Consistent parameter bounding identification using cross-covariance constraints on the noise

Cross-covariance constraints on the noise are introduced into bounded error identification as an alternative to the standard time-domain noise constraints. The constraints are represented by a small number of linear inequalities, which can be used in parameter bounding by linear programming. An important feature of this new type of noise bound is that under fairly general conditions the feasible parameter set converges to the true parameter vector, the noise bounds need not be tight. A procedure is presented to estimate the cross-covariance bounds on the noise from data, such that asymptotically they will be correct with any prespecified probability desired. Also another noise constraint, a bound on the amplitude of the discrete Fourier transform of the noise, is introduced into time-domain parameter bounding identification. This frequency domain constraint on the noise is analysed as well.<<ETX>>

[1]  E. Walter,et al.  Estimation of parameter bounds from bounded-error data: a survey , 1990 .

[2]  P. V. D. Hof,et al.  Quantification of model uncertainty from data: input design, interpolation, and connection with robust control design specifications , 1992 .

[3]  Carl N. Nett,et al.  Control oriented system identification: a worst-case/deterministic approach in H/sub infinity / , 1991 .

[4]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[5]  Sandor M. Veres,et al.  Structure selection for bounded-parameter models: consistency conditions and selection criterion , 1991 .

[6]  D. Brillinger.  Time Series: Data Analysis and Theory. , 1981 .

[7]  E. Fogel.  System identification via membership set constraints with energy constrained noise , 1979 .

[8]  Richard G. Hakvoort.  A Linear Programming Approach to the Identification of Frequency Domain Error Bounds , 1994 .

[9]  P. Khargonekar,et al.  Linear and nonlinear algorithms for identification in H/sub infinity / with error bounds , 1992 .

[10]  Antonio Vicino,et al.  Optimal estimation theory for dynamic systems with set membership uncertainty: An overview , 1991, Autom..

[11]  P. V. D. Hof,et al.  A generalized orthonormal basis for linear dynamical systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  O. Bosgra,et al.  Approximate system identification using system based orthonormal functions , 1990, 29th IEEE Conference on Decision and Control.

[14]  D. S. Bayard,et al.  Statistical Plant Set Estimation using Schroeder-Phased Multisinusoidal Input Design , 1992, 1992 American Control Conference.

[15]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[16]  J. Norton,et al.  Structure identification of parameter-bounding models by use of noise-structure bounds , 1989 .