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4
tex/chapters/conclusion.tex
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@@ -1,6 +1,6 @@
\section{Conclusion}
We presented a novel approach for integrating prior navigation knowledge by using realistic human walking paths.
Based on a weighted graph, two different models for walking in a more targeted and natural manner were introduced.
We presented a novel approach to integrate prior navigation knowledge by using realistic human walking paths.
Based on a weighted graph, two different models for walking in a targeted and natural manner were introduced.
It could be shown that adding this additional knowledge causes an overall improvement of the localisation results, while maintaining flexibility for unexpected behaviour.
Furthermore, our approach is able to provide accurate and robust position estimations, even when (usually) necessary calibration processes are omitted.

19
tex/chapters/experiments.tex
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@@ -6,15 +6,15 @@
Evaluation took place within all floors (0 to 3) of the
faculty building, each of which about \SI{77}{\meter} x \SI{55}{\meter} in size.
%
We conducted 4 distinct walks, for testing short distances, long distances, critical sections
We conducted 4 distinct walks, to test short distances, long distances, critical sections
and ignoring the shortest-path suggested by the system.
Due to an in-house exhibition during that time, many places were crowded and \docWIFI{} signals
are attenuated more than usual.
Each acquired path is backed by ground truth information to enable error calculation.
This ground truth is measured by recording a timestamp at a marked spot on the walking route.
During the walk, the pedestrian had to click a button on the smartphone application
are attenuated.
To enable error calculation, each acquired path is backed by ground truth information.
The ground truth is measured by recording a timestamp at marked spots on the walking route.
While walking, the pedestrian clicked a button on the smartphone application
when passing a marker. Between two consecutive points, a constant movement speed is assumed.
Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough to conduct
Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for
error measurements. All walks were performed using a Motorola Nexus 6 and a Samsung Galaxy S5.
As the Samsung Galaxy S5's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only,
@@ -47,8 +47,8 @@
%\commentByFrank{$\mUsePath$ erklaert}
As we start with a discrete uniform distribution for $\mStateVec_0$ (random position and heading), the first few estimations
are omitted from the error calculation to allow the system to somewhat settle its initial state. Even though, the error
As we start with a uniform distribution (random position and heading) for $\mStateVec_0$, the first few estimations
are omitted from error calculations to allow the system to somewhat settle its initial state. Even though, the error
during the following few seconds is expected to be much higher than the error when starting with a well known initial
position and heading.
%
@@ -111,7 +111,6 @@
Starting with both, known position and heading, reduced the error by about \SI{15}{\percent} when using prior knowledge and
by \SI{25}{\percent} when omitting prior knowledge. As prior knowledge directs the density towards a known target,
it is able to compensate unknown initial headings which explains the \SI{10}{\percent} difference.
\commentByFrank{bekannter startpunkt getestet und kurz beschrieben}
%
However, as soon as the pedestrian starts moving down the hallway \refSeg{2} the error is reduced dramatically.
Adding prior knowledge centres the density in the middle of the floor, ensures that the heading is directed towards
@@ -157,7 +156,7 @@
%\end{figure}
The median error values for all other paths and the other smartphone are listed in table
\ref{tbl:errNexus} and \ref{tbl:errGalaxy}. Furthermore, fig. \ref{fig:errorDistNexus}
\ref{tbl:errNexus}. Furthermore, fig. \ref{fig:errorDistNexus}
depicts the error development for several percentile values. As can be seen, adding prior
knowledge is able to improve the localisation for all examined situations, even when
leaving the suggested path or when facing bad/slow sensor readings.

