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recursive section done

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toni
2018-04-03 13:14:59 +02:00
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tex/chapters/introduction.tex
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@@ -33,8 +33,8 @@ However, this is contrary to most costumers expectations of a fast to deploy and
In addition, this is not only a question of costs incurred, but also for buildings under monumental protection, what does not allow for larger construction measures. In addition, this is not only a question of costs incurred, but also for buildings under monumental protection, what does not allow for larger construction measures.
To sum up, this work presents a smartphone-based localization system using a particle filter to incorporate different probabilistic models. To sum up, this work presents a smartphone-based localization system using a particle filter to incorporate different probabilistic models.
We omit time-consuming approaches like classic fingerprinting or measuring the exact positions of access-points by using a simple optimization scheme. We omit time-consuming approaches like classic fingerprinting or measuring the exact positions of access-points.
\todo{der satz davor macht keinen sinn. fingerprint vs opt?!} Instead we use a simple optimization scheme based on reference measurements to estimate a corresponding Wi-Fi model.
The pedestrian's movement is modeled realistically using a navigation mesh, based on the building's floorplan. The pedestrian's movement is modeled realistically using a navigation mesh, based on the building's floorplan.
A barometer based activity recognition enables going into the third dimension and problems occurring from multimodalities and impoverishment are taken into account. A barometer based activity recognition enables going into the third dimension and problems occurring from multimodalities and impoverishment are taken into account.

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tex/chapters/system.tex
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@@ -1,13 +1,41 @@
\section{Recursive State Estimation} \section{Recursive State Estimation}
\label{sec:rse} \label{sec:rse}
1/2 Seite, also kurz halten.
\begin{itemize}
\item klassiker.. also eigenltich alles beim alten.
\end{itemize}
We consider indoor localization to be a time-sequential, non-linear and non-Guassian state estimation problem.
The filtering equation to calculated the posterior is given by the recursion
%
\begin{equation}
\arraycolsep=1.2pt
\begin{array}{ll}
&p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\
&\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}}
\end{array}
\enspace ,
\label{equ:bayesInt}
\end{equation}
%
where $\mState$ is the hidden state and $\mObs_t$ provides the corresponding observation vector at time $t$.
As realization of \eqref{equ:bayesInt} we use the well-known CONDENSATION algorithm \cite{Isard98:CCD}.
Here, the transition is used as proposal distribution and a resampling step is utilized to handle the phenomenon of weight degeneracy.
The state $\mState$ is given by
%
\begin{equation}
\mStateVec = (x, y, z, \mStateHeading),\enskip
x, y, z, \mStateHeading \in \R \enspace,
\end{equation}
%
where $x, y, z$ represent the position in 3D space and $\mStateHeading$ is the user's current (absolute) heading.
The observation vector is defined as
%
\begin{equation}
\mObsVec = (\mRssiVec_\text{wifi}, \mObsHeading, \mObsSteps, \mObsActivity) \enspace .
\end{equation}
%
Here, $\mRssiVec_\text{wifi}$ contains the signal strength measurements of all \docAP{}s currently visible to the phone. $\mObsHeading$ provides the relative angular change and $\mObsSteps$ the number of steps since the last filter-step.
The result of a simple activity recognition using the phone's barometer is given by $\mObsActivity$, which is one of: unknown, standing, walking, walking up the stairs or walking down the stairs.