Fast Kernel Density Estimation using Gaussian Filter Approximation

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 best estimate of the underlying problem, e.g. the position of a robot. This is often done by means of simple parametric point estimators, providing the sample statistics. 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 solve the state estimation problem i.e. finding the "real" most probable state, but comes with high computational costs. 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 box filter. Our approach outperforms other state of the art solutions, due to a fully linear complexity and a negligible overhead, even for small sample sets. Finally, our findings are evaluated and tested within a real world sensor fusion system.