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near to final draft

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toni
2016-05-11 16:30:36 +02:00
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tex/chapters/system.tex
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@@ -4,7 +4,7 @@
As mentioned before, most smoothing methods require a preceding filtering.
Similar to our previous works, we consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem.
Therefore, a Bayes filter that satisfies the Markov property is used to calculate the posterior, which is given by
Therefore, a Bayes filter that satisfies the Markov property is used to calculate the posterior:
%
\begin{equation}
\arraycolsep=1.2pt
@@ -12,16 +12,16 @@ Therefore, a Bayes filter that satisfies the Markov property is used to calculat
&p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\
&\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}} \enspace.
\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}}
\end{array}
\label{equ:bayesInt}
\end{equation}
%
Here, the previous observation $\mObsVec_{t-1}$ is included into the state transition \cite{Koeping14-PSA}.
Here, the previous observation $\mObsVec_{t-1}$ is included into the state transition \cite{Ebner-15}.
For approximating eq. \eqref{equ:bayesInt} by means of MC methods, the transition is used as proposal distribution, also known as CONDENSATION algorithm \cite{isard1998smoothing}.
This algorithm also performs a resampling step to handle the phenomenon of weight degeneracy.
In context of indoor localisation, the hidden state $\mStateVec$ is defined as follows:
In the context of indoor localisation, the hidden state $\mStateVec$ is defined as follows:
\begin{equation}
\mStateVec = (x, y, z, \mStateHeading, \mStatePressure),\enskip
x, y, z, \mStateHeading, \mStatePressure \in \R \enspace,