FHWS/Fusion2016
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recent presentation

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minor fixes
added summary
changed theme
changed some gfx
This commit is contained in:
FrankE
2016-07-03 20:18:23 +02:00
parent 473bff7c70
commit cdfb1decc6
15 changed files with 983 additions and 371 deletions
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116
presentation/main.tex
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@@ -7,7 +7,8 @@
%\usetheme{m}
\usetheme[everytitleformat=regular]{m}
%\usetheme[everytitleformat=regular]{m}
\usetheme[subsectionpage=progressbar]{metropolis}
% Costumizing the m-theme here
\setbeamertemplate{footline}[text line]{%
@@ -33,8 +34,8 @@
% End Costumizing
\usepackage{tikz}
\usetikzlibrary{backgrounds}
\usepackage[utf8]{inputenc}
\usepackage{mathptmx}
@@ -109,15 +110,33 @@
\begin{document}
\maketitle
%\frame{\tableofcontents[currentsection]}
\frame{\tableofcontents}
%\frametitle{Agenda}
%\frame{\tableofcontents}
\begin{frame}
\frametitle{Agenda}
\tableofcontents
\end{frame}
\section{Overview}
% set background
\setbeamertemplate{background}{
%\begin{tikzpicture}%
% %\coordinate (Origin) at (0,0);
% %\draw[fill=blue!10] (0,1) circle (1cm);%
% %\draw[fill=red!10] (3,1) circle (1cm);%
% \begin{scope} \fill[white!80!black] (0.0, 0.0) rectangle (6.5, 8.4); \end{scope}
% \begin{scope} \fill[white!60!black] (6.5, 3.8) rectangle (13.0, 0.0); \end{scope}
% \begin{scope} \fill[white!80!black] (6.5, 8.4) rectangle (13.0, 3.8); \end{scope}
% %\fill[red] (6.5, 4.0) rectangle (13.0, 8.4);
%\end{tikzpicture}%
\includegraphics[width=12.8cm]{gfx/sysbg.eps}
}
\begin{frame}
\begin{tabular}{lcr}
% icons: https://thenounproject.com/search/?q=graph
@@ -144,6 +163,9 @@
\end{frame}
% reset
\setbeamertemplate{background}{}
\section{System}
\subsection{Recursive Density Estimation}
@@ -156,18 +178,18 @@
\overbrace{\qTurn \in \R}^{\text{heading}},\enskip{}
\overbrace{\qBaro \in \R}^{\text{rel. pressure}}
$ \\
$\vec{q_0} = $ uniformly distributed
$\vec{q}_0 = $ uniformly distributed, $\qBaro = 0$
\ispace
\item<2-> Observation\\
$\vec{o} = (\vec{\oWifi}, \vec{\oBeacons}, \oStep, \oTurn, \oBaro)$
\ispace
\item<3-> \small$
\underbrace{ p(\vec{q_t}\mid \vec{o}_{1:t})}_{\text{estimation}}
\underbrace{ p(\vec{q}_t\mid \vec{o}_{1:t})}_{\text{estimation}}
\propto %
\underbrace{ p(\vec{o_t} \mid \vec{q_t}) }_{\text{evaluation}}%
\underbrace{ p(\vec{o}_t \mid \vec{q}_t) }_{\text{evaluation}}%
\int
\underbrace{ p(\vec{q_t} \mid \vec{q_{t-1}}, \vec{o_{t-1}}) }_{\text{transition}}%
\underbrace{ p(\vec{q_{t-1}} \mid \vec{o}_{1:t-1})}_{\text{recursion}}%
\underbrace{ p(\vec{q}_t \mid \vec{q}_{t-1}, \vec{o}_{t-1}) }_{\text{transition}}%
\underbrace{ p(\vec{q}_{t-1} \mid \vec{o}_{1:t-1})}_{\text{recursion}}%
d\vec{q}_{t-1}%
$
\end{itemize}
@@ -230,12 +252,20 @@
\frametitle{Observation - Wi-Fi/iBeacons}
\begin{itemize}
\item<1->
$p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}=$
$p(\vec{\oWifi} \mid \vec{q}_t) = \prod_{\oWifi} \NDist(s_i \mid P_r(d_i, \Delta f_i), \sigma_{\text{wifi}}^2)$,\\
\ispace
\item<2-> 3D signal strength prediction\\\ispace
%\only<1>{
\item<1->
$p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}=$
