# Scenario Optimisation and Sensitivity Analysis for Safe Automated Driving Using Gaussian Processes
## 7 Conclusions and Future Work  
In this article, we showed how Gaussian Process models can be used to test AVs in a scenario-based setting. We used a vehicle simulation of scenarios to compile concrete scenario data and train probabilistic models to predict the scenario outcomes. GPs were formally introduced and it was shown that GP models can predict the outcomes of a logical scenario including several actors and their interactions.  
We presented a method to optimise the parameter space of a logical scenario towards critical scenarios, measured by their minimal time-to-collision. This active learning method, as presented in Algorithm 1, was then evaluated on an exemplary functional scenario of a pedestrian stepping onto the road in front of the ego vehicle. The scenario was parametrised with 5 scenario parameters and the optimisation method sampled between 71-75% of new concrete scenarios within 0.5 s of the targeted, critical time-to-collision of 1.5 s. The Mean Absolute Error was between 0.086 and 0.146, while the Root-Mean-Squared Error was between 1.297 and 1.516, measured in seconds and for differently seeded initialisations of the method. The resulting data set of critical scenarios consisted of the targeted 100 concrete scenarios.  
Furthermore, we formally introduced and conducted a probabilistic sensitivity analysis on the optimised data set and found that the configurations of ego speeds, actor speeds and the geometric layout of the scenario had the strongest effect on the scenario outcome. Sensor parameter variations were found to have a lower impact. This information can be used to further restrict the parameter space of the logical scenarios and denser sampling of the most important parameters.  
The same probabilistic sensitivity analysis was also conducted on a simpler scenario data set of a functional scenario describing a traffic jam approach, taken from literature. On this functional scenario, a visual analysis of the parameter influences was possible and could therefore be linked to the results of the probabilistic sensitivity analysis and validate the sensitivity results. For the functional scenario of the pedestrian stepping onto the road, it is not possible to visually analyse the scenario parameter influences, due to the higher number of parameters.  
A limitation of the optimisation method is the fitting of GP models in every iteration step, which is computationally expensive. This could be improved if the GP model fitting is adapted to only incorporate the newly found concrete scenario, instead of refitting the GP models in every iteration. Further research is also necessary into the efficacy of different selection heuristics, which trade off exploration and exploitation of the logical scenario parameter space. This is something we plan for future work, along with extending the GPmodelling to be able to classify multiple possible outcomes of the scenario, for example in several criticality classes and with different criticality metrics.  
Conceptualization, F.B. and A.D.; methodology, F.B.; software, F.B.; validation, F.B.; formal analysis, F.B. and A.D; data curation, F.B.; writing--original draft preparation, F.B. and A.D.; writing--review and editing, F.B. and A.D.; visualization, F.B.; supervision, A.D., V.P. and M.C.; project administration, A.D., V.P. and M.C.; funding acquisition, M.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by a joint initiative called the Centre for Connected and Autonomous Automotive Research. The joint initiative is between Coventry University and HORIBA MIRA Ltd.  
The authors declare no conflict of interest.