further small changes

tex_review/chapters/experiments.tex

@@ -69,7 +69,7 @@ It implements the standard Android sensor functionalities and provides a very si
 As smartphones we used either a Samsung Note 2, Google Pixel One or Motorola Nexus 6.
 The computation of the state estimation as well as the \docWIFI{} optimization are done offline using an Intel Core i7-4702HQ CPU with a frequency of \SI{2.2}{GHz} running \add{\SI{8}{threads} on \SI{4}{cores}} and \SI{16}{GB} main memory. 
 \add{An offline computation has practical advantages, such as easier evaluation of the results or shorter waiting times due to higher computing power. 
-Nevertheless, Android App and offline application are both based on the same C++ backend for localization.}
+Nevertheless, Android app and offline application are both based on the same C++ backend for localization.}
 
 
 %However, similar to our \add{previously presented system}, the setup is able to run completely on commercial smartphones as it \add{is} written in high performant C++ code \cite{torres2017smartphone}. 
@@ -118,7 +118,9 @@ Finally, the respective estimation methods are discussed in section \ref{sec:eva
 \end{figure}
 
 To compare our old graph-based model with our novel transition model presented within section \ref {sec:transition}, we chose a simple scenario, in which a tester walks up and down a staircase several times. 
-We used 1000 particles and did not perform an evaluation and resampling step to maintain the pure performance of the transition (step and heading).
+We used \SI{5000}{} particles and did not perform an evaluation and resampling step to maintain the pure performance of the transition (step and heading).
+\add{The number of particles was heuristically chosen and is based on our previous experience from other scenarios and competitions.
+In addition, it sill allows a stable performance of our Android app for localization.}
 The filter starts at a fixed position and is updated after every newly recognized step. 
 We set $\sigma_\text{step} = 0.1$ and $\sigma_\text{turn} = 0.1$ likewise. 
 The cells of the gridded graph were \SI{20}{} x \SI{20}{\centi\meter} in size and the transition implemented as described in \cite{Ebner-16}. 
@@ -268,7 +270,7 @@ Here, we differ between the respective anti-impoverishment techniques presented
 The simple anti-impoverishment method is added to the resampling step and thus uses the transition method presented in chapter \ref{sec:transition}.
 In contrast, the $D_\text{KL}$-based method extends the transition and thus uses a standard cumulative resampling step. 
 We set $l_\text{max} =$ \SI{-75}{dBm} and $l_\text{min} =$ \SI{-90}{dBm}.
-For a better overview, we only used the KDE-based estimation, as the errors compared to the weighted-average estimation differ by only a few centimeter.
+For a better overview, we only used the KDE-based estimation, as the errors compared to the weighted-average estimation differ by only a few centimeter. 
 
 \begin{table}[t]
 	\centering
@@ -310,7 +312,7 @@ Walking down the stairs at \SI{80}{\second} does also recover the localization s
 \begin{figure}
 	\centering
 	\input{gfx/errorOverTimeWalk0/errorOverTime.tex}
-	\caption{Error development over time of a single Monte Carlo run of walk 0. Between \SI{10}{\second} and \SI{24}{\second} the Wi-Fi signal was highly attenuated, causing the system to get stuck and producing high errors. Both, the simple and the $D_\text{KL}$ anti-impoverishment method are able to recover early. However, between \SI{65}{\second} and \SI{74}{\second} the simple method produces high errors due to the high random factor involved.} 
+	\caption{Error development over time of a single particle filter run of walk 0. Between \SI{10}{\second} and \SI{24}{\second} the Wi-Fi signal was highly attenuated, causing the system to get stuck and producing high errors. Both, the simple and the $D_\text{KL}$ anti-impoverishment method are able to recover early. However, between \SI{65}{\second} and \SI{74}{\second} the simple method produces high errors due to the high random factor involved.} 
 	\label{fig:errorOverTimeWalk0}
 \end{figure}
 
@@ -379,7 +381,8 @@ Ironically, this is again some type of sample impoverishment, caused by the afor
 \subsection{Activity Recognition}
 \label{sec:eval:act}
 
-Wie gut ist die Activity...
+\commentByToni{Wie gut ist die Activity...}
+
 
 
 %%estimation
@@ -421,7 +424,7 @@ Due to a right turn the lower red particles are walking against a wall and thus
 
 Although, situations as displayed in fig. \ref{fig:walk1:kde} frequently occur, the KDE-estimation is not able to improve the overall estimation results.
 This can be seen in the corresponding error development over time plot given by fig. \ref{fig:walk1:kdeovertime}. 
-Here, the KDE-estimation performs slightly better then the weighted-average, however after deploying \SI{100}{} Monte Carlo runs, the difference becomes insignificant.
+Here, the KDE-estimation performs slightly better then the weighted-average, however after deploying \SI{100}{} runs of the particle filter, the difference becomes insignificant.
 It is obvious, that the above mentioned "correct" mode, not always provides the lowest error. 
 In some situations the weighted-average estimation is often closer to the ground truth. 
 Within our experiments this happened especially when entering or leaving thick-walled rooms, causing slow and attenuated Wi-Fi signals. 
@@ -472,7 +475,8 @@ We hope to further improve such situations in future work by enabling the transi
 
 To summarize, the KDE-based approach for estimation is able to resolve multimodalities. 
 It does not provide a smooth estimated path, since it depends more on an accurate sensor model than a weighted-average approach, but is suitable as a good indicator about the real performance of a sensor fusion system. 
-At the end, in the here shown examples we only searched for a global maxima, even though the KDE approach opens a wide range of other possibilities for finding a best estimate.
+At the end, in the here shown examples we only searched for a global maxima, even though the KDE approach opens a wide range of other possibilities for finding a best estimate. 
+\add{A detailed examination of the runtime performance of the used estimation methods in comparison to the state-of-the-art can be found in \cite{Bullmann-18}.}
 
 \commentByToni{Diskussion, wie die Contributions uns jetzt geholfen haben. Nochmal zusammengefasst.}