Many state-of-the-art methods for safety assessment and motion planning for automated driving require estimation of the probability of collision (POC). To estimate the POC, a shape approximation of the colliding actors and probability density functions of the associated uncertain kinematic variables are required. Even with such information available, the derivation of the POC is in general, i.e., for any shape and density, only possible with Monte Carlo sampling (MCS). Random sampling of the POC, however, is challenging as computational resources are limited in real-world applications. We present expressions for the POC in the presence of Gaussian uncertainties, based on multi-circular shape approximations. In addition, we show that the proposed approach is computationally more efficient than MCS. Lastly, we provide a method for upper and lower bounding the estimation error for the POC induced by the used shape approximations.

翻译：自动驾驶领域许多先进的安全评估与运动规划方法都需要对碰撞概率（POC）进行估计。为估计POC，需要获取碰撞参与者的形状近似及其相关不确定运动变量的概率密度函数。即使获得这些信息，对于任意形状和密度分布，POC的推导通常只能通过蒙特卡洛采样（MCS）实现。然而在实际应用中，由于计算资源有限，对POC进行随机采样具有挑战性。本文基于多圆形形状近似，推导了存在高斯不确定性时的POC表达式。此外，我们证明所提方法在计算效率上优于MCS。最后，我们提出了一种针对所用形状近似引起的POC估计误差进行上下界定界的方法。