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latest TeX: grid, experiments, conclusion. some gfx changed

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FrankE
2016-02-14 18:35:33 +01:00
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tex/chapters/experiments.tex
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@@ -13,13 +13,13 @@
During the walk, the pedestrian had to click a button on the smartphone application
when passing a marker. Between two consecutive points, a constant movement speed is assumed.
Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough to conduct
error measurements. All walks were performed using a Google Nexus 6 and a Samsung Galaxy S5.
error measurements. All walks were performed using a Motorola Nexus 6 and a Samsung Galaxy S5.
As the Samsung Galaxy S5's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only,
its scans take much longer than those of the Google Nexus 6:
its scans take much longer than those of the Motorola Nexus 6:
\SI{3500}{\milli\second} vs. \SI{600}{\milli\second}.
Also, the Nexus' barometer sensor provides readings both more frequent and far more accurate than
the Galaxy does. This results in a much better localisation using the Nexus smartphone.
the Galaxy does. This results in a better localisation using the Nexus smartphone.
Despite being fast enough to run in realtime on the smartphone itself, computation was done offline using
the CONDENSATION particle filter with \SI{7500}{} particles as realization.
@@ -28,21 +28,24 @@
As mentioned earlier, the position of all \docAP{}s (about 5 per floor) is known beforehand.
Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures.
Additionally, we used three \docIBeacon{}s for slight enhancements in some areas.
The empirically chosen values for \docWIFI{} were $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}$,
The empirically chosen values for \docWIFI{} were
$P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}, \mWAF_{\text{wifi}} = \SI{8}{\dB}$,
and $\mPLE_{\text{ib}} = \SI{1.5}{}$ for the \docIBeacon{}s, respectively.
%
Due to omitting a time-consuming calibration process for those values we expect the localisation process to perform generally worse compared to standard fingerprinting methods \cite{Ville09}.
However, incorporating prior knowledge will often compensate for those poorly chosen system parameters.
Due to omitting a time-consuming calibration process for those values we expect the localisation process to
perform generally worse compared to standard fingerprinting methods \cite{Ville09}. However, incorporating
prior knowledge will often compensate for those poorly chosen system parameters.
As uncertainties we used $\sigma_\text{wifi} = \sigma_\text{ib} = 8.0$, both growing with each measurement's age.
While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters
are determined automatically (see \ref{sec:sensBaro}). The step size for the transition was configured to be \SI{70}{\centimeter}
with an allowed derivation of \SI{10}{\percent}. The heading deviation in \refeq{eq:transSimple} was \SI{25}{\degree}.
with an allowed derivation of \SI{10}{\percent}. The heading deviation in
\refeq{eq:transSimple}, \refeq{eq:transShortestPath} and \refeq{eq:transMultiPath} was \SI{25}{\degree}.
As we start with a discrete uniform distribution for $\mStateVec_0$ (random position and heading), the first few estimations
are omitted from the error calculation to allow the system to somewhat settle its initial state. Even though, the error
during the following few seconds is expected to be much higher than the error when starting with a well known initial
position and heading.
position and heading.
The following evaluations will depict the improvements that the prior path knowledge is able to provide,
even when other system parameters are badly chosen.
@@ -65,21 +68,19 @@ position and heading.
\label{fig:paths}
\end{figure}
\commentByFrank{verlassen vom shortest path fuehrt zu weniger verbesserung, aber es wird nach wie vor besser als ohne!}
\commentByFrank{in den ersten paar sec ist die pfad-info teils hinderlich, da die genaue position noch sehr unklar ist und sich erst einstellen muss.
deshalb geht der fehler hier oft leicht hoch}
% error development over time while walking along a path
% error development over time while walking along a path
\begin{figure}
\input{gfx/eval/error_timed_nexus}
\caption{Development of the error while walking along
%path 1 (upper) and
path 4 (lower) using the Google Nexus 6.
path 4 (lower) using the Motorola Nexus 6.
