\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}. 

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}. 

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. 

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. 

Nevertheless, most corridors 

...and walking into a rooms unwahrscheinlich.

deshalb grided tessellation graph. blabalba for 2D environments. later for 3D .. 

also hyprid version of both like presented in. they use blabal.. balab 



remove degrees of freedom from the map -> less particles

\subsection{State Transition}

In computer games like the sims or starcraft, intelligent npc movement is a key factor. hierbei geht es nicht nur um das umlaufen von hindernissen sondern auch um eine möglichst natürliche art der bewegung. 


ansätze die dijkstra einfach zum navigieren nutzen.

ansätze aus der robotic um einen roboter von a nach b zu schicken


the idea of using navigational knowledge to simulate the human movement 

\begin{itemize}
	\item Allgemein indoor localizations systeme
	\subitem was ist state of the art? 
	\subitem klarstellen was wir anders/besser machen
	\item graphen-basierte systeme
	\subitem probability graph / transition
	\item pathfinding for humans
	\subitem computerspiele machen das schon ewig. robotor auch.
	\subitem auf menschliches verhalten anpassen. gibt es viele theoritsche ansätze und simulationen aber in noch keinem system.
\end{itemize}


