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The safety assessment of automated vehicles (AVs) is an important aspect ofthe development cycle of AVs. A scenario-based assessment approach is acceptedby many players in the field as part of the complete safety assessment. Ascenario is a representation of a situation on the road to which the AV needsto respond appropriately. One way to generate the required scenario-based testdescriptions is to parameterize the scenarios and to draw these parameters froma probability density function (pdf). Because the shape of the pdf is unknownbeforehand, assuming a functional form of the pdf and fitting the parameters tothe data may lead to inaccurate fits. As an alternative, Kernel DensityEstimation (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 theneed of evaluating the actual pdf, which makes it suitable for drawing randomsamples for, e.g., Monte Carlo methods. Sampling from a KDE while the samplessatisfy a linear equality constraint, however, has not been described in theliterature, 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 analgorithm of our method in pseudo-code. The method can be used to generatingscenarios that have, e.g., a predetermined starting speed or to generatedifferent types of scenarios. This paper also shows that the method forsampling scenarios can be used in case a Singular Value Decomposition (SVD) isused to reduce the dimension of the parameter vectors.

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