experiments set values, added csv files radius error and graphic stuff

tex/chapters/experiments.tex

@@ -15,7 +15,7 @@ It was created using our 3D map editor software based on architectural drawings
 
 Sensor measurements are recorded using a simple mobile application that implements the standard Android sensor functionalities.
 As smartphones we used either a Samsung Note 2, Google Pixel One or Motorola Nexus 6.
-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. 
+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. 
 
@@ -66,9 +66,9 @@ Other transmitters like smart TVs or smartphone hotspots are ignored as they mig
 \end{figure}
 %
 The 4 chosen walking paths can be seen in fig. \ref{fig:floorplan}. 
-Walk 0 is \SI{152}{\meter} long and took about \SI{2.30}{\minutes} to walk.
-Walk 2 has a length of \SI{223}{\meter} and Walk 3 a length of \SI{231}{\meter}, both required about \SI{6}{\minutes} to walk. 
-Finally, walk 3 is \SI{310}{\meter} long and needs \SI{10}{\minutes} to walk.
+Walk 0 is \SI{152}{\meter} long and took about \SI{2.30}{\minute} to walk.
+Walk 2 has a length of \SI{223}{\meter} and Walk 3 a length of \SI{231}{\meter}, both required about \SI{6}{\minute} to walk. 
+Finally, walk 3 is \SI{310}{\meter} long and needs \SI{10}{\minute} to walk.
 All walks 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.
 The picked walks intentionally contain erroneous situations, in which many of the above treated problems occur. 
@@ -146,17 +146,10 @@ Without a method to recover from impoverishment, the system lost track in \SI{10
 By using the simple method, the overall error can be reduced and the impoverishment resolved. Nevertheless, unpredictable jumps of the estimation are causing the system to be highly uncertain in some situations, even if those jumps do not last to long.
 Only the use of the $D_\text{KL}$ method is able to produce reasonable results.
 
-\begin{figure}[bt]
-	\centering
-  	\includegraphics[width=0.9\textwidth]{gfx/wifiOptGlobalFloor/combined_dummy.png}
-	\caption{A small section of walk 3. Optimizing the system with a global Wi-Fi optimization scheme (blue) causes a big jump and thus high errors. This happens due to highly attenuated Wi-Fi signals and inappropriate Wi-Fi parameters. We compare this to a system optimized for each floor individually (red), resolving the situation a producing reasonable results.}
-	\label{fig:wifiopt}
-\end{figure}
-%
 As described in chapter \ref{sec:wifi}, we use a Wi-Fi model optimized for each floor instead of a single global one.
 A good example why we do this, can be seen in fig. \ref{fig:wifiopt}, considering a small section of walk 3.
 Here, the system using the global Wi-Fi model makes a big jump into the right-hand corridor and requires \SI{5}{\second} to recover.
-This happens through a combination of environmental occurrences, like the many different materials and thus attenuation factors, as well as the limitation of the here used Wi-Fi model, only considering ceilings and ignoring walls. 
+This happens through a combination of environmental occurrences, like the many different materials and thus attenuation factors, as well as the limitation of the here used Wi-Fi model, only considering ceilings and ignoring walls.
 Following, \docAPshort{}'s on the same floor level, which are highly attenuated by \SI{2}{\meter} thick stone walls, are neglected and \docAPshort{}'s from the floor above, which are only separated by a thin wooden ceiling, have a greater influence within the state evaluation process.
 Of course, we optimize the attenuation per floor, but at the end this is just an average value summing up the \docAPshort{}'s surrounding materials. 
 Therefore, the calculated signal strength predictions do not fit the measurements received from the above in a optimal way.
@@ -164,6 +157,14 @@ In contrast, the model optimized for each floor only considers the respective \d
 A major disadvantage of the method is the reduced number of visible \docAPshort{}'s and thus measurements within an area. 
 This could lead to an underrepresentation of \docAPshort{}'s for triangulation.
 
