We propose a general framework for group synchronization with adversarial corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently infer the corrupted group ratios and solve the synchronization problem. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further show that under a uniform corruption model, the recovery results are sharp in terms of an information-theoretic bound.

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This paper intends to analyze the Light Detection and Ranging (Lidar) sensor performance on detecting pedestrians under different weather conditions. Lidar sensor is the key sensor in autonomous vehicles, which can provide high-resolution object information. Thus, it is important to analyze the performance of Lidar. This paper involves an autonomous bus operating several pedestrian detection tests in a parking lot at the University at Buffalo. By comparing the pedestrian detection results on rainy days with the results on sunny days, the evidence shows that the rain can cause unstable performance and even failures of Lidar sensors to detect pedestrians in time. After analyzing the test data, three logit models are built to estimate the probability of Lidar detection failure. The rainy weather still plays an important role in affecting Lidar detection performance. Moreover, the distance between a vehicle and a pedestrian, as well as the autonomous vehicle velocity, are also important. This paper can provide a way to improve the Lidar detection performance in autonomous vehicles.

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm ofÖzyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee for camera locations was established for the ShapeFit algorithm by Hand, Lee and Voroninski, but with typically less corruption. * This work was supported by NSF award DMS-14-18386. We are grateful for the anonymous reviewers and the action editor for the careful reading of the manuscript and the useful suggestions.