Safe driving requires autonomous vehicles to anticipate potential hidden traffic participants and other unseen objects, such as a cyclist hidden behind a large vehicle, or an object on the road hidden behind a building. Existing methods are usually unable to consider all possible shapes and orientations of such obstacles. They also typically do not reason about observations of hidden obstacles over time, leading to conservative anticipations. We overcome these limitations by (1) modeling possible hidden obstacles as a set of states of a point mass model and (2) sequential reasoning based on reachability analysis and previous observations. Based on (1), our method is safer, since we anticipate obstacles of arbitrary unknown shapes and orientations. In addition, (2) increases the available drivable space when planning trajectories for autonomous vehicles. In our experiments, we demonstrate that our method, at no expense of safety, gives rise to significant reductions in time to traverse various intersection scenarios from the CommonRoad Benchmark Suite.