\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 a 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} 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 \changed{-- up to an average error of \SI{1}{\meter} --} due to real-world comparisons,
	aforementioned approaches suffer from tremendous setup- and maintenance 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 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}.
	
	% log distance model. optimization of path-loss-exponent.
	% uses least-squares to solve for 3 unknowns: x, y, path-loss
	% based on triangulation by converting the rssi back to a distance based on the model
	% whole walk/dataset must be known beforehand?!
	\changed{%
		While signal strength models are used to predict a signal strength given the distance from the transmitter, 
		some also allow to infer the distance based on a known signal strength.
		Given several signal strength measurements from transmitters at known locations
		it is thus possible to perform trilateration. Such an approach is presented in \cite{rssModelOpt1},
		where the pedestrian's 2D location and one model parameter are optimized using
		a non-linear least square approach.
		Optimizing location and model parameter together yields a setup which is invariant
		to temporal environmental changes affecting the signal strength propagation.
		However, all transmitters are assumed to have the same optimized model parameter, which
		is an oversimplification for most environments. This issue is addressed in
		\cite{autoRssModel}, where this parameter is estimated per transmitter
		to increase the accuracy.
		However, due to the used optimized strategy it is hard to include additional constraints,
		such as knowledge given by a floorplan that would prevent the estimation from
		returning unreachable areas within a building.
		Likewise, the approach will not work smoothly for 3D location estimation,
		as the corresponding signal strength propagation models are usually non-continuous
		due to impact of floors/ceilings.
	}%
	
	\changed{%
		As the presented drawbacks denote, using just \docWIFI{} signal strengths as location estimation is erroneous.
		It thus makes sense to combine several other sensors
		via sensor fusion, to leverage the positive aspects of each individual source. 
		Recursive state estimation, e.g. based on an (extended) Kalman filter, allows for combining
		absolute \docWIFI{} location information, absolute landmarks, and relative pedestrian dead reckoning (PDR),
		as presented in \cite{indoorKalman,indoorKalman2}.%
	}%
	
	\changed{%
		Besides signal strengths, other RF characteristics
		like the signal's time of arrival (TOA) and time difference of arrival (TDOA),
		as used within the GPS, or its angle of arrival (AOA) can be used.
		They %
	}
	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 only allow for a limited number of use-cases.
		
	We therefore focus on the RSSI that is available on each commercial smartphone, and use 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.
	\changed{%
		Finally, we include additional smartphone sensors using sensor fusion via recursive state estimation to
		enhance the system's accuracy.
	}%