near to final draft

tex/chapters/experiments.tex

@@ -10,8 +10,8 @@
 	\label{fig:paths}
 \end{figure}
 %
-The experiments were carried out on all floors (0 to 3) of the faculty building. 
-Each floor is about \SI{77}{\meter} x \SI{55}{\meter} in size, with a ceiling height of \SI{3}{\meter}.
+The experiments were carried out on all four floors of the faculty building. 
+Each floor is about \SI{77}{\meter} x \SI{55}{\meter} in size, with a ceiling height of about \SI{3.0}{\meter}.
 To resemble real-world conditions, the evaluation took place during an in-house exhibition. 
 Thus, many places were crowded and Wi-Fi signals attenuated.
 As can be seen in fig. \ref{fig:paths} we arranged 4 distinct walks, covering different distances, critical sections and uncertain decisions leading to multimodalities. 
@@ -29,7 +29,7 @@ Even though, the error during the following few seconds is expected to be much h
 
 The measurements were recorded using a Motorola Nexus 6 and a Samsung Galaxy S5.
 As the Galaxy's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only, its scans take much longer than those of the Nexus: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}.
-Additionally, the Galaxy's barometer sensor provides fare more inaccurate and less frequent readings than the Nexus does. 
+Additionally, the Galaxy's barometer sensor provides far more inaccurate and less frequent readings than the Nexus does. 
 This results in a better localisation using the Nexus smartphone.	
 The computation for both filtering and smoothing was done offline using the aforementioned \mbox{CONDENSATION} algorithm and multinomal (cumulative) resampling. 
 For each path we deployed 10 MC runs using \SI{2500}{} particles. BS uses $500$ sample realisations drawn with a cumulative frequency.
@@ -89,8 +89,8 @@ Now, the positional average error along all 4 paths using the Nexus and the Gala
 The BS performs with an average error of \SI{2.21}{\meter} for filtering and  \SI{1.51}{\meter} for smoothing.
 The difference between both filtering steps is of course based upon the randomized behaviour of the respective probabilistic models. 
 It is interesting to note, that the positional error is very similar for both used smartphones, although the approximation error varies greatly. 
-Using the FBS, the Galaxy donates an average approximation error of \SI{4.03}{\meter} by filtering with \SI{7.74}{\meter}. 
-In contrast the Nexus 6 filters at \SI{5.11}{\meter} and results in \SI{3.87}{\meter} for smoothing.
+Using the FBS, the Galaxy provides an average approximation error of \SI{4.03}{\meter} while filtering resulted in \SI{7.74}{\meter}. 
+In contrast, the Nexus 6 filters with an error of \SI{5.11}{\meter} and \SI{3.87}{\meter} for smoothing.
 The BS has a similar improvement rate.
 
 
@@ -106,7 +106,7 @@ It can be clearly seen, how the smoothing compensates for the faulty detected fl
 Additionally, the initial error is reduced extremely, approximating the pedestrian's starting position down to a few centimetres.
 In the context of reducing the error as far as possible, fig. \ref{fig:int_path2} b) is a very interesting example. 
 Here, the filter offers a lower approximation and positional error in regard to the ground truth. 
-However it is obvious that smoothing causes the estimation to behave more natural instead of walking the supposed path. 
+However it is obvious that smoothing causes the estimation to behave more natural, due to the restrictive smoothing transition, instead of walking the supposed path. 
 This phenomena could be observed for both smoothers respectively.
 
 At next, we discuss the advantages and disadvantages of utilizing FBS and BS as fixed-lag smoother. 
@@ -128,8 +128,8 @@ For better distinction, the path was divided into $10$ individual segments.
 	\label{fig:lag_error_path4}
 \end{figure}
 %
-Again it can be observed, that both smoother enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 7). 
-Immediately after the first floor change, a long and straight walk down the hallway follows. 
+Again it can be observed, that both smoothers enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 7). 
+Immediately after the \newline first floor change, a long and straight walk down the hallway follows. 
 While the Wi-Fi component pulls the pedestrian into the rooms on the right side, the actual walking route was located on the left side of the floor (see ground truth in fig. \ref{fig:lag_comp_path4} seg. 6). 
 Here, the BS is able to slightly improve the path, whereas the FBS follows the filtering until the upcoming staircase provides the necessary information for adjustments.
 %It follows a critical area with high errors and multimodalities.
@@ -141,7 +141,7 @@ Especially in seg. 8 and 9 a big crowd was gathered and highly attenuated the Wi
 For an excessive amount of time, the absolute location estimated by the Wi-Fi component got stuck in the middle of seg. 8 and therefore delayed the estimation.
 The next viable measurements were then provided at the end of seg. 9.
 This suggests that the here presented smoothing transition is able to improve the estimated path visibly, but does not compensate for those jumps in a timely manner.  
-Finally, the BS provides an approximation error alongside all paths of $\SI{6.48}{\meter}$ for the Galaxy and $\SI{4.47}{\meter}$ for the Nexus by filtering with $\SI{7.92}{\meter}$ and $\SI{5.50}{\meter}$ respectively. 
+Finally, the BS provides an approximation error alongside all paths of $\SI{6.48}{\meter}$ for the Galaxy and $\SI{4.47}{\meter}$ for the Nexus, while filtering resulted in $\SI{7.92}{\meter}$ and $\SI{5.50}{\meter}$ respectively. 
 Whereas FBS improves the Galaxy's estimation from $\SI{7.73}{\meter}$ to $\SI{6.68}{\meter}$ and from $\SI{5.66}{\meter}$ to $\SI{4.80}{\meter}$ for the Nexus.
 As stated before, the main advantage of BS over FBS is the better computational time by just using a sub-set of particles for calculations.