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

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

de Gelder, E. (TU Delft Team Bart De Schutter; TNO)
Cator, Eric (Radboud Universiteit Nijmegen)
Paardekooper, Jan Pieter (Radboud Universiteit Nijmegen; TNO)
Op den Camp, Olaf (TNO)
De Schutter, B.H.K. (TU Delft Team Bart De Schutter)

2021

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.

http://resolver.tudelft.nl/uuid:1116d92a-4951-4f0b-840a-5184073a4d62

https://doi.org/10.1109/IVWorkshops54471.2021.9669213

IEEE

978-1-6654-7922-6

Proceedings of the 2021 IEEE Intelligent Vehicles Symposium Workshops (IV Workshops)

2021 IEEE Intelligent Vehicles Symposium Workshops (IV Workshops), 2021-07-11 → 2021-07-17, Virtual at Nagoya, Japan

Accepted Author Manuscript

Institutional Repository

conference paper

© 2021 E. de Gelder, Eric Cator, Jan Pieter Paardekooper, Olaf Op den Camp, B.H.K. De Schutter