Subspace-based spectrum estimation in frequency-domain by regularized nuclear norm minimization

Signal Processing

Volumn 99, Issue , 2014, Pages 69-85

  Akçay, Hüseyin ^a  

^a ANADOLU UNIVERSITY   (Turkey)

Author keywords

Frequency domain; Identification; Nuclear norm; Power spectrum; Subspace method

Indexed keywords

CROSS-POWER SPECTRAL DENSITY; FREQUENCY DOMAINS; INSTRUMENTAL VARIABLES; LINEAR TIME-INVARIANT SYSTEM; LOW SIGNAL-TO-NOISE RATIO; NUCLEAR NORM; NUCLEAR NORM MINIMIZATIONS; SUB-SPACE METHODS;

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FREQUENCY DOMAIN ANALYSIS; IDENTIFICATION (CONTROL SYSTEMS); POWER SPECTRAL DENSITY; POWER SPECTRUM; SPECTRUM ANALYSIS;

MATRIX ALGEBRA;

EID: 84892774077     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2013.12.028     Document Type: Article

References (40)

1. P. Van Overschee, and B. De Moor Subspace Identification for Linear Systems Theory, Implementation, Applications 1996 Kluwer Academic Publishers Dordrecht, The Netherlands
2. T. Katayama Subspace Methods for System Identification 2005 Springer-Verlag London
3. M. Verhaegen, and V. Verdult Filtering and System Identification A Least Squares Approach 2007 Cambridge University Press New York
4. R. Fraanje, M. Verhaegen, and A. Berkhoff Optimal and robust feedback controller estimation for a vibrating plate Control Eng. Pract. 12 2004 1017 1027 (Pubitemid 38708435)
5. H. Akçay, and S. Türkay A study of vibration characteristics of the quarter-car model J. Sound Vib. 282 2005 111 124
6. P. Van Overschee, B. De Moor, W. Dehandschutter, and J. Swevers A subspace algorithm for the identification of discrete-time frequency domain power spectra Automatica 33 1997 2147 2157 (Pubitemid 127380280)
7. G.C. Carter Coherence and Time Delay Estimation 1993 IEEE Press Piscataway, NJ
8. H. Pozidis, and A.P. Petropulu Cross-spectrum based blind channel identification IEEE Trans. Signal Process. 45 1997 2977 2992
9. H. Akaike, Some problems in the application of the cross-spectral method, in: Proceedings of Advanced Seminar Conducted by the Mathematical Research Center, 1996, pp. 81-107.
10. M.J. Schulz, P.F. Pai, A.S. Naser, S.K. Thyagarajan, G.J. Brannon, J. Chung, Locating structural damage using frequency response reference functions and curvatures, in: Proceedings of International Workshop on Structural Health Monitoring, Stanford University, 1997, pp. 690-701.
11. H. Akçay, and S. Türkay Frequency domain subspace-based identification of discrete-time power spectra from nonuniformly spaced measurements Automatica 40 2004 1333 1347
12. H. Akçay Frequency domain subspace-based identification of discrete-time power spectra from uniformly spaced measurements Automatica 47 2011 363 367
13. H. Akçay, Estimation of cross-power and auto-power spectral densities in frequency domain by subspace methods, in: Proceedings of 51st IEEE Conference on Decision and Control, Maui, HI, December 2012, pp. 3445-3450.
14. H. Akçay Subspace-based rational interpolation of analytic functions from phase data IEEE Trans. Signal Process. 58 2010 1069 1081
15. K. Hinnen, M. Verhaegen, and N. Doelman Robust spectral factor approximation of discrete-time frequency domain power spectra Automatica 41 2005 1791 1798 (Pubitemid 41119036)
16. M. Fazel, H. Hindi, S. Boyd, A rank minimization heuristic with application to minimum order system identification, in: Proceedings of American Control Conference, 2001, pp. 4734-4739. (Pubitemid 32837075)
17. Z. Liu, and L. Vandenberghe Interior-point method for nuclear norm approximation with application to system identification SIAM J. Matrix Anal. Appl. 31 2009 1235 1256
