added heading and step detection to transition

tex/chapters/experiments.tex

@@ -259,7 +259,7 @@ Walking down the stairs at \SI{80}{\second} does also recover the localization s
 	\label{fig:errorOverTimeWalk0}
 \end{figure}
 
-A similar behaviour as the above can be seen in walk 3. 
+A similar behavior as the above can be seen in walk 3. 
 Without a method to recover from impoverishment, the system lost track in \SI{100}{\percent} of the runs due to a not detected floor change in the last third of the walk. 
 By using the simple method, the overall error can be reduced and the impoverishment resolved. Nevertheless, unpredictable jumps of the estimation are causing the system to be highly uncertain in some situations, even if those jumps do not last to long.
 Only the use of the $D_\text{KL}$ method is able to produce reasonable results.
@@ -379,7 +379,7 @@ Nevertheless, even if both estimated paths look very different, they produce sim
 The purple square displays a situation in which a sample impoverishment was successfully resolved. 
 Due to a poorly working \docAPshort{}, in the lower corner of the big room the pedestrians passes before walking down the stairs, the majority of particles is dragged into the upper right corner of  that room and unable to walk down. 
 By allowing some particles to walk through the wall and thus down the stairs, the impoverishment could be dissolved. 
-The KDE-based estimation illustrates this behaviour very accurate.
+The KDE-based estimation illustrates this behavior very accurate.
 Another situation in which the estimated paths do not provide sufficient results can be seen inside the teal square. 
 The room is very isolated from the rest of the building, which is reflected by the fact that only 3 \docAPshort{}'s are detected.
 The pedestrians have been asked to cross the room at a quick pace, leading to a higher step rate and therefore update rate of the filter.