tex

presentation/beamerthemefhws.sty

@@ -71,7 +71,7 @@
 	\ifnum \value{page}=1
 		\includegraphics[width=\pagewidth,height=\paperheight]{style/background.pdf}
 	\else
-		\includegraphics[width=\paperwidth,height=\paperheight]{style/slide-background.pdf}
+		%\includegraphics[width=\paperwidth,height=\paperheight]{style/slide-background.pdf}
 	\fi
 }
 

presentation/chapters/system.tex

@@ -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}

presentation/presentation.tex

@@ -80,6 +80,8 @@
 	
 	\input{chapters/achievements}
 	
+	\input{chapters/system}
+
 
 \end{document}