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FrankE
2016-02-12 20:48:38 +01:00
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tex/chapters/experiments.tex
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% introduction
Evaluation took place within all floors (0 to 3) of the
faculty building, each of which about \SI{77}{\meter} x \SI{55}{\meter} in size.
%
We conducted 4 distinct walks, for testing short distances, long distances, critical sections
and ignoring the shortest-path suggested by the system. Each path is backed by ground truth information
to enable error calculation. This ground truth is measured by recording a timestamp at a marked spot
on the walking route. During the walk, the pedestrian has 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 good enough to conduct error measurements.
All walks were conducted using a Google Nexus 6 and a Samsung Galaxy S5.
and ignoring the shortest-path suggested by the system.
Due to an inhouse exhibition during that time, many places were crowded and \docWIFI{} signals
are attenuated more than usual.
Each acquired path is backed by ground truth information to enable error calculation.
This ground truth is measured by recording a timestamp at a marked spot on the walking route.
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 conducted using a Google 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: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}. Also, the Nexus' barometer sensor
provides readings more frequent and far more accurate than the Galaxy does. This results in a much better
localisation for the Nexus smartphone.
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:
\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 of the Nexus smartphone.
Despite being fast enough to run in realtime on the smartphone itself, computation was done offline using
the condensation algorithm with \SI{7500}{} particles as realization of the recursive density estimation \cite{todo}
and the weighted arithmetic mean of those for the state estimation.
the condensation algorithm with \SI{7500}{} particles as realization of the recursive density estimation \cite{todo}.
The weighted arithmetic mean of the particles was used as state estimation.
As mentioned earlier, the position of all \docAP{}s (about 5 per floor) is known beforhand.
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 $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}$,
and $\mPLE_{\text{ib}} = \SI{1.5}{}$ for the \docIBeacon{}s, respectively. Due to omitting a time-consuming calibration
process for those values, the sensor readings are considered somewhat faulty.
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 localistation
process to perform generally worse compared to fingerpring methods \todo{cite}. 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}.
\commentByFrank{describe what was evaluated: 2 phones (differences), 4 paths, building, several floors, ibeacons, access points}
As we start with a uniformation 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 follwing few seconds is expected to be much higher than the error when starting with a well known initial
position and heading.
The follwing evaluations will depict the improvements prior path knowledge is able to provide
even when other system parameters are badly chosen.
Just adding importance-factors described in \ref{sec:wallAvoidance} and \ref{sec:doorDetection}
to the simple transition \refeq{eq:transSimple} addresses only minor local errors
% like not sticking too close to walls. In most cases this lead only to slight improvements
and is therefore not further evaluated.
%
\commentByFrank{bergwerk\_path3\_galaxy}
As we start with a uniformation distribution for $\mStateVec_0$, the first few estimations
are omitted from the error calculation to allow the system to settle its initial state.
Adding the importance factors described in \ref{sec:wallAvoidance} and \ref{sec:doorDetection}
to the simple transition \refeq{eq:transSimple} addresses only minor local errors like not
sticking too close to walls. In most cases this lead only to minor, if any, improvements
and is therefore not fruther evaluated.
\begin{figure}
\input{gfx/eval/paths}
\caption{The four paths that were part of the evaluation.
Starting positions are marked with black circles.
For a better visualisation they were slightly shifted to avoid overlapping.}
\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}
\begin{figure}
%\includegraphics{eval/bergwerk_path2_nexus_shortest}
\end{figure}
% 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 shows increasing errors for our methods when leaving the shortest path and when facing multimodalities between two
staircases at the end.}
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}