A New Formalism of the Sliding Window Recursive Least Squares Algorithm and Its Fast Version

Kiyoshi NISHIYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.6   pp.1394-1400
Publication Date: 2011/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1394
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
recursive least squares algorithm,  sliding window,  forgetting factor,  fast algorithm,  system identification,  adaptive filter,  

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Summary: 
A new compact form of the sliding window recursive least squares (SWRLS) algorithm, the I-SWRLS algorithm, is derived using an indefinite matrix. The resultant algorithm has a form similar to that of the traditional recursive least squares (RLS) algorithm, and is more computationally efficient than the conventional SWRLS algorithm including two Riccati equations. Furthermore, a computationally reduced version of the I-SWRLS algorithm is developed utilizing a shift property of the correlation matrix of input data. The resulting fast algorithm reduces the computational complexity from O(N2) to O(N) per iteration when the filter length (tap number) is N, but retains the same tracking performance as the original algorithm. This fast algorithm is much easier to implement than the existing SWC FTF algorithms.