On the Role of Constraints in System Identification

System identification is concerned with the estimation of parameters characterizing an unknown system. The estimation is usually based on observations of the system’s (possibly noisy) input(s) and output(s). In the so-called “blind” system identification scenario, the estimation is based on the observed output(s) only, aided by some general knowledge about statistical properties of the input(s), rather than by actual observations thereof. Quite commonly, the discussion is limited to discrete-time systems, assumed to be linear and time-invariant (LTI), stable and causal. As such, their input-output relation can always 1 be described as

[1]  Bart De Moor,et al.  Misfit versus latency , 2000, Autom..

[2]  Arie Yeredor,et al.  On homogeneous least-squares problems and the inconsistency introduced by mis-constraining , 2004, Comput. Stat. Data Anal..

[3]  T. Söderström,et al.  Instrumental variable methods for system identification , 1983 .

[4]  J. Willems,et al.  Application of structured total least squares for system identification and model reduction , 2005, IEEE Transactions on Automatic Control.

[5]  Andreas Spanias,et al.  System identification based on bounded error constraints , 1995, IEEE Trans. Signal Process..

[6]  Graham C. Goodwin,et al.  L2-overbiased, L2-underbiased and L2-unbiased estimation of transfer functions , 1994, Autom..

[7]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[8]  Roberto López-Valcarce,et al.  An algorithm for unit-norm equation error system identification based on the method of multipliers , 2003, IEEE Trans. Signal Process..

[9]  Dennis S. Bernstein,et al.  Quadratically constrained least squares identification , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[10]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[11]  Robert J. Vanderbei,et al.  Linear Programming: Foundations and Extensions , 1998, Kluwer international series in operations research and management service.

[12]  Mats Viberg,et al.  Subspace-based methods for the identification of linear time-invariant systems , 1995, Autom..

[13]  Hing-Cheung So,et al.  Analysis of an LMS algorithm for unbiased impulse response estimation , 2003, IEEE Trans. Signal Process..

[14]  장윤희,et al.  Y. , 2003, Industrial and Labor Relations Terms.

[15]  Eric M. Dowling,et al.  Total least squares with linear constraints , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[16]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[17]  D. Bernstein,et al.  Subspace identification with guaranteed stability using constrained optimization , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[18]  Phillip A. Regalia.  An unbiased equation error identifier and reduced-order approximations , 1994, IEEE Trans. Signal Process..

[19]  Sabine Van Huffel,et al.  Improved methods for exponential parameter estimation in the presence of known poles and noise , 1997, IEEE Trans. Signal Process..

[20]  T. Söderström,et al.  Bias correction in least-squares identification , 1982 .