The fusion of a 3D reconstruction up to a similarity transformation from monocular videos and the metric positional measurements from GPS usually relies on the alignment of the two coordinate systems. When positional measurements provided by a low-cost GPS are corrupted by high-level noises, this approach becomes problematic. In this paper, we introduce a novel framework that uses similarity invariants to form a tetrahedral network of views for the fusion. Such a tetrahedral network decouples the alignment from the fusion to combat the high-level noises. Then, we update the similarity transformation each time a well-conditioned motion of cameras is successfully identified. Moreover, we develop a multi-scale sampling strategy to reduce the computational overload and to adapt the algorithm to different levels of noises. It is important to note that our optimization framework can be applied in both batch and incremental manners. Experiments on simulations and reed datasets demonstrate the robustness and the efficiency of our method.
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