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+\section{Indoor Positioning System}
+
+	Our smartphone-based indoor localization system estimates the current location and heading
+	using recursive density estimation.
+	A graph based movement model provides the transition,
+	%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
+	while the smartphone's accelerometer, gyroscope, magnetometer provide the observations  
+	for the following evaluation step to infer the hidden state, namely the pedestrian's location and heading
+	\cite{Ebner-16, Fetzer-16}.
+	
+	\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}
+	
+	The hidden state $\mStateVec$ is given by
+	\begin{equation}
+		\mStateVec = (x, y, z, \mStateHeading),\enskip
+		x, y, z, \mStateHeading \in \R \enspace,
+	\end{equation}
+	%
+	where $x, y, z$ represent the pedestrian's position in 3D space
+	and $\mStateHeading$ his current (absolute) heading.
+	%
+	The corresponding observation vector is defined as
+	%
+	\begin{equation}
+		\mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mObsGPS) \enspace.
+	\end{equation}
+	%
+	$\mRssiVecWiFi$ contains the measurements of all nearby \docAP{}s (\docAPshort{}s),
+	$\mObsSteps$ describes the number of steps detected since the last filter-step,
+	$\mObsHeadingRel$ the (relative) angular change since the last filter-step,
+	$\mObsHeadingAbs$ the current, vague absolute heading and
+	$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon )$ the current location (if available) given by the GPS.
+	
+	Assuming statistical independence, the state evaluation's density can be written as 
+	%
+	\begin{equation}
+		%\begin{split}
+			p(\vec{o}_t \mid \vec{q}_t) = 
+			p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}\enskip
+			p(\vec{o}_t \mid \vec{q}_t)_\text{gps}
+			\enspace.
+		\label{eq:evalDensity}
+	\end{equation}
+	%
+
+	The remaining observations, 
+	namely: detected steps, relative- and absolute heading are 
+	used within the transition model, where potential movements 
+	$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ are sampled 
+	based on those sensor values.
+
+	Thus, the overall system works as described in \cite{Ebner-16}.
+	Since then, absolute heading and GPS have been added as additional sensors
+	to further enhance the localization.
+	\todo{neues resampling?}
+		
+	
+	\todo{ueberleitung}
+	\todo{
+		die absolute positionierung kommt aus dem wlant,
+		dafür braucht man entweder viele fingerprints oder ein modell
+	}
+	As GPS will only work outdoors, e.g. when moving from one building into another,
+	the system's absolute position is solely provided by the \docWIFI{} component.
+	Therefore its crucial for this component to provide location estimations 
+	that are as accurate as possible, while ensuring fast setup and
+	maintenance times.