Abstract-Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finiteorder autoregressive processes with unidirectional information flow between two variables, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.

This article presents a robust approach to navigating at high speed across desert terrain. A central theme of this approach is the combination of simple ideas and components to build a capable and robust system. A pair of robots were developed, which completed a 212 km Grand Challenge desert race in approximately 7 h. A pathcentric navigation system uses a combination of LIDAR and RADAR based perception sensors to traverse trails and avoid obstacles at speeds up to 15 m/s. The onboard navigation system leverages a human-based preplanning system to improve reliability and robustness. The robots have been extensively tested, traversing over 3500 km of desert trails prior to completing the challenge. This article describes the mechanisms, algorithms, and testing methods used to achieve this performance.

This article presents a robust approach to navigating at high speed across desert terrain. A central theme of this approach is the combination of simple ideas and components to build a capable and robust system. A pair of robots were developed, which completed a 212 km Grand Challenge desert race in approximately 7 h. A pathcentric navigation system uses a combination of LIDAR and RADAR based perception sensors to traverse trails and avoid obstacles at speeds up to 15 m/s. The onboard navigation system leverages a

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