OLRIV: A new fast adaptive algorithm for rectangular-block toeplitz systems

IEEE Transactions on Signal Processing

Volumn 48, Issue 9, 2000, Pages 2519-2534

  Buzenac Settineri, Véronique ^a,b   Najim, Mohamed ^a,b  

^a Motorola Labs   (France)

^b Informatique et Radiocommunications de Bordeaux   (France)

Author keywords

Adaptive filtering; High order statistics; Instrumental variables; Overdetermined systems; Toeplitz matrices

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; STATISTICAL METHODS; VECTORS;

BLIND IDENTIFICATION; HIGH ORDER STATISTICS; INSTRUMENTAL VARIABLES; OVERDETERMINED SYSTEMS; TOEPLITZ MATRICES;

ADAPTIVE FILTERING;

EID: 0034259410     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.863055     Document Type: Article

References (32)

1. D. Aboutajdine, A. Meziane, A. Adib, and M. Najim, Algorithme rapide transversal pour l'estimation des paramètres AR dans le cas non gaussien, in Proc. GRETSI, Juan les Pins, France, Sept. 1993.
2. H. Akaike, Block Toeplitz matrix inversion, J. SIAM Appl. Math., vol. 24, pp. 334-341, Mar. 1973.
3. J. W. Brewer, Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits Syst., vol. CAS-25, Sept. 1978.
4. V. Buzenac, R. Settineri, and M. Najim, Overview of cumulant-based adaptive AR identification methods, Proc. ATHOS Workshop Identification Higher Order Statist., Sept. 1993.
5. _, A recursive instrumental variable lattice algorithm for adaptive identification of non gaussian multichannel AR processes, Proc. GRETSI, Sept. 1995.
6. S. L. Campbell and C. D. Meyer, Generalized inverse of linear transformations, in Surveys and Reference Works in Mathematics. New York: Pitman, 1979.
7. G. Carayannis, D. G. Manolakis, and N. Kalouptsidis, A fast sequential algorithm for least square filtering and prediction, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 1394-1402, 1983.
8. J. F. Cardoso, Eigenstructure of the fourth-order cumulant tensor with application to blind source separation, in Proc. ICASSP, Albuquerque, NM, Apr. 1990.
9. J. M. Cioffi and T. Kailath, Fast recursive least squares transversal filters for adaptive filtering, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 304-337, 1984.
10. D. D. Falconer and L. Ljung, Application of fast Kaiman estimation to adaptive equalization, IEEE Trans. Commun., vol. COMM-26, pp. 1439-1446, 1978.
11. J. A. R. Fonollosa, J. Vidal, and E. Masgrau, Adaptive system identification based on higher order statistics, in Proc. ICASSP, Toronto, ON, Canada, 1991.
12. J. A. R. Fonollosa and J. Vidal, Adaptive ARMA identification using cumulants, in Proc. Int. Signal Processing Workshop HOS, Chamrousse, France, July 1991.
13. _, Analytic performance evaluation of cumulant-based ARMA system identification methods, in Proc. IEEE Signal Processing Workshop HOS, Lake Tahoe, CA, June 1993.
14. B. Friedlander, Lattice filters for adaptive filtering, Proc. IEEE, vol. 70, pp. 829-867, 1982.
15. _, The overdetermined recursive instrumental variable method, IEEE Trans. Automat. Contr., vol. AC-29, pp. 353-356, Apr. 1984.
16. B. Friedlander and B. Porat, Adaptive IIR algorithms based on high-order statistics, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 485-495, Apr. 1989.
17. G. B. Giannakis, On the identifiability of non gaussian ARMA models using cumulants, IEEE Trans. Automat. Contr., vol. 35, June 1990.
18. G. B. Giannakis and A. Swami, Identifiability of general ARMA processes using linear cumulant-based estimators, Automatica, vol. 28, no. 4, pp. 771-779, 1992.
19. S. Haykin, Adaptive Filter Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1991.
20. D. T. L. Lee, M. Morf, and B. Friedlander, Recursive least square ladder estimation algorithms, IEEE Trans. Circuits Syst., vol. CAS-28, pp. 467-481, 1981.
21. H. Lev-Ari, T. Kailath, and J. Cioffi, Least square adaptive lattice and transversal filters: A unified geometric theory, IEEE Trans. Inform. Theory, vol. IT-30, pp. 222-236, 1984.
22. N. Levinson, The wiener RMS (root mean square) error criteria in filter design and prediction, J. Math. Phys., vol. 25, pp. 261-178, 1947.
23. X. Liu and M. Najim, A two-dimensional fast lattice recursive least squares algorithm, IEEE Trans. Signal Processing, vol. 44, Oct. 1996.
24. J. M. Mendel, Tutorial on higher order statistics (spectra) in signal processing and systems theory: Theoretical results and some applications, Proc. IEEE, vol. 79, pp. 278-305, 1991.
25. R. L. Moses, J. A. Cadzow, and A. A. Beex, A recursive procedure for ARMA modeling, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 1188-1196, Apr. 1984.
26. C. L. Nikias and A. P. Petropulu, Higher Order Spectra Analysis: A Non Linear Signal Processing Framework. Englewood Cliffs, NJ: Prentice-Hall, 1993.
27. M. B. Priestley, Spectral Analysis and Time Series. London, U.K.: Academic, 1981.
28. A. Swami, System identification using cumulants, Ph.D. dissertation, Univ. Southern Calif., Los Angeles, Dec. 1988.
29. A. Swami and J. Mendel, Adaptive system identification using cumulants, in Proc. ICASSP, New York, 1988.
30. _, Identifiability of non gaussian ARMA process using cumulants, IEEE Trans. Automat. Contr., vol. 37, Feb. 1992.
31. A. Swami, G. Giannakis, and S. Shamsunder, Multichannel ARMA processes, IEEE Trans. Signal Processing, vol. 42, Apr. 1994.
32. J. Vidal, Non-gaussian ARMA estimation based on higher-order statistics, Ph.D. dissertation, Univ. Polytech. Catalogne, Catalogne, France, 1993.