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fixed Wi-Fi

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toni
2018-09-18 12:36:41 +02:00
parent 1f44af390d
commit 4134f949b3
5 changed files with 66 additions and 54 deletions
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9
tex/bare_conf.tex
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@@ -70,6 +70,15 @@ $^{2}$ \quad University of Siegen - Pattern Recognition Group; marcin.grzegorzek
\input{misc/keywords}
\input{misc/functions}
% footnote hack for thanks
\newcommand{\blfootnote}[1]{%
\begingroup
\renewcommand\thefootnote{}\footnote{#1}%
\addtocounter{footnote}{-1}%
\endgroup
}
\graphicspath{{gfx/}{gfx/groundTruth/}{gfx/wifiOptGlobalFloor/}{gfx/errorOverTimeWalk3/}{gfx/estimationPath2/}{gfx/optimization/}{gfx/optimization/side/}{gfx/transEval/}}
\input{chapters/abstract}

96
tex/chapters/eval.tex
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@@ -37,77 +37,81 @@ The comparison between a single RSSI measurement $\mRssi_i$ and the reference is
\begin{equation}
p(\mRssi_i \mid \mPosVec) =
\mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma_{i,\mPosVec}^2)
\mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma_{\text{wifi}}^2)
\enskip ,
\label{eq:wifiProb}
\end{equation}
\commentByFrank{ich wuerde einfach $\sigma_\text{wifi}$ nehmen. es haengt nicht von der pos $\mPosVec$ ab, und wir hatten immer fuer jeden AP das gleiche}
\noindent where $\mu_{i,\mPosVec}$ denotes the (predicted) average signal strength and $\sigma_{i,\mPosVec}^2$ a corresponding standard deviation for the \docAPshort{} identified by $i$, regarding the location $\mPosVec$.
Within this work $\mu_{\mPosVec}$ is calculated by a modified version of the wall-attenuation-factor model as presented in \cite{Ebner-17}. Here, the prediction depends on the 3D distance $d$ from the \docAPshort{} and the number of floors $\Delta f$ between the \docAPshort{} and $\mPosVec$ of the state-in-question:
%\commentByFrank{ich wuerde einfach $\sigma_\text{wifi}$ nehmen. es haengt nicht von der pos $\mPosVec$ ab, und wir hatten immer fuer jeden AP das gleiche}
\noindent where $\mu_{i,\mPosVec}$ denotes the (predicted) signal strength for the \docAPshort{} identified by $i$, regarding the location $\mPosVec$.
A certain noise is allowed by the corresponding standard deviation $\sigma_{\text{wifi}}$.
Within this work $\mu_{\mPosVec}$ is calculated by a modified version of the wall-attenuation-factor model as presented in \cite{Ebner-17}.
Here, the prediction depends on the 3D distance $d$ between the \docAPshort{} in question and the location $\mPosVec$ as well as the number of floors $\Delta f$ between them:
\begin{equation}
\mu_{\mPosVec} = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF
\label{eq:wallAtt}
\end{equation}
\commentByFrank{
hier sollte das $i$, das du vorher hattest, wohl wieder mit rein?
was genau $d$ bzw $d_i$ oder $d_{i,\mPosVec}$ ist, muessten wir vermutlich auch kurz erklären.
Ich hatte auch immer unterschieden zwischen der fraglichen position (z.B. $\vec{\rho}$)
und der position des access points (z.B. $\mPosVec_i$). also, zwei verschiedene zeichen, dass das klar wird.
ich weis aber nicht, ob $\vec{\rho}$ noch frei ist, bzw was auf den folgenden seiten nocht kommt.
eigentlich gehoert das $i$ dann auch noch ans $P_0$ und $\gamma$ und $d_0$.. aber der einfachheit halber, reicht das ja im text.
vorschlag wäre etwas wie:
}
\begin{equation}
\mu(i,\vec{\rho}) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF
,\enskip
d = \| \vec{\rho} - \mPosVec_i \|
\label{eq:wallAtt}
\end{equation}
%\commentByFrank{
% hier sollte das $i$, das du vorher hattest, wohl wieder mit rein?
% was genau $d$ bzw $d_i$ oder $d_{i,\mPosVec}$ ist, muessten wir vermutlich auch kurz erklären.
