FHWS/IPIN2018
Archived
4
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

erster schwung grafiken

Browse Source
This commit is contained in:
toni
2018-09-11 22:45:40 +02:00
parent a29aac498c
commit 7ed0415cc2
22 changed files with 12096 additions and 51 deletions
Download Patch File Download Diff File Expand all files Collapse all files

70
tex/chapters/experiments.tex
View File

@@ -4,7 +4,7 @@ As explained at the very beginning of this work, we wanted to explore the limits
By utilizing it to a 13th century historic building, we created a challenging scenario not only because of the various architectural factors, but also because of its function as a museum.
During all experiments, the museum was open to the public and had a varying number of \SI{10}{} to \SI{50}{} visitors while recording.
The \SI{2500}{\square\meter} building consists of \SI{6}{} different levels, which are grouped into 4 floors (see fig. \ref{fig:apfingerprint}).
The \SI{2500}{\square\meter} building consists of \SI{6}{} different levels, which are grouped into 3 floors (see fig. \ref{fig:apfingerprint}).
Thus, the ceiling height is not constant over one floor and varies between \SI{2.6}{\meter} to \SI{3.6}{\meter}.
In the middle of the building is an outdoor area, which is only accessible from one side.
While most of the exterior and ground level walls are made of massive stones, the floors above are half-timbered constructions.
@@ -78,10 +78,25 @@ looking at the optimziation errors, this can be varified... etc pp
\subsection{Localization Error}
\begin{figure}[ht]
\begin{figure}[t]
\centering
\includegraphics[width=0.9\textwidth]{gfx/floorplanDummy.png}
\caption{All conducted walks.}
\begin{subfigure}{0.32\textwidth}
\def\svgwidth{\columnwidth}
{\input{gfx/groundTruth/gt_unten_final.eps_tex}}
\caption{Ground floor}
\end{subfigure}
\begin{subfigure}{0.32\textwidth}
\def\svgwidth{\columnwidth}
{\input{gfx/groundTruth/gt_mitte_final.eps_tex}}
\caption{First floor}
\end{subfigure}
\begin{subfigure}{0.32\textwidth}
\def\svgwidth{\columnwidth}
{\input{gfx/groundTruth/gt_oben_final.eps_tex}}
\caption{Second floor}
\end{subfigure}
\caption{All conducted walks within the building. The arrows indicate the running direction and a cross marks the end. For a better overview we have divided the building into 3 floors. However, each floor consists of different high levels. They are separated from each other by different shades of grey, dark is lower then light.}
\label{fig:floorplan}
\end{figure}
%
@@ -112,7 +127,7 @@ Here, we differ between the respective anti-impoverishment techniques presented
The simple anti-impoverishment method is added to the resampling step and thus uses the transition method presented in chapter \ref{sec:transition}.
In contrast, the $D_\text{KL}$-based method extends the transition and thus uses a standard cumulative resampling step.
We set $l_\text{max} =$ \SI{-75}{dBm} and $l_\text{min} =$ \SI{-90}{dBm}.
For a better overview, we only used the KDE-based estimation, as the errors compared to the weighted average estimation differ by only a few centimetres.
For a better overview, we only used the KDE-based estimation, as the errors compared to the weighted-average estimation differ by only a few centimetres.
\newcommand{\STAB}[1]{\begin{tabular}{@{}c@{}}#1\end{tabular}}
@@ -124,10 +139,10 @@ For a better overview, we only used the KDE-based estimation, as the errors comp
\hline
& $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ \\
\hline \hline
Walk 0 & \SI{1340}{\centi\meter} & \SI{1115}{\centi\meter} & \SI{2265}{\centi\meter} & \SI{715}{\centi\meter} & \SI{660}{\centi\meter} & \SI{939}{\centi\meter} & \SI{576}{\centi\meter} & \SI{494}{\centi\meter} & \SI{734}{\centi\meter} \\ \hline
Walk 1 & \SI{320}{\centi\meter} & \SI{242}{\centi\meter} & \SI{406}{\centi\meter} & \SI{322}{\centi\meter} & \SI{258}{\centi\meter} & \SI{404}{\centi\meter} & \SI{379}{\centi\meter} & \SI{317}{\centi\meter} & \SI{463}{\centi\meter} \\ \hline
Walk 2 & \SI{834}{\centi\meter} & \SI{412}{\centi\meter} & \SI{1092}{\centi\meter} & \SI{356}{\centi\meter} & \SI{232}{\centi\meter} & \SI{486}{\centi\meter} & \SI{362}{\centi\meter} & \SI{234}{\centi\meter} & \SI{484}{\centi\meter} \\ \hline
Walk 3 & \SI{704}{\centi\meter} & \SI{589}{\centi\meter} & \SI{1350}{\centi\meter} & \SI{538}{\centi\meter} & \SI{469}{\centi\meter} & \SI{782}{\centi\meter} & \SI{476}{\centi\meter} & \SI{431}{\centi\meter} & \SI{648}{\centi\meter} \\
walk 0 & \SI{1340}{\centi\meter} & \SI{1115}{\centi\meter} & \SI{2265}{\centi\meter} & \SI{715}{\centi\meter} & \SI{660}{\centi\meter} & \SI{939}{\centi\meter} & \SI{576}{\centi\meter} & \SI{494}{\centi\meter} & \SI{734}{\centi\meter} \\ \hline
walk 1 & \SI{320}{\centi\meter} & \SI{242}{\centi\meter} & \SI{406}{\centi\meter} & \SI{322}{\centi\meter} & \SI{258}{\centi\meter} & \SI{404}{\centi\meter} & \SI{379}{\centi\meter} & \SI{317}{\centi\meter} & \SI{463}{\centi\meter} \\ \hline
walk 2 & \SI{834}{\centi\meter} & \SI{412}{\centi\meter} & \SI{1092}{\centi\meter} & \SI{356}{\centi\meter} & \SI{232}{\centi\meter} & \SI{486}{\centi\meter} & \SI{362}{\centi\meter} & \SI{234}{\centi\meter} & \SI{484}{\centi\meter} \\ \hline
walk 3 & \SI{704}{\centi\meter} & \SI{589}{\centi\meter} & \SI{1350}{\centi\meter} & \SI{538}{\centi\meter} & \SI{469}{\centi\meter} & \SI{782}{\centi\meter} & \SI{476}{\centi\meter} & \SI{431}{\centi\meter} & \SI{648}{\centi\meter} \\
\hline
\end{tabular}
\caption{Overall localization results using the different impoverishment methods. The error is given by the \SI{75}{\percent}-quantil Used only kde for estimation, since kde and avg nehmen sich nicht viel. fehler kleiner als 10 cm im durchschnitt deshalb der übersichtshalber weggelassen. }
