  We propose a method for optimal Bayesian filtering with deterministic
particles. In order to avoid particle degeneration, the filter step is not
performed at once. Instead, the particles progressively flow from prior to
posterior. This is achieved by splitting the filter step into a series of
sub-steps. In each sub-step, optimal resampling is done by a map that replaces
non-equally weighted particles with equally weighted ones. Inversions of the
maps or monotonicity constraints are not required, greatly simplifying the
procedure. The parameters of the mapping network are optimized w.r.t.\ to a
particle set distance. This distance is differentiable, and compares
non-equally and equally weighted particles. Composition of the map sequence
provides a final mapping from prior to posterior particles. Radial basis
function neural networks are used as maps. It is important that no intermediate
continuous density representation is required. The entire flow works directly
with particle representations. This avoids costly density estimation.

Machine Learning;Systems and Control;Systems and Control