Abstract
Maximum likelihood estimation has been widely applied in system identification because of consistency, its asymptotic efficiency and sufficiency. However, gradient-based optimisation of the likelihood function might end up in local convergence. In this article we derive various new non-local-minimum conditions in both open and closed-loop system when the noise distribution is a Gaussian process. Here we consider different model structures, in particular ARARMAX, BJ and OE models.
Acknowledgements
The authors would like to thank Dr. Daniel Coca and Dr. Tim Breikin for their constructive comments on the way of discussing the simulation examples. The authors are sincerely grateful to the anonymous reviewers for their useful suggestions in the literature survey, theory presentation and simulation illustration.