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tex/chapters/experiments.tex
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@@ -1,12 +1,5 @@
experiments
\todo{obwohl das angepasste modell doch recht gut laeuft und der fehler recht klein wird, sind immernoch stellen dabei,
wo es einfach nicht gut passt, unguenstige mehrdeutigkeiten vorliegen, oder regionen einfach nicht passen wie sie sollten.
das liegt teils auch daran, dass die fingerprints drehend aufgenommen wurden und beim laufen nach hinten durch den
menschen abgeschottet wird. auch zeitlicher verzug kann ein problem darstellen.}
\todo{GPS ist leider kaum eine hilfe. entweder kein empfang wegen ueberdachung oder abschattung, oder
zu kurz draußen um einen guten gps-fix zu bekommen.}
\section{Experiments}
wir betrachten nur die fest-installierten APs die man meist anhand einer bestimmten mac-range ausmachen kann
portable geraete von studenten, beamer, aehnliches werden ignoriert
@@ -37,90 +30,248 @@ optimierungs input: alle 4 walks samt ground-truth
dann kommt fuer die 4 typen [fixed, all same par, each par, each par pos]
log probability 50 75, meter 50, 75
path1
31.8|38.9 7.8|11.6
27.3|36.8 7.2|9.8
24.0|30.3 5.8|10.24
22.9|29.9 5.0|7.6
hoherer fehler weil mehr outdoor anteil
path2
32.0|42.4 12.6|20.9
28.4|35.2 10.1|16.1
27.0|34.0 7.0|10.1
25.4|33.3 8.0|17.2
je mehr outdoor, desto schlechter wird es.
outdoor schadet auch der optimierung
outdoor schadet mehr als indoor, weil das wifi modell fuer indoor noch halbwegs passt
aber fuer outdoor so garned
fenster sind metallbedampft und schirmen stark ab
siehe beispielgrafik
gps wird so schnell nicht warm, versagt denn auf dem hof als hilfestellung
reines wifi eval mittels num-opt springt stark durch die gegend
d.h. das bewegungsmodell rettet uns
kann man auch testen wenn man beim particle-filter das resampling ganz aus macht
\todo{
we analyzed various paths throughout the whole building
}
\todo{
mit grafik: exp-dist vergroesert teils den abstand zu anderen locations , der GT selbst wird also besser,
aber an anderen stellen geht dafür der fehler hoch und kann zu verlaufen führen (z.B. treppenhaus)
}
% -------------------------------- optimization -------------------------------- %
% used reference measurements
\begin{figure}
{
\centering
\input{gfx/all_fingerprints.tex}
}
\label{fig:referenceMeasurements}
\caption{
Locations of the 121 reference measurements.
The size of each square denotes the number of permanently installed \docAPshort{}s
that are visible at this location,
and ranges between 2 and 22 with an average of 9.
}
\end{figure}
% visible APs:
% cnt(121) min(2.000000) max(22.000000) range(20.000000) med(8.000000) avg(9.322314) stdDev(4.386709)
\begin{figure}
\input{gfx/wifi_model_error_0_95.tex}
\input{gfx/wifi_model_error_95_100.tex}
\label{fig:wifiModelError}%
\caption{%
Comparison between different optimization strategies by examining the error (in \decibel) at each reference measurement.%
The higher the number of variable parameters, the better the model resembles real world conditions. %
}%
\end{figure}
\begin{figure}
\centering
\input{gfx/compare-wifi-in-out.tex}
\caption{
Measurable signal strengths of a testing \docAPshort{} (black dot).
While the signal diminishes slowly along the corridor (upper rectangle)
the metallised windows (dashed outline) attenuate the signal by over \SI{30}{\decibel} (lower rectangle).
}
\end{figure}
fenster sind metallbedampft und schirmen stark ab
siehe beispielgrafik
\todo{
distance between AP pos estimation and real position???
}
% -------------------------------- number of fingerprints -------------------------------- %
wie viele fingerprints sind genug?
