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added section recursive state estimation, and 3/4 of related work

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Toni
2016-04-19 07:45:23 +02:00
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tex/chapters/relatedwork.tex
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@@ -18,16 +18,20 @@ 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 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?}
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 the field of computer vision and ... Here, ...
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 ...