  We revisit the computation of a probability of collision in the context of
automotive collision avoidance (also referred to as conflict detection in other
contexts). After reviewing existing approaches to the definition and
computation of a collision probability we argue that the question "What is the
probability of collision within the next three seconds?" can be answered on the
basis of a collision probability rate.
  Using results on level crossings for vector stochastic processes we derive a
general expression for the upper bound of the distribution of the collision
probability rate. This expression is valid for arbitrary prediction models
including process noise.
  We demonstrate in several examples that distributions obtained by large-scale
Monte-Carlo simulations obey this bound and in many cases approximately
saturate the bound. We derive an approximation for the distribution of the
collision probability rate that can be computed on an embedded platform. An
upper bound of the probability of collision is then obtained by one-dimensional
numerical integration over the time period of interest.
  A straightforward application of this method applies to the collision of an
extended object with a second point-like object. Using an abstraction of the
second object by salient points of its boundary we propose an application of
this method to two extended objects with arbitrary orientation.
  Finally, the distribution of the collision probability rate is compared to
approximations of time-to-collision distributions for one-dimensional motions
that have been obtained previously.
