Adaptive Set-Membership Identification in O(m) Time for Linear-in-Parameters Models

IEEE Transactions on Signal Processing

Volumn 41, Issue 5, 1993, Pages 1906-1924

  Deller, John R ^a   Odeh, Souheil F ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SYSTEMS; ALGORITHMS; IDENTIFICATION (CONTROL SYSTEMS); LEAST SQUARES APPROXIMATIONS; OPTIMIZATION;

LINEAR-IN-PARAMETERS MODELS; SET-MEMBERSHIP IDENTIFICATION;

SIGNAL PROCESSING;

EID: 0027589615     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.215308     Document Type: Article

References (42)

1. E. Walter, Ed., Math. Comput. in Simulation (Special Issue on Parameter Identifications with Error Bound), vol. 32, Dec. 1990.
2. Cs. Banyasz and L. Keviczky, Eds., Proc. 9th IFAC/IFORS Symp. Identification Syst. Parameter Estim., vol. 1, 2, Budapest, Hungary, July 1991.
3. E. Walter and H. Piet-Lahanier, “Estimation of parameter bounds from bounded-error data: A survey,” Math. Comput. in Simulation, vol. 32, pp. 449–468, 1990.
4. M. Milanese and A. Vicino, “Estimation theory for dynamic systems with unknown but bounded uncertainty: An overview,” in Proc. 9th IFAC/IFORS Symp. Identification Syst. Parameter Estim., vol. 2, Budapest, Hungary, July 1991, pp. 859–867.
5. J. R. Deller, Jr., “Set-membership identification in digital signal processing,” IEEE ASSP Mag., vol. 6, pp. 4–22, Oct. 1989.
6. E. Fogel and Y. F. Huang, “On the value of information in system identification—bounded noise case,” Automatica, vol. 18, pp. 229–238, 1982.
7. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns-Hopkins Univ. Press, 1983, ch. 6.
8. J. P. Norton, An Introduction to Identification. London and Orlando, FL: Academic, 1986.
9. C. R. Johnson, Lectures on Adaptive Parameter Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1988.
10. D. Graupe, Time Series Analysis, Identification, and Adaptive Systems. Malabar, FL: Kreiger, 1989, ch. 5.
11. L. Ljung and T. Soderstrom, Theory and Practice of Recursive Identification. Cambridge, MA: M.I.T. Press, 1983, pp. 14–15 and sect. 2.2.1.
12. T. C. Luk and J. R. Deller, Jr., “A nonclassical WRLS algorithm,” in Proc. 23rd Annu. Allerton Conf., 1985, pp. 732–741.
13. J. R. Deller, Jr., and D. Hsu, “An alternative adaptive sequential regression algorithm and its application to the recognition of cerebral palsy speech,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 782–787, July 1987.
14. J. R. Deller, Jr., and G. P. Picache, “Advantages of a Givens rotation approach to temporally recursive linear prediction analysis of speech,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 429–431, Mar. 1989.
15. J. R. Deller, Jr., “A ‘systolic array’ formulation of the optimal bounding ellipsoid algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 1432–1436, Sept. 1989.
16. S. F. Odeh, “Algorithms and architecture for adaptive set membership-based signal processing,” Ph.D. dissertation, Michigan State Univ., East Lansing, 1990.
17. S. F. Odeh and J. R. Deller, Jr., “Systolic algorithms for adaptive set-membership identification,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing ’90, Albuquerque, NM, vol. 5, Apr. 1990, pp. 2419–2422.
18. S. H. Mo and J. P. Norton, “Fast and robust algorithm to compute exact polytope parameter bounds,” Math. Comput. in Simulation, vol. 32, pp. 481–493, 1990.
19. V. Broman and M. J. Shensa, “A compact algorithm for the intersection and approximation of N-dimensional polytopes,” Math. Com put. in Simulation, vol. 32, pp. 469–480, 1990.
20. E. Walter and H. Piet-Lahanier, “Exact recursive polyhedral description of the feasible parameter set for bounded-error models,” IEEE Trans. Automat. Contr., vol. AC-34, pp. 911–915, 1989.
