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A New Approach To Estimate The Collision Probability For Automotive Applications
We revisit the computation of probability of collision in the context of
automotive collision avoidance (the estimation of a potential collision is 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. In order to efficiently sample this probability rate
distribution for determination of its characteristic shape an adaptive method
to obtain the sampling points is proposed. 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
identified as the distribution of the time-to-collision.Comment: Revised and restructured version, discussion of extended vehicles
expanded, section on TTC expanded, references added, other minor changes, 17
pages, 18 figure
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