@@ -167,7 +182,7 @@ By using the simple method, the overall error can be reduced and the impoverishm
Only the use of the $D_\text{KL}$ method is able to produce reasonable results.
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.
A good example why we do this, can be seen in fig. \ref{fig:walk3: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.
@@ -175,13 +190,25 @@ Of course, we optimize the attenuation per floor, but at the end this is just an
Therefore, the calculated signal strength predictions do not fit the measurements received from the above in a optimal way.
In contrast, the model optimized for each floor only considers the respective \docAPshort{}'s on that floor, allowing to calculate better fitting parameters.
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.
This could lead to an underrepresentation of \docAPshort{}'s for triangulation.
Such a scenario can be seen in fig. \ref{fig:walk3:time} between \SI{200}{\second} and \SI{220}{\second}, where the pedestrian enters an isolated room.
Only two \docAPshort{}'s provide a solid signal within this area, leading to a higher error, while the global scheme still receives RSSI readings from above.
\begin{figure}[t!]
\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}
\begin{subfigure}{0.48\textwidth}
\def\svgwidth{\columnwidth}
{\input{gfx/wifiOptGlobalFloor/wifiOptGlobalFloor.eps_tex}}
\caption{}
\label{fig:walk3:wifiopt}
\end{subfigure}
\begin{subfigure}{0.50\textwidth}
\resizebox{1\textwidth}{!}{\input{gfx/errorOverTimeWalk3/errorOverTime.tex}}
\caption{}
\label{fig:walk3:time}
\end{subfigure}
\caption{(a) 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 (orange), resolving the situation a producing reasonable results. (b) Error development over time for this section. The high error can be seen at \SI{190}{\second}. }
\label{fig:walk3}
\end{figure}
@@ -240,7 +267,7 @@ 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:walk1:kde}.
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}.
Thus, a weighted average estimation (blue line) results in a position of the pedestrian somewhere outside the building (light green area).
Thus, a weighted-average estimation (blue line) results in a position of the pedestrian somewhere outside the building (light green area).
The ground truth is given by the black solid line.
The KDE-based estimation (orange line) is able to provide reasonable results by choosing the "correct" mode of the density.
After \SI{20.8}{\second} the setting returns to be unimodal again.
@@ -255,14 +282,14 @@ Within our experiments this happened especially when entering or leaving thick-w
While the system’s dynamics are moving the particles outside, the faulty Wi-Fi readings are holding back a majority by assigning corresponding weights.
Only with new measurements coming from the hallway or other parts of the building, the distribution and thus the KDE-estimation are able to recover.
This leads 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.
A comparison between both methods is illustrated in fig. \ref{fig:estimationcomp} using a measuring sequence of walk 2.
We have highlighted some interesting areas with coloured squares.
The greatest difference between the respective estimation methods can be seen inside the green square, the gallery wing of the museum.
While the weighted average (blue) produces a very straight estimated path, the KDE-based method (red) is much more volatile.
While the weighted-average (blue) produces a very straight estimated path, the KDE-based method (red) is much more volatile.
This can be explained by the many small rooms that pedestrians pass through.
The doors act like a bottleneck, which is why many particles run against walls and are thus either drawn on a new position within a reachable area (cf. section \ref{sec:estimation}) or walk along the wall towards the door.
This causes a higher uncertainty and diversity of the posterior, what is more likely to be reflected by the KDE method than by the weighted average.
This causes a higher uncertainty and diversity of the posterior, what is more likely to be reflected by the KDE method than by the weighted-average.
Additionally, the pedestrian was forced seven times to look at paintings (stop walking) between \SI{10}{\second} and \SI{20}{\second}, just in this small area.
Nevertheless, even if both estimated paths look very different, they produce similar errors.
@@ -281,13 +308,14 @@ We hope to further improve such situations in future work by enabling the transi
\begin{figure}[t]
\centering
\includegraphics[width=0.9\textwidth]{gfx/estimationPath2/combined_dummy.png}
\caption{Estimation results of walk 2 using the KDE method (orange) and the weighted-average (blue).}
\def\svgwidth{0.8\columnwidth}
{\input{gfx/estimationPath2/est.eps_tex}}
\caption{Estimation results of walk 2 using the KDE method (blue) and the weighted-average (orange). While the latter provides a more smooth representation of the estimated locations, the former provides a better idea of the quality of the underlying processes. In order to keep a better overview, the top level of the last floor was hidden. The coloured squares are used as references within the text.}
\label{fig:estimationcomp}
\end{figure}
To summarize, the KDE-based approach for estimation is able to resolve multimodalities.
It does not provide a smooth estimated path, 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.
It does not provide a smooth estimated path, 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 the KDE approach opens a wide range of other possibilities for finding a best estimate.