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4
tex_review/chapters/estimation.tex
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@@ -15,7 +15,7 @@
% Problems: larger error compared to WA and bandwidth selection
Each particle is a realization of one possible system state, here, the position of a pedestrian within a building.
Each particle is a realization of one possible system state, here the position of a pedestrian within a building.
The set of all particles represents the posterior of the system.
In other words, the particle filter naturally generates a sample based representation of the posterior.
With this representation a point estimator can directly be applied to the sample data to derive a sample statistic serving as a \qq{best guess}.
@@ -30,7 +30,7 @@ In the case of particle filters the MMSE estimate equals to the weighted-average
where $W_t=\sum_{i=1}^{N}w^i_t$ is the sum of all weights.
While producing an overall good result in many situations, it fails when the posterior is multimodal.
In these situations the weighted-average estimate will find the estimate somewhere between the modes.
\del{Clearly}\add{It is expected that}, such a position between modes is extremely unlikely the position of the pedestrian.
\del{Clearly}\add{It is expected that} such a position between modes is extremely unlikely the position of the pedestrian.
The real position is more likely to be found at the position of one of the modes, but virtually never somewhere between.
In the case of a multimodal posterior the system should estimate the position based on the highest mode.

2
tex_review/chapters/eval.tex
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@@ -51,7 +51,7 @@ A certain noise is allowed by the corresponding standard deviation $\sigma_{\tex
Within this work $\mu_{i,\mPosVec}$ is calculated by a compromise between the log-distance model and the
wall-attenuation factor model \cite{radar}, as presented in \cite{Ebner-17}.
\add{
The model only considers floors/ceilings, as including walls demands for costly intersection tests to determine all walls along the signal's line-of-sight.
In contrary to its name the model only considers floors/ceilings, as including walls demands for costly intersection tests to determine all walls along the signal's line-of-sight.
While including walls within the model would increase the accuracy of the model's prediction \cite{PropagationModelling, radar},
for many use-cases it is sufficient to just consider floors/ceilings,
to reduce the performance impact when being used on smartphones.

48
tex_review/chapters/experiments.tex
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@@ -8,54 +8,54 @@ The \del{\SI{2500}{\square\meter}} building consists of \SI{6}{} different level
Thus, the ceiling height is not constant over one floor and varies between \SI{2.6}{\meter} to \SI{3.6}{\meter}.
While most of the exterior and ground level walls are made of massive stones, the floors above are half-timbered constructions.
In the middle of the building is an outdoor area, which is only accessible from one side.
\add{The complete walkable indoor area for a visitor is \SI{2500}{\square\meter} in size.
\add{The total walkable indoor area for a visitor is \SI{2500}{\square\meter} in size.
Due to objects like exhibits, cabinets or signs not all positions within the building were freely accessible.}
For the sake of simplicity we did not incorporate such knowledge into the floorplan.
Thus, the floorplan consists only of walls, ceilings, doors, windows and stairs.
For the sake of simplicity we did not incorporate such knowledge into the floor plan.
Thus, the floor plan consists only of walls, ceilings, doors, windows and stairs.
It was created using our 3D map editor software (see fig. \ref{fig:mapeditor}) based on architectural drawings from the 1980s.
\add{The mesh is then created automatically, which only takes a few seconds to compute.}
\add{Our map editor is also used to automatically create the navigation mesh, which only takes a few seconds to compute.}
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{gfx/apps/editor_light.png}
\caption{\add{The 3D map editor we developed to create the floorplans. This screenshot shows the ground level of the building. The window is split into toolbar (left), layers (upper right), parameters of current selection (lower right), drawing mode (upper center) and 3D view (lower center).}}
\caption{\add{The 3D map editor we developed to create the floor plans. This screenshot shows the ground level of the building. The window is split into toolbar (left), layers (upper right), parameters of current selection (lower right), drawing mode (upper center) and 3D view (lower center).}}
\label{fig:mapeditor}
\end{figure}
%wie haben wir die ap aufgehängt
\add{As described in section \ref{sec:wifi} we used \SI{42}{} WEMOS D1 mini to provide a \docWIFI{} infrastructure throughout the building.
