  A Maximum Likelihood recursive state estimator is derived for non-linear and
non-Gaussian state-space models. The estimator combines a particle filter to
generate the conditional density and the Expectation Maximization algorithm to
compute the maximum likelihood state estimate iteratively. Algorithms for
maximum likelihood state filtering, prediction and smoothing are presented. The
convergence properties of these algorithms, which are inherited from the
Expectation Maximization algorithm, are proven and examined in two examples. It
is shown that, with randomized reinitialization, which is feasible because of
the algorithm simplicity, these methods are able to converge to the Maximum
Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as
well as those of disjoint support.
