changed some gfx
added tex comments
This commit is contained in:
kazu
@@ -1,8 +1,8 @@
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\section{Conclusion}
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Within this work a novel approach for utilizing the forward-backward smoother and backward simulation to problems of indoor localisation was presented.
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Within this work a novel approach for utilizing \commentByFrank{utiliSing?} the forward-backward smoother and backward simulation to problems of indoor localisation was presented.
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Both were implemented as fixed-lag and fixed-interval smoother.
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It was shown that smoothing methods are able to decrease the estimation error and improving the overall localisation.
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Especially fixed-lag smoothing is a great tool for runtime support by reducing timely errors and improving the overall estimation with affordable costs.
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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.
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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.
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However, a fixed-lag smoother is not able to change the lag dynamically, as its name suggests.
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Therefore, a dynamic-lag smoother could be able to further improve the estimation by considering higher lags in critical areas.
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@@ -73,8 +73,12 @@ Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{s
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\label{fig:particles}
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\end{figure}
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At first, both FBS and BS are compared in context of fixed-interval smoothing.
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As a reminder, fixed-interval smoother are using all observations until time $T$ therefore run offline, after the filtering procedure is finished.
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Thus, we calculate only the positional error between estimation and ground truth, since timely information are negligible.
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As a reminder, fixed-interval smoother are \commentByFrank{smootherS? oder IS using?} using all observations until time $T$
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\commentByFrank{AND therefore run offline?}
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therefore run offline, after the filtering procedure is finished.
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Thus, we calculate only the positional error between estimation and ground truth, since timely
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\commentByFrank{timeLY passt IMHO hier nicht weil auf information bezogen -> kein adverb. time information? time-based information? timed information?}
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information are negligible.
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%
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In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position.
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Fig. \ref{fig:particles} illustrates the filtered and smoothed particle set at a certain time step on path 4.
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@@ -110,9 +114,13 @@ Here, the filter offers a lower approximation and positional error in regard to
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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.
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This phenomena could be observed for both smoothers respectively.
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At next, we discuss the advantages and disadvantages of utilizing FBS and BS as fixed-lag smoother.
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Compared to fixed-interval smoothing, timely errors are now of higher importance due to an interest on real-time localization.
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Especially interesting in this context are small lags $\tau < 10$ considering filter updates near \SI{500}{\milli\second}.
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At next, we discuss the advantages and disadvantages of utilising FBS and BS as fixed-lag smoother.
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Compared to fixed-interval smoothing, timely
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\commentByFrank{timeLY ist IMHO hier falsch, weil es sich auf error bezieht -> kein adverb. timeED errors? timing errors? time errors? time-based errors?}
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errors are now of higher importance due to an interest on real-time localization.
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Especially interesting in this context are small lags $\tau < 10$
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\commentByFrank{WARUM sind die interesining? -> weil es fuer echtzeitsysteme brauchbar ist? falls noch platz ist, kurzer satz?}
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considering filter updates near \SI{500}{\milli\second}.
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Fig. \ref{fig:lag_comp_path4} illustrates the different estimations for path 4 using a fixed-lag $\tau = 5$.
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The associated approximation errors alongside the path can additionally be seen in fig. \ref{fig:lag_error_path4}.
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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.
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@@ -127,7 +135,11 @@ For better distinction, the path was divided into $10$ individual segments.
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\begin{figure}
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\centering
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\input{gfx/eval/lag_path4_comp/error_timed}
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\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.}
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\caption{%
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Error development while walking along Path 4 using the Nexus 6.
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Especially in segments including floor changes, the error is reduced visibly by using smoothing methods.
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The black line denotes the activity detected during each timestep.
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}
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\label{fig:lag_error_path4}
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\end{figure}
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%
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@@ -139,18 +151,18 @@ Here, the BS is able to slightly improve the path, whereas the FBS follows the f
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%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.
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By looking at fig. \ref{fig:lag_comp_path4} seg. 9 it seems that both smoothing methods are highly improving the error.
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However, the approximation error in this area is similar to the filter and only the positional error decreases.
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This timely error is caused by a phenomenon we call Wi-Fi jump.
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This timely error \commentByFrank{same here: LY} is caused by a phenomenon we call Wi-Fi jump.
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Especially in seg. 8 and 9 a big crowd was gathered and highly attenuated the Wi-Fi signal.
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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.
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The next viable measurements were then provided at the end of seg. 9.
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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.
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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}
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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.
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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.
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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.
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Reducing the number of particles down to $500$ does not necessarily worsen the estimation.
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In most cases smoothing compensates for this reduction and maintains the good results.
