Constrained Sampling from a Kernel Density Estimator to Generate Scenarios for the Assessment of Automated Vehicles
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914924493537280 |
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| author | de Gelder, Erwin Cator, Eric Paardekooper, Jan-Pieter Camp, Olaf Op den De Schutter, Bart |
| author_facet | de Gelder, Erwin Cator, Eric Paardekooper, Jan-Pieter Camp, Olaf Op den De Schutter, Bart |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_05278 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Constrained Sampling from a Kernel Density Estimator to Generate Scenarios for the Assessment of Automated Vehicles de Gelder, Erwin Cator, Eric Paardekooper, Jan-Pieter Camp, Olaf Op den De Schutter, Bart Artificial Intelligence 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. |
| title | Constrained Sampling from a Kernel Density Estimator to Generate Scenarios for the Assessment of Automated Vehicles |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2107.05278 |