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toni
2016-05-11 16:30:36 +02:00
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tex/chapters/smoothing.tex
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\section{Smoothing}
\label{sec:smoothing}
The main purpose of this work is to provide MC smoothing methods in context of indoor localisation.
The main purpose of this work is to provide MC smoothing methods in the context of indoor localisation.
As mentioned before, those algorithms are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$ and are therefore able to make use of future observations between $t$ and $T$, where $t \ll T$.
%Especially fixed-lag smoothing is very promising in context of pedestrian localisation.
In the following we discuss the algorithmic details of the forward-backward smoother and the backward simulation.
@@ -9,7 +9,7 @@ Further, a novel approach for incorporating them into the localisation system is
\subsection{Forward-backward Smoother}
The forward-backward smoother (FBS) of \cite{Doucet00:OSM} is a well established alternative to the simple filter-smoother. The foundation of this algorithm was again laid by Kitagawa in \cite{kitagawa1987non}.
The forward-backward smoother (FBS) of \cite{doucet2000} is a well established alternative to the simple filter-smoother. The foundation of this algorithm was again laid by Kitagawa in \cite{kitagawa1987non}.
An approximation is given by
\begin{equation}
p(\vec{q}_t \mid \vec{o}_{1:T}) \approx \sum^N_{i=1} W^i_{t \mid T} \delta_{\vec{X}^i_{t}}(\vec{q}_{t}) \enspace,