+\begin{figure}[t!]
+	\centering
+  	\includegraphics[width=0.9\textwidth]{gfx/wifiOptGlobalFloor/combined_dummy.png}
+	\caption{A small section of walk 3. Optimizing the system with a global Wi-Fi optimization scheme (blue) causes a big jump and thus high errors. This happens due to highly attenuated Wi-Fi signals and inappropriate Wi-Fi parameters. We compare this to a system optimized for each floor individually (red), resolving the situation a producing reasonable results.}
+	\label{fig:wifiopt}
+\end{figure}
+
+
 %walk 1 
 Looking at the results of table \ref{table:overall} again, it can be seen that the $D_\text{KL}$ method is able to improve the results in three of the four walks. 
 Those walks have in common, that they suffer in some way from sample impoverishment or other problems causing the system to stuck. 
@@ -182,8 +183,8 @@ As a result, the radius $r_\text{sub}$ increases and thus the diversity of parti
 We are able to confirm the above by examining the different scenarios integrated into walk 1.
 For this, we compared the error development with the corresponding radius $r_\text{sub}$ over time. 
 In situations where the errors given by the $D_\text{KL}$ method and the simple method differ the most, $r_\text{sub}$ also increases the most. 
-Here, the radius grows to a maximum of $r_\text{sub} = $ \SI{666}{\meter}.
-In contrast, a real sample impoverishment scenario, as seen in walk 0 (cf. fig. \ref{fig:errorOverTimeWalk0}), provides a maximum radius of \SI{777}{\meter}.
+Here, the radius grows to a maximum of $r_\text{sub} = $ \SI{8.4}{\meter}, using the same measurement series as in fig. \ref{fig:walk1:kdeovertime}.
+In contrast, a real sample impoverishment scenario, as seen in walk 0 (cf. fig. \ref{fig:errorOverTimeWalk0}), has a maximum radius of \SI{19.6}{\meter}.
 Nevertheless, such an slightly increased diversity is enough to influence the estimation error of the $D_\text{KL}$ in a negative way (cf. walk 1 in table \ref{table:overall}). 
 Ironically, this is again some type of sample impoverishment, caused by the aforementioned environmental restrictions not allowing particles inside walls or other out of reach areas. 
 
@@ -191,21 +192,32 @@ Ironically, this is again some type of sample impoverishment, caused by the afor
 \subsection{Estimation}
 \label{sec:eval:est}
 
+\todo{boxkde 0.2 point2(1,1);}
+
 As mentioned before, the single estimation methods (cf. chapter \ref{sec:estimation}) only vary by a few centimetres in the overall localization error. 
 That means, they differ mainly in the representation of the estimated locations. 
 More easily spoken, in which way the estimated path is drawn and thus presented to the user.
 Regarding the underlying particle set, different shapes of probability distributions need to be considered, especially those with multimodalities. 
 %
-\begin{figure}
+\begin{figure}[t]
 	\centering
-	\input{gfx/walk.tex}
-	\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of walk 1. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides a high error compared to the ground truth (solid black), while the KDE approach (orange) does not. }
-	\label{fig:realWorldMulti}
+	\begin{subfigure}{0.48\textwidth}
+		\resizebox{1\textwidth}{!}{\input{gfx/walk.tex}}
+        \caption{}
+        \label{fig:walk1:kde}
+    \end{subfigure}
+	\begin{subfigure}{0.50\textwidth}
+		\resizebox{1\textwidth}{!}{\input{gfx/errorOverTimeWalk1/errorOverTime.tex}}
+        \caption{}
+        \label{fig:walk1:kdeovertime}
+    \end{subfigure}
+	\caption{(a) Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of walk 1. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides a high error compared to the ground truth (solid black), while the KDE approach (orange) does not. (b) Error development over time for the complete walk. From \SI{230}{\second} to \SI{290}{\second} to pedestrian was not moving. }
+	\label{fig:walk1}
 \end{figure}
 %
 The main advantage of a KDE-based estimation is that it provides the "correct" mode of a density, even under a multimodal setting (cf. section \ref{sec:estimation}). 
 That is why we again have a look at walk 1.
-A situation in which the system highly benefits from this is illustrated in fig. \ref{fig:realWorldMulti}.
+A situation in which the system highly benefits from this is illustrated in fig. \ref{fig:walk1:kde}.
 Here, a set of particles splits apart, due to uncertain measurements and multiple possible walking directions.
 Indicated by the black dotted line, the resulting bimodal posterior reaches its maximum distance between the modes at \SI{13.4}{\second}.
 Thus, a weighted average estimation (blue line) results in a position of the pedestrian somewhere outside the building (light green area). 
@@ -214,8 +226,8 @@ The KDE-based estimation (orange line) is able to provide reasonable results by
 After \SI{20.8}{\second} the setting returns to be unimodal again. 
 Due to a right turn the lower red particles are walking against a wall and thus punished with a low weight.
 
