Maximum Likelihood and Lower Bounds in System Identification with Non-Gaussian Inputs

IEEE Transactions on Information Theory

Volumn 40, Issue 2, 1994, Pages 328-339

  Shalvi, Ofir ^a   Weinstein, Ehud ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

blind deconvolution equalization; Cramer Rao lower bound; maximum likelihood estimation; non Gaussianity; Nonminimum phase ARMA models; system identification

Indexed keywords

ALGORITHMS; DISCRETE TIME CONTROL SYSTEMS; EQUALIZERS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; PERFORMANCE; POLES AND ZEROS; PROBABILITY; RANDOM PROCESSES; SIGNAL FILTERING AND PREDICTION;

ASYMPTOTIC ERROR VARIANCE; BLIND DECONVOLUTION EQUALIZATION; CRAMER-RAO LOWER BOUND; MAXIMUM LIKELIHOOD ESTIMATION; NON GAUSSIAN; NONMINIMUM PHASE; PROBABILITY DISTRIBUTION FUNCTION;

PARAMETER ESTIMATION;

EID: 0028385548     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.312156     Document Type: Article

References (43)

1. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 718-723, 1977.
2. K. J. Astrom, “Maximum likelihood and prediction error methods,” Automatica, vol. 16, pp. 551-574, 1980.
3. K. J. Astrom and T. Soderstrom, “Uniqueness of the maximum likelihood estimates of the parameters of an ARMA model,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 769-773, 1974.
4. S. Bellin and F. Rocca, “Asymptotically efficient blind deconvolution,” Signal Processing, vol. 20, pp. 193-209, 1990.
5. A. Benveniste, M. Goursat, and G. Ruget, “Robust identification of a non-minimum phase system: Blind adjustment of a linear equalizer in data communication,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 385-399. June 1980.
6. G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control. San Francisco, CA: Holden-Day, 1970.
7. D. Burshtein, “An efficient algorithm for calculating the likelihood and likelihood gradient of ARMA models,” IEEE Trans. Automat. Contr., Feb. 1993.
8. D. Burshtein and E. Weinstein, “On the application of the Wald statistic to order estimation of ARMA models,” IEEE Trans. Automat. Contr., vol. 36, Sept. 1991.
9. T. Cover, Elements of Information Theory. New York: Wiley, 1991.
10. H. Cramer, Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press, 1951.
11. D. L. Donoho, “On minimum entropy deconvolution,” in Applied Time Series Analysis, II, D. F. Findley, Ed. New York: Academic, 1981.
12. R. Durrett, Probability Theory and Examples. CA: Wadsworth and Brooks/Cole.
13. B. Friedlander, “On the computation of the Cramer-Rao bound for ARMA parameter estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 721-727, 1984.
14. G. B. Giannakis and J. M. Mendel, “Identification of non-minimum phase systems using higher order statistics,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 360-377, Mar. 1989.
15. D. Godard, “Self recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun., vol COM-28, pp. 1867-1875, Nov. 1980.
16. I. C. Gohberg and I. A. Feldman, Convolution Equations and Projection Methods for Their Solution, American Mathematical Society, 1974.
17. E. J. Hannan and J. Rissanen, “Recursive estimation of ARMA order,” Biometrika, vol. 69, pp. 81-94, 1982.
18. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1991, 2nd ed.
19. S. Haykin, Ed. Blind Deconvolution, Englewood Cliffs, NJ: Prentice-Hall, 1994.
20. S. M. Kay and S. L. Marple, “Spectrum Analysis—A Modern Perspective,” Proc. IEEE, vol. 69, 1981.
21. K. S. Lii and M. Rosenblatt, “Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear procesess,” Ann. Statist., vol. 10, pp. 1195-1208, 1982.
22. L. Ljung, System Identification Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, 1987.
23. R. D. Martin, “The Cramer-Rao bound and robust M-estimates for autoregressions,” Blometrika, vol. 62, no. 2, pp. 437-442, 1982.
24. I. Meilijson, “A fast improvement to the EM algorithm on its own terms,” J. Roy. Statist. Soc. B., vol. 51, pp. 127-138, 1989.
25. J. M. Mendel, Optimal Siesmic Deconvolution. New York: Academic 1987.
26. C. L. Nikias and M. R. Raghuveer, “Bispectrum estimation: A digital signal processing framework,” Proc. IEEE, vol. 75, pp. 869-891, July 1987.
27. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing Englewood Cliffs, NJ: Prentice-Hall, 1989.
28. C. R. Rao, Linear Statistical Inference and Its Applications. New York Wiley, 1973.
29. R. A. Render and H. F. Walker, “Mixture densities, maximum likelihood and the EM algorithm,” SIAM Rev., vol. 26, pp. 195-239, 1984.
30. J. Rissanen, “Modeling by shortest data description,” Automatica, vol 14, pp. 465-471, 1978.
31. D. Sengupta and S. Kay, “Efficient estimation of parameters for non- Gaussian autoregressive processes,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 785-794, June 1989.
32. D. Sengupta and S. Kay, “Recent advances in non-Gaussian autoregressive processes,” in Advances in Spectrum Analysis and Array Processing, S. Haykin Ed. Englewood Cliffs, NJ: Prentice-Hall, 1991, pp. 141-210.
33. M. I. Sezan and A. M. Tekalp, “Survey of recent developments in digital image restoration,” Opt. Eng., vol. 29, pp. 393-404, May 1990.
34. B. M. Silverman, Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall, 1986.
35. O. Shalvi and E. Weinstein, “New criteria for blind deconvolution of nonminimum phase systems (channels),” IEEE Trans. Inform. Theory, vol. 36, pp. 312-321, Mar. 1990.
36. O. Shalvi and E. Weinstein, “Super exponential methods for blind deconvolution,” IEEE Trans. Inform. Theory, pp. 504-519, Mar. 1993.
37. O. Shalvi and E. Weinstein, “Universal methods for blind deconvolution,” in Blind Deconvolution, S. Haykin, Ed. Englewood Cliffs, NJ: Prentice-Hall.
38. H. Stark, Ed., Image Recovery: Theory and Applications. New York: Academic. 1987.
39. D. M. Titterington, “Recursive parameter estimation using incomplete data,” J. Roy. Stat. Soc., vol. 46(B), pp. 257-267, 1984.
40. A. T. Walden, “Non-Gaussian reflectivity, entropy and deconvolution,” Geophys., vol. 50, pp. 2862-2888.
41. P. White, “Estimation and information in stationary time series,” Arkiv fur Mathematik, vol. 2, pp. 423-434, 1952.
42. E. Weinstein, “Estimation of trajectory parameters from passive array measurements,” Ph.D. dissertation, Yale University, 1978.
43. R. A. Wiggins, “Minimum entropy deconvolution,” Geoexploration, vol. 16, pp. 21-35, 1977.