\section{Related Work}
\label{sec:relatedWork}
% 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 $p(\mStateVec_t \mid \mObsVec_{1:t})$.
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, 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}. 


%historie des smoothings und entwicklung der methoden.
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}.

%wo werden diese eingesetzt, paar beispiele. offline, online 
In recent years, smoothing gets attention mainly in the field of computer vision and ... Here, ...

Nevertheless, their are some promising approach for indoor localisation systems as well. For example ...

%smoothing im bezug auf indoor
Smoothing solutions in indoor localisation werden bisher nicht wirklich behandelt.  das liegt hauptsächlich daran das es sehr langsam ist \cite{}. es gibt ansätze von ... und ... diese benutzen blah und blah. wir machen das genauso/besser.