-Although, situations as displayed in fig. \ref{fig:realWorldMulti} frequently occur, the KDE-estimation is not able to improve the overall estimation results.
-This can be seen in the corresponding error development over time plot given by fig. \ref{fig:realWorldTime}. 
+Although, situations as displayed in fig. \ref{fig:walk1:kde} frequently occur, the KDE-estimation is not able to improve the overall estimation results.
+This can be seen in the corresponding error development over time plot given by fig. \ref{fig:walk1:kdeovertime}. 
 Here, the KDE-estimation performs slightly better then the weighted-average, however after deploying \SI{100}{} Monte Carlo runs, the difference becomes insignificant.
 It is obvious, that the above mentioned "correct" mode, not always provides the lowest error. 
 In some situations the weighted-average estimation is often closer to the ground truth. 
@@ -223,30 +235,22 @@ Within our experiments this happened especially when entering or leaving thick-w
 While the system’s dynamics are moving the particles outside, the faulty Wi-Fi readings are holding back a majority by assigning corresponding weights.
 Only with new measurements coming from the hallway or other parts of the building, the distribution and thus the KDE-estimation are able to recover. 
 
-\begin{figure}
-	\centering
-	\input{gfx/errorOverTimeWalk1/errorOverTime.tex}
-	\caption{Error development over time of a single Monte Carlo run of the walk calculated between estimation and ground truth. Between \SI{230}{\second} and \SI{290}{\second} to pedestrian was not moving.}
-	\label{fig:realWorldTime}
-\end{figure}
-
 This leads to the conclusion, that a weighted average approach provides a more smooth representation of the estimated locations and thus a higher robustness.
 
-\todo{bild vom gesamten walk 2 und den unterschied zwischen weighted average estimation und kde estimation zeigen. wie sich das auf dne estimated path auswirkt. also der eine pfad springt viel und der andere ist halt smoother}
+\todo{bild vom gesamten walk 2 und den unterschied zwischen weighted average estimation und kde estimation zeigen. wie sich das auf dne estimated path auswirkt. also der eine pfad springt viel und der andere ist halt smoother
+
+vielleicht noch fig. 8 raus dafür. }
 
 In contrast, a KDE-based approach for estimation is able to resolve multimodalities. 
 It does not always provide the lowest error, since it depends more on an accurate sensor model then a weighted average approach, but is very suitable as a good indicator about the real performance of a sensor fusion system. 
 At the end, in the here shown examples we only searched for a global maxima, even though this approach opens a wide range of other possibilities for finding a best estimate.
 
-\todo{boxkde 0.2 point2(1,1);}
-
-\todo{
-BILD: Von einem Pfad der steckenbleibt und den beiden anderen verfahren mit fehler über die zeit. 
-
-BILD: WIFI-Fehler unten bei den Kellern. 
-
-BILD: Estimation Fehler 
-}
+\begin{figure}[t]
+	\centering
+	\input{gfx/errorOverTimeWalk1/errorOverTime.tex}
+	\caption{Error development over time of a single Monte Carlo run of the walk calculated between estimation and ground truth. Between \SI{230}{\second} and \SI{290}{\second} to pedestrian was not moving.}
+	\label{}
+\end{figure}