A divide and conquer strategy for multinomial particle filter resampling

Abstract

This work provides a new multinomial resampling procedure for particle filter resampling, focused on the case where the number of samples required is less than or equal to the size of the underlying discrete distribution. This setting is common in ensemble mixture model filters such as the Gaussian mixture filter. We show superiority of our approach with respect two of the best known multinomial sampling procedures both through a computational complexity analysis and through a numerical experiment.

Figures (2)

• Figure 1: A visual representation of the divide and conquer sampler. The $W$ indicate the cumulative weights from which samples are determined and the $U$ indicate the sorted list of uniform random samples. The dashed lines indicate matching an element to its corresponding weight. Dashed boxes indicate the scope both in $W$ and $U$ of the current steps.
• Figure 2: Numerical comparison of the three multinomial sampling algorithms. The $x$ axis in all panels represents the number of samples, $N$, requested, and the $y$ axis represents the runtime in seconds. The three panels represent different sizes of the underlying distribution, $M$.