Different maximum likelihood formulations have been proposed in the literature for dynamic system identification in the time and frequency domains. In this paper we present numerical examples to study and compare these approaches for short and long data sets. In particular, in the time domain, different likelihood functions are obtained depending on whether or not the initial state is considered as a random vector, as a deterministic parameter, or equal to zero. Similar assumptions can be made in the frequency domain regarding an extra term that contains the difference between the initial and final state.
15th IFAC Symposium on System Identification (SYSID 2009). Proceedings of the 15th IFAC Symposium on System Identification (Saint-Malo, France 6-8 July, 2009) p. 1133-1138