Haengt vom modell ab
bei den einfachen modellen aendert sich erstmal nicht viel. man hat ja viele testdaten für ein modell mit wenigen parametern.
je mehr variable wird, z.B. position, und das ganze pro AP und nicht füer alle, desto wichtiger wird, dass die fingerprints passen.
neuralgische schwachpunkte wie betonierte treppenhäuser kann man weglassen, dadurch wird der rest etwas besser,
die treppenhäuser ansich aber natürlich nochmal schlechter. siehe \ref{fig:wifiNumFingerprints}
\begin{figure}
\input{gfx/wifi_model_error_num_fingerprints_method_5_0_90.tex}
\input{gfx/wifi_model_error_num_fingerprints_method_5_90_100.tex}
\label{fig:wifiNumFingerprints}%
\caption{%
number of fingerprints
}%
\end{figure}
% -------------------------------- wifi walk error -------------------------------- %
Using aforementioned model setups and the measurements $\mRssiVec$ determined by scanning for nearby \docAPshort{}s,
we can directly perform a location estimation by rewriting \refeq{eq:wifiProb}:
\begin{equation}
p(\mPosVec \mid \mRssiVec) =
\frac{p(\mRssiVec \mid \mPosVec) p(\mPosVec)}{p(\mRssiVec)}
\approx p(\mRssiVec \mid \mPosVec),\enskip
p(\mPosVec) = p(\mRssiVec) = \text{const}
.
\label{eq:wifiBayes}
\end{equation}
The pedestrian's current location $\mPosVec^*$ given $\mRssiVec$ satisfies
\begin{equation}
\mPosVec^* = \argmax_{\mPosVec}
p(\mRssiVec \mid \mPosVec)
.
\label{eq:bestWiFiPos}
\end{equation}
The quality of the estimated location is determined by comparing the estimation
$\mPosVec^*$ with the pedestrian's ground truth at the time the scan $\mRssiVec$
has been received.
We therefore conducted 10 walks on 5 different paths within our building,
each of which is defined by connecting several marker points at well known positions
(see figure \ref{fig:allWalks}).
Whenever the pedestrian reached such a marker, the current time was recorded.
Due to constant walking speeds, the ground-truth for any timestamp can be approximated
using linear interpolation between adjacent markers.
% walked paths
\begin{figure}
{
\centering
\input{gfx/all_walks.tex}
}
\label{fig:allWalks}
\caption{
Overview of all conducted paths.
Outdoor areas are marked in green.
}
\end{figure}
To estimate the performance of the prediction models, we compare the position estimation
for each \docWIFI{} measurement within the recorded paths (3756 \docAPshort{} scans in total)
against the corresponding ground-truth, which indicates the absolute 3D error in meter.
\begin{figure}
\input{gfx/modelPerformance_meter.tex}
\label{fig:modelPerformance}
\caption{
Error between ground truth and estimation using \refeq{eq:bestWiFiPos} depending
on the underlying signal strength prediction model
}
\end{figure}
As can be seen in figure \ref{fig:modelPerformance}, the quality of the location estimation
directly scales with the quality of the signal strength prediction model.
However, depending on the model, the maximal estimation error might increase (see \optParamsPosEachAP{}).
%
This is either due to multimodalities, where more than one area is possible based on the recent
\docWIFI{} observation, or optimization yields an overadaption where the average signal
strength prediction error is small, but the maximum error is dramatically increased for some regions.
% -------------------------------- plots indicating optimization issues -------------------------------- %
\begin{figure}
\input{gfx/wifiMultimodality.tex}
\label{fig:wifiMultimodality}
\caption{
Location probability \refeq{eq:bestWiFiPos} for three scans. Higher color intensities are more likely.
Ideally, places near the ground truth (black) are highly highly probable (green).
Often, other locations are just as likely as the ground truth (blue),
or the location with the highest probability does not match at all (red).
}
\end{figure}
Figure \ref{fig:wifiMultimodality} depicts aforementioned issues of multimodal (blue) or wrong (red) location
estimations. Filtering (\refeq{eq:recursiveDensity}) thus is highly recommended as minor errors are compensated
using other sensors and/or a movement model that prevents the estimation from leaping within the building.
However, if wrong sensor values (red) are observed for longer time periods, even filtering will produce erroneous
results and might get stranded (density is trapped e.g. within a room),
as the movement model is constrained by the actual floorplan.
% -------------------------------- other distributions, unseen APs, etc -------------------------------- %
To reduce the amount of misclassifications, where other locations within the building are (almost)
as likely (see \refeq{eq:wifiProb}) as the pedestrians actual location, we examined various
approaches. Unfortunately, none of which provided a viable enhancement under all conditions within
the performed walks.
