Data-reuse recursive least-squares algorithm with Riemannian manifold constraint

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 traditi...

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Bibliographic Details
Published in:Signal processing Vol. 234; p. 109982
Main Authors: Zhao, Haiquan, Wang, Haolin, Peng, Yi
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2025
Subjects:
Adaptive filtering
Convergence speed
DR-RLS
Riemannian manifold constraints
Steady-state error
Tracking performance
Steady-state error
Adaptive filtering
DR-RLS
Riemannian manifold constraints
Tracking performance
Convergence speed
ISSN:0165-1684
Online Access:Get full text
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Summary: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.
ISSN:0165-1684
DOI:10.1016/j.sigpro.2025.109982