Givens Rotation Based Least Squares Lattice and Related Algorithms

IEEE Transactions on Signal Processing

Volumn 39, Issue 7, 1991, Pages 1541-1551

  Ling, Fuyun ^a  

^a Codex Corp ^*  (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EQUALIZERS; SIGNAL PROCESSING - COMPUTER AIDED ANALYSIS;

GIVENS ROTATION; LATTICE ALGORITHMS; LEAST SQUARES ESTIMATION ALGORITHMS;

MATHEMATICAL TECHNIQUES;

EID: 0026186386     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.134393     Document Type: Article

References (24)

1. J. G. McWhirter, “Recursive least-squares minimization using a systolic array,” Proc. SPIE Int. Soc. Opt. Eng., 1983, pap. 431–15.
2. H. T. Kung and W. M. Gentleman, “Matrix triangularization by systolic arrays,” Proc. SPIE Int. Soc. Opt. Eng., vol. 298, 1981.
3. W. M. Gentleman, “Least squares computation by Givens transformation without square roots,” J. Inst. Math. Its Appl., vol. 12, pp. 329–336, 1973.
4. F. Ling and J. G. Proakis, “A recursive modified Gram-Schmidt algorithm with applications to least squares estimation and adaptive filtering,” in IEEE Proc. ISCS’84 (Montreal, Que., Canada), May, 1984.
5. F. Ling, D. Manolakis, and J. G. Proakis, “A recursive modified Gram-Schmidt algorithm for least squares estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 829–836, Aug. 1986.
6. J. M. Cioffi, “The fast QR adaptive filter,” in IEEE Proc. ICASSP’87 (Dallas, TX), Apr. 1987.
7. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1986.
8. A. Bjorck, “Solving linear least squares problems by Gram-Schmidt orthogonalization,” BIT, vol. 7, pp. 1–21, 1967.
9. F. Ling, D. Manolakis, and J. G. Proakis, “A flexible, numerically robust array processing algorithm and its relationship to the Given’s transformation,” in IEEE Proc. ICASSP’86 (Tokyo, Japan), Apr. 1986.
10. F. Ling, “Systolic arrays for implementation of order-recursive least squares adaptive filtering algorithms,” in Proc. 1988 Int. Conf. Syst. Arrays (San Diego, CA), June 1988.
11. S. Kalson and K. Yao, “Geometrical approach to generalized least squares estimation with systolic array processing.” in Proc. Twenty-Second Annu. Allerton Conf. Commun. Contr., Comput., Oct. 1984.
12. D. D. Falconer and L. Ljung, “Application of fast Kalman estimation to adaptive equalization,” IEEE Trans. Commun., vol. COM-26, pp. 1349–1446, 1978.
13. H. Lev-Ari, T. Kailath, and J. Cioffi, “Least squares adaptive lattice and transversal filters: A unified geometric theory,” IEEE Trans. Inform. Theory, vol. IT-30, Mar. 1984.
14. D. T. L. Lee, M. Morf, and B. Friedlander, “Recursive least squares ladder estimation algorithms,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 3, pp. 627–641, June 1981.
15. F. Ling, D. Manolakis, and J. G. Proakis, “Numerically robust least squares lattice-ladder algorithms with direct updating of the reflection coefficients,” IEEE Trans. Acoust., Speech, Signal Processing, Aug. 1986.
16. F. Ling and J. G. Proakis, “A family of order- and time-recursive least squares adaptive algorithms with systolic array implementation,” in Proc. IEEE New England Mini-Conf. ASSP (Boston, MA), May 15–16, 1987.
17. F. Ling, “Order-recursive least squares adaptive algorithms—a unified framework,” in IEAC Symp. Syst. Identification Parameter Estimation (Beijing, China), Aug. 1988.
18. S. T. Alexander, “Fast adaptive filters: A geometric approach,” IEEE ASSP Mag., vol. 3, no. 4, pp. 18–28, Oct. 1986.
19. S. Yuen, K. Abend, and R. S. Berkowitz, “A recursive least squares algorithm for multiple inputs and outputs and a cylindrical systolic implementation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-36, no. 12, pp. 1917–1923, Dec. 1988.
20. F. Ling and J. G. Proakis, “A generalized multichannel least squares lattice algorithm based on sequential processing stages,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 2, pp. 381–389, Apr. 1984.
21. H. Lev-Ari, “Modular architecture for adaptive multichannel lattice algorithms,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-87, no. 4, pp. 543–552, Apr. 1987.
22. F. Ling, “Efficient least squares lattice algorithm based on Givens rotations with systolic array implementation,” in IEEE Proc. ICASSP'89 (Glasgow, U.K.), May 1989, pap. 40.D9.4.
23. I. K. Proudler et al., “QRD-based lattice filter algorithm,” in Proc. SPIE’89 (San Diego, CA), Aug. 1989.
24. P. A. Regalia and M. G. Bellanger, “On the duality between fast QR methods and lattice methods in least squares adaptive filtering,” IEEE Trans. Signal Processing, vol. 39, no. 4, pp. 879–891, Apr. 1991.