$p(\vec{\oWifi} \mid \vec{q}_t) = \prod_{\oWifi} \NDist(s_i \mid \overbrace{P_r(d_i, \Delta f_i)}^\text{model prediction}, \sigma_{\text{wifi}}^2)$,\\
\ispace
\only<1>{%
\small{\textit{probability to measure all currently received signal-strengths $\vec{\oWifi}$ at a location $\vec{q}_t$, by comparing them with corresponding estimations from a prediction model}}%
%\vspace{2.9cm}%
}
%}
\item<2->
3D signal strength prediction\\\ispace
$
P_r(d,\Delta f) =
\underbrace{P_0}_{\text{reference}}\enskip
@@ -249,10 +279,15 @@
% \underbrace{\lambda \approx -8}_{\text{attenuation per floor}}
%$
%\ispace
\only<3>{ \includegraphics[width = 0.4\textwidth]{gfx/wifi1.png} }%
\only<4->{ \includegraphics[width = 0.4\textwidth]{gfx/wifi2.png} }%
\only<5>{ \includegraphics[width = 0.4\textwidth]{gfx/wifi3.png} }%
\only<6->{ \includegraphics[width = 0.4\textwidth]{gfx/wifi4.png} }%
\newline
\raisebox{5.0cm}{
%\only<2>{ \vspace{4.0cm} }
\only<3>{ \includegraphics[width = 0.35\textwidth]{gfx/wifi1.png} }%
\only<4->{ \includegraphics[width = 0.35\textwidth]{gfx/wifi2.png} }%
\only<5>{ \includegraphics[width = 0.35\textwidth]{gfx/wifi3.png} }%
\only<6->{ \includegraphics[width = 0.35\textwidth]{gfx/wifi4.png} }%
}
%\vspace{6mm}
\end{itemize}
\end{frame}
@@ -261,14 +296,18 @@
\begin{frame}
\frametitle{Observation - Barometer}
\begin{itemize}
\item<1-> $p(\vec{o}_t \mid \vec{q}_t)_{\text{baro}} = $
$\NDist(o_t^{\oBaro} \mid q_t^{\qBaro}, \sigma_{\text{baro}}^2)$
\ispace
\item<2-> each transition performs a relative pressure prediction:\\
\ispace
$q_t^{\qBaro} = q_{t-1}^{\qBaro} + \Delta z \cdot b$, \enskip
$\underbrace{\Delta z = q_{t-1}^z - q_{t}^z}_{\text{height change}}$, \enskip
$\underbrace{b \in \R}_{\text{pressure change / meter}}$\\
\item<1->
$p(\vec{o}_t \mid \vec{q}_t)_{\text{baro}} = $
$\NDist(o_t^{\oBaro} \mid q_t^{\qBaro}, \sigma_{\text{baro}}^2)$\\
\ispace
\small{\textit{probability to measure the pressure $o_t^{\oBaro}$ (relative to the start) at a location $\vec{q}_t$}, by comparing it with the corresponding prediction}
\item<2->
each transition performs a relative pressure prediction:\\
\ispace
$q_t^{\qBaro} = q_{t-1}^{\qBaro} + \Delta z \cdot b$, \enskip
$\underbrace{\Delta z = q_{t-1}^z - q_{t}^z}_{\text{height change}}$, \enskip
$\underbrace{b \in \R}_{\text{pressure change / meter}}$\\
%
\vspace{5mm}
\begin{figure}
@@ -339,7 +378,7 @@
\begin{frame}
\frametitle{Transition - Random Walk}
\begin{minipage}{0.49\textwidth}
$p(\vec{q}_t \mid \vec{q}_{t-1})$:
$p(\vec{q}_t \mid \vec{q}_{t-1}, \vec{o}_{t-1})$:
\begin{enumerate}
\item get node $\vec{q}_{t-1}$ belongs to
\item draw distance $\leDistance$ to walk%\\ \textit{depends on the number of detected steps}
@@ -501,4 +540,17 @@
\end{frame}
\section{Summary}
\begin{frame}
\frametitle{Summary}
\begin{itemize}
\item Wi-Fi, iBeacons and a barometer infer the probability for a pedestrian to reside at a location
\item step- and turn detection serve as prediction for the pedestrian's movement
\item incorporating the building's floorplan by using a graph allows only valid movements
\item weighting the graph's nodes allows a realistic shortest-path calculation
\item adding prior knowledge like the pedestrian's destination further enhances the movement prediction
\end{itemize}
\end{frame}
\end{document}