Linear pushbroom cameras are widely used in passive remote sensing from space as they provide high resolution images. In earth observation applications, where several pushbroom sensors are mounted in a single focal plane, small dynamic disturbances of the satellite's orientation lead to noticeable geometrical distortions in the images. In this paper, we present a global method to estimate those disturbances, which are effectively vibrations. We exploit the geometry of the focal plane and the stationary nature of the disturbances to recover undistorted images. To do so, we embed the estimation process in a Bayesian framework. An autoregressive model is used as a prior on the vibrations. The problem can be seen as a global image registration task where multiple pushbroom images are registered to the same coordinate system, the registration parameters being the vibration coefficients. An alternating maximisation procedure is designed to obtain Maximum a Posteriori estimates (MAP) of the vibrations as well as of the autoregressive model coefficients. We illustrate the performance of our algorithm on various datasets of satellite imagery.