Merge branch 'master' of https://git.frank-ebner.de/FHWS/IPIN2018

tex/chapters/eval.tex

@@ -1,4 +1,5 @@
 \section{Evaluation}
+\label{sec:evaluation}
 
 The probability density of the state evaluation in \eqref{equ:bayesInt} is given by 
 %

tex/chapters/experiments.tex

@@ -102,61 +102,62 @@ This is more difficult using the mesh and requires the handling of baricentric c
 \subsection{\docWIFI{} Optimization}
 \label{sec:exp:opti}
 
-\commentByToni{Work in Progress... Irgendwie passt die Grafik nicht so wirklich. Im Gegensatz zum 2017 Paper würde ich gerne ein wenig über die geschätzten Positionen reden. Die Unterschiede zwischen Local und Global dabei. Warum machne Schätzungen gar so weit weg von der Realität sind und das es oft auch gar nicht so schlimm ist, falls das passiert. Tipps sind Willkommen}
+%\commentByToni{Work in Progress... Irgendwie passt die Grafik nicht so wirklich. Im Gegensatz zum 2017 Paper würde ich gerne ein wenig über die geschätzten Positionen reden. Die Unterschiede zwischen Local und Global dabei. Warum machne Schätzungen gar so weit weg von der Realität sind und das es oft auch gar nicht so schlimm ist, falls das passiert. Tipps sind Willkommen. Vielleicht b) weglassen und in a einfach noch die fingerprint positionen mit rein. damit man ein gefühlt dafür bekommt wie viel wir in Vorleistung gehen müssen. An sich erkannt man ja dann das von "oben" das die optimierung manchmal gut und manchmal schlecht ist.}
 
