\chapter{Appendix}

\section{List of Abbreviations}

\begin{acronym}[ABCDEFGH]
	\setlength{\itemsep}{-\parsep}
	
	%\acro{ABC}{Alphabet}
	\acro{AOA}{Angle Of Arrival}
	\acro{AP}{Access Point}
	\acro{API}{Application Programming Interface}
	\acro{BRDF}{Bidirectional Reflectance Distribution Function}
	\acro{CPU}{Central Processing Unit}
	\acro{GPS}{Global Positioning System}
	\acro{GPU}{Graphics Processing Unit}
	\acro{GSM}{Global System for Mobile Communications}
	\acro{HMM}{Hidden Markov Model}
	\acro{HTTP}{Hypertext Transfer Protocol}
	\acro{IEEE}{Institute of Electrical and Electronics Engineers}
	\acro{LMSE}{Least Mean Squared Error}
	\acro{LOS}{Line Of Sight}
	\acro{LDS}{Linear Dynamic System}
	\acro{LE}{Localization Error}
	\acro{NLOS}{None Line Of Sight}
	\acro{OpenGL}{Open Graphics Library}
	\acro{OpenMP}{Open Multi-Processing}
	\acro{PF}{Particle Filter}
	\acro{PDF}{Probability Density Function}
	\acro{RPE}{Radio Propagation Error}
	\acro{RSSI}{Received Signal Strength Indication}
	\acro{SSID}{Service Set IDentification}
	\acro{SSM}{Signal Strength Map}
	\acro{TDOA}{Time Difference Of Arrival}
	\acro{TOA}{Time Of Arrival}
	\acro{UTD}{Uniform Theory of Diffraction}
	\acro{WAF}{Wall Attenuation Factor}
	
\end{acronym}

\section{Localization Paths}

\begin{figure}[h]
  \begin{center}
    \includegraphics[trim=0px 0px 0px 0px, clip=true, scale=0.355]{figures/path_eg_room_change.png}
  \end{center}
  \caption{The path \emph{eg-room-change} starts in a room in the lower floor and visits 2 other rooms on the same level. In the middle room (greenish) the localization target holds its position for around 5 seconds. The path has a length of $40m$ and is covered by an average of 9 APs.} 
  \label{fig:path_eg_room_change}
\end{figure}

\begin{figure}
  \begin{center}
    \includegraphics[trim=0px 0px 0px 0px, clip=true, scale=0.355]{figures/path_og1_classic.png}
  \end{center}
  \caption{The path \emph{og1-classic} start in a room on the right side of the first level. It leaves the room and visits another room by circling around the core room (Hardware Pool) of the level. The path has an length of $36m$ and is covered by 12 APs.} 
  \label{fig:path_og1_classic}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_og1_eg.png}
  \end{center}
  \caption{The path \emph{og1-eg} starts deep in the left side of the ground level and leads by the stairways to the right side of the first level of the building. The path has distance of $60m$ and is covered by an average of 7 APs over all positions.} 
  \label{fig:path_og1_eg}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_og1_eg_right.png}
  \end{center}
  \caption{The path \emph{og1-eg-right} starts in the same room as \emph{og1-classic}. It leads from the first level to the right side of the ground level by passig the stairways. The total covered distance is $70m$ and an average of 10 APs are seen during the transition.} 
  \label{fig:path_og1_eg_right}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_og1_long_rooms.png}
  \end{center}
  \caption{the path \emph{og1-long-rooms} starts at the right side of the first level and leads deep into the left side of the same level. There, a room is covered and the path leads back again into some sort of kitchen zone. In that zone, the mobile device rests for around 5 seconds. The path has a length of $81m$ and is covered by an average of 7 APs over all positions.} 
  \label{fig:path_og1_long_rooms}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_og1_long_straight.png}
  \end{center}
  \caption{The path \emph{og1-long-straight} forms a straight line from one side to the other side of the building and remains on one level. The path is $42m$ long and is covered by an average of 8 APs.} 
  \label{fig:path_og1_long_straight}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_og1_room_change.png}
  \end{center}
  \caption{The path \emph{og1-room-changes} represents a short room transtions. At the start and the end of the path, the device rests around 5 seconds and does not move. The scene is covered by 10 APs and the path has a length of $14m$.} 
  \label{fig:path_og1_room_change}
\end{figure}

\begin{figure} 
  \begin{center}
    \includegraphics[scale=0.355]{figures/path_stairs_upward.png}
  \end{center}
  \caption{The path \emph{og1-stairs-upward} starts at the ground level and uses the stairways to relocate to the second level. It has a length of around $50m$ and is covered by an average of 4 APs over all positions.} 
  \label{fig:path_stairs_upward}
\end{figure}

