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MBulli
2018-03-12 21:03:15 +01:00
parent 1fb9461a5f
commit c224967b19
3 changed files with 3 additions and 3 deletions
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tex/chapters/introduction.tex
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@@ -18,7 +18,7 @@ Additionally, in most practical scenarios the sample size and therefore the reso
It is obvious, that a computation of the full posterior could solve the above, but finding such an analytical solution is an intractable problem, which is the reason for applying a sample representation in the first place.
Another promising way is to recover the probability density function from the sample set itself, by using a non-parametric estimator like a kernel density estimation (KDE).
With this, it is easy to recover the \qq{real} most probable state and thus to avoid the aforementioned drawbacks.
With this, the \qq{real} most probable state is given by the maxima of the density estimation and thus avoids the aforementioned drawbacks.
However, non-parametric estimators tend to consume a large amount of computational time, which renders them unpractical for real time scenarios.
Nevertheless, the availability of a fast processing density estimate might improve the accuracy of today's sensor fusion systems without sacrificing their real time capability.

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tex/chapters/realworld.tex
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@@ -17,7 +17,7 @@ The bivariate state estimation was calculated whenever a step was recognized, ab
\begin{figure}
\input{gfx/walk.tex}
\caption{Occurring bimodal distribution at the start of the walk, caused by uncertain measurements. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides an high error compared to the ground truth (solid black), while the boxKDE approach (orange) does not. }
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of the walk. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides an high error compared to the ground truth (solid black), while the boxKDE approach (orange) does not. }
\label{fig:realWorldMulti}
\end{figure}
%

2
tex/egbib.bib
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@@ -3017,7 +3017,7 @@ year = {2003}
@article{oBrien2016fast,
title={A fast and objective multidimensional kernel density estimation method: fastKDE},
author={O’Brien, Travis A and Kashinath, Karthik and Cavanaugh, Nicholas R and Collins, William D and O’Brien, John P},
author={O'Brien, Travis A and Kashinath, Karthik and Cavanaugh, Nicholas R and Collins, William D and O'Brien, John P},
journal={Computational Statistics \& Data Analysis},
volume={101},
pages={148--160},