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.
Cator, E.
Paardekooper, J.P.
op den Camp, O.M.G.C.
de Schutter, B.

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.

Monte Carlo methods
Shape
Intelligent vehicles
Conferences
Roads
Estimation
Probability density function

http://resolver.tudelft.nl/uuid:7da7263d-96bc-4832-8fdf-005d612b970b

https://doi.org/10.1109/ivworkshops54471.2021.9669213

962973

IEEE

9781665479219

IEEE Intelligent Vehicles Symposium Workshops (IV Workshop), 203-208

conference paper