Path 4 shows increasing errors for our methods when leaving the shortest path (3) and when facing multimodalities between two
staircases just before the destination (9).}
\label{fig:errorTimedNexus}
\end{figure}
% detailed analysis of path 4
\begin{figure}
\input{gfx/eval/path_nexus_detail}
\caption{Detailed path analysis depicting the individual segments of path 4. Their corresponding error contribution can
@@ -89,8 +90,7 @@ position and heading.
\end{figure}
%
\newcommand{\refSeg}[1]{$(#1)$}
Fig. \ref{fig:errorTimedNexus} shows the error for path 4 recorded with the Google Nexus 6.
\commentByToni{heisst das teil nicht motorola nexus 6?}
Fig. \ref{fig:errorTimedNexus} depicts the error for path 4 recorded with the Motorola Nexus 6.
For a better understanding of the following discussion, the path was divided into $10$ individual segments.
Remember that we start with a uniform distribution instead of a well known pedestrian location.
Therefore, the first few estimations
@@ -98,33 +98,36 @@ position and heading.
as illustrated in fig. \ref{fig:nexusPathDetails} \refSeg{1}.
%
Even when removing those initial estimations from the error calculation, the next few seconds are still erroneous
due to (intentionally) bad system parameters introduced in section \ref{sec:sensors}. Furthermore, as the pedestrian is not yet walking,
our proposed method is also not yet able to address those errors. This can be seen
at the red area in the upper left corner of fig. \ref{fig:nexusPathDetails} \refSeg{1} and within segment \refSeg{1} of fig. \ref{fig:errorTimedNexus}.
due to (intentionally) bad system parameters introduced in section \ref{sec:sensors}.
Furthermore, as the pedestrian is not yet walking, our proposed method is also not yet able to address those errors.
This can be seen at the red area in the upper left corner of fig. \ref{fig:nexusPathDetails} \refSeg{1} and within
segment \refSeg{1} of fig. \ref{fig:errorTimedNexus}.
%
However, as soon as the pedestrian starts moving down the hallway \refSeg{2} the error is reduced dramatically.
Adding prior knowledge centres the density in the middle of the floor, ensures the heading is directed towards
Adding prior knowledge centres the density in the middle of the floor, ensures that the heading is directed towards
the shortest path and thus produces even better localisation results.
%
Directly hereafter, we ignore the shortest path \refSeg{3'} determined by the system and walk along \refSeg{3}
instead. Of course, this leads to a temporally increasing error, as the system needs to detect this path change
and takes some time to recover (see fig. \ref{fig:errorDistNexus} \refSeg{3}). The new path to the desired destination
is \refSeg{3''} which is also ignored. Instead, we took a much longer route down the stairwell \refSeg{4}.
After this change is detected by the system, prior knowledge is able to reduce the error for segment \refSeg{5}.
After this change is detected by the system, prior knowledge is again able to reduce the error for segment \refSeg{5}.
%
Immediately hereafter follows a long, straight walk down the hallway. While the \docWIFI{} component pulls
the pedestrian into the rooms on the right side, the actual walking route was located on the left side
of the wall (see ground truth in fig. \ref{fig:nexusPathDetails} \refSeg{6}). While prior knowledge prevents
the density being dragged into the office-rooms, the estimated path is still located on the wrong side
of the floor (see ground truth in fig. \ref{fig:nexusPathDetails} \refSeg{6}). While prior knowledge prevents
the density from being dragged into the office-rooms, the estimated path is still located on the wrong side
of the hallway. As both sides of the floor result in a route with almost the same length,
just knowing the pedestrian's destination is not able to provide further improvements.
Thus, a constant error of approximately the floor's width remains. This is clearly visible in fig. \ref{fig:nexusPathDetails} \refSeg{6}.
Thus, a constant error of approximately the floor's width remains.
This is clearly visible in fig. \ref{fig:nexusPathDetails} \refSeg{6}.
%
Due to the excellent barometer installed within the Nexus 6, changing the floor provides only small estimation errors in segment \refSeg{7}.
