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latest TeX: grid, experiments, conclusion. some gfx changed

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FrankE
2016-02-14 18:35:33 +01:00
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tex/chapters/sensors.tex
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@@ -4,33 +4,40 @@
\subsection{Barometer}
\label{sec:sensBaro}
As stated by \cite{Muralidharan14-BPS}, ambient pressure readings are highly influenced by environmental conditions like the weather, time-of-day and others.
Thus, relative pressure readings are preferred over absolute ones.
However, due to noisy sensors, one single reading is not enough as a relative base.
Harnessing the usual setup time of a navigation-system (route calculation, user checking the route) we use the average of all barometer readings during this timeframe as relative base $\overline{\mObsPressure}$.
However, it is often necessary to omit the first few sensors readings, as the sensor needs some time to settle.
Otherwise the estimated base would be far off the real values as shown in fig. \ref{fig:baroSetupError}.
Besides, we use the system's setup time to estimate the sensors uncertainty $\sigma_\text{baro}$ for later use within the evaluation.
%
As stated by \cite{Muralidharan14-BPS}, ambient pressure readings are highly influenced by environmental conditions
like the weather, time-of-day and others. Thus, relative pressure readings are preferred over absolute ones.
However, due to noisy sensors, more than one reading is required to estimate the relative base.
Harnessing the usual setup time of a navigation-system (route calculation, user checking the route, etc.)
we use the average of all barometer readings during this timeframe as estimated base $\overline{\mObsPressure}$.
Moreover, it is often necessary to omit some initial sensors readings, as the smartphone's sensor needs some time
to settle. Besides, we use the setup timeframe to estimate the sensors uncertainty $\sigma_\text{baro}$ for later
use within the evaluation. Fig. \ref{fig:baroSetupError} depicts actual sensor-readings including aforementioned
error conditions.
%
\begin{figure}
\include{gfx/baro/baro_setup_issue}
\caption{Sometimes the barometer provides erroneous \SI{}{\hpa} readings during the first seconds. Those
need to be omitted before $\sigma_\text{baro}$ and $\overline{\mObsPressure}$ are estimated.}
\label{fig:baroSetupError}
\end{figure}
%
During each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$, we need a corresponding, relative pressure prediction $\mStatePressure$ which is adjusted according to the resulting $z$-change, if any:
%
%
During each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$, we need a corresponding, relative
pressure prediction $\mStatePressure$ which is adjusted according to the resulting $z$-change:
%
\begin{equation}
\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot \SI{0.105}{\hpa}
\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
.
\label{eq:baroTransition}
\end{equation}
%
The evaluation following the transition then compares the predicted relative pressure with the observed one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
%
In \refeq{eq:baroTransition}, $b$ denotes the usual pressure change in $\frac{\text{hPa}}{\text{m}}$.
The evaluation, following the transition, compares the predicted relative pressure with the observed
one using a normal distribution utilizing 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}).
\label{eq:baroEval}
@@ -39,45 +46,51 @@ The evaluation following the transition then compares the predicted relative pre
\subsection{Wi-Fi \& iBeacons}
For additional absolute location hints, we use the smartphones Wi-Fi and iBeacon sensor to measure the signal-strengths
of nearby transmitters. As the positions of both \docAP{}s and \docIBeacon{}s are known beforehand, we compare
each measurement with its corresponding signal strength prediction which is defined by the 3D distance $d$
and the number of floors $\Delta f$ between the \docAPshort{} and the particle
%
Additional absolute location hints, are provided by the smartphone's \docWIFI{} and \docIBeacon{} component,
measuring the signal-strengths of nearby transmitters. As the positions of both \docAP{}s and \docIBeacon{}s
are known beforehand, we compare each measurement with its corresponding signal strength prediction using
the wall-attenuation-factor model \cite{Ebner-15}. This prediction depends on the 3D distance $d$ from the
\docAPshort{} and the number of floors $\Delta f$ between the \docAPshort{} and the state-in-question:
%
\begin{equation}
P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF,
\end{equation}
%
and calculate the resulting probability as described in \cite{Ebner-15}:
%
%
The probability to measure this prediction given a 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).
\label{eq:wifiTotal}
\end{equation}
For the \docWIFI{} component we thus need two parameters per \docAPshort{}: $\mTXP$ measured at a distance
$\mMdlDist_0$ (usually \SI{1}{\meter}) and the path-loss exponent $\mPLE$ describing the environment.
For the \docWIFI{} component we thus need three parameters per \docAPshort{}: $\mTXP$ measured at a distance
$\mMdlDist_0$ (usually \SI{1}{\meter}), the path-loss exponent $\mPLE$ describing the environment
and $\mWAF$ denoting the attenuation per floor.
To reduce complexity and system setup time, we use the same values for all \docAP{}s at the cost of accuracy.
While, $\mTXP$ is best determined using averaged measurements at a single location,
a good estimation of $\mPLE$ requires several measurements and numerical optimization \cite{PathLossPredictionModelsForIndoor}.
$\mPLE$ is thus chosen empirically.
a good estimation of $\mPLE$ and $\mWAF$ requires several measurements and numerical optimization
\cite{PathLossPredictionModelsForIndoor}. $\mPLE$ and $\mWAF$ are thus chosen empirically.
For the \docIBeacon{} component we also use \refeq{eq:wifiTotal} but $\mTXP$ is transmitted by each beacon.
Due to the short-range coverage the model parameters require less consideration of the senders ambient conditions (e.g. walls).
Therefore, a smaller $\mPLE$ can be chosen to model the signal strength prediction for \docIBeacon{}s.
Due to the short-range coverage the model parameters require less consideration of the senders ambient conditions
(e.g. walls). Therefore, a smaller $\mPLE$ can be chosen to model the signal strength prediction for \docIBeacon{}s.
\subsection{Step- \& Turn-Detection}
\subsection{Step- \& Turn-Detection}
A big disadvantage of using the state transition as proposal distribution is the high possibility of sample impoverishment due to a small measurement noise.
This happens since accurate observations result in high peaks of the evaluation density and therefore the proposal density is not able to sample outside that peak \cite{Isard98:CCD}.
Additionally, erroneous or delayed measurements from absolute positioning sensors like \docWIFI{} may lead to misplaced turns.
This causes a downvoting of particles with increased heading deviation.
Therefore, we incorporate the turn-detection, as well as the related step-detection, directly into the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$. This leads to a more directed sampling instead of a truly random one.
Step- and turn-detection uses the smartphone's IMU and is implemented as described in \cite{Ebner-15}.
%
However, a big disadvantage of using the state transition as proposal distribution is the high possibility of sample
impoverishment due to a small measurement noise. This happens since accurate observations result in high peaks
of the evaluation density and therefore the proposal density is not able to sample outside that peak \cite{Isard98:CCD}.
Additionally, erroneous or delayed measurements from absolute positioning sensors like \docWIFI{} may lead to misplaced turns.
This causes a downvoting of particles with increased heading deviation.
Therefore, we incorporate the turn-detection, as well as the related step-detection, directly into the state transition
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$, which leads to a more directed sampling instead of a truly random one.