\section{Experiments}
We now empirically evaluate the accuracy of our method and compare its runtime performance with other state of the art approaches.
To conclude our findings we present a real world example from a indoor localisation system.

All tests are performed on a Intel Core \mbox{i5-7600K} CPU with a frequency of $4.5 \text{GHz}$, which supports the AVX2 instruction set, hence 256-bit wide SIMD registers are available.
We compare our C++ implementation of the box filter based KDE to the KernSmooth R package and the \qq{FastKDE} implementation \cite{fastKDE}.
The KernSmooth packages provides a FFT-based BKDE implementation based on optimized C functions at its core.

\subsection{Error}
In order to quantity the accuracy of our method the mean integrated squared error (MISE) is used.
The ground truth is given as a synthetic data set drawn from a mixture normal density.
Clearly, the choice of the ground truth distribution affects the resulting error.
However, as our method approximates the KDE it is only of interest to evaluate the closeness to the KDE and not to the ground truth itself.
Therefore, the particular choice of the ground truth is only of minor importance here.

At first we evaluate the accuracy of our method as a function of the bandwidth $h$ in comparison to the exact KDE and the BKDE.



% kde, box filter, exbox in abhänigkeit von h (bild)
% sample size und grid size text
% fastKDE fehler vergleich macht kein sinn weil kernel und bandbreite unterschiedlich sind


\subsection{Performance}

\subsection{Real World}
