diff --git a/tex_review/chapters/misc.tex b/tex_review/chapters/misc.tex
index 47a0922..6c5f8a8 100644
--- a/tex_review/chapters/misc.tex
+++ b/tex_review/chapters/misc.tex
@@ -53,14 +53,21 @@ This allows the primary filter to recover, while retaining prior knowledge.
 However, we believe that such a combination of two independent filters is not necessary for most scenarios and thus the resulting overhead can be avoided.
 
 %neue methode:
-For the simplified version we distribute \SI{10000}{} samples uniformly within the complete building to approximate $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ as presented in section \ref{sec:wifi}.
-From the resulting probability grid $\probGrid_{t, \text{wifi}}$ we are able to identify the areas where the \docWIFI{} model assumes the pedestrian is most likely located. 
-Of course, this often results in a multimodal representation of the probability density and thus multiple possible whereabouts.  
+\add{For the simplified version we draw a number of $N_{\probGrid}$ locations $\mPosVec_{\probGrid} = (x,y,z)^T$ uniformly from the underlying navigation mesh.
+Based on this locations we then approximate $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ as described in section \ref{sec:wifi}. 
+This results in a set of probabilities associated with $\mPosVec_{\probGrid}$, we call probability grid $\probGrid_{t, \text{wifi}}$.
+It is important to notice, that $\probGrid_{t, \text{wifi}}$ is newly created in every filter update, independently of the filter's current particle set. 
+Based on the grid, we are able to identify the areas where the (standalone) \docWIFI{} model assumes the pedestrian to be most likely located.}
+This often results in a multimodal representation of the probability density and thus multiple possible whereabouts.  
 However, compared to the used particle filter, this representation enables us to monitor the complete building without any environmental restrictions and can thus be deployed as an indicator to detect sample impoverishment. 
 If $\probGrid_{t, \text{wifi}}$ and the current posterior $p(\mStateVec_{t} \mid \mObsVec_{1:t})$ show a significant difference, we can assume that either the posterior got stuck and suffers from impoverishment or the \docWIFI{} quality is low due to factors like attenuation or bad coverage. 
 A good measure of how one probability distribution differs from a second is the well-established Kullback-Leibler divergence $D_\text{KL}$ \cite{Fetzer-17}.
 To calculate $D_\text{KL}$, we need to sample densities from both probability density functions likewise. 
 For the posterior we use the results provided by our \del{rapid} kernel density estimation performed in the state estimation procedure, while $\probGrid_{t, \text{wifi}}$ is already in the desired form.
+\add{The number of $N_{\probGrid}$ is chosen empirically, depending on the size of the building and the detail of approximation required. 
+Based on our experience $N_{\probGrid} = \SI{10000}{}$ is a reasonable amount and keeps the workload stable for real time system.}
+%Using more then \SI{10000}{} locations would of course improve the approximation of $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$, however 
+
 %To handle $D_\text{KL}$ as probability, we use a positive exponential distribution 
 
 %	\begin{equation}