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competition/tex/chapters/components.tex

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+\section{Component Description}
+	
+	Our indoor localisation solely uses the sensors provided by almost each commodity smartphone.
+	The readings of all those sensors are fused using recursive density estimation, directly on the phone:
+	
+	\commentByFrank{state beschreiben: x, y, z, heading. oder machst du das schon weiter oben? dann kann vermutlicha uch die formel hier weg}
+	
+	\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}} \enspace,
+		\end{array}
+		\label{eq:recursiveDensity}
+	\end{equation}
+	
+	\docWIFI{} and (if available) \docIBeacon{}s serve as absolute positioning component. If the smartphone provides
+	a barometer, its measurements are used as an additional, relative verification for the current $z$-component
+	of the pedestrian's location.
+	
+	The transition in \refeq{eq:recursiveDensity} is carried out using random walks on a graph, which is built offline, and uses
+	the building's floorplan. During the localisation process, the smartphone's IMU (accelerometer, gyroscope) is used to constrain the random walk
+	in both, distance and heading.
+	
+	The recursive density estimation is implemented using a particle-filter.
+	
+	\input{chapters/barometer.tex}
+	\input{chapters/wifi.tex}
+	\input{chapters/stepturn.tex}
+	\input{chapters/graph.tex}
+