  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.