\add{As described in section \ref{sec:wifi} we used \SI{42}{} WEMOS D1 mini to provide a \docWIFI{} signal coverage throughout the building.
The distribution of the beacons on ground floor can be seen in fig. \ref{fig:apfingerprint} (black dots) as well as the references (fingerprints) for optimization.
The position of the beacons were chosen depending on available power sources.
We have tried to have at least two beacons in one room and a third beacon visible in an approximate radius of 10 meters.
Due to the difficult architecture and the extremely thick walls of the museum, we decided on this procedure, which explains the rather unusual number of \SI{42}{} transmitters compared to modern buildings.
Another reason for the high number of beacons is that we did not want to analyze the quality of the Wi-Fi infrastructure for further improvements, as this can be a very time-consuming task.
Care was taken to have at least two beacons in each room and a third beacon visible in an approximate radius of \SI{10}{\meter}.
Due to the difficult architecture and the extremely thick walls of the museum, we decided on this procedure, which explains the rather large number of \SI{42}{} transmitters compared to modern buildings.
Another reason for the high number of beacons is that we did not want to analyze the quality of the Wi-Fi signal coverage for further improvements, as this can be a very time-consuming task.
In many areas of the building an improvement would not even be possible due to the lack of power sockets.
As an alternative, the beacons could also be operated using a battery, but we consider this approach less practicable, so we did not take this option.
The power sockets had different heights ranging from \SI{0.2}{\meter} to \SI{2.5}{\meter}.
So there were no prior requirements how to place a single beacon exactly and their position is thus similar to the sockets position.
To compensate that, battery powered beacons could be used but we consider this approach less practicable, so we did not take this option.
The power sockets are located at different heights ranging from \SI{0.2}{\meter} to \SI{2.5}{\meter}.
Consequently, there were no prior requirements on how a single beacon should be placed exactly and its position is dictated by the socket's position.
Considering all the above, the beacons were placed more or less freely and to the best of our knowledge.}
\add{A very similar approach was chosen for placing the fingerprints.
The positions of the fingerprints are set within our 3D map editor (see fig. \ref{fig:mapeditor}) software by simply dragging the fingerprinting icon on the desired position or by entering the position manually.
The reference points were placed every \SI{3}{\meter} to \SI{7}{\meter} from each other, however as can be seen in fig. \ref{fig:apfingerprint} not very accurately.
A perfect distance between the single points is not a crucial factor for the optimization and thus we consider such an accurate approach to be pointless.
\add{A similar approach was chosen for placing the fingerprints.
The positions of the fingerprints are set within our 3D map editor (see fig. \ref{fig:mapeditor}) software by dragging the fingerprinting icon on the desired position or by entering the position manually.
The reference points were placed every \SI{3}{\meter} to \SI{7}{\meter} from each other, however as can be seen in fig. \ref{fig:apfingerprint} not necessarily accurate.
As the optimization scheme does not require equally spaced reference points, doing so would result in superfluous effort.
Furthermore, it is not easy to adopt the exact position to take the reference measurements in the building later on.
Of course, this could be done with appropriate hardware (e.g. laser-scanner), but again this costs a lot of time, which in our opinion does not justify a presumably increased accuracy of some decimeters.}
Of course, this could be achieved with appropriate hardware (e.g. laser-scanner), but again, this requires more time and care, which in our opinion does not justify a presumably increased accuracy of some decimeters.}
\add{Summing up the above, the following initial steps are required to utilize our localization system to a building:
\begin{enumerate}
\item Acquiring a blueprint or architectural drawing of the building including at minimum the walls and stairs of the respective floors.
\item Based on this 2D drawing, the floorplan is created using our 3D map editor (cf. fig. \ref{fig:mapeditor}). This requires manual effort, comparable to software like Inkscape or FreeCAD.
\item If necessary, creating or improving the Wi-Fi infrastructure by plugging in beacons to available power sockets and write all MAC-addresses into a whitelist.
