current TeX

tex/chapters/relatedwork.tex

@@ -54,7 +54,7 @@
 	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 uses a 
+	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.

tex/chapters/system.tex

@@ -15,33 +15,21 @@
 		\label{eq:recursiveDensity}
 	\end{equation}
 	
-	A movement model, based on random walks on a graph, samples only those transitions,
+	The pedestrian's hidden state $\mStateVec$ is given by
-	that are allowed by the buildings floorplan.
-	%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
-	The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide
-	the observations for both, the transition and the following evaluation step to infer the hidden state,
-	namely the pedestrian's location and heading
-	\cite{Ebner2016OPN, Fetzer2016OMC}.
-
-	
-	This hidden state $\mStateVec$ is given by
 	\begin{equation}
 		\mStateVec = (x, y, z, \mStateHeading),\enskip
 		x, y, z, \mStateHeading \in \R \enspace,
 	\end{equation}
 	%
-	where $x, y, z$ represent the pedestrian's position in 3D space
+	where $x, y, z$ represent its position in 3D space and $\mStateHeading$ his current (absolute) heading.
-	and $\mStateHeading$ his current (absolute) heading.
 	
-	
+	The corresponding observation vector, given by the smartphone's sensors, is defined as
-	
-	The corresponding observation vector is defined as
 	%
 	\begin{equation}
 		\mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mPressure, \mObsGPS) \enspace.
 	\end{equation}
 	%
-	$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the smartphone,
+	$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the phone,
 	$\mObsSteps$ describes the number of steps detected since the last filter-step,
 	$\mObsHeadingRel$ the (relative) angular change since the last filter-step,
 	$\mObsHeadingAbs$ the vague absolute heading as provided by the magnetometer,
@@ -49,7 +37,7 @@
 	$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS.
 	
 	
-	Assuming statistical independence, the state-evaluation density can be written as 
+	Assuming statistical independence, the state-evaluation density from \refeq{eq:recursiveDensity} can be written as 
 	%
 	\begin{equation}
 		p(\vec{o}_t \mid \vec{q}_t) = 
@@ -61,6 +49,15 @@
 		\label{eq:evalDensity}
 	\end{equation}
 	%
+	
+	Besides the evaluation, a movement model, based on random walks on a graph, samples only those transitions
+	(= pedestrian movements), that are allowed by the building's floorplan.
+	%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
+	The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide
+	the observations for both, the transition and the following evaluation step to infer the hidden state,
+	namely the pedestrian's location and heading
+	\cite{Ebner2016OPN, Fetzer2016OMC}.
+	
 
 	Absolute location information is provided by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ and 
 	$p(\vec{o}_t \mid \vec{q}_t)_\text{gps}$, if available.
@@ -69,30 +66,58 @@
 	$p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}$. Finally, the barometer is used
 	to distinguish between normal walking and climbing stairs within
 	$p(\vec{o}_t \mid \vec{q}_t)_\text{activity}$.
-	%
+	
-	The remaining observations, derived from aforementioned smartphone sensors,
+	Furthermore, the smartphone's IMU is used to infer the number of steps
-	namely: detected steps, and relative heading are 
+	and the relative turn angle the pedestrian has taken since the last filter-update.
-	used within the transition model, where potential movements 
+	While those values could be used within the evaluation \refeq{eq:evalDensity}
-	$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ 
+	we apply them within the transition model to estimate the pedestrian's potential
-	are not only constrained by the buildings floorplan but also by
+	movement $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ within the building.
-	those additional observations.
+	Using real values to perform this movement-update instead of just scattering randomly 
-
+	along the floorplan followed by downvoting within the evaluation \refeq{eq:evalDensity}
-	As this work focuses on \docWIFI{} optimization, not all parts of
+	provides a more stable result.
-	the localization system are discussed in detail.
+	
-	For missing explanations please refer to \cite{Ebner2016OPN}.
+	As this work focuses on \docWIFI{} optimization, not all parts of the localization system were discussed in detail.
+	For missing explanations and further details on aforementioned practices,
+	please refer to \cite{Ebner2016OPN}.
 	%
 	Compared to this reference, absolute heading and GPS have been added as additional sensors
-	to further enhance the localization. Their values are incorporated by simply
+	to further enhance the localization. As can be seen in \refeq{eq:evalAbsHead} and \refeq{eq:evalGPS},
-	comparing the sensor readings against a distribution that models the sensor's uncertainty.
+	their values are incorporated using a simple distribution that models each sensor's uncertainty.
 	
