  We consider approximate maximum likelihood parameter estimation in nonlinear
state-space models. We discuss both direct optimization of the likelihood and
expectation--maximization (EM). For EM, we also give closed-form expressions
for the maximization step in a class of models that are linear in parameters
and have additive noise. To obtain approximations to the filtering and
smoothing distributions needed in the likelihood-maximization methods, we focus
on using Gaussian filtering and smoothing algorithms that employ sigma-points
to approximate the required integrals. We discuss different sigma-point schemes
based on the third, fifth, seventh, and ninth order unscented transforms and
the Gauss--Hermite quadrature rule. We compare the performance of the methods
in two simulated experiments: a univariate nonlinear growth model as well as
tracking of a maneuvering target. In the experiments, we also compare against
approximate likelihood estimates obtained by particle filtering and extended
Kalman filtering based methods. The experiments suggest that the higher-order
unscented transforms may in some cases provide more accurate estimates
