Worst Time To Collision (WTTC)#

Description#

The WTTC metric extends the usual TTC by considering multiple traces of actors as predicted by an over-approximating DMM, i.e.

\[\mathit{WTTC}(A_1,A_2,t) = \min_{p_1 \in \mathit{Tr}_1(t), p_2 \in \mathit{Tr}_2(t)} (\{ \tilde{t} \ge 0 \,\mid\, d(p_1(t+\tilde{t}),p_2(t+\tilde{t})) = 0 \} \cup \{ \infty \}),\]

where \(\mathit{Tr}_1(t)\) resp. \(\mathit{Tr}_2(t)\) denotes the set of all possible trajectories available to actor \(A_1\) resp. \(A_2\) at time \(t\), as constraint by the employed DMM. Similar to the TTC, the WTTC can be extended to multi-actor scenarios. Defined by Wachenfeld et al. [Wachenfeld2016], it excels in selective data recording and data filtering applications.

Properties#

Run-time capability#

Yes

Target values#

1 s (scenario classification) [Huber2020], comparison with ACC \(\tau\) (gap time) made in [Wachenfeld2016]

Subject type#

Optimal for road vehicles (automated and human), sub-optimal for VRUs

Scenario type#

Overlapping predicted trajectories for a significant time span in the scenario

Inputs#

Static/dynamic objects and their state (pose, shape, etc.) at time t

Output scale#

\([0,\infty]\), time (s), ratio scale

Reliability#

Medium, as over-approximating DMM robustly assesses criticality increases (expert-based evaluation [Wachenfeld2016]), but decreases potentially not reliably reflected

Validity#

Medium, as most critical scenarios can be detected depending on the DMM, but also not able to distinguish many uncritical ones, initial expert-based evaluation on four scenarios has been published [Wachenfeld2016]

Sensitivity#

Almost maximal, due to over-approximation of possible trajectories, depends on DMM (e.g. whether unstable dynamics are considered)

Specificity#

Low, due to over-approximation of possible trajectories, depends on DMM

Prediction model#

Time window#

Unbound, but usefulness depends on DMM

Time mode#

Branching time