The motion of a driving car is highly constrained and we claim that powerful predictors can be built that learn the typical egomotion statistics, and support the typical tasks of feature matching, tracking, and egomotion estimation. We analyze the statistics of the ground truth data given in the KITTI odometry benchmark sequences and confirm that a coordinated turn motion model, overlaid by moderate vibrations, is a very realistic model. We develop a predictor that is able to significantly reduce the uncertainty about the relative motion when a new image frame comes in. Such predictors can be used to steer the matching process from frame n to frame n + 1. We show that they can also be employed to detect outliers in the temporal sequence of egomotion parameters.