deletions | additions       diff --git a/Methodolofy Measurement Definitions.tex b/Methodolofy Measurement Definitions.tex  index ec0988c..a4061a6 100644  --- a/Methodolofy Measurement Definitions.tex  +++ b/Methodolofy Measurement Definitions.tex 
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While vehicle trajectories offer a rich set of observed behavioural data, they do not provide much collision data; this is by design of the proactive road safety approach: predicting collisions should be performed without observing them directly. In order to study collisions, they need to be extrapolated from traffic events with potential for collision. This potential is modeled by predicting future positions of vehicles using motion prediction at every instant in time and examining i) situations of particular risk (i.e. threshold) or ii) evolution of the risk. Several motion prediction models are proposed for study:  \begin{itemize}  \item \textbf{Constant velocity} is the classic motion prediction model, wherin vehicles are projected along straight paths at a constant speed and heading using the velocity vector at that moment in time. This model is the simplest but also makes the most assumptions: only one movement is predicted at every instant, both users do not enter evasive action in the event of a collision course, and the natural (non-reacting) motion of a moving object is a straight path (not always true). These assumptions may be adequate for niche applications of the methodology, e.g. highways \cite{St_Aubin_2013}. The current implementation is based off of \cite{Laureshyn_2010}.  \item \textbf{Normal adaptation} uses constant velocity to project trajectories, but modifies the velocity vector to account for normal variation. This model benefits from a wider range of possible outcome velocity vectors, but otherwise suffers the same problems and makes the same assumptions as constant velocity. The implementation of normal adaption studied is based off of \cite{Mohamed_2013}, using a acceleration maxima $\alpha$ of  \begin{equation} \label{eqn:norm-adapt-accel-maxima} \alpha = \pm \frac{2}{f^2} \end{equation}