Algorithm for recursive Frisch scheme ientification and errors-in-variables filtering

  • Jens Linden

    Student thesis: Doctoral ThesisDoctor of Philosophy


    This thesis deals with the development of algorithms for recursive estimation within the errors-in-variables framework. Within this context attention is focused on two major threads of research: Recursive system identification based on the Frisch scheme and the extension and application of errors-in-variables Kalman filtering techniques.

    In the first thread, recursive algorithms for the approximate update of the estimates obtained via the Frisch scheme, which makes use of the Yule-Walker model selection criterion, are developed for the case of white measurement noise. Gradient-based techniques are utilised to update the Frisch scheme equations, which involve the minimisation of the model selection criterion as well as the solution of an eigenvalue problem, in a recursive manner. The computational complexity of the resulting algorithms is critically analysed and, by introducing additional approximations, fast recursive Frisch scheme algorithms are developed, which reduce the computational complexity from cubic to quadratic order. In addition, it is investigated how the singularity condition within the Frisch scheme is affected when the estimates are computed recursively. Whilst this first group of recursive Frisch scheme algorithms is developed directly from the offline Frisch scheme equations, it is also possible to interpret the Frisch scheme within an extended bias compensating least squares framework. Consequently, the development of recursive algorithms, which update the estimate obtained from the extended bias compensated least squares technique, is considered. These algorithms make use of the bilinear parametrisation principle or, alternatively, the variable projection method. Finally, two recursive Frisch scheme algorithms are developed for the case of coloured output noise.

    The second thread, which considers the theory of errors-in-variables filtering for linear systems, extends the approach to deal with a class of bilinear systems, a frequently used subset of nonlinear systems. The application of errors-in-variables filtering for the purpose of system identification is also considered. This leads to the development of a prediction error method based on symmetric innovations, which resembles the joint output method. Both the offline and online implementation of this novel identification technique are investigated.
    Date of Award2008
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorKeith Burnham (Supervisor)


    • recursive systems
    • Frisch scheme
    • algorithms

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