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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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10
tex/chapters/experiments.tex
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@@ -147,6 +147,8 @@
% error values
\begin{table}
\caption{Median error for walks conducted with the Nexus 6.}
\label{tbl:errNexus}
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
@@ -155,12 +157,12 @@
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
\end{tabular}
\caption{Median error for walks conducted with the Nexus 6.}
\label{tbl:errNexus}
\end{table}
\begin{table}
\centering
\caption{Median error for walks conducted with the Galaxy S5.}
\label{tbl:errGalaxy}
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
& Path1 & Path2 & Path3 & Path4 \\\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
Multipath (\refeq{eq:transMultiPath}) & \SI{ 6.35}{\meter} & \SI{4.21}{\meter} & \SI{5.03}{\meter} & \SI{6.79}{\meter} \\\hline
\end{tabular}
\caption{Median error for walks conducted with the Galaxy S5.}
\label{tbl:errGalaxy}
\end{table}
%\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
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
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.
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 $\{\lambda_1, \lambda_2 \mid \lambda_1 > \lambda_2\}$
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
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
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
$\pathCentroid$. After advancing the starting-vertex by three times this deviation
@@ -283,8 +283,8 @@
\subsubsection{Multipath}
The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the
$\fLength{v}{\dot{v}}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $
The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the distance
$\fDistance{v}{\dot{v}}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $
for the path from $v$ to the pedestrian's destination $\dot{v}$.
We thus apply the same assumption as \refeq{eq:transShortestPath} and downvote edges
not decreasing the distance to the destination:
@@ -296,7 +296,7 @@
\mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
\alpha &=
\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}
\end{cases}
\end{split}