## 2 Materials and Methods
### Pre-Crash Systems in Compliance with International Safety Standards
The lowest ASIL safety relevant classification is A and the highest is D. Additionally, there is a QM level which means that the system has a low safety relevance and the risk should be considered during quality management process. In addition to ISO 26262, ISO/PAS 21448 focuses on the safety of the intended functionality (SOTIF) of road vehicles and addresses functional insufficiencies of the system on the vehicle level as well as foreseeable misuse [14]. SOTIF standards are not intended to replace the established standards, but to enhance them, especially for advanced driver-assistance systems (ADAS) and autonomous driving (AD) development. It considers system boundaries, in particular sensor, controller and actuator boundaries. For this purpose, the intended functionality of the system is defined and the SOTIF HARA, which can identify additional hazards and risks to ISO 26262, is performed. SOTIF also focuses on scenario-based testing and classifies the relevant use cases into four categories: known safe scenarios, known unsafe scenarios, unknown unsafe scenarios and unknown safe scenarios. While known safe scenarios should be maximized, known unsafe scenarios should be minimized through functional modification and unknown unsafe scenarios should be identified through test data acquisition [14]. Since Pre-Crash systems are perception-based and safety-relevant systems, development according only to ISO 26262 is not sufficient, and the international standard ISO/PAS 21448 should be taken into account [12]. A Schematic representation of the multi-level crash prediction function and a generic Pre-Crash system is shown in Figure 2. The crash prediction function estimates the probability of the collision, the time to collision (TTC) and the collision configuration for both host and opponent vehicles based on sensors' perceptions and real-time data processing. The collision configuration is described by In-Crash variables at the time \(t_{0}\), the time of the first impact. In-Crash variables, such as impact zone or impact points, impact angle and collision velocity for both accident participants, define the collision configuration. Crash severity prediction function is designed to predict the technical crash severity, which can be defined by various crash severity parameters, such as crash velocity, crash pulse, delta-v, occupant load criterion (OLC), energy equivalent speed (EES), intrusion zone and depth and others. The reliable and accurate prediction of relevant crash severity parameters enables Pre-Crash activation of irreversible restraint systems. However, activation of QM systems is possible based only on crash prediction without the associated crash severity. Once the targeted PCS is classified as ASIL A+ (ASIL of at least A or higher), system activation is inconceivable without an additional crash severity estimation. Collision constellation optimization based on crash prediction should contribute to the lowest injury severity within the possible collisions. A machine learning approach to estimate the trajectory of the lowest crash severity for unavoidable collisions is shown in [6]. However, the injury severity of the occupants is unknown even for the host vehicle, as there are no real-time models for the predictive estimation of injury severity. In addition, a conflict of interest arises between the safety of host and opponent. The protection of other road users cannot be neglected and is directly addressed by the SOTIF standard. Predicting injury severity distributions for host and opponent occupants for all possible collision constellations in real time is necessary for targeted collision constellation  
Figure 2: Schematic representation of the multi-level crash prediction function and a generic Pre-Crash system. The illustration is modified and extended according to [5]. optimization. This is not possible according to the current state of the art and is therefore not part of the testing scope, but could be considered in the future.