From a8b91b141d786b559de778602cd696bf0ff4f4eb Mon Sep 17 00:00:00 2001 From: toni Date: Thu, 25 Feb 2016 15:03:10 +0100 Subject: [PATCH] 8 pages.. --- tex/chapters/experiments.tex | 30 +++++++++++++----------------- tex/chapters/grid.tex | 4 +--- 2 files changed, 14 insertions(+), 20 deletions(-) diff --git a/tex/chapters/experiments.tex b/tex/chapters/experiments.tex index 9685914..70276e6 100644 --- a/tex/chapters/experiments.tex +++ b/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 diff --git a/tex/chapters/grid.tex b/tex/chapters/grid.tex index 4d2aa6e..e9321d9 100644 --- a/tex/chapters/grid.tex +++ b/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. % %