Numerical stability issues of the conventional recursive least squares algorithm

Author

Liavas, Athanasios P. ; Regalia, Phillip A.

Author_Institution

Dept. Signal et Image, Inst. Nat. des Telecommun., Evry, France

Volume

3

fYear

1998

fDate

12-15 May 1998

Firstpage

1409

Abstract

The continuous use of adaptive algorithms is strongly dependent on their behavior in finite-precision environments. We study the nonlinear round-off error accumulation system of the conventional RLS algorithm and we derive bounds for the relative precision of the computations and the accumulated round-off error, which guarantee the numerical stability of the finite-precision implementation of the algorithm. The bounds depend on the conditioning of the problem and the exponential forgetting factor. Simulations agree with our theoretical results

Keywords

adaptive filters; error analysis; least squares approximations; numerical stability; recursive filters; RLS algorithm; accumulated round-off error; adaptive algorithms; conventional recursive least squares algorithm; exponential forgetting factor; finite-precision environments; finite-precision implementation; nonlinear round-off error accumulation system; numerical stability; simulations; Adaptive algorithm; Computational modeling; Convergence; Difference equations; Ear; Explosives; Least squares methods; Numerical stability; Roundoff errors; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on

Conference_Location

Seattle, WA

ISSN

1520-6149

Print_ISBN

0-7803-4428-6

Type

conf

DOI

10.1109/ICASSP.1998.681711

Filename

681711