  This paper considers the problem of computing Bayesian estimates of both
states and model parameters for nonlinear state-space models. Generally, this
problem does not have a tractable solution and approximations must be utilised.
In this work, a variational approach is used to provide an assumed density
which approximates the desired, intractable, distribution. The approach is
deterministic and results in an optimisation problem of a standard form. Due to
the parametrisation of the assumed density selected first- and second-order
derivatives are readily available which allows for efficient solutions. The
proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in
two numerical examples.
