, repetitive, nanomeasurements in the near future. Thus, there is a clear need to develop automation strategies for these microscopes.This paper introduces an adaptive minimum variance control scheme to compensate specimen drift, a common cause of image blurring in long-exposure images. The controller, which is new in the electron microscope literature, makes use of ARMASA, a statistical toolbox designed to identify linear models from finite-length data sets, to generate ARMA models of the drift process 'on-the-fly'. These models are then used as part of a controller designed to reduce the drift variance. The benefits of the proposed scheme, which can be quite substantial, are illustrated through a set of simulations that use a model of the drift present in a sequence of experimental images.