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added wi-fi part, path lengths, discussion to walk1

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toni
2018-07-03 14:45:28 +02:00
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6
tex/chapters/conclusion.tex
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@@ -1,3 +1,9 @@
\section{Conclusion}
KDE besser machen, nicht nur maximumg
simple impoverishment nur dann einschalten wenn wirklich gebraucht
wifi optimierung noch besser machen und wände mitnehmen also raytracing
Conclusion Conclusion

96
tex/chapters/experiments.tex
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@@ -22,9 +22,8 @@ However, similar to our previous, award-winning system, the setup is able to run
The experiments are separated into four sections:
At first, we discuss the performance of the novel transition model and compare it to a grid-based approach.
In section \ref{sec:exp:opti} we have a look at \docWIFI{} optimization and how the real \docAPshort{} positions differ from it.
Following, we conducted several test walks throughout the building to examine the estimation accuracy (in \SI{}{\meter}) of the localisation system and try to resolve sample impoverishment with the here presented methods.
Finally, the different estimation methods are compared in section \ref{sec:exp:est}.
Following, we conducted several test walks throughout the building to examine the estimation accuracy (in \SI{}{\meter}) of the localisation system and discuss the here presented solutions for sample impoverishment.
Finally, the respective estimation methods are discussed in section \ref{sec:eval:est}.
\subsection{Transition}
To make a statement about the performance of our novel transition model presented within section \ref {}, we chose a simple scenario, in which a tester walks up and down a staircase three times.
@@ -67,8 +66,10 @@ 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}.
\todo{wie lang sind die walks meter und zeit?}
They 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.
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.
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.
Thus we are able to discuss everything in detail.
@@ -145,8 +146,15 @@ 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.
As described in chapter \ref{}, 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{}, considering walk 3.
\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.
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.
@@ -156,48 +164,47 @@ 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.
%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.
The only exception is walk 1.
It was set up to provide a challenging scenario, leading to as many multimodalities as possible.
We intentionally searched for situations in which there was a great chance that the particle set would separate, e.g. by providing multiple possible whereabouts through crossings or by blocking and thus separating a straight path with objects like movable walls.
Similar to the other walks, we added different pausing intervals of \SI{10}{\second} to \SI{60}{\second}.
This helps to analyse how the particles behave in such situations, especially in this multimodal setting.
\todo{fuer eins brauchen wir aber noch estimated path}
\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
}
%To analyse the drawbacks and benefits of the here presented method to resolve sample impoverishment,
%The benefits of the here presented solution to resolve sample impoverishment can be seen in the example shown in fig. \ref{}.
%probleme mit impoverishment aufzeigen, wo bringt es was, was macht es kaputt etc pp
Besides uncertain measurements, one of the main sources for multimodalities are restrictive transition models, e.g. no walking through walls.
As shown in section \ref{sec:impo}, the $D_\text{KL}$ method compares the current posterior $p(\mStateVec_{t} \mid \mObsVec_{1:t})$ with the probability grid $\probGrid_{t, \text{wifi}}$ using the Kullback-Leibler divergence and a Wi-Fi quality factor.
Environmental restriction like walls are not considered while creating $\probGrid_{t, \text{wifi}}$, that is why the grid is not effected by a transition-based multimodal setting.
Given accurate Wi-Fi measurements, it is therefore very likely that $\probGrid_{t, \text{wifi}}$ represents a unimodal distribution, even if the particles got separated by an obstacle or wall.
This leads to a situation, in which posterior and grid differ.
As a result, the radius $r_\text{sub}$ increases and thus the diversity of particles.
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}.
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.
%%estimation
\subsection{Estimation Methods}
\label{sec:exp:est}
\subsection{Estimation}
\label{sec:eval:est}
As discussed before, the single estimation methods only vary by a few centimetres in the overall localization error.
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}
\centering
\input{gfx/walk.tex}
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of the walk. 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 BoxKDE approach (orange) does not. }
\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}
\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}.
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}.
@@ -223,15 +230,24 @@ Only with new measurements coming from the hallway or other parts of the buildin
\label{fig:realWorldTime}
\end{figure}
This lead to the conclusion, that a weighted average approach provides a more smooth representation of the estimated locations and thus a higher robustness.
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}
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.
%wie in bulli paper.
\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
}
%letzer absatz nochmal gesamtergebniss des gesamten systems
%was läuft noch schief? wo macht was probleme?

2
tex/chapters/introduction.tex
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@@ -45,3 +45,5 @@ 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?}