added heading and step detection to transition

tex/chapters/relatedwork.tex

@@ -4,7 +4,7 @@
 We consider indoor localization to be a time-sequential, non-linear and non-Gaussian state estimation problem. 
 Such problems are often solved using Bayesian filters, which update a state estimation recursively
 with every new incoming measurement. 
-A powerful method to obtain numerical results for this approach are particle filters.
+A powerful group of methods to obtain numerical results for this approach are particle filter.
 
 In context of indoor localization, particle filter approximate a probability distribution describing the pedestrian's possible whereabouts by using a set of weighted random samples (particles).
 Here, new particles are drawn according to some importance distribution, often represented by the state transition, which models the dynamics of the system.
@@ -21,25 +21,20 @@ 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.
-
-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{Ebner-15}.
-
+Obviously, the answer to this question depends on the pedestrian's walking behavior, any nearby architecture and thus the building's floorplan.
+%
+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{Ebner-15}.
+%
 Despite its simplicity, this approach suffers from several drawbacks. 
 The intersection-test can be costly, depending on the number of used particles and the complexity of the building. 
 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 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}.
 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}.
+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 
@@ -88,7 +83,7 @@ Additionally, we will show that such an optimization scheme can partly compensat
 
 %immpf
 Besides well chosen probabilistic models, the system's performance is also highly affected by handling problems which are based on the nature of particle filter.
-They are often caused by restrictive assumptions about the dynamic system, like the aforementioned sample impoverishment. 
+They are often caused by restrictive assumptions about the dynamic system, like seen from the aforementioned problem of sample impoverishment. 
 The authors of \cite{Sun2013} handled the problem by using an adaptive number of particles instead of a fixed one. 
 The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
 The problem of sample impoverishment is then addressed by adapting the number of particles dependent upon the system's current uncertainty \cite{Fetzer-17}.