%\item Store floorplan and whitelist of MAC-addresses onto the smartphone.
\item Record the reference measurements based on the reference positions given in the floorplan.
\item Based on this 2D drawing, the floor plan is created manually using our 3D map editor (cf. fig. \ref{fig:mapeditor}), comparable to software like Inkscape or FreeCAD.
\item If necessary, create or improve the Wi-Fi infrastructure by plugging in beacons to available power sockets and compose a whitelist of MAC-addresses of the involved access points or beacons.
%\item Store floor plan and whitelist of MAC-addresses onto the smartphone.
\item Record the reference measurements based on the reference positions given in the floor plan.
\item The Wi-Fi model is optimized using the previously obtained reference measurements.
\item The navigation mesh is created automatically based on the before created floorplan as can be seen in fig. \ref{fig:museumMapMesh}.
\item The navigation mesh is created automatically based on the before created floor plan as can be seen in fig. \ref{fig:museumMapMesh}.
\end{enumerate}
For the building considered within this work, we were able to perform this steps in less then \SI{160}{\minute} by a person, which is familiar with the system, and the janitor of the museum.
Step 1 and 2 were conducted off-site.
The blueprint was initially provided by the director of the museum as digital photography.
Creating the floorplan including walls and stairs took us approximately \SI{40}{\minute} and is then stored onto the smartphone after creation.
Creating the floor plan including walls and stairs took us approximately \SI{40}{\minute} and is then stored onto the smartphone after creation.
Adding knowledge like semantic information such as room numbers would of course take additional time.
All other steps were performed on-site using our smartphone app for localization, which can be seen in fig. \ref{fig:yasmin}.
As the museum did not provide any Wi-Fi infrastructure, we installed the \SI{42}{} beacons as explained above.
@@ -82,7 +82,7 @@ In addition, the above steps do not require a high level of detail in their exec
\label{fig:simple}
\end{subfigure}
\caption{\add{The two mobile applications developed for Android. The localization app in (a) is used to record the Wi-Fi reference measurements based on the positions provided by the floorplan. In this screenshot the dialog for recording them is visible. The app also implements the here presented approach and can thus be used for localization. However, for the utilized experiments we used a simpler client (b) allowing for user input like a ground truth or activity button.}}
\caption{\add{The two mobile applications developed for Android. The localization app in (a) is used to record the Wi-Fi reference measurements based on the positions provided by the floor plan. In this screenshot the dialog for recording them is visible. The app also implements the here presented approach and can thus be used for localization. However, for the utilized experiments we used a simpler client (b) allowing for user input like a ground truth or activity button.}}
\label{fig:applications}
\end{figure}

23
tex_review/chapters/introduction.tex
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@@ -19,7 +19,7 @@ Thus, this paper presents a \del{robust but realistic} \add{continuous} movement
In localization systems using a sample based density representation, like particle filters, aforementioned problems can further lead to more advanced problems like sample impoverishment \cite{Fetzer-17} or multimodalities \cite{Fetzer-16}.
Sample impoverishment refers to a situation, in which the filter is unable to sample enough particles into proper regions of the building, caused by a high concentration of misplaced particles.
Within this work we present a simple yet efficient method that enables a particle filter to fully recover from sample impoverishment.
We also use \del{a novel} \add{an} approach for finding an exact estimation of the pedestrian's current position by using a \del{rapid computation} \add{approximation} scheme of the kernel density estimation (KDE) \cite{Bullmann-18}.
We also use \del{a novel} \add{an} approach for finding an exact estimation of the pedestrian's current position by using an \del{rapid computation} \add{approximation} scheme of the kernel density estimation (KDE) \cite{Bullmann-18}.
Many historical buildings, especially bigger ones like castles, monasteries or churches, are built of massive stone walls and have annexes from different historical periods out of different construction materials.
\del{This leads to problems} \add{This makes it more challenging to ensure good radio coverage of the entire building, especially} for technologies using received signal strengths indications (RSSI) from \docWIFI{} or Bluetooth.
