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second draft - check toni

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Toni
2016-02-17 22:25:39 +01:00
parent b79b3746c0
commit 3fd0db82fe
2 changed files with 11 additions and 11 deletions
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8
tex/chapters/experiments.tex
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@@ -147,6 +147,8 @@
% error values % error values
\begin{table} \begin{table}
\caption{Median error for walks conducted with the Nexus 6.}
\label{tbl:errNexus}
\centering \centering
\begin{tabular}{|l|c|c|c|c|} \begin{tabular}{|l|c|c|c|c|}
\hline \hline
@@ -155,11 +157,11 @@
Shortest (\refeq{eq:transShortestPath}) & \SI{2.72}{\meter} & \SI{2.98}{\meter} & \SI{2.48}{\meter} & \SI{3.06}{\meter} \\\hline Shortest (\refeq{eq:transShortestPath}) & \SI{2.72}{\meter} & \SI{2.98}{\meter} & \SI{2.48}{\meter} & \SI{3.06}{\meter} \\\hline
Multipath (\refeq{eq:transMultiPath}) & \SI{2.62}{\meter} & \SI{2.14}{\meter} & \SI{2.46}{\meter} & \SI{2.75}{\meter} \\\hline Multipath (\refeq{eq:transMultiPath}) & \SI{2.62}{\meter} & \SI{2.14}{\meter} & \SI{2.46}{\meter} & \SI{2.75}{\meter} \\\hline
\end{tabular} \end{tabular}
\caption{Median error for walks conducted with the Nexus 6.}
\label{tbl:errNexus}
\end{table} \end{table}
\begin{table} \begin{table}
\caption{Median error for walks conducted with the Galaxy S5.}
\label{tbl:errGalaxy}
\centering \centering
\begin{tabular}{|l|c|c|c|c|} \begin{tabular}{|l|c|c|c|c|}
\hline \hline
@@ -168,8 +170,6 @@
Shortest (\refeq{eq:transShortestPath}) & \SI{ 5.86}{\meter} & \SI{4.14}{\meter} & \SI{5.14}{\meter} & \SI{5.20}{\meter} \\\hline Shortest (\refeq{eq:transShortestPath}) & \SI{ 5.86}{\meter} & \SI{4.14}{\meter} & \SI{5.14}{\meter} & \SI{5.20}{\meter} \\\hline
Multipath (\refeq{eq:transMultiPath}) & \SI{ 6.35}{\meter} & \SI{4.21}{\meter} & \SI{5.03}{\meter} & \SI{6.79}{\meter} \\\hline Multipath (\refeq{eq:transMultiPath}) & \SI{ 6.35}{\meter} & \SI{4.21}{\meter} & \SI{5.03}{\meter} & \SI{6.79}{\meter} \\\hline
\end{tabular} \end{tabular}
\caption{Median error for walks conducted with the Galaxy S5.}
\label{tbl:errGalaxy}
\end{table} \end{table}
%\begin{figure} %\begin{figure}

12
tex/chapters/grid.tex
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@@ -87,7 +87,7 @@
A* using the previously created graph would obviously lead to non-realistic paths sticking to walls and A* using the previously created graph would obviously lead to non-realistic paths sticking to walls and
walking many diagonals. Pedestrian's however, will probably keep a small gap between themselves and walking many diagonals. Pedestrian's however, will probably keep a small gap between themselves and
nearby walls. To calculate paths that resemble this behaviour, an importance-factor is derived for nearby walls. To calculate paths that resemble this behaviour, an importance-factor is derived for
each vertex. Those will be used to modify the euclidean distance $\fDistance{u}{v}$ between two vertices each vertex. Those will be used to modify the distance $\fDistance{u}{v}$ between two vertices
$u,v$, examined by the shortest-path algorithm. $u,v$, examined by the shortest-path algorithm.
To downvote vertices near walls, we need to determine the distance of each vertex from its nearest wall. To downvote vertices near walls, we need to determine the distance of each vertex from its nearest wall.
@@ -139,7 +139,7 @@
% %
For $\mat{\Sigma}$, the two largest eigenvalues $\{\lambda_1, \lambda_2 \mid \lambda_1 > \lambda_2\}$ For $\mat{\Sigma}$, the two largest eigenvalues $\{\lambda_1, \lambda_2 \mid \lambda_1 > \lambda_2\}$
are calculated. If their ratio $^{\lambda_1}/_{\lambda_2}$ is above a certain are calculated. If their ratio $^{\lambda_1}/_{\lambda_2}$ is above a certain
threshold, the neighbourhood describes a flat ellipse and thus either a door or a straight wall threshold, the neighbourhood describes a flat ellipse and thus either a door or a straight wall.
% %
To filter the latter, we enforce the euclidean distance \mbox{$\| \fPos{v} - \vec{c} \|$} between To filter the latter, we enforce the euclidean distance \mbox{$\| \fPos{v} - \vec{c} \|$} between
the centroid and the vertex to be very small. Hereafter, only vertices located directly within a the centroid and the vertex to be very small. Hereafter, only vertices located directly within a
@@ -251,7 +251,7 @@
% %
As new states $\mStateVec_{t}$ should approach the pedestrian's destination As new states $\mStateVec_{t}$ should approach the pedestrian's destination
we use a reference $\pathRef$ all states try to reach. This references must we use a reference $\pathRef$ all states try to reach. This references must
both, part of the shortest path and located somewhere outside of the sample-set. be both, part of the shortest path and located somewhere outside of the sample-set.
% %
We thus calculate the standard deviation of the distance of all samples from the centre We thus calculate the standard deviation of the distance of all samples from the centre
$\pathCentroid$. After advancing the starting-vertex by three times this deviation $\pathCentroid$. After advancing the starting-vertex by three times this deviation
@@ -283,8 +283,8 @@
\subsubsection{Multipath} \subsubsection{Multipath}
The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the distance
$\fLength{v}{\dot{v}}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $ $\fDistance{v}{\dot{v}}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $
for the path from $v$ to the pedestrian's destination $\dot{v}$. for the path from $v$ to the pedestrian's destination $\dot{v}$.
We thus apply the same assumption as \refeq{eq:transShortestPath} and downvote edges We thus apply the same assumption as \refeq{eq:transShortestPath} and downvote edges
not decreasing the distance to the destination: not decreasing the distance to the destination:
@@ -296,7 +296,7 @@
\mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\ \mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
\alpha &= \alpha &=
\begin{cases} \begin{cases}
0.9 & \fLength{v'}{\dot{v}} < \fLength{v}{\dot{v}} \\ 0.9 & \fDistance{v'}{\dot{v}} < \fDistance{v}{\dot{v}} \\
0.1 & \text{else} 0.1 & \text{else}
\end{cases} \end{cases}
\end{split} \end{split}