added gfx

tex/chapters/smoothing.tex

@@ -115,7 +115,7 @@ In the following a simple and inexpensive approach for receiving this informatio
 
 By writing
 \begin{equation}
-p(\vec{q}_{t+1} \mid \vec{q}_t, \mObsVec_t)_{\text{step}} = \mathcal{N}(\Delta d_t \mid \mu_{\text{step}}, \sigma_{\gDist}^2)
+p(\vec{q}_{t+1} \mid \vec{q}_t, \mObsVec_t)_{\text{step}} = \mathcal{N}(\Delta d_t \mid \mu_{\text{step}}, \sigma_{\text{step}}^2)
 \label{eq:smoothingTransDistance}
 \end{equation}
 we receive a statement about how likely it is to cover a distance $\Delta d_t$ between two states $\vec{q}_{t+1}$ and $\vec{q}_{t}$.
@@ -123,8 +123,8 @@ In the easiest case, $\Delta d_t$ is the linear distance between two states.
 Of course, based on the graph structure, one could calculate the shortest path between both and sum up the respective edge lengths. 
 However, this requires tremendous calculation time for negligible improvements. 
 Therefore this is not further discussed within this work. 
-The average step length $\mu_{\text{step}}$ is based on the pedestrian's walking speed and $\sigma_{\gDist}^2$ denotes the step length's variance. 
-Both values are chosen depending on the activity $x$ recognized at time $t$. 
+The average step length $\mu_{\text{step}}$ is based on the pedestrian's walking speed and $\sigma_{\text{step}}^2$ denotes the step length's variance. 
+Both values are chosen depending on the activity $\mObsActivity$ recognized at time $t$. 
 For example $\mu_{\text{step}}$ gets smaller while a pedestrian is walking upstairs, than just walking straight.
 This requires to extend the smoothing transition by the current observation $\mObsVec_t$.
 Since $\mStateVec$ is hidden and the Markov property is satisfied, we are able to do so.