{"title":"Data-reuse recursive least-squares algorithm with Riemannian manifold constraint","authors":"Haiquan Zhao, Haolin Wang, Yi Peng","doi":"10.1016/j.sigpro.2025.109982","DOIUrl":null,"url":null,"abstract":"<div><div>Actual signals often contain nonlinear manifold structures, but traditional filtering algorithms assume data are embedded in Euclidean space, which makes them less effective when handling complicated noise and manifold data. To address these challenges, Riemannian geometry constraints to the traditional data-reuse recursive least-squares (DR-RLS) algorithm is proposed in this paper. Therefore, a novel adaptive filtering algorithm combining the DR-RLS algorithm with Riemannian manifolds is proposed. This algorithm constrains the filter update process on the Riemannian manifold through exponential mapping, enabling better adaptation to nonlinear manifold data structures. Additionally, the tracking performance and convergence speed of the algorithm are enhanced by data reuse. The convergence and computational complexity of the proposed algorithm on the Riemannian manifold are also analyzed. Finally, the effectiveness of the proposed algorithm relative to other methods is demonstrated through simulation results.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"234 ","pages":"Article 109982"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425000969","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
Actual signals often contain nonlinear manifold structures, but traditional filtering algorithms assume data are embedded in Euclidean space, which makes them less effective when handling complicated noise and manifold data. To address these challenges, Riemannian geometry constraints to the traditional data-reuse recursive least-squares (DR-RLS) algorithm is proposed in this paper. Therefore, a novel adaptive filtering algorithm combining the DR-RLS algorithm with Riemannian manifolds is proposed. This algorithm constrains the filter update process on the Riemannian manifold through exponential mapping, enabling better adaptation to nonlinear manifold data structures. Additionally, the tracking performance and convergence speed of the algorithm are enhanced by data reuse. The convergence and computational complexity of the proposed algorithm on the Riemannian manifold are also analyzed. Finally, the effectiveness of the proposed algorithm relative to other methods is demonstrated through simulation results.
期刊介绍:
Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing.
Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.