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updated tex. sensors done.

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Toni
2016-02-12 15:40:52 +01:00
parent f0215731ce
commit 6b02336277
6 changed files with 40 additions and 54 deletions
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tex/chapters/grid.tex
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@@ -1,10 +1,10 @@
\section{Transition Model}
\label{sec:trans}
To sample only transitions $p(\mStateVec_{t} \mid \mStateVec_{t-1})$ that are actually feasible
To sample only transitions that are actually feasible
within the environment, we utilize a \SI{20}{\centimeter}-gridded graph
$G = (V,E)$, $v_{x,y,z} \in V$, $e_{v_{x,y,z}}^{v_{x',y',z'}} \in E$
derived from the buildings floorplan as described in \cite{ipin2015}.
derived from the buildings floorplan as described in section \ref{sec:relatedWork}.
However, we add improved $z$-transitions by also modelling realistic
stairwells using nodes and edges as can be seen in fig. \ref{fig:gridStairs}.
@@ -21,6 +21,7 @@
The corresponding vertices are determined using intersections of the segments with the bounding-box
for each vertex.
\commentByToni{Der Teil wird mir gar nicht klar irgendwie. Kann mir vor allem den letzten Satz nicht vorstellen.}
\commentByFrank{mention?: clean z-transitions, remove x/y nodes by adding bounding boxes}
To reduce the system's memory footprint, we search for the largest connected region within the graph and
@@ -29,29 +30,26 @@
\newcommand{\gHead}{\theta}
\newcommand{\gDist}{d}
Walking the grid is now possible by moving along adjacent nodes into a given walking-direction
until a desired distance is reached \cite{ipin2015}.
until a desired distance $\gDist$ is reached \cite{Ebner-15}.
In order to use meaningful headings $\gHead$ and distances $\gDist$
(matching the pedestrian's real heading and walking speed) for each transition,
we use the current sensor-readings $\mObsVec_{t}$ for hinted instead of truly random adjustments.
During a walk, each edge has an assigned probability $p(e)$ which depends on a chosen implementation.
Usually, this probability describes aspects like a comparison of the edge's angle $\angle e$ with the
current heading $\gHead$. However, it is also possible to incorporate additional prior knowledge to favor
some vertices/edges
\commentByFrank{im system-teil anmerken: $\mObsVec_t^{\mObsSteps} \in \N$}
\begin{align}
%
\begin{align}
\mStateVec_{t}^{\mStateHeading} = \gHead &= \mStateVec_{t-1}^{\mStateHeading} + \mObsVec_t^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
\gDist &= \mObsVec_t^{\mObsSteps} \cdot \SI{0.7}{\meter} + \mathcal{N}(0, \sigma_{\gDist}^2)
\end{align}
%
During a walk, each edge has an assigned probability $p(e)$ which depends on a chosen implementation.
Usually, this probability describes aspects like a comparison of the edge's angle $\angle e$ with the
current heading $\gHead$. However, it is also possible to incorporate additional prior knowledge to favor
some vertices/edges.
For comparison purpose we define a simple weighting method that assigns a probability to each edge
based on the deviation from the currently estimated heading $\gHead$:
\commentByFrank{das erste $=$ ist komisch. bessere option?}
\commentByToni{Find ich jetzt nicht tragisch. Eher notwendig fuers Verstaendnis.}
\begin{equation}
p(e) = p(e \mid \gHead) = N(\angle e \mid \gHead, \sigma_\text{dev}^2).
\label{eq:transSimple}
@@ -61,20 +59,18 @@
\section{TITLE?}
\section{Navigation Knowledge}
Assuming navigation, the pedestrian wants to reach a well-known destination and represents additional
prior knowledge. Most probabily, the pedestrian will stick to the path presented by
a navigation system. However, some deviations like chatting to someone or taking another router
cannot be strictly ruled out. We will therefor describe a system that is able to deal with such variants
as well as present an algorithm to calculate realistic routes based on aforemention grid.
prior knowledge. Most probably, the pedestrian will stick to the path presented by
a navigation system. However, some deviations like chatting to someone or taking another route
cannot be strictly ruled out. We will therefore describe a system that is able to deal with such variants
as well as present an algorithm to calculate realistic routes based on the aforementioned grid.
Simply running a shortest-path algorithm as Dijkstra or A* \todo{cite} using the previously created floorplan
would oviously lead to non-realistic paths sticking to the walls and walking many diagonals. In order
to calculate paths the resemble pedestrian walking behaviour we thus need some adjustments to the
route calculation.
As discussed in section \ref{sec:relatedWork}, simply running a shortest-path algorithm as Dijkstra or A* using the previously created graph would obviously lead to non-realistic paths sticking to the walls and walking many diagonals.
In order to calculate paths the resemble pedestrian walking behavior we thus need some adjustments to the route calculation.
\subsection{wall avoidance}
\subsection{Wall Avoidance}
\label{sec:wallAvoidance}
As already mentioned, shortest-path calculation usually sticks close to walls to reduce the path's length.
@@ -102,7 +98,7 @@
\subsection{door detection}
\subsection{Door Detection}
\label{sec:doorDetection}
Doors are usually anchored between two (thin) walls and have a normed width. Examining only a limited region
@@ -144,7 +140,7 @@
\subsection{path estimation}
\subsection{Path Estimation}
\label{sec:pathEstimation}
Based on aforementioned assumptions, the final importance for each node is