\section{Conclusion}

Within this paper a novel approach for rapid approximation of the KDE was presented. 
This is achieved by considering the discrete convolution structure of the BKDE and thus elaborating its connection to digital signal processing, especially the Gaussian filter.
Using a box filter as an appropriate approximation results in an efficient computation scheme with a fully linear complexity and a negligible overhead, as demonstrated by the experiments.

The analysis of the error showed that the method shows an similar error behaviour compared to the BKDE.
In terms of calculation time, our approach outperforms other state of the art implementations.
Despite being more efficient than other methods, the algorithmic complexity still increases in its exponent with an increasing number of dimensions. 

%future work kurz
Finally, such a fast approximation scheme makes the KDE more attractive for real time use cases.
In a sensor fusion context, the availability of a reconstructed density of the posterior enables many new approaches and techniques for finding a best estimate of the system's current state.

