final version of paper

tex/chapters/experiments.tex

@@ -73,12 +73,8 @@ Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{s
 	\label{fig:particles}
 \end{figure}
 At first, both FBS and BS are compared in context of fixed-interval smoothing.
-As a reminder, fixed-interval smoother are \commentByFrank{smootherS? oder IS using?} using all observations until time $T$
-\commentByFrank{AND therefore run offline?}
-therefore run offline, after the filtering procedure is finished.
-Thus, we calculate only the positional error between estimation and ground truth, since timely
-\commentByFrank{timeLY passt IMHO hier nicht weil auf information bezogen -> kein adverb. time information? time-based information? timed information?}
-information are negligible. 
+As a reminder, fixed-interval smoothers are using all observations until time $T$ and therefore run offline, after the filtering procedure is finished.
+%Thus, we calculate only the positional error between estimation and ground truth, since temporal information are negligible. 
 %
 In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position.
 Fig. \ref{fig:particles} illustrates the filtered and smoothed particle set at a certain time step on path 4. 
@@ -114,18 +110,6 @@ Here, the filter offers a lower approximation and positional error in regard to
 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 utilising FBS and BS as fixed-lag smoother. 
-Compared to fixed-interval smoothing, timely 
-\commentByFrank{timeLY ist IMHO hier falsch, weil es sich auf error bezieht -> kein adverb. timeED errors? timing errors? time errors? time-based errors?}
-errors are now of higher importance due to an interest on real-time localization. 
-Especially interesting in this context are small lags $\tau < 10$
-\commentByFrank{WARUM sind die interesining? -> weil es fuer echtzeitsysteme brauchbar ist? falls noch platz ist, kurzer satz?}
-considering filter updates near \SI{500}{\milli\second}.
-Fig. \ref{fig:lag_comp_path4} illustrates the different estimations for path 4 using a fixed-lag $\tau = 5$. 
-The associated approximation errors alongside the path can additionally be seen in fig. \ref{fig:lag_error_path4}. 
-Due to the small number of sample realisations for BS and the additional resampling for FBS, the errors are changing very frequently in contrast to the filter.
-For better distinction, the path was divided into $10$ individual segments.
-%
 \begin{figure}
 	\centering
 	\input{gfx/eval/lag_path4_comp/path4_lag_comp}
@@ -138,67 +122,46 @@ For better distinction, the path was divided into $10$ individual segments.
 	\caption{%
 		Error development while walking along Path 4 using the Nexus 6.
 		Especially in segments including floor changes, the error is reduced visibly by using smoothing methods.
-		The black line denotes the activity detected during each timestep.
+		The black line denotes the activity detected during each time step.
 	}
 	\label{fig:lag_error_path4}
 \end{figure}
 %
+At next, we discuss the advantages and disadvantages of utilising FBS and BS as fixed-lag smoother. 
+Compared to fixed-interval smoothing, timing errors are now of higher importance due to an interest on real-time localization. 
+Especially interesting in this context are small lags $\tau < 10$ considering filter updates near \SI{500}{\milli\second}.
+Fig. \ref{fig:lag_comp_path4} illustrates the different estimations for path 4 using a fixed-lag $\tau = 5$. 
+The associated approximation errors alongside the path can additionally be seen in fig. \ref{fig:lag_error_path4}. 
+Due to the small number of sample realisations for BS and the additional resampling for FBS, the errors are changing very frequently in contrast to the filter.
+For better distinction, the path was divided into $10$ individual segments.
 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. 
+The black line denotes the activity detect during each time step. 
+Here, the camel humps while changing a floor can be explained by a flat area in the middle of the stairs.
+Further, two short false detections can be observed in seg. 2 and seg. 6. 
+Immediately after the 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.
 %Due to an in-house exhibition during the time of recording, we had to leave the ground truth by a few meters and Wi-Fi was strongly attenuated.
 By looking at fig. \ref{fig:lag_comp_path4} seg. 9 it seems that both smoothing methods are highly improving the error. 
 However, the approximation error in this area is similar to the filter and only the positional error decreases.
-This timely error \commentByFrank{same here: LY} is caused by a phenomenon we call Wi-Fi jump. 
+This temporal error is caused by a phenomenon we call Wi-Fi jump. 
 Especially in seg. 8 and 9 a big crowd was gathered and highly attenuated the Wi-Fi signal. 
 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. \commentByFrank{hier auch, denke ich}
+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 temporal 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, 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.
 
