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FrankE
2017-04-25 18:34:37 +02:00
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tex/chapters/abstract.tex
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@@ -6,3 +6,7 @@ und optimierung durch einige referenzmessungen
floorplan wird für die navigation bzw orientierung des anwenders eh gebraucht floorplan wird für die navigation bzw orientierung des anwenders eh gebraucht
dann kann man ihn auch gleich für ein bewegungsmodell nutzen dann kann man ihn auch gleich für ein bewegungsmodell nutzen
es sollte klar werden, dass es auch darum geht, effizient
auf einem normalen smartphone lauffähig zu sein [passend zum journal]

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tex/chapters/experiments.tex
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@@ -89,6 +89,8 @@
{\em\optPerFloor{}} and {\em\optPerRegion{}} are just like \optParamsPosEachAP{} except that {\em\optPerFloor{}} and {\em\optPerRegion{}} are just like \optParamsPosEachAP{} except that
there are several sub-models that are optimized for one floor / region instead of the whole building. there are several sub-models that are optimized for one floor / region instead of the whole building.
\todo{grafik, die die regionen zeigt???}
Figure \ref{fig:wifiModelError} shows the optimization results for all strategies, which are as expected: Figure \ref{fig:wifiModelError} shows the optimization results for all strategies, which are as expected:
The estimation error is indirectly proportional to the number of optimized parameters. The estimation error is indirectly proportional to the number of optimized parameters.
However, even with {\em \optPerRegion{}} the maximal error is relatively high due to some locations that do However, even with {\em \optPerRegion{}} the maximal error is relatively high due to some locations that do
@@ -165,33 +167,45 @@
\subsection{Location estimation error} \subsection{Location estimation error}
Using the optimized model setups and the measurements $\mRssiVec$ determined by scanning for nearby \docAPshort{}s, \todo{übergang holprig}
we can directly perform a location estimation by rewriting \refeq{eq:wifiProb}:
%Using the optimized 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}:
For each of the discussed optimization strategies we can now determine the resulting localization accuracy.
The position within the building that best fits some signal strength measurements $\mRssiVec$ received by the smartphone
is the one that maximizes $p(\mPosVec \mid \mRssiVec)$ and can be rewritten as:
\begin{equation} \begin{equation}
p(\mPosVec \mid \mRssiVec) = p(\mPosVec \mid \mRssiVec) =
\frac{p(\mRssiVec \mid \mPosVec) p(\mPosVec)}{p(\mRssiVec)} \frac{p(\mRssiVec \mid \mPosVec) p(\mPosVec)}{p(\mRssiVec)}
\approx p(\mRssiVec \mid \mPosVec),\enskip \propto p(\mRssiVec \mid \mPosVec),\enskip
p(\mPosVec) = p(\mRssiVec) = \text{const} p(\mPosVec) = p(\mRssiVec) = \text{const}
. .
\label{eq:wifiBayes} \label{eq:wifiBayes}
\end{equation} \end{equation}
The pedestrian's current location $\mPosVec^*$ given $\mRssiVec$ satisfies Following \refeq{eq:wifiObs} and \refeq{eq:wifiProb}, the best
location $\mPosVec^*$ given $\mRssiVec$ is the one that satisfies
\begin{equation} \begin{equation}
\mPosVec^* = \argmax_{\mPosVec} \mPosVec^* = \argmax_{\mPosVec}
p(\mRssiVec \mid \mPosVec) \prod_{\mRssi_{i} \in \mRssiVec{}}
. \mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma^2)
\label{eq:bestWiFiPos} \label{eq:bestWiFiPos}
\end{equation} \end{equation}
where $\mu_{i,\mPosVec}$ is the signal strength for \docAP{} $i$
at location $\mPosVec$ returned from the to-be-examined prediction model.
For all comparisons we use a constant uncertainty $\sigma = $\SI{8}{\decibel}.
The quality of the estimated location is determined by comparing the estimation The quality of the estimated location is determined by comparing the estimation
$\mPosVec^*$ with the pedestrian's ground truth at the time the scan $\mRssiVec$ $\mPosVec^*$ with the pedestrian's ground truth position at the time the scan $\mRssiVec$
has been received. has been received.
We therefore conducted 10 walks on 5 different paths within our building, 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 each of which is defined by connecting marker points at well known positions
(see figure \ref{fig:allWalks}). (see figure \ref{fig:allWalks}).
Whenever the pedestrian reached such a marker, the current time was recorded. 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 Due to constant walking speeds, the ground-truth for any timestamp can be approximated
@@ -210,10 +224,6 @@
} }
\end{figure} \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}[b] \begin{figure}[b]
\input{gfx/modelPerformance_meter.tex} \input{gfx/modelPerformance_meter.tex}
\label{fig:modelPerformance} \label{fig:modelPerformance}
@@ -223,12 +233,17 @@
} }
\end{figure} \end{figure}
As can be seen in figure \ref{fig:modelPerformance}, the quality of the location estimation %To estimate the overall performance of the prediction models, we compare the position estimation
directly scales with the quality of the signal strength prediction model. %for each \docWIFI{} measurement within the recorded paths (3756 \docAPshort{} scans in total)
However, depending on the model, the maximal estimation error might increase (see \optParamsPosEachAP{}). %against the corresponding ground-truth, which indicates the absolute 3D error in meter.
The position estimation for each \docWIFI{} measurement within the recorded walks (3756 \docAPshort{} scans in total)
is compared against its corresponding ground-truth, indicating the absolute 3D error.
The resulting cumulative error distribution 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, as discussed earlier, the maximal estimation error might increase for some setups.
% %
This is either due to multimodalities, where more than one area is possible based on the recent 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 \docWIFI{} observation, or optimization yielded an overadaption where the average signal
strength prediction error is small, but the maximum error is dramatically increased for some regions. strength prediction error is small, but the maximum error is dramatically increased for some regions.
@@ -247,7 +262,7 @@
\end{figure} \end{figure}
Figure \ref{fig:wifiMultimodality} depicts aforementioned issues of multimodal (blue) or wrong (red) location 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 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. 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 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), results and might get stranded (density is trapped e.g. within a room),
@@ -379,15 +394,13 @@ die treppe richtung h.1.5 hochgehen und durch das wlan sehr sehr hoch gewichtet
die mittelwert-estimation versagt hier die mittelwert-estimation versagt hier
\input{gfx/wifi-opt-error-hist-methods.tex} % was ist das??
%\input{gfx/wifi-opt-error-hist-methods.tex}
\input{gfx/wifi-opt-error-hist-stair-outdoor.tex} %\input{gfx/wifi-opt-error-hist-stair-outdoor.tex}
outdoor hat insgesamt nicht all zu viel einfluss, da die meisten APs %outdoor hat insgesamt nicht all zu viel einfluss, da die meisten APs
an den outdoor punkten kaum gesehen werden. auf einzelne APs kann %an den outdoor punkten kaum gesehen werden. auf einzelne APs kann
der einfluss jedoch recht groß sein, siehe den fingerprint plot von %der einfluss jedoch recht groß sein, siehe den fingerprint plot von
dem einen ausgewählten AP %dem einen ausgewählten AP
wenn noch zeit ist: wie aendert sich die model prediction wenn man z.B. nur die haelfte der referenzmessungen nimmt?
\todo{anfaenglich falsches heading ist gift, wegen rel. heading, weil sich dann alles verlaeuft. fix: anfaenglich große heading variation erlauben} \todo{anfaenglich falsches heading ist gift, wegen rel. heading, weil sich dann alles verlaeuft. fix: anfaenglich große heading variation erlauben}