110 lines
5.6 KiB
TeX
110 lines
5.6 KiB
TeX
\section{Filtering}
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\label{sec:filtering}
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\commentByToni{Bin mir nicht sicher ob wir diese Section überhaupt brauchen. Könnte man bestimmt auch einfach unter Section 3 packen. Aber dann können wir ungestört voneinander schreiben.}
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\subsection{Evaluation}
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\section{Barometer}
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\label{sec:sensBaro}
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%
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The probability of currently residing on a given floor is evaluated using the smartphone's barometer.
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Environmental influences are circumvented by using relative pressure readings instead of absolute ones.
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To reduce the impact of noisy sensors, we calculate the average of several sensor reading, carried out
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while the pedestrian chooses his destination. This $\overline{\mObsPressure}$ serves as relative base.
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Likewise, we estimate the sensor's uncertainty $\sigma_\text{baro}$ for later use within the evaluation step.
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In order to evaluate relative pressure readings, we need a prediction to compare them with. Therefore, each
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transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ estimates the state's relative pressure prediction
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$\mStatePressure$ by examining every height-change ($z$-axis):
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%
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\begin{equation}
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\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot b
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,\enskip
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\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
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,\enskip
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b \in \R
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\enspace .
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\label{eq:baroTransition}
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\end{equation}
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%
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In \refeq{eq:baroTransition}, $b$ denotes the common pressure change in $\frac{\text{hPa}}{\text{m}}$.
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The evaluation step compares the predicted relative pressure with the observed
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one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
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%
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\begin{equation}
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p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace.
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\label{eq:baroEval}
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\end{equation}
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%
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%
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%
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\subsection{Wi-Fi \& iBeacons}
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%
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The smartphone's \docWIFI{} and \docIBeacon{} component provides absolute location estimation by
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measuring the signal-strengths of nearby transmitters. The positions of detected \docAP{}s (\docAPshort{}) and \docIBeacon{}s
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are known beforehand. This allows a comparison of each measurement with a corresponding estimation
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using the wall-attenuation-factor signal strength prediction model \cite{Ebner-15}. This model uses the 3D distance $d$ and the
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number of floors $\Delta f$ between transmitter and the state-in-question:
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%
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\begin{equation}
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P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace ,
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\end{equation}
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%
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As transmitters are assumed to be statistically independent, the overall probability to measure their predictions at a given location is:
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\begin{equation}
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\mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} =
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\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace .
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\label{eq:wifiTotal}
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\end{equation}
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%
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The prediction model itself needs three parameters per \docAPshort{}: $\mTXP$ measured at a distance
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$\mMdlDist_0$ (usually \SI{1}{\meter}), the path-loss exponent $\mPLE$ describing the environment
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and the attenuation per floor $\mWAF$.
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\commentByFrank{aufs andere paper beziehen zum kuerzen?}
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To reduce the system's setup time, we use the same values for all \docAP{}s at the cost of accuracy.
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All parameters are chosen empirically. Further details on how to determine this parameters exactly,
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can be found in \cite{PathLossPredictionModelsForIndoor}.
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The same holds for the \docIBeacon{} component, except $\mTXP$, which is broadcasted by each beacon.
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As \docIBeacon{}s cover only a small area, $\mPLE$ is usually much smaller compared to the one needed for \docWIFI{}.
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%
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\subsection{Transition}
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The transition step depends on random walks on a graph, generated from the buildings floorplan
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\todo{cite}. This setup allows only valid movements, as ambient conditions (walls, doors, etc.) are considered.
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Furthermore, we assume the pedestrian's desired destination to be known beforehand. This prior knowledge is evaluated
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during the random walk, to favour movements approaching the chosen destination.
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To ensure the transition step provides a viable posterior distribution, we include some sensors directly into the transition step.
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Adding them to the evaluation instead, would lead to sample impoverishment when using Monte Carlo methods.
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\subsection{Step- \& Turn-Detection}
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%
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Steps and turns are detected using the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
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%
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\subsection{Activity-Detection}
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% Activity Recognition
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% Naives Bayes als Klassifikator
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% Features -> 1: Variance of mean 2: Differenz zwischen Barometer
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% Zeitintervall für das die Merkmale berechnet werden
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The transition model includes a simple recognizer of different locomotion modes like normal walking or ascending/descending stairs. The reasoning behind this is to favour paths that correspond with the detected locomotion mode.
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We use a Naives Bayes classifier with two features. For this, the sensor signals are split in sliding windows. Each window has a length of one second and overlaps 500 ms with its prior window.
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The first feature is the variance of the accelerometer's magnitude during a window and the second feature is the difference between the last and first barometer measurement of the particular window.
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Based on these features the classifier assigns an activity to each sliding window.
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\todo{Was passiert wenn ein überlappendes Fenster zwei verschiedene Aktivitäten zugewiesen bekommt? Sliding windows evtl. weglassen?}
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