\newpage

\section{Synthetic Localization Error Tables}
\label{appendix_synth_errors}

\begin{center}
    \begin{tabularx}{1.013\textwidth}{|X|c|c|c|c|c|c|c|}\hline
    \rowcolor[gray]{.85}
    \multicolumn{8}{|>{\columncolor[gray]{.8}}c|}{\textbf{Online and Offline LEs in $m$ for Noise: $\sigma=0dBm$ (forward$+$backward)}}  \\ \hline
    \rowcolor[gray]{.92}
    \textbf{Path} & {\small HMM/off} & {\small HMM} & {\small HMM/avg} & {\small LMSE} & {\small PF/off} & {\small PF} & {\small PF/avg}\\ \hline\hline
    {\small eg-room-change} & 1.78 & 2.30 & 2.04 & 4.88 & 2.43 & 2.93 & 2.40\\ \hline
    {\small eg-room-change-r} & 1.75 & 2.38 & 2.13 & 5.07 & 2.60 & 3.07 & 2.62\\ \hline
    {\small og1-classic} & 1.11 & 1.79 & 1.58 & 3.65 & 2.26 & 2.76 & 2.36\\ \hline
    {\small og1-classic-r} & 1.07 & 1.52 & 1.25 & 3.54 & 1.95 & 2.16 & 1.73\\ \hline
    {\small og1-eg} & 1.49 & 2.31 & 2.08 & 4.98 & 3.29 & 3.72 & 3.36\\ \hline
    {\small og1-eg-r} & 1.70 & 2.56 & 2.38 & 5.03 & 2.79 & 3.37 & 3.09\\ \hline
    {\small og1-eg-right} & 1.44 & 2.17 & 1.97 & 5.34 & 3.08 & 3.54 & 3.25\\ \hline
    {\small og1-eg-right-r} & 1.59 & 2.36 & 2.11 & 5.43 & 2.98 & 3.39 & 3.05\\ \hline
    {\small og1-long-rooms} & 1.86 & 2.50 & 2.31 & 6.19 & 3.12 & 3.68 & 3.25\\ \hline
    {\small og1-long-rooms-r} & 1.80 & 2.56 & 2.36 & 5.91 & 3.01 & 3.66 & 3.32\\ \hline
    {\small og1-long-straight} & 1.29 & 2.06 & 1.89 & 4.29 & 2.13 & 2.60 & 2.30\\ \hline
    {\small og1-long-straight-r} & 1.47 & 2.08 & 1.85 & 4.10 & 2.16 & 2.62 & 2.26\\ \hline
    {\small og1-room-change} & 1.60 & 2.06 & 1.82 & 3.63 & 2.51 & 2.73 & 2.35\\ \hline
    {\small og1-room-change-r} & 1.67 & 2.04 & 1.86 & 3.58 & 2.39 & 2.75 & 2.33\\ \hline
    {\small stairs-upward} & 1.17 & 1.80 & 1.58 & 5.92 & 2.62 & 2.96 & 2.56\\ \hline
    {\small stairs-upward-r} & 1.22 & 2.81 & 2.63 & 6.03 & 2.76 & 3.21 & 2.95\\ \hline
\hline Mean in $m$ & 1.50 & 2.21 & 1.99 & 4.85 & 2.63 & 3.07 & 2.70 \\ \hline
Stdev in $m$ & 0.25 & 0.32 & 0.34 & 0.91 & 0.39 & 0.44 & 0.47 \\ \hline
    \end{tabularx}
\end{center}
\begin{center}
    \begin{tabularx}{1.013\textwidth}{|X|c|c|c|c|c|c|c|}\hline
    \rowcolor[gray]{.85}
    \multicolumn{8}{|>{\columncolor[gray]{.8}}c|}{\textbf{Online and Offline LEs in $m$ for Noise: $\sigma=4dBm$ (forward$+$backward)}}  \\ \hline
    \rowcolor[gray]{.92}
    \textbf{Path} & {\small HMM/off} & {\small HMM} & {\small HMM/avg} & {\small LMSE} & {\small PF/off} & {\small PF} & {\small PF/avg}\\ \hline\hline
    {\small eg-room-change} & 1.78 & 2.30 & 2.04 & 4.88 & 2.43 & 2.93 & 2.40\\ \hline
    {\small eg-room-change-r} & 1.75 & 2.38 & 2.13 & 5.07 & 2.60 & 3.07 & 2.62\\ \hline
    {\small og1-classic} & 1.11 & 1.79 & 1.58 & 3.65 & 2.26 & 2.76 & 2.36\\ \hline
