conclusion done

tex/chapters/conclusion.tex

@@ -1,17 +1,13 @@
 \section{Conclusion}
 
-map information into smoothing. better way and faster then just dijkstra. compensate big jumps caused by wifi. better method for estimation and drawing of particles in backward simulation. more advanced smoothing transition. not used evaluating using the observations, but using the given information for more advanced approaches. 
+Within this work a novel approach for utilizing the forward-backward smoother and backward simulation to problems of indoor localisation was presented.
+Both were implemented as fixed-lag and fixed-interval smoother. 
+It was shown that smoothing methods are able to decrease the estimation error and improving the overall localisation.
+Especially fixed-lag smoothing is a great tool for runtime support by reducing timely errors and improving the overall estimation with affordable costs.
+However, a fixed-lag smoother is not able to change the lag dynamically, as its name suggests. 
+Therefore, a dynamic-lag smoother could be able to further improve the estimation by considering higher lags in critical areas. 
 
-fixed-lag gap dynamic interval dependend upon estimation error variance
+Finally, the smoothing transition does not use any information provided by the underlying graph structure. 
+This would allow to use environmental informations and to replace the current line-of-sight model with a graph-based one.
+By incorporating the Wi-Fi's signal strength measurements a more advanced smoothing transition should be able to compensate for faulty Wi-Fi measurements and the hereby resulting jumps.
 
-\begin{figure}
-	\input{gfx/activity/activity_over_time}
-	\caption{activity recognition}
-	\label{fig:activityRecognition}
-\end{figure}
-
-\begin{figure}
-	\input{gfx/particles/particles}
-	\caption{particles. green = avg50, black = avg. gnuplot zickt bei der legende}
-	\label{fig:activityRecognition}
-\end{figure}

tex/chapters/experiments.tex

@@ -1,6 +1,15 @@
 \section{Experiments}
 
-
+% all paths we evaluated
+\begin{figure}
+	\input{gfx/eval/paths}
+	\caption{The four paths that were part of the evaluation.
+	Starting positions are marked with black circles.
+	For a better visualisation they were slightly shifted to avoid overlapping.}
+	%\commentByFrank{font war korrekt, aber die groesse war zu gross im vgl. zu den anderen}
+	\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}.
 To resemble real-world conditions, the evaluation took place during an in-house exhibition. 
@@ -43,18 +52,13 @@ For smoothing we set $\sigma^2_{\text{turn}} = \SI{5}{\degree}$ and $\sigma^2_z
 If walking or unknown are the current activities, $ \mu_{\text{step}} = \SI{0.7}{\meter}$, $ \mu_{\text{step}} = \SI{0.5}{}$ and $ \mu_z = \SI{0.0}{\meter}$ are used. 
 Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{step}}^2 = \SI{0.2}{}$ and $ \mu_z = \SI{-0.3}{\meter}$, otherwise $ \mu_{\text{step}} = \SI{0.5}{\meter}$, $ \sigma_{\text{step}}^2 = \SI{0.3}{}$ and $ \mu_z = \SI{0.3}{\meter}$ for walking downstairs.
 
-% all paths we evaluated
-\begin{figure}
-	\input{gfx/eval/paths}
-	\caption{The four paths that were part of the evaluation.
-	Starting positions are marked with black circles.
-	For a better visualisation they were slightly shifted to avoid overlapping.}
-	%\commentByFrank{font war korrekt, aber die groesse war zu gross im vgl. zu den anderen}
-	\label{fig:paths}
-\end{figure}
-
 
 %kurz zeigen das activity recognition was bringt
+\begin{figure}
+	\input{gfx/activity/activity_over_time}
+	\caption{activity recognition}
+	\label{fig:activityRecognition}
+\end{figure}
 By adding the activity recognition to the system of \cite{Ebner-16}, we are able to further improve the overall localisation results. 
 The approximation error decreases by an average of \SI{66666}{\centimeter} for all 4 paths on 10 MC runs.
 Due to this additional knowledge, the state transition samples mostly depending upon the current activity and therefore limits the possibility of false floor changes.
@@ -66,8 +70,13 @@ At first, both FBS and BS are compared in context of fixed-interval smoothing.
 As a reminder, fixed-interval smoother 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 timely information are negligible. 
 
+\begin{figure}
+	\input{gfx/particles/particles}
+	\caption{particles. green = avg50, black = avg. gnuplot zickt bei der legende}
+	\label{fig:particles}
+\end{figure}
 In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position. 
-As illustrated in fig. \ref{}, the estimated position for filtering and FBS is identical although the weights are highly different. 
+As illustrated in fig. \ref{fig:particles}, the estimated position for filtering and FBS is identical although the weights are highly different. 
 To address this problem, we are calculating the average state using the \SI{50}{\percent} best weighted particles.
 For evaluating the FBS this estimation method was applied to filtering and smoothing likewise.
 We deployed 10 MC runs using \SI{2500}{} particles for approximation. 
@@ -101,29 +110,33 @@ At next, we discuss the advantages and disadvantages of utilizing FBS and BS as
 Compared to fixed-interval smoothing, timely 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}.
 
-%as seen fbs war im fixed interval schon nicht so gut, im lag ist sein einfluss vernachlässigbar. optische und error technische verbesserung sind kaum vorhanden. lediglich eine verbesserung von  deshalb konzentrieren wir uns bei der diskussion auf den BS. trotzdem verschlechtert sich das ergebniss aber auch nicht. die verbesserung ist nur nicht so signifikant wie bei bs
-
 %wie gut ist fixed-lag mit einem lag = 5. was fällt so auf?
 Fig. \ref{} illustrates the estimation results for path 4 using \SI{2500}{particles}, \SI{500}{sample realisations} for BS and a fixed-lag $\tau = 5$. 
 It can be seen that again BS provides a better overall estimation, especially in areas where the user is changing floors. 
 Besides the positional quality, also the timely error could be reduced by both algorithms using this fixed-lag.
 Once more, the BS outperforms the FBS by providing an overall approximation error of $\SI{55}{\centimeter}$ by filtering with $\SI{55}{\centimeter}$, while FBS improves to $\SI{55}{\centimeter}$.
+The median errors for all conducted walks are listed in table \ref{}. 
+Similar to fixed-interval smoothing, decreasing the number of particles does not necessarily worsen the estimation. 
+In most cases smoothing compensates for this reduction and maintains the good results.
+For example estimating path for using \SI{50}{particles} results in an approximation error for BS of \SI{}{\meter}.
 
+%lag vergrößern was passiert beschreiben
 Besides changing the number of particles, it is also possible 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 in fig. \ref{}. 
 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 
+Nevertheless, there are practical applications like accurately verifying hit checkpoints or continuously optimizing a recurring segment of the path.
+The different approximation errors alongside path 4 can now be seen in fig. \ref{}. 
 
-\todo{Experimente noch etwas theoretisch verfeinert. Nicht nur bloße beobachtungen}
 
-%lag vergrößern was passiert beschreiben
 
-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. 
+
+
+%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.
+%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.
 
@@ -134,7 +147,7 @@ bei weniger partikeln bringt fixed-lag und fixed-interval smoothing im verhältn
 
 %beispiel multimodalität
 
-%Tabelle mit spalten interval partikel, lag partikel; spalten: filter, BS, FBS
+%Tabelle mit spalten interval partikel, lag, partikel; spalten: filter, BS, FBS
 
 %Evaluation:
 %\begin{itemize}