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Correction-Based Diffusion LMS Algorithms for Distributed Estimation

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Abstract

In this paper, we consider distributed estimation problems where a set of agents are used for jointly estimating an interesting parameter from the noise measurements. By using the adaptation-then-combination rule in the traditional diffusion least mean square (DLMS), a DLMS is proposed by introducing a correction step with a gain factor between the adaptation and combination steps. An explicit expression for the network mean-square deviation is derived for the proposed algorithm, and a sufficient condition is established to guarantee the mean stability. Simulation results are provided to verify theoretical results, and it is shown that the proposed algorithm outperforms the traditional DLMS.

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References

  1. R. Abdolee, B. Champagne, A.H. Sayed, A diffusion LMS strategy for parameter estimation in noisy regressor applications, in 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Bucharest, pp. 749–753 (2012)

  2. P. Braca, S. Marano, V. Matta, Running consensus in wireless sensor networks, in Proceedings of the IEEE International Conference on Information Fusion, Cologne, Germany, p. 1C6 (2008)

  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. B. Chen, L. Xing, N. Zheng, J.C. Prncipe, Quantized minimum error entropy criterion. IEEE Trans. Neural Netw. Learn. Syst. 30(5), 1370–1380 (2019)

    Article  MathSciNet  Google Scholar 

  5. J. Chen, A.H. Sayed, Diffusion adaptation strategies for distributed optimization and learning over networks. IEEE Trans. Signal Process. 60(8), 4289C4305 (2012)

    MathSciNet  Google Scholar 

  6. J. Chen, A.H. Sayed, On the learning behavior of adaptive networks part I: transient analysis. IEEE Trans. Inf. Theory 61(6), 3487C3517 (2015)

    MathSciNet  Google Scholar 

  7. J. Chen, A.H. Sayed, On the learning behavior of adaptive networks part II: performance analysis. IEEE Trans. Inf. Theory 61(6), 3518C3548 (2015)

    MathSciNet  Google Scholar 

  8. R.H. Koning, H. Neudecker, T. Wansbeek, Block Kronecker products and the vecb operator. Linear Algebra Appl. 149, 165–184 (1991)

    Article  MathSciNet  Google Scholar 

  9. J. Lee, S.E. Kim, W.J. Song, Data-selective diffusion LMS for reducing communication overhead. Signal Process. 113(7), 211–217 (2015)

    Article  Google Scholar 

  10. Y. Liu, C. Li, Secure distributed estimation over wireless sensor networks under attacks. IEEE Trans. Aerosp. Electron. Syst. 54(4), 1815–1831 (2018)

    Article  Google Scholar 

  11. C.G. Lopes, A.H. Sayed, Diffusion least-mean squares over adaptive networks: formulation and performance analysis. IEEE Trans. Signal Process. 56(7), 31223136 (2008)

    Article  MathSciNet  Google Scholar 

  12. L. Lu, H. Zhao, W. Wang, Y. Yu, Performance analysis of the robust diffusion normalized least mean \({p} \)-power algorithm. IEEE Trans. Circuits Syst. II Express Briefs 65(12), 2047–2051 (2018)

    Article  Google Scholar 

  13. L. Lu, Z. Zheng, B. Champagne, X. Yang, W. Wu, Self-regularized nonlinear diffusion algorithm based on levenberg gradient descent. Signal Process. 163, 107–114 (2019)

    Article  Google Scholar 

  14. L. Lu, H. Zhao, B. Champagne, Diffusion total least-squares algorithm with multi-node feedback. Signal Process. 153, 243–254 (2018)

    Article  Google Scholar 

  15. R. Mohammadloo, G. Azarnia, M. A. Tinati, Increasing the initial convergence of distributed diffusion LMS algorithm by a new variable tap-length variable step-size method, in 21st Iranian Conference on Electrical Engineering (ICEE), Mashhad, pp. 1–5 (2013)

  16. R. Nassif, C. Richard, A. Ferrari, A.H. Sayed, Diffusion LMS for multitask problems with local linear equality constraints. IEEE Trans. Signal Process. 65(19), 4979–4993 (2017)

    Article  MathSciNet  Google Scholar 

  17. R. Olfati-Saber, J.S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, in Proceedings of IEEE Conference on Decision and Control (CDC). IEEE, p. 66986703 (2005)

  18. M. Omer Bin Saeed, A. Zerguine, S.A. Zummo, Variable step-size least mean square algorithms over adaptive networks, in 10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010), Kuala Lumpur, pp. 381–384 (2010)

  19. S. Sardellitti, M. Giona, S. Barbarossa, Fast distributed average consensus algorithms based on advection-diffusion processes. IEEE Trans. Signal Process. 58(2), 826842 (2010)

    Article  MathSciNet  Google Scholar 

  20. A.H. Sayed, Diffusion strategies for adaptation and learning over networks. IEEE Signal Process. Mag. 30(3), 155–171 (2013)

    Article  Google Scholar 

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

    Google Scholar 

  22. A.H. Sayed, Adaptive networks, in Proceedings of the IEEE, vol. 102, no. 4, p. 460C497 (2014)

  23. A.H. Sayed, Adaptation, learning, