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