abstract first draft

tex/bare_conf.tex

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-\title{Fast Kernel Density Estimation using blah und blub}
+\title{Fast Kernel Density Estimation using Gaussian Filter Approximation}
 
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tex/chapters/abstract.tex

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-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