deletions | additions       diff --git a/Methodolofy Measurement Definitions.tex b/Methodolofy Measurement Definitions.tex  index abde249..520cb18 100644  --- a/Methodolofy Measurement Definitions.tex  +++ b/Methodolofy Measurement Definitions.tex 
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\item \textbf{Motion patterns} are a family of models which use machine learning to calculate future position likelihoods from past behaviour\cite{Saunier}. This type of model is the most promising as motion prediction is probabilistic in nature and inherently models naturalistic behaviour. However, they may not be able to model erratic behaviour such as roadway departures. Motion patterns are also complex to implement and expensive to process. The type of motion pattern being studied for implementation is a discretised motion pattern \cite{St_Aubin_2014}.  \end{itemize}  As illustrated in Figure~\ref{fig:prob-collision-space}, motion prediction is performed for each user pair over each interaction-instant $t_0$ for a number of timesteps of size $\Delta t$ between $t_0$ and some chosen timehorizon. Each motion prediction may generate for two road users a series or a matrix of collision points with a sum of probabilities inferior or equal to 1. This is significantly larger and more difficult to handle than trajectory data, and currently cannot be performed in real time. 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-mp-weight-avg} TTC'_i = \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}.  It's quite clear from both this figure and the trajectories themselves that constant velocity motion prediction is inadequate for roundabout conflict analysis: it's quite clear that the trajectories share the same destination yet they only share similar headings for a brief period of time.