commit for merge

tex/chapters/experiments.tex

@@ -77,6 +77,8 @@ Now, the positional error along all 4 paths could be improved from \SI{}{} to \S
 
 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{fig:intcomp}.
+The estimation of BS (blue) looks way more realistic and adapts better to the ground truth path.
+However, in this particular example the FBS (red) starts at an earlier position, better handling the initial uniform distribution. 
 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.
 \begin{figure}
@@ -103,6 +105,18 @@ Especially interesting in this context are small lags $\tau < 10$ considering fi
 
 %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 $\SI{55}{\centimeter}$.
+
+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 
+
+\todo{Experimente noch etwas theoretisch verfeinert. Nicht nur bloße beobachtungen}
 
 %lag vergrößern was passiert beschreiben