diff --git a/competition/tex/chapters/components.tex b/competition/tex/chapters/components.tex
index cf4fef8..811e3c2 100644
--- a/competition/tex/chapters/components.tex
+++ b/competition/tex/chapters/components.tex
@@ -1,6 +1,26 @@
 \section{Component Description}
 	
-	Our indoor localisation solely uses the sensors provided by almost each commodity smartphone.
+	As described above, our indoor localisation solely uses the sensors provided by almost each commodity smartphone. 
+By assuming statistical independence of all sensors, the probability density of the state evaluation of eq. \eqref{eq:recursiveDensity} is given by 
+	%
+	\begin{equation}
+		%\begin{split}
+			p(\vec{o}_t \mid \vec{q}_t) = 
+			p(\vec{o}_t \mid \vec{q}_t)_\text{baro} 
+			\,p(\vec{o}_t \mid \vec{q}_t)_\text{ib}
+			\,p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}
+			\enspace.
+		%\end{split}
+		\label{eq:evalBayes}
+	\end{equation}
+	%
+	Here, every single component refers to a probabilistic sensor model. 
+	The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$,
+	whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for
+	\docIBeacon{}s and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. 
+	
+  Compared to other state-of-the-art system, the step- and turn-detection is not incorporated into the evaluation step. 
+  In our approach it stabilizes and improves the sampling of states $\vec{q}$ into moving more realistically. The transition step is the carried out using random walks on a graph, which is built offline, and uses the building's floorplan \cite{ebner-16}. 
 
 	
 	\input{chapters/barometer.tex}
diff --git a/competition/tex/chapters/introduction.tex b/competition/tex/chapters/introduction.tex
index acb98dd..c417540 100644
--- a/competition/tex/chapters/introduction.tex
+++ b/competition/tex/chapters/introduction.tex
@@ -32,8 +32,7 @@ where $\mObsVec_{1:t} = \mObsVec_{1}, \mObsVec_{1}, ..., \mObsVec_{t}$ is a seri
 	%
 	where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the relative atmospheric pressure prediction in hectopascal (hPa). 
 	The recursive part of the density estimation contains all information up to time $t-1$.
-	Furthermore, the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ models the pedestrian's movement and is carried out using random walks on a graph, which is built offline, and uses the building's floorplan \cite{ebner-16}. 
-
+	Furthermore, the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ models the pedestrian's movement, whereby the evaluation provides a likelihood for every sensor.
 	Containing all relevant sensor measurements to evaluate the current state, the observation vector is defined as follows:
 	%
 	\begin{equation}