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refactored sample impoverishment a littel

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toni
2018-05-24 12:12:24 +02:00
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tex/chapters/misc.tex
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@@ -102,10 +102,13 @@ For this, the state transition model is extended.
Compared to the resampling step, as used by the first method, the transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ enables us to use prior measurements, which is obviously necessary for all \docWIFI{} related calculations. Compared to the resampling step, as used by the first method, the transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ enables us to use prior measurements, which is obviously necessary for all \docWIFI{} related calculations.
As described in chapter \ref{sec:transition}, our transition method only allows to sample particles at positions, that are actual feasible for a humans within a building e.g. no walking trough walls. As described in chapter \ref{sec:transition}, our transition method only allows to sample particles at positions, that are actual feasible for a humans within a building e.g. no walking trough walls.
If a particle targets a position which is not walk-able e.g. behind a wall, we draw a new position within a very small, but reachable area around its current position. If a particle targets a position which is not walk-able e.g. behind a wall, we draw a new position within a very small, but reachable area around its current position.
%To prevent sample impoverishment we extend our transition method. %
Instead of such a small are or even the complete building, as suggested in method one, we now define a sphere. %Instead of such a small area or even the complete building, as suggested in method one, we now define a sphere.
\todo{radius ist falsch! all connected triangles... warte aber noch aufs franks transition teil.} To prevent sample impoverishment we extend this transition method by making the reachable area depended upon $D_\text{KL}$ and the \docWIFI{} quality factor.
The radius is given by $D_\text{KL} \cdot q(\mObsVec_t^{\mRssiVec_\text{wifi}})$ and particles are drawn uniformly on the mesh enclosed by the sphere. Particles are thus drawn uniformly on a sub-region of the mesh, given by a radius $ r_\text{sub} = D_\text{KL} \cdot q(\mObsVec_t^{\mRssiVec_\text{wifi}})$.
The sub-region consists of all walk-able and connected triangles within $r_\text{sub}$, including stairs and elevators.
%\todo{radius ist falsch! all connected triangles... warte aber noch aufs franks transition teil.}
%The radius is given by $D_\text{KL} \cdot q(\mObsVec_t^{\mRssiVec_\text{wifi}})$ and particles are drawn uniformly on the mesh enclosed by the sphere.
This allows to increase the diversity of particles by the means of \docWIFI{}, allowing to ignore any restrictions made by the system, as long as the difference between $\probGrid_{t, \text{wifi}}$ and the posterior is high. This allows to increase the diversity of particles by the means of \docWIFI{}, allowing to ignore any restrictions made by the system, as long as the difference between $\probGrid_{t, \text{wifi}}$ and the posterior is high.
The subsequent evaluation step of the particle filter then reweights the particles, so that only those in proper regions will survive the resampling. The subsequent evaluation step of the particle filter then reweights the particles, so that only those in proper regions will survive the resampling.