diff --git a/tex/chapters/filtering.tex b/tex/chapters/filtering.tex
index e3f8ec0..539328b 100644
--- a/tex/chapters/filtering.tex
+++ b/tex/chapters/filtering.tex
@@ -1,20 +1,97 @@
 \section{Filtering}
-\label{sec:filtering}
+	
+	\label{sec:filtering}
 
-\commentByToni{Bin mir nicht sicher ob wir diese Section überhaupt brauchen. Könnte man bestimmt auch einfach unter Section 3 packen. Aber dann können wir ungestört voneinander schreiben.}
+	\commentByToni{Bin mir nicht sicher ob wir diese Section überhaupt brauchen. Könnte man bestimmt auch einfach unter Section 3 packen. Aber dann können wir ungestört voneinander schreiben.}
 
-\subsection{Evaluation}
+	\subsection{Evaluation}
 
-\begin{itemize}
-  \item Umfang: 1/2 Seite (so kurz wie halt geht)
-	\item Welche Sensoren benutzen wir? 
-	\item Wie kommen wir auf die Wahrscheinlichkeit?
-\end{itemize}
+\section{Barometer}
 
-\subsection{Transition}
+	\label{sec:sensBaro}
+		%
+		The probability of currently residing on a given floor is evaluated using the smartphone's barometer.
+		Environmental influences are circumvented by using relative pressure readings instead of absolute ones.
+		To reduce the impact of noisy sensors, we calculate the average of several sensor reading, carried out
+		while the pedestrian chooses his destination. This $\overline{\mObsPressure}$ serves as relative base.
+		Likewise, we estimate the sensor's uncertainty $\sigma_\text{baro}$ for later use within the evaluation step.		
+	
+		In order to evaluate relative pressure readings, we need a prediction to compare them with. Therefore, each
+		transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ estimates the state's relative pressure prediction
+		$\mStatePressure$ by examining every height-change ($z$-axis):
+		%		
+		\begin{equation}
+			\mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot b
+			,\enskip
+			\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
+			,\enskip
+			b \in \R
+			\enspace .
+			\label{eq:baroTransition}
+		\end{equation}
+		%
+		In \refeq{eq:baroTransition}, $b$ denotes the common pressure change in $\frac{\text{hPa}}{\text{m}}$.
+		The evaluation step compares the predicted relative pressure with the observed
+		one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
+		%
+		\begin{equation}
+			p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace.
+			\label{eq:baroEval}
+		\end{equation}
+		%		
+		%
+		%
+	\subsection{Wi-Fi \& iBeacons}
+		%
+		The smartphone's \docWIFI{} and \docIBeacon{} component provides absolute location estimation by
+		measuring the signal-strengths of nearby transmitters. The positions of detected \docAP{}s  (\docAPshort{}) and \docIBeacon{}s
+		are known beforehand. This allows a comparison of each measurement with a corresponding estimation
+		using the wall-attenuation-factor signal strength prediction model \cite{Ebner-15}. This model uses the 3D distance $d$ and the
+		number of floors $\Delta f$ between transmitter and the state-in-question:
+		%	
+		\begin{equation}
+			P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace ,
+		\end{equation}
+		%
+		As transmitters are assumed to be statistically independent, the overall probability to measure their predictions at a given location is:
+		%		
+		\begin{equation}
+			\mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} =
+			\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace .
+			\label{eq:wifiTotal}
+		\end{equation}
+		%
+		The prediction model itself needs three parameters per \docAPshort{}: $\mTXP$ measured at a distance 
+		$\mMdlDist_0$ (usually \SI{1}{\meter}), the path-loss exponent $\mPLE$ describing the environment
+		and the attenuation per floor $\mWAF$.
+		\commentByFrank{aufs andere paper beziehen zum kuerzen?}
+		To reduce the system's setup time, we use the same values for all \docAP{}s at the cost of accuracy.
+		All parameters are chosen empirically. Further details on how to determine this parameters exactly,
+		can be found in \cite{PathLossPredictionModelsForIndoor}.
+			
+		The same holds for the \docIBeacon{} component, except $\mTXP$, which is broadcasted by each beacon.
+		As \docIBeacon{}s cover only a small area, $\mPLE$ is usually much smaller compared to the one needed for \docWIFI{}.
+	
+		%
+		
+
+	\subsection{Transition}
+	
+		The transition step depends on random walks on a graph, generated from the buildings floorplan
+		\todo{cite}. This setup allows only valid movements, as ambient conditions (walls, doors, etc.) are considered.
+		
+		Furthermore, we assume the pedestrian's desired destination to be known beforehand. This prior knowledge is evaluated
+		during the random walk, to favour movements approaching the chosen destination.
+	
+		To ensure the transition step provides a viable posterior distribution, we include some sensors directly into the transition step.
+		Adding them to the evaluation instead, would lead to sample impoverishment when using Monte Carlo methods.
+	
+		\subsection{Step- \& Turn-Detection}
+			%
+			Steps and turns are detected using the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
+			
+			%
+			
+		\subsection{Activity-Detection}
+			\todo{write}
 
-\begin{itemize}
-  \item Umfang: 1 Seite
-	\item Im Prinzip nochmal das gleiche wie im Fusion Paper nur kürzer
-	\item Lukas-Teil hat hier bestimmt Platz
-\end{itemize}