diff --git a/tex/chapters/relatedwork.tex b/tex/chapters/relatedwork.tex index 39cd2c7..e7b794e 100755 --- a/tex/chapters/relatedwork.tex +++ b/tex/chapters/relatedwork.tex @@ -54,7 +54,7 @@ to estimate parameters like signal-runtime or signal-phase-shifts. Those requirements usually allow only for some use-cases. - We therefore focus on the RSSI, that is available on each commodity smartphone and uses a + We therefore focus on the RSSI, that is available on each commodity smartphone, and use a a simple signal strength prediction model to estimate the most probable location given the phone's observations. Furthermore, we propose a new model based on multiple simple ones, which will reduce the prediction error. Several strategies to optimize simple models and the resulting accuracies are hereafter evaluated and discussed. diff --git a/tex/chapters/system.tex b/tex/chapters/system.tex index 053d3fc..04bc5f8 100755 --- a/tex/chapters/system.tex +++ b/tex/chapters/system.tex @@ -15,33 +15,21 @@ \label{eq:recursiveDensity} \end{equation} - A movement model, based on random walks on a graph, samples only those transitions, - that are allowed by the buildings floorplan. - %$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ - The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide - the observations for both, the transition and the following evaluation step to infer the hidden state, - namely the pedestrian's location and heading - \cite{Ebner2016OPN, Fetzer2016OMC}. - - - This hidden state $\mStateVec$ is given by + The pedestrian's hidden state $\mStateVec$ is given by \begin{equation} \mStateVec = (x, y, z, \mStateHeading),\enskip x, y, z, \mStateHeading \in \R \enspace, \end{equation} % - where $x, y, z$ represent the pedestrian's position in 3D space - and $\mStateHeading$ his current (absolute) heading. + where $x, y, z$ represent its position in 3D space and $\mStateHeading$ his current (absolute) heading. - - - The corresponding observation vector is defined as + The corresponding observation vector, given by the smartphone's sensors, is defined as % \begin{equation} \mObsVec = (\mRssiVecWiFi{}, \mObsSteps, \mObsHeadingRel, \mObsHeadingAbs, \mPressure, \mObsGPS) \enspace. \end{equation} % - $\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the smartphone, + $\mRssiVecWiFi$ contains the signal strength measurements of all \docAP{}s (\docAPshort{}s) currently visible to the phone, $\mObsSteps$ describes the number of steps detected since the last filter-step, $\mObsHeadingRel$ the (relative) angular change since the last filter-step, $\mObsHeadingAbs$ the vague absolute heading as provided by the magnetometer, @@ -49,7 +37,7 @@ $\mObsGPS = ( \mObsGPSlat, \mObsGPSlon, \mObsGPSaccuracy)$ the current location (if available) given by the GPS. - Assuming statistical independence, the state-evaluation density can be written as + Assuming statistical independence, the state-evaluation density from \refeq{eq:recursiveDensity} can be written as % \begin{equation} p(\vec{o}_t \mid \vec{q}_t) = @@ -61,6 +49,15 @@ \label{eq:evalDensity} \end{equation} % + + Besides the evaluation, a movement model, based on random walks on a graph, samples only those transitions + (= pedestrian movements), that are allowed by the building's floorplan. + %$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ + The smartphone's accelerometer, gyroscope, magnetometer, GPS- and \docWIFI{}-module provide + the observations for both, the transition and the following evaluation step to infer the hidden state, + namely the pedestrian's location and heading + \cite{Ebner2016OPN, Fetzer2016OMC}. + Absolute location information is provided by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ and $p(\vec{o}_t \mid \vec{q}_t)_\text{gps}$, if available. @@ -69,30 +66,58 @@ $p(\vec{o}_t \mid \vec{q}_t)_\text{abshead}$. Finally, the barometer is used to distinguish between normal walking and climbing stairs within $p(\vec{o}_t \mid \vec{q}_t)_\text{activity}$. - % - The remaining observations, derived from aforementioned smartphone sensors, - namely: detected steps, and relative heading are - used within the transition model, where potential movements - $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ - are not only constrained by the buildings floorplan but also by - those additional observations. - - As this work focuses on \docWIFI{} optimization, not all parts of - the localization system are discussed in detail. - For missing explanations please refer to \cite{Ebner2016OPN}. + + Furthermore, the smartphone's IMU is used to infer the number of steps + and the relative turn angle the pedestrian has taken since the last filter-update. + While those values could be used within the evaluation \refeq{eq:evalDensity} + we apply them within the transition model to