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deactivated comments from frank

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toni
2016-02-23 15:41:56 +01:00
parent 822f71f633
commit 208c0869bf
3 changed files with 19 additions and 19 deletions
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26
tex/chapters/grid.tex
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@@ -8,7 +8,7 @@
To sample only transitions that are actually feasible
within the environment, we utilize a \SI{20}{\centimeter}-gridded graph
$G = (V,E)$ with vertices $v_i \in V$ and undirected edges $e_{i,j} \in E$
\commentByFrank{notation geaendert. so ok?}
%\commentByFrank{notation geaendert. so ok?}
derived from the buildings floorplan as described in section \ref{sec:relatedWork}.
However, we add improved $z$-transitions by also modelling realistic
stairwells using nodes and edges, depicted in fig. \ref{fig:gridStairs}.
@@ -36,7 +36,7 @@
New states $\mStateVec_{t}$ may now be sampled by starting at the vertex for
position $\fPos{\mStateVec_{t-1}} = (x,y,z)^T$
\commentByFrank{eingefuehrt}
%\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 $\mObsVec_{t}$
@@ -48,21 +48,21 @@
\gDist &= \mObs_t^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2)
.
\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}
%\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}
%
During the random walk, each edge has its own probability $p(\mEdgeAB)$
which e.g. depends on the edge's direction $\angle \mEdgeAB$ and the
pedestrian's current heading $\gHead$.
Furthermore, section \ref{sec:nav} uses $p(\mEdgeAB)$ to incorporate prior path knowledge to
favour edges leading towards the pedestrian's desired target $\mVertexDest$.
\commentByFrank{fixed}
%\commentByFrank{fixed}
For each single movement on the graph, we calculate $p(\mEdgeAB)$ for all edges
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 $\mStepSize$.
\commentByFrank{step-size als variable}
%\commentByFrank{step-size als variable}
To quantify the improvement prior knowledge is able to provide,
we define a simple reference for $p(\mEdgeAB)$ that assigns a probability to each edge
@@ -105,7 +105,7 @@
themselves and nearby walls. To calculate paths that resemble this behaviour, an importance-factor is derived for
each vertex. Those will be used to scale the distance between two nodes, just like navigation systems use
the speed-limit as scaling-factor.
\commentByFrank{so besser? der ganze absatz.}
%\commentByFrank{so besser? der ganze absatz.}
To downvote vertices near walls, we need to determine the distance of each vertex from its nearest wall.
We therefore derive an inverted version $G' = (V', E')$ of the graph $G$, just describing walls and
obstacles. A nearest-neighbour search \cite{Cover1967} $\fNN{\mVertexA}{V'}$ within $V'$ provides the vertex
@@ -121,7 +121,7 @@
\enskip .
\label{eq:wallAvoidance}
\end{equation}
\commentByFrank{fixed. WA war WallAvoidance. hatte statt ll immer $\|$ gelesen und deshalb nicht verstanden}
%\commentByFrank{fixed. WA war WallAvoidance. hatte statt ll immer $\|$ gelesen und deshalb nicht verstanden}
%
%The parameters of the normal distribution and the scaling-factors were chosen empirically.
%While this approach provides good results for most areas, doors are downvoted by
@@ -155,7 +155,7 @@
\end{equation}
%
For $\mat{\Sigma}$, the two largest eigenvalues $\lambda_1, \lambda_2$ with $\lambda_1 > \lambda_2$
\commentByFrank{fixed}
%\commentByFrank{fixed}
are calculated. If their ratio $^{\lambda_1}/_{\lambda_2}$ is above a certain
threshold, the neighbourhood describes a flat ellipse and thus either a door or a straight wall.
%
@@ -180,7 +180,7 @@
the distance of a vertex $\mVertexA$ from its nearest door and a deviation
of \SI{1.0}{\meter}:
%
%\commentByFrank{distanzrechnung: formel ok?}
%%\commentByFrank{distanzrechnung: formel ok?}
\begin{equation}
\fDD{\mVertexA} = \mathcal{N}( \| \fPos{\mVertexA} - \vec{c} \| \mid 0.0, 1.0^2 )
\label{eq:doorDetection}
@@ -265,7 +265,7 @@
represents the most proper state of the posterior distribution at time $t-1$, is calculated.
%
%
%\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
%%\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
%\commentByToni{Das ist gar nicht so einfach... wir haben nie ein Sample Set eingefuehrt. Nicht mal einen Sample. Wir haben immer nur diesen State... Man könnte natuerlich einfach sagen das $\Upsilon_t$ an set of random samples representing the posterior distribution ist oder einfach nur ein set von partikeln. habs mal eingefuegt wie ich denke}
%
This centre serves as the starting point for the shortest-path calculation.
@@ -279,7 +279,7 @@ represents the most proper state of the posterior distribution at time $t-1$, is
%
We thus calculate the standard deviation of the distance of all sample-positions
$\fPos{\mStateVec_{t-1}}$ from aforementioned centre $\pathCentroid$.
\commentByFrank{so klarer? platz fuer groese Eq. fehlt und Notation zum ansprechen jedes einzelnen Particles vermeide ich lieber...}
%\commentByFrank{so klarer? platz fuer groese Eq. fehlt und Notation zum ansprechen jedes einzelnen Particles vermeide ich lieber...}
%\begin{equation}
% d_\text{cen} = \| pos(q_{t-1}) - \pathCentroid \|
@@ -309,7 +309,7 @@ represents the most proper state of the posterior distribution at time $t-1$, is
\enskip .
\label{eq:transShortestPath}
\end{equation}
\commentByFrank{$\mUsePath$ als variable}
%\commentByFrank{$\mUsePath$ als variable}
%
@@ -348,7 +348,7 @@ represents the most proper state of the posterior distribution at time $t-1$, is
Both possible paths are covered and slight deviations are possible.
Additionally shows the shortest-path calculation without (dashed) and with (solid) importance-factors
used for edge-weight-adjustment.}
\commentByFrank{so besser?}
%\commentByFrank{so besser?}
\label{fig:multiHeatMap}
\end{figure}