98 lines
4.6 KiB
TeX
98 lines
4.6 KiB
TeX
\section{Filtering}
|
|
|
|
\label{sec:filtering}
|
|
|
|
\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.}
|
|
|
|
\subsection{Evaluation}
|
|
|
|
\section{Barometer}
|
|
|
|
\label{sec:sensBaro}
|
|
%
|
|
The probability of currently residing on a given floor is evaluated using the smartphone's barometer.
|
|
Environmental influences are circumvented by using relative pressure readings instead of absolute ones.
|
|
To reduce the impact of noisy sensors, we calculate the average of several sensor reading, carried out
|
|
while the pedestrian chooses his destination. This $\overline{\mObsPressure}$ serves as relative base.
|
|
Likewise, we estimate the sensor's uncertainty $\sigma_\text{baro}$ for later use within the evaluation step.
|
|
|
|
In order to evaluate relative pressure readings, we need a prediction to compare them with. Therefore, each
|
|
transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ estimates the state's relative pressure prediction
|
|
$\mStatePressure$ by examining every height-change ($z$-axis):
|
|
%
|
|
\begin{equation}
|
|
\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot b
|
|
,\enskip
|
|
\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
|
|
,\enskip
|
|
b \in \R
|
|
\enspace .
|
|
\label{eq:baroTransition}
|
|
\end{equation}
|
|
%
|
|
In \refeq{eq:baroTransition}, $b$ denotes the common pressure change in $\frac{\text{hPa}}{\text{m}}$.
|
|
The evaluation step compares the predicted relative pressure with the observed
|
|
one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
|
|
%
|
|
\begin{equation}
|
|
p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace.
|
|
\label{eq:baroEval}
|
|
\end{equation}
|
|
%
|
|
%
|
|
%
|
|
\subsection{Wi-Fi \& iBeacons}
|
|
%
|
|
The smartphone's \docWIFI{} and \docIBeacon{} component provides absolute location estimation by
|
|
measuring the signal-strengths of nearby transmitters. The positions of detected \docAP{}s (\docAPshort{}) and \docIBeacon{}s
|
|
are known beforehand. This allows a comparison of each measurement with a corresponding estimation
|
|
using the wall-attenuation-factor signal strength prediction model \cite{Ebner-15}. This model uses the 3D distance $d$ and the
|
|
number of floors $\Delta f$ between transmitter and the state-in-question:
|
|
%
|
|
\begin{equation}
|
|
P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace ,
|
|
\end{equation}
|
|
%
|
|
As transmitters are assumed to be statistically independent, the overall probability to measure their predictions at a given location is:
|
|
%
|
|
\begin{equation}
|
|
\mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} =
|
|
\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace .
|
|
\label{eq:wifiTotal}
|
|
\end{equation}
|
|
%
|
|
The prediction model itself needs three parameters per \docAPshort{}: $\mTXP$ measured at a distance
|
|
$\mMdlDist_0$ (usually \SI{1}{\meter}), the path-loss exponent $\mPLE$ describing the environment
|
|
and the attenuation per floor $\mWAF$.
|
|
\commentByFrank{aufs andere paper beziehen zum kuerzen?}
|
|
To reduce the system's setup time, we use the same values for all \docAP{}s at the cost of accuracy.
|
|
All parameters are chosen empirically. Further details on how to determine this parameters exactly,
|
|
can be found in \cite{PathLossPredictionModelsForIndoor}.
|
|
|
|
The same holds for the \docIBeacon{} component, except $\mTXP$, which is broadcasted by each beacon.
|
|
As \docIBeacon{}s cover only a small area, $\mPLE$ is usually much smaller compared to the one needed for \docWIFI{}.
|
|
|
|
%
|
|
|
|
|
|
\subsection{Transition}
|
|
|
|
The transition step depends on random walks on a graph, generated from the buildings floorplan
|
|
\todo{cite}. This setup allows only valid movements, as ambient conditions (walls, doors, etc.) are considered.
|
|
|
|
Furthermore, we assume the pedestrian's desired destination to be known beforehand. This prior knowledge is evaluated
|
|
during the random walk, to favour movements approaching the chosen destination.
|
|
|
|
To ensure the transition step provides a viable posterior distribution, we include some sensors directly into the transition step.
|
|
Adding them to the evaluation instead, would lead to sample impoverishment when using Monte Carlo methods.
|
|
|
|
\subsection{Step- \& Turn-Detection}
|
|
%
|
|
Steps and turns are detected using the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
|
|
|
|
%
|
|
|
|
\subsection{Activity-Detection}
|
|
\todo{write}
|
|
|