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

Kiyoshi NISHIYAMA

doi:10.1587/transfun.E94.A.1394

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

Kiyoshi NISHIYAMA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.6 pp.1394-1400

Publication Date: 2011/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.1394

Type of Manuscript: PAPER

Category: Digital Signal Processing

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Kiyoshi NISHIYAMA, "A New Formalism of the Sliding Window Recursive Least Squares Algorithm and Its Fast Version" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 6, pp. 1394-1400, June 2011, doi: 10.1587/transfun.E94.A.1394.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1394/_p

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@ARTICLE{e94-a_6_1394,
author={Kiyoshi NISHIYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Formalism of the Sliding Window Recursive Least Squares Algorithm and Its Fast Version},
year={2011},
volume={E94-A},
number={6},
pages={1394-1400},
abstract={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.},
keywords={},
doi={10.1587/transfun.E94.A.1394},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - A New Formalism of the Sliding Window Recursive Least Squares Algorithm and Its Fast Version
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1394
EP - 1400
AU - Kiyoshi NISHIYAMA
PY - 2011
DO - 10.1587/transfun.E94.A.1394
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2011
AB - 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.
ER -