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toni changes in franks part

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toni
2016-02-23 15:34:00 +01:00
parent 8889c4cf83
commit 822f71f633
4 changed files with 19 additions and 21 deletions
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10
tex/chapters/experiments.tex
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@@ -65,9 +65,8 @@
\input{gfx/eval/paths}
\caption{The four paths that were part of the evaluation.
Starting positions are marked with black circles.
For a better visualisation they were slightly shifted to avoid overlapping.
For a better visualisation they were slightly shifted to avoid overlapping.}
\commentByFrank{font war korrekt, aber die groesse war zu gross im vgl. zu den anderen}
}
\label{fig:paths}
\end{figure}
% error development over time while walking along a path
@@ -76,9 +75,8 @@
\caption{Development of the error while walking along Path 4 using the Motorola Nexus 6.
When leaving the suggested route (3), the error of \textbf{shortest} path \refeq{eq:transShortestPath}
and \textbf{multi}path \refeq{eq:transMultiPath} increases.
The same issues arise when facing multimodalities between two staircases just before the destination (9).
The same issues arise when facing multimodalities between two staircases just before the destination (9).}
\commentByFrank{hilft das bold vlt. schon um die legende zu verstehen?}
}
\label{fig:errorTimedNexus}
\end{figure}
% detailed analysis of path 4
@@ -139,8 +137,8 @@
\begin{figure}
\input{gfx/eval/error_dist_nexus}
\caption{Error distribution of all walks conducted with the Motorola Nexus 6 for distinct percentile values.
Our proposed methods clearly provide an enhancement for the overall localization process.
\commentByFrank{percentile erwaehnt}}
Our proposed methods clearly provide an enhancement for the overall localization process.}
\commentByFrank{percentile erwaehnt}
\label{fig:errorDistNexus}
\end{figure}
%\begin{figure}

12
tex/chapters/grid.tex
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@@ -258,9 +258,11 @@
\newcommand{\pathRef}{v_\text{ref}}
Before every transition, the centre-position $\pathCentroid = (x,y,z)^T$ of the current
\commentByFrank{reicht das so schon?}
sample-set, representing the posterior distribution at time $t-1$, is calculated.
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}
represents the most proper state of the posterior distribution at time $t-1$, is calculated.
%
%
%\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
@@ -345,8 +347,8 @@
\caption{Heat-Map showing the number of visits per vertex after $30.000$ walks using \refeq{eq:transMultiPath}.
Both possible paths are covered and slight deviations are possible.
Additionally shows the shortest-path calculation without (dashed) and with (solid) importance-factors
used for edge-weight-adjustment.
\commentByFrank{so besser?}}
used for edge-weight-adjustment.}
\commentByFrank{so besser?}
\label{fig:multiHeatMap}
\end{figure}

14
tex/chapters/sensors.tex
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@@ -18,8 +18,8 @@
\include{gfx/baro/baro_setup_issue}
\caption{Sometimes the smartphone's barometer (here: Motorola Nexus 6) provides erroneous pressure readings
during the first seconds. Those need to be omitted before $\sigma_\text{baro}$ and
$\overline{\mObsPressure}$ are estimated.
\commentByFrank{fixed}}
$\overline{\mObsPressure}$ are estimated.}
\commentByFrank{fixed}
\label{fig:baroSetupError}
\end{figure}
%
@@ -84,17 +84,15 @@
\subsection{Step- \& Turn-Detection}
Step- and turn-detection use the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
%
However, a big disadvantage of using the state transition as proposal distribution is the high possibility of sample
A big disadvantage of using the state transition as proposal distribution is the high possibility of sample
impoverishment due to a small measurement noise. This happens since accurate observations result in high peaks
of the evaluation density and therefore the proposal density is not able to sample outside that peak \cite{Isard98:CCD}.
Additionally, erroneous or delayed measurements from absolute positioning sensors like \docWIFI{} may lead to misplaced turns.
This causes a downvoting of all states $\mStateVec_t$ with increased heading deviation.
\commentByFrank{so besser?: downvoting of states statt particles}
Therefore, we incorporate the turn-detection, as well as the related step-detection, directly into the state transition
This causes a downvoting of the posterior distribution in areas where the heading deviates.
Therefore, we incorporate the pedestrian's heading $\mObsHeading$, as well as the number of steps $\mObsSteps$, directly into the state transition
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$, which leads to a more directed sampling instead of a truly random one.
Steps and turns are detected using the smartphone's IMU and are implemented as described in \cite{Ebner-15}.

4
tex/chapters/system.tex
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@@ -24,7 +24,7 @@
where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the
relative atmospheric pressure prediction in hectopascal (hPa).
The recursive part of the density estimation contains all information up to time $t-1$.
Furthermore, the state transition models the pedestrian's movement as described in section \ref{sec:trans}.
Furthermore, the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ models the pedestrian's movement as described in section \ref{sec:trans}.
%It should be noted, that we also include the current observation $\mObsVec_{t}$ in it.
As \cite{Koeping14-PSA} has proven, we are able to include the observation $\mObsVec_{t-1}$ into the state transition.
@@ -62,7 +62,7 @@
Therefore, numerical solutions like Gaussian filters or the broad class of Monte Carlo methods are deployed \cite{sarkka2013bayesian}.
Since we assume indoor localisation to be a time-sequential, non-linear and non-Gaussian process,
a particle filter is chosen as approximation of the posterior distribution.
Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t})$ is used as proposal distribution,
Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ is used as proposal distribution,
what is also known as CONDENSATION algorithm \cite{Isard98:CCD}.