One possibility to dissolve an equal \docWIFI{}-likelihood between two (or more) locations within in the building
is, to not only consider the \docAPshort{}s seen by the Smartphone, but also the \docAPshort{}s not seen
by the Smartphone. Maybe there is an \docAP{} that should be visible at the other locations. However,
as the Smartphone did not see this \docAPshort{} the other location can be ruled out.
While this works in theory, evaluations revealed several issues:
There is a chance that an \docAPshort{} is unseen during a scan due to packet collisions or
temporal effects within the surrounding. It thus might make sense to opt-out other locations
only, if at least two \docAPshort{}s are missing. On the other hand, this obviously requires (at least)
two \docAPshort{}s to actually be different between the two locations, which might not always be
the case.
Also, this requires the signal strength prediction model to be fairly accurate. Within our testing
walks there are several places surrounded by concrete walls, which cause a harsh, local drop in signal strength.
The models used within this work will not accurately predict the signal strength for such locations.
Including \docAPshort{}s unseen by the Smartphone thus often increases the estimation error instead
of fixing the multimodality.
We therefore examined variations of the probability calculation from \refeq{eq:wifiProb}.
Removing the strongest/weakest \docAPshort{} from $\mRssiVecWiFi{}$ yielded similar results.
While some estimations were improved, the overall estimation error increased for our walks,
as there are many situations where only a handful \docAP{}s can be seen. Removing (valid)
information will highly increase the error for such situations.
Using a more strict exponential distribution for
\begin{figure}
\input{gfx/wifiCompare_normalVsExp_cross.tex}
\input{gfx/wifiCompare_normalVsExp_meter.tex}
\label{fig:normalVsExponential}
\caption{
Comparison between normal- (black) and exponential-distribution (red) for \refeq{eq:wifiProb}.
While misclassifications are slightly reduced (upper chart),
the error between ground-truth and estimation (lower chart) increases by
about \SI{1}{\meter} for the median.
To reduce the amount such of misclassifications, where other locations within the building are
as likely as the pedestrians actual location, we examined various approaches.
Unfortunately, none of which provided a viable enhancement under all conditions for the performed walks:
One possibility to dissolve an equal \docWIFI{}-likelihood between two (or more) locations within in the building
is, to not only consider the \docAPshort{}s seen by the Smartphone, but also the \docAPshort{}s not seen
by the Smartphone. This additional information can be used to rule out all locations where this
\docAP{} should be received (high signal strength from the prediction model).
% There might be an \docAP{} that should be visible at the other locations. However,
%as the Smartphone did not see this \docAPshort{} the other location can be ruled out.
While this works in theory, evaluations revealed several issues:
There is a chance that even a nearby \docAPshort{} is unseen during a scan due to packet collisions or
temporal effects within the surrounding. It thus might make sense to opt-out other locations
only, if at least two \docAPshort{}s are missing. On the other hand, this obviously requires (at least)
two \docAPshort{}s to actually be different between the two locations, and requires a lot of permanently
installed transmitters to work out.
Furthermore, this requires the signal strength prediction model to be fairly accurate. Within our testing
walks, several places are surrounded by concrete walls, which cause a harsh, local drop in signal strength.
The models used within this work will not accurately predict the signal strength for such locations.
Including \docAPshort{}s unseen by the Smartphone thus often increases the estimation error instead
of fixing the multimodality.
We therefore examined variations of the probability calculation from \refeq{eq:wifiProb}.
Removing the strongest/weakest \docAPshort{} from $\mRssiVecWiFi{}$ yielded similar results.
While some estimations were improved, the overall estimation error increased for our walks,
as there are many situations where only a handful \docAP{}s can be seen. Removing (valid)
information will highly increase the error for such situations.
Using a more strict exponential distribution for the model vs. scan comparison in \refeq{eq:wifiProb}
had a positive effect on the misclassification error for some of the walks, but slightly increased
the estimation error (see figure \reffig{fig:normalVsExponential}) and thus produced negative side effects.
\begin{figure}
\input{gfx/wifiCompare_normalVsExp_cross.tex}
\input{gfx/wifiCompare_normalVsExp_meter.tex}
\label{fig:normalVsExponential}
\caption{
Comparison between normal- (black) and exponential-distribution (red) for \refeq{eq:wifiProb}.
While misclassifications are slightly reduced (upper chart),
the median error between ground-truth and estimation (lower chart) increases by
about \SI{1}{\meter}.
