Estimation of the parameters of a bilinear model with applications to submarine detection and system identification

Authors:
Richard Abrahamsson;Steven M. Kay;Petre Stoica
Affiliations:
Department of Information Technology, Division of Systems and Control, Uppsala University, P.O. Box 337, SE-75105 Uppsala, Sweden;Department of Electrical and Computer Engineering, University of Rhode Island, Kelley Hall, 4 East Alumni Avenue, Kingston, RI 02881, USA;Department of Information Technology, Division of Systems and Control, Uppsala University, P.O. Box 337, SE-75105 Uppsala, Sweden
Venue:
Digital Signal Processing
Year:
2007

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Abstract

In this work we study the problem of estimating the parameters of a bilinear model describing, e.g., the amplitude modulation of extremely low frequency electromagnetic (ELFE) signatures of submarines. A similar problem arises in estimation of a nonlinear dynamic system using a Hammerstein-Wiener model, where two nonlinear static blocks surround a linear dynamic block. For these purposes a new method is derived. It is also shown in the same context that a two-stage method for parameter estimation of Hammerstein-Wiener models can be interpreted as an approximate least squares method. We also show the similarities with the problem of weighted low-rank approximation and the fact that these problems can be solved exactly in finite time using solvers for global optimization of systems of polynomials based on self dual optimization.