Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Approach To Estimate The Collision Probability For Automotive
  Applications   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.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat