changed colors of boxkde and weighted average

tex/chapters/misc.tex

@@ -1,7 +1,7 @@
 \section{Particle Filtering}
 
 As described earlier, we use a CONDENSATION particle filter to implement the recursive state estimator described in section \ref{sec:rse}.
-A set of particles is defined by $\{\vec{X}^i_{t}, w^i_{t} \}_{i=1}^N$, where $\mParticleVec^{i}_{t}$ is sampled based on the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$.
+A set of $N$ particles is defined by $\{\vec{X}^i_{t}, w^i_{t} \}_{i=1}^N$, where $\mParticleVec^{i}_{t}$ is sampled based on the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$.
 The weight $w_t^i$ is obtained by the probability density of the state evaluation $p(\mObsVec_{t} \mid \mStateVec_{t})$.
 A particle set approximates the posterior as follows:
 
@@ -103,10 +103,11 @@ Finally, we have all necessary tools to implement the second method to prevent i
 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.
 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 deploy a strategy how to handle this. 
+For example, drawing a new position within a very small, but reachable area around the particle's current position. 
 %
 %Instead of such a small area or even the complete building, as suggested in method one, we now define a sphere.
-To prevent sample impoverishment we extend this transition method by making the reachable area depended upon $D_\text{KL}$ and the \docWIFI{} quality factor.
+To prevent sample impoverishment we extend this transition strategy by making the reachable area depended upon $D_\text{KL}$ and the \docWIFI{} quality factor.
 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.}