latest TeX

many new gfx and data
worked on eval

tex/chapters/experiments.tex

@@ -1,4 +1,118 @@
 \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)
@@ -12,7 +126,12 @@
 \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}