 %wie viele ap sind es insgesamt?
 As described in section \ref{sec:wifi} we used \SI{42}{} WEMOS D1 mini to provide a \docWIFI{} infrastructure throughout the building.
 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.
-The position of every installed beacon was measured using a laser scanner. 
-This allows a comparison with the optimized \docAPshort{} positions.
-Fig. \ref{fig:apfingerprint} illustrates the results of the global and the per-floor method for all \docAPshort{}'s installed to ground level. 
+The references (fingerprints) we used to optimize the Wi-Fi models as well as the real position of the \docAPshort{}s (black dot) can be seen in fig. \ref{fig:apfingerprint} for ground level.
+Each reference location was scanned \SI{30}{} times ($\approx \SI{25}{\second}$ scan time) using a Motorola Nexus 6 at \SI{2.4}{GHz} band only.
+The resulting measurements were grouped per physical transmitter and aggregated to form the average signal strength per transmitter.
+The real position of every installed beacon was measured using a laser scanner. 
+This allows a comparison with the optimized \docAPshort{} positions, what can also be seen in fig. \ref{fig:apfingerprint}.
+
 %
 \begin{figure}[t]
 	\centering
-	\begin{subfigure}{0.49\textwidth}
-		\def\svgwidth{\columnwidth}
-		\input{gfx/optimization/wifiOptTopView.eps_tex}
-        \caption{Top view}
-    \end{subfigure}
-	\begin{subfigure}{0.49\textwidth}
-		\def\svgwidth{\columnwidth}
-		\input{gfx/optimization/side/sideplot2.eps_tex}
-        \caption{Side view}
-    	\label{fig:apfingerprint:b}
-    \end{subfigure}
-    \caption{Position of Ap's optimized with global and per floor and real.}
+	\def\svgwidth{\columnwidth}
+	\input{gfx/optimization/wifiOptTopView.eps_tex}
+    \caption{Ground level of the building in the $xz$-plane from above. Includes the locations of the reference points, the ground truth and the optimized \docAPshort{}s. The grey line connects an \docAPshort{} with the corresponding optimization. The coloured squares are areas of special interest and are discussed within the text. The corresponding pictures on the right side show the museum in these places.}
     \label{fig:apfingerprint}
 \end{figure}
-%
-Here, the respective optimized positions are connected by a grey line with the corresponding ground truth.
-In order not to be confused by overlaps, the side view in fig. \ref{fig:apfingerprint:b} only shows the eight \docAPshort{}'s installed on the right side of the building.
+%Positionsfehler und wo?
+It illustrates the results of the global (blue) and the per-floor (orange) method for all \docAPshort{}'s installed to ground level. 
+The respective optimized positions $\mPosAPVec$ are connected by a grey line with the corresponding ground truth, providing the position error on the $xz$-plane.
+The average error between the \docAPshort{}'s real position and the optimized ones is \SI{5.4}{\meter} ($\mu =$ \SI{5.1}{}) for the per-floor and \SI{4.8}{\meter} ($\mu =$ \SI{5.6}{}) for global strategy.
+However, it is easy to see that the results are better in some areas (green) than in others (red and purple).
+While the green square encloses an area that has a high number of \docAPshort{}s with line of sight conditions, the \docAPshort{}s in red and purple are shielded by very thick stone walls and have a lower number of reference points with direct visual contact (cf. fig. \ref{fig:apfingerprint}).
+The maximum position error for the global scheme is \SI{25.3}{\meter} and \SI{18.4}{\meter} for the per-floor one.
+Both are related to the \docAPshort{} in the red square.
+
+%Gesamtfehler und wieso?
+Of course, the position alone does not provide sufficient information of the overall performance, however it provides a good visual impression of how the optimization behaves.
+The overall optimization error is measured using the difference between model predictions and real-world values for each reference measurement. 
+These differences can be positive or negative, which is why we indicate an absolute or signed error.
+The (absolute) optimization error of the respective strategies is \SI{4.7}{\decibel} ($\mu =$ \SI{3.8}{}) for global and \SI{2.6}{\decibel} ($\mu =$ \SI{2.7}{}) for per-floor in average.
+Again, the highest errors occur from \docAPshort{}s within the red and purple area, whereby the local maxima for the signed difference are \SI{-31.4}{\decibel} and \SI{17.5}{\decibel} for global and \SI{-12.7}{\decibel} and \SI{13.4}{\decibel} for local.
+%global vs local
+Thus, the per-floor optimization scheme provides a smaller overall error, whereby the positioning error is higher compared to the global one. 
+The reason for the latter can be found within the purple area. 
+It marks a vaulted cellar, that is \SI{1.7}{\meter} deeper then ground level and connect by a narrow staircase.
+Here, RSSI measurements taken from outside the ground level are strongly attenuated, while measurements taken from above are more moderately attenuated. 
+Since the per-floor scheme uses only references from the current floor in question, while the global scheme uses all available references and thus more meaningful information in this area. 
+However, as the overall error suggests, this is not always an advantage, which we will see later on in the localization.
+
+%warum ist die optimierung tdz. ganz gut?
+As mentioned above, some areas are heavily attenuated by big walls, what simply does not fit the used signal strength prediction model. 
+As discussed in section \ref{sec:relatedWork} and \ref{sec:wifi}, we only consider ceilings within the model to avoid computational expensive wall intersection-tests. 
+A far higher number of reference measurements in bad areas can therefore only increase the accuracy to a limited extent. 
+Nevertheless, by optimizing all parameters (\mPosAPVec, \mTXP{}, \mPLE{} and \mWAF{}) the system provides far better localization results compared to using the \docAPshort{}'s real positions with empirical values or even optimized values only for \mTXP{}, \mPLE{} and \mWAF{}. 
+The reason for this is obvious.
+The optimized parameters fit the (unrealistic) signal strength prediction model much better than the real ones and thus provide for a smaller error between measured RSSI and predicted RSSI. 
+Since walls are ignored by the model, optimizing the position of the access points can compensate for the resulting effects. 
+This is also the reason why the optimized positions of \docAPshort{}'s attached to walls always have a certain distance to them, as can be seen in fig. \ref{fig:apfingerprint}.
+A more realistic model would not only mean an overall improvement of the results, but also a further approximation to the real conditions in the building. It is to be expected that the estimated positions of the access points will then approach the ground truth. 
+Further evaluations and discussions regarding the here used optimization can be found in \cite{Ebner-17}.
 
 
-Looking at fig. \ref{fig:apfingerprint}, it can be seen that most optimized positions differ in the lower single-digit meter range.
-
-gives a good idea on how optimizing a simplified signal-strength prediction model behaves. 
-
-
-
-of course, the position alone does not provide sufficient information of the overall performance of the optimiziation since they give no information about the other optimized parameters (bla, blub and bliib). 
-%Nevertheless, fig. \ref{} gives an idea on how optimizing a simplified signal-strength prediction model behaves. 
-By only considering ceillings, the attenuation factore... and thus most z coordinates for the ap's are similiar. 
-The main message from this is, that wherever the ap's are optimized they are optimized to perfectly fit the underlying signal-strength model. 
-thus the optimized parameters provide far better localization results compared to just using the real ones. simply because modelling the realistic incidents is very time consuming. 
-
-difference stockwerk, global
-looking at the optimziation errors, this can be varified... etc pp
-
-%wie fingerprints aufgenommen, wie viele ...
-
-\todo{die werte "results from the (absolute) difference between model predictions and real-world values for each reference measurement", wie im other 2017 und dann darauf referenzieren.}
-
-%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{Localization Error}
 

