Frequency domain subspace-based identification of discrete-time power spectra from nonuniformly spaced measurements

In this paper, we present a new subspace-based algorithm for the identification of multi-input/multi-output, square, discrete-time, linear-time invariant systems from nonuniformly spaced power spectrum measurements. The algorithm is strongly consistent and it is illustrated with one practical example that solves a stochastic road modeling problem.

[1]  Jan Swevers,et al.  A subspace algorithm for the identification of discrete time frequency domain power spectra , 1997, Autom..

[2]  Michel Verhaegen,et al.  Identification of the deterministic part of MIMO state space models given in innovations form from input-output data , 1994, Autom..

[3]  Bart De Moor,et al.  The singular value decomposition and long and short spaces of noisy matrices , 1993, IEEE Trans. Signal Process..

[4]  J. Willems,et al.  Parametrizations of linear dynamical systems: Canonical forms and identifiability , 1974 .

[5]  Rik Pintelon,et al.  Identification of Linear Systems: A Practical Guideline to Accurate Modeling , 1991 .

[6]  Michel Verhaegen,et al.  Robust spectral factor approximation of discrete-time frequency domain power spectras , 2005, Autom..

[7]  L. Ljung,et al.  Subspace-based multivariable system identification from frequency response data , 1996, IEEE Trans. Autom. Control..

[8]  J. D. Robson,et al.  The description of road surface roughness , 1973 .

[9]  Lennart Ljung,et al.  On-line structure selection for multivariable state-space models , 1982, Autom..

[10]  P. Caines Linear Stochastic Systems , 1988 .

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

[12]  Michel Verhaegen A Subspace Model Identification Solution to the Identification of Mixed Causal, Anti-Causal LTI Systems , 1996, SIAM J. Matrix Anal. Appl..

[13]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[14]  Roberto Guidorzi,et al.  Invariants and canonical forms for systems structural and parametric identification , 1981, Autom..

[15]  Wallace E. Larimore,et al.  Canonical variate analysis in identification, filtering, and adaptive control , 1990, 29th IEEE Conference on Decision and Control.

[16]  R. Guidorzi Canonical structures in the identification of multivariable systems , 1975, Autom..

[17]  Lennart Ljung,et al.  Subspace-based identification of infinite-dimensional multivariable systems from frequency-response data , 1996, Autom..

[18]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[19]  Michel Verhaegen,et al.  Optimal and robust feedback controller estimation for a vibrating plate , 2004 .

[20]  Robert N. Jacques,et al.  Frequency domain structural system identification by observability range space extraction , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[21]  Rik Pintelon,et al.  A frequency domain subspace algorithm for mixed causal, anti-causal LTI systems , 2003 .

[22]  Mats Viberg,et al.  Subspace Methods in System Identification , 1994 .

[23]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

[24]  H. Ahrens CHUNG, K. L.: A course in probability theory. Harcourt & Brace, New York 1968. VIII, 331 S. , 1973 .

[25]  Semiha Turkay,et al.  A study of random vibration characteristics of the quarter-car model , 2005 .

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

[27]  Bart De Moor,et al.  Continuous-time frequency domain subspace system identification , 1996, Signal Process..