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  • Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions

    Author(s)
    Celka, Patrick
    Griffith University Author(s)
    Celka, Patrick
    Year published
    2001
    Metadata
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    Abstract
    This paper investigates the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system (WHS) with Gaussian inputs. The WHS nonlinearity is assumed to be expandable in a series of orthogonal Hermite polynomials. The sequential procedure uses (1) a gradient search for the unknown coefficients of the Hermite polynomials, (2) an LMS adaptive filter to partially identify the input and output linear filters of the WHS, and (3) the higher order terms in the Hermite expansion to identify each of the linear filters. The third step requires the iterative solution ...
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    This paper investigates the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system (WHS) with Gaussian inputs. The WHS nonlinearity is assumed to be expandable in a series of orthogonal Hermite polynomials. The sequential procedure uses (1) a gradient search for the unknown coefficients of the Hermite polynomials, (2) an LMS adaptive filter to partially identify the input and output linear filters of the WHS, and (3) the higher order terms in the Hermite expansion to identify each of the linear filters. The third step requires the iterative solution of a set of coupled nonlinear equations in the linear filter coefficients. An alternative scheme is presented if the two filters are known a priori to be exponentially shaped. The mean behavior of the various gradient recursions are analyzed using small step-size approximations (slow learning) and yield very good agreement with Monte Carlo simulations. Several examples demonstrate that the scheme provides good estimates of the WHS parameters for the cases studied.
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    Journal Title
    IEEE Transaction on Signal Processing
    Volume
    49
    DOI
    https://doi.org/10.1109/78.917809
    Subject
    PRE2009-Signal Processing
    Publication URI
    http://hdl.handle.net/10072/58838
    Collection
    • Journal articles

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