34 lines
1.5 KiB
TeX
34 lines
1.5 KiB
TeX
\section{Component Description}
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Our indoor localisation solely uses the sensors provided by almost each commodity smartphone.
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The readings of all those sensors are fused using recursive density estimation, directly on the phone:
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\commentByFrank{state beschreiben: x, y, z, heading. oder machst du das schon weiter oben? dann kann vermutlicha uch die formel hier weg}
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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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\docWIFI{} and (if available) \docIBeacon{}s serve as absolute positioning component. If the smartphone provides
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a barometer, its measurements are used as an additional, relative verification for the current $z$-component
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of the pedestrian's location.
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The transition in \refeq{eq:recursiveDensity} is carried out using random walks on a graph, which is built offline, and uses
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the building's floorplan. During the localisation process, the smartphone's IMU (accelerometer, gyroscope) is used to constrain the random walk
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in both, distance and heading.
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The recursive density estimation is implemented using a particle-filter.
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\input{chapters/barometer.tex}
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\input{chapters/wifi.tex}
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\input{chapters/stepturn.tex}
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\input{chapters/graph.tex}
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