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recursive section done

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toni
2018-04-03 13:14:59 +02:00
parent b237667950
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6
tex/chapters/introduction.tex
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@@ -21,7 +21,7 @@ We also use a novel approach for finding an exact estimation of the pedestrian's
Many historical buildings, especially bigger ones like castles, monasteries or churches, are built of massive stone walls and have annexes from different historical periods out of different construction materials.
This leads to problems for methods using received signal strengths (RSS) from \docWIFI{} or Bluetooth, due to a high signal attenuation between different rooms.
Many unknown quantities like the walls definitive material or thickness make it expensive to determine important parameters, \eg{} the signal's depletion over distance.
Many unknown quantities like the walls definitive material or thickness make it expensive to determine important parameters, \eg{} the signal's depletion over distance.
Additionally, most wireless approaches require a line-of-sight assumption.
Thus, the performance will be even more limited due to the irregularly shaped spatial structure of such buildings.
Our approach tries to avoid those problems.
@@ -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.
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.
\todo{der satz davor macht keinen sinn. fingerprint vs opt?!}
We omit time-consuming approaches like classic fingerprinting or measuring the exact positions of access-points.
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.
A barometer based activity recognition enables going into the third dimension and problems occurring from multimodalities and impoverishment are taken into account.

42
tex/chapters/system.tex
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@@ -1,13 +1,41 @@
\section{Recursive State Estimation}
\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.