current TeX

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}.