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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, François Chapeau-Blondeau3, and Derek Abbott4 |
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 |
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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.
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Received: 16 July 2025
Revised: 17 August 2025
Accepted manuscript online: 26 August 2025
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PACS:
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02.50.-r
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(Probability theory, stochastic processes, and statistics)
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02.50.Fz
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(Stochastic analysis)
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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05.40.Ca
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(Noise)
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| Fund: This project was supported by the National Natural Science Foundation of China (Grant No. 62001271). |
Corresponding Authors:
Yan Pan
E-mail: panyan87@sdust.edu.cn
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Cite this article:
Li Zhang(张莉), Yan Pan(潘燕), Fabing Duan(段法兵), François Chapeau-Blondeau, and Derek Abbott Sequential noise-boosted M-estimation for robust parameter estimation under impulsive noise 2026 Chin. Phys. B 35 030204
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