Provable safety is one of the most critical challenges in automated driving. The behavior of numerous traffic participants in a scene cannot be predicted reliably due to complex interdependencies and the indiscriminate behavior of humans. Additionally, we face high uncertainties and only incomplete environment knowledge. Recent approaches minimize risk with probabilistic and machine learning methods -even under occlusions. These generate comfortable behavior with good traffic flow, but cannot guarantee safety of their maneuvers. Therefore, we contribute a safety verification method for trajectories under occlusions. The field-of-view of the ego vehicle and a map are used to identify critical sensing field edges, each representing a potentially hidden obstacle. The state of occluded obstacles is unknown, but can be over-approximated by intervals over all possible states. Then set-based methods are extended to provide occupancy predictions for obstacles with state intervals. The proposed method can verify the safety of given trajectories (e.g. if they ensure collision-free fail-safe maneuver options) w.r.t. arbitrary safe-state formulations. The potential for provably safe trajectory planning is shown in three evaluative scenarios.

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Estimating and understanding the current scene is an inevitable capability of automated vehicles. Usually, maps are used as prior for interpreting sensor measurements in order to drive safely and comfortably. Only few approaches take into account that maps might be outdated and lead to wrong assumptions on the environment. This work estimates a lanelevel intersection topology without any map prior by observing the trajectories of other traffic participants.We are able to deliver both a coarse lane-level topology as well as the lane course inside and outside of the intersection using Markov chain Monte Carlo sampling. The model is neither limited to a number of lanes or arms nor to the topology of the intersection.We present our results on an evaluation set of 1000 simulated intersections and achieve 99.9% accuracy on the topology estimation that takes only 36ms, when utilizing tracked object detections. The precise lane course on these intersections is estimated with an error of 15cm on average after 140ms. Our approach shows a similar level of precision on 14 realworld intersections with 18cm average deviation on simple intersections and 27cm for more complex scenarios. Here the estimation takes only 113ms in total.

Let L be a lattice in R n . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in R n . The first method is based on the observation that if the sphere is sufficiently small then the lattice points contained in the sphere give rise to a spherical code with a certain minimum angle. The second method involves Gaussian measures on L in the sense of Banaszczyk (Math Ann 296: [625][626][627][628][629][630][631][632][633][634][635] 1993). Examples where the obtained bounds are optimal include some root lattices in small dimensions and the Leech lattice. We also present a natural decoding algorithm for lattices constructed from lattices of smaller dimension, and apply our results on the number of lattice points in a small sphere to conclude on the performance of this algorithm.

We consider an extension of Massey's construction of secret sharing schemes using linear codes. We describe the access structure of the scheme and show its connection to the dual code. We use the g-fold joint weight enumerator and invariant theory to study the access structure.