Reference
E. de Gelder, E. Cator, J.-P. Paardekooper, O. Op den Camp, and B. De Schutter,
"Constrained sampling from a kernel density estimator to generate scenarios for
the assessment of automated vehicles,"
Proceedings of the 2021
IEEE Intelligent Vehicles Symposium Workshops (IV Workshops), Nagoya,
Japan, pp. 203-208, July 2021.
Abstract
The safety assessment of Automated Vehicles (AVs) is an important aspect of the
development cycle of AVs. A scenario-based assessment approach is accepted by
many players in the field as part of the complete safety assessment. A scenario
is a representation of a situation on the road to which the AV needs to respond
appropriately. One way to generate the required scenario-based test
descriptions is to parameterize the scenarios and to draw these parameters from
a probability density function (pdf). Because the shape of the pdf is unknown
beforehand, assuming a functional form of the pdf and fitting the parameters to
the data may lead to inaccurate fits. As an alternative, Kernel Density
Estimation (KDE) is a promising candidate for estimating the underlying pdf,
because it is flexible with the underlying distribution of the parameters.
Drawing random samples from a pdf estimated with KDE is possible without the
need of evaluating the actual pdf, which makes it suitable for drawing random
samples for, e.g., Monte Carlo methods. Sampling from a KDE while the samples
satisfy a linear equality constraint, however, has not been described in the
literature, as far as the authors know.
In this paper, we propose a method to sample from a pdf estimated using KDE,
such that the samples satisfy a linear equality constraint. We also present an
algorithm of our method in pseudo-code. The method can be used to generating
scenarios that have, e.g., a predetermined starting speed or to generate
different types of scenarios. This paper also shows that the method for
sampling scenarios can be used in case a Singular Value Decomposition (SVD) is
used to reduce the dimension of the parameter vectors.
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BibTeX
@inproceedings{deGCat:21-015,
author = {de Gelder, Erwin and Cator, Eric and Paardekooper, Jan-Pieter
and Op den Camp, Olaf and De Schutter, Bart},
title = {Constrained Sampling from a Kernel Density Estimator to
Generate Scenarios for the Assessment of Automated Vehicles},
booktitle = {Proceedings of the 2021 IEEE Intelligent Vehicles Symposium
Workshops (IV Workshops)},
address = {Nagoya, Japan},
pages = {203--208},
month = jul,
year = {2021}
}