  Particle filtering is used to compute good nonlinear estimates of complex
systems. It samples trajectories from a chosen distribution and computes the
estimate as a weighted average. Easy-to-sample distributions often lead to
degenerate samples where only one trajectory carries all the weight, negatively
affecting the resulting performance of the estimate. While much research has
been done on the design of appropriate sampling distributions that would lead
to controlled degeneracy, in this paper our objective is to \emph{learn}
sampling distributions. Leveraging the framework of algorithm unrolling, we
model the sampling distribution as a multivariate normal, and we use neural
networks to learn both the mean and the covariance. We carry out unsupervised
training of the model to minimize weight degeneracy, relying only on the
observed measurements of the system. We show in simulations that the resulting
particle filter yields good estimates in a wide range of scenarios.