-	\todo{verteilung fuer gps und abs-heading}
+	\begin{equation}
+		p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}
+		=
+		\begin{cases}
+			0.7 & 	| \mObsVec_{\mObsHeadingAbs} - \mStateVec_{\mStateHeading} | < \SI{120}{\degree}	\\
+			0.3	&	\text{else}
+		\end{cases}
+		\label{eq:evalAbsHead}
+	\end{equation}
+	
+	\begin{equation}
+		p(\vec{o}_t \mid \vec{q}_t)_\text{gps} = 
+			\mathcal{N}(
+				d
+				\mid
+				0,
+				\sigma^2
+			), \enskip
+			d = \text{distance}(
+					(\mObsGPS_\text{lat}, \mObsGPS_\text{lon}),
+					(\mStateVec_x, \mStateVec_y)
+				), \enskip
+			\sigma = \mObsGPS_\text{accuracy}
+		\label{eq:evalGPS}
+	\end{equation}
 	
 	%\todo{neues resampling? je nach dem was sich noch in der eval zeigt}
 	
-	As GPS will only work outdoors, e.g. when moving from one building into another,
+	The GPS sensor should enhance scenarios where multiple, unconnected buildings are involved
-	the system's absolute position indoors is solely provided by \docWIFI{}.
+	and the pedestrian is required to move outdoors to enter the next facility.
-	Therefore its crucial for this component to supply location estimations 
+	Indoors the GPS will usually not provide viable location estimations and the system has to
-	that are as accurate as possible, while ensuring fast setup and
+	solely rely on the smartphone's \docWIFI{} observations.
-	maintenance times.
+	Therefore its crucial for this component to supply location
+	estimations that are as accurate as possible,
+	while the component itself must be easy to set-up and maintain.
 
-	\todo{ueberleitung holprig?}
+	\todo{ueberleitung besser?}

tex/chapters/work.tex

@@ -3,7 +3,9 @@
 		
 	The \docWIFI{} sensor infers the pedestrian's current location based on a comparison between live observations
 	(the smartphone continuously scans for nearby \docAP{}s) and fingerprints or
-	signal strength predictions for well known locations:
+	signal strength predictions for well known locations. The location that fits the observations best,
+	is the pedestrian's current location. Assuming statistical independence of all transmitters
+	installed within a building, this matching probability can be written as
 	
 	\begin{equation}
 		p(\vec{o}_t \mid \vec{q}_t)_\text{wifi} = 
@@ -11,12 +13,16 @@
 		\prod_{\mRssi_{i} \in \mRssiVec{}} p(\mRssi_{i} \mid \mPosVec),\enskip
 		%\mPos = (x,y,z)^T
 		\mPosVec \in \R^3
+		\enskip ,
 		\label{eq:wifiObs}
 	\end{equation}
-	%
+	
+	where matching a single signal strength observation against the reference is given by
+	
 	\begin{equation}
 		p(\mRssi_i \mid \mPosVec) = 
 		\mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma_{i,\mPosVec}^2)
+		\enskip .
 		\label{eq:wifiProb}
 	\end{equation}
 	
@@ -45,7 +51,9 @@
 		to also serve for indoor purposes.
 		%
 		It predicts an \docAP{}'s signal strength 
-		for an arbitrary location $\mPosVec{}$ given the distance between both and two environmental parameters:
+		for an arbitrary location 
+		%$\mPosVec{}$
+		given the distance $d$ between both and two environmental parameters:
 		The \docAPshort{}'s signal strength \mTXP{} measurable at a known distance $d_0$ (usually \SI{1}{\meter}) and
 		the signal's depletion over distance \mPLE{}, which depends on the \docAPshort{}'s surroundings like walls
 		and other obstacles.
@@ -78,7 +86,7 @@
 		In \refeq{eq:logNormShadowModel}, a constant attenuation factor \mWAF{} is
 		multiplied by the number \numFloors{} of floors/ceilings between sender and the location in question. 
 		The attenuation \mWAF{} (per element) depends on the building's architecture and for common,
-		steel enforced concrete floors $\approx 8.0$ is a viable choice \cite{ElectromagneticPropagation}.
+		steel enforced concrete floors $\mWAF \approx \SI{-8.0}{\decibel}$ is a viable choice \cite{ElectromagneticPropagation}.