Deterministic Proposal Sampling Using Projected Cumulative Distributions

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.