tex/gfx/optimization/plot.gp

@@ -7,17 +7,17 @@ set terminal x11 size 2000,1500
 
 set ticslevel 0
 #unset key 
-set xrange [15.000000:71.300003]
+#set xrange [15.000000:71.300003]
 set xtics  autofreq 
 set format x '%h'
 #unset xlabel 
 
-set yrange [-0.500000:51.700001]
+#set yrange [-0.500000:51.700001]
 set ytics  autofreq 
 set format y '%h'
 #unset ylabel 
 
-set zrange [-6:11]
+#set zrange [-6:11]
 set ztics  autofreq 
 set format z '%h'
 #unset zlabel 
@@ -30,20 +30,20 @@ set view 0,90
 set ticslevel 0
 #set view equal xy
 
-set lmargin at screen 0
-set rmargin at screen 1
-set tmargin at screen 0.8
-set bmargin at screen 0
+#set lmargin at screen 0
+#set rmargin at screen 1
+#set tmargin at screen 0.8
+#set bmargin at screen 0
 
 #unset lmargin
 #unset rmargin
 #unset tmargin
 #unset bmargin
 
-unset border
-unset xtics
-unset ytics
-unset ztics
+#unset border
+#unset xtics
+#unset ytics
+#unset ztics
 
 # Building
 load 'building2.gp.inc'

tex/gfx/optimization/side/plot.gp

@@ -1,7 +1,7 @@
 reset
 
-#set terminal x11 size 2000,1500
-set terminal windows size 2000,1500
+set terminal x11 size 2000,1500
+#set terminal windows size 2000,1500
 #set terminal epslatex size 15cm,22cm
 #set output "plot.tex"
 
@@ -63,6 +63,6 @@ splot \
  'perFloor.csv'          using 2:3:4 with point  pt 7 ps 1 lc rgb '#FCAF3E' notitle ,\
  'global.csv'            using 2:3:4 with point  pt 7 ps 1 lc rgb '#0D6DCD' notitle ,\
  
-
+pause -1
 
 

tex/gfx/optimization/wifiOptTopView.eps_tex

@@ -38,7 +38,7 @@
   \newcommand*\fsize{\dimexpr\f@size pt\relax}%
   \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
   \ifx\svgwidth\undefined%
-    \setlength{\unitlength}{446.52248112bp}%
+    \setlength{\unitlength}{707.99998847bp}%
     \ifx\svgscale\undefined%
       \relax%
     \else%
@@ -50,12 +50,15 @@
   \global\let\svgwidth\undefined%
   \global\let\svgscale\undefined%
   \makeatother%
-  \begin{picture}(1,1.19347493)%
+  \begin{picture}(1,0.71927962)%
     \lineheight{1}%
     \setlength\tabcolsep{0pt}%
     \put(0,0){\includegraphics[width=\unitlength]{wifiOptTopView.eps}}%
-    \put(0.06667645,1.0782626){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}local optim.\end{tabular}}}}%
-    \put(0.03905654,1.13354086){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}global optim.\end{tabular}}}}%
-    \put(0.04173314,1.01929418){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}ground truth\end{tabular}}}}%
+    \put(0.0420516,0.65683794){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}floor optim.\end{tabular}}}}%
+    \put(0.02675088,0.68947947){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}global optim.\end{tabular}}}}%
+    \put(0.24620002,0.68934834){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}ground truth\end{tabular}}}}%
+    \put(0.2303965,0.65687677){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}reference point\end{tabular}}}}%
+    \put(0.70550855,0.26588974){\color[rgb]{1,0.99607843,1}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}\textbf{DUMMY}\end{tabular}}}}%
+    \put(0.70396481,0.01662141){\color[rgb]{1,0.99607843,1}\makebox(0,0)[lt]{\lineheight{38.57500076}\smash{\begin{tabular}[t]{l}\textbf{DUMMY}\end{tabular}}}}%
   \end{picture}%
 \endgroup%