Identification of noisy linear systems with discrete random input

IEEE Transactions on Information Theory

Volumn 44, Issue 5, 1998, Pages 1941-1952

  Gassiat, Elisabeth ^a   Gautherat, Emmanuelle ^a  

^a UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

Contrast function, deconvolution, discrete linear systems, hankel matrix, non minimum phase systems

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; IDENTIFICATION (CONTROL SYSTEMS); LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; PROBABILITY; RANDOM PROCESSES; SIGNAL TO NOISE RATIO;

BLIND DECONVOLUTION; CONTRAST FUNCTION; HANKEL MATRIX;

SIGNAL FILTERING AND PREDICTION;

EID: 0032166613     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.705571     Document Type: Article

References (27)

1. R. Azencott and D. Dacunha-Castelle, Séries d'observations irréglières. Modevision et Prévision, 1984.
2. G. K. Golubev, "Nonparameteric estimation of smooth spectral densities of gaussian stationary sequences," Theory Probab. Appt., vol. 38, no. 4, pp. 630-639, 1993.
3. J. P. Kreiss, "On adaptive estimation in stationary a.r.m.a. processes," Ann. Stat., no. 1, pp. 112-133, 1987.
4. K. S. Lii and M. Rosenblatt, "Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes," Ann. Stat., vol. 10, pp. 1195-1208.
5. C. L. Nikias and M. Rghuveer, "Bispectrum estimation: A digital signal processing framework," Proc. IEEE, vol. 75, pp. 869-891, 1987.
6. D. Donoho, "On minimum entropy deconvolution," in Applied Time Series Analysis II, D. F. Findley, Ed. New York: Academic, 1981, pp. 564-608.
7. A. Benveniste, M. Goursat, and G. Rüget, "Robust identification of a non-minimum phase system: Blind adjustment of a linear equalizer in data communications," IEEE Trans. Automat. Contr., vol. AC-25, pp. 385-399, 1980.
8. E. Gassiat, "Estimation semi-paramétrique d'un modèle autorégressif stationnaire muliindice non nécessairement causal," Ann. Institut Henri Poincaré, vol. 26, no. 1, pp. 181-205, 1990.
9. O. Shalvi and E. Weinstein, "On new criteria for blind deconvolution of non-minimum phase systems (channels)," IEEE Trans. Inform. Theory, vol. 36, pp. 312-321, 1990.
10. F. J. Breidt, R. A. Davis, K. S. Lii, and M. Rosenblatt, "Maximum likelihood estimation for non causal autoregressive processes," J. Multivariate Anal., vol. 36, pp. 175-198, 1991.
11. E. Gassiat, "Adaptive estimation in non causal ar processes," Ann. Stat., vol. 21, no. 4, pp. 2022-2042, 1993.
12. R. A. Davis and M. Rosenblatt, "Parameter estimation for some time series models without contiguity," Stat. Prob. Lett., vol. 11, pp. 515-521.
13. K. Feher, Advanced Digital Communications-Systems and Signal Processing Techniques. Englewood Cliffs: NJ, Prentice-Hall, 1987.
14. T. H. Li, "Blind identification and deconvolution of linear systems driven by binary random sequences," IEEE Trans. Inform. Theory, vol. 38, pp. 26-38, 1992.
15. _, "Blind deconvolution of linear systems with multilevel nonstationary inputs," Ann. Stat., vol. 23, pp. 690-704, 1995.
16. F. Gamboa and E. Gassiat, "Blind deconvolution of discrete linear systems," Ann. Stat., 1993, to be published.
17. E. Gassiat, "Deconvolution aveugle de systems linéaries discrets bruités, C.R.A.S. Séries I, vol. 319, pp. 489-492, 1994.
18. D. Dacunha-Castelle and E. Gassiat, "Estimation of the order of a mixture model," Tech. Rep., Univ. d'Evry-Val d'Essonne, France, and Univ. Paris-Sud, Orsay, France, 1994.
19. F. Gamboa and E. Gassiat, "Source separation when the input sources are discrete or have constant modulus," Tech. Rep. Univ. Paris-Sud, Orsay, France, 1994.
20. V. Petrov, Sums of Independent Variables. Moscow, USSR: Nauka, 1975.
21. M. G. Krein and A. A. Nudel'man, The Markov Moment Problem and Extremal Problems, vol. 50, 1977.
22. F. Gamboa and E. Gassiat, "Bayesian methods and maximum entropy for ill posed inverse problems," Ann. Stat., 1993, to be published.
23. P. Doukhan, "Mixing properties and examples," in Lecture Notes in Statistics, vol. 85. New York: Springer-Verlag, 1994.
24. P. Hall and C. C. Heyde, Martingale limit theory and its applications. New York: Academic, 1980.
25. H. Linhart and W. Zucchini, Model Selection. New York: Wiley, 1986.
26. E. Gassiat and E. Gautherat, "Blind deconvolution of a multilevel input series with unknown alphabet and using noisy observations," Tech. Rep., Univ. d'Evry-Val d'Essonne, France, 1995.
27. B. G. Lindsay, "On the determinant of moment matrices," Ann. Stat., vol. 17, pp. 711-721, 1989.