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FrankE
2017-05-05 16:10:24 +02:00
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tex/chapters/system.tex
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@@ -15,33 +15,21 @@
\label{eq:recursiveDensity}
\end{equation}
A movement model, based on random walks on a graph, samples only those transitions,
that are allowed by the buildings floorplan.
%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide
the observations for both, the transition and the following evaluation step to infer the hidden state,
namely the pedestrian's location and heading
\cite{Ebner2016OPN, Fetzer2016OMC}.
This hidden state $\mStateVec$ is given by
The pedestrian's hidden state $\mStateVec$ 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 pedestrian's position in 3D space
and $\mStateHeading$ his current (absolute) heading.
where $x, y, z$ represent its position in 3D space and $\mStateHeading$ his current (absolute) heading.
The corresponding observation vector is defined as
The corresponding observation vector, given by the smartphone's sensors, is defined as
%
\begin{equation}
\mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mPressure, \mObsGPS) \enspace.
\end{equation}
%
$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the smartphone,
$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the phone,
$\mObsSteps$ describes the number of steps detected since the last filter-step,
$\mObsHeadingRel$ the (relative) angular change since the last filter-step,
$\mObsHeadingAbs$ the vague absolute heading as provided by the magnetometer,
@@ -49,7 +37,7 @@
$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS.
Assuming statistical independence, the state-evaluation density can be written as
Assuming statistical independence, the state-evaluation density from \refeq{eq:recursiveDensity} can be written as
%
\begin{equation}
p(\vec{o}_t \mid \vec{q}_t) =
@@ -61,6 +49,15 @@
\label{eq:evalDensity}
\end{equation}
%
Besides the evaluation, a movement model, based on random walks on a graph, samples only those transitions
(= pedestrian movements), that are allowed by the building's floorplan.
%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide
the observations for both, the transition and the following evaluation step to infer the hidden state,
namely the pedestrian's location and heading
\cite{Ebner2016OPN, Fetzer2016OMC}.
Absolute location information is provided by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ and
$p(\vec{o}_t \mid \vec{q}_t)_\text{gps}$, if available.
@@ -69,30 +66,58 @@
$p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}$. Finally, the barometer is used
to distinguish between normal walking and climbing stairs within
$p(\vec{o}_t \mid \vec{q}_t)_\text{activity}$.
%
The remaining observations, derived from aforementioned smartphone sensors,
namely: detected steps, and relative heading are
used within the transition model, where potential movements
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
are not only constrained by the buildings floorplan but also by
those additional observations.
As this work focuses on \docWIFI{} optimization, not all parts of
the localization system are discussed in detail.
For missing explanations please refer to \cite{Ebner2016OPN}.
Furthermore, the smartphone's IMU is used to infer the number of steps
and the relative turn angle the pedestrian has taken since the last filter-update.
While those values could be used within the evaluation \refeq{eq:evalDensity}
we apply them within the transition model to estimate the pedestrian's potential
movement $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ within the building.
Using real values to perform this movement-update instead of just scattering randomly
along the floorplan followed by downvoting within the evaluation \refeq{eq:evalDensity}
provides a more stable result.
As this work focuses on \docWIFI{} optimization, not all parts of the localization system were discussed in detail.
For missing explanations and further details on aforementioned practices,
please refer to \cite{Ebner2016OPN}.
%
Compared to this reference, absolute heading and GPS have been added as additional sensors
to further enhance the localization. Their values are incorporated by simply
comparing the sensor readings against a distribution that models the sensor's uncertainty.
to further enhance the localization. As can be seen in \refeq{eq:evalAbsHead} and \refeq{eq:evalGPS},
their values are incorporated using a simple distribution that models each sensor's uncertainty.
\todo{verteilung fuer gps und abs-heading}
\begin{equation}
p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}
=
\begin{cases}
0.7 & | \mObsVec_{\mObsHeadingAbs} - \mStateVec_{\mStateHeading} | < \SI{120}{\degree} \\
0.3 & \text{else}
\end{cases}
\label{eq:evalAbsHead}
\end{equation}
\begin{equation}
p(\vec{o}_t \mid \vec{q}_t)_\text{gps} =
\mathcal{N}(
d
\mid
0,
\sigma^2
), \enskip
d = \text{distance}(
(\mObsGPS_\text{lat}, \mObsGPS_\text{lon}),
(\mStateVec_x, \mStateVec_y)
), \enskip
\sigma = \mObsGPS_\text{accuracy}
\label{eq:evalGPS}
\end{equation}
%\todo{neues resampling? je nach dem was sich noch in der eval zeigt}
As GPS will only work outdoors, e.g. when moving from one building into another,
the system's absolute position indoors is solely provided by \docWIFI{}.
Therefore its crucial for this component to supply location estimations
that are as accurate as possible, while ensuring fast setup and
maintenance times.
The GPS sensor should enhance scenarios where multiple, unconnected buildings are involved
and the pedestrian is required to move outdoors to enter the next facility.
Indoors the GPS will usually not provide viable location estimations and the system has to
solely rely on the smartphone's \docWIFI{} observations.
Therefore its crucial for this component to supply location
estimations that are as accurate as possible,
while the component itself must be easy to set-up and maintain.
\todo{ueberleitung holprig?}
\todo{ueberleitung besser?}