On estimation of errors caused by non-linear undermodelling in system identification

References

• ANDERSON , T. W. 1963 . Asymptotic theory for principal component analysis . Ann. Math. Stat. , 34 : 122 – 148 .
   Google Scholar
• BILLINGS , S. A. 1980 . Identification of nonlinear systems - a survey . Proceedings of the IEE, Part D , 127 : 272 – 285 .
   Web of Science ®Google Scholar
• BILLINGS , S. A. and FAKHOURI , S. Y. 1978 . Theory of separable processes with applications to the identification of nonlinear systems . Proceedings of the IEE , 125 : 1051 – 1058 .
   Google Scholar
• BURL , J. B. 1998 . H estimation for nonlinear systems . IEEE Signal Processing Letters , S : 199 – 202 .
   Google Scholar
• CHEN , J. and VANDEWALLE , J. study of adaptive nonlinear echo canceller with Volterra expansion . Proceedings of the ICASSP . pp. 1376 – 1379 .
   Google Scholar
• CRAMER , H. and LEADBETTER , M. R. 1957 . Stationary and Related Stochastic Processes , New York : Wiley .
   Google Scholar
• GOLUB , G. H. and VAN LOAN , C. F. 1989 . Matrix Computations , Baltimore , MD : Johns Hopkins University Press .
   Google Scholar
• GOODWIN , G. C. , GEVERS , M. and NINNESS , B. M. 1992 . Quantifying the error in estimated transfer functions with application to model order selection . IEEE Transactions on Automatic Control , 37 : 913 – 928 .
   Web of Science ®Google Scholar
• GOODWIN , G. C. and SALGADO , M. 1939 . A stochastic embedding approach for quantifying uncertainty in the estimation of restricted complexity models . International Journal of Adaptive Control and Signal Processing , 3 : 333 – 356 .
   Google Scholar
• Gu , G. and KHARGONEKAR , P. 1992 . A class of algorithms for identification in H . Automatica , 28 : 299 – 312 .
   Web of Science ®Google Scholar
• GUPTA , R. P. 1965 . Asymptotic theory for principal component analysis in the complex case . Journal of the Indian Statistical Association , 3 : 97 – 106 .
   Google Scholar
• HELMICKI , A. , JACOBSON , C. and NETT , C. H, identification of stable LSI systems: A scheme with direct application to controller design . Proceedings of the American Control Conference . pp. 1428 – 1434 .
   Google Scholar
• HUNG , G. and STARK , L. 1977 . The Kernel Identification Method (1910-1977) - Review of theory, calculation, application and interpretation . Mathematical Biosciences , 37 : 135 – 190 .
   Web of Science ®Google Scholar
• HUNTER , I. W. and KORENBERG , M. J. 1986 . The identification of nonlinear biological systems: Wiener and Hammerstein cascade models . Biological Cybernetics , 55 : 135 – 144 .
   PubMed Web of Science ®Google Scholar
• LJUNG , L. 1987 . System Identification , New Jersey : PrenticeHall Inc. .
   Google Scholar
• MERRINGTON , G. , KWON , O-K. , GOODWIN , G. C. and CARLSSON , B. 1991 . Fault detection and diagnosis in gas turbines . ASME Journal of Engineering for Gas Turbines and Power , 113 : 276 – 282 .
   Web of Science ®Google Scholar
• MILANESE , M. and BELFORTE , G. 1982 . Estimations theory and uncertainty intervals evaluation in the presence of unknown but bounded errors: Linear families of models and estimators . IEEE Transactions on Automatic Control , 27 : 408 – 414 .
   Web of Science ®Google Scholar
• NINNESS , B. M. 1993 . Stochastic and deterministic modelling , N.S.W. , , Australia : University of Newcastle . PhD dissertation
   Google Scholar
• NINNESS , B. and GOODWIN , G. C. 1995 . Estimation of modelquality . Automatica , 31 : 1771 – 1797 .