    {\small og1-classic-r} & 1.07 & 1.52 & 1.25 & 3.54 & 1.95 & 2.16 & 1.73\\ \hline
    {\small og1-eg} & 1.49 & 2.31 & 2.08 & 4.98 & 3.29 & 3.72 & 3.36\\ \hline
    {\small og1-eg-r} & 1.70 & 2.56 & 2.38 & 5.03 & 2.79 & 3.37 & 3.09\\ \hline
    {\small og1-eg-right} & 1.44 & 2.17 & 1.97 & 5.34 & 3.08 & 3.54 & 3.25\\ \hline
    {\small og1-eg-right-r} & 1.59 & 2.36 & 2.11 & 5.43 & 2.98 & 3.39 & 3.05\\ \hline
    {\small og1-long-rooms} & 1.86 & 2.50 & 2.31 & 6.19 & 3.12 & 3.68 & 3.25\\ \hline
    {\small og1-long-rooms-r} & 1.80 & 2.56 & 2.36 & 5.91 & 3.01 & 3.66 & 3.32\\ \hline
    {\small og1-long-straight} & 1.29 & 2.06 & 1.89 & 4.29 & 2.13 & 2.60 & 2.30\\ \hline
    {\small og1-long-straight-r} & 1.47 & 2.08 & 1.85 & 4.10 & 2.16 & 2.62 & 2.26\\ \hline
    {\small og1-room-change} & 1.60 & 2.06 & 1.82 & 3.63 & 2.51 & 2.73 & 2.35\\ \hline
    {\small og1-room-change-r} & 1.67 & 2.04 & 1.86 & 3.58 & 2.39 & 2.75 & 2.33\\ \hline
    {\small stairs-upward} & 1.17 & 1.80 & 1.58 & 5.92 & 2.62 & 2.96 & 2.56\\ \hline
    {\small stairs-upward-r} & 1.22 & 2.81 & 2.63 & 6.03 & 2.76 & 3.21 & 2.95\\ \hline
\hline Mean in $m$ & 1.50 & 2.21 & 1.99 & 4.85 & 2.63 & 3.07 & 2.70 \\ \hline
Stdev in $m$ & 0.25 & 0.32 & 0.34 & 0.91 & 0.39 & 0.44 & 0.47 \\ \hline
    \end{tabularx}
\end{center}
\begin{center}
    \begin{tabularx}{1.013\textwidth}{|X|c|c|c|c|c|c|c|}\hline
    \rowcolor[gray]{.85}
    \multicolumn{8}{|>{\columncolor[gray]{.8}}c|}{\textbf{Online and Offline LEs in $m$ for Noise: $\sigma=8dBm$ (forward$+$backward)}}  \\ \hline
    \rowcolor[gray]{.92}
    \textbf{Path} & {\small HMM/off} & {\small HMM} & {\small HMM/avg} & {\small LMSE} & {\small PF/off} & {\small PF} & {\small PF/avg}\\ \hline\hline
    {\small eg-room-change} & 1.78 & 2.30 & 2.04 & 4.88 & 2.43 & 2.93 & 2.40\\ \hline
    {\small eg-room-change-r} & 1.75 & 2.38 & 2.13 & 5.07 & 2.60 & 3.07 & 2.62\\ \hline
    {\small og1-classic} & 1.11 & 1.79 & 1.58 & 3.65 & 2.26 & 2.76 & 2.36\\ \hline
    {\small og1-classic-r} & 1.07 & 1.52 & 1.25 & 3.54 & 1.95 & 2.16 & 1.73\\ \hline
    {\small og1-eg} & 1.49 & 2.31 & 2.08 & 4.98 & 3.29 & 3.72 & 3.36\\ \hline
    {\small og1-eg-r} & 1.70 & 2.56 & 2.38 & 5.03 & 2.79 & 3.37 & 3.09\\ \hline
    {\small og1-eg-right} & 1.44 & 2.17 & 1.97 & 5.34 & 3.08 & 3.54 & 3.25\\ \hline
    {\small og1-eg-right-r} & 1.59 & 2.36 & 2.11 & 5.43 & 2.98 & 3.39 & 3.05\\ \hline
    {\small og1-long-rooms} & 1.86 & 2.50 & 2.31 & 6.19 & 3.12 & 3.68 & 3.25\\ \hline
    {\small og1-long-rooms-r} & 1.80 & 2.56 & 2.36 & 5.91 & 3.01 & 3.66 & 3.32\\ \hline
    {\small og1-long-straight} & 1.29 & 2.06 & 1.89 & 4.29 & 2.13 & 2.60 & 2.30\\ \hline
