39 lines
2.6 KiB
TeX
39 lines
2.6 KiB
TeX
\section{Related Work}
|
|
\label{sec:relatedWork}
|
|
% 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 $\mStateVec_t$.
|
|
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.
|
|
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 $\mathcal{O}(N)$.
|
|
However, it gives a poor representation of previous states \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, ...
|
|
|
|
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.
|
|
|
|
|
|
|
|
|
|
|