@@ -27,19 +27,19 @@ Many historical buildings, especially bigger ones like castles, monasteries or c
Many unknown quantities, like the walls definitive material or thickness, make it expensive to determine important parameters, \eg{} the signal's depletion over distance.
Additionally, \del{most wireless} \add{many of these} approaches are based on a line-of-sight assumption.
Thus, the performance will be even more limited due to the irregularly shaped spatial structure of such buildings.
Our approach tries to avoid those problems using an optimization scheme for Wi-Fi based on a \del{few} \add{set of} reference measurements.
Our approach tries to avoid those problems using an optimization scheme based on a \del{few} \add{set of} Wi-Fi reference measurements.
We distribute a \del{small number} \add{set} of \del{simple} \add{small (\SI{2.8}{\centi\meter} x \SI{3.5}{\centi\meter})} and cheap \add{($\approx \$10$)} \docWIFI{} beacons over the whole building \add{to ensure a reasonable coverage} and instead of measuring their position \add{and necessary parameters, we use our optimization scheme, initially presented in \cite{Ebner-17}}.
\add{An optimization scheme is able to compensate for wrongly measured access point positions, inaccurate building plans or other knowledge necessary for the Wi-Fi component.
\add{This optimization scheme is able to compensate for wrongly measured access point positions, inaccurate building plans or other knowledge necessary for the Wi-Fi component.
}
%An optimization scheme also avoids inaccuracies like wrongly measured access point positions or outdated fingerprints caused by changes of the environment or inaccurate building plans.
%\commentByFrank{warum fingerprints? das verwirrt mich an der stelle. willst du sagen, dass opt. besser ist, als ueberhaupt fingerprints zu nehmen? dann kommt es nicht so rueber. unsicher, deshalb kein direkter fix sondern comment}
\del{It is obvious, that} \add{Of course, } this could be solved by re-measuring the building, however this is a very time-consuming process requiring specialized hardware and a surveying engineer.
\del{It is obvious, that} \add{Of course, } this could be solved by re-measuring the building, however this is a very time-consuming process requiring specialized hardware and surveying engineer.
\add{Depending on the size of the building, such a complex and time-consuming process is} contrary to most costumers expectations of a fast to deploy \del{and low-cost} solution.
%
In addition, this is not just a question of \del{costs incurred} \add{initial effort}, but also for buildings under monumental protection, not allowing for larger construction measures.
In addition, this is not just a question of \del{costs incurred} \add{initial effort}, but it is also problematic for buildings under monumental protection, not allowing larger construction measures.
\add{That is why the compact Wi-Fi beacons are a reasonable alternative to conventional access points for localization.
The access points of a classic Wi-Fi infrastructure are mostly mounted to the ceilings of the building to presume a cost efficient setting receiving the highest possible coverage.
The access points of a regular Wi-Fi network infrastructure are mostly mounted to the ceilings of the building to presume a cost efficient setting receiving the highest possible coverage.
However, this usually requires new cabling, e.g. an extra power over Ethernet connection.
In contrast, the beacons can simply be plugged into already existing power outlets and due to their low price they can be distributed in large quantities, if necessary.
In the here presented scenario, the beacons do not establish a wireless network and thus serve only to provide signal strengths.}
@@ -53,20 +53,21 @@ To sum up, \add{this work presents an updated version of the winning localizatio
This is the first time that all these previously acquired findings have been fully combined and applied simultaneously.
During the here presented update, the following novel contributions will be presented and added to the system:
\begin{itemize}
\item The pedestrian's movement is modelled in a more realistic way using a navigation mesh, based on the building's floorplan. This only allows movements that are actually feasible, e.g. no walking through walls. Compared to the gridded-graph structure we used before \cite{Ebner-16}, the mesh allows continuous transitions and reduces the required storage space drastically.
