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added smoothing and performance

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Toni
2016-07-11 17:51:32 +02:00
parent 668248fa79
commit f8d5449dbc
4 changed files with 57 additions and 9 deletions
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competition/tex/chapters/components.tex
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@@ -27,4 +27,4 @@ By assuming statistical independence of all sensors, the probability density of
\input{chapters/wifi.tex} \input{chapters/wifi.tex}
\input{chapters/stepturn.tex} \input{chapters/stepturn.tex}
\input{chapters/graph.tex} \input{chapters/graph.tex}
\input{chapters/smoothing.tex}

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competition/tex/chapters/introduction.tex
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@@ -68,11 +68,4 @@ System setup is very easily and no fingerprinting is required.
\input{chapters/components.tex} \input{chapters/components.tex}
\input{chapters/performance.tex}
\begin{itemize}
\item Fixed-lag smoother
\end{itemize}
\section{Performance Overview}
Wie toll sind wir? kurzer ueberblick der ergebnisse in einer tabelle und paar worte dazu. eventl graphic.

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competition/tex/chapters/performance.tex Normal file
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\section{Performance Overview}
% all paths we evaluated
\begin{figure}
\input{gfx/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.}
%\commentByFrank{font war korrekt, aber die groesse war zu gross im vgl. zu den anderen}
\label{fig:paths}
\end{figure}
%
To give a brief overview of the system's performance we look back at the evaluation provided in \cite{ebner-16}.
Here, 4 distinct walks were conducted within the faculty building (cf. fig. \ref{fig:paths}).
No smoothing was carried out.
We used \SI{7500}{particles} as realization and calculated the weighted arithmetic mean of the particles as state estimation.
The ground truth was measured by recording a timestamp at marked spots on the walking route, similar as described in the competition guidelines.
Starting uniformly distributed, the median error for all conducted walks are listed in table \ref{tbl:errNexus} for the Motorola Nexus 6 and the Samsung Galaxy S5.
Additionally performing a smoothing step, would further improve the results and reduces temporal errors, as shown in \cite{fetzer-16}.
%
\begin{table}[h]
\caption{Median error for all conducted walks.}
\label{tbl:errNexus}
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
\textbf{Device:} & Path1 & Path2 & Path3 & Path4 \\\hline
Motorola Nexus 6 & \SI{2.62}{\meter} & \SI{2.14}{\meter} & \SI{2.46}{\meter} & \SI{2.75}{\meter} \\\hline
Samsung Galaxy S5 & \SI{ 6.35}{\meter} & \SI{4.21}{\meter} & \SI{5.03}{\meter} & \SI{6.79}{\meter} \\\hline
\end{tabular}
\end{table}

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competition/tex/chapters/smoothing.tex Normal file
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\subsection{Fixed-lag smoothing}
Within \cite{fetzer-16} we added an additional smoothing step to the localisation procedure.
In contrast to normal filtering, smoothing methods are able to incorporate future measurements instead of just using current and past data.
Therefore, they are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$.
Especially interesting for real-time applications is the so-called fixed-lag smoothing.
In fixed-lag smoothing, one tries to estimate the current state, given measurements up to a time $t + \tau$, where $\tau$ is a predefined lag.
By running backwards in time, they are able to remove multimodalities and improve the overall localisation result.
We can distinguish between two different smoothing algorithms: Forward-backward smoothing \cite{doucet2000} and backward simulation \cite{Godsill04:MCS}.
Both perform very similar and are reweighting possible states based on a smoothing transition model.
The smoothing transition model calculates the probability of being in a state $\vec{q}_{t+1}$ in regard to previous states and the pedestrian's walking behaviour.
Therefore, we compare the distance, angle and height between $\vec{q}_{t+1}$ and $\vec{q}_{t}$ in regard to the measurements gettered at time $t$.
The resulting likelihood is then used for reweighting.
%By writing
%\begin{equation}
%p(\vec{q}_{t+1} \mid \vec{q}_t, \mObsVec_t)_{\text{step}} = \mathcal{N}(\Delta d_t \mid \mu_{\text{step}}, \sigma_{\text{step}}^2)
%\label{eq:smoothingTransDistance}
%\end{equation}
%we receive a statement about how likely it is to cover a distance $\Delta d_t$ between two states $\vec{q}_{t+1}$ and $\vec{q}_{t}$.
%In the easiest case, $\Delta d_t$ is the euclidean distance between two states.
%The average step length $\mu_{\text{step}}$ is based on the pedestrian's walking speed and $\sigma_{\text{step}}^2$ denotes the step length's variance.