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added mc sampling and fixed some stuff in smoothing

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Toni
2016-04-26 20:46:32 +02:00
parent 33f8acbcab
commit df1be331a6
2 changed files with 6 additions and 16 deletions
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15
tex/chapters/smoothing.tex
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@@ -1,16 +1,13 @@
\section{Smoothing}
\label{sec:smoothing}
The main purpose of this work is to provide MC smoothing methods in context of indoor localisation.
As mentioned before, those algorithm 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 $T$.
The main purpose of this work is to provide smoothing methods in context of indoor localisation.
As mentioned before, those algorithm 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 $T$.
%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.
Further, two novel approaches for incorporating them into the localisation system are shown.
\todo{Einfuehren von $X$ und etwas konkreter schreiben.}
\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}.
@@ -31,8 +28,6 @@ The weights are obtained through the backward recursion in line 9.
\caption{Forward-Backward Smoother}
\label{alg:forward-backwardSmoother}
\begin{algorithmic}[1] % The number tells where the line numbering should start
\Statex{\textbf{Input:} Prior $\mu(\vec{X}^i_1)$}
\Statex{~}
\For{$t = 1$ \textbf{to} $T$} \Comment{Filtering}
\State{Obtain the weighted trajectories $ \{ W^i_t, \vec{X}^i_t\}^N_{i=1}$}
\EndFor
@@ -65,8 +60,6 @@ Therefore, \cite{Godsill04:MCS} presented the backward simulation (BS). Where a
\caption{Backward Simulation Smoothing}
\label{alg:backwardSimulation}
\begin{algorithmic}[1] % The number tells where the line numbering should start
\Statex{\textbf{Input:} Prior $\mu(\vec{X}^i_1)$}
\Statex{~}
\For{$t = 1$ \textbf{to} $T$} \Comment{Filtering}
\State{Obtain the weighted trajectories $ \{ W^i_t, \vec{X}^i_t\}^N_{i=1}$}
\EndFor
@@ -88,7 +81,3 @@ This method can be seen in algorithm \ref{alg:backwardSimulation} in pseudo-algo
\subsection{Transition for Smoothing}
%komplexität eingehen
The reason for not behandeln liegt ...
However, \cite{} and \cite{} have proven this wrong and reduced the complexity of different smoothing methods.