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\section{Related Work}
Indoor localization based on \docWIFI{} signal strengths dates back to the year
2000 and the work of Bahl and Padmanabhan \cite{radar}. During an offline-phase, a
multitude of reference measurements are conducted once. Those measurements are compared
against live readings during an online-phase. The pedestrian's location is inferred
using the $k$-nearest neighbor(s) based on the Euclidean distance between currently
received signal strengths and the readings during the offline phase.
Indoor localization based on received \docWIFI{} signal strengths (RSSI) dates back to the year
2000 and the work of Bahl and Padmanabhan \cite{radar}. During an one-time offline-phase, a
multitude of reference measurements are conducted. During the online-phase, where the pedestrian
walks along the building, those prior measurements are compared against live readings.
The pedestrian's location is inferred using the $k$-nearest neighbor(s) based on the Euclidean distance between currently
received signal strengths and the readings during the offline-phase.
Inspired by this initial work, Youssef et al. \cite{horus} proposed a more robust, probabilistic
approach. Fingerprints were placed every \SI{1.52}{\meter} and estimated by scanning each location
100 times. The resulting signal strength propagation for one location is hereafter denoted by a histogram.
approach. Their fingerprints were placed every \SI{1.52}{\meter} and estimated by scanning each location
100 times. The resulting signal strength distribution for each location is hereafter encoded by a histogram.
The latter can be compared against live measurements to infer its matching-probability. The center
of mass among the $k$ highest probabilities, including their weight, describes the pedestrian's current location.
%
In \cite{ProbabilisticWlan}, a similar approach is used and compared against nearest neighbor and machine learning.
Furthermore, they mention potential issues of unseen transmitters and describe a simple heuristic of how to handle such cases.
In \cite{ProbabilisticWlan}, a similar approach is used and compared against nearest neighbor, kernel-density-estimation and machine learning.
Furthermore, they mention potential issues of (temporarily) invisible transmitters and describe a simple heuristic of how to handle such cases.
Meng et al \cite{secureAndRobust} further discuss several fingerprinting issues like environmental changes
after the fingerprints were recorded. They propose an outlier detected based on RANSAC to remove potentially
Meng et al. \cite{secureAndRobust} further discuss several fingerprinting issues like environmental changes
after the fingerprints were recorded. They propose an outlier detection based on RANSAC to remove potentially
distorted measurements and thus improve the matching process.
Despite a very high accuracy due to real-world comparisons, all approaches suffer from tremendous setup-
and maintainance times.
Despite a very high accuracy due to real-world comparisons, aforementioned approaches suffer from tremendous setup-
and maintainance times.
Using robots instead of human workforce to accurately gather the necessary
fingerprints might thus be a viable choice \cite{robotFingerprinting}.
Being cheaper and more accurate, this technique can also
be combined with SLAM for cases where the floorplan is unavailable.
Therefore it makes sense to replace those time consuming fingerprints by model predictions.
Those are a well established research field, mainly used to determine the \docWIFI{}-coverage
for new installations. \cite{ANewPathLossPrediction, PredictingRFCoverage, empiricalPathLossModel}
Besides using real world measurements via fingerprinting, model predictions can be used to determine
signal strengths for arbitrary locations. Propagation models are a well established field of research,
initially used to determine the \docWIFI{}-coverage for new installations.
While many of them are intended for outdoor and line-of-sight purposes, they are often applied to indoor use-cases as well
\cite{ANewPathLossPrediction, PredictingRFCoverage, empiricalPathLossModel}.
The model-based approach presented by Chintalapudi et al. \cite{WithoutThePain} works without any prior knowledge.
During a setup phase, pedestrians just walk within the building and transmit all observations to a central
server. Some GPS fixes with well known position (e.g. entering and leaving the building) observed by the pedestrians
are used as reference points. A genetic optimization algorithm hereafter estimates both, the parameters for a
signal strength prediction model and the pedestrian's locations during the walk. The estimated parameters
can be refined using additional walks and may hereafter be used for the indoor localization process.
Likewise, it is possible to apply a global optimization that also determines a vague floorplan for the building \cite{crowdinside}.
einfach messen, ab und zu einen GPS fix und danach genetisch alles zuusammenoptimieren. also kein vorwissen
\cite{WithoutThePain}
As described in previous works, signal strength propagation strongly depends on the transmitter's surroundings and thus on the buildings
architecture.
%This induces both, the need for more complex prediction models and the need for filtering approaches
%to limit the impact of potentially erroneous readings.
%
Approaches based on timing like TOA and TDOA as used within the GPS or methods estimating the signal's angle-of-arrival (AOA)
are more accurate, and mostly invariant to architectural obstacles \cite{TimeDifferenceOfArrival1, TOAAOA}.
However, each of those requires special hardware to work.
%
We therefore focus on the well-known RSSI that is available on each commodity smartphone and use a
a simple signal strength prediction model to estimate the most probable location given the phone's observations.
To reduce the prediction error, we propose a new model based on multiple simple ones.
Several strategies to optimize such a model and the to-be-expected accuracy are hereafter discussed and evaluated.
das muesste noch was aehnliches sein:
\cite{crowdinside}
neben signalstärke gibt es noch viele andere methoden über laufzeiten wie beim gps etc.
diese erfordern meist aber spezial-hardware und laufen deshalb nicht so einfach auf dem smartphone [= ueberleitung!]
\cite{secureAndRobust}
andere methoden neben signalstärke
\cite{TimeDifferenceOfArrival1} \cite{TOAAOA}
\cite{Ebner-15}