  We introduce two new classes of exact Markov chain Monte Carlo (MCMC)
samplers for inference in latent dynamical models. The first one, which we coin
auxiliary Kalman samplers, relies on finding a linear Gaussian state-space
model approximation around the running trajectory corresponding to the state of
the Markov chain. The second, that we name auxiliary particle Gibbs samplers
corresponds to deriving good local proposals in an auxiliary Feynman--Kac model
for use in particle Gibbs. Both samplers are controlled by augmenting the
target distribution with auxiliary observations, resulting in an efficient
Gibbs sampling routine. We discuss the relative statistical and computational
performance of the samplers introduced, and show how to parallelise the
auxiliary samplers along the time dimension. We illustrate the respective
benefits and drawbacks of the resulting algorithms on classical examples from
the particle filtering literature.
