changed colors of boxkde and weighted average

tex/chapters/transition.tex

@@ -121,7 +121,7 @@
 	that might be reachable. Increasing $\sigma_\text{step}$ and $\sigma_\text{turn}$ for those cases might also be a viable choice.
 	Likewise, just using some random position, omitting heading/steps might be viable as well.
 
-The detected steps $\mObsSteps$ and the heading change $\mObsHeading$ are obtained using the smartphones IMU. 
+The detected steps $\mObsSteps$ and the heading change $\mObsHeading$ are obtained using the smartphone's IMU. 
 To provide a robust heading change, we first need to rotate the gyroscope onto the east-north-up frame using a suitable transformation matrix.
 After the rotation, integrating over the gyros $z$-axis for a predefined time interval provides the user’s heading change (yaw) \cite{Ebner-15}.
 To obtain the matrix in the first place, we assume that the acceleration during walking is cyclic and thus the average acceleration over several cycles has to be almost zero. 
@@ -132,7 +132,7 @@ To receive the number of steps, we use a very simple step detection based on the
 For this, we calculated the difference between the average magnitude over the last \SI{200}{\milli\second} and the gravity vector.
 If this difference is above a certain threshold ($> \SI{0.32}{\m\per\square\s}$), a step is detected. 
 To prevent multiple detections within an unrealistic short interval, we block the complete process for \SI{250}{\milli\second} \cite{Koeping14}.
-
+Of course, there are much more advanced methods as surveyed in \cite{davidson2017survey}, however this simple method has served us very well in the past.
 	
 	%\commentByFrank{es gaebe noch ganz andere ansaetze etc. aber wir haben wohl nicht mehr genug platz :P}
 	%\commentByToni{ich denke aber auch, es langt.}