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Diffusion-Probabilistic Least Mean Square Algorithm

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Abstract

In this paper, a novel diffusion estimation algorithm is proposed from a probabilistic perspective by combining the diffusion strategy and the probabilistic least mean square (LMS) at all distributed network nodes. The proposed method, namely diffusion-probabilistic LMS (DPLMS), is more robust to the input signal and impulsive noise than previous algorithms like the diffusion sign-error LMS (DSE-LMS), diffusion robust variable step-size LMS (DRVSSLMS), and diffusion least logarithmic absolute difference (DLLAD) algorithms. Instead of minimizing the estimation error, the DPLMS algorithm is based on approximating the posterior distribution with an isotropic Gaussian distribution. In this paper, the stability of the mean estimation error and the computational complexity of the DPLMS algorithm are analyzed theoretically. Simulation experiments are conducted to explore the mean estimation error for the DPLMS algorithm with varied conditions for input signals and impulsive interferences, compared to the DSE-LMS, DRVSSLMS, and DLLAD algorithms. Both results from the theoretical analysis and simulation suggest that the DPLMS algorithm has superior performance than the DSE-LMS, DRVSSLMS, and DLLAD algorithms when estimating the unknown linear system under the changeable impulsive noise environments.

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References

  1. S. Ashkezari-Toussi, H. Sadoghi-Yazdi, Robust diffusion LMS over adaptive networks. Signal Process. 158, 201–209 (2019)

    Article  Google Scholar 

  2. F.S. Cattivelli, C.G. Lopes, A.H. Sayed, Diffusion recursive least-squares for distributed estimation over adaptive networks. IEEE Trans. Signal Process. 56(5), 1865–1877 (2008)

    Article  MathSciNet  Google Scholar 

  3. F.S. Cattivelli, A.H. Sayed, Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58(3), 1035–1048 (2010)

    Article  MathSciNet  Google Scholar 

  4. F. Chen, T. Shi et al., Diffusion least logarithmic absolute difference algorithm for distributed estimation. Signal Process. 142, 423–430 (2018)

    Article  Google Scholar 

  5. H. Eavani, T.D. Satterthwaite et al., Identifying sparse connectivity patterns in the brain using resting-state fMRI. NeuroImage 105, 286–299 (2015)

    Article  Google Scholar 

  6. J. Fernández-Bes, V. Elvira, S. Van Vaerenbergh, A probabilistic least mean squares filter, in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, QLD, 2015, pp. 2199–2203

  7. Y. Gao, J. Ni, J. Chen et al., Steady-state and stability analyses of diffusion sign-error LMS algorithm. Signal Process. 149, 62–67 (2018)

    Article  Google Scholar 

  8. S. Haykin, Adaptive Filter Theory (Prentice-Hall, Englewood Cliffs, 2001)

    MATH  Google Scholar 

  9. W. Huang, L. Li, Q. Li et al., Diffusion robust variable step-size LMS algorithm over distributed networks. IEEE Access 6, 47511–47520 (2018)

    Article  Google Scholar 

  10. F. Huang, J. Zhang, S. Zhang, Mean-square-deviation analysis of probabilistic LMS algorithm. Digit. Signal Process. 92, 26–35 (2019)

    Article  Google Scholar 

  11. C. Jie, C. Richard, A.H. Sayed, Diffusion LMS over multitask networks. IEEE Trans. Signal Process. 63(11), 2733–2748 (2015)

    Article  MathSciNet  Google Scholar 

  12. H.S. Lee, S.H. Yim, W.J. Song, z2-proportionate diffusion LMS algorithm with mean square performance analysis. Signal Process. 131, 154–160 (2017)

    Article  Google Scholar 

  13. Z. Li, G. Sihai, Diffusion normalized Huber adaptive filtering algorithm. J. Frank. Inst. 355(8), 3812–3825 (2018)

    Article  MathSciNet  Google Scholar 

  14. Y. Liu, C. Li, Z. Zhang, Diffusion sparse least-mean squares over networks. IEEE Trans. Signal Process. 60(8), 4480–4485 (2012)

    Article  MathSciNet  Google Scholar 

  15. C.G. Lopes, A.H. Sayed, Diffusion least-mean squares over adaptive networks: formulation and performance analysis. IEEE Trans. Signal Process. 56(7), 3122–3136 (2008)

    Article  MathSciNet  Google Scholar 

  16. P.D. Lorenzo, A.H. Sayed, Sparse distributed learning based on diffusion adaptation. IEEE Trans. Signal Process. 61(6), 1419–1433 (2013)

    Article  MathSciNet  Google Scholar 

  17. J. Ni, Diffusion sign subband adaptive filtering algorithm for distributed estimation. IEEE Signal Process. Lett. 22(11), 2029–2033 (2015)

    Article  Google Scholar 

  18. J. Ni, J. Chen, X. Chen, Diffusion sign-error LMS algorithm: formulation and stochastic behavior analysis. Signal Process. 128, 142–149 (2016)

