Common factor estimation and two applications in signal processing

Authors:
Monika Agrawal;Petre Stoica;Per Åhgren
Affiliations:
Department of Systems and Control, Information Technology, Uppsala University, P.O. Box 27, SE-75103 Uppsala, Sweden;Department of Systems and Control, Information Technology, Uppsala University, P.O. Box 27, SE-75103 Uppsala, Sweden;Department of Systems and Control, Information Technology, Uppsala University, P.O. Box 27, SE-75103 Uppsala, Sweden
Venue:
Signal Processing - Special issue on independent components analysis and beyond
Year:
2004

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Abstract

The problem of finding common factors (or common roots) of a set of polynomials without rooting is of interest in many fields of research. When the polynomials are observed in noise, i.e., their coefficients are corrupted by errors, the problem becomes challenging. In this paper we suggest a method of estimating the greatest common divisor of a set of polynomials whose coefficients are perturbed by noise. The corresponding algorithm is called COFE (COmmon Factor Estimation). The COFE algorithm has several applications of which in this paper we discuss two in detail. One of these is MUSIC (MUltiple SIgnal Classification) which is reformulated as a COFE problem. The advantages of COFE MUSIC over the existing MUSIC is the case by which we estimate the parameters. The other application is system identification, where maximum likelihood estimates of the parameters of an ARARX system can be directly obtained by the suggested COFE algorithm in a simple manner.