    {\small og1-long-straight-r} & 1.47 & 2.08 & 1.85 & 4.10 & 2.16 & 2.62 & 2.26\\ \hline
    {\small og1-room-change} & 1.60 & 2.06 & 1.82 & 3.63 & 2.51 & 2.73 & 2.35\\ \hline
    {\small og1-room-change-r} & 1.67 & 2.04 & 1.86 & 3.58 & 2.39 & 2.75 & 2.33\\ \hline
    {\small stairs-upward} & 1.17 & 1.80 & 1.58 & 5.92 & 2.62 & 2.96 & 2.56\\ \hline
    {\small stairs-upward-r} & 1.22 & 2.81 & 2.63 & 6.03 & 2.76 & 3.21 & 2.95\\ \hline
\hline Mean in $m$ & 1.50 & 2.21 & 1.99 & 4.85 & 2.63 & 3.07 & 2.70 \\ \hline
Stdev in $m$ & 0.25 & 0.32 & 0.34 & 0.91 & 0.39 & 0.44 & 0.47 \\ \hline
    \end{tabularx}
\end{center}
\begin{center}
    \begin{tabularx}{1.013\textwidth}{|X|c|c|c|c|c|c|c|}\hline
    \rowcolor[gray]{.85}
    \multicolumn{8}{|>{\columncolor[gray]{.8}}c|}{\textbf{Online and Offline LEs in $m$ for Noise: $\sigma=12dBm$ (forward$+$backward)}}  \\ \hline
    \rowcolor[gray]{.92}
    \textbf{Path} & {\small HMM/off} & {\small HMM} & {\small HMM/avg} & {\small LMSE} & {\small PF/off} & {\small PF} & {\small PF/avg}\\ \hline\hline
    {\small eg-room-change} & 1.78 & 2.30 & 2.04 & 4.88 & 2.43 & 2.93 & 2.40\\ \hline
    {\small eg-room-change-r} & 1.75 & 2.38 & 2.13 & 5.07 & 2.60 & 3.07 & 2.62\\ \hline
    {\small og1-classic} & 1.11 & 1.79 & 1.58 & 3.65 & 2.26 & 2.76 & 2.36\\ \hline
    {\small og1-classic-r} & 1.07 & 1.52 & 1.25 & 3.54 & 1.95 & 2.16 & 1.73\\ \hline
    {\small og1-eg} & 1.49 & 2.31 & 2.08 & 4.98 & 3.29 & 3.72 & 3.36\\ \hline
    {\small og1-eg-r} & 1.70 & 2.56 & 2.38 & 5.03 & 2.79 & 3.37 & 3.09\\ \hline
    {\small og1-eg-right} & 1.44 & 2.17 & 1.97 & 5.34 & 3.08 & 3.54 & 3.25\\ \hline
    {\small og1-eg-right-r} & 1.59 & 2.36 & 2.11 & 5.43 & 2.98 & 3.39 & 3.05\\ \hline
    {\small og1-long-rooms} & 1.86 & 2.50 & 2.31 & 6.19 & 3.12 & 3.68 & 3.25\\ \hline
    {\small og1-long-rooms-r} & 1.80 & 2.56 & 2.36 & 5.91 & 3.01 & 3.66 & 3.32\\ \hline
    {\small og1-long-straight} & 1.29 & 2.06 & 1.89 & 4.29 & 2.13 & 2.60 & 2.30\\ \hline
    {\small og1-long-straight-r} & 1.47 & 2.08 & 1.85 & 4.10 & 2.16 & 2.62 & 2.26\\ \hline
    {\small og1-room-change} & 1.60 & 2.06 & 1.82 & 3.63 & 2.51 & 2.73 & 2.35\\ \hline
    {\small og1-room-change-r} & 1.67 & 2.04 & 1.86 & 3.58 & 2.39 & 2.75 & 2.33\\ \hline
    {\small stairs-upward} & 1.17 & 1.80 & 1.58 & 5.92 & 2.62 & 2.96 & 2.56\\ \hline
    {\small stairs-upward-r} & 1.22 & 2.81 & 2.63 & 6.03 & 2.76 & 3.21 & 2.95\\ \hline
\hline Mean in $m$ & 1.50 & 2.21 & 1.99 & 4.85 & 2.63 & 3.07 & 2.70 \\ \hline
Stdev in $m$ & 0.25 & 0.32 & 0.34 & 0.91 & 0.39 & 0.44 & 0.47 \\ \hline
    \end{tabularx}
\end{center}
\begin{center}
    \begin{tabularx}{1.013\textwidth}{|X|c|c|c|c|c|c|c|}\hline
    \rowcolor[gray]{.85}
