Paper:
Translation Synchronization via Truncated Least Squares
In this paper, we introduce a robust algorithm, TranSync, for the 1D translation synchronization problem, in which the aim is to recover the global coordinates of a set of nodes from noisy measurements of relative coordinates along an observation graph. The basic idea of TranSync is to apply truncated least squares, where the solution at each step is used to gradually prune out noisy measurements. We analyze TranSync under both deterministic and randomized noisy models, demonstrating its robustness and stability. Experimental results on synthetic and real datasets show that TranSync is superior to state-of-the-art convex formulations in terms of both efficiency and accuracy.

Review:
In this paper the authors describe a robust and scalable algorithm,TranSync, for solving the 1D translation synchronization problem. The algorithm is quite simple, to solve a truncated least squares at each iteration, and then the computational efficiency is superior to state-of-the-art methods for solving the linear programming formulation. On the other hand, the analyze TranSync under both deterministic and randomized noise models, demonstrating its robustness and stability. In particular, when the pair-wise measurement is biased, TranSync can still achieve sub-constant recovery rate, while the linear programming approach can tolerate no more
than 50% of the measurements being biased. The paper is very readable and
the proofs of main theorems are clear and appear correct. However, it will be good if the authors can provide more intuition behind the theorem. The numerical experiments are complete and clear.