Abstract
There are a large number of algorithms that solve the least-squares problem in a recursive form. In particular, the algorithms based on the lattice realization are very attractive because they allow modular implementation and require a reduced number of arithmetic operations (of order N) [1]–[7]. As a consequence, the lattice recursive least-squares (LRLS) algorithms are considered fast implementations of the RLS problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. L. Lee, M. Morf, and B. Friedlander, “Recursive least squares ladder estimation algorithms,” IEEE Trans. on Acoust., Speech, and Signal Processing, vol. ASSP-29, pp. 627–641, June 1981.
B. Friedlander, “Lattice filters for adaptive processing,” Proceedings of the IEEE, vol. 70, pp. 829–867, Aug. 1982.
F. Ling, D. Manolakis, and J. G. Proakis, “Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients,” IEEE Trans. on Acoust., Speech, and Signal Processing, vol. ASSP-34, pp. 837–845, Aug. 1986.
M. Bellanger, Adaptive Digital Filters and Signal Processing, Marcel Dekker Inc., New York, NY, 1987.
S. Haykin, Adaptive Filter Theory, Prentice Hall, Englewood Cliffs, NJ, 2nd edition 1991.
J. G. Proakis, C. M. Rader, F. Ling, and C. L. Nikias, Advanced Digital Signal Processing, MacMillan, New York, NY, 1992.
C. G. Samson, and V. U. Reddy, “Fixed point error analysis of the normalized ladder algorithm,” IEEE Trans. on Acoust., Speech, and Signal Processing, vol. ASSP-31, pp. 1177–1191, Oct. 1983.
R. C. North, J. R. Zeidler, W. H. Ku, and T. R. Albert, “A floatingpoint arithmetic error analysis of direct and indirect coefficient updating techniques for adaptive lattice filters,” IEEE Trans. on Signal Processing, vol. 41, pp. 1809–1823, May 1993.
H. Lev-Ari, T. Kailath, and J. Cioffi, “Least-squares adaptive lattice and transversal filters: A unified geometric theory,” IEEE Trans. on Information Theory, vol. IT-30, pp. 222–236, March 1984.
J. Cioffi, “An unwindowed RLS adaptive lattice algorithm,” IEEE Trans. on Acoust., Speech, and Signal Processing, vol. 36, pp. 365–371, March 1988.
H. Lev-Ari, K.-F. Chiang, and T. Kailath, “Constrained-input/constrained-output stability for adaptive RLS lattice filters,” IEEE Trans. on Circuits and Systems, vol. 38, pp. 1478–1483, Dec. 1991.
V. J. Mathews, and Z. Xie, “Fixed-point error analysis of stochastic gradient adaptive lattice filters,” IEEE Trans. on Signal Processing, vol. 31, pp. 70–80, Jan. 1990.
M. Reed, and B. Liu, “Analysis of simplified gradient adaptive lattice algorithms using power-of-two quantization,” Proc. 1990 IEEE Intern. Symp. on Circuits and Systems, New Orleans, LA, pp. 792–795, May 1990.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Diniz, P.S.R. (1997). Adaptive Lattice-Based RLS Algorithms. In: Adaptive Filtering. The Springer International Series in Engineering and Computer Science, vol 399. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8660-3_6
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8660-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4660-9
Online ISBN: 978-1-4419-8660-3
eBook Packages: Springer Book Archive