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added conclusion

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toni
2018-02-21 15:17:17 +01:00
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tex/chapters/conclusion.tex
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\section{Conclusion} \section{Conclusion}
The conclusion goes here.
Within this paper a novel approach for rapid computation of the KDE was presented.
This is achieved by considering the discrete convolution structure of the BKDE and thus elaborate its connection to digital signal processing, especially the Gaussian filter.
Using a box filter as an appropriate approximation results in an efficient computation scheme with a fully linear complexity \landau{N} and a negligible overhead, as confirmed by the utilized experiments.
The analysis of the error showed that the method exhibits an expected error behaviour compared to the BKDE.
In terms of calculation time, our approach outperforms other state of the art implementations.
Despite being more efficient than other methods, the algorithmic complexity still increases in its exponent with increasing number of dimensions.
%future work kurz
Finally, such a fast computation scheme makes the KDE more attractive for real time use cases.
In a sensor fusion context, the availability of a reconstructed density of the posterior enables many new approaches and techniques for finding a best estimate of the system's current state.

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tex/chapters/realworld.tex
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@@ -11,7 +11,8 @@ We arranged a \SI{223}{\meter} long walk within the first floor of a \SI{2500}{m
%The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only. %The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only.
% %
Since this work only focuses on processing a given sample set, further details of the localisation system and the described scenario can be looked up in \cite{Ebner17} and \cite{Fetzer17}. Since this work only focuses on processing a given sample set, further details of the localisation system and the described scenario can be looked up in \cite{Ebner17} and \cite{Fetzer17}.
The spacing $\delta$ of the grid was set to \SI{20}{\centimeter} and a state estimation was calculated whenever a step was recognized, about every \SI{500}{\milli \second}. The spacing $\delta$ of the grid was set to \SI{20}{\centimeter} for $x$ and $y$-direction.
The bivariate state estimation was calculated whenever a step was recognized, about every \SI{500}{\milli \second}.
%The intention of a real world experiment is to investigate the advantages and disadvantages of the here proposed method for finding a best estimate of the pedestrian's position in the wild, compared to conventional used methods like the weighted-average or choosing the maximum weighted particle. %The intention of a real world experiment is to investigate the advantages and disadvantages of the here proposed method for finding a best estimate of the pedestrian's position in the wild, compared to conventional used methods like the weighted-average or choosing the maximum weighted particle.
\begin{figure} \begin{figure}