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Besides changing the number of particles, it is also possible the variate the lag.
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Besides changing the number of particles, it is also possible the \commentByFrank{possible TO?} variate the lag.
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As one would expect, increasing the lag causes the smoothed estimation to approach the results provided by fixed-interval smoothing.
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%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}).
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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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File diff suppressed because it is too large
Load Diff
@@ -79,39 +79,39 @@
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\fi%
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\setlength{\fboxrule}{0.5pt}%
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\setlength{\fboxsep}{1pt}%
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\begin{picture}(4896.00,2014.00)%
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\begin{picture}(4896.00,2160.00)%
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\gplgaddtomacro\gplbacktext{%
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\csname LTb\endcsname%
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\put(475,1284){\makebox(0,0)[r]{\strut{}\footnotesize{walk}}}%
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\put(475,1469){\makebox(0,0)[r]{\strut{}\footnotesize{stairs}}}%
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\put(475,220){\makebox(0,0)[r]{\strut{}\footnotesize{0.0 m}}}%
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\put(475,405){\makebox(0,0)[r]{\strut{}\footnotesize{2.0 m}}}%
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\put(475,590){\makebox(0,0)[r]{\strut{}\footnotesize{4.0 m}}}%
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\put(475,775){\makebox(0,0)[r]{\strut{}\footnotesize{6.0 m}}}%
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\put(475,960){\makebox(0,0)[r]{\strut{}\footnotesize{8.0 m}}}%
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\put(639,0){\makebox(0,0){\strut{}\footnotesize{20 s}}}%
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\put(1286,0){\makebox(0,0){\strut{}\footnotesize{40 s}}}%
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\put(1932,0){\makebox(0,0){\strut{}\footnotesize{60 s}}}%
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\put(2579,0){\makebox(0,0){\strut{}\footnotesize{80 s}}}%
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\put(3226,0){\makebox(0,0){\strut{}\footnotesize{100 s}}}%
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\put(3872,0){\makebox(0,0){\strut{}\footnotesize{120 s}}}%
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\put(4519,0){\makebox(0,0){\strut{}\footnotesize{140 s}}}%
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\put(409,1383){\makebox(0,0)[r]{\strut{}\footnotesize{walk}}}%
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\put(409,1585){\makebox(0,0)[r]{\strut{}\footnotesize{stairs}}}%
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\put(409,220){\makebox(0,0)[r]{\strut{}\footnotesize{0.0 m}}}%
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\put(409,422){\makebox(0,0)[r]{\strut{}\footnotesize{2.0 m}}}%
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\put(409,624){\makebox(0,0)[r]{\strut{}\footnotesize{4.0 m}}}%
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\put(409,827){\makebox(0,0)[r]{\strut{}\footnotesize{6.0 m}}}%
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\put(409,1029){\makebox(0,0)[r]{\strut{}\footnotesize{8.0 m}}}%
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\put(574,0){\makebox(0,0){\strut{}\footnotesize{20 s}}}%
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\put(1230,0){\makebox(0,0){\strut{}\footnotesize{40 s}}}%
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\put(1887,0){\makebox(0,0){\strut{}\footnotesize{60 s}}}%
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\put(2544,0){\makebox(0,0){\strut{}\footnotesize{80 s}}}%
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\put(3200,0){\makebox(0,0){\strut{}\footnotesize{100 s}}}%
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\put(3857,0){\makebox(0,0){\strut{}\footnotesize{120 s}}}%
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\put(4514,0){\makebox(0,0){\strut{}\footnotesize{140 s}}}%
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}%
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\gplgaddtomacro\gplfronttext{%
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\csname LTb\endcsname%
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\put(866,1654){\makebox(0,0){\strut{}\footnotesize{2}}}%
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\put(1464,1654){\makebox(0,0){\strut{}\footnotesize{3}}}%
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\put(1868,1654){\makebox(0,0){\strut{}\footnotesize{4}}}%
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\put(2240,1654){\makebox(0,0){\strut{}\footnotesize{5}}}%
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\put(2886,1654){\makebox(0,0){\strut{}\footnotesize{6}}}%
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\put(3565,1654){\makebox(0,0){\strut{}\footnotesize{7}}}%
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\put(3937,1654){\makebox(0,0){\strut{}\footnotesize{8}}}%
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\put(4325,1654){\makebox(0,0){\strut{}\footnotesize{9}}}%
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\put(4680,1654){\makebox(0,0){\strut{}\footnotesize{10}}}%
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\put(1031,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0.6,0}{\footnotesize{filtered}}}}%
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\put(1878,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{BS}}}}%
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\put(2725,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{FBS}}}}%
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\put(3995,1887){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{activity}}}}%
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\put(804,1787){\makebox(0,0){\strut{}\footnotesize{2}}}%
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\put(1411,1787){\makebox(0,0){\strut{}\footnotesize{3}}}%
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\put(1821,1787){\makebox(0,0){\strut{}\footnotesize{4}}}%
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\put(2199,1787){\makebox(0,0){\strut{}\footnotesize{5}}}%
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\put(2856,1787){\makebox(0,0){\strut{}\footnotesize{6}}}%
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\put(3545,1787){\makebox(0,0){\strut{}\footnotesize{7}}}%
