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Accurately perceiving location and scene is crucial for autonomous driving and mobile robots. Recent advances in deep learning have made it possible to learn egomotion and depth from monocular images in a self-supervised manner, without requiring highly precise labels to train the networks. However, monocular vision methods suffer from a limitation known as scale-ambiguity, which restricts their application when absolute-scale is necessary. To address this, we propose SelfOdom, a self-supervised dual-network framework that can robustly and consistently learn and generate pose and depth estimates in global scale from monocular images. In particular, we introduce a novel coarse-to-fine training strategy that enables the metric scale to be recovered in a two-stage process. Furthermore, SelfOdom is flexible and can incorporate inertial data with images, which improves its robustness in challenging scenarios, using an attention-based fusion module. Our model excels in both normal and challenging lighting conditions, including difficult night scenes. Extensive experiments on public datasets have demonstrated that SelfOdom outperforms representative traditional and learning-based VO and VIO models.