68
tex/chapters/grid.tex
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@@ -1,10 +1,10 @@
\section{Transition Model}
\label{sec:trans}
%
\newcommand{\spoint}{l}
\newcommand{\gHead}{\theta_\text{walk}}
\newcommand{\gDist}{d_\text{walk}}
%
To sample only transitions that are actually feasible
within the environment, we utilize a \SI{20}{\centimeter}-gridded graph
$G = (V,E)$ with vertices $v_i \in V$ and undirected edges $e_{i,j} \in E$
@@ -12,7 +12,7 @@
derived from the buildings floorplan as described in section \ref{sec:relatedWork}.
However, we add improved $z$-transitions by also modelling realistic
stairwells using nodes and edges, depicted in fig. \ref{fig:gridStairs}.
%
\begin{figure}
\centering
\input{gfx/grid/grid}
@@ -29,7 +29,6 @@
direction (see fig. \ref{fig:gridStairs}). The grid-vertices corresponding to the starting-edge are determined using an
intersection of the segment $[ \vec{\spoint}_1 \vec{\spoint}_2 ]$ with the \SI{20}{\centimeter} bounding-box around each
node's centre $\fPos{v} = (x,y,z)^T$.
To reduce the system's memory footprint, we search for the largest connected region within the graph and
remove all nodes and edges that are not connected to this region.
@@ -72,14 +71,14 @@
p(\mEdgeAB) = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{dev}^2).
\label{eq:transSimple}
\end{equation}
%
%
%
%
%
\section{Navigational Knowledge}
\label{sec:nav}
%
Considering navigation, a pedestrian wants to reach a well-known destination which represents additional
prior knowledge. Most probably, the user will stick to the path presented by
a navigation system. However, some deviations like chatting to someone or taking another route
@@ -88,7 +87,7 @@
\subsection{Wall Avoidance}
\label{sec:wallAvoidance}
%
%As discussed in section \ref{sec:relatedWork}, simply applying a shortest-path algorithm such as Dijkstra or
%A* using the previously created graph would obviously lead to non-realistic paths sticking to walls and
%walking many diagonals. Pedestrians however, will probably keep a small gap between themselves and
@@ -96,7 +95,7 @@
%To calculate paths that resemble this behaviour, an importance-factor is derived for
%each vertex. Those will be used to modify the weight $\fDistance{v}{v'}$ between two vertices
%$v,v'$, examined by the shortest-path algorithm.
%
Shortest-path algorithms such as Dijkstra use a scalar weight $\fDistance{v_1}{v_2}$ between two vertices
to determine the path with the lowest overall weight.
As discussed in section \ref{sec:relatedWork}, simply using the distance
@@ -130,12 +129,12 @@
While rendering wall-regions less likely, \refeq{eq:wallAvoidance}
will obviously have the same effect on doors as they are just a small gap between
consecutive walls. Therefore, a door-detection is necessary, to upvote them again.
%
%
%
\subsection{Door Detection}
\label{sec:doorDetection}
%
To automatically detect doors within the floorplan, we utilize the fact that doors are usually
anchored between two straight walls and have a normed width. Examining the region directly
around it, the door and its surrounding walls thus describe a flat ellipse with the door as its centre.
@@ -205,11 +204,11 @@
passages depict a high importance.}
\label{fig:importance}
\end{figure}
%
\subsection{Path Estimation}
\label{sec:pathEstimation}
For routing the pedestrian towards his desired target, a modified version
%
To route the pedestrian towards his desired target, a modified version
of Dijkstra's algorithm is used. Instead of calculating the shortest path from the start to the end,
the direction is inverted and the calculated terminates as soon as every single node was evaluated.
Hereafter, every node in the grid knows the distance and shortest path to the pedestrian's target.
@@ -237,32 +236,31 @@
%
Fig. \ref{fig:multiHeatMap} depicts the difference between the shortest path calculated without (dashed) and
with importance-factors (solid), where the latter is clearly more realistic.
%
%\begin{figure}
% \includegraphics[angle=-90, width=\columnwidth, trim=20 19 17 9, clip]{floorplan_paths}
% \caption{Comparision of shortest-path calculation without (dotted) and with (solid) importance-factors
% use for edge-weight-adjustment.}
% \label{fig:shortestPath}
%\end{figure}
%
%
\subsection{Guidance}
%
Based on the previous considerations, we propose two approaches to utilize prior
knowledge within the transition.
\subsubsection{Shortest Path}
%
\newcommand{\pathCentroid}{{\vec{\overline{c}}_{t-1}}}
\newcommand{\pathDev}{\sigma_{t-1}}
\newcommand{\pathRef}{v_\text{ref}}
%
Before every transition, the centre-position $\pathCentroid = \fPos{\mStateVec_{t-1}^*}$ of the current sample-set, where
\begin{equation}
\mStateVec_{t-1}^* = \underset{\mStateVec_{t-1}}{\argmax} \enspace p(\mStateVec_{t-1} | \mObsVec_{t-1})
\end{equation}
represents the most proper state of the posterior distribution at time $t-1$, is calculated.
\begin{equation}
\mStateVec_{t-1}^* = \underset{\mStateVec_{t-1}}{\argmax} \enspace p(\mStateVec_{t-1} | \mObsVec_{t-1})
\end{equation}
represents the most proper state of the posterior distribution at time $t-1$, is calculated.
%
%
%%\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
@@ -280,13 +278,13 @@ represents the most proper state of the posterior distribution at time $t-1$, is
We thus calculate the standard deviation of the distance of all sample-positions
$\fPos{\mStateVec_{t-1}}$ from aforementioned centre $\pathCentroid$.
%\commentByFrank{so klarer? platz fuer groese Eq. fehlt und Notation zum ansprechen jedes einzelnen Particles vermeide ich lieber...}
%
%\begin{equation}
% d_\text{cen} = \| pos(q_{t-1}) - \pathCentroid \|
% \sigma_\text{cen} = stdDev(distance)
%\end{equation}
After advancing the starting-vertex by three times this deviation
After advancing the starting-vertex by three times this deviation
we get the new point $\pathRef$ that is: part of the shortest path, outside of the sample-set
and closer (but not too close) to the desired destination.
%
@@ -313,10 +311,10 @@ represents the most proper state of the posterior distribution at time $t-1$, is
\end{equation}
%\commentByFrank{$\mUsePath$ als variable}
%
%
%
\subsubsection{Multipath}
%
The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the distance
$\fLength{\mVertexA}{\mVertexDest}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $
for the path from $\mVertexA$ to the pedestrian's destination $\mVertexDest$.