\item The pedestrian's movement is modelled in a more realistic way using a navigation mesh, generated from the building's floor plan. This only allows movements that are actually feasible, e.g. no walking through walls. Compared to the gridded-graph structure we used before \cite{Ebner-16}, the mesh allows continuous transitions and reduces the required storage space drastically.
\item To enabled more smooth floor changes, a threshold-based activity recognition using barometer and accelerometer readings is added to the state evaluation process of the particle filter. The method is able to distinguish between standing, walking, walking up and walking down.
\item To address the problem of sample impoverishment in a wider scope, we present a simplification of our previous method \cite{Fetzer-17}. This reduces the overhead of adapting an existing system to the method and allows to incorporate it as independent component of the state transition of any approach using a general particle filter methodology.
\item To address the problem of sample impoverishment in a wider scope, we present a simplification of our previous method \cite{Fetzer-17}. This reduces the overhead of adapting an existing system to the proposed method and allows to incorporate it as an independent component of the state transition of any approach using a general particle filter methodology. \commentByMarkus{Satzbau}
\end{itemize}
}
%We then further omit time-consuming approaches like classic fingerprinting or measuring the exact positions of access points.
%Instead we use a simple optimization scheme based on reference measurements to estimate a corresponding \docWIFI{} model.
The goal of this work is to propose a fast to deploy \del{and low-cost} localization solution, that provides reasonable results in a high variety of situations.
\add{However, many state-of-the-art solutions are evaluating their systems within office or faculty buildings, offering a modern environment and well described infrastructure.}
\add{However, many state-of-the-art solutions tend to be evaluated within office or faculty buildings, offering a modern environment and well described infrastructure.} \commentByMarkus{Brauchen wir hier Quellen um das zu belegen?}
Consequently, we believe that by utilizing our localization approach to such a challenging scenario, it is possible to prove those characteristics.
\add{To initially set up the system we only require a blueprint to create the floorplan, some Wi-Fi infrastructure, without any further information about access point positions or parameters, and a smartphone carried by the pedestrian to be localized.
\commentByMarkus{Statt challenging "a more realistic scenario"?!}
\add{To initially set up the system we only require a blueprint to create the floor plan, some Wi-Fi infrastructure, without any further information about access point positions or parameters, and a smartphone carried by the pedestrian to be localized.
The existing Wi-Fi infrastructure can consist of the aforementioned Wi-Fi beacons and/or already existing access points.
The combination of both technologies is feasible, depending on the scenario and building.
The combination of both technologies is feasible, depending on the scenario and building. \commentByMarkus{depending on was genau? Würde den Nebensatz einfach weg lassen}
Nevertheless, the museum considered in this work has no Wi-Fi infrastructure at all, not even a single access point.
Thus, we distributed a set of \SI{42}{beacons} throughout the complete building by simply plugging them into available power outlets.
In addition to evaluating the novel contributions and the overall performance of the system, we have carried out further experiments to determine the performance of our Wi-Fi optimization in such a complex scenario as well as a detailed comparison between KDE-based and weighted-average position estimation.}

14
tex_review/chapters/relatedwork.tex
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@@ -21,7 +21,7 @@ Most localization approaches differ mainly in how the transition and evaluation
The system's dynamics describe a pedestrian's potential movement within the building.
This can be formulated as the question \emph{``Given the pedestrian's current position and heading are known, where could he be after a certain amount of time?''}.
Obviously, the answer to this question depends on the pedestrian's walking behavior, any nearby architecture and thus the building's floorplan.
Obviously, the answer to this question depends on the pedestrian's walking behavior, any nearby architecture and thus the building's floor plan.
%
Assuming the pedestrian to walk almost straight towards his current heading with a known, constant walking speed, the most basic form of state transition simply rejects all movements, where the line-of-sight between current position and potential destination is blocked by an obstacle \cite{Woodman08-PLF, Blanchart09}.
%
@@ -30,14 +30,14 @@ The intersection-test can be costly, depending on the number of used particles a
Furthermore, it is limited mainly to 2D transitions within the plane.
Smooth 3D transitions, like walking stairs, would require much more complex intersection tests \cite{Afyouni2012}.
