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@@ -52,8 +52,8 @@ However, both cases do not give a deeper insight of the error behavior of our me
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\subsection{Performance}
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\subsection{Performance}
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In the following, we underpin the promising theoretical linear time complexity of our method with empirical time measurements compared to other methods.
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In the following, we underpin the promising theoretical linear time complexity of our method with empirical time measurements compared to other methods.
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All tests are performed on a Intel Core \mbox{i5-7600K} CPU with a frequency of \SI{4.2}{\giga\hertz}, and \SI{16}{\giga\byte} main memory.
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All tests are performed on a Intel Core \mbox{i5-7600K} CPU with a frequency of \SI{4.2}{\giga\hertz}, and \SI{16}{\giga\byte} main memory.
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We compare our C++ implementation of the extended box filter based KDE approximation to the KernSmooth R package and the \qq{FastKDE} Python implementation \cite{oBrien2016fast}.
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We compare our C++ implementation of the box filter based KDE approximation to the \texttt{ks} R package and the fastKDE Python implementation \cite{oBrien2016fast}.
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The KernSmooth packages provides a FFT-based BKDE implementation based on optimized C functions at its core.
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The \texttt{ks} packages provides a FFT-based BKDE implementation based on optimized C functions at its core.
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% Vergleich zu weighted average (in c++) um unseren großen Geschwindigkeitsvorteil zu zeigen.
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% Vergleich zu weighted average (in c++) um unseren großen Geschwindigkeitsvorteil zu zeigen.
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With state estimation problems in mind, we additionally provide a C++ implementation of a weighted average estimator.
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With state estimation problems in mind, we additionally provide a C++ implementation of a weighted average estimator.
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\commentByToni{Vielleicht sollten wir hier noch paar Worte über die Implementierung verlieren. Ist das alles std c++? nehmen wir iwas mega kraßes? usw. vielleicht im camera ready sogar nen link zum coder oder sowas.}
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\commentByToni{Vielleicht sollten wir hier noch paar Worte über die Implementierung verlieren. Ist das alles std c++? nehmen wir iwas mega kraßes? usw. vielleicht im camera ready sogar nen link zum coder oder sowas.}
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@@ -46,6 +46,7 @@ Additionally, in most real world scenarios many particles share the same weight
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\end{figure}
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\end{figure}
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Further investigating fig. \ref{fig:realWorldTime}, the boxKDE performs slightly better then the weighted-average, however after deploying \SI{100} MC runs, the difference becomes insignificant.
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Further investigating fig. \ref{fig:realWorldTime}, the boxKDE performs slightly better then the weighted-average, however after deploying \SI{100} MC runs, the difference becomes insignificant.
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\commentByMarkus{Was sind MC Runs? Die Abkürzung kommt das erste mal vor.}
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The main reason for this are again multimodalities caused by faulty or delayed measurements, especially when entering or leaving rooms.
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The main reason for this are again multimodalities caused by faulty or delayed measurements, especially when entering or leaving rooms.
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Within our experiments the problem occurred due to slow and attenuated Wi-Fi signals inside thick-walled rooms.
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Within our experiments the problem occurred due to slow and attenuated Wi-Fi signals inside thick-walled rooms.
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While the system's dynamics are moving the particles outside, the faulty Wi-Fi readings are holding back a majority by assigning corresponding weights.
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While the system's dynamics are moving the particles outside, the faulty Wi-Fi readings are holding back a majority by assigning corresponding weights.
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