% Ich hatte auch immer unterschieden zwischen der fraglichen position (z.B. $\vec{\rho}$)
% und der position des access points (z.B. $\mPosVec_i$). also, zwei verschiedene zeichen, dass das klar wird.
% ich weis aber nicht, ob $\vec{\rho}$ noch frei ist, bzw was auf den folgenden seiten nocht kommt.
% eigentlich gehoert das $i$ dann auch noch ans $P_0$ und $\gamma$ und $d_0$.. aber der einfachheit halber, reicht das ja im text.
% vorschlag wäre etwas wie:
%}
%\begin{equation}
% \mu(i,\vec{\rho}) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF
% ,\enskip
% d = \| \vec{\rho} - \mPosVec_i \|
% \label{eq:wallAtt}
%\end{equation}
\noindent Here, $\mTXP$ is the \docAPshort{}'s signal strength measurable at a known distance $\mMdlDist_0$ (usually \SI{1}{\meter}) and $\mPLE$ denotes the signals depletion over distance, which depends on the \docAPshort{}'s surroundings like walls and other obstacles.
The attenuation per floor is given by $\mWAF$.
For example, a viable choice for steel enforced concrete floors is $\mWAF \approx \SI{-8.0}{dB}$ \cite{Ebner-15}.
Of course, eq. \eqref{eq:wallAtt} needs to be calculated separately for every $i$ and thus available \docAPshort{}.
It should be noted, that we omitted the index $i$ in eq. \eqref{eq:wallAtt} for the sake of clarity and consistency with other literature.
Of course, the environmental parameters $\mTXP$, $\mPLE$ and $\mWAF$ need to be known beforehand and often vary greatly between single \docAPshort{}'s.
The environmental parameters $\mTXP$, $\mPLE$ and $\mWAF$ need to be known beforehand and often vary greatly between single \docAPshort{}'s.
Nevertheless, for simplicity's sake it is common practice to use some fixed empirically chosen values, the same for every \docAPshort{}.
This might already provide enough accuracy for some use-cases and buildings, but fails in complex scenarios, as discussed in section \ref{sec:intro}.
Therefore, instead of using a pure empiric model, we deploy an optimization scheme to find a well-suited set of parameters ($\mPosAPVec{}, \mTXP{}, \mPLE{}, \mWAF{}$) per \docAPshort{}, where $\mPosAPVec{} = (x,y,z)^T$ denotes the \docAPshort{}'s estimated position.
The optimization is based on a few reference measurements $s_{\mPosVec}$ throughout the building, e.g. every \SI{3}{} to \SI{5}{\meter} centred within a corridor and between \SI{1}{} and \SI{4}{} references per room, depending on the room's size.
The optimization is based on a few reference measurements $\vec{s_{\text{opt}}}$ throughout the building, e.g. every \SI{3}{} to \SI{5}{\meter} centred within a corridor and between \SI{1}{} and \SI{4}{} references per room, depending on the room's size.
Compared to classical fingerprinting, where reference measurements are recorded on small grids between \SI{1}{} to \SI{2}{\meter}, this highly reduces their required number and thus the overall setup-time.
The target function to optimize the $6$ model parameters for one \docAPshort{} is given by
\begin{equation}
\epsilon^* =
\min_{\mPosAPVec, \mTXP, \mPLE, \mWAF}
\sum_{s_{\mPosVec} \in \vec{s}}
(s_{\mPosVec} - \mu_{\mPosVec})^2
(\mPosAPVec, \mTXP, \mPLE, \mWAF) =
\argmin_{\mPosAPVec, \mTXP, \mPLE, \mWAF}
\sum_{s_{i} \in \vec{s_{\text{mac}}}}
(s_{i} - \mu_{\mPosVec})^2
\enskip,\enskip\enskip
\mu_{\mPosVec} =
\mTXP{} + 10 \mPLE{} \log_{10} \| \mPosVec-\mPosAPVec \| + \Delta f \mWAF{}
\enspace .
\label{eq:optTarget}
\end{equation}
\commentByFrank{hier muesste dann auch das $i$ rein, bzw die funktion $\mu()$. vorschlag waere dann:}
\begin{equation}
(\mPosAPVec, \mTXP, \mPLE, \mWAF)_i =
\argmin_{\mPosVec, \mTXP, \mPLE, \mWAF}
\sum_{s_{i,\vec{\rho}} \in \vec{s}_i}
\big(s_{i,\vec{\rho}} - \mu(i,\mPosVec) \big)^2
\enspace .