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\put(3923,1787){\makebox(0,0){\strut{}\footnotesize{8}}}%
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\put(4317,1787){\makebox(0,0){\strut{}\footnotesize{9}}}%
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\put(4678,1787){\makebox(0,0){\strut{}\footnotesize{10}}}%
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\put(1616,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0.6,0}{\footnotesize{filtered}}}}%
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\put(2304,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{BS}}}}%
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\put(2907,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{FBS}}}}%
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\put(3638,2042){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{activity}}}}%
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}%
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\gplbacktext
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\put(0,0){\includegraphics{error_timed}}%
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@@ -1,5 +1,5 @@
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#set terminal epslatex size 3.4,2.8
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set terminal epslatex size 3.4,1.4
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set terminal epslatex size 3.4,1.5
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set output "error_timed.tex"
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#set multiplot layout 2,1
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@@ -12,7 +12,7 @@ set xtics nomirror
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set ytics nomirror
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set key at graph 1,1 opaque box samplen 1.0 spacing 0.8 width -13
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set lmargin 4.6
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set lmargin 4.1
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set tmargin 1.0
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set rmargin 0.4
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set bmargin 1.0
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@@ -114,11 +114,11 @@ set object 10 rectangle from 140,0 to 150,17 fs solid noborder fc rgb "#dddddd"
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set label 10 "\\footnotesize{10}" at 145,15.5 center rotate by 0 front
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set object 900 rectangle at graph 0.5, 1.06 size graph 1.0,0.12 fs solid fc rgb "#ffffff" lc rgb "#000000"
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set label 901 "\\textcolor[rgb]{0,0.6,0}{\\footnotesize{filtered}}" at graph 0.1, 1.06 center front
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set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{BS}}" at graph 0.3, 1.06 center front
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set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{FBS}}" at graph 0.5, 1.06 center front
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set label 904 "\\textcolor[rgb]{0,0,0}{\\footnotesize{activity}}" at graph 0.8, 1.06 center front
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set object 900 rectangle at graph 0.485, 1.06 size graph 0.65,0.12 fs solid fc rgb "#ffffff" lc rgb "#000000"
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set label 901 "\\textcolor[rgb]{0,0.6,0}{\\footnotesize{filtered}}" at graph 0.25, 1.06 center front
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set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{BS}}" at graph 0.41, 1.06 center front
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set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{FBS}}" at graph 0.55, 1.06 center front
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set label 904 "\\textcolor[rgb]{0,0,0}{\\footnotesize{activity}}" at graph 0.72, 1.06 center front
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unset key
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set yrange[0:17.0]
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File diff suppressed because it is too large
Load Diff
@@ -84,11 +84,17 @@
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}%
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\gplgaddtomacro\gplfronttext{%
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\csname LTb\endcsname%
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\put(4453,2553){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}%
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\put(1222,582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}%
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\csname LTb\endcsname%
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\put(4453,2333){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}%
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\put(1222,362){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}%
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\csname LTb\endcsname%
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\put(4453,2113){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}%
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\put(1222,142){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}%
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\csname LTb\endcsname%
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\put(1222,582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (FBS)}}}%
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\csname LTb\endcsname%
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\put(1222,362){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}%
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\csname LTb\endcsname%
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\put(1222,142){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}%
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\csname LTb\endcsname%
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\put(1297,2415){\makebox(0,0){\strut{}\footnotesize{2}}}%
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\put(1790,2559){\makebox(0,0){\strut{}\footnotesize{3}}}%
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@@ -11,7 +11,7 @@ unset xtics
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unset ytics
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unset ztics
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set key at screen 0.99,1.0 samplen 0.5 width -7.0
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set key at screen 0.33,0.26 samplen 0.5 width -7.0 box opaque
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#set label 1 "\\footnotesize{1}" at 1692.27, 2721.79, 932.453-70 center front
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set label 2 "\\footnotesize{2}" at 1086.04, 2622.65, 1058.51+100 center front
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