Open Access

New Insights into the RLS Algorithm

EURASIP Journal on Advances in Signal Processing20042004:243857

Received: 21 July 2003

Published: 21 March 2004


The recursive least squares (RLS) algorithm is one of the most popular adaptive algorithms that can be found in the literature, due to the fact that it is easily and exactly derived from the normal equations. In this paper, we give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We also give a very efficient way to recursively estimate the condition number of the input signal covariance matrix thanks to fast versions of the RLS algorithm. Finally, we quantify the misalignment of the RLS algorithm with respect to the condition number.

Keywords and phrases

adaptive algorithms normal equations RLS fast RLS condition number linear interpolation

Authors’ Affiliations

INRS-EMT, Université du Québec
Agere Systems Inc.


© Benesty and Gänsler. 2004