}
\end{figure}
\todo{
wir wollen nicht, dass die position des ground-truths durch das wifi so wahrscheinlich wie möglich ist,
wir wollen dass die position des ground-truth einfach eine höhere wahrscheinlichkeit hat, als alle anderen punkte im gebäude
das pruefen wir ab
}
\end{figure}
\todo{
erkenntnisse:
@@ -141,32 +292,33 @@ kann man auch testen wenn man beim particle-filter das resampling ganz aus macht
}
\todo{
das bbox modell hat probleme an den uebergängen zwischen bboxes da dort teils starke spruenge sind
die nicht immer in der realität so auch vorliegen. z.B. z-wechsel machen teils probleme.
hier wäre ein kontinuierliches modell hilfreich bzw interpolation in randbereichen
}
\todo{
wenn ich beim fingerprinten einen AP an einer stelle NICHT gesehen habe,
ist das auch eine aussage für die model optimierung.. da kann dann sicher keine signatlstaerke > -90 an der stelle raus kommen
}
% REAL WALKS
\todo{obwohl das angepasste modell doch recht gut laeuft und der fehler recht klein wird, sind immernoch stellen dabei,
wo es einfach nicht gut passt, unguenstige mehrdeutigkeiten vorliegen, oder regionen einfach nicht passen wie sie sollten.
das liegt teils auch daran, dass die fingerprints drehend aufgenommen wurden und beim laufen nach hinten durch den
menschen abgeschottet wird. auch zeitlicher verzug kann ein problem darstellen.}
\todo{GPS ist leider kaum eine hilfe. entweder kein empfang wegen ueberdachung oder abschattung, oder
zu kurz draußen um einen guten gps-fix zu bekommen.}
\todo{
das bbox modell hat probleme an den uebergängen zwischen bboxes da dort teils starke spruenge sind
die nicht immer in der realität so auch vorliegen. z.B. z-wechsel machen teils probleme.
hier wäre ein kontinuierliches modell hilfreich bzw interpolation in randbereichen
}
\todo{
wenn ich beim fingerprinten einen AP an einer stelle NICHT gesehen habe,
ist das auch eine aussage für die model optimierung.. da kann dann sicher keine signatlstaerke > -90 an der stelle raus kommen
}
\todo{gps wird so schnell nicht warm, versagt denn auf dem hof als hilfestellung}
\todo{
wir wollen nicht, dass die position des ground-truths durch das wifi so wahrscheinlich wie möglich ist,
wir wollen dass die position des ground-truth einfach eine höhere wahrscheinlichkeit hat, als alle anderen punkte im gebäude
das pruefen wir ab
}
\begin{figure}
\centering
\input{gfx/compare-wifi-in-out.tex}
\caption{
Measurable signal strengths of a testing \docAPshort{} (black dot).
While the signal diminishes slowly along the corridor (upper rectangle)
the metallised windows (dashed outline) attenuate the signal by over \SI{30}{\decibel} (lower rectangle).
}
\end{figure}
ware das grid-model nicht da, wuerde der outdoor teil richtig schlecht laufen,
weil das wlan hier absolut ungenau ist.. da die partikel aber aufgrund des vorherigen
@@ -200,3 +352,6 @@ der einfluss jedoch recht groß sein, siehe den fingerprint plot von
dem einen ausgewählten AP
wenn noch zeit ist: wie aendert sich die model prediction wenn man z.B. nur die haelfte der referenzmessungen nimmt?

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tex/chapters/relatedwork.tex
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@@ -1,5 +1,10 @@
relatedwork
wifi anfänge von radar (microsoft) etc
\cite{radar} \cite{horus} \cite{secureAndRobust}
andere methoden neben signalstärke
\cite{TimeDifferenceOfArrival1} \cite{TOAAOA}
\cite{Ebner-15}

10
tex/misc/keywords.tex
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@@ -24,3 +24,13 @@
\newcommand{\docsRSSI}{RSSI}
\newcommand{\docDSimplex}{downhill-simplex}
% optimizations
\newcommand{\noOptEmpiric}{empiric params}
\newcommand{\optParamsAllAP}{optimization 1}
\newcommand{\optParamsEachAP}{optimization 2}
\newcommand{\optParamsPosEachAP}{optimization 3}
\newcommand{\optPerFloor}{model per floor}
\newcommand{\optPerRegion}{model per region}