\subsection{Transition}
	
	To enhance the quality of the proposal distribution, the transition step is 
	based on a \SI{20}{\centimeter}-gridded graph $G = (V,E)$
	with vertices $v_i \in V$ and undirected edges $e_{i,j} \in E$
	derived from the buildings floorplan. This ensures that only valid
	movements can be sampled from the previous state.%
	
	\todo{wenn platz dann bild?}
	
	The graph is built once and offline using the floorplan created by our editor.
	Besides realistic stairwells, additional semantic information (e.g. doors)
	can be included. Hereafter, the built graph is transmitted to the smartphone
	and is used during the online phase.
	
	If the pedestrian's destination is know beforehand, this information can
	be included as prior knowledge into the transition step. A shortest-path
	calculation imposes additional constraints to the transition by favouring
	movements that approach the desired destination (pedestrian sticking to the shortest path)
	over movements that depart from the destination.
	
	To ensure that the calculated shortest path is realistic (resembled human walking paths)
	each node within the graph contains a weight, denoting the likelyhood for being visited
	by the pedestrian. Using this approach, nodes near to walls receive a lower likelyhood.
	During the path-calculation this importance is used to artificially increase/decrease the
	weight $\delta(\mEdgeAB)$ between two nodes. This ensures that the resulting path is 
	farther away from obstacles and looks much more realistic
	
	\todo{wenn platz dann bild?}
	

