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added some comments. more to-do

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FrankE
2018-09-17 19:31:03 +02:00
parent 93082818ef
commit ed46dd65dd
5 changed files with 67 additions and 31 deletions
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13
tex/chapters/transition.tex
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@@ -84,7 +84,7 @@
\newcommand{\stepSize}{\mathcal{S}}
This data structure yields room for various strategies to be applied within the transition step.
The most simple approach uses an average pedestrian step size together with the
number of detected steps $\mObsSteps$ together and change in heading $\mObsHeading$
number of detected steps $\mObsSteps$ and change in heading $\mObsHeading$
gathered from sensor observations $\mObsVec_{t-1}$.
Combined with previously estimated position $(x,y)^T$ and heading $\mStateHeading$
%from $\mStateVec_{t-1}$
@@ -95,8 +95,9 @@
%
\begin{equation}
\begin{aligned}
x_t &=& \overbrace{x_{t-1}}^{\text{old pos.}}& & &+& \overbrace{\mObsSteps \cdot \stepSize}^{\text{distance}}& & &\cdot& \overbrace{\cos(\mStateHeading + \turnNoise)}^{\text{direction}}& & ,\enskip \turnNoise &\sim \mathcal{N}(\mObsHeading, \sigma_\text{turn}^2) \\
y_t &=& y_{t-1}\phantom{.}& & &+& \mObsSteps \cdot \stepSize& & &\cdot& \sin(\mStateHeading + \turnNoise)& & ,\enskip \stepSize &\sim \mathcal{N}(\SI{70}{\centi\meter}, \sigma_\text{step}^2)
x_t &=& \overbrace{x_{t-1}}^{\text{old pos.}}& & &+& \overbrace{\mObsSteps \cdot \stepSize}^{\text{distance}}& & &\cdot& \overbrace{\cos(\mStateHeading_{t})}^{\text{direction}}& & ,\enskip \turnNoise &\sim \mathcal{N}(\mObsHeading, \sigma_\text{turn}^2) \\
y_t &=& y_{t-1}\phantom{.}& & &+& \mObsSteps \cdot \stepSize& & &\cdot& \sin(\mStateHeading_{t})& & ,\enskip \stepSize &\sim \mathcal{N}(\SI{70}{\centi\meter}, \sigma_\text{step}^2) \\
\mStateHeading_{t} &=& \mStateHeading_{t-1} + \turnNoise\\
\end{aligned}
\end{equation}
\noindent{}with
@@ -105,7 +106,7 @@
\enskip\enskip\enskip
\text{and}
\enskip\enskip\enskip
x_{t-1},y_{t-1},\mStateHeading \in \mStateVec_{t-1}
x_{t-1},y_{t-1},\mStateHeading_{t-1} \in \mStateVec_{t-1}
\enskip.
\end{equation*}
@@ -120,6 +121,6 @@
that might be reachable. Increasing $\sigma_\text{step}$ and $\sigma_\text{turn}$ for those cases might also be a viable choice.
Likewise, just using some random position, omitting heading/steps might be viable as well.
\commentByFrank{es gaebe noch ganz andere ansaetze etc. aber wir haben wohl nicht mehr genug platz :P}
\commentByToni{ich denke aber auch, es langt.}
%\commentByFrank{es gaebe noch ganz andere ansaetze etc. aber wir haben wohl nicht mehr genug platz :P}
%\commentByToni{ich denke aber auch, es langt.}