86 lines
3.5 KiB
TeX
Executable File
86 lines
3.5 KiB
TeX
Executable File
\section{Indoor Positioning System}
|
|
\label{sec:system}
|
|
|
|
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}
|
|
\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}} \enspace,
|
|
\end{array}
|
|
\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{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,
|
|
\end{equation}
|
|
%
|
|
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 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
|
|
$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS.
|
|
|
|
|
|
Assuming statistical independence, the state-evaluation density can be written as
|
|
%
|
|
\begin{equation}
|
|
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, 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 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}.
|
|
%
|
|
{\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? 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 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?}
|