To overcome both limitations, the building's floorplan can be used to derive a graph-based structure, like voronoi diagrams or fixed-distance grids, moving all costly intersection tests into a one-time offline phase \cite{Ebner-16, Hilsenbeck2014}.
To overcome both limitations, the building's floor plan can be used to derive a graph-based structure, like voronoi diagrams or fixed-distance grids, moving all costly intersection tests into a one-time offline phase \cite{Ebner-16, Hilsenbeck2014}.
Hereafter, graph-based random walks along the created data-structure can be used as a fast transition approximation.
Smooth transitions in 3D space can be achieved by generating nodes and edges along stairs and elevators.
Furthermore, the nodes can be used to store additional information, like their distance towards a pedestrian's desired destination.
Such information can be included during the transitions step, \eg{} increasing the likelihood of all potential movements that approach this destination \cite{Ebner-16}.
However, the graph-based approach also imposes some potential issues. When using a gridded graph, the spacing between adjacent
nodes directly represents the transition's accuracy. Likewise, the amount of required memory to represent the floorplan
nodes directly represents the transition's accuracy. Likewise, the amount of required memory to represent the floor plan
scales about quadratically with this spacing. Even though nodes/edges are only created for actually walkable areas (like a sparse cube),
large buildings require millions of nodes and might not fit into memory at once.
Furthermore, (large) outdoor regions between adjacent buildings require unnecessarily large amounts
@@ -46,7 +46,7 @@ they usually suffer from reduced accuracy for large open spaces, as many impleme
We therefore present a novel technique based on continuous walks along a navigation mesh.
Like the graph, the mesh, consisting of triangles sharing adjacent edges,
is created once during an offline phase, based on the building's 3D floorplan.
is created once during an offline phase, based on the building's 3D floor plan.
Using large triangles reduces the memory footprint dramatically (a few megabytes for large buildings)
while still increasing the quality (triangle-edges directly adhere to architectural-edges) and allows
for truly continuous transitions along the surface spanned by all triangles.
@@ -60,12 +60,12 @@ During a one-time offline-phase, a multitude of reference measurements are condu
During the online-phase the pedestrian's location is then inferred by comparing those prior measurements against live readings.
Based on this pioneering work, many further improvements where made within this field of research \cite{PropagationModelling, ProbabilisticWlan, meng11}.
However, despite a very high accuracy up to \SI{1}{\meter}, classic fingerprinting approaches suffer from tremendous setup- and maintenance times.
\add{For this reason, some alternative approaches were presented to speed up the offline phase.
\add{For this reason, some alternative approaches were presented to speed up the offline-phase.
In \cite{Guimaraes16} the positions of recorded references are interpolated between the start and end of some reference path, based on the pedestrians gait cycle.
Unrecorded positions are then interpolated using the flood fill algorithm.
Unrecorded positions are then obtained using the flood fill algorithm.
However, for old buildings with many nooks and crannies this might cause problems as the RSSI can differ highly within a few meter, especially in the entrance area of thick-walled rooms.
This could open the need for more advanced map interpolation methods or a higher number and density of reference paths to walk.
Another often considered alternative is using robots instead of human workforce \cite{he2016wi, yeh2009indoor}}, still this seems not to be a valid option for old buildings with limited accessibility due to uneven grounds and small stairs.
Another often considered alternative is using robots instead of human workforce \cite{he2016wi, yeh2009indoor}}, still this seems not to be a valid option for old buildings with limited accessibility for robots due to uneven grounds and small stairs.
%wifi, signal strength
Signal strength prediction models are a well-established field of research to determine signal strengths for arbitrary locations by using an estimation model instead of real measurements.

24
tex_review/chapters/transition.tex
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@@ -6,7 +6,7 @@
\begin{subfigure}{0.325\textwidth}
\centering
\includegraphics[width=5.1cm]{gfx/transition/museumMap.pdf}
\caption{3D Floorplan}
\caption{3D Floor plan}
\label{fig:museumMap}
\end{subfigure}
\begin{subfigure}{0.325\textwidth}
@@ -22,7 +22,7 @@
\label{fig:museumMapMesh}
\end{subfigure}
\caption{
Floorplan and automatically generated transition data structures for the ground floor of the historic building (\SI{71}{\meter}~x~\SI{53}{\meter}).
