Paul St-Aubin edited Results.tex  almost 10 years ago

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A sample analysis for a single pair of road users at a single site over a timeseries of 64 interaction-instants, lasting just over 4 seconds is presented in Figure~\ref{fig:conflict-video} and Figure~\ref{fig:conflict-series}. In this scenario, vehicle # 304 is approaching at high velocity vehicle # 303 which is enganged in an illegal u-turn (in a right-hand roundabout, users are supposed to travel counter-clockwise around the center island at all times). The differential velocity $\Delta v$, realtive distance $d$, and corresponding time $t$ is measured for every interaction-instant. In a matter of just under 4 seconds, the differential velocity changes from 9.63 m/s to 2.26 while the relative distance changes from 28.57 metres to 9.57 metres. For every interation-instant of this user pair, motion prediction is used to calculate resulting TTC under each motion prediction's respective hypothesis. These predicted collisions and associated TTC measures are presented in Figure~\ref{fig:ttc-timeseries}. Motion pattern prediction generates many more possible collision points than constant velocity prediction, though each of these points has a significantly lower associated probability. For beterr instant-to-instant comparison, a summary $TTC'_i$ at time $t_i$ is calculated as the probability-weighted TTC average   \begin{equation} \label{eqn:TTC-mot-pat-weight-avg} \label{eqn:TTC-mp-weight-avg}  TTC'_i = \frac{\sum_{j=1}^{n}{TTC_i_j*Prob(collision)_i_j} \frac{\sum_{j=1}^{n}{TTC_{ij} Prob(collision)_{ij}}  }{n} \end{equation} of all possible collision points $j=1..m$ with $Prob(collision)$ \cite{St_Aubin_2014}.