Time To Closest Encounter (TTCE)

Description

The TTCE is a distance-dependent risk indicator, which generalizes the concept of the TTC to the non-collision case [Eggert2014]. At time \(t\), the TTCE measures the time \(\tilde{t}>0\) for which the distance to other actors in a scenario becomes minimal. The corresponding minimal distance is called the DCE. The formulae are

\[\mathit{DCE}(A_1,A_2,t) = \min_{\tilde{t} \ge 0} d(p_1(t+\tilde{t}),p_2(t+\tilde{t}))\,,\]

\[\mathit{TTCE}(A_1,A_2,t) = \text{arg}\,\text{min}_{\tilde{t} \ge 0} d(p_1(t+\tilde{t}),p_2(t+\tilde{t}))\,.\]

In particular, as \(\mathit{DCE} \rightarrow 0\), \(\mathit{TTCE} \rightarrow \mathit{TTC}\) which implies \(\mathit{DCE} = 0\) if and only if \(\mathit{TTCE} = \mathit{TTC}\). Building on the TTCE and DCE, Eggert uses an exponential transform together with a survival function in order to estimate the future event probability of a collision for the distance-dependent risk [Eggert2014].

Properties

Run-time capability

Yes

Target values

None found

Subject type

Road vehicles (automated and human)

Scenario type

Any scenario

Inputs

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

Output scale

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

Reliability

Higher than TTC as the DMM is not constraint to a predict a collision

Validity

Low, as the closest encounter is not necessarily a critical event, increased when used with a DCE threshold to delineate critical from non-critical encounters

Sensitivity

High, as many critical scenes exhibit temporal proximity to a close encounter

Specificity

Low, as a closest encounter is not always a critical event

Prediction model

Time window

Unbound, but usefulness depends on DMM

Time mode

Linear time