Predictive Encroachment Time (PrET)

Description

Here, we summarize the various predictive versions of the PET. The PrET [Neurohr2021] is the anticipated PET relative to an intersection point as predicted by the employed DMM, hence

\[\mathit{PrET}(A_1,A_2,t) = \min (\{|\tilde{t}_1 - \tilde{t}_2| \,\mid\, p_1(t+\tilde{t}_1) = p_2(t+\tilde{t}_2), \, \tilde{t}_1, \tilde{t}_2 \ge 0 \} \cup \{ \infty \})\,.\]

The Time Advantage (TA) metric [Hansson1975] can be interpreted as a special case of PrET for a constant velocity model, i.e. \(p_i(s+t) = p_i(t) + s v_i(t)\). A scaled variant of the PrET, labeled Scaled Predictive Encroachment Time (SPrET), modifies the value of PrET by multiplication with the factor \((\tilde{t}_1+\tilde{t}_2)\), i.e.

\[\mathit{SPrET}(A_1,A_2,t) = \min (\{|\tilde{t}_1^2 - \tilde{t}_2^2| \,\mid\, p_1(t+\tilde{t}_1) = p_2(t+\tilde{t}_2), \, \tilde{t}_1, \tilde{t}_2 \ge 0 \} \cup \{ \infty \})\,,\]

in order to decrease the weight of situations long before the predicted intersection [Neurohr2021]. Therefore, the SPrET incorporates prediction uncertainty.

Properties

Note

Includes properties for SPrET and TA.

Run-time capability

Yes

Target values

2 s (threshold for critical) and \([2,3]\) s (normal traffic) for TA [Laureshyn2010], 3 s (threshold for critical) for SPrET [Neurohr2021]

Subject type

Any two actors

Scenario type

Any scenario with a conflict area (containing a potential intersection point)

Inputs

Static/dynamic objects and their state at time t, DMM for each object

Output scale

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

Reliability

Comparable to PET, but additionally dependent on DMM

Validity

Comparable to PET, but additionally dependent on DMM, increased validity for run-time applications; no empirical analysis available

Sensitivity

Comparable to PET, but additionally dependent on DMM

Specificity

Comparable to PET, but specificity decreases with increasing distance to intersection

Prediction model

Time window

Unbound, but usefulness depends on DMM

Time mode

Linear time