added optimization results, finished chapter estimation in experiments

tex/chapters/experiments.tex

@@ -241,22 +241,41 @@ While the system’s dynamics are moving the particles outside, the faulty Wi-Fi
 Only with new measurements coming from the hallway or other parts of the building, the distribution and thus the KDE-estimation are able to recover. 
 
 This leads to the conclusion, that a weighted average approach provides a more smooth representation of the estimated locations and thus a higher robustness.
+A comparison between both methods is illustrated in fig. \ref{fig:estimationcomp} using a measuring sequence of walk 2.
+We have highlighted some interesting areas with coloured squares.
+The greatest difference between the respective estimation methods can be seen inside the green square, the gallery wing of the museum.
+While the weighted average (blue) produces a very straight estimated path, the KDE-based method (red) is much more volatile. 
+This can be explained by the many small rooms that pedestrians pass through. 
+The doors act like a bottleneck, which is why many particles run against walls and are thus either drawn on a new position within a reachable area (cf. section \ref{sec:estimation}) or walk along the wall towards the door.
+This causes a higher uncertainty and diversity of the posterior, what is more likely to be reflected by the KDE method than by the weighted average.
+Additionally, the pedestrian was forced seven times to look at paintings (stop walking) between \SI{10}{\second} and \SI{20}{\second}, just in this small area. 
+Nevertheless, even if both estimated paths look very different, they produce similar errors. 
 
-\todo{bild vom gesamten walk 2 und den unterschied zwischen weighted average estimation und kde estimation zeigen. wie sich das auf dne estimated path auswirkt. also der eine pfad springt viel und der andere ist halt smoother
+The purple square displays a situation in which a sample impoverishment was successfully resolved. 
+Due to a poorly working \docAPshort{}, in the lower corner of the big room the pedestrians passes before walking down the stairs, the majority of particles is dragged into the upper right corner of  that room and unable to walk down. 
+By allowing some particles to walk through the wall and thus down the stairs, the impoverishment could be dissolved. 
+The KDE-based estimation illustrates this behaviour very accurate.
+Another situation in which the estimated paths do not provide sufficient results can be seen inside the teal square. 
+The room is very isolated from the rest of the building, which is reflected in the fact that only 3 \docAPshort{}'s are detected.
+The pedestrians have been asked to cross the room at a quick pace, leading to a higher step rate and therefore update rate of the filter.
+The results within this area lead to the assumption, that even if Wi-Fi has a bad coverage, it influences the estimation results the most. 
+The PDR based transition alone is able to walk alongside the ground truth in an accurate manner. 
+However, this is of course only true if we consider this area individually, without the rest of the walk due to the accumulating bias of the relative sensors involved.
+In the end, it is a question of optimal harmony between transition and evaluation. 
+We hope to further improve such situations in future work by enabling the transition step to provide a weight to particles that walk very likely, especially in situation were Wi-Fi provides bad readings.
 
-vielleicht noch fig. 8 raus dafür. }
-
-In contrast, a KDE-based approach for estimation is able to resolve multimodalities. 
-It does not always provide the lowest error, since it depends more on an accurate sensor model then a weighted average approach, but is very 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 this approach opens a wide range of other possibilities for finding a best estimate.
-
-\begin{figure}[bt]
+\begin{figure}[t]
 	\centering
   \includegraphics[width=0.9\textwidth]{gfx/estimationPath2/combined_dummy.png}
 	\caption{Estimation results of walk 2 using the KDE method (orange) and the weighted-average (blue).}
-	\label{fig:apfingerprint}
+	\label{fig:estimationcomp}
 \end{figure}
 
+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 then a weighted average approach, but is very 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.
+
+
 
 
 

tex/gfx/optimization/results.txt

@@ -0,0 +1,14 @@
+Global Optimization:
+
+[  WiFiOptLDC] optimization result: 
+[  WiFiOptLDC]  - AvgPerAP   cnt(73)	min(0.000000)	max(9.555109)	range(9.555109)	med(4.985681)	avg(3.982592)	stdDev(2.942827)	
+[  WiFiOptLDC]  - Single:    cnt(1607)	min(-31.389175)	max(17.544662)	range(48.933838)	med(0.000305)	avg(-0.209369)	stdDev(6.079994)	
+[  WiFiOptLDC]  - SingleAbs: cnt(1607)	min(0.000000)	max(31.389175)	range(31.389175)	med(3.839722)	avg(4.713982)	stdDev(3.845587)
+
+
+Local Optimization:
+
+[  WiFiOptLDC] optimization result: 
+[  WiFiOptLDC]  - AvgPerAP   cnt(35)	min(0.000152)	max(7.472599)	range(7.472447)	med(1.253041)	avg(1.844023)	stdDev(1.933329)	
+[  WiFiOptLDC]  - Single:    cnt(312)	min(-12.710892)	max(13.446358)	range(26.157249)	med(-0.000275)	avg(-0.137351)	stdDev(3.787940)	
+[  WiFiOptLDC]  - SingleAbs: cnt(312)	min(0.000023)	max(13.446358)	range(13.446335)	med(1.721626)	avg(2.637260)	stdDev(2.722538)