97 lines
4.1 KiB
TeX
Executable File
97 lines
4.1 KiB
TeX
Executable File
\section{Indoor Positioning System}
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\label{sec:system}
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Our smartphone-based indoor localization system estimates a pedestrian's current location and heading
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using recursive density estimation seen in \refeq{eq:recursiveDensity}.
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\begin{equation}
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%\arraycolsep=1.2pt
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%\begin{array}{ll}
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p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\
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\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
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\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
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\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}} \enspace,
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%\end{array}
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\label{eq:recursiveDensity}
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\end{equation}
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A movement model, based on random walks on a graph, samples only those transitions,
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that are allowed by the buildings floorplan.
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%$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
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The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide
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the observations for both, the transition and the following evaluation step to infer the hidden state,
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namely the pedestrian's location and heading
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\cite{Ebner2016OPN, Fetzer2016OMC}.
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This hidden state $\mStateVec$ is given by
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\begin{equation}
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\mStateVec = (x, y, z, \mStateHeading),\enskip
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x, y, z, \mStateHeading \in \R \enspace,
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\end{equation}
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%
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where $x, y, z$ represent the pedestrian's position in 3D space
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and $\mStateHeading$ his current (absolute) heading.
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The corresponding observation vector is defined as
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%
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\begin{equation}
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\mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mPressure, \mObsGPS) \enspace.
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\end{equation}
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%
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$\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the smartphone,
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$\mObsSteps$ describes the number of steps detected since the last filter-step,
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$\mObsHeadingRel$ the (relative) angular change since the last filter-step,
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$\mObsHeadingAbs$ the current, vague absolute heading,
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$\mPressure$ the ambient pressure in hPa and
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$\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS.
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Assuming statistical independence, the state-evaluation density can be written as
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%
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\begin{equation}
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p(\vec{o}_t \mid \vec{q}_t) =
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p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}\enskip
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p(\vec{o}_t \mid \vec{q}_t)_\text{gps}\enskip
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p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}\enskip
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p(\vec{o}_t \mid \vec{q}_t)_\text{activity}\enskip
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\enspace.
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\label{eq:evalDensity}
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\end{equation}
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%
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Absolute location information is provided by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ and
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$p(\vec{o}_t \mid \vec{q}_t)_\text{gps}$, if available.
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The vague absolute heading provided by
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the smartphone's magnetometer is included using a simple heuristic for
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$p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}$. Finally, the barometer is used
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to distinguish between normal walking and climbing stairs within
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$p(\vec{o}_t \mid \vec{q}_t)_\text{activity}$.
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%
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The remaining observations, derived from aforementioned smartphone sensors,
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namely: detected steps, and relative heading are
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used within the transition model, where potential movements
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$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$
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are not only constrained by the buildings floorplan but also by
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those additional observations.
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As this work focuses on \docWIFI{} optimization, not all parts of
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the localization system are discussed in detail.
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For missing explanations please refer to \cite{Ebner2016OPN}.
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%
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Compared to this reference, absolute heading and GPS have been added as additional sensors
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to further enhance the localization. Their values are incorporated by simply
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comparing the sensor readings against a distribution that models the sensor's uncertainty.
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%\todo{neues resampling? je nach dem was sich noch in der eval zeigt}
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As GPS will only work outdoors, e.g. when moving from one building into another,
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the system's absolute position indoors is solely provided by \docWIFI{}.
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Therefore its crucial for this component to supply location estimations
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that are as accurate as possible, while ensuring fast setup and
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maintenance times.
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\todo{ueberleitung holprig?}
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