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Merge branch 'master' of https://git.frank-ebner.de/FHWS/Fusion2016

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FrankE
2016-02-29 12:13:15 +01:00
parent 020cbc5d94 cabf60c851
commit 44120a63a5
5 changed files with 26 additions and 29 deletions
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14
tex/chapters/grid.tex
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@@ -38,14 +38,14 @@
%\commentByFrank{eingefuehrt}
and walking along adjacent nodes into a given walking-direction $\gHead$ until a distance $\gDist$ is
reached \cite{Ebner-15}.
Both, heading and distance, are supplied by the current sensor readings $\mObsVec_{t}$
Both, heading and distance, are supplied by the previous sensor readings $\mObsVec_{t-1}$
and thus reflect the pedestrian's real heading and walking speed including uncertainty.
Working with relative sensor readings, the state's heading is updated during each transition:
%
\begin{align}
\gHead &= \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_t^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
\gDist &= \mObs_t^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2)
.
\gHead &= \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_{t-1}^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
\gDist &= \mObs_{t-1}^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2)
\enspace .
\end{align}
%\commentByFrank{fixed. war das falsche makro in (2) und dem satz darunter. das delta musste weg. der state hat ein absolutes heading. step-size als variable}
%
@@ -60,7 +60,7 @@
connected to a vertex $\mVertexA$, and, hereafter, randomly draw the to-be-walked edge
depending on those probabilities. This step is repeated until the sum
of the length of all used edges exceeds $d$. The latter depends on the number of
detected steps $\mObs_t^{\mObsSteps}$ and the pedestrian's step-size $\mStepSize$.
detected steps $\mObs_{t-1}^{\mObsSteps}$ and the pedestrian's step-size $\mStepSize$.
%\commentByFrank{step-size als variable}
To quantify the improvement prior knowledge is able to provide,
@@ -68,7 +68,7 @@
just based on its deviation from the currently estimated heading $\gHead$:
%
\begin{equation}
p(\mEdgeAB) = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{dev}^2).
p(\mEdgeAB) = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{dev}^2) \enspace .
\label{eq:transSimple}
\end{equation}
%
@@ -210,7 +210,7 @@
%
To route the pedestrian towards his desired target, a modified version
of Dijkstra's algorithm is used. Instead of calculating the shortest path from the start to the end,
the direction is inverted and the calculated terminates as soon as every single node was evaluated.
the direction is inverted and the calculation terminates as soon as every single node was evaluated.
Hereafter, every node in the grid knows the distance and shortest path to the pedestrian's target.
To get realistic path suggestions, we use the importance-factors to adjust the edge-weight