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chhhhaaaaaannnggggees von Toni F.

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toni
2016-02-17 17:44:35 +01:00
parent bcb84a9138
commit e7ae0f7fef
4 changed files with 15 additions and 6 deletions
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8
tex/chapters/system.tex
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@@ -8,7 +8,7 @@
\begin{array}{ll}
&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})}_{\text{transition}}
\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,
\end{array}
\label{equ:bayesInt}
@@ -22,11 +22,11 @@
\end{equation}
%
where $x, y, z$ represent the position in 3D space, $\mObsHeading$ the user's heading and $\mStatePressure$ the
relative pressure prediction in hectopascal (hPa).
The recursive part of the density estimation contains all information up to time $t$.
relative atmospheric pressure prediction in hectopascal (hPa).
The recursive part of the density estimation contains all information up to time $t-1$.
Furthermore, the state transition models the pedestrian's movement as described in section \ref{sec:trans}.
%It should be noted, that we also include the current observation $\mObsVec_{t}$ in it.
Differing from the usual notation, the state transition also includes the current observation $\mObsVec_{t}$ \cite{Koeping14}.
As \cite{Koeping14-PSA} has proven, we are able to include the observation $\mObsVec_{t-1}$ into the state transition.
Containing all relevant sensor measurements to evaluate the current state, the observation vector is defined as follows:
%