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toni
2016-05-09 16:46:32 +02:00
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tex/chapters/experiments.tex
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@@ -96,24 +96,16 @@ The BS has a similar improvement rate.
\begin{figure}
\begin{subfigure}{0.175\textwidth}
\input{gfx/eval/interval_path2_good/path2_interval_good}
\caption{}
\label{fig:int_path2_a}
\end{subfigure}
\begin{subfigure}{0.175\textwidth}
\input{gfx/eval/interval_path2_bad/path2_interval}
\caption{}
\label{fig:int_path2_b}
\end{subfigure}
\caption{a) Exemplary results for path 2 where BS (blue) and filtering (green) using 2500 particles and 500 sample realisations. b) A situation where smoothing provides a worse error in regard to the ground truth, but obviously a more realistic path.}
\label{fig:int_path2}
\centering
\input{gfx/eval/interval_path2_compare/path2_interval_compare}
\caption{Left: Exemplary results for path 2 where BS (blue) and filtering (green) using 2500 particles and 500 sample realisations. Right: A situation where smoothing provides a worse error in regard to the ground truth, but obviously a more realistic path.}
\label{fig:int_path2}
\end{figure}
%
Two visual examples of the smoothing outcome for path 2 are illustrated in fig. \ref{fig:int_path2}.
It can be clearly seen, how the smoothing compensates for the faulty detected floor changes using future knowledge.
Additionally, the initial error is reduced extremely, approximating the pedestrian's starting position down to a few centimetres.
In the context of reducing the error as far as possible, fig. \ref{fig:int_path2b} is a very interesting example.
In the context of reducing the error as far as possible, the right side of fig. \ref{fig:int_path2} is a very interesting example.
Here, the filter offers a lower approximation and positional error in regard to the ground truth.
However it is obvious that smoothing causes the estimation to behave more natural instead of walking the supposed path.
This phenomena could be observed for both smoothers respectively.
@@ -123,8 +115,8 @@ Compared to fixed-interval smoothing, timely errors are now of higher importance
Especially interesting in this context are small lags $\tau < 10$ considering filter updates near \SI{500}{\milli\second}.
Fig. \ref{} 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}.
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.
For better distinction, the path was divided into $10$ individual segments.
%
\begin{figure}
\input{gfx/eval/lag_path4_error/error_timed_costum}
@@ -132,12 +124,13 @@ For better distinction, the path was divided into $10$ individual segments.
\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.
Again it can be observed, that both smoother enable 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 clearly.
The BS provides 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.