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added tex comments
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kazu
2016-05-22 14:39:19 +02:00
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6
tex/chapters/conclusion.tex
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@@ -1,8 +1,8 @@
\section{Conclusion} \section{Conclusion}
Within this work a novel approach for utilizing the forward-backward smoother and backward simulation to problems of indoor localisation was presented. Within this work a novel approach for utilizing \commentByFrank{utiliSing?} the forward-backward smoother and backward simulation to problems of indoor localisation was presented.
Both were implemented as fixed-lag and fixed-interval smoother. 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. It was shown that smoothing methods are able to decrease the estimation error and improving \commentByFrank{are able to decrease ... and improve. ING weg?} 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. Especially fixed-lag smoothing is a great tool for runtime support by reducing timely \commentByFrank{wieder} 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. 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. Therefore, a dynamic-lag smoother could be able to further improve the estimation by considering higher lags in critical areas.

30
tex/chapters/experiments.tex
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@@ -73,8 +73,12 @@ Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{s
\label{fig:particles} \label{fig:particles}
\end{figure} \end{figure}
At first, both FBS and BS are compared in context of 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 $T$ therefore run offline, after the filtering procedure is finished. As a reminder, fixed-interval smoother are \commentByFrank{smootherS? oder IS using?} using all observations until time $T$
Thus, we calculate only the positional error between estimation and ground truth, since timely information are negligible. \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.
% %
In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position. 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. Fig. \ref{fig:particles} illustrates the filtered and smoothed particle set at a certain time step on path 4.
@@ -110,9 +114,13 @@ 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. 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. This phenomena could be observed for both smoothers respectively.
At next, we discuss the advantages and disadvantages of utilizing FBS and BS as fixed-lag smoother. At next, we discuss the advantages and disadvantages of utilising 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. Compared to fixed-interval smoothing, timely
Especially interesting in this context are small lags $\tau < 10$ considering filter updates near \SI{500}{\milli\second}. \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 $\tau = 5$. 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}. 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. 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.
@@ -127,7 +135,11 @@ For better distinction, the path was divided into $10$ individual segments.
\begin{figure} \begin{figure}
\centering \centering
\input{gfx/eval/lag_path4_comp/error_timed} \input{gfx/eval/lag_path4_comp/error_timed}
\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.} \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.
}
\label{fig:lag_error_path4} \label{fig:lag_error_path4}
\end{figure} \end{figure}
% %
@@ -139,18 +151,18 @@ Here, the BS is able to slightly improve the path, whereas the FBS follows the f
%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. %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. 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. However, the approximation error in this area is similar to the filter and only the positional error decreases.
This timely error is caused by a phenomenon we call Wi-Fi jump. This timely error \commentByFrank{same here: LY} 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. 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. 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. 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. 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}
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. 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. 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. 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. 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. In most cases smoothing compensates for this reduction and maintains the good results.
Besides changing the number of particles, it is also possible the variate the lag. Besides changing the number of particles, it is also possible the \commentByFrank{possible TO?} variate the lag.
As one would expect, increasing the lag causes the smoothed estimation to approach the results provided by fixed-interval smoothing. 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}). %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. 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.

