A Provably Robust Multiple Rotation Averaging Scheme for SO(2)

We give adversarial robustness results for synchronization on the rotation group over $\mathbb{R}^2$, $\mathrm{SO}(2)$. In particular, we consider an adversarial corruption setting, where an adversary can choose which measurements to corrupt as well as what to corrupt them to. In this setting, we first show that some common nonconvex formulations, which are categorized as "multiple rotation averaging", may fail. We then discuss a new fast algorithm, called Trimmed Averaging Synchronization, which has exact recovery and linear convergence up to an outlier percentage of $1/4$.