On the equivalence of time and frequency domain maximum likelihood estimation

Authors:
Juan C. Agüero;Juan I. Yuz;Graham C. Goodwin;Ramón A. Delgado
Affiliations:
ARC Centre for Complex Dynamics Systems and Control (CDSC), School of Electrical Engineering and Computer Science, The University of Newcastle, Australia;Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile;ARC Centre for Complex Dynamics Systems and Control (CDSC), School of Electrical Engineering and Computer Science, The University of Newcastle, Australia;Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

Maximum likelihood estimation has a rich history. It has been successfully applied to many problems including dynamical system identification. Different approaches have been proposed in the time and frequency domains. In this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data. A key point in this context is how initial (and final) conditions are considered and how they are introduced in the likelihood function.