From c224967b1961fb88c2eafac225781918114112f4 Mon Sep 17 00:00:00 2001 From: MBulli Date: Mon, 12 Mar 2018 21:03:15 +0100 Subject: [PATCH] Fixed FD --- tex/chapters/introduction.tex | 2 +- tex/chapters/realworld.tex | 2 +- tex/egbib.bib | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/tex/chapters/introduction.tex b/tex/chapters/introduction.tex index f915131..af59233 100644 --- a/tex/chapters/introduction.tex +++ b/tex/chapters/introduction.tex @@ -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. diff --git a/tex/chapters/realworld.tex b/tex/chapters/realworld.tex index fd87bf5..33595ca 100644 --- a/tex/chapters/realworld.tex +++ b/tex/chapters/realworld.tex @@ -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} % diff --git a/tex/egbib.bib b/tex/egbib.bib index d66a6a1..2c514ec 100644 --- a/tex/egbib.bib +++ b/tex/egbib.bib @@ -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},