A subspace method for frequency selective identification of stochastic systems

A parametric method for the estimation of vector valued discrete-time stochastic systems or equivalently the spectrum of a stochastic process is presented. The key feature is that the method can be used to frequency selectively fit the model to the data. This means that parts of the spectrum can be modeled with a lower model order than otherwise would be necessary if the entire spectrum would be modeled. The method is based on a frequency domain subspace method which delivers a state-space model. It explicitly takes into account that the frequency domain data is derived from finite data and hence suppresses the leakage effects. Furthermore the method employs convex optimization to guarantee that the estimated parametric model represents a non-negative spectrum.

[1]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[2]  Petre Stoica,et al.  MA estimation in polynomial time , 2000, IEEE Trans. Signal Process..

[3]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[4]  B. Anderson.  A SYSTEM THEORY CRITERION FOR POSITIVE REAL MATRICES , 1967 .

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

[6]  Anders Lindquist,et al.  From Finite Covariance Windows to Modeling Filters: A Convex Optimization Approach , 2001, SIAM Rev..

[7]  D. Bernstein,et al.  First-order-hold sampling of positive real systems and subspace identification of positive real models , 2004, Proceedings of the 2004 American Control Conference.

[8]  T. McKelvey,et al.  A robust frequency domain subspace algorithm for multi-component harmonic retrieval , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[9]  Tomas McKelvey,et al.  Consistency analysis of a frequency domain subspace algorithm for multi-component harmonic retrieval , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.

[11]  M. Tismenetsky,et al.  Kronecker Products and Matrix Calculus (Alexander Graham) , 1983 .

[12]  B. Porat,et al.  Digital Spectral Analysis with Applications. , 1988 .

[13]  S. O. Reza Moheimani,et al.  Estimation of phase constrained MIMO transfer functions with application to flexible structures with , 2005 .

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

[15]  A. Rantzer.  On the Kalman-Yakubovich-Popov lemma , 1996 .

[16]  Bart De Moor,et al.  A subspace algorithm for the identification of discrete time frequency domain power spectra , 1997 .

[17]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[18]  Petre Stoica,et al.  Vector ARMA estimation: a reliable subspace approach , 2000, IEEE Trans. Signal Process..