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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| Vydané v: | Signal processing Ročník 234; s. 109982 |
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| Jazyk: | English |
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Elsevier B.V
01.09.2025
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| ISSN: | 0165-1684 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 109982 |
| Author | Zhao, Haiquan Peng, Yi Wang, Haolin |
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| Cites_doi | 10.1007/s00245-019-09564-3 10.1109/LSP.2022.3153207 10.1007/s11182-018-1326-5 10.1109/TPAMI.2007.70735 10.1016/j.ymssp.2024.111716 10.1109/TSP.2002.801893 10.1038/s41598-023-36127-y 10.4153/CJM-1967-036-6 10.1109/TAC.2013.2254619 10.1109/TSP.2017.2752695 10.1080/00036811.2019.1566530 10.1145/2185520.2185529 10.1109/JSEN.2023.3348521 10.1007/s00034-021-01720-x 10.1109/TCSII.2023.3305482 10.1115/1.3662552 10.1007/s11265-021-01711-w 10.1016/j.ins.2024.121242 10.1137/23M1589463 10.1007/s10470-024-02261-4 10.1109/TVT.2002.1002509 |
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| Keywords | Steady-state error Adaptive filtering DR-RLS Riemannian manifold constraints Tracking performance Convergence speed |
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