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first draft

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toni
2016-05-06 02:25:14 +02:00
parent 605ec85aff
commit 787d109cc4
5 changed files with 59 additions and 45 deletions
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4
code/Settings.h
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@@ -17,9 +17,9 @@ namespace MiscSettings {
const int timeSteps = 500;
const int numParticles = 2500;
const int numParticles = 500;
const int numBSParticles = 500;
const int numBSParticles = 100;
const int lag = 5;

48
code/main.cpp
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@@ -87,42 +87,42 @@ void testModelWalk() {
int main(void) {
// {SmoothingEval1 eval;
// eval.fixedIntervallSimpleTransPath4();
// eval.run();}
{SmoothingEval1 eval;
eval.fixedIntervallSimpleTransPath4();
eval.run();}
for(int i = 0; i < 10; ++i){
// for(int i = 0; i < 10; ++i){
//nexus
std::string name = "bergwerk_path1_nexus_simple_interval_" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path1_nexus_multi(name); eval.run();}
// //nexus
// std::string name = "bergwerk_path1_nexus_simple_interval_" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path1_nexus_multi(name); eval.run();}
name = "bergwerk_path2_nexus_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path2_nexus_multi(name); eval.run();}
// name = "bergwerk_path2_nexus_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path2_nexus_multi(name); eval.run();}
name = "bergwerk_path3_nexus_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path3_nexus_multi(name); eval.run();}
// name = "bergwerk_path3_nexus_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path3_nexus_multi(name); eval.run();}
name = "bergwerk_path4_nexus_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path4_nexus_multi(name); eval.run();}
// name = "bergwerk_path4_nexus_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path4_nexus_multi(name); eval.run();}
//galaxy
name = "bergwerk_path1_galaxy_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path1_galaxy_multi(name); eval.run();}
// //galaxy
// name = "bergwerk_path1_galaxy_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path1_galaxy_multi(name); eval.run();}
name = "bergwerk_path2_galaxy_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path2_galaxy_multi(name); eval.run();}
// name = "bergwerk_path2_galaxy_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path2_galaxy_multi(name); eval.run();}
name = "bergwerk_path3_galaxy_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path3_galaxy_multi(name); eval.run();}
// name = "bergwerk_path3_galaxy_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path3_galaxy_multi(name); eval.run();}
name = "bergwerk_path4_galaxy_simple_interval" + std::to_string(i);
{SmoothingEval1 eval; eval.bergwerk_path4_galaxy_multi(name); eval.run();}
// name = "bergwerk_path4_galaxy_simple_interval" + std::to_string(i);
// {SmoothingEval1 eval; eval.bergwerk_path4_galaxy_multi(name); eval.run();}
std::cout << "We are in loop number: " << i << "of " << 10 << std::endl;
}
// std::cout << "We are in loop number: " << i << "of " << 10 << std::endl;
// }
return 0;

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tex/bare_conf.dvi
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2
tex/bare_conf.tex
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@@ -117,7 +117,7 @@
% gfx include folder
\graphicspath{ {gfx/baro/},{gfx/graph/},{gfx/paths/},{gfx/eval/},{gfx/},{gfx/grid/},{gfx/activity/},{gfx/eval/interval_path4_comp/},{gfx/eval/interval_path3_bad/},{gfx/particles/}}
\graphicspath{ {gfx/baro/},{gfx/graph/},{gfx/paths/},{gfx/eval/},{gfx/},{gfx/grid/},{gfx/activity/},{gfx/eval/interval_path4_comp/},{gfx/eval/interval_path3_bad/},{gfx/particles/}, {gfx/eval/lag_path4_error/}}
% correct bad hyphenation here

