The Error Variance of LMS with Time-Varying Weights

IEEE Transactions on Signal Processing

Volumn 40, Issue 4, 1992, Pages 803-813

  Solo, Victor ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL STATISTICS; MATHEMATICAL TECHNIQUES - ERROR ANALYSIS; MATHEMATICAL TECHNIQUES - LEAST SQUARES APPROXIMATIONS;

FAST ADAPTATION; LMS ERROR VARIANCE; MATCHED ADAPTATION; PERTURBATION EXPANSION; SLOW ADAPTATION; TIME-VARYING WEIGHTS;

SIGNAL FILTERING AND PREDICTION;

EID: 0026848021     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.127953     Document Type: Article

References (15)

1. P. Billingsley, Convergence of Probability Measure. New York: Wiley, 1968.
2. D. Brillinger, Time Series, Data Analysis, and Theory. Holt, Rein-hart, Winston, 1975.
3. A. Benveniste and G. Ruget, “A measure of the tracking capability of recursive stochastic algorithms with constant gains,” IEEE Trans. Automat. Contr., vol. AC-27, pp. 639–649, 1982.
4. A. Benveniste, “Design of adaptive algorithms for the tracking of time-varying systems,” Int. J. Adapt. Contr. Signal Processing, pp. 3–29, 1987.
5. 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, 1980.
6. 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, 1980.
7. R. R. Bitmead, “Convergence in distribution of LMS-type adaptive parameter estimates,” IEEE Trans. Automat. Contr., vol. AC-28, pp. 54–60, 1983.
8. R. R. Bitmead, “Convergence properties of LMS adaptive estimates with unbounded dependent inputs,” in Proc. 20th IEEE Conf. Dec. Contr. (San Diego, CA), 1981, pp. 607–612.
9. A. Feuer and E. Weinstein, “Convergence analysis of LMS filters with uncorrelated Gaussian data,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 222–230, 1985.
10. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic System Theory. Cambridge, MA: M.I.T. Press, 1984.
11. L. Ljung, “Adaptation and tracking in system identification—A survey,” Automatica, vol. 26, pp. 7–21, 1990.
12. O. Macchi, “Optimization of adaptive identification for time varying filters.” IEEE Trans. Automat. Contr., vol. AC-31, pp. 283–287, 1986.
13. O. Macchi and E. Eweda, “Second-order convergence analysis of stochastic adaptive linear filtering,” IEEE Trans. Automat. Contr., vol. AC-28, pp. 76–85, 1983.
14. K. H. Shi and F. Kozin, “On almost sure convergence of adaptive algorithms,” IEEE Trans. Automat. Contr., vol. AC-31, pp. 471–474, 1986.
15. V. Solo, “The limiting behavior of LMS,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-37, pp. 1909–1922, 1989.