Scale drift is a crucial challenge for monocular autonomous driving to emulate the performance of stereo. This paper presents a real-time monocular SFM system that corrects for scale drift using a novel cue combination framework for ground plane estimation, yielding accuracy comparable to stereo over long driving sequences. Our ground plane estimation uses multiple cues like sparse features, dense inter-frame stereo and (when applicable) object detection. A data-driven mechanism is proposed to learn models from training data that relate observation covariances for each cue to error behavior of its underlying variables. During testing, this allows per-frame adaptation of observation covariances based on relative confidences inferred from visual data. Our framework significantly boosts not only the accuracy of monocular self-localization, but also that of applications like object localization that rely on the ground plane. Experiments on the KITTI dataset demonstrate the accuracy of our ground plane estimation, monocular SFM and object localization relative to ground truth, with detailed comparisons to prior art.