Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm

Shuning Chen; Die Gan; Kexin Liu; Jinhu Lü

doi:10.1016/j.ifacol.2023.10.905

Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm

Shuning Chen^*
, Die Gan
, Kexin Liu
, Jinhu Lü

^*Corresponding author for this work

School of Automation Science and Electrical Engineering

CAS - Academy of Mathematics and System Sciences
Zhongguancun Laboratory

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

To identify the unknown sparse time-varying parameters of the stochastic dynamic system, we integrate compressive sensing theory with the traditional recursive least squares with forgetting factor (FFLS) algorithm, and propose a compressed adaptive filtering algorithm. Our algorithm is designed to first compress the original high-dimensional sparse regression vector by using the sensing matrix, and then apply the FFLS algorithm to estimate the compressed parameters. Subsequently, the original high-dimensional sparse parameters can be well recovered by a reconstruction technique. We introduce an excitation condition on the compressed stochastic regressors, under which the stability of the proposed algorithm (i.e., the upper bound of the estimation error) is established without assuming independence, stationarity or ergodicity of the system signals. The effectiveness of our theoretical results is demonstrated by a numerical example, which also shows that our proposed algorithm has better performance than both the compressed least mean squares algorithm and the uncompressed FFLS algorithm for tracking high-dimensional sparse parameters.

Original language	English
Title of host publication	IFAC-PapersOnLine
Editors	Hideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
Publisher	Elsevier B.V.
Pages	10240-10245
Number of pages	6
Edition	2
ISBN (Electronic)	9781713872344
DOIs	https://doi.org/10.1016/j.ifacol.2023.10.905
State	Published - 1 Jul 2023
Event	22nd IFAC World Congress - Yokohama, Japan Duration: 9 Jul 2023 → 14 Jul 2023

Publication series

Name	IFAC-PapersOnLine
Number	2
Volume	56
ISSN (Electronic)	2405-8963

Conference

Conference	22nd IFAC World Congress
Country/Territory	Japan
City	Yokohama
Period	9/07/23 → 14/07/23

Keywords

Stochastic dynamic system
compressive sensing
excitation condition
forgetting factor
recursive least squares
time-varying sparse parameters

Access to Document

10.1016/j.ifacol.2023.10.905

Cite this

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title = "Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm",

abstract = "To identify the unknown sparse time-varying parameters of the stochastic dynamic system, we integrate compressive sensing theory with the traditional recursive least squares with forgetting factor (FFLS) algorithm, and propose a compressed adaptive filtering algorithm. Our algorithm is designed to first compress the original high-dimensional sparse regression vector by using the sensing matrix, and then apply the FFLS algorithm to estimate the compressed parameters. Subsequently, the original high-dimensional sparse parameters can be well recovered by a reconstruction technique. We introduce an excitation condition on the compressed stochastic regressors, under which the stability of the proposed algorithm (i.e., the upper bound of the estimation error) is established without assuming independence, stationarity or ergodicity of the system signals. The effectiveness of our theoretical results is demonstrated by a numerical example, which also shows that our proposed algorithm has better performance than both the compressed least mean squares algorithm and the uncompressed FFLS algorithm for tracking high-dimensional sparse parameters.",

keywords = "Stochastic dynamic system, compressive sensing, excitation condition, forgetting factor, recursive least squares, time-varying sparse parameters",

author = "Shuning Chen and Die Gan and Kexin Liu and Jinhu L{\"u}",

note = "Publisher Copyright: Copyright {\textcopyright} 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",

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Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm. / Chen, Shuning; Gan, Die; Liu, Kexin et al.
IFAC-PapersOnLine. ed. / Hideaki Ishii; Yoshio Ebihara; Jun-ichi Imura; Masaki Yamakita. 2. ed. Elsevier B.V., 2023. p. 10240-10245 (IFAC-PapersOnLine; Vol. 56, No. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm

AU - Chen, Shuning

AU - Gan, Die

AU - Liu, Kexin

AU - Lü, Jinhu

PY - 2023/7/1

Y1 - 2023/7/1

N2 - To identify the unknown sparse time-varying parameters of the stochastic dynamic system, we integrate compressive sensing theory with the traditional recursive least squares with forgetting factor (FFLS) algorithm, and propose a compressed adaptive filtering algorithm. Our algorithm is designed to first compress the original high-dimensional sparse regression vector by using the sensing matrix, and then apply the FFLS algorithm to estimate the compressed parameters. Subsequently, the original high-dimensional sparse parameters can be well recovered by a reconstruction technique. We introduce an excitation condition on the compressed stochastic regressors, under which the stability of the proposed algorithm (i.e., the upper bound of the estimation error) is established without assuming independence, stationarity or ergodicity of the system signals. The effectiveness of our theoretical results is demonstrated by a numerical example, which also shows that our proposed algorithm has better performance than both the compressed least mean squares algorithm and the uncompressed FFLS algorithm for tracking high-dimensional sparse parameters.

AB - To identify the unknown sparse time-varying parameters of the stochastic dynamic system, we integrate compressive sensing theory with the traditional recursive least squares with forgetting factor (FFLS) algorithm, and propose a compressed adaptive filtering algorithm. Our algorithm is designed to first compress the original high-dimensional sparse regression vector by using the sensing matrix, and then apply the FFLS algorithm to estimate the compressed parameters. Subsequently, the original high-dimensional sparse parameters can be well recovered by a reconstruction technique. We introduce an excitation condition on the compressed stochastic regressors, under which the stability of the proposed algorithm (i.e., the upper bound of the estimation error) is established without assuming independence, stationarity or ergodicity of the system signals. The effectiveness of our theoretical results is demonstrated by a numerical example, which also shows that our proposed algorithm has better performance than both the compressed least mean squares algorithm and the uncompressed FFLS algorithm for tracking high-dimensional sparse parameters.

KW - Stochastic dynamic system

KW - compressive sensing

KW - excitation condition

KW - forgetting factor

KW - recursive least squares

KW - time-varying sparse parameters

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U2 - 10.1016/j.ifacol.2023.10.905

DO - 10.1016/j.ifacol.2023.10.905

M3 - 会议稿件

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A2 - Ishii, Hideaki

A2 - Ebihara, Yoshio

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PB - Elsevier B.V.

T2 - 22nd IFAC World Congress

Y2 - 9 July 2023 through 14 July 2023

ER -

Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm

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