Convergence Properties of LMS Adaptive Estimators with Unbounded Dependent Inputs

IEEE Transactions on Automatic Control

Volumn 29, Issue 5, 1984, Pages 477-479

  Bitmead, Robert R ^a,b  

^a JAMES COOK UNIVERSITY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS - THEORY;

LMS ALGORITHM;

COMPUTER PROGRAMMING;

EID: 0021422494     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1984.1103562     Document Type: Article

References (22)

1. B. Widrow, J. M. McCool, ?. ?. Larimore, and C. R. Johnson Jr., “Stationary and nonstationary learning characteristics of the LMS adaptive filter.” Proc. IEEE, vol. 64. pp. 1151-1162. Aug. 1976.
2. J. M. Mendel. Discrete Techniques of Parameter Estimation: The Equation Error Formulation. New York Marcel-Dekker, 1973.
3. A. Gersho, “Adaptive equalization of highly dispersive channels for data transmission,” Bell Syst. Tech. J., vol. 48, pp. 55-70, Jan. 1969.
4. A. Weiss and D. Mitra, “Digital adaptive filters: Conditions for convergence, rates of convergence, effects of noise and errors arising from implementation,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 537-652, Nov. 1979.
5. L. D. Davisson, “Steady-state error in adaptive mean-square minimization,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 382-385, July 1970.
6. T. P. Daniell, “Adaptive estimation with mutually correlated training sequences,” IEEE Trans. Syst. Sci. Cybern., vol. SSC-6, pp. 12-19, Jan. 1970.
7. J.-K. Kim and L. D. Davisson, “Adaptive linear estimation for stationary M-dependent processes,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 23-31, Jan. 1975.
8. S. K. Jones, “Adaptive filtering with correlated training samples: A mean square root analysis,” Ph.D. dissertation, Dep. Elec. Eng., Southern Methodist Univ., Dallas, TX, Jan. 1973.
9. D. C. Farden, J. C. Goding, and K. Sayood, “On the “desired behavior” of adaptive signal processing algorithms,” in Proc. Int. Conf. Acoust., Speech, Signal Processing, Washington, DC, Apr. 1979.
10. S. K. Jones, R. K. Cavin, III, and W. M. Reed, “Analysis of error-gradient adaptive linear estimators for a class of stationary dependent processes,” IEEE Trans. Inform Theory, vol. IT-28, pp. 318-329. Mar. 1982.
11. R. R. Bitmead and B. D. O. Anderson, “Performance of adaptive estimation algorithms in dependent random environments,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 788-794, Aug. 1980.
12. R. R. Bitmead, “Convergence in distribution of LMS-type adaptive parameter estimates,” IEEE Trans. Automat, Contr., vol. AC-28, pp. 54-60, Jan. 1983.
13. W. Phillip, “The central limit problem for mixing sequences of random variables,” Z. Wahrscheinlichkeitstheorie und verw. Geb., vol. 12, pp. 155-171, 1969.
14. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
15. R. R. Bitmead and B. D. O. Anderson, “Lyapunov techniques for the exponential stability of linear difference equations with random coefficients,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 782-787, Aug. 1980.
16. C. R. Johnson, Jr., “Input matching, error augmentation, self-tuning and output error identification: Algorithmic similarities in discrete adaptive model following,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 697-703, Aug. 1980.
17. M. Iosifescu and R. Theodorescu, Random Processes and Learning. New York: Springer-Verlag, 1969.
18. B. D. O. Anderson and R. M. Johnstone, “Robust Lyapunov stability results and adaptive systems,” presented at the 20th IEEE Conf. Decision and Contr., San Diego, CA. 1981.
19. K. L. Chung, A Course in Probability Theory. New York: Harcourt, Brace and World, 1968.
20. I. A. Ibragimov, Yu. V. Linnik, Independent and Stationary Sequences of Random Variables. Groningen: Wolters-Noordhoff, 1971.
21. B. D. O. Anderson and C. R. Johnson, Jr., “Exponential convergence of adaptive identification and control algorithms,” Automatica, vol. 18, pp. 1-13, Jan. 1982.
22. R. R. Bitmead, “Convergence properties for LMS adaptive estimators with unbounded dependent inputs,” presented at the 20th IEEE Conf. Decision Contr. San Diego, CA, 1981, pp. 607-612.