estimate the pedestrian's potential + movement $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ within the building. + Using real values to perform this movement-update instead of just scattering randomly + along the floorplan followed by downvoting within the evaluation \refeq{eq:evalDensity} + provides a more stable result. + + As this work focuses on \docWIFI{} optimization, not all parts of the localization system were discussed in detail. + For missing explanations and further details on aforementioned practices, + please refer to \cite{Ebner2016OPN}. % Compared to this reference, absolute heading and GPS have been added as additional sensors - to further enhance the localization. Their values are incorporated by simply - comparing the sensor readings against a distribution that models the sensor's uncertainty. + to further enhance the localization. As can be seen in \refeq{eq:evalAbsHead} and \refeq{eq:evalGPS}, + their values are incorporated using a simple distribution that models each sensor's uncertainty. - \todo{verteilung fuer gps und abs-heading} + \begin{equation} + p(\vec{o}_t \mid \vec{q}_t)_\text{abshead} + = + \begin{cases} + 0.7 & | \mObsVec_{\mObsHeadingAbs} - \mStateVec_{\mStateHeading} | < \SI{120}{\degree} \\ + 0.3 & \text{else} + \end{cases} + \label{eq:evalAbsHead} + \end{equation} + + \begin{equation} + p(\vec{o}_t \mid \vec{q}_t)_\text{gps} = + \mathcal{N}( + d + \mid + 0, + \sigma^2 + ), \enskip + d = \text{distance}( + (\mObsGPS_\text{lat}, \mObsGPS_\text{lon}), + (\mStateVec_x, \mStateVec_y) + ), \enskip + \sigma = \mObsGPS_\text{accuracy} + \label{eq:evalGPS} + \end{equation} %\todo{neues resampling? je nach dem was sich noch in der eval zeigt} - As GPS will only work outdoors, e.g. when moving from one building into another, - the system's absolute position indoors is solely provided by \docWIFI{}. - Therefore its crucial for this component to supply location estimations - that are as accurate as possible, while ensuring fast setup and - maintenance times. + The GPS sensor should enhance scenarios where multiple, unconnected buildings are involved + and the pedestrian is required to move outdoors to enter the next facility. + Indoors the GPS will usually not provide viable location estimations and the system has to + solely rely on the smartphone's \docWIFI{} observations. + Therefore its crucial for this component to supply location + estimations that are as accurate as possible, + while the component itself must be easy to set-up and maintain. - \todo{ueberleitung holprig?} + \todo{ueberleitung besser?} diff --git a/tex/chapters/work.tex b/tex/chapters/work.tex index cc84f03..14dc6f8 100755 --- a/tex/chapters/work.tex +++ b/tex/chapters/work.tex @@ -3,7 +3,9 @@ The \docWIFI{} sensor infers the pedestrian's current location based on a comparison between live observations (the smartphone continuously scans for nearby \docAP{}s) and fingerprints or - signal strength predictions for well known locations: + signal strength predictions for well known locations. The location that fits the observations best, + is the pedestrian's current location. Assuming statistical independence of all transmitters + installed within a building, this matching probability can be written as \begin{equation} p(\vec{o}_t \mid \vec{q}_t)_\text{wifi} = @@ -11,12 +13,16 @@ \prod_{\mRssi_{i} \in \mRssiVec{}} p(\mRssi_{i} \mid \mPosVec),\enskip %\mPos = (x,y,z)^T \mPosVec \in \R^3 + \enskip , \label{eq:wifiObs} \end{equation} - % + + where matching a single signal strength observation against the reference is given by + \begin{equation} p(\mRssi_i \mid \mPosVec) = \mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma_{i,\mPosVec}^2) + \enskip . \label{eq:wifiProb} \end{equation} @@ -45,7 +51,9 @@ to also serve for indoor purposes. % It predicts an \docAP{}'s signal strength - for an arbitrary location $\mPosVec{}$ given the distance between both and two environmental parameters: + for an arbitrary location + %$\mPosVec{}$ + given the distance $d$ between both and two environmental parameters: The \docAPshort{}'s signal strength \mTXP{} measurable at a known distance $d_0$ (usually \SI{1}{\meter}) and the signal's depletion over distance \mPLE{}, which depends on the \docAPshort{}'s surroundings like walls and other obstacles. @@ -78,7 +86,7 @@ In \refeq{eq:logNormShadowModel}, a constant attenuation factor \mWAF{} is multiplied by the number \numFloors{} of floors/ceilings between sender and the location in question. The attenuation \mWAF{} (per element) depends on the building's architecture and for common, - steel enforced concrete floors $\approx 8.0$ is a viable choice \cite{ElectromagneticPropagation}. + steel enforced concrete floors $\mWAF \approx \SI{-8.0}{\decibel}$ is a viable choice \cite{ElectromagneticPropagation}.