\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 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 $\mathcal{O}(N)$.
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. 
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 other areas as indoor localisation. 
The early work of \cite{isard1998smoothing} demonstrates the possibilities of smoothing for visual tracking.
They used a combination of the CONDENSATION particle filter with a forward-backward smoother. 
Based on this pioneering approach, many different solutions for visual and multi-target tracking have been developed \cite{Perez2004}.
For example, in \cite{Platzer:2008} a particle smoother is used to reduce multimodalities in a blood flow simulation for human vessels. Or \cite{} 



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.