\label{eq:optTarget}
\end{equation}
%\commentByFrank{hier muesste dann auch das $i$ rein, bzw die funktion $\mu()$. vorschlag waere dann:}
%\begin{equation}
% (\mPosAPVec, \mTXP, \mPLE, \mWAF)_i =
% \argmin_{\mPosVec, \mTXP, \mPLE, \mWAF}
% \sum_{s_{i,\vec{\rho}} \in \vec{s}_i}
% \big(s_{i,\vec{\rho}} - \mu(i,\mPosVec) \big)^2
%\enspace .
% \label{eq:optTarget}
%\end{equation}
%\commentByFrank{argmin liefert die argumente, nicht den fehler. da muesste nur min stehen}
\commentByFrank{
hier braucht es drigend eine unterscheidung zwischen den beiden positionen. der vom fingerprint und der vom ap
$\mPosAPVec$ ist, wegen dem $\hat{ }$ einfach nur die \emph{beste}. aber sie ist halt generell anders als der fingerprint.
deshalb brauchen wir da zwei formel zeichen.
und wir muessen einheitlich machen, ob wir das $i$ jetzt mitnehmen, oder nicht. sonst wirkt es verwirrend
}
\noindent Here, one reduces the squared error between reference measurements $s_{\mPosVec} \in \vec{s}$ with well-known location $\mPosVec$ and corresponding model predictions $\mu_{\mPosVec}$ (cf. eq. \eqref{eq:wallAtt}).
%\commentByFrank{
% hier braucht es drigend eine unterscheidung zwischen den beiden positionen. der vom fingerprint und der vom ap
% $\mPosAPVec$ ist, wegen dem $\hat{ }$ einfach nur die \emph{beste}. aber sie ist halt generell anders als der fingerprint.
% deshalb brauchen wir da zwei formel zeichen.
% und wir muessen einheitlich machen, ob wir das $i$ jetzt mitnehmen, oder nicht. sonst wirkt es verwirrend
%}
\noindent Here, one reduces the squared error between reference measurements $s_{i} \in \vec{s_{\text{mac}}}$ with well-known location $\mPosVec$ and corresponding model predictions $\mu_{\mPosVec}$ (cf. eq. \eqref{eq:wallAtt}).
Whereas $\vec{s_{\text{mac}}}$ is the subset of $\vec{s_{\text{opt}}}$ for the \docAPshort{} in question, identified by its MAC-adress.
The number of floors between $\mPosVec$ and $\mPosAPVec$ is again given by $\Delta f$.
As discussed by \cite{Ebner-17}, optimizing all 6 parameters, especially the unknown \docAPshort{} position $\mPosAPVec$, usually results in optimizing a non-convex, discontinuous function.
A promising way to deal with non-convex functions is using a genetic algorithm, which is inspired by the process of natural selection \cite{goldberg89}.
@@ -119,8 +123,8 @@ During each iteration, the best \SI{25}{\percent} of the population are kept.
The remaining entries are then re-created by modifying the best entries with uniform random values within $\pm$\SI{10}{\percent} of the known limits.
Inspired by {\em cooling} known from simulated annealing \cite{Kirkpatrick83optimizationby}, the result is stabilized by narrowing the allowed modification limits over time and thus decrease in the probability of accepting worse solutions.
\commentByToni{Wollen wir das mal genauer beschreiben? Also wie genau funktioniert das cooling. Das ist ja alles sehr wischi waschi gehalten}
\commentByFrank{ich wuerde es so lassen. da gibts genug in der literatur ueber ideen und potentielle ansaetze}
%\commentByToni{Wollen wir das mal genauer beschreiben? Also wie genau funktioniert das cooling. Das ist ja alles sehr wischi waschi gehalten}
%\commentByFrank{ich wuerde es so lassen. da gibts genug in der literatur ueber ideen und potentielle ansaetze}
To further improve the results, we optimize a model for each floor of the building instead of a single global one, using only the reference measurements that belong to the corresponding floor.
The reason for this comes from the assumptions made in eq. \eqref{eq:wallAtt}.
@@ -130,8 +134,8 @@ For example, if a pedestrian walks on a staircase and thus is in-between multipl
%man muss zwar messungen machen, dafür muss man aber die position der ap's nicht mehr kennen. daher kostet das jetzt nicht viel mehr zeit.
