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tex/chapters/introduction.tex

@@ -8,6 +8,26 @@ In our previous work we were able to present such a localisation system based on
 
 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 for this. The main advantage of such an approach is that the graph only samples 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 graphs, which are based upon the heading of the pedestrian. However, this suffers from several drawbacks, we want to address within this work. 
 
+The transition model presented in \cite{Ebner-15} uses discrete floors. Changing the floor on a discrete basis is like jumping down the staircase. This does not resemble real world floor changes and it could be shown that a correct estimation strongly depends on the quality of $z$-transitions. To address this problem we extended the graph by identically shaped stairs, allowing a step-wise transition in the $z$-direction.
+
+
+However, we also discovered that correct estimation
+strongly depends on the quality of z-transitions. If one is
+missed or incorrectly detected, the estimation only slowly re-
+covers. The presented discrete transition does not resemble real
+world floor changes and thus not always works as expected.
+
+Our current transition model uses discrete floors. Chang-
+ing the floor on a discrete basis is like jumping down the
+staircase. Such a transition would e.g. require the barometer
+to detect an immediate pressure change. In reality, the pressure
+slowly increases while walking down the stairs. This traps the
+density on the previous floor until the pedestrian has reached
+the end of the staircase and the sensor values actually match
+a floor-change. However, until then, the density might have
+already passed the stairwell and thus has no chance of changing
+the floor
+
 senkrechte stockwerke, wehcseln schwer blabal.. Therefore, we extend the graph by additional non-discrete nodes which resemble the shape of the stairs.
 
 blumenverteilung, kurven laufen fällt schwer... bessers ziehen.