Particle filters are an important class of algorithms for Bayesian estimation. One of their drawbacks is the socalled particle degeneration where only very few particles with a meaningful weight remain after the filter step. This effect is typically remedied by regularly resampling the particles, yielding a set of equally weighted particles. This paper investigates an approach to deterministically sample particles from the proposal distribution in such a way to automatically have equally weighted particles at the end of the filter step. The proposed method is first motivated and presented for the one-dimensional case. Using the Radon transform and projected cumulative distributions, the one-dimensional algorithm is extended to multivariate problems. Some examples of the usefulness of the proposed algorithm are also shown.
Prossel et al. (Wed,) studied this question.