From ba83665c74bfe26ff472ca08eb65b75ae22ea620 Mon Sep 17 00:00:00 2001 From: toni Date: Wed, 21 Feb 2018 15:17:17 +0100 Subject: [PATCH] added conclusion --- tex/chapters/conclusion.tex | 14 +++++++++++++- tex/chapters/realworld.tex | 3 ++- 2 files changed, 15 insertions(+), 2 deletions(-) diff --git a/tex/chapters/conclusion.tex b/tex/chapters/conclusion.tex index 62fd97f..cc1a6cc 100644 --- a/tex/chapters/conclusion.tex +++ b/tex/chapters/conclusion.tex @@ -1,2 +1,14 @@ \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. + diff --git a/tex/chapters/realworld.tex b/tex/chapters/realworld.tex index 2dbd05b..47e135e 100644 --- a/tex/chapters/realworld.tex +++ b/tex/chapters/realworld.tex @@ -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. % 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. \begin{figure}