diff --git a/tex/bare_conf.tex b/tex/bare_conf.tex index f0460e0..b478a7d 100644 --- a/tex/bare_conf.tex +++ b/tex/bare_conf.tex @@ -141,12 +141,12 @@ % affiliations \author{ - \IEEEauthorblockN{Toni Fetzer, Frank Ebner and Frank Deinzer}% + \IEEEauthorblockN{Frank Ebner, Toni Fetzer and Frank Deinzer}% \IEEEauthorblockA{% Faculty of Computer Science and Business Information Systems\\ University of Applied Sciences W\"urzburg-Schweinfurt\\ W\"urzburg, Germany\\ - \{toni.fetzer, frank.ebner, frank.deinzer\}@fhws.de\\ + \{frank.ebner, toni.fetzer, frank.deinzer\}@fhws.de\\ } } @@ -186,8 +186,6 @@ \input{chapters/sensors} -\input{chapters/floorplan} - \input{chapters/grid} \input{chapters/experiments} diff --git a/tex/chapters/sensors.tex b/tex/chapters/sensors.tex index fa6bdfa..fb31fd1 100644 --- a/tex/chapters/sensors.tex +++ b/tex/chapters/sensors.tex @@ -3,26 +3,23 @@ \subsection{Barometer} \label{sec:sensBaro} - As stated by \cite{ipin2015} \todo{and the other paper directly}, 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 \todo{cite oder grafik? je nach platz}, 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 realtive base $\overline{\mObsPressure}$. However, it is often necessary to omit the first few - sensors readings, as the sensor needs some time to settle and the estimated base would otherwise be far off - the real values (see 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, 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. +% \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, if any: +% \begin{equation} \mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot \SI{0.105}{\hpa} ,\enskip @@ -30,10 +27,8 @@ . \label{eq:baroTransition} \end{equation} - - \commentByToni{Woher kommen die 0.105hPa? Sollte man dazu schreiben.} - The evaluation following the transition then compares the predicted relative pressure with the observed one - using a normal distribution with the previously estimated $\sigma_\text{baro}$: +% +The evaluation following the transition then compares the predicted relative pressure with the observed one using a normal distribution with the previously estimated $\sigma_\text{baro}$: \begin{equation} p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}). @@ -46,17 +41,17 @@ \subsection{Wi-Fi \& iBeacons} - For additional absolute location hints, we use the Smartphones Wi-Fi and iBeacon sensor to measure the signal-strengths + 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 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 - +% \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{ipin2015}: - +% + and calculate the resulting probability as described in \cite{Ebner-15}: +% \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). @@ -67,24 +62,30 @@ $\mMdlDist_0$ (usually \SI{1}{\meter}) and the path-loss exponent $\mPLE$ describing the environment. 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{etwas_aus_der_MA}. + a good estimation of $\mPLE$ requires several measurements and numerical optimization \cite{PathLossPredictionModelsForIndoor}. $\mPLE$ is thus chosen empirically. - For the \docIBeacon{} component we also use \refeq{eq:wifiTotal} but $\mTXP$ is transmitted by each beacon. - Again, $\mPLE$ is determined emprically. \todo{faellt hier meist kleiner aus, weil ja kuerzere reichweite etc} + 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. - - - - \subsection{Step- \& Turn-Detection} - - To prevent degradation within the particle-filter \cite{??} due to downvoting of particles with increased - heading deviation, we incorporate the turn-detection as control-data -\commentByToni{ich würde es jetzt nicht unbedingt controldata nennen. einfach nur das wir die observation in die transition integrieren. fertig. für den cite oben habe ich eine sehr sehr gute quelle. der beschreibt das ganz gut. hab das bei mir in der MA so begründet: Another big disadvantage 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 importance density is not able to sample outside that peak [IB98b].} +\subsection{Step- \& Turn-Detection} + +\commentByToni{da muessen wir nochmal drueber reden. das problem ist glaube ich. das die state transition vorher zu wenig gestreut hat und dadurch auch zu wenige particles in "hochwinkligen" bereichen hatte. dann haben die turns immer entsprechen einen delay gehabt. bin mir also nicht sicher ob es wirklich das downvoting / sample impoverishment ist. hast du da vielleicht noch ein paar infos für mich? weil unser sigma war ja immer rießig... quasi fast gleichverteilt.} + +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}. This causes a downvoting of particles with increased heading deviation. ... + + +To prevent degradation within the particle-filter \cite{??} due to downvoting of particles with increased heading deviation, we incorporate the step- and turn-detection within the transition step. + + + directly into the transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$. \cite{thrun?}\cite{lukas2014?} to get a more directed sampling instead of a truly random one. + +This happens since accurate observations result in high peaks of the evaluation density and therefore the importance density is not able to sample outside that peak [IB98b]. diff --git a/tex/chapters/system.tex b/tex/chapters/system.tex index 3efe5f4..af15b5b 100644 --- a/tex/chapters/system.tex +++ b/tex/chapters/system.tex @@ -41,8 +41,6 @@ By assuming statistical independence of all sensor models, the probability densi \begin{equation} \begin{split} &p(\vec{o}_t \mid \vec{q}_t, \vec{q}_{t-1}) = \\ - &p(\vec{o}_t \mid \vec{q}_t, \vec{q}_{t-1})_\text{turn} - \,p(\vec{o}_t \mid \vec{q}_t, \vec{q}_{t-1})_\text{step} \\ &p(\vec{o}_t \mid \vec{q}_t)_\text{baro} \,p(\vec{o}_t \mid \vec{q}_t)_\text{ib} \,p(\vec{o}_t \mid \vec{q}_t)_\text{wifi} @@ -50,9 +48,9 @@ By assuming statistical independence of all sensor models, the probability densi \label{eq:evalBayes} \end{equation} % -\commentByFrank{die zeile in der mitte (step/turn) faellt ganz weg. also generell kein $q_{t-1}$ mehr} -% Here, every single component refers to a probabilistic sensor model. -The heading information is evaluated using $p(\vec{o}_t \mid \vec{q}_t, \vec{q}_{t-1})_\text{turn}$, the step length using a step detection process by $p(\vec{o}_t \mid \vec{q}_t, \vec{q}_{t-1})_\text{step}$, using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$ the barometer evaluates the current floor, whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for iBeacons and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for Wi-Fi. +The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$, whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for iBeacons and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for Wi-Fi. + +\todo{art unseres particle filters hier einfuehren. transition als proposal. dann kann man spaeter bei step und turn besser begruenden warum wir es in die transition ziehen.}