 Reducing the number of particles down to $500$ does not necessarily worsen the estimation. 
 In most cases smoothing compensates for this reduction and maintains the good results.
-Besides changing the number of particles, it is also possible the \commentByFrank{possible TO?} variate the lag. 
+Besides changing the number of particles, it is also possible to the variate the lag. 
 As one would expect, increasing the lag causes the smoothed estimation to approach the results provided by fixed-interval smoothing. 
 %This can be verified by looking at fig. \ref{}, which is a detailed view of segment XX of path 4 (cf. fig. \ref{fig:intcomp}). 
 It is obvious that a lag of \SI{30}{} time steps has access to much more future observations and is therefore able to obtain such a result. 
 Considering an update interval of \SI{500}{\milli\second}, a lag of \SI{30}{} would however mean that the smoother is \SI{15}{\second} behind the filter.
 Nevertheless, there are practical applications like accurately verifying hit checkpoints or continuously optimizing a recurring segment of the path.
 
-%verlgeich noch zwischen bs und fbs. bs weniger partikel und somit schneller. ändern der estimations kann aber auch ein möglichkeit sein.
-
-
-
-
-%fixed-lag reduces the error about... however, as seen in fig. \ref{} ist der bloße error nicht unbedingt ausschlaggebend für die verbesserung. fast immer liefert smoothing pfade die realistischer sind, aber die error erhöhen. 
-
-%conclusion der experimente
-%bei weniger partikeln bringt fixed-lag und fixed-interval smoothing im verhältnis sogar mehr! weil es da mehr zum "aufräumen" gibt. trotzdem hängt die performane natürlich stark vom vorwärtsschritt ab und man sollte nicht all zu wenige waehlen und lieber auf nummer sicher gehen. bs ist im vergleich zu fbs ein gutes stück besser in unserem fall. das hängt auch stark mit dem bereits sehr guten filtering schritt zusammen. man könnte aber trotzdem schlussfolgern das bs besser für indoor ist.
-
-%fbs ist hier mies und liegt direkt über dem filter? oder ein fbs mit anderer estimaton und den filter nicht anzeigen?! das ist doch quatsch... wennn ich den filter net anzeige. notfalls einfach den fbs nicht nehmen. sondern sagen das er net taugt und rauswerfen.
-
-%Smoothing mit großen lag kann die zeitliche information schwer halten. das liegt hauptsächlich daran, das im smoothing nur die relativen positionsinfos genutzt werden. das wi-fi wird nicht beachtet und deswegen können absolute justierungen der position (sprünge) nur sehr schlecht abgefedert werden. 
-
-
-%fixed lag smoothing verbessert den pfad ein wenig und vor allem bügelt unrealistische sprunge aus. daher wird der zeitlich verzug gut herrausgerechnet. 
-
-%beispiel multimodalität
-
-%Tabelle mit spalten interval partikel, lag, partikel; spalten: filter, BS, FBS
-
-%Evaluation:
-%\begin{itemize}
-%	\item Filter ist immer der gleiche mit MultiPathPrediction und Importance Factors
-%	\item FBS Interval mit 500 und 2500 Partikeln auf 4 Pfaden mit SimpleSmoothingTrans
-%	\item BS Interval mit 500 zu 100 und 2500 zu 500 Partikeln auf auf 4 Pfaden mit SimpleSmoothingTrans
-%	\item FBS Lag = 5 mit 500 und 2500 Partikeln auf 4 Pfaden mit SimpleSmoothingTrans
-%	\item BS Lag = 5 mit 500 zu 100 und 2500 zu 500 Partikeln auf auf 4 Pfaden mit SimpleSmoothingTrans
-%	\item BS Lag zu Error Plot. Lag von 0 bis 100, wie verhält sich der Error. Am besten auf Pfad 4 mit SimpleSmoothingTrans.
-%\end{itemize}
-