Stochastic Approximation with Correlated Data

IEEE Transactions on Information Theory

Volumn 27, Issue 1, 1981, Pages 105-113

  Farden, David C ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SIGNAL PROCESSING;

EID: 0019396845     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1981.1056300     Document Type: Article

References (33)

1. H. Robbins and S. Monro, “A stochastic approximation method,” Ann. Math. Statist., Vol. 22, pp. 400–407, 1951.
2. J. Kiefer and J. Wolfowitz, “Stochastic estimation of the maximum of a regression function,” Ann. Math. Statist., Vol. 23, pp. 462–466, 1952.
3. D. C. Farden, “Stochastic approximation with correlated data,” Ph.D. Dissertation, Colorado St. Univ., Ft. Collins. Also ONR Technical Report, No. 11, May 1975.
4. L. L. Scharf, “On stochastic approximation and the hierarchy of adaptive array algorithms,” in Proc. 1972 IEEE Conf. on Decision and Control, pp. 258–261, New Orleans, Dec. 13–15, 1972.
5. D. G. Lupberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
6. L. J. Griffiths, “A simple algorithm for real-time processing in antenna arrays,” Proc. IEEE, Vol. 57, pp. 1696–1704, Oct. 1969.
7. B. Widrow, P. E. Mantey, L. J. Griffiths, and B. B. Goode, “Adaptive antenna systems,” Proc. IEEE, Vol. 55, pp. 2145–2159, Dec. 1967.
8. C. W. Niessen and D. K. Willim, “Adaptive equalizer for pulse transmission,” IEEE Trans. Commun. Technol., Vol. COM-18, pp. 377–395, Aug. 1970.
9. A. Gersho, “Adaptive equalization of highly dispersive channels for data transmission,” Bell Syst. Tech. J., Vol. 48, pp. 55–70, Jan. 1969.
10. T. J. Schonfeld and M. Schwartz, “A rapidly converging first-order training algorithm for an adaptive equalizer,” IEEE Trans. Inform. Theory, Vol. IT-17, pp. 431–439, July 1971.
11. D. C. Farden, J. C. Goding, Jr., and K. Sayood, “On the ‘desired behavior’ of adaptive signal processing algorithms,” in Proc. 1979 IEEE International Conf. on Acoustics, Speech, and Signal Processing, pp. 941–944, Apr. 1979.
12. D. C. Farden and K. Sayood, “Tracking properties of adaptive signal processing algorithms,” in Proc. 1980 IEEE International Conf. on Acoustics, Speech, and Signal Processing, pp. 466–469, Apr. 1980.
13. T. P. Daniell, “Adaptive estimation with mutually correlated training sequences,” IEEE Trans. Syst. Sci. Cybern., Vol. SSC-6, pp. 12–19, Jan. 1970.
14. J. L. 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.
15. S. K. Jones, “Adaptive filtering with correlated training samples: A mean square error analysis,” Ph.D. dissertation, Dept. of Elec. Eng., Southern Methodist Univ., Dallas, TX, Jan. 1973.
16. R. T. Lacross, “Adaptive combining of wideband array data for optimal reception,” IEEE Trans. Geosci. Electron., Vol. GE-6, pp. 78–86, May 1968.
17. O. L. Frost, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE, Vol. 60, pp. 922–935, Aug. 1972.
18. L. Schmetterer, “Stochastic approximation,” in Proc. Fourth Berke-ley Symposium on Mathematical Statistics and Probability, Vol. 1. Berkeley and Los Angeles: Univ. California, pp. 587–609, 1961.
19. L. Schmetterer, “Multidimensional stochastic approximation,” Multivariate Analysis II, Proc. 2nd Int. Symp., P. R. Krishnaiah, Ed. New York and London: Academic Press, pp. 443–460, 1969.
20. D. J. Sakrison, “Stochastic approximation: A recursive method for solving regression problems,” Advances in Comm. Sys. 2, A. V. Balakrishnan, Ed. New York and London: Academic, pp. 51–106, 106, 1966.
21. D. J. Sakrison, “A continuous Kiefer-Wolfowitz procedure for random processes,” Ann. Math. Statist., Vol. 35, pp. 590–599, 1964.
22. L. Ljung, “Analysis of recursive stochastic algorithms,” IEEE Trans. Automat. Contr., Vol. AC-22, pp. 551–575, Aug. 1977.
23. H. J. Kushner and D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Applied Mathematical Sciences, Vol. 26. New York: Springer, 1978.
24. R. J. Serfling, “Moment Inequalities for the Maximum Cumulative Sum,” Ann. Math. Statist., Vol. 41, pp. 1227–1234, 1970.
25. R. J. Serfling, “Convergence properties of Sn under moment restrictions,” Ann. Math. Statist., Vol. 41, pp. 1235–1248, 1970.
26. M. M. Sondhi and D. Mitra, “New results on the performance of a well-known class of adaptive filters,” Proc. IEEE, Vol. 64, pp. 1583–1597, Nov. 1976.
27. A. E. Albert and L. A. Gardner, Jr., Stochastic Approximation and Nonlinear Regression. Cambridge, MA: M.I.T. 1967.
28. W. F. Stout, Almost Sure Convergence. New York: Academic, 1974.
29. D. C. Farden and L. L. Scharf, “Stochastic approximation with correlated data I: Applications,” Tech. Rep., Dept. of Elec. Eng., Univ. Rochester, Rochester, NY, Jan. 1979.
30. R. S. Varga, Matrix Iterative Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1962.
31. D. C. Farden, “Stochastic approximation with correlated data II: Analysis,” Tech. Rep., Dept. of Elec. Eng., Univ. Rochester, Rochester, NY, Jan. 1979.
32. A. Weiss and D. Mitra, “Digital adaptive filters: Conditions for convergence, rates of convergence, effects of noise and errors arising from the implementation,” IEEE Trans. Inform. Theory, Vol. IT-25, pp. 637–652, Nov. 1979.
33. R. R. Bitmead and B. D. O. Anderson, “Exponentially convergent behavior of simple stochastic adaptive estimation algorithms,” in Proc. 17th IEEE Conf. on Decision and Control, 1979, pp. 580–585.