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