18. K. Mohan, M. Fazel, Reweighted nuclear norm minimization with application to system identification, in: Proceedings of American Control Conference, 2010, pp. 2953-2959.
19. R.S. Smith, Nuclear norm minimization methods for frequency domain subspace identification, in: Proceedings of 2012 American Control Conference, Montreal, CA, June 2012, pp. 2689-2694.
20. Z. Liu, A. Hansson, and L. Vandenberghe Nuclear norm system identification with missing inputs and outputs Syst. Control Lett. 62 2013 605 612
21. M. Fazel, T.K. Pong, D. Sun, and P. Tseng Hankel matrix rank minimization with applications to system identification and realization SIAM J. Matrix Anal. Appl. 34 2013 946 977
22. C. Grosmann, C.N. Jones, M. Morari, System identification via nuclear norm regularization for simulated bed processes from incomplete data sets, in: Proceedings of 48th IEEE Conference on Decision and Control, 2009, pp. 4692-4697.
23. P.M.O. Gebraad, J.W. Van Wingerden, G.J. Van der Veen, M. Verhaegen, LPV subspace identification using a novel nuclear norm regularization method, in: Proceedings of American Control Conference, 2011, pp. 165-170.
24. B. Recht, M. Fazel, and P.A. Parrilo Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization SIAM Rev. 52 2010 471 501
25. E.J. Candes, and T. Tao The power of convex relaxation: near-optimal matrix completion IEEE Trans. Inf. Theory 56 2010 2053 2080
26. T. McKelvey, H. Akçay, and L. Ljung Subspace-based multivariable system identification from frequency response data IEEE Trans. Autom. Control 41 7 1996 960 979 (Pubitemid 126768477)
27. H. Akçay, S. Türkay, Subspace-based spectrum estimation by nuclear norm minimization, in: Proceedings of 21st European Signal Processing Conference, Marrakech, Morocco, September 2013, p. 1569743059.
28. H. Akçay Frequency domain subspace-based identification of discrete-time singular power spectra Signal Process. 92 2012 2075 2081
29. J. Mari Modifications of rational transfer matrices to achieve positive realness Signal Process. 80 2000 615 635 (Pubitemid 30582738)
30. T. McKelvey, Frequency domain system identification with instrumental variable based subspace algorithm, in: Proceedings of 1997 ASME Design Engineering Technical Conference, Sacremento, CA, 1997, pp. 1-8.
31. H. Akçay An insight into instrumental variable frequency domain subspace identification Automatica 46 2010 375 382
32. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein Distributed optimization and statistical learning via alternating direction method of multipliers Found. Trends Mach. Learn. 3 2010 1 122
33. R. Tibshirani Regression shrinkage and selection via the LASSO J. R. Stat. Soc. Ser. B 58 1996 267 288
34. G. Tang, and A. Nehorai Lower bounds on the mean-squared error of low-rank matrix reconstruction IEEE Trans. Signal Process. 59 2011 4559 4571
35. G. Tang, and A. Nehorai Constrained Cramér-Rao bound on robust principal component analysis IEEE Trans. Signal Process. 59 2011 5070 5076
36. H. Akçay, S. Türkay, A spectral estimation case study in frequency domain by subspace methods, in: Proceedings of ECC'13 European Control Conference, Zurich, Switzerland, July 2013.
37. C.J. Dodds, and J.D. Robson The description of road surface roughness J. Sound Vib. 31 1973 175 183
38. S.M. Kay Modern Spectral Estimation Theory & Application 1988 Prentice-Hall Upper Saddle River, Englewood Cliffs, NJ
39. R. Pintelon, and J. Schoukens System Identification A Frequency Domain Approach 2001 IEEE Press Piscataway, NJ
40. S.M. Kay Fundamentals of Statistical Signal Processing Estimation Theory 1993 Prentice-Hall Upper Saddle River, NJ