add activity recognition

tex/chapters/system.tex

@@ -17,11 +17,11 @@ The filtering equation to calculated the posterior is given by the recursion
 	\label{equ:bayesInt}
 \end{equation}
 %
-where $\mState$ is the hidden state and $\mObs_t$ provides the corresponding observation vector at time $t$.
+where $\mStateVec_t$ is the hidden state and $\mObsVec_t$ provides the corresponding observation vector at time $t$.
 As realization of \eqref{equ:bayesInt} we use the well-known CONDENSATION particle filter \cite{Isard98:CCD}.
 Here, the transition is used as proposal distribution and a resampling step is utilized to handle the phenomenon of weight degeneracy.
 
-The state $\mState$ is given by 
+The state $\mStateVec$ is given by 
 %
 \begin{equation}
 	\mStateVec = (x, y, z, \mStateHeading),\enskip
@@ -29,6 +29,7 @@ The state $\mState$ is given by
 \end{equation}
 %
 where $x, y, z$ represent the position in 3D space and $\mStateHeading$ is the user's current (absolute) heading. 
+In context of particle filtering, a particle is thus a weighted representation of one possible state $\mStateVec$.
 The observation vector is defined as 
 %
 \begin{equation}