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We therefore examined variations of the probability calculation from \refeq{eq:wifiProb}.
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Removing the strongest/weakest \docAPshort{} from $\mRssiVec{}$ yielded similar results.
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While some estimations were improved, the overall estimation error increased for our walks,
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as there are many situations where only a handful \docAP{}s can be seen. Removing (valid)
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information will highly increase the error for such situations.
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Despite the results show in \cite{PotentialRisks}, removing weak \docAPshort{}s from $\mRssiVec{}$
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yielded similar results. While some estimations were improved, the overall estimation error increased
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for our walks, as there are many situations where only a handful \docAP{}s can be seen.
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Removing this (valid) information will highly increase the error for such situations.
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Incorporating additional knowledge provided by virtual \docAP{}s (see section \ref{sec:vap}) mitigated this issues.
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If only one out of six virtual networks is observed, this observation is likely to be erroneous, no matter
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@@ -1,7 +1,48 @@
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relatedwork
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\section{Related Work}
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wifi anfänge von radar (microsoft) etc
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\cite{radar} \cite{horus} \cite{secureAndRobust}
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Indoor localization based on \docWIFI{} signal strengths dates back to the year
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2000 and the work of Bahl and Padmanabhan \cite{radar}. During an offline-phase, a
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multitude of reference measurements are conducted once. Those measurements are compared
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against live readings during an online-phase. The pedestrian's location is inferred
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using the $k$-nearest neighbor(s) based on the Euclidean distance between currently
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received signal strengths and the readings during the offline phase.
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Inspired by this initial work, Youssef et al. \cite{horus} proposed a more robust, probabilistic
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approach. Fingerprints were placed every \SI{1.52}{\meter} and estimated by scanning each location
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100 times. The resulting signal strength propagation for one location is hereafter denoted by a histogram.
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The latter can be compared against live measurements to infer its matching-probability. The center
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of mass among the $k$ highest probabilities, including their weight, describes the pedestrian's current location.
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%
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In \cite{ProbabilisticWlan}, a similar approach is used and compared against nearest neighbor and machine learning.
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Furthermore, they mention potential issues of unseen transmitters and describe a simple heuristic of how to handle such cases.
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Meng et al \cite{secureAndRobust} further discuss several fingerprinting issues like environmental changes
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after the fingerprints were recorded. They propose an outlier detected based on RANSAC to remove potentially
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distorted measurements and thus improve the matching process.
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Despite a very high accuracy due to real-world comparisons, all approaches suffer from tremendous setup-
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and maintainance times.
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Therefore it makes sense to replace those time consuming fingerprints by model predictions.
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Those are a well established research field, mainly used to determine the \docWIFI{}-coverage
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for new installations. \cite{ANewPathLossPrediction, PredictingRFCoverage, empiricalPathLossModel}
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einfach messen, ab und zu einen GPS fix und danach genetisch alles zuusammenoptimieren. also kein vorwissen
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\cite{WithoutThePain}
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das muesste noch was aehnliches sein:
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\cite{crowdinside}
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neben signalstärke gibt es noch viele andere methoden über laufzeiten wie beim gps etc.
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diese erfordern meist aber spezial-hardware und laufen deshalb nicht so einfach auf dem smartphone [= ueberleitung!]
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\cite{secureAndRobust}
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andere methoden neben signalstärke
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@@ -118,7 +118,7 @@
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Just optimizing \mTXP{} and \mPLE{} with constant \mWAF{} and known transmitter position
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usually means optimizing a convex function as can be seen in figure \ref{fig:wifiOptFuncTXPEXP}.
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For such error functions, algorithms like gradient descent \cite{TODO} and (downhill) simpelx \cite{TODO}
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For such error functions, algorithms like gradient descent and simplex \cite{gradientDescent, downhillSimplex1, downhillSimplex2}
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are well suited and will provide the global minima:
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\begin{equation}
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