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toni
2018-05-23 20:48:00 +02:00
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@@ -101,12 +101,13 @@ Finally, we have all necessary tools to introduce a second method to prevent imp
For this, the state transition model is extended. 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 it. 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. %To prevent sample impoverishment we extend our transition method.
Instead of drawing particles like this or even the complete building, as suggested in method one, we define a sphere. Instead of such a small are or even the complete building, as suggested in method one, we now define a sphere.
The radius is given by $D_\text{KL} \cdot q(\mObsVec_t^{\mRssiVec_\text{wifi}})$. \todo{radius ist falsch! all connected triangles... warte aber noch aufs franks transition teil.}
This allows to increase the diversity of particles by the means of \docWIFI{}. 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.
The subsequent evaluation of the particle filter then reweights the particles, so that only those in proper regions will survive the resampling. 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.
To further improve the method we give particles a chance of \SI{0.01}{\percent} to walk trough a nearby wall, if the destination is not outside. To further improve the method we give particles a chance of \SI{0.01}{\percent} to walk trough a nearby wall, if the destination is not outside.
This enables to handle sample impoverishment more quickly in situations caused by environmental restrictions, even when the \docWIFI{} quality is low. This enables to handle sample impoverishment more quickly in situations caused by environmental restrictions, even when the \docWIFI{} quality is low.