This paper considers parameter estimation for nonlinear state-space models,
which is an important but challenging problem. We address this challenge by
employing a variational inference (VI) approach, which is a principled method
that has deep connections to maximum likelihood estimation. This VI approach
ultimately provides estimates of the model as solutions to an optimisation
problem, which is deterministic, tractable and can be solved using standard
optimisation tools. A specialisation of this approach for systems with additive
Gaussian noise is also detailed. The proposed method is examined numerically on
a range of simulated and real examples focusing on the robustness to parameter
initialisation; additionally, favourable comparisons are performed against
state-of-the-art alternatives