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We propose a method for optimal Bayesian filtering with deterministicparticles. In order to avoid particle degeneration, the filter step is notperformed at once. Instead, the particles progressively flow from prior toposterior. This is achieved by splitting the filter step into a series ofsub-steps. In each sub-step, optimal resampling is done by a map that replacesnon-equally weighted particles with equally weighted ones. Inversions of themaps or monotonicity constraints are not required, greatly simplifying theprocedure. The parameters of the mapping network are optimized w.r.t.\ to aparticle set distance. This distance is differentiable, and comparesnon-equally and equally weighted particles. Composition of the map sequenceprovides a final mapping from prior to posterior particles. Radial basisfunction neural networks are used as maps. It is important that no intermediatecontinuous density representation is required. The entire flow works directlywith particle representations. This avoids costly density estimation.

Progressive Bayesian Particle Flows based on Optimal Transport Map Sequences