\section{Sensors}

	\subsection{Barometer}
		As stated by \cite{ipin2015} \todo{and the other paper directly}, ambient pressure readings are highly influenced
		by environmental conditions like the weather, time-of-day and others. Thus, relative pressure readings are
		preferred over absolute ones. However, due to noisy sensors \todo{cite oder grafik? je nach platz}, one
		single reading is not enough as a relative base. Harnessing the usual setup time of a navigation-system (
		route calculation, user checking the route) we use the average of all barometer readings during this
		timeframe as realtive base $\overline{\mPressure}$.
		
		During each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$, the predicted pressure $\mStatePressure$ is
		adjusted according to the resulting $z$-change, if any:
		
		\begin{equation}
			\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot \SI{0.105}{\hpa}
			,\enskip
			\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
			.
		\end{equation}
		
		
	\subsection{Wi-Fi \& iBeacons}
		For additional absolute location hints, we use the Smartphones Wi-Fi and iBeacon sensor to measure the signal-strengths
		of nearby transmitters. As the positions of both \docAP{}s and and \docIBeacon{}s are known beforehand, we compare
		each measurement with its corresponding signal strength prediction which is defined by the 3D distance $d$
		and the number of floors $\Delta f$ between the \docAPshort{} and the particle
		
		\begin{equation}
			P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF,
		\end{equation}
		
		and calculate the resulting probability as described in \cite{ipin2015}:
		
		\begin{equation}
			\mProb(\mObsVec \mid \mStateVec)_\text{wifi} =
			\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2).
			\label{eq:wifiTotal}
		\end{equation}
				
		For the \docWIFI{} component we thus need two parameters per \docAPshort{}: $\mTXP$ measured at a distance 
		$\mMdlDist_0$ (usually \SI{1}{\meter}) and the path-loss exponent $\mPLE$ describing the environment.
		To reduce complexity and system setup time, we use the same values for all \docAP{}s at the cost of accuracy.
		While, $\mTXP$ is best determined using averaged measurements at a single location,
		a good estimation of $\mPLE$ requires several measurements and numerical optimization \cite{etwas_aus_der_MA}.
		$\mPLE$ is thus chosen empirically.
		
		For the \docIBeacon{} component we also use \refeq{eq:wifiTotal} but $\mTXP$ is transmitted by each beacon.
		Again, $\mPLE$ is determined emprically. \todo{faellt hier meist kleiner aus, weil ja kuerzere reichweite etc}
	
	
	\subsection{Step- \& Turn-Detection}
		
		To prevent degradation within the particle-filter \cite{??} due to downvoting of particles with increased
		heading deviation, we incorporate the turn-detection as control-data directly into the transition
		$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$.
		\cite{thrun?}\cite{lukas2014?} to get a more directed sampling instead of a truly random one.
		
		
		
		\commentByFrank{todo: wie wird die unsicherheit in der transition eingebracht, sigma, ..}