To ensure safe operation of autonomous vehicles (AVs), trajectory planners should account for occlusions. These are areas invisible to the AV that might contain vehicles. Set-based methods can guarantee safety by calculating the reachable set, which is the set of possible states, for each potentially hidden vehicle. A recently published method proved in simulation experiments to reduce the cautiousness by reasoning about these occluded areas over time, assuming perfect input data. We present a novel algorithm that uses this reasoning and is applicable on a real AV with its accompanying uncertainties and imperfect sensor data. The uncertainties include sensor errors and noise, computation and communication delays and control errors in the trajectory following. This is achieved by modelling the error distributions and accounting for them in the calculations, where the confidence interval for each error is exposed as a setting. Experiments indicate that our algorithm can reduce the traversal time through an intersection by 2.2 seconds with reasoning. An ablation study of the different error measures shows that the errors in the construction of the field of view (FOV) limit the performance the most. Reducing the errors in the FOV construction is therefore the most important recommendation, besides making the method interaction-aware.