\section{Experiments}
	
	% introduction
	Evaluation took place within all floors (0 to 3) of the
	faculty building, each of which about \SI{77}{\meter} x \SI{55}{\meter} in size.
	We conducted 4 distinct walks, for testing short distances, long distances, critical sections
	and ignoring the shortest-path suggested by the system. Each path is backed by ground truth information
	to enable error calculation. This ground truth is measured by recording a timestamp at a marked spot
	on the walking route. During the walk, the pedestrian has to click a button on the smartphone
	application when passing a marker. Between two consecutive points, a constant movement speed is assumed.
	Thus, the ground truth might not be \SI{100}{\percent} accurate, but good enough to conduct error measurements.
	All walks were conducted using a Google Nexus 6 and a Samsung Galaxy S5.
	
	As the Samsung Galaxy S5's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only, its scans take much
	longer than those of the Google Nexus 6: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}. Also, the Nexus' barometer sensor
	provides readings more frequent and far more accurate than the Galaxy does. This results in a much better
	localisation for the Nexus smartphone.
	
	Despite being fast enough to run in realtime on the smartphone itself, computation was done offline using
	the condensation algorithm with \SI{7500}{} particles as realization of the recursive density estimation \cite{todo}
	and the weighted arithmetic mean of those for the state estimation.
	
	As mentioned earlier, the position of all \docAP{}s (about 5 per floor) is known beforhand. 
	Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures.
	Additionally we used three \docIBeacon{}s for slight enhancements in some areas.
	The empirically chosen values for \docWIFI{} were $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}$,
	and $\mPLE_{\text{ib}} = \SI{1.5}{}$ for the \docIBeacon{}s, respectively. Due to omitting a time-consuming calibration
	process for those values, the sensor readings are considered somewhat faulty.
	
	As uncertainties we used $\sigma_\text{wifi} = \sigma_\text{ib} = 8.0$, both growing with each measurement's age.
	While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters
	are determined automatically (see \ref{sec:sensBaro}). The step size for the transition was configured to be \SI{70}{\centimeter}
	with an allowed derivation of \SI{10}{\percent}. The heading deviation in \refeq{eq:transSimple} was \SI{25}{\degree}.
	


	\commentByFrank{describe what was evaluated: 2 phones (differences), 4 paths, building, several floors, ibeacons, access points}

	\commentByFrank{bergwerk\_path3\_galaxy}
	
	As we start with a uniformation distribution for $\mStateVec_0$, the first few estimations
	are omitted from the error calculation to allow the system to settle its initial state.

	Adding the importance factors described in \ref{sec:wallAvoidance} and \ref{sec:doorDetection} 
	to the simple transition \refeq{eq:transSimple} addresses only minor local errors like not
	sticking too close to walls. In most cases this lead only to minor, if any, improvements
	and is therefore not fruther evaluated.

	\commentByFrank{verlassen vom shortest path fuehrt zu weniger verbesserung, aber es wird nach wie vor besser als ohne!}
	
	\commentByFrank{in den ersten paar sec ist die pfad-info teils hinderlich, da die genaue position noch sehr unklar ist und sich erst einstellen muss.
	deshalb geht der fehler hier oft leicht hoch}
	
	\begin{figure}
		%\includegraphics{eval/bergwerk_path2_nexus_shortest}
	\end{figure}
	
	% error development over time while walking along a path
	\begin{figure}
		\input{gfx/eval/error_timed_nexus}
		\caption{Development of the error while walking along path 1 (upper) and path 4 (lower) using the Google Nexus 6.
		Path 4 shows increasing errors for our methods when leaving the shortest path and when facing multimodalities between two
		staircases at the end.}
		\label{fig:errorTimedNexus}
	\end{figure}
	
