Constrained Sampling from a Kernel Density Estimator to Generate Scenarios for the Assessment of Automated Vehicles

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}
   }


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