FHWS/OTHER2017
Archived
3
0
Fork 0
Code Issues 4 Pull Requests Releases Wiki Activity

TeX

Browse Source
This commit is contained in:
FrankE
2017-04-25 11:39:33 +02:00
parent aea38def0b
commit 8a3de63075
4 changed files with 131 additions and 125 deletions
Download Patch File Download Diff File Expand all files Collapse all files

64
tex/chapters/system.tex
View File

@@ -1,15 +1,10 @@
\section{Indoor Positioning System}
\label{sec:system}
Our smartphone-based indoor localization system estimates the current location and heading
using recursive density estimation.
A graph based movement model provides the transition,
%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
while the smartphone's accelerometer, gyroscope, magnetometer provide the observations
for the following evaluation step to infer the hidden state, namely the pedestrian's location and heading
\cite{Ebner-16, Fetzer-16}.
Our smartphone-based indoor localization system estimates a pedestrian's current location and heading
using recursive density estimation seen in \refeq{eq:recursiveDensity}.
\begin{equation}
\begin{equation}
\arraycolsep=1.2pt
\begin{array}{ll}
&p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\
@@ -20,7 +15,16 @@
\label{eq:recursiveDensity}
\end{equation}
The hidden state $\mStateVec$ is given by
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{Ebner-16, Fetzer-16}.
This hidden state $\mStateVec$ is given by
\begin{equation}
\mStateVec = (x, y, z, \mStateHeading),\enskip
x, y, z, \mStateHeading \in \R \enspace,
@@ -28,54 +32,54 @@
%
where $x, y, z$ represent the pedestrian's position in 3D space
and $\mStateHeading$ his current (absolute) heading.
%
The corresponding observation vector is defined as
%
\begin{equation}
\mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mObsGPS) \enspace.
\end{equation}
%
$\mRssiVecWiFi$ contains the measurements of all nearby \docAP{}s (\docAPshort{}s),
$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the smartphone,
$\mObsSteps$ describes the number of steps detected since the last filter-step,
$\mObsHeadingRel$ the (relative) angular change since the last filter-step,
$\mObsHeadingAbs$ the current, vague absolute heading and
$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon )$ the current location (if available) given by the GPS.
$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS.
Assuming statistical independence, the state evaluation's density can be written as
Assuming statistical independence, the state-evaluation density can be written as
%
\begin{equation}
%\begin{split}
p(\vec{o}_t \mid \vec{q}_t) =
p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}\enskip
p(\vec{o}_t \mid \vec{q}_t)_\text{gps}
\enspace.
p(\vec{o}_t \mid \vec{q}_t) =
p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}\enskip
p(\vec{o}_t \mid \vec{q}_t)_\text{gps}
\enspace.
\label{eq:evalDensity}
\end{equation}
%
The remaining observations,
The remaining observations, derived from aforementioned smartphone sensors,
namely: detected steps, relative- and absolute heading are
used within the transition model, where potential movements
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ are sampled
based on those sensor values.
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
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{Ebner-16}.
%
Since then, absolute heading and GPS have been added as additional sensors
to further enhance the localization by comparing the sensor values
using some distribution.
{\bf Since then}, 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.
\todo{neues resampling?}
\todo{neues resampling? je nach dem was sich noch in der eval zeigt}
\todo{ueberleitung}
\todo{
die absolute positionierung kommt aus dem wlant,
dafür braucht man entweder viele fingerprints oder ein modell
}
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 the \docWIFI{} component.
Therefore its crucial for this component to provide location estimations
that are as accurate as possible, while ensuring fast setup and
maintenance times.
\todo{ueberleitung holprig?}