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fixed bubus in abstract

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toni
2018-02-15 14:55:43 +01:00
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tex/chapters/abstract.tex
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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.
However, in complex scenarios this frequently results in a poor representation, due to multimodal densities and limited sample sizes.
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.
Especially in time critical and time sequential scenarios, this turns 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.