Floor plan and automatically generated transition data structures for the ground floor of the historic building (\SI{71}{\meter}~x~\SI{53}{\meter}).
\add{
To reach every nook and cranny, the generated graph (b) requires many nodes and edges.
The depicted version uses a coarse node-spacing of \SI{90}{\centi\meter} (1700 nodes) but barely reaches all doors and stairs.
@@ -33,9 +33,9 @@
\end{figure}
Within previous works, we used a graph of equidistant nodes (see \reffig{fig:museumMapGrid})
to model the building's floorplan, representing the basis for the transition step \cite{Ebner-15, Ebner-16}.
to model the building's floor plan, representing the basis for the transition step \cite{Ebner-15, Ebner-16}.
\add{
It is created \emph{automatically}, based on the building's floorplan,
It is created \emph{automatically}, based on the building's floor plan,
which, in turn, results from \emph{manually} tracing available blueprint pictures within our editing software.
}
% in 15 und 16 haben wir stueckweise den graph eingefuhert
@@ -49,9 +49,9 @@
As cells are equidistant and axis aligned for performance reasons,
the algorithm works reasonably well for rectangular buildings,
matching the graph's coordinate system.
For skewed floorplans, however, many periphery cells will intersect
For skewed floor plans, however, many periphery cells will intersect
with walls and are thus omitted, reducing the quality of the representation.
While smaller cells thus allow for a more accurate representation of the building,
While smaller cells allow for a more accurate representation of the building,
more cells are needed in total, increasing memory requirements for the smartphone.
}
After placement, each cell is connected with their, up to 8, potential
@@ -60,8 +60,8 @@
Those connections are only added, if the neighbor is actually available,
and the connection itself does not intersect any obstacles.
}
Doing so creates a walkable graph \add{of nodes and edges} for each floor.
The graphs for each floor are hereafter connected via stairs or elevators,
Doing so creates a walkable graph \add{consisting of nodes and edges} for each floor.
These graphs are hereafter connected via stairs or elevators,
to form the final, walkable data structure for the whole building.
This allows for (semi-)random walks along the graph, \add{modeling potential pedestrian movements}.
\add{
@@ -88,7 +88,7 @@
model \add{depending on the spacing},
we developed a new basis for the transition step, that is still able to answer
$p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$,
\add{but has a much smaller memory footprint while representing the real floorplan
\add{but has a much smaller memory footprint while representing the real floor plan
more accurately.}
%
The new foundation is provided by well-known navigation meshes \cite{navMesh1},
@@ -103,10 +103,10 @@
is presented by shared outline edges between adjacent polygons.
It thus is always possible to walk from one polygon into another,
if they are adjacent.
Similar to the graph-based approach, adjacent polygons thus
Similar to the graph-based approach, adjacent polygons
denote some sort of walkable surface.
Just as before, the navigation mesh can be \emph{automatically}
generated from the building's floorplan, based on
generated from the building's floor plan, based on
various algorithms \cite{navMeshAlg1}.
}
Using variably shaped/sized elements instead of rigid grid-cells
@@ -182,7 +182,7 @@
Whether the newly obtained destination $(x_t, y_t)^T$ is actually reachable from the start $(x_{t-1}, y_{t-1})^T$ can be determined
by checking if there is a way from the starting triangle towards some other, nearby triangle that contains these coordinates.
If so, the discarded $z$-component $z_t$ is determined using the barycentric coordinates of $(x_t, y_t)^T$
within a 2D projection of the triangle the position belongs to, and applying them to the original 3D triangle.
within a 2D projection of the triangle which the position belongs to, and applying them to the original 3D triangle.
This can be though of walking along a 2D floor, and determining the floor's altitude for the 2D destination.
}
\add{