# Measuring and maintaining consistency: a hybrid FTF algorithm

James Bunch; Richard Le Borne; Ian Proudler

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 5, page 1203-1216
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topBunch, James, Le Borne, Richard, and Proudler, Ian. "Measuring and maintaining consistency: a hybrid FTF algorithm." International Journal of Applied Mathematics and Computer Science 11.5 (2001): 1203-1216. <http://eudml.org/doc/207551>.

@article{Bunch2001,

abstract = {Due to the versatility as well as its ease of implementation, the Fast Transversal Filters algorithm is attractive for many adaptive filtering applications. However, it is not widely used because of its undesirable tendency to diverge when operating in finite precision arithmetic. To compensate, modifications to the algorithm have been introduced that are either occasional (performed when a predefined condition(s) is violated) or structured as part of the normal update iteration. However, in neither case is any confidence explicitly given that the computed parameters are in fact close to the desired ones. Here, we introduce a time invariant parameter that provides the user with more flexibility in establishing confidence in the consistency of the updated filter parameters. Additionally, we provide evidence through the introduction of a hybrid FTF algorithm that when sufficient time is given prior to catastrophic divergence, the update parameters of the FTF algorithm can be adjusted so that consistency can be acquired and maintained.},

author = {Bunch, James, Le Borne, Richard, Proudler, Ian},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {consistency; FTF; numerical stability; fast transversal filter algorithms; numerical instability; finite precision arithmetic},

language = {eng},

number = {5},

pages = {1203-1216},

title = {Measuring and maintaining consistency: a hybrid FTF algorithm},

url = {http://eudml.org/doc/207551},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Bunch, James

AU - Le Borne, Richard

AU - Proudler, Ian

TI - Measuring and maintaining consistency: a hybrid FTF algorithm

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 5

SP - 1203

EP - 1216

AB - Due to the versatility as well as its ease of implementation, the Fast Transversal Filters algorithm is attractive for many adaptive filtering applications. However, it is not widely used because of its undesirable tendency to diverge when operating in finite precision arithmetic. To compensate, modifications to the algorithm have been introduced that are either occasional (performed when a predefined condition(s) is violated) or structured as part of the normal update iteration. However, in neither case is any confidence explicitly given that the computed parameters are in fact close to the desired ones. Here, we introduce a time invariant parameter that provides the user with more flexibility in establishing confidence in the consistency of the updated filter parameters. Additionally, we provide evidence through the introduction of a hybrid FTF algorithm that when sufficient time is given prior to catastrophic divergence, the update parameters of the FTF algorithm can be adjusted so that consistency can be acquired and maintained.

LA - eng

KW - consistency; FTF; numerical stability; fast transversal filter algorithms; numerical instability; finite precision arithmetic

UR - http://eudml.org/doc/207551

ER -

## References

top- Chaitin-Chatelin F. and Frayssé V. (1996): Lectures on FinitePrecision Computations. - Philadelphia: SIAM. Zbl0846.65020
- Cioffi J.M. and Kailath T. (1984): Fast, recursive-least-squares transversalfilters for adaptive filtering. - IEEE Trans. s Acoust. Speech Sign.Process., Vol.32, No.2, pp.304-337. Zbl0577.93073
- Haykin S. (1991): Adaptive Filter Theory, 2nd Edn. - Englewood Cliffs, NJ: Prentice-Hall. Zbl0723.93070
- Lin D. (1984): On digital implementation of the fast Kalman algorithms. - IEEE Trans. Acoust. Speech Sign. Process., Vol.32,No.5, pp.998-1005. Zbl0576.65061
- Regalia P. (1992): Numerical stability issues in fast least-squaresadaptation algorithms. - Opt. Eng., Vol.31, No.6, pp.1144-1152.
- Slock D.T.M. and Kailath T. (1991): Numerically stable fast transversalfilters for recursive least squares adaptive filtering. - IEEE Trans. Signal Process., Vol.39, No.1, pp.92-114. Zbl0728.93085
- Slock D.T.M. and Kailath T. (1992): Backward consistency concept andround-off error propagation dynamics in recursive least-squares algorithms. - Opt. Eng., Vol.31, No.6, pp.1153-1169.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.