    Article  Google Scholar 

  19. Y. Renping, L. Qiao, M. Chen et al., Weighted graph regularized sparse brain network construction for MCI identification. Pattern Recognit. 90, 220–231 (2019)

    Article  Google Scholar 

  20. A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley, New York, 2003)

    Google Scholar 

  21. A.H. Sayed, Adaptive networks. Proc. IEEE 102(4), 460–497 (2014)

    Article  Google Scholar 

  22. M. Shao, C.L. Nikias, Signal processing with fractional lower order moments: stable processes and their applications. Proc. IEEE 81(7), 986–1010 (1993)

    Article  Google Scholar 

  23. K. Smith, L. Spyrou, J. Escudero, Graph-variate signal analysis. IEEE Trans. Signal Process. 67(2), 293–305 (2019)

    Article  MathSciNet  Google Scholar 

  24. J. Song, Y. Xu, Y. Liu et al., Investigation on estimator of chirp rate and initial frequency of LFM signals based on modified discrete chirp Fourier transform. Circuits Syst. Signal Process. 38, 5861–5882 (2019)

    Article  Google Scholar 

  25. V. Stojanovic, V. Filipovic, Adaptive input design for identification of output error model with constrained output. Circuits Syst. Signal Process. 33(1), 97–113 (2014)

    Article  MathSciNet  Google Scholar 

  26. V. Stojanovic, N. Nedic, Joint state and parameter robust estimation of stochastic nonlinear systems. Int. J. Robust Nonlinear Control 26(14), 3058–3074 (2015)

    Article  MathSciNet  Google Scholar 

  27. V. Stojanovic, N. Nedic, Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non-Gaussian noise. Int. J. Robust Nonlinear Control 26(3), 445–460 (2015)

    Article  MathSciNet  Google Scholar 

  28. V. Stojanovic, N. Nedic, Robust identification of OE model with constrained output using optimal input design. J. Frank. Inst. 353(2), 576–593 (2016)

    Article  MathSciNet  Google Scholar 

  29. S.Y. Tu, A.H. Sayed, Diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks. IEEE Trans. Signal Process. 60(12), 6217–6234 (2012)

    Article  MathSciNet  Google Scholar 

  30. E.T. Wagner, M.I. Doroslovački, Distributed LMS estimation of scaled and delayed impulse responses, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016, pp. 4154–4158

  31. F. Wen, Diffusion least-mean p-power algorithms for distributed estimation in alpha-stable noise environments. Electron. Lett. 49(21), 1355–1356 (2013)

    Article  Google Scholar 

  32. P. Wen, J. Zhang, Variable step-size diffusion normalized sign-error algorithm. Circuits Syst. Signal Process. 37(20), 4993–5004 (2018)

    Article  MathSciNet  Google Scholar 

  33. X.J. Yang, Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems. Therm. Sci. 21(3), 1161–1171 (2016)

    Article  Google Scholar 

  34. X.J. Yang, A new integral transform operator for solving the heat-diffusion problem. Appl. Math. Lett. 64, 193–197 (2017)

    Article  MathSciNet  Google Scholar 

  35. X.J. Yang, Y.Y. Feng, C. Cattani et al., Fundamental solutions of anomalous diffusion equations with the decay exponential kernel. Math. Methods Appl. Sci. 42(11), 4054–4060 (2019)

    Article  MathSciNet  Google Scholar 

  36. X.J. Yang, F. Gao, Y. Ju et al., Fundamental solutions of the general fractional-order diffusion equations. Math. Methods Appl. Sci. 41(18), 9312–9320 (2018)

    Article  MathSciNet  Google Scholar 

  37. X.-J. Yang, M.J.A. Tenreiro, A new fractional operator of variable order: application in the description of anomalous diffusion. Phys. A Stat. Mech. Appl. 481, 276–283 (2017)

    Article  MathSciNet  Google Scholar 

  38. S. Zhang, H.C. So, W. Mi et al., A family of adaptive decorrelation NLMS algorithms and its diffusion version over adaptive networks. IEEE Trans. Circ. Syst. I Regul. Pap. 99, 1–12 (2017)

    Google Scholar 

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Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant: 61871420).

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Authors and Affiliations

  1. The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Laboratory for Neuroinformation, Center for Information in Medicine, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China

    Sihai Guan, Chun Meng & Bharat Biswal

  2. Department of Biomedical Engineering, New Jersey Institute of Technology (NJIT), Newark, NJ, USA

    Bharat Biswal

Authors
  1. Sihai Guan
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  2. Chun Meng
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  3. Bharat Biswal
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Correspondence to Sihai Guan, Chun Meng or Bharat Biswal.

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Guan, S., Meng, C. & Biswal, B. Diffusion-Probabilistic Least Mean Square Algorithm. Circuits Syst Signal Process 40, 1295–1313 (2021). https://doi.org/10.1007/s00034-020-01518-3

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  • DOI: https://doi.org/10.1007/s00034-020-01518-3

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