The Cramer-Rao lower bound for bilinear systems

IEEE Transactions on Signal Processing

Volumn 54, Issue 5, 2006, Pages 1666-1680

  Zou, Qiyue ^a,b   Lin, Zhiping ^a   Ober, Raimund J ^c,d  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b University of California   (United States)

^c The University of Texas at Dallas   (United States)

^d UNIVERSITY OF TEXAS SOUTHWESTERN MEDICAL CENTER   (United States)

Author keywords

Bilinear systems; Cramer Rao lower bound (CRLB); Fisher information matrix, local identifiability; Parameter estimation; Surface plasmon resonance experiments; System identification

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; IDENTIFICATION (CONTROL SYSTEMS); LYAPUNOV METHODS; PARAMETER ESTIMATION; SURFACE PLASMON RESONANCE;

BILINEAR SYSTEMS; COVARIANCE MATRIX; CRAMER-RAO LOWER BOUND;

LINEAR CONTROL SYSTEMS;

EID: 33646063509     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2005.863006     Document Type: Article

References (32)

1. R. S. Baheti, R. R. Mohler, and H. A. Spang III, "Second-order correlation method for bilinear system identification," IEEE Trans. Autom. Control, vol. AC-25, no. 6, pp. 1141-1146, Dec. 1980.
2. W. Favoreel, B. D. Moor, and P. V. Overschee, "Subspace identification of bilinear systems subject to white inputs," IEEE Trans. Autom. Control, vol. 44, no. 6, pp. 1157-1165, Jun. 1999.
3. Z. Zhu and H. Leung, "Adaptive identification of nonlinear systems with application to chaotic communications," IEEE Trans. Circuits Syst., I Reg. Papers, vol. 47, no. 7, pp. 1072-1080, Jul. 2000.
4. N. Kalouptsidis, P. Koukoulas, and V. J. Mathews, "Blind identification of bilinear systems," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 484-499, Feb. 2003.
5. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993, vol. I.
6. H. L. Van Trees, Detection, Estimation, and Modulation Theory. New York: Wiley, 1968, vol. I.
7. B. Friedlander, "On the computation of the Cramer-Rao bound for ARMA parameter estimation," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, no. 4, pp. 721-727, Aug. 1984.
8. B. Hanzon, Identifiability, Recursive Identification and Spaces of Linear Dynamical Systems: Part 1, CWI Tract. Amsterdam, The Netherlands: Centrum voor Wiskunde and Informatica, 1989, vol. 63.
9. P. Stoica and B. C. Ng, "Performance bounds for blind channel estimation," in Signal Processing Advances in Wireless and Mobile Communications. ser. Trends in Channel Estimation and Equalization, G. B. Giannakis, Y. Hua, P. Stoica, and L. Tong, Eds. Englewood Cliffs, NJ: Prentice-Hall, 2001, vol. I, ch. 2.
10. R. J. Ober, "The Fisher information matrix for linear systems," Syst. Control Lett., vol. 47, pp. 221-226, 2002.
11. R. J. Ober, Q. Zou, and Z. Lin, "Calculation of the Fisher information matrix for multidimensional data sets," IEEE Trans. Signal Process., vol. 51, no. 10, pp. 2679-2691, Oct. 2003.
12. G. S. J. Young and R. Chellappa, "3-D motion estimation using a sequence of noisy stereo images: Models, estimation, and uniqueness results," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 8, pp. 735-759, Aug. 1990.
13. A. K. R. Chowdhury and R. Chellappa, "Stochastic approximation and rate-distortion analysis for robust structure and motion estimation," Int. J. Comput. Vision, vol. 55, pp. 27-53, Oct. 2003.
14. R. R. Mohler, Nonlinear Systems, Vol. II, Applications to Bilinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
15. S. Zacks, The Theory of Statistical Inference. New York: Wiley, 1971.
16. P. E. Caines, Linear Stochastic Systems. New York: Wiley, 1988.
17. P. Stoica and A. Nehorai, "MUSIC, maximum likelihood, and Cramer-Rao bound," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-37, no. 5, pp. 720-741, May 1989.
18. L. Ljung, System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, 1999.
19. T. J. Rothenberg, "Identification in parametric models," Econometrica, vol. 39, pp. 577-591, May 1971.
20. P. Stoica and T. Soderstrom, "On nonsingular information matrices and local identifiability," Int. J. Control, vol. 36, pp. 323-329, 1982.
21. W. J. Rugh, Nonlinear System Theory: The Volterra/Wiener Approach. Baltimore, MD: The Johns Hopkins Univ. Press, 1981.
22. R. J. Ober and E. S. Ward, "A system theoretic formulation of NMR experiments," J. Math. Chem., vol. 20, pp. 47-65, 1996.
23. K. A. Grasse, "Reachability of interior states by piecewise constant controls," Forum Math., vol. 7, pp. 607-628, 1995.
24. R. J. Ober and E. S. Ward, "On the role of reachability and observability in NMR experimentation," J. Math. Chem., vol. 26, pp. 15-26, 1999.
25. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
26. F. R. Gantmacher, The Theory of Matrices. New York: Chelsea, 1959, vol. I and II.
27. S. Lofas and B. Johnsson, "A novel hydrogel matrix on gold surfaces in surface plasmon resonance sensors for fast and efficient covalent immobilization of ligands," J. Chem. Soc. Chem. Commun., vol. 21, pp. 1526-1528, 1990.
28. P. Schuck, "Reliable determination of binding affinity and kinetics using surface plasmon resonance biosensors," Curr. Opin. Biotechnol., vol. 8, pp. 498-502, 1997.
29. R. J. Ober and E. S. Ward, "The influence of signal noise on the accuracy of kinetic constants measured by surface plasmon resonance experiments," Anal. Biochem., vol. 273, pp. 49-59, 1999.
30. Q. Zou, "System Theory in Biomedical Applications," M. Eng. Thesis, School of Electrical and Electronic Engineering, Nanyang Technological Univ., Singapore, 2003.
31. T. M. Apostol, Mathematical Analysis, 2nd ed. Reading, MA: Addison-Wesley, 1974.
32. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.