中国物理B ›› 2026, Vol. 35 ›› Issue (3): 30204-030204.doi: 10.1088/1674-1056/adfefe

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Sequential noise-boosted M-estimation for robust parameter estimation under impulsive noise

Li Zhang(张莉)1, Yan Pan(潘燕)1,†, Fabing Duan(段法兵)2, Fran?ois Chapeau-Blondeau3, and Derek Abbott4   

  1. 1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    2 Institute of Complexity Science, Qingdao University, Qingdao 266071, China;
    3 Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Université d'Angers, 62 Avenue Notre Dame du Lac, 49000 Angers, France;
    4 Centre for Biomedical Engineering (CBME) and School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia
  • 收稿日期:2025-07-16 修回日期:2025-08-17 接受日期:2025-08-26 出版日期:2026-02-11 发布日期:2026-03-19
  • 通讯作者: Yan Pan E-mail:panyan87@sdust.edu.cn
  • 基金资助:
    This project was supported by the National Natural Science Foundation of China (Grant No. 62001271).

Sequential noise-boosted M-estimation for robust parameter estimation under impulsive noise

Li Zhang(张莉)1, Yan Pan(潘燕)1,†, Fabing Duan(段法兵)2, Fran?ois Chapeau-Blondeau3, and Derek Abbott4   

  1. 1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    2 Institute of Complexity Science, Qingdao University, Qingdao 266071, China;
    3 Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Université d'Angers, 62 Avenue Notre Dame du Lac, 49000 Angers, France;
    4 Centre for Biomedical Engineering (CBME) and School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia
  • Received:2025-07-16 Revised:2025-08-17 Accepted:2025-08-26 Online:2026-02-11 Published:2026-03-19
  • Contact: Yan Pan E-mail:panyan87@sdust.edu.cn
  • Supported by:
    This project was supported by the National Natural Science Foundation of China (Grant No. 62001271).

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摘要： We propose a sequential noise-boosted M-estimation algorithm for estimating system parameters in environments characterized by impulsive (heavy-tailed) noise. This algorithm extends the conventional M-estimation framework by strategically injecting artificial noise into the observations, thereby facilitating the estimation procedure and ensuring convergence to the desired estimator. A fundamental criterion theorem is established to determine the conditions under which injecting scale-family noise enhances the efficacy of the M-estimator in heavy-tailed background noise. For cases where noise injection is beneficial, it is rigorously proved that the sequential noise-boosted M-estimation algorithm converges with probability one. Experimental results demonstrate that the proposed algorithm outperforms traditional M-estimation methods, both under a given injected noise intensity and when the noise injection is adaptively optimized via Bayesian optimization. Furthermore, it is observed that the proposed algorithm can asymptotically achieve the performance of the maximum likelihood estimator (MLE) for system parameter estimation.

关键词: sequential estimation, noise-boosted m-estimation, convergence analysis, stochastic resonance

Abstract: We propose a sequential noise-boosted M-estimation algorithm for estimating system parameters in environments characterized by impulsive (heavy-tailed) noise. This algorithm extends the conventional M-estimation framework by strategically injecting artificial noise into the observations, thereby facilitating the estimation procedure and ensuring convergence to the desired estimator. A fundamental criterion theorem is established to determine the conditions under which injecting scale-family noise enhances the efficacy of the M-estimator in heavy-tailed background noise. For cases where noise injection is beneficial, it is rigorously proved that the sequential noise-boosted M-estimation algorithm converges with probability one. Experimental results demonstrate that the proposed algorithm outperforms traditional M-estimation methods, both under a given injected noise intensity and when the noise injection is adaptively optimized via Bayesian optimization. Furthermore, it is observed that the proposed algorithm can asymptotically achieve the performance of the maximum likelihood estimator (MLE) for system parameter estimation.

Key words: sequential estimation, noise-boosted m-estimation, convergence analysis, stochastic resonance

中图分类号:  (Probability theory, stochastic processes, and statistics)

  • 02.50.-r
02.50.Fz (Stochastic analysis) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.40.Ca (Noise)