	% overall error-distribution for nexus and galaxy
	\begin{figure}
		\input{gfx/eval/error_dist_nexus}
		\caption{Error distribution for all walks conducted with the Google Nexus 6. Our proposed methods
		clearly provide an enhancement for the overall localization process.}
		\label{fig:errorDistNexus}
	\end{figure}
	\begin{figure}
		\input{gfx/eval/error_dist_galaxy}
		\caption{Nicht so markant beim galaxy, denke aber der platz reicht eh nicht, also einfach kurz erwaehnen}
	\end{figure}

	\begin{table}
		\centering
		\begin{tabular}{|l|c|c|c|c|}
			\hline
														& Path1 			& Path2				& Path3 			& Path4 \\\hline
			Simple (\refeq{eq:transSimple})				&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
			Shortest (\refeq{eq:transShortestPath})		&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
			Multipath (\refeq{eq:transMultiPath})		&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
		\end{tabular}
		\caption{Median error for walks conducted with the Nexus 6.}
	\end{table}
	
	\begin{table}
		\centering
		\begin{tabular}{|l|c|c|c|c|}
			\hline
														& Path1				& Path2				& Path3				& Path4 \\\hline
			Simple (\refeq{eq:transSimple})				&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
			Shortest (\refeq{eq:transShortestPath})		&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
			Multipath (\refeq{eq:transMultiPath})		&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	&	\SI{}{\meter}	\\\hline
		\end{tabular}
		\caption{Median error for walks conducted with the Galaxy S5.}
	\end{table}
	
	\begin{figure}
		\includegraphics{gfx/eval/bergwerk_path1_galaxy}
		\caption{Path 1 recorded with the Galaxy S5. Using prior knowledge improves the staircase (left) and the target area (right) where
		both the barometer and \docWIFI{} provided bad readings.}
		\label{fig:bergwerkPath1Galaxy}
	\end{figure}
	
	\begin{figure}
		\includegraphics{gfx/eval/bergwerk_path3_galaxy}
		\caption{Path 3 recorded with the Galaxy S5. Even though both paths look similar, the version with prior knowledge ended
		much closer to the real destination due to reduced delays.}
		\label{fig:bergwerkPath3Galaxy}
	\end{figure}

\begin{itemize}
  \item Nochmal kurz auf die Probleme des letzten Systems eingehen (schon teil der introduction)
	\item Da letztes mal nur 1 Pfad, machen wir dieses mal mehrere! 
	\item Stelle normale Lokalisation der Pfad Lokalisation gegenüber und überlege wo Probleme auftreten
	\item nutze den "natürlichen Pfad" und einen normalen dijkstra
	\item Analysiere Probleme ggf. mit schönen Grafiken.
	\item Vergleich zum Schluss das neue System mit dem Alten um eine schöne Conclusion der Verbesserungen einzuleiten. 
\end{itemize}

\commentByFrank{we start with a uniform distribution $\mStateVec_0$}

\commentByFrank{hinweis auf die verschiedenen geraete (smartphones) und unterschiede, wlan/baro}
\commentByFrank{
	PATH4 HAELT SICH NICHT AN DEN SHORTEST PATH.
	GUTES BEISPIEL.
	der pfad wechselt sogar 2x! (3. stock)
	der shortest wird am ende etwas ungenau bei der treppe
}

\commentByFrank{sensorausfall simulieren, z.b. in der mitte, oder auf einer treppe}
\commentByFrank{zwischendrin mal stehenbleiben und schauen ob auch das klappt}
\commentByFrank{pfad verlassen und ganz wo anders hingehen}

\commentByFrank{die reine importance selbst auf dem graphen hilft, aber nur minimal weiter}

\commentByFrank{pfad4 nexus. pfadlos laeuft mit ach und krach richtig (treppenhaus, wlan schlecht)
mit pfad laeuft es falsch, weil die andere treppe kuerzer zum ziel ist und das wlan dort besser passt}

\commentByFrank{zu grosser einfluss vom pfad ist also kein allheilmittel.. kann, wie beim treppenhaus, auch nach hinten los gehen}


\commentByFrank{path1: bad start due to nearby AP and bad parameters (path-loss too high): high starting errors: median better}