   Web of Science ®Google Scholar
• NORDSJO , A. E. 1997 . Cramér-Rao bounds for a class of systems described by Wiener and Hammerstein models . International journal of Control , 68 : 1067 – 1083 .
   Web of Science ®Google Scholar
• NORDSJÖ , A. E. , NINNESS , B. M. and WIGREN , T. Quantifying model errors caused by nonlinear undermodeling in linear systems identification . 13th World Congress of IFAC . San Francisco, CA , USA. Vol. I , pp. 145 – 149 .
   Google Scholar
• NORDSJÖ , A. E. and ZETTERBERG , L. H. 2001 . Identification of certain time-varying nonlinear Wiener and Hammerstein systems . IEEE Transactions on Signal Processing , 49 : 577 – 592 .
   Web of Science ®Google Scholar
• NORTON , J. 1987 . Identification and application of bounded parameter models . Automatica , 23 : 497 – 507 .
   Web of Science ®Google Scholar
• PANAYIRC , E. and BAR-NESS , E. Y. 1996 . New approach for evaluating the performance of a symbol timing recovery system employing a general type of nonlinearity . IEEE Transactions on Communications , 44 : 29 – 33 .
   Web of Science ®Google Scholar
• PARKER , P. and BITMEAD , R. Adaptive frequency response estimation . Proceedings of the Conference on Decision and Control . pp. 348 – 353 .
   Google Scholar
• SCHWEPPE , F. 1968 . Recursive state estimation-unknown but bounded errors and system inputs . IEEE Transactions on Automatic Control , : 22 – 28 .
   Web of Science ®Google Scholar
• SÖDERSTRÖM , T. and STOICA , P. 1989 . System Identification , UK : Prentice-Hall International .
   Google Scholar
• STEWART , G. W. 1973 . Error and perturbation bounds forsubspaces associated with certain eigenvalue problems . SIAM Review , 15 : 727 – 764 .
   Web of Science ®Google Scholar
• STOUT , W. F. 1974 . Almost Sure Convergence , New York : Academic Press .
   Google Scholar
• WAX , M. and KAILATH , T. 1985 . Detection of signals by information theoretic criteria . IEEE Transactions on ASSP , 33 : 387 – 392 .
   Google Scholar
• WAX , M. and ZISKIND , I. 1989 . Detection of the number of coherent signals by the MDL principle . IEEE Transactions on ASSP , 37 : 1190 – 1196 .
   Google Scholar
• VIBERG , M. , OTTERSTEN , B. and KAILATH , T. 1991 . Detection and estimation in sensor arrays using weighted subspace fitting . IEEE Transactions on Signal Processing , 39 : 2436 – 2449 .
   Web of Science ®Google Scholar
• WIGREN , T. 1993 . Recursive prediction error identification using the nonlinear Wiener model . Automatica , 29 : 1011 – 1025 .
   Web of Science ®Google Scholar
• WIGREN , T. 1994 . Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model . IEEE Transactions on Automatic Control , 39 : 2191 – 2206 .
   Web of Science ®Google Scholar
• WIGREN , T. 1995 . Approximate gradients, convergence and positive realness in recursive identification of a class of nonlinear systems . International Journal of Adaptive Control Signal Processing , 9 : 325 – 354 .
   Web of Science ®Google Scholar
• WIGREN , T. 1997 . Circle criteria in recursive identification . IEEE Transactions on Automatic Control , 42 : 975 – 979 .
   Web of Science ®Google Scholar
• WIGREN , T. 1998 . Adaptive filtering using quantized output measurements . IEEE Transactions on Signal Processing , 46 : 3423 – 3426 .
   Web of Science ®Google Scholar
• WILKINSON , J. H. 1965 . The Algebraic Eigenvalue Problem , Oxford , , UK : Clarendon Press .
   Google Scholar
• WYNN , W. D. 1969 . A second order statistical analysis of the operation of a limiter-phase detector-filter cascade . Bell System Technical Journal , 48 : 233 – 248 .
   Google Scholar