Basically, any kind of \docAPshort{} providing RSSI measurements can be used for the above.
\commentByMarkus{Provieded der AP die RSSI? Misst nicht das Smartphone an seiner Antenne?}
Basically, any kind of wireless network which allows to measure RSSI can be used for the above.
%\commentByMarkus{Provieded der AP die RSSI? Misst nicht das Smartphone an seiner Antenne?}
However, most buildings do not provide a satisfying and well covered \docWIFI{} infrastructure, e.g. staircases or hallways are often neglected for office spaces.
This applies in particular to historical buildings, as discussed in section \ref{sec:intro}.
To improve $\docWIFI$ coverage we are able to distribute a small number of simple and cheap \docWIFI{} beacons.

7
tex/chapters/introduction.tex
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@@ -28,8 +28,8 @@ Thus, the performance will be even more limited due to the irregularly shaped sp
Our approach tries to avoid those problems.
We distribute a small number of simple and cheap \docWIFI{} beacons over the whole building and instead of measuring their position, we use an optimization scheme based on a few reference measurements.
An optimization scheme also avoids inaccuracies like wrongly positioned access points or fingerprints caused by outdated or inaccurate building plans.
\commentByFrank{warum fingerprints? das verwirrt mich an der stelle. willst du sagen, dass opt. besser ist, als ueberhaupt fingerprints zu nehmen? dann kommt es nicht so rueber. unsicher, deshalb kein direkter fix sondern comment}
An optimization scheme also avoids inaccuracies like wrongly measured access point positions or outdated fingerprints caused by changes of the environment or inaccurate building plans.
%\commentByFrank{warum fingerprints? das verwirrt mich an der stelle. willst du sagen, dass opt. besser ist, als ueberhaupt fingerprints zu nehmen? dann kommt es nicht so rueber. unsicher, deshalb kein direkter fix sondern comment}
It is obvious, that this could be solved by re-measuring the building, however this is a very time-consuming process requiring specialized hardware and a surveying engineer.
Clearly, this is contrary to most costumers expectations of a fast to deploy and low-cost solution.
In addition, this is not only a question of costs incurred, but also for buildings under monumental protection, not allowing for larger construction measures.
@@ -44,5 +44,4 @@ The goal of this work is to propose a fast to deploy and low-cost localization s
Consequently, we believe that by utilizing our localization approach to such a challenging scenario, it is possible to prove those characteristics.
Finally, it should be mentioned that the here presented work is an highly updated version of the winner of the smartphone-based competition at IPIN 2016 \cite{Ebner-15}.
\todo{Dankesagung Moehring oder einfach mit als Autor?}
\blfootnote{Dankesagung und so weiter.}

4
tex/chapters/relatedwork.tex
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@@ -91,8 +91,8 @@ Besides well chosen probabilistic models, the system's performance is also highl
They are often caused by restrictive assumptions about the dynamic system, like the aforementioned sample impoverishment.
The authors of \cite{Sun2013} handled the problem by using an adaptive number of particles instead of a fixed one.
The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
The problem of sample impoverishment is then encountered by adapting the number of particles dependent upon the system's current uncertainty \cite{Fetzer-17}.
\commentByFrank{ich glaube encountered ist das falsche wort. du willst doch auf 'es wird gefixed' raus, oder? addressed? mitigated?}
The problem of sample impoverishment is then addressed by adapting the number of particles dependent upon the system's current uncertainty \cite{Fetzer-17}.
%\commentByFrank{ich glaube encountered ist das falsche wort. du willst doch auf 'es wird gefixed' raus, oder? addressed? mitigated?}
In practice, sample impoverishment is often a problem of environmental restrictions and system dynamics.
Therefore, the method above fails, since it is not able to propagate new particles into the state space due to environmental restrictions e.g. walls or ceilings.

2
tex/misc/functions.tex
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@@ -12,7 +12,7 @@
\newcommand{\mMdlRSSI}{\ensuremath{\varsigma}} % model's signal-strength
\newcommand{\mPosAP}{\hat\varrho} % char for access point position vector
\newcommand{\mPos}{\varrho} % char for positions
\newcommand{\mPos}{\rho} % char for positions
\newcommand{\mPosVec}{\vec{\mPos}} % position vector
\newcommand{\mPosAPVec}{\ensuremath{\vec{\mPosAP}}} % AP position vector