  In this work, a novel sequential Monte Carlo filter is introduced which aims
at efficient sampling of high-dimensional state spaces with a limited number of
particles. Particles are pushed forward from the prior to the posterior density
using a sequence of mappings that minimizes the Kullback-Leibler divergence
between the posterior and the sequence of intermediate densities. The sequence
of mappings represents a gradient flow. A key ingredient of the mappings is
that they are embedded in a reproducing kernel Hilbert space, which allows for
a practical and efficient algorithm. The embedding provides a direct means to
calculate the gradient of the Kullback-Leibler divergence leading to quick
convergence using well-known gradient-based stochastic optimization algorithms.
Evaluation of the method is conducted in the chaotic Lorenz-63 system, the
Lorenz-96 system, which is a coarse prototype of atmospheric dynamics, and an
epidemic model that describes cholera dynamics. No resampling is required in
the mapping particle filter even for long recursive sequences. The number of
effective particles remains close to the total number of particles in all the
experiments.