12
tex/chapters/relatedwork.tex
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@@ -7,9 +7,9 @@ They differ mainly by the used sensors, their probabilistic models and how envir
For example \cite{Li2015} recently presented an approach combining methods of pedestrian dead reckoning (PDR), \docWIFI{}
fingerprinting and magnetic matching using a Kalman filter. While providing good results, fingerprinting methods
require an extensive offline calibration phase. Therefore, many other systems like \cite{Fang09} or \cite{Ebner-15}
use signal strength prediction models like the log-distance model or wall-attenuation-factor model.
Additionally, the sensors noise is not always Gaussian or satisfies the central limit theorem, what makes the
usage of Kalman filters problematic \cite{sarkka2013bayesian, Nurminen2014}.
use signal strength prediction models like the log-distance or wall-attenuation-factor model.
Additionally, the sensors noise is not always Gaussian or satisfies the central limit theorem. Using
Kalman filters is therefore problematic \cite{sarkka2013bayesian, Nurminen2014}.
All this shows, that sensor models differ in many ways and are a subject in itself.
A good discussion on different sensor models can be found in \cite{Yang2015}, \cite{Gu2009} or \cite{Khaleghi2013}.
@@ -56,9 +56,9 @@ Likewise, cells occupied by obstacles or walls are less likely.
Additionally, every grid cell is able to hold some context information about the environment (e.g. elevators or stairs)
or the behaviour of a pedestrian at this particular position (e.g. jumping or running).
A similar approach is presented in \cite{Li2010}, \cite{Ebner-15} and is also used within this work.
By assuming that the floorplan is given beforehand, the occupied cells can be removed.
The remaining cells are described by their centre/bounding-box and represent all free spaces in the indoor environment.
A similar approach, presented in \cite{Li2010}, \cite{Ebner-15}, is also used within this work.
Assuming the floorplan is given beforehand, occupied cells can be removed.
The remaining cells are described by their centre/bounding-box and represent free spaces within the environment.
A graph is defined by using the centres as nodes and connecting direct neighbours with edges.
In order to enable floor changes, some approaches suggest to simply connect the nodes at staircases \cite{Ebner-15, Hilsenbeck2014}.

30
tex/chapters/sensors.tex
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@@ -3,7 +3,7 @@
\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, more than one reading is required to estimate the relative base.
@@ -19,7 +19,6 @@
\caption{Sometimes the smartphone's barometer (here: Motorola Nexus 6) provides erroneous pressure readings
during the first seconds. Those need to be omitted before $\sigma_\text{baro}$ and
$\overline{\mObsPressure}$ are estimated.}
%\commentByFrank{fixed}
\label{fig:baroSetupError}
\end{figure}
%
@@ -39,19 +38,17 @@
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 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).
\label{eq:baroEval}
\end{equation}
%
%
%
\subsection{Wi-Fi \& iBeacons}
Additional absolute location hints are provided by the smartphone's \docWIFI{} and \docIBeacon{} component,
%
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
@@ -69,7 +66,7 @@
\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 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.
@@ -81,8 +78,8 @@
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}
%
A big disadvantage of using the state transition as proposal distribution is the high possibility of sample
@@ -91,9 +88,6 @@
Additionally, erroneous or delayed measurements from absolute positioning sensors like \docWIFI{} may lead to misplaced turns.
This causes a downvoting of the posterior distribution in areas where the heading deviates.
Therefore, we incorporate the pedestrian's heading $\mObsHeading$, as well as the number of steps $\mObsSteps$, 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.
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$, which leads to a directed sampling instead of a random one.
Steps and turns are detected using the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
%

4
tex/chapters/system.tex
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@@ -26,7 +26,7 @@
The recursive part of the density estimation contains all information up to time $t-1$.
Furthermore, the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ models the pedestrian's movement as described in section \ref{sec:trans}.
%It should be noted, that we also include the current observation $\mObsVec_{t}$ in it.
As \cite{Koeping14-PSA} has proven, we are able to include the observation $\mObsVec_{t-1}$ into the state transition.
As proven in \cite{Koeping14-PSA}, we may include the observation $\mObsVec_{t-1}$ into the state transition.
Containing all relevant sensor measurements to evaluate the current state, the observation vector is defined as follows:
%
@@ -37,7 +37,7 @@
where $\mRssiVec_\text{wifi}$ and $\mRssiVec_\text{ib}$ contain the measurements of all nearby \docAP{}s (\docAPshort{})
and \docIBeacon{}s, respectively. $\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number
of steps detected for the pedestrian.
Finally, $\mObsPressure$ is the relative barometric pressure with respect to some fixed point in time.
Finally, $\mObsPressure$ is the relative barometric pressure with respect to a fixed reference.
For further information on how to incorporate such highly different sensor types,
one should refer to the process of probabilistic sensor fusion \cite{Khaleghi2013}.
By assuming statistical independence of all sensors, the probability density of the state evaluation is given by