84 lines
4.7 KiB
TeX
84 lines
4.7 KiB
TeX
\section{Sensors}
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\subsection{Barometer}
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\label{sec:sensBaro}
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As stated by \cite{Muralidharan14-BPS}, ambient pressure readings are highly influenced by environmental conditions like the weather, time-of-day and others.
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Thus, relative pressure readings are preferred over absolute ones.
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However, due to noisy sensors, one single reading is not enough as a relative base.
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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 $\overline{\mObsPressure}$.
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However, it is often necessary to omit the first few sensors readings, as the sensor needs some time to settle.
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Otherwise the estimated base would be far off the real values as shown in fig. \ref{fig:baroSetupError}.
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Besides, we use the system's setup time to estimate the sensors uncertainty $\sigma_\text{baro}$ for later use within the evaluation.
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%
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\begin{figure}
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\include{gfx/baro/baro_setup_issue}
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\caption{Sometimes the barometer provides erroneous \SI{}{\hpa} readings during the first seconds. Those
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need to be omitted before $\sigma_\text{baro}$ and $\overline{\mObsPressure}$ are estimated.}
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\label{fig:baroSetupError}
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\end{figure}
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%
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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:
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%
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\begin{equation}
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\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot \SI{0.105}{\hpa}
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,\enskip
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\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
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.
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\label{eq:baroTransition}
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\end{equation}
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%
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The evaluation following the transition then compares the predicted relative pressure with the observed one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
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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}).
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\label{eq:baroEval}
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\end{equation}
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\subsection{Wi-Fi \& iBeacons}
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For additional absolute location hints, we use the smartphones Wi-Fi and iBeacon sensor to measure the signal-strengths
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of nearby transmitters. As the positions of both \docAP{}s and \docIBeacon{}s are known beforehand, we compare
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each measurement with its corresponding signal strength prediction which is defined by the 3D distance $d$
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and the number of floors $\Delta f$ between the \docAPshort{} and the particle
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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,
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\end{equation}
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%
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and calculate the resulting probability as described in \cite{Ebner-15}:
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%
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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).
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\label{eq:wifiTotal}
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\end{equation}
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For the \docWIFI{} component we thus need two parameters per \docAPshort{}: $\mTXP$ measured at a distance
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$\mMdlDist_0$ (usually \SI{1}{\meter}) and the path-loss exponent $\mPLE$ describing the environment.
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To reduce complexity and system setup time, we use the same values for all \docAP{}s at the cost of accuracy.
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While, $\mTXP$ is best determined using averaged measurements at a single location,
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a good estimation of $\mPLE$ requires several measurements and numerical optimization \cite{PathLossPredictionModelsForIndoor}.
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$\mPLE$ is thus chosen empirically.
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For the \docIBeacon{} component we also use \refeq{eq:wifiTotal} but $\mTXP$ is transmitted by each beacon.
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Due to the short-range coverage the model parameters require less consideration of the senders ambient conditions (e.g. walls).
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Therefore, a smaller $\mPLE$ can be chosen to model the signal strength prediction for \docIBeacon{}s.
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\subsection{Step- \& Turn-Detection}
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A big disadvantage of using the state transition as proposal distribution is the high possibility of sample impoverishment due to a small measurement noise.
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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}.
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Additionally, erroneous or delayed measurements from absolute positioning sensors like \docWIFI{} may lead to misplaced turns.
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This causes a downvoting of particles with increased heading deviation.
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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.
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