fixed minor typos

added some comments

tex/chapters/relatedwork.tex

@@ -3,13 +3,13 @@
 % 3/4 Seite ca.
 
 %kurze einleitung zum smoothing
-Filtering algorithm, like the before mentioned particle filter, use all observations $\mObsVec_{1:t}$ until the current time $t$ for computing an estimation of the state $\mStateVec_t$. 
+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 $p(\mStateVec_t \mid \mObsVec_{1:t})$.
 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.
 
 Within this work we utilise two types of smoothing: fixed-lag and fixed-interval smoothing. 
-In fixed-lag smoothing, one tries to estimate the current state, give measurements up to a time $t + \tau$, where $\tau$ is a predefined lag. 
+In fixed-lag smoothing, one tries to estimate the current state, given measurements up to a time $t + \tau$, where $\tau$ is a predefined lag. 
 This makes the fixed-lag smoother able to run online. 
 On the other hand, fixed-interval smoothing requires all observations until time $T$ and therefore only runs offline, after the filtering procedure is finished \cite{chen2003bayesian}. 
 
@@ -19,7 +19,9 @@ 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 can produce an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with computational complexity of only $\mathcal{O}(N)$.
+\commentByFrank{kleines n?}
 However, it gives a poor representation of previous states \cite{Doucet11:ATO}.
+\commentByFrank{wenn noch platz, einen satz mehr dazu warum es schlecht ist?}
 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. 
 Algorithmic details will be shown in section \ref{sec:smoothing}.