boxkde nur ein cite dazu...
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@@ -55,10 +55,9 @@ For our system we choose the Gaussian kernel in favour of computational efficien
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The great flexibility of the KDE comes at the cost of a high computational time, which renders it unpractical for real time scenarios.
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The complexity of a naive implementation of the KDE is \landau{MN}, given by $M$ evaluations and $N$ particles as input size.
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A fast approximation of the KDE can be applied if the data is stored in a equidistant bins.
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A fast approximation of the KDE can be applied if the data is stored in equidistant bins as suggested by \cite{silverman1982algorithm}.
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Computation of the KDE with a Gaussian kernel on the binned data becomes analogous to applying a Gaussian filter, which can be approximated by iterated box filter in \landau{N} \cite{Bullmann-18}.
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Our rapid computation scheme of the KDE is fast enough to estimate the density of the posterior in each time step.
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This allows us to recover the most prober state from occurring multimodal posterior.
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\todo{Hier ist es mir tatsächlich noch etwas zu dünn. Könnte man nicht noch ein paar essentielle Details über den boxKDE verlieren? Spontan fällt mir zwar nichts ein. Aber der Wunsch ist da.}
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