\section{Introduction}

Since the advent of smartphones, location aware apps and services are ubiquitous and have become a natural part of our everyday life.
Whether driving a car, jogging or shopping in the streets, GNSS-based applications are making orientation easier,
point the way and even track our fitness achievements. But as soon as we drive into an underground car park or visit a shopping mall, most of them do not work at all.
That is because satellite signals are to weak to pass through obstacles like buildings' ceilings.
Moreover, their accuracy is not sufficient for individual parking spaces or office rooms.
Therefore, many different solutions for localizing a moving object within buildings have been developed in most recent years \cite{Ebner-15, Yang2015, Khaleghi2013, Fang09, Nurminen2014}.
Especially the hard problem of pedestrian localization and navigation has lately attracted a lot of interest. 

Most modern indoor localisation systems primarily use smartphones for determining the position of a pedestrian.
Especially the phone's inertial measurement unit (IMU) as well as external information like Wi-Fi or Bluetooth
are used for collecting the necessary data. Additionally, environmental knowledge is often incorporated by using
floor maps. This combination of highly different sensor types is also known as sensor fusion.

Here, probabilistic methods like particle- or Kalman filters are often used to approximate a probability
distribution describing describing the pedestrian's possible whereabouts.

This procedure can be separated into two probabilistic models:
The transition model represents the dynamics of the pedestrian
and predicts the next accessible locations,
while the evaluation model estimates the probability for the position also corresponding to the recent sensor measurements.
 %Therefore, the most accurate position is represented by a peak of the probability distribution. 
In our previous work we were able to present such a localisation system based on all the above mentioned
sensors including the phone's barometer \cite{Ebner-15}.

In pedestrian navigation, the human movement underlies the characteristics of walking speed and walking direction.
Additionally, environmental restrictions need to be considered as well, for example, walking through walls is in
most cases impossible. Therefore, incorporating environmental knowledge is a necessary and gainful step.
Like other systems, we are using a graph-based approach to sample only valid locations.
The unique feature of our approach is the way in how we model the human movement.
This is done by using random walks on a graph, which are based upon the heading of the
pedestrian. 
Despite very good results

However, the system presented in \cite{Ebner-15} suffers from two major drawbacks, we want to solve within this work.


\commentByFrank{unser unique feature ist also, dass es nicht geht? :P so liest sich der absatz}

Firstly, the transition model of our past \commentByFrank{previous?} approach uses discrete floors.
\commentByFrank{floor-changes. die floors sind immernoch discrete}.
Although the overall systems prevoides viable results, it does not resemble real-world floor changes.
Especially the barometric sensor is affected due to its continuous pressure measurements.
The discrete model restricts the barometer to exploit its full potential.
\commentByFrank{komischer satz, schraenkt ein um das ganze potential zu nutzen? wie waers mit:
prevents using the baromters full potential?}

It could further be shown that a correct estimation strongly depends on the quality of $z$-transitions.
To address this problem we extended the graph by realistically shaped stairs, allowing a step-wise transition
in the $z$-direction.

Secondly, the heading for modeling the pedestrian's walking behaviour is calculated between two adjacent nodes.
This restricts the transition to perform only \SI{45}{\degree} turns. In most scenarios this assumption performs
well, since the... However, walking sharp turns and ... is not 
 \commentByToni{Ich denke hier kann Frank E. noch bissle was schreiben, oder?} 
\commentByFrank{ja das werde ich noch anpassen, dass es stimmt und die probleme beschreibt}

The problem of localization can be simplified by assuming a person navigation.
\commentByFrank{???}
Such applications are used to navigate a pedestrian to his desired destination.
So, based on this assumption the starting point, which is the current position of the pedestrian,
as well as the destination are known beforehand.
\commentByFrank{die aktuelle post ist nicht vorher bekannt, jedenfalls verwenden wir es nicht so}

Regarding a graph-based transition model, one could suggest to calculate the shortest path
between start and destination. However, this often leads to paths running very unnatural alongside walls.
\commentByFrank{zumindest bei unserem graphen layout. auf nem voronoi koennte es sogar besser sein}
Additionally, the human walking behaviour is highly affected by visual distractions, comfort, disorientation
and many other factors. Therefore, we present a novel method for pedestrian navigation by using \todo{XXX} methods
to calculate a preferably realistic path:
areas near a wall are less likely to be chosen for the path then a door or a small hallway. ... probability map/graph ... 
\commentByToni{Wissen ja noch nicht was wir hier genau nehmen, deswegen erstmal leer}
to address the problem of walking on a corridor with higher probability ... a method for detecting doors and
reducing the proabability of walking alongside walls will be presentend within this work...


The work is structured as follows... 