    \multicolumn{8}{|>{\columncolor[gray]{.8}}c|}{\textbf{Online and Offline LEs in $m$ for Noise: $\sigma=16dBm$ (forward$+$backward)}}  \\ \hline
    \rowcolor[gray]{.92}
    \textbf{Path} & {\small HMM/off} & {\small HMM} & {\small HMM/avg} & {\small LMSE} & {\small PF/off} & {\small PF} & {\small PF/avg}\\ \hline\hline
    {\small eg-room-change} & 1.78 & 2.30 & 2.04 & 4.88 & 2.43 & 2.93 & 2.40\\ \hline
    {\small eg-room-change-r} & 1.75 & 2.38 & 2.13 & 5.07 & 2.60 & 3.07 & 2.62\\ \hline
    {\small og1-classic} & 1.11 & 1.79 & 1.58 & 3.65 & 2.26 & 2.76 & 2.36\\ \hline
    {\small og1-classic-r} & 1.07 & 1.52 & 1.25 & 3.54 & 1.95 & 2.16 & 1.73\\ \hline
    {\small og1-eg} & 1.49 & 2.31 & 2.08 & 4.98 & 3.29 & 3.72 & 3.36\\ \hline
    {\small og1-eg-r} & 1.70 & 2.56 & 2.38 & 5.03 & 2.79 & 3.37 & 3.09\\ \hline
    {\small og1-eg-right} & 1.44 & 2.17 & 1.97 & 5.34 & 3.08 & 3.54 & 3.25\\ \hline
    {\small og1-eg-right-r} & 1.59 & 2.36 & 2.11 & 5.43 & 2.98 & 3.39 & 3.05\\ \hline
    {\small og1-long-rooms} & 1.86 & 2.50 & 2.31 & 6.19 & 3.12 & 3.68 & 3.25\\ \hline
    {\small og1-long-rooms-r} & 1.80 & 2.56 & 2.36 & 5.91 & 3.01 & 3.66 & 3.32\\ \hline
    {\small og1-long-straight} & 1.29 & 2.06 & 1.89 & 4.29 & 2.13 & 2.60 & 2.30\\ \hline
    {\small og1-long-straight-r} & 1.47 & 2.08 & 1.85 & 4.10 & 2.16 & 2.62 & 2.26\\ \hline
    {\small og1-room-change} & 1.60 & 2.06 & 1.82 & 3.63 & 2.51 & 2.73 & 2.35\\ \hline
    {\small og1-room-change-r} & 1.67 & 2.04 & 1.86 & 3.58 & 2.39 & 2.75 & 2.33\\ \hline
    {\small stairs-upward} & 1.17 & 1.80 & 1.58 & 5.92 & 2.62 & 2.96 & 2.56\\ \hline
    {\small stairs-upward-r} & 1.22 & 2.81 & 2.63 & 6.03 & 2.76 & 3.21 & 2.95\\ \hline
\hline Mean in $m$ & 1.50 & 2.21 & 1.99 & 4.85 & 2.63 & 3.07 & 2.70 \\ \hline
Stdev in $m$ & 0.25 & 0.32 & 0.34 & 0.91 & 0.39 & 0.44 & 0.47 \\ \hline
    \end{tabularx}
\end{center}

\newpage

\section{2D Localization Result}

\begin{figure}[ht]
  \begin{center}
    \includegraphics[scale=0.44]{figures/offline-online-error.png}
  \end{center}
  \caption{Visualization of the HMM driven localization results for the path \emph{og1-classic-r}. The first result is only available at the end of the path, whereas an online user would be more interested in last two results.}
  \label{appendix:2d_offline_classic}
\end{figure}

\section{Optimization Process}
\begin{figure}
  \begin{center}
    \includegraphics[scale=0.685, angle=270]{figures/optimize_process.png}
  \end{center}
  \caption{Convergence of material parameters during an optimization run with genetic algorithms. The optimization target can be seen in the upper left corner, it is the average delta between the simulation results and the real world measurements.}
  \label{appendix:optimize}
\end{figure}
