Fast RLS adaptive algorithms and Chandrasekhar equations

Guy Demoment; Roger Reynaud

doi:10.1117/12.49791

1 December 1991 Fast RLS adaptive algorithms and Chandrasekhar equations

Guy Demoment, Roger Reynaud

Proceedings Volume 1565, Adaptive Signal Processing; (1991) https://doi.org/10.1117/12.49791
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

Fast recursive least squares (FRLS) algorithms have been extensively studied since the mid- 1970s for adaptive signal processing applications. Despite their large number and apparent diversity, they were almost exclusively derived using only two techniques: partitioned matrix inversion lemma or least squares geometric theory. Surprisingly, Chandrasekhar factorizations, that were introduced in the early 1970s to derive fast Kalman filters, were little used, even though fast RLS algorithms can also be derived with this technique, under various forms, either unnormalized or over-normalized. For instance, the well-known FTF algorithm corresponds exactly to a particular case of the Chandrasekhar equations. The aim of this paper is to take stock of the interest of the Chandrasekhar technique for FRLS estimation. The corresponding equations have a somewhat generic character which can help to show the links between FRLS algorithms and other least squares estimation problems, since they were successfully used to derive fast algorithms for estimating random variables through regularization techniques, or for computing cross-validation criteria in statistics. These Chandrasekhar factorizations can also help teach fast adaptive algorithms: they are easy to understand, they can be used in a large variety of algorithmic problems, and, in a least squares algorithmic context, there is no need to learn the FRLS algorithms separately.

Citation Download Citation

Guy Demoment and Roger Reynaud "Fast RLS adaptive algorithms and Chandrasekhar equations", Proc. SPIE 1565, Adaptive Signal Processing, (1 December 1991); https://doi.org/10.1117/12.49791

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available