Maximum likelihood estimation of rational transfer function parameters

The problem of estimating unknown transfer function parameters from finite input-output records which have been disturbed by additive Gaussian noise with unknown correlation is considered. A rational sampled-data model of preselected order is assumed appropriate, and following the work of Klein, Åström and Bohlin, and Mayne, the likelihood function is generated from the data by numerical filtering. The maximum likelihood criterion leads to nonlinear regression equations for the unknown parameters, which are solved by damped Gauss-Newton iteration. Some computational experiments are described.