50
tex/chapters/experiments.tex
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@@ -60,7 +60,7 @@ Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{s
\label{fig:activityRecognition}
\end{figure}
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.
The approximation error decreases by an average of \SI{XX}{\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{fig:activityRecognition} 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.
@@ -69,31 +69,32 @@ Despite a short misdetection caused by faulty pressure readings, the recognition
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.
%
\begin{figure}
\input{gfx/particles/particles}
\caption{particles. green = avg50, black = avg. gnuplot zickt bei der legende}
\label{fig:particles}
\end{figure}
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{fig:particles}, 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.
As illustrated in fig. \ref{fig:particles}, the estimated position (black dot) 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 (green dot).
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.
Now, the positional average error along all 4 paths could be improved from \SI{2.49}{\meter} to \SI{2.2}{\meter} for the Galaxy and from \SI{1.76}{\meter} to \SI{1.54}{\meter} 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.
However, BS still outperforms the FBS with an average error of \SI{1.74}{\meter} for the Galaxy and \SI{1.41}{\meter} for the Nexus on all 4 paths using the same number of particles and $500$ 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.
The estimation of BS looks way more realistic and adapts better to the ground truth path.
However, in this particular example the FBS starts at an earlier position (cf. fig. \ref{fig:intcomp} seg. 2), 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}
\input{gfx/eval/interval_path4_comp/path4_interval}
\caption{Comparison between FBS (red) and BS (blue) on path 4 (black). Both were approximated using \SI{2500}{} particles and \SI{500}{} sample realisations for BS. The measurements were recorded using the Nexus 6.}
\caption{Comparison between FBS (red) and BS (blue) on path 4 (black). Both were approximated using $2500$ particles and \SI{500}{} sample realisations for BS. The measurements were recorded using the Nexus 6. }
\label{fig:intcomp}
\todo{Filter mit rein}
\end{figure}
\begin{figure}
@@ -109,25 +110,38 @@ This shows that the smoothing results are of course highly depend upon the filte
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}.
%
%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 $\SI{55}{\centimeter}$.
The median errors for all conducted walks are listed in table \ref{}.
Fig. \ref{fig:lag_error_path4} illustrates the different approximation errors alongside path 4 using $500$ particles, \SI{100}{sample realisations} for BS and a fixed-lag $\tau = 5$.
%
\begin{figure}
\input{gfx/eval/lag_path4_error/error_timed_costum}
\caption{Hier muss ich noch was schreiben. Bin aber seeeehr muede. Geh jetzt ins Bett. Nachti.}
\label{fig:lag_error_path4}
\end{figure}
%
Due to the small number of sample realisations for BS and the different estimation method for FBS, the errors are changing very frequently in contrast to the filter.
It can be seen that again BS provides a better overall estimation, especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 9).
Besides the positional quality, also the timely error could be reduced by both algorithms in fig. \ref{fig:lag_error_path4}.
Once more, the BS outperforms the FBS by providing an overall approximation error of $\SI{4.86}{\meter}$ for the Galaxy and $\SI{2.97}{\meter}$ for the Nexus by filtering with $\SI{5.68}{\meter}$ and $\SI{3.15}{\meter}$ respectively.
Whereas FBS is not able to reduce the filtering error, obtaining $\SI{5.59}{\meter}$ using the Nexus and $\SI{3.12}{\meter}$ the Galaxy.
However, this does not mean, that the FBS is unpracticable for problems of fixed-lag smoothing.
By looking at the data in detail, high errors similar as seen in fig. \ref{fig:lag_error_path4} occur on path 3, which cause the estimation to behave more natural instead of walking the supposed path.
This phenomena could be observed for both smoothers respectively.
Also note the difference between this error, including timely information, and the positional error used before.
%The median errors for all conducted walks are listed in table \ref{}.
Similar to fixed-interval smoothing, decreasing the number of particles does not necessarily worsen the estimation.
In most cases smoothing compensates for this reduction and maintains the good results.
For example estimating path for using \SI{50}{particles} results in an approximation error for BS of \SI{}{\meter}.
%For example estimating path for using \SI{50}{particles} results in an approximation error for BS of \SI{}{\meter}.
%lag vergrößern was passiert beschreiben
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{}.
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.
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 continuously optimizing a recurring segment of the path.
The different approximation errors alongside path 4 can now be seen in fig. \ref{}.