21. M. Milanese and G. Belaforte, “Estimation theory and uncertainty intervals evaluation in the presence of unknown but bounded errors: Linear families of models and estimators,” IEEE Trans. Automat. Contr., vol. AC-27, pp. 408–414, 1982.
22. G. Belforte, B. Bona, and V. Cerone, “Parameter estimation algorithms for a set-membership description of uncertainty,” Automatica, vol. 26, pp. 887–898, 1990.
23. A. K. Rao, Y. F. Huang, and S. Dasgupta, “ARMA parameter estimation using a novel recursive estimation algorithm with selective updating,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 447–457, Mar. 1990.
24. A. K. Rao and Y. F. Huang, “Recent developments in optimal bounding ellipsoid parameter estimation,” Math. Comput. in Simulation, vol. 32, pp. 515–526, Dec. 1990.
25. L. Pronzato, E. Walter, and H. Piet-Lahanier, “Mathematical equivalence of two ellipsoid algorithms for bounded error estimation,” in Proc. 28th IEEE Conf. Decision Contr., Tampa, FL, 1989, pp. 1952–1955.
26. J. R. Deller, Jr. and T. C. Luk, “Linear prediction analysis of speech based on set-membership theory,” Comput. Speech and Language, vol. 3, pp. 301–327, Oct. 1989.
27. S. Dasgupta and Y. F. Huang, “Asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 383–392, 1987.
28. J. P. Norton, “Identification of parameter bounds for ARMAX models from records with bounded noise,” Int. J. Contr., vol. 45, pp. 375–390, 1987.
29. Y. F. Huang, “A recursive estimation algorithm using selective updating for spectral analysis and adaptive signal processing,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1331— 1334, 1986.
30. J. P. Norton, “Recursive computation of inner bounds for the parameters of linear models,” Int. J. Contr., vol. 50, pp. 2423–2430, 1989.
31. A. Vicino and M. Milanese, “Optimal approximation of feasible parameter set in estimation with unknown but bounded noise,” in Proc. 9th IFAC/IFORS Symp. Identification and Syst. Parameter Estim., vol. 2, Budapest, Hungary, July, 1991, pp. 1365–1369.
32. J. R. Deller, Jr. and S. F. Odeh, “SM-WRLS algorithms with an efficient test for innovation,” in Proc. 9th IFAC/IFORS Symp. Identification Syst. Parameter Estim., vol. 2, Budapest, Hungary, July, 1991, pp. 1044–1049.
33. J. P. Norton and S. H. Mo, “Parameter bounding for time-varying systems,” Math. Comput. in Simulation, vol. 32, pp. 527–534, 1990.
34. J. R. Deller, Jr., M. Nayeri, and S. F. Odeh, “Least squares identification with error bounds for real-time signal processing and control,” Proc. IEEE, to be published, June 1993.
35. L. E. Dickson, A First Course in the Theory of Equations. New York: Wiley, 1952.
36. J. Makhoul, “Linear prediction: A tutorial review,” Proc. IEEE, vol. 63, pp. 561–580, 1975.
37. W. M. Gentleman and H. T. Kung, “Matrix triangularization by systolic arrays,” Proc. Soc. Photo-Optical Instrumentation Engineers: Real-Time Signal Processing IV, vol. 298, pp. 19–26, 1981.
38. H. T. Kung and C. Leiserson, “Algorithms for VLSI processor arrays,” Rep. MU-CS-79-103, Dept. Comput. Sci., Camegie-Mellon Univ., 1978; reprinted in C. Mead and L. Conway, Introduction to VLSI Systems. Reading, MA: Addison-Wesley, 1980, section 8.3.
39. J. R. Deller, Jr. and S. F. Odeh, “Implementing the optimal bounding ellipsoid algorithm on a fast processor,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing ’89, Glasgow, vol. 2, May 1989, pp. 1067–1070.
40. J. G. McWhirter, “Recursive least squares minimization using a systolic array,” Proc. Soc. Photo-Optical Instrumentation Engineers: Real-Time Signal Processing VI, vol. 431, pp. 105–112, 1983.
41. W. M. Gentleman, “Least squares computations by Givens transformations without square roots,” J. Inst. Math. Its Appl., vol. 12, pp. 329–336, 1973.
42. S. Y. Kung, VLSI Array Processors. Englewood Cliffs, NJ: Prentice-Hall, 1988, ch. 3.