experimante weiter gemacht

tex/chapters/estimation.tex

@@ -1,4 +1,5 @@
 \subsection{State Estimation}
+\label{sec:estimation}
 
 1/2 bis 3/4 Seite
 

tex/chapters/eval.tex

@@ -1,6 +1,5 @@
 \section{Evaluation}
 
-
 The probability density of the state evaluation in \eqref{equ:bayesInt} is given by 
 %
 \begin{equation}

tex/chapters/experiments.tex

@@ -1,6 +1,96 @@
 \section{Experiments}
 
-3 1/2 seiten sollten das schon werden. also eine ausführliche evaluation. 
+As explained at the very beginning of this work, we wanted to explore the limits of the here presented localization system.
+By utilizing it to a 13th century historic building, we created a challenging scenario not only because of the various architectural factors, but also because of its function as a museum.
+During all experiments, the museum was open to the public and had a varying number of \SI{10}{} to \SI{50}{} visitors while recording.
+
+The \SI{2500}{\square\meter} building consists of \SI{6}{} different levels, which are grouped into 4 floors (see fig. \ref{fig:apfingerprint}). 
+Thus, the ceiling height is not constant over one floor and varies between \SI{2.6}{\meter} to \SI{3.6}{\meter}.
+In the middle of the building is an outdoor area, which is only accessible from one side. 
+While most of the exterior and ground level walls are made of massive stones, the floors above are half-timbered constructions.
+Due to different objects like exhibits, cabinets or signs not all positions within the building were walkable. 
+For the sake of simplicity we did not incorporate such knowledge into the floorplan. 
+Thus, the floorplan consists only of walls, ceilings, doors, windows and stairs.
+It was created using our 3D map editor software based on architectural drawings from the 1980s. 
+
+The computation of the state estimation as well as the \docWifi{} optimization are done offline using an Intel Core i7-4702HQ CPU with a frequency of \SI{2.2}{GHz} running \SI{8}{cores} and \SI{16}{GB} main memory. 
+However, similar to our previous, award-winning system, the setup is able to run completely on commercial smartphones as well as it uses C++ code \cite{torres2017smartphone}. 
+%Sensor measurements are recorded using a simple mobile application that implements the standard Android SensorManager. 
+
+The experiments are separated into three sections:
+At first, we discuss the performance of the novel transition model and compare it to a grid-based approach.  
+In section \ref{sec:exp:opti} we have a look at \docWIFI{} optimization and how the real \docAPshort{} positions differ from it.
+Following, we conducted several test walks throughout the building to examine the estimation accuracy (in \SI{}{\meter}) of the localisation system. 
+We try to resolve sample impoverishment with the here presented method and compare the different estimation methods as presented in section \ref{sec:estimation}. 
+
+
+\subsection{Transition}
+To make a statement about the performance of our novel transition model presented within section \ref {}, we 
+
+\todo{Unser liebes Treppensteigen. Vergleich altes und neues Bewegungsmodell.}
+
+\subsection{\docWIFI{} Optimization}
+\label{sec:exp:opti}
+
+%wie viele ap sind es insgesamt?
+The \docAPshort{} positions as well as the fingerprints used for optimization can be seen in fig. \ref{fig:apfingerprint}.
+As described in section \ref{sec:wifi} we used \SI{42}{} WEMOS D1 mini to provide a \docWIFI{} infrastructure throughout the building.
+The position of every installed beacon was measured using a laser scanner. 
+This allows a comparison with the optimized \docAPshort{} positions. 
+Within all Wi-Fi observations, we only consider the beacons, which are identified by their well-known MAC address. 
+Other transmitters like smart TVs or smartphone hotspots are ignored as they might cause estimation errors.
+%wie fingerprints aufgenommen, wie viele ...
+
+\begin{figure}[bt]
+	\centering
+  \includegraphics[width=0.9\textwidth]{gfx/floorplanDummy.png}
+	\caption{Floorplan Dummy}
+	\label{fig:apfingerprint}
+\end{figure}
+
+
+%kurze beschreibung was wir jetzt alles testen wollen.
+
+
+%was kommt bei der optimierung raus. vergleichen mit ground truth. auch den fehler gegenüberstellen. 
+%man sollte sehen das ohne optimierung gar nichts geht.
+
+\subsection{Location Estimation Error}
+
+
+\begin{figure}[ht]
+	\centering
+  \includegraphics[width=0.9\textwidth]{gfx/floorplanDummy.png}
+	\caption{Floorplan Dummy}
+	\label{fig:floorplan}
+\end{figure}
+%
+The 4 arranged walks can be seen in fig. \ref{fig:floorplan}.
+They were carried out be 4 different male testers using either a Samsung Note 2, Google Pixel One or Motorola Nexus 6 for recording the measurements. 
+All in all, we recorded \SI{28}{} distinct measurement series, \SI{7}{} for each walk.
+A walk is indicated by a set of numbered markers, fixed to the ground. 
+Small icons on those markers give the direction of the next marker and in some cases provide instructions to pause walking for a certain time.
+The intervals for pausing vary between \SI{10}{\second} to \SI{60}{\second}. 
+The ground truth is then measured by recording a timestamp while passing a marker. 
+For this, the tester clicks a button on the smartphone application. 
+Between two consecutive points, a constant movement speed is assumed.
+Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for error measurements. 
+The approximation error is then calculated by comparing the interpolated ground truth position with the current estimation \cite{Fetzer-16}.
+
+%computation und monte carlo runs
+For each walk we deployed 50 runs using a varying size of particles. 
+Instead of an initial position and heading, all walks start with a uniform distribution (random position and heading) as prior.
+
+
+%probleme mit impoverishment aufzeigen, wo bringt es was, was macht es kaputt etc pp
+
+%%estimation
+
+%wie in bulli paper.
+
+%letzer absatz nochmal gesamtergebniss des gesamten systems
+%was läuft noch schief? wo macht was probleme?
+
 
 \begin{itemize}
 	\item Noch ein paar Dinge über das gebäude und das setup an sich