\section{Related Work}

	Indoor localization based on \docWIFI{} and received signal strength indications (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. 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, 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 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, 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.
	
	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}.
	
	
	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}.
	Especially signal runtimes are unaffected by walls and thus allow for stable distance estimations, if the used components
	support measuring time-delays down to a few picoseconds. This is why those techniques often need special (measurement) hardware
	to estimate parameters like signal-runtime or signal-phase-shifts. Those requirements usually allow only for some use-cases.
	
	
	We therefore focus on the 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.
	Furthermore, we propose a new model based on multiple simple ones, which will reduce the prediction error.
	Several strategies to optimize simple models and the resulting accuracies are hereafter evaluated and discussed.
	
