8 pages..

tex/chapters/experiments.tex

@@ -10,12 +10,12 @@
 	and ignoring the shortest-path suggested by the system.
 	Due to an in-house exhibition during that time, many places were crowded and \docWIFI{} signals
 	are attenuated.
-	To enable error calculation, each acquired path is backed by ground truth information.
+%	To enable error calculation, each acquired path is backed by ground truth information.
 	The ground truth is measured by recording a timestamp at marked spots on the walking route.
 	While walking, the pedestrian clicked a button on the smartphone application
 	when passing a marker. Between two consecutive points, a constant movement speed is assumed.
-	Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for
-	error measurements. All walks were performed using a Motorola Nexus 6 and a Samsung Galaxy S5.
+	Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for error measurements. 
+All walks were performed using a Motorola Nexus 6 and a Samsung Galaxy S5.
 	
 	As the Samsung Galaxy S5's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only,
 	its scans take much longer than those of the Motorola Nexus 6:
@@ -53,15 +53,11 @@
 	%
 	
 	
-	The following evaluations will depict the improvements that the prior path knowledge is able to provide,
-	even when other system parameters are badly chosen.
-	Just adding importance-factors (described in \ref{sec:wallAvoidance} and \ref{sec:doorDetection})
-	to the simple transition \refeq{eq:transSimple} addresses only minor local errors
+	The following evaluations will depict the improvements that the prior path knowledge is able to provide, even when other system parameters are badly chosen.
+	Just adding importance-factors (described in \ref{sec:wallAvoidance} and \ref{sec:doorDetection}) to the simple transition \refeq{eq:transSimple} addresses only minor local errors
 	% like not sticking too close to walls. In most cases this lead only to slight improvements
 	and is therefore not further evaluated.
-	To examine the contribution our approach is able to provide, we will have a closer look
-	at a long walk with many stairs, intentionally leaving the shortest path several times,
-	named path 4 (see fig. \ref{fig:paths}).
+	To examine the contribution our approach is able to provide, we will have a closer look at a long walk with many stairs, intentionally leaving the shortest path several times, named path 4 (see fig. \ref{fig:paths}). 
 	%
 	% all paths we evaluated
 	\begin{figure}
@@ -107,7 +103,7 @@
 	This can be seen at the red area in the upper left corner of fig. \ref{fig:nexusPathDetails} \refSeg{1} and within
 	segment \refSeg{1} of fig. \ref{fig:errorTimedNexus}.
 	%
-	Starting with both, known position and heading, reduced the error by about \SI{15}{\percent} when using prior knowledge and
+	Starting instead with both, known position and heading, reduced the error by about \SI{15}{\percent} when using prior knowledge and
 	by \SI{25}{\percent} when omitting prior knowledge. As prior knowledge directs the density towards a known target,
 	it is able to compensate unknown initial headings which explains the \SI{10}{\percent} difference.
 	%
@@ -127,8 +123,8 @@
 	the density from being dragged into the office-rooms, the estimated path is still located on the wrong side
 	of the hallway. As both sides of the floor result in a route with almost the same length,
 	just knowing the pedestrian's destination is not able to provide further improvements.
-	Thus, a constant error of approximately the floor's width remains.
-	This is clearly visible in fig. \ref{fig:nexusPathDetails} \refSeg{6}.
+	Thus, a constant error of approximately the floor's width remains
+as seen in fig. \ref{fig:nexusPathDetails} \refSeg{6}.
 	%
 	Due to the excellent barometer installed within the Nexus 6, changing the floor provides only small estimation
 	errors in segment \refSeg{7}. 
@@ -136,7 +132,7 @@
 	Due to an in-house exhibition during the time of recording, we had to leave the ground truth by a few meters.
 	Furthermore, the overcrowded areas lead to attenuated \docWIFI{} signals. Both reasons move the
 	density into another stairwell (see fig. \ref{fig:nexusPathDetails}, red lines in the lower right).
-	The resulting multimodality (two staircases possible at the same time) leads to a rising error
+	The resulting multimodality (two staircases possible) leads to a rising error
 	\refSeg{8}, \refSeg{9}. At the end of the walk \refSeg{10} the system is able to recover, again.
 	
 	
@@ -154,11 +150,11 @@
 	%	\caption{Nicht so markant beim galaxy, denke aber der platz reicht eh nicht, also einfach kurz erwaehnen}
 	%\end{figure}
 
-	The median error values for all other paths and the other smartphone are listed in table
-	\ref{tbl:errNexus}. Furthermore, fig. \ref{fig:errorDistNexus} 
+	 The median errors for all conducted walks are listed in table \ref{tbl:errNexus}. Furthermore, fig. \ref{fig:errorDistNexus} 
 	depicts the error development for several percentile values. As can be seen, adding prior
-	knowledge is able to improve the localisation for all examined situations, even when
+	knowledge improves the localisation for all examined situations, even when
 	leaving the suggested path or when facing bad/slow sensor readings.
+\newpage
 	%\commentByFrank{fig. \ref{fig:errorDistNexus} erwaehnt}
 
 	% error values

tex/chapters/grid.tex

@@ -257,9 +257,7 @@
 			\newcommand{\pathRef}{v_\text{ref}}
 			%
 			Before every transition, the centre-position $\pathCentroid = \fPos{\mStateVec_{t-1}^*}$ of the current sample-set, where 
-			\begin{equation}
-				\mStateVec_{t-1}^* = \underset{\mStateVec_{t-1}}{\argmax} \enspace p(\mStateVec_{t-1} | \mObsVec_{t-1}) 
-			\end{equation}
+			$\mStateVec_{t-1}^* = \argmax_{\mStateVec_{t-1}} \enspace p(\mStateVec_{t-1} \mid \mObsVec_{t-1})$
 			represents the most proper state of the posterior distribution at time $t-1$, is calculated.
 			%
 			%