The Steiglitz-McBride identification algorithm revisited--Convergence analysis and accuracy aspects

The convergence and accuracy properties of the Steiglitz and McBride identification method are examined. The analysis is valid for a sufficiently large number of data. It is shown that the method can converge to the true parameter vector only when the additive output noise is white. In that case the method is proved to be locally convergent to the true parameters. The global convergence properties are also investigated. It is pointed out that the method is not always globally convergent. Some sufficient conditions guaranteeing global convergence are given. Assuming convergence takes place the estimates are shown to be asymptotically Gaussian distributed. An explicit expression is given for their asymptotic covariance matrix.

[1]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[2]  K. Narendra,et al.  An iterative method for the identification of nonlinear systems using a Hammerstein model , 1966 .

[3]  Kenneth Steiglitz,et al.  ESTIMATION OF DISTRIBUTED LAGS , 1970 .

[4]  C. Weygandt,et al.  Extension of the Steiglitz and McBride identification technique , 1971 .

[5]  T. Söderström.  On the uniqueness of maximum likelihood identification , 1975, Autom..

[6]  P. Gallman,et al.  An iterative method for the identification of nonlinear systems using a Uryson model , 1975 .

[7]  P. Gallman.  A comparison of two Hammerstein model identification algorithms , 1976 .

[8]  J. Cadzow.  Recursive digital filter synthesis via gradient based algorithms , 1976 .

[9]  K. Steiglitz.  On the simultaneous estimation of poles and zeros in speech analysis , 1977 .

[10]  Lennart Ljung,et al.  A theoretical analysis of recursive identification methods , 1978, Autom..

[11]  An Iterative Identification Procedure for Systems with a Nonlinear Gain in the Feedback or Feedforward Paths , 1978 .

[12]  Craig K. Rushforth,et al.  Evaluation of the Steiglitz algorithm for estimating the parameters of an ARMA process , 1979, ICASSP.

[13]  Petre Stoica,et al.  On the stability of dynamic models obtained by least-squares identification , 1981 .

[14]  Petre Stoica,et al.  Comparison of some instrumental variable methods - Consistency and accuracy aspects , 1981, Autom..

[15]  Petre Stoica,et al.  Some properties of the output error method , 1982, Autom..