added missing legend to gfx

fixed some typos and refactored some sentences

tex/chapters/introduction.tex

@@ -1,8 +1,8 @@
 \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.
+Whether driving a car, jogging or shopping in the streets, GNSS-based applications simplify orientation,
+guide 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 too weak to pass through obstacles like ceilings.
 Moreover, their accuracy is not sufficient for individual parking spaces or office rooms.
 Therefore, many different solutions for localising a moving object within buildings have been developed in 
@@ -26,12 +26,12 @@ In pedestrian navigation, the human movement is subject to the characteristics o
 Additionally, environmental restrictions need to be considered as well, for example, walking through walls is 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 movements.
-The unique feature of our approach is the way how we model the human movement.
+The unique feature of our approach is the way how human movement is modelled. 
 This is done by using random walks on a graph, which are based on the heading of the pedestrian. 
 Despite very good results, the system presented in \cite{Ebner-15} suffers from two drawbacks, we want to solve within this work.
 
 First, the transition model of our previous approach uses discrete floor-changes.
-Although the overall systems provides viable results, it does not resemble real-world floor changes.
+Although the overall system provides 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 prevents the barometer's full potential.
 It could further be shown that a correct estimation strongly depends on the quality of $z$-transitions.
@@ -40,8 +40,8 @@ To address this problem we extended the graph by adding realistic stairs, allowi
 Second, the heading for modelling the pedestrian's walking behaviour is calculated between two adjacent nodes
 and restricts the transition to perform only discrete \SI{45}{\degree} turns. While this is sufficient
 for most cases, minor heading changes are often ignored and the posterior distribution (after walking)
-is not smoothly spread. 
-\commentByToni{Und was machen wir dagegen?}
+is not smoothly spread. The heading-change of our new approach is solely controlled by the smartphone's turn detection.
+During the random walk, matching edges are sampled according to their deviation from this change.
 
 To improve the complex problem of localising a person indoors, prior knowledge given by a navigation system can be used.
 Such applications are used to navigate a user to his desired destination.
@@ -49,15 +49,16 @@ This limits the unpredictability of human movement to a certain degree.
 So, based on this assumption, the destination is known beforehand and the starting point is the pedestrian's currently estimated position. 
 Regarding a graph-based transition model, one could suggest to use the shortest route between start and destination as the user's most-likely-to-walk path. 
 By incorporating this prior knowledge into the state transition step, a new state can be sampled in a more targeted manner. 
-However, for regular tessellated (grid) graphs, as used in \cite{Ebner-15}, this often leads to paths running very unnatural alongside walls. 
-Therefore, we present a novel approach that detects walls using the inverted graph (representing walls and obstacles) and a nearest-neighbour search.
+However, for regularly tessellated (grid) graphs, as used in \cite{Ebner-15}, this would lead to unnatural paths e.g.
+directly adhering to walls. 
+Therefore, we present a novel approach that detects walls using an inverted graph (representing walls and obstacles) and a nearest-neighbour search.
 %\commentByFrank{hier kann man, wenn platz fehlt, vlt noch etwas details weglassen (inverted-graph, knn, etc)}
 
 Since areas near walls are less likely to be chosen for walking, a probabilistic weight is assigned to every node of the graph.
 This allows a variety of options for integrating additional knowledge about the environment and enables us to address another problem:
 Entering or leaving rooms is very unlikely as only a few nodes are representing doors and allow doing so.
 This can be tackled by making such areas more likely.
-Therefore, a novel approach for detecting doors using again the inverted graph and a principal component analysis (PCA) \cite{Hotelling1933} is presented within this work.
+Therefore, a novel approach for detecting doors using the inverted graph and a principal component analysis (PCA) \cite{Hotelling1933} is presented within this work.
 %\commentByFrank{auch hier vlt das inverted erstmal noch weg lassen wegen platz}
 
 Finally, it is now possible to calculate more natural and realistic paths using the weighted graph.