Progressive Particle Filtering Using Projected Cumulative Distributions

We propose a progressive particle filter that inherently avoids sample degeneracy by splitting the likelihood into a product of wider functions applied step by step. Between steps, the particle distribution is resampled using projected cumulative distributions (PCDs). To be able to handle weighted Dirac mixture distributions, their corresponding one-dimensional densities are interpolated with a piecewise constant function. Both Cramér-von-Mises and 2-Wasserstein distance are used as base objective functions for PCDs to deterministically and optimally resample such distributions. The proposed filter is compared with a standard SIR particle filter on a simulated tracking problem.