diff --git a/tex/chapters/relatedwork.tex b/tex/chapters/relatedwork.tex
index 18e7ce9..451d807 100644
--- a/tex/chapters/relatedwork.tex
+++ b/tex/chapters/relatedwork.tex
@@ -3,8 +3,9 @@
 % 3/4 Seite ca.
 
 %kurze einleitung zum smoothing
-Filtering algorithm, like aforementioned particle filter, use all observations $\mObsVec_{1:t}$ until the current time $t$ for computing an estimation of the state $\mStateVec_t$. 
-In a Bayesian setting, this can be formalized as the computation of the posterior distribution $p(\mStateVec_t \mid \mObsVec_{1:t})$.
+Sequential MC filter, like aforementioned particle filter, use all observations $\mObsVec_{1:t}$ until the current time $t$ for computing an estimation of the state $\mStateVec_t$. 
+In a Bayesian setting, this can be formalized as the computation of the posterior distribution $p(\mStateVec_t \mid \mObsVec_{1:t})$ using a sample of $N$ independent random variables, $\vec{X}^i_{t} \sim (\mStateVec_t \mid \mObsVec_{1:t})$ for $i = 1,...,N$ for approximation. 
+Due to importance sampling, a weight $W^i_t$ is assigned to each sample $\vec{X}^i_{t}$.
 By considering a situation given all observations $\vec{o}_{1:T}$ until a time step $T$, where $t \ll T$, standard filtering methods are not able to make use of this additional data for computing $p(\mStateVec_t \mid \mObsVec_{1:T})$.
 This problem can be solved with a smoothing algorithm.
 
@@ -18,7 +19,7 @@ On the other hand, fixed-interval smoothing requires all observations until time
 The origin of MC smoothing can be traced back to Genshiro Kitagawa. 
 In his work \cite{kitagawa1996monte} he presented the simplest form of smoothing as an extension to the particle filter. 
 This algorithm is often called the filter-smoother since it runs online and a smoothing is provided while filtering. 
-This approach uses the particle filter steps to update weighted paths $\{(\vec{q}_{1:t}^i , w^i_t)\}^N_{i=1}$, producing an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with a computational complexity of only $\mathcal{O}(N)$.
+This approach uses the particle filter steps to update weighted paths $\{(\vec{X}_{1:t}^i , W^i_t)\}^N_{i=1}$, producing an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with a computational complexity of only $\mathcal{O}(N)$. 
 However, it gives a poor representation of previous states due a monotonic decrease of distinct particles caused by resampling of each weighted path \cite{Doucet11:ATO}.
 Based on this, more advanced methods like the forward-backward smoother \cite{doucet2000} and backward simulation \cite{Godsill04:MCS} were developed.
 Both methods are running backwards in time to reweight a set of particles recursively by using future observations. 
diff --git a/tex/chapters/smoothing.tex b/tex/chapters/smoothing.tex
index 02f31ed..aac81d2 100644
--- a/tex/chapters/smoothing.tex
+++ b/tex/chapters/smoothing.tex
@@ -1,16 +1,13 @@
 \section{Smoothing}
 \label{sec:smoothing}
 
+The main purpose of this work is to provide MC smoothing methods in context of indoor localisation.
+As mentioned before, those algorithm are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$ and are therefore able to make use of future observations between $t$ and $T$.
 
-
-The main purpose of this work is to provide smoothing methods in context of indoor localisation.
-As mentioned before, those algorithm are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$ and are therefore able to make use of future observations between $t$ and $T$. 
 %Especially fixed-lag smoothing is very promising in context of pedestrian localisation. 
 In the following we discuss the algorithmic details of the forward-backward smoother and the backward simulation. 
 Further, two novel approaches for incorporating them into the localisation system are shown.
 
-\todo{Einfuehren von $X$ und etwas konkreter schreiben.}
-
 \subsection{Forward-backward Smoother}
 
 The forward-backward smoother (FBS) of \cite{Doucet00:OSM} is a well established alternative to the simple filter-smoother. The foundation of this algorithm was again laid by Kitagawa in \cite{kitagawa1987non}. 
@@ -31,8 +28,6 @@ The weights are obtained through the backward recursion in line 9.
     \caption{Forward-Backward Smoother}
     \label{alg:forward-backwardSmoother}
     \begin{algorithmic}[1] % The number tells where the line numbering should start
-		\Statex{\textbf{Input:} Prior $\mu(\vec{X}^i_1)$}
-		\Statex{~}
 			\For{$t = 1$ \textbf{to} $T$} \Comment{Filtering}
 				\State{Obtain the weighted trajectories $ \{ W^i_t, \vec{X}^i_t\}^N_{i=1}$}
 			\EndFor
@@ -65,8 +60,6 @@ Therefore, \cite{Godsill04:MCS} presented the backward simulation (BS). Where a
     \caption{Backward Simulation Smoothing}
     \label{alg:backwardSimulation}
     \begin{algorithmic}[1] % The number tells where the line numbering should start
-		\Statex{\textbf{Input:} Prior $\mu(\vec{X}^i_1)$}
-		\Statex{~}
 			\For{$t = 1$ \textbf{to} $T$} \Comment{Filtering}
 				\State{Obtain the weighted trajectories $ \{ W^i_t, \vec{X}^i_t\}^N_{i=1}$}
 			\EndFor
@@ -88,7 +81,3 @@ This method can be seen in algorithm \ref{alg:backwardSimulation} in pseudo-algo
 
 \subsection{Transition for Smoothing}
 
-
-%komplexität eingehen
-The reason for not behandeln liegt ... 
-However, \cite{} and \cite{} have proven this wrong and reduced the complexity of different smoothing methods.