push before merge

tex/chapters/experiments.tex

@@ -23,9 +23,9 @@ As the Galaxy's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band
 Additionally, the Galaxy's barometer sensor provides fare 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. 
-The state was then estimated using the weighted arithmetic mean of the particles. 
 However, the filter itself would be fast enough to run on the smartphone itself ($ \approx \SI{100}{\milli\second} $ per transition, single-core Intel\textsuperscript{\textregistered} Atom{\texttrademark} C2750).
 The computational times of the different smoothing algorithm will be discussed later. 
+Unless explicitly stated, the state was estimated using the weighted arithmetic mean of the particles. 
 
 As mentioned earlier, the position of all \docAP{}s (about 5 per floor) is known beforehand. 
 Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures.
@@ -40,7 +40,6 @@ While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text
 The step size $\mStepSize$ for the transition was configured to be \SI{70}{\centimeter} with an allowed derivation of \SI{10}{\percent}. The heading deviation in \refeq{eq:transSimple}, \refeq{eq:transShortestPath} and \refeq{eq:transMultiPath} was \SI{25}{\degree}.
 Edges departing from the pedestrian's destination are downvoted using $\mUsePath = 0.9$.
 
-
 % all paths we evaluated
 \begin{figure}
 	\input{gfx/eval/paths}
@@ -53,10 +52,54 @@ Edges departing from the pedestrian's destination are downvoted using $\mUsePath
 
 
 %kurz zeigen das activity recognition was bringt
+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.
+Fig. \ref{dd} shows the recognized activities for path 4 using the Nexus 6.
+Despite a short misdetection caused by faulty pressure readings, the recognition can be considered to be very robust and accurate.
+
+%Fixed Interval Smoothing
+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. 
+
+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. 
+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. 
+%The resulting positional error between estimated and ground truth along path 4 can be seen in fig. \ref{}. 
+Now, the positional error along all 4 paths could be improved from \SI{}{} to \SI{}{} for the galaxy and from \SI{}{} to \SI{}{} for the nexus.
+%Similar outcomes can be observed by adding a resampling step at the end of every smoothing iteration. 
+
+However, BS still outperforms the FBS by an average of \SI{}{} on all 4 paths using the same number of particles and \SI{500}{} sample realisations. 
+A visual example comparing both smoothing methods on path 4 is illustrated in fig. \ref{}.
+Another advantage of BS over FBS, is the ability to still improve the filtering results even while reducing the number of particles radical. 
+For example \SI{50}{} particles and \SI{25}{} sample realisations are providing reliable estimations similar to above experiments, though the risk of losing track is higher.
+
+Despite the very good outcomes provided by both interval smoother, there are some rare situations in which smoothing does not improve the filtered estimation or even improves the visual path. 
+For example fig. \ref{} depicts such a situation for path 3 using BS and measurements provided by the Galaxy S5.
+This shows that the smoothing results are of course highly depend upon the filtering performance.
+
+At next, we discuss the advantages and disadvantages of utilizing FBS and BS as fixed-lag smoother. 
+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. lediglich eine verbesserung von... deshalb konzentrieren wir uns bei der diskussion auf den BS.
+
+Fig. \ref{} illustrates the estimation results for path 4 using \SI{2500}{particles}, \SI{50}{sample realisations} for BS and a fixed-lag $\tau = 5$. 
+
+%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
+
+%ein paar worte zur berechenzeit.
+
 %Evaluation:
 %\begin{itemize}
 %	\item Filter ist immer der gleiche mit MultiPathPrediction und Importance Factors