  Maximum likelihood (ML) estimation using Newton's method in nonlinear state
space models (SSMs) is a challenging problem due to the analytical
intractability of the log-likelihood and its gradient and Hessian. We estimate
the gradient and Hessian using Fisher's identity in combination with a
smoothing algorithm. We explore two approximations of the log-likelihood and of
the solution of the smoothing problem. The first is a linearization
approximation which is computationally cheap, but the accuracy typically varies
between models. The second is a sampling approximation which is asymptotically
valid for any SSM but is more computationally costly. We demonstrate our
approach for ML parameter estimation on simulated data from two different SSMs
with encouraging results.