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tex/gfx/eval/lag_path4_comp/error_timed.eps
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tex/gfx/eval/lag_path4_comp/error_timed.tex
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@@ -79,39 +79,39 @@
\fi% \fi%
\setlength{\fboxrule}{0.5pt}% \setlength{\fboxrule}{0.5pt}%
\setlength{\fboxsep}{1pt}% \setlength{\fboxsep}{1pt}%
\begin{picture}(4896.00,2014.00)% \begin{picture}(4896.00,2160.00)%
\gplgaddtomacro\gplbacktext{% \gplgaddtomacro\gplbacktext{%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(475,1284){\makebox(0,0)[r]{\strut{}\footnotesize{walk}}}% \put(409,1383){\makebox(0,0)[r]{\strut{}\footnotesize{walk}}}%
\put(475,1469){\makebox(0,0)[r]{\strut{}\footnotesize{stairs}}}% \put(409,1585){\makebox(0,0)[r]{\strut{}\footnotesize{stairs}}}%
\put(475,220){\makebox(0,0)[r]{\strut{}\footnotesize{0.0 m}}}% \put(409,220){\makebox(0,0)[r]{\strut{}\footnotesize{0.0 m}}}%
\put(475,405){\makebox(0,0)[r]{\strut{}\footnotesize{2.0 m}}}% \put(409,422){\makebox(0,0)[r]{\strut{}\footnotesize{2.0 m}}}%
\put(475,590){\makebox(0,0)[r]{\strut{}\footnotesize{4.0 m}}}% \put(409,624){\makebox(0,0)[r]{\strut{}\footnotesize{4.0 m}}}%
\put(475,775){\makebox(0,0)[r]{\strut{}\footnotesize{6.0 m}}}% \put(409,827){\makebox(0,0)[r]{\strut{}\footnotesize{6.0 m}}}%
\put(475,960){\makebox(0,0)[r]{\strut{}\footnotesize{8.0 m}}}% \put(409,1029){\makebox(0,0)[r]{\strut{}\footnotesize{8.0 m}}}%
\put(639,0){\makebox(0,0){\strut{}\footnotesize{20 s}}}% \put(574,0){\makebox(0,0){\strut{}\footnotesize{20 s}}}%
\put(1286,0){\makebox(0,0){\strut{}\footnotesize{40 s}}}% \put(1230,0){\makebox(0,0){\strut{}\footnotesize{40 s}}}%
\put(1932,0){\makebox(0,0){\strut{}\footnotesize{60 s}}}% \put(1887,0){\makebox(0,0){\strut{}\footnotesize{60 s}}}%
\put(2579,0){\makebox(0,0){\strut{}\footnotesize{80 s}}}% \put(2544,0){\makebox(0,0){\strut{}\footnotesize{80 s}}}%
\put(3226,0){\makebox(0,0){\strut{}\footnotesize{100 s}}}% \put(3200,0){\makebox(0,0){\strut{}\footnotesize{100 s}}}%
\put(3872,0){\makebox(0,0){\strut{}\footnotesize{120 s}}}% \put(3857,0){\makebox(0,0){\strut{}\footnotesize{120 s}}}%
\put(4519,0){\makebox(0,0){\strut{}\footnotesize{140 s}}}% \put(4514,0){\makebox(0,0){\strut{}\footnotesize{140 s}}}%
}% }%
\gplgaddtomacro\gplfronttext{% \gplgaddtomacro\gplfronttext{%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(866,1654){\makebox(0,0){\strut{}\footnotesize{2}}}% \put(804,1787){\makebox(0,0){\strut{}\footnotesize{2}}}%
\put(1464,1654){\makebox(0,0){\strut{}\footnotesize{3}}}% \put(1411,1787){\makebox(0,0){\strut{}\footnotesize{3}}}%
\put(1868,1654){\makebox(0,0){\strut{}\footnotesize{4}}}% \put(1821,1787){\makebox(0,0){\strut{}\footnotesize{4}}}%
\put(2240,1654){\makebox(0,0){\strut{}\footnotesize{5}}}% \put(2199,1787){\makebox(0,0){\strut{}\footnotesize{5}}}%
\put(2886,1654){\makebox(0,0){\strut{}\footnotesize{6}}}% \put(2856,1787){\makebox(0,0){\strut{}\footnotesize{6}}}%
\put(3565,1654){\makebox(0,0){\strut{}\footnotesize{7}}}% \put(3545,1787){\makebox(0,0){\strut{}\footnotesize{7}}}%
\put(3937,1654){\makebox(0,0){\strut{}\footnotesize{8}}}% \put(3923,1787){\makebox(0,0){\strut{}\footnotesize{8}}}%
\put(4325,1654){\makebox(0,0){\strut{}\footnotesize{9}}}% \put(4317,1787){\makebox(0,0){\strut{}\footnotesize{9}}}%
\put(4680,1654){\makebox(0,0){\strut{}\footnotesize{10}}}% \put(4678,1787){\makebox(0,0){\strut{}\footnotesize{10}}}%
\put(1031,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0.6,0}{\footnotesize{filtered}}}}% \put(1616,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0.6,0}{\footnotesize{filtered}}}}%
\put(1878,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{BS}}}}% \put(2304,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{BS}}}}%
\put(2725,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{FBS}}}}% \put(2907,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{FBS}}}}%
\put(3995,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{activity}}}}% \put(3638,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{activity}}}}%
}% }%
\gplbacktext \gplbacktext
\put(0,0){\includegraphics{error_timed}}% \put(0,0){\includegraphics{error_timed}}%

14
tex/gfx/eval/lag_path4_comp/path4_error_verlauf.gp
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@@ -1,5 +1,5 @@
#set terminal epslatex size 3.4,2.8 #set terminal epslatex size 3.4,2.8
set terminal epslatex size 3.4,1.4 set terminal epslatex size 3.4,1.5
set output "error_timed.tex" set output "error_timed.tex"
#set multiplot layout 2,1 #set multiplot layout 2,1
@@ -12,7 +12,7 @@ set xtics nomirror
set ytics nomirror set ytics nomirror
set key at graph 1,1 opaque box samplen 1.0 spacing 0.8 width -13 set key at graph 1,1 opaque box samplen 1.0 spacing 0.8 width -13
set lmargin 4.6 set lmargin 4.1
set tmargin 1.0 set tmargin 1.0
set rmargin 0.4 set rmargin 0.4
set bmargin 1.0 set bmargin 1.0
@@ -114,11 +114,11 @@ set object 10 rectangle from 140,0 to 150,17 fs solid noborder fc rgb "#dddddd"
set label 10 "\\footnotesize{10}" at 145,15.5 center rotate by 0 front set label 10 "\\footnotesize{10}" at 145,15.5 center rotate by 0 front
set object 900 rectangle at graph 0.5, 1.06 size graph 1.0,0.12 fs solid fc rgb "#ffffff" lc rgb "#000000" set object 900 rectangle at graph 0.485, 1.06 size graph 0.65,0.12 fs solid fc rgb "#ffffff" lc rgb "#000000"
set label 901 "\\textcolor[rgb]{0,0.6,0}{\\footnotesize{filtered}}" at graph 0.1, 1.06 center front set label 901 "\\textcolor[rgb]{0,0.6,0}{\\footnotesize{filtered}}" at graph 0.25, 1.06 center front
set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{BS}}" at graph 0.3, 1.06 center front set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{BS}}" at graph 0.41, 1.06 center front
set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{FBS}}" at graph 0.5, 1.06 center front set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{FBS}}" at graph 0.55, 1.06 center front
set label 904 "\\textcolor[rgb]{0,0,0}{\\footnotesize{activity}}" at graph 0.8, 1.06 center front set label 904 "\\textcolor[rgb]{0,0,0}{\\footnotesize{activity}}" at graph 0.72, 1.06 center front
unset key unset key
set yrange[0:17.0] set yrange[0:17.0]

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tex/gfx/eval/lag_path4_comp/path4_lag_comp.eps
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12
tex/gfx/eval/lag_path4_comp/path4_lag_comp.tex
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@@ -84,11 +84,17 @@
}% }%
\gplgaddtomacro\gplfronttext{% \gplgaddtomacro\gplfronttext{%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(4453,2553){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}% \put(1222,582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(4453,2333){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% \put(1222,362){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(4453,2113){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% \put(1222,142){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}%
\csname LTb\endcsname%
\put(1222,582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}%
\csname LTb\endcsname%
\put(1222,362){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}%
\csname LTb\endcsname%
\put(1222,142){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}%
\csname LTb\endcsname% \csname LTb\endcsname%
\put(1297,2415){\makebox(0,0){\strut{}\footnotesize{2}}}% \put(1297,2415){\makebox(0,0){\strut{}\footnotesize{2}}}%
\put(1790,2559){\makebox(0,0){\strut{}\footnotesize{3}}}% \put(1790,2559){\makebox(0,0){\strut{}\footnotesize{3}}}%

2
tex/gfx/eval/lag_path4_comp/path4_sections.gp
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@@ -11,7 +11,7 @@ unset xtics
unset ytics unset ytics
unset ztics unset ztics
set key at screen 0.99,1.0 samplen 0.5 width -7.0 set key at screen 0.33,0.26 samplen 0.5 width -7.0 box opaque
#set label 1 "\\footnotesize{1}" at 1692.27, 2721.79, 932.453-70 center front #set label 1 "\\footnotesize{1}" at 1692.27, 2721.79, 932.453-70 center front
set label 2 "\\footnotesize{2}" at 1086.04, 2622.65, 1058.51+100 center front set label 2 "\\footnotesize{2}" at 1086.04, 2622.65, 1058.51+100 center front