Christian Reichenbächer

Christian Reichenbächer, Philipp Rank, Jochen Hipp et al.

This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario parameters is essential for scenario-based safety assessment, where risk quantification depends on the likelihood of concrete parameter combinations. Gaussian Mixture Copula Models bring together the multimodal expressivity of Gaussian Mixture Models and the flexibility of copulas, enabling separate modeling of marginal distributions and dependencies. We benchmark Gaussian Mixture Copula Models against previously proposed approaches - Gaussian Mixture Models and Gaussian Copula Models - using real-world driving data drawn from scenarios defined in United Nations Regulation No. 157. Our evaluation across approximately 18 million scenario instances demonstrates that Gaussian Mixture Copula Models consistently surpass Gaussian Copula Models and perform better than, or at least comparably to, Gaussian Mixture Models, as measured by both log-likelihood and Sinkhorn distance. These results are promising for the adoption of Gaussian Mixture Copula Models as a statistical foundation for future scenario-based validation frameworks.

Florian Wirthmüller, Jochen Hipp, Christian Reichenbächer et al.

The prediction of surrounding traffic participants behavior is a crucial and challenging task for driver assistance and autonomous driving systems. Today's approaches mainly focus on modeling dynamic aspects of the traffic situation and try to predict traffic participants behavior based on this. In this article we take a first step towards extending this common practice by calculating location-specific a-priori lane change probabilities. The idea behind this is straight forward: The driving behavior of humans may vary in exactly the same traffic situation depending on the respective location. E.g. drivers may ask themselves: Should I pass the truck in front of me immediately or should I wait until reaching the less curvy part of my route lying only a few kilometers ahead? Although, such information is far away from allowing behavior prediction on its own, it is obvious that today's approaches will greatly benefit when incorporating such location-specific a-priori probabilities into their predictions. For example, our investigations show that highway interchanges tend to enhance driver's motivation to perform lane changes, whereas curves seem to have lane change-dampening effects. Nevertheless, the investigation of all considered local conditions shows that superposition of various effects can lead to unexpected probabilities at some locations. We thus suggest dynamically constructing and maintaining a lane change probability map based on customer fleet data in order to support onboard prediction systems with additional information. For deriving reliable lane change probabilities a broad customer fleet is the key to success.