# Scenario Optimisation and Sensitivity Analysis for Safe Automated Driving Using Gaussian Processes
## 2 Related Work  
### Scenario-Based Validation of AVs  
Scenario-based testing has emerged as an active field of research, pursuing the aim of validating the safety of AVs. It is inherently connected to the definition of scenarios in automated driving research ([7; 9]), and examines the interactions and relations of the AV (also called ego vehicle) with one or several other actors in defined environmental conditions [10]. By testing the AV in concrete scenarios, the decision making of the AV can be validated based on the outcome of the concrete scenario. It is here assumed that the decision making of the AV changes, depending on the specified behaviour of other involved actors and the various environmental conditions, similar to human decision making while driving. The execution of such scenario-based tests is predominantly done with vehicle simulation software, which combines the dynamics of the ego vehicle with a virtual representation of the world and other traffic participants, as well as sensor emulation. Most of the subsequently presented methods for scenario-based testing utilise simulation. Scenario-based testing of AVs is however not limited to simulation and can also be done with Hardware-in-the-Loop or field-operational tests on the road or proving ground [6]. Using simulation in executing the tests offers however benefits in terms of cost and execution time, as large numbers of concrete scenarios can easily be carried out. A scenario-based validation process should cover all functional scenarios defined in the concept phase of the development process [7]. After these functional scenarios are defined, the respective logical scenarios can be constructed, by specifying the parameters and value ranges. To actually carry out a scenario, a concrete scenario needs to be drawn from the logical scenario space by setting the values of each parameter. The simplest approach is to sample values from specified probability distributions of each parameter, such as Monte Carlo (MC) sampling. The values of the concrete scenarios in Reference [11] are, for example, drawn from a uniform distribution. The MC simulation approach would however only yield accurate outcomes, if a high number of concrete scenarios were carried out, making it computationally expensive. But when a sufficient number of concrete scenario are carried out, this approach covers the whole parameter space of a logical scenario, and is thus often used as a baseline for comparison to other methods [12]. The MC sampling based approach can be improved, if the probability distributions used for sampling concrete values are changed from uniform distributions to distributions which are closer to the true distributions of the parameters characterising the functional scenarios. [PERSON] et al. [5] proposed a related approach to improve the computational efficiency of the MC method by starting with MC sampling, but benefiting from the important sampling concept to sample from a tractable distribution, which can be considered a close distribution to the true one. The proposed method achieved much higher computational efficiency in the magnitude of hundreds to thousands of times greater compared to the original MC method. This results in more scenarios being evaluated that can be classed as rare events and might be problematic for AVs [5]. Importance sampling methods are especially suited here and have been used to evaluate adaptive cruise control systems [13]. Further, they were found to improve the evaluation time of testing a car following scenario by a factor of up to 100,000 and a lane change scenario by up to 20,000 [14; 15]. An improvement over MC simulation was also shown by using subset simulation on the test case of a lane change scenario [5]. It was shown to offer a similar improvement as importance sampling by focusing on a subset of scenarios that have a higher probability of failure.