Selecting appropriately the proposal kernel of particle filters is an issue
of significant importance, since a bad choice may lead to deterioration of the
particle sample and, consequently, waste of computational power. In this paper
we introduce a novel algorithm approximating adaptively the so-called optimal
proposal kernel by a mixture of integrated curved exponential distributions
with logistic weights. This family of distributions is broad enough to be used
in the presence of multi-modality or strongly skewed distributions. This
"mixture of experts" is fitted, via Monte Carlo EM or online-EM methods, to the
optimal kernel through minimization of the Kullback-Leibler divergence between
the auxiliary target and instrumental distributions of the particle filter. The
algorithm requires only one optimization problem to be solved for the whole
sample, as opposed to existing methods solving one problem per particle. In
addition, we illustrate in a simulation study how the method can be
successfully applied to optimal filtering in nonlinear state-space models.