  Exact Bayesian inference on state-space models~(SSM) is in general
untractable, and unfortunately, basic Sequential Monte Carlo~(SMC) methods do
not yield correct approximations for complex models. In this paper, we propose
a mixed inference algorithm that computes closed-form solutions using belief
propagation as much as possible, and falls back to sampling-based SMC methods
when exact computations fail. This algorithm thus implements automatic
Rao-Blackwellization and is even exact for Gaussian tree models.