Due to the excellent barometer installed within the Nexus 6, changing the floor provides only small estimation
errors in segment \refSeg{7}.
It follows a critical area with high errors and multimodalities.
Due to an in-house exhibition during the time of recording, we had to leave the ground truth by a few meters.
Furthermore, the overcrowded areas lead to attenuated \docWIFI{} signals. Both reasons cause the
density being dragged into another stairwell (see fig. \ref{fig:nexusPathDetails}, red lines in the lower right).
Furthermore, the overcrowded areas lead to attenuated \docWIFI{} signals. Both reasons move the
density into another stairwell (see fig. \ref{fig:nexusPathDetails}, red lines in the lower right).
The resulting multimodality (two staircases possible at the same time) leads to a rising error
\refSeg{8}, \refSeg{9}. At the end of the walk \refSeg{10} the system is able to recover, again.
@@ -132,7 +135,7 @@ position and heading.
% overall error-distribution for nexus and galaxy
\begin{figure}
\input{gfx/eval/error_dist_nexus}
\caption{Error distribution for all walks conducted with the Google Nexus 6. Our proposed methods
\caption{Error distribution for all walks conducted with the Motorola Nexus 6. Our proposed methods
clearly provide an enhancement for the overall localization process.}
\label{fig:errorDistNexus}
\end{figure}
@@ -141,7 +144,7 @@ position and heading.
% \caption{Nicht so markant beim galaxy, denke aber der platz reicht eh nicht, also einfach kurz erwaehnen}
%\end{figure}
The error values for all other paths and the other smartphone are listed in table
The median error values for all other paths and the other smartphone are listed in table
\ref{tbl:errGalaxy} and \ref{tbl:errNexus}. As can be seen, adding prior knowledge
is able to improve the localisation for all examined situations, even when
leaving the suggested path or when facing bad/slow sensor readings.
@@ -173,20 +176,20 @@ position and heading.
\end{tabular}
\end{table}
\begin{figure}
\includegraphics{gfx/eval/bergwerk_path1_galaxy}
\caption{Path 1 recorded with the Galaxy S5. Using prior knowledge improves the staircase (left) and the target area (right) where
both the barometer and \docWIFI{} provided bad readings.}
\label{fig:bergwerkPath1Galaxy}
\end{figure}
\begin{figure}
\includegraphics{gfx/eval/bergwerk_path3_galaxy}
\caption{Path 3 recorded with the Galaxy S5. Even though both paths look similar, the version with prior knowledge ended
much closer to the real destination due to reduced delays.}
\label{fig:bergwerkPath3Galaxy}
\end{figure}
%\begin{figure}
% \includegraphics{gfx/eval/bergwerk_path1_galaxy}
% \caption{Path 1 recorded with the Galaxy S5. Using prior knowledge improves the staircase (left) and the target area (right) where
% both the barometer and \docWIFI{} provided bad readings.}
% \label{fig:bergwerkPath1Galaxy}
%\end{figure}
%
%\begin{figure}
% \includegraphics{gfx/eval/bergwerk_path3_galaxy}
% \caption{Path 3 recorded with the Galaxy S5. Even though both paths look similar, the version with prior knowledge ended
% much closer to the real destination due to reduced delays.}
% \label{fig:bergwerkPath3Galaxy}
%\end{figure}
\commentByFrank{sensorausfall simulieren, z.b. in der mitte, oder auf einer treppe}
\commentByFrank{zwischendrin mal stehenbleiben und schauen ob auch das klappt}
\commentByFrank{zu grosser einfluss vom pfad ist also kein allheilmittel.. kann, wie beim treppenhaus, auch nach hinten los gehen}
%\commentByFrank{sensorausfall simulieren, z.b. in der mitte, oder auf einer treppe}
%\commentByFrank{zwischendrin mal stehenbleiben und schauen ob auch das klappt}
%\commentByFrank{zu grosser einfluss vom pfad ist also kein allheilmittel.. kann, wie beim treppenhaus, auch nach hinten los gehen}