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k-a-z-u
2018-06-05 13:19:53 +02:00
parent 0e91d778be
commit cfe1ea6717
3 changed files with 82 additions and 1 deletions
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2
presentation/beamerthemefhws.sty
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@@ -71,7 +71,7 @@
\ifnum \value{page}=1 \ifnum \value{page}=1
\includegraphics[width=\pagewidth,height=\paperheight]{style/background.pdf} \includegraphics[width=\pagewidth,height=\paperheight]{style/background.pdf}
\else \else
\includegraphics[width=\paperwidth,height=\paperheight]{style/slide-background.pdf} %\includegraphics[width=\paperwidth,height=\paperheight]{style/slide-background.pdf}
\fi \fi
} }

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presentation/chapters/system.tex Normal file
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@@ -0,0 +1,79 @@
\newcommand{\mPosVec}{\vec{\mPos}} % position vector
\newcommand{\mRssiVec}{\vec{s}} % client signal strength measurements
\newcommand{\mState}{q} % state variable
\newcommand{\mStateVec}{\vec{q}} % state vector variable
\newcommand{\mObs}{o} % observation variable
\newcommand{\mObsVec}{\vec{o}} % observation vector variable
\newcommand{\mObsWifi}{\vec{o}_{\text{wifi}}} % wifi observation
\newcommand{\mPressure}{\rho}
\newcommand{\mObsPressure}{\mPressure_\text{rel}} % symbol for observation pressure
\newcommand{\mStatePressure}{\hat{\mPressure}_\text{rel}} % symbol for state pressure
\newcommand{\mHeading}{\theta}
\newcommand{\mObsHeading}{\Delta\mHeading} % symbol used for the observation heading
\newcommand{\mStateHeading}{\mHeading} % symbol used for the state heading
\newcommand{\mSteps}{n_\text{steps}}
\newcommand{\mObsSteps}{\mSteps}
\newcommand{\mActivity}{\Omega}
\newcommand{\mObsActivity}{\mActivity}
\newcommand{\R}{\mathbb{R}}
%\newcommand{\N}{\mathbb{N}}
\begin{frame}[fragile]
\frametitle{System}
%\includegraphics[width=4cm]{gfx/map1}
\small
\begin{minipage}{0.49\textwidth}
Unbekannter Zustand
\begin{equation*}
\mStateVec = (\underbrace{x, y, z}_{\text{Position}}, \underbrace{\mStateHeading}_{\text{Richtung}}),\enskip
x, y, z, \mStateHeading \in \R
\end{equation*}
\vspace{1mm}
\end{minipage}
%
\begin{minipage}{0.49\textwidth}
Smartphone Sensordaten
\begin{equation*}
\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{beacon}, \mObsSteps, \mObsHeading, \mStateHeading, \mObsActivity, ) \enspace .
\end{equation*}
\vspace{1mm}
\end{minipage}
Sensorfusion über rekursive Dichteschätzung
\begin{equation*}
\arraycolsep=1.2pt
%\begin{array}{ll}
p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto
\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}}
%\end{array}
%\label{equ:bayesInt}
\end{equation*}
%\vspace{1mm}
%
\begin{equation*}
\begin{aligned}
p(\vec{o}_t \mid \vec{q}_t) &=
\,p(\mRssiVec_\text{wifi} \mid \vec{q}_t)%_\text{wifi}
\,p(\mRssiVec_\text{beacon} \mid \vec{q}_t)%_\text{beacon}
\,p(\mStateHeading \mid \vec{q}_t)%_\text{kompass}
\,p(\mObsActivity \mid \vec{q}_t)%_\text{activity}
\footnote{\tiny Annahme: Sensoren sind statistisch unabhängig}
\\
p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1}) &= \text{Bewegungsmodell mit Zusatzwissen}
\end{aligned}
\end{equation*}
\end{frame}

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presentation/presentation.tex
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@@ -79,6 +79,8 @@
\input{chapters/bib} \input{chapters/bib}
\input{chapters/achievements} \input{chapters/achievements}
\input{chapters/system}
\end{document} \end{document}