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In earlier work closed-form trajectory bending was shown to provide an efficient and accurate out-of-core solution for loop-closing exactly sparse trajectories. Here we extend it to fuse exactly sparse trajectories, obtained from relative pose estimates, with absolute orientation data. This allows us to close-the-loop using absolute orientation data only. The benefit is that our approach does not rely on the observations from which the trajectory was estimated nor on the probabilistic links between poses in the trajectory. It therefore is highly efficient. The proposed method is compared against regular fusion and an iterative trajectory bending solution using a 5 km long urban trajectory. Proofs concerning optimality of our method are provided.

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