diff --git a/tex/bare_conf.tex b/tex/bare_conf.tex index d4fd48e..c3d9a39 100644 --- a/tex/bare_conf.tex +++ b/tex/bare_conf.tex @@ -183,7 +183,7 @@ % not capitalized unless they are the first or last word of the title. % Linebreaks \\ can be used within to get better formatting as desired. % Do not put math or special symbols in the title. -\title{Fast Kernel Density Estimation using blah und blub} +\title{Fast Kernel Density Estimation using Gaussian Filter Approximation} % author names and affiliations % use a multiple column layout for up to three different diff --git a/tex/chapters/abstract.tex b/tex/chapters/abstract.tex index a9b4ce2..2da1a69 100644 --- a/tex/chapters/abstract.tex +++ b/tex/chapters/abstract.tex @@ -1,5 +1,14 @@ -This is the abstract stract stract +\begin{abstract} +It is common practice to use a sample-based representation to solve problems having a probabilistic interpretation. +In many real world scenarios one is then interested in finding a \qq{best estimate} of the underlying problem, e.g. the position of a robot. +This is often done by means of simple parametric point estimator, providing the sample statistics. +However, in complex scenarios this frequently results in a poor representation, due to a multimodal posteriors and a limited sample size. -linear complexity +Recovering the probability density function using a kernel density estimation yields a promising approach to find the \qq{real} most probable state, but comes with high computational costs. +Especially in time critical and time sequential scenarios, this turn out to be impractical. +Therefore, this work uses techniques from digital signal processing in the context of estimation theory, to allow rapid computations of kernel density estimates. +The gains in computational efficiency are realized by substituting the Gaussian filter with an approximate filter based on the moving average filter. +Our approach outperforms other state of the art solutions, due to a fully linear complexity \landau{N} and a negligible overhead, even for small sample sets. +Finally, our findings are tried and tested within a real world sensor fusion system. +\end{abstract} -This will be shown in an a theoritical bases and also realistic ... blah