Brief paper: Maximum likelihood identification of noisy input-output models

Authors:
Roberto Diversi;Roberto Guidorzi;Umberto Soverini
Affiliations:
Dipartimento di Elettronica, Informatica e Sistemistica, Universití di Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy;Dipartimento di Elettronica, Informatica e Sistemistica, Universití di Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy;Dipartimento di Elettronica, Informatica e Sistemistica, Universití di Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cramer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations.