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\section{Related Work}
Like mentioned before, most state-of-the-art systems use recursive state estimators like Kalman filters and particle filters. They differ mainly by the sensors used, their probabilistic models and how the environmental information is incorporated. For example \cite{Li2015} recently presented an approach combining methods of pedestrian dead reckoning (PDR), Wi-Fi fingerprinting and magnetic matching using a Kalman filter. Regardless of the good results, fingerprinting methods require an extensive offline calibration phase. Therefore, many other systems like \cite{Fang09} or \cite{Ebner-15} are using 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}.
Like mentioned before, most state-of-the-art systems use recursive state estimators like Kalman- and particle filters.
They differ mainly by the sensors used, their probabilistic models and how the environmental information are incorporated.
For example \cite{Li2015} recently presented an approach combining methods of pedestrian dead reckoning (PDR), Wi-Fi
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}
are using 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}.
All this shows, that sensor models differ in many ways and are a subject in itself. However, in regard of this work, we are not that interested in the different sensor representations but more in the state transition as well as incorporating environmental and navigational knowledge. A good discussion on different sensor models can be found in \cite{Yang2015}, \cite{Gu2009} or \cite{Khaleghi2013}.
All this shows, that sensor models differ in many ways and are a subject in itself.
\commentByFrank{sagt man das so? meinst du: haben ihr eigenes forschungsgebiet?}
A good discussion on different sensor models can be found in \cite{Yang2015}, \cite{Gu2009} or \cite{Khaleghi2013}.
A widely used and easy method for modelling the movement of a pedestrian, is the prediction of a new position by adding an approximated covered distance to the current position. In most cases, the heading serves as walking direction. If the connection line between the new and the old position intersects a wall, the probability for the new position is set to zero \cite{Woodman08-PLF, Blanchert09-IFF}. However, as \cite{Nurminen13-PSI} already stated, it "gives more probability to a short step". An additional drawback of these approaches is that for every transition an intersection-test must be executed. This can result in a high computational complexity.
\commentByFrank{However, within this work, we use simple models, configured using a handful of parameters
and address their inaccuracies by harnassing prior information like the pedestrian's desired destination.}
However, in regard of this work, we are not that interested in the different sensor representations but more in
the state transition as well as incorporating environmental and navigational knowledge.
These disadvantages can be avoided, from the outset, by using spatial models like indoor graphs. Regarding modelling approaches, two main classes are inferred: symbolic and geometric spatial models \cite{Afyouni2012}. Especially geometric spatial models (coordinate-based approaches) are very popular, since they integrate metric properties to provide highly accurate location and distance information. One of the most common environmental representations in indoor localization literature is the Voronoi diagram \cite{Liao2003}. It represents the topological skeleton of the building's floorplan as an irregular tessellation of space. In the work of \cite{Nurminen2014} a Voronoi diagram is used to approximate the human movement. It is assumed that the pedestrian can be anywhere on the topological links. The choice probabilities of changing to the next link are proportional to the total link lengths. However, for highly accurate localisation and large-scale buildings, this network of one-dimensional curves is not suitable \cite{Afyouni2012}. Therefore, \cite{Hilsenbeck2014} searches for large open spaces (e.g. a lobby) and extends the Voronoi diagram by adding those two-dimensional areas. The final graph is then created by sampling nodes in regular intervals from this structure. Similar to \cite{Ebner-15}, they provide a state transition model that selects and edge and a node from the graph according to a sampled distance and heading.
A widely used and easy method for modelling the movement of a pedestrian, is the prediction of a new position
by adding an approximated covered distance to the current position. In most cases, a heading serves as
walking direction. If the connection line \commentByFrank{graph? oder generell?: line-of-sight?}
between the new and the old position intersects a wall, the probability for the new position is set to
zero \cite{Woodman08-PLF, Blanchert09-IFF}.
\commentByFrank{das hatte ich auch mit fast-0 auf der ipin2014. koennen wir auch noch citen}
However, as \cite{Nurminen13-PSI} already stated, it "gives more probability to a short step".
\commentByFrank{waende bevorzugen kurze schritte? wird das klar was hier gemeint ist?}
An additional drawback of these approaches is that for every transition an intersection-test
must be executed. This can result in a high computational complexity.
\commentByFrank{ohja.. ipin2014 war brechend langsam}
These disadvantages can be avoided, from the outset\commentByFrank{??}, by using spatial models
like indoor graphs. Regarding modelling approaches, two main classes are inferred: \commentByFrank{richtiges wort hier?}
symbolic and geometric spatial models \cite{Afyouni2012}.
Especially geometric spatial models (coordinate-based approaches) are very popular,
since they integrate metric properties to provide highly accurate location and distance information.
One of the most common environmental representations in indoor localization literature is the Voronoi
diagram \cite{Liao2003}. It represents the topological skeleton of the building's floorplan as an irregular
tessellation of space. In the work of \cite{Nurminen2014} a Voronoi diagram is used to approximate the human
movement. It is assumed that the pedestrian can be anywhere on the topological links.
The choice probabilities \commentByFrank{??} of changing to the next link are proportional to the total link
lengths. However, for highly accurate localisation and large-scale buildings, this network of one-dimensional
curves is not suitable \cite{Afyouni2012}.
Therefore, \cite{Hilsenbeck2014} searches for large open spaces (e.g. a lobby) and extends the Voronoi diagram by
adding those two-dimensional areas. \commentByFrank{was passsiert hier? wird nicht klar}
The final graph is then created by sampling nodes in regular intervals from this structure.
Similar to \cite{Ebner-15}, they provide a state transition model that selects an edge and a node
from the graph according to a sampled distance and heading.
Nevertheless, most corridors