Fast Collision Probability Estimation Based on Finite-Dimensional Monte Carlo Method

Abstract: The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned system and the obstacles, including both moving and static objects, accounts for a great proportion of the system abnormalities. The route planning and corresponding controller are established in order to avoid the collision, whereas, in the presence of uncertainties, it is possible that the unmanned system would deviate from the predetermined route and collide with the obstacles. Therefore, for the safety of unmanned systems, collision probability estimation and further safety decision are very important. To estimate the collision probability, the Monte Carlo method could be applied, however, it is generally rather slow. This paper introduces a fast collision probability estimation method based on finite-dimensional distribution, whose main idea is to filter out the sampling points needed and generate the states directly by samples of finite-dimensional distribution, reducing the estimation time significantly. Besides, further techniques including the probabilistic equidistance sampling and dimension reduction, also serve to reduce the estimation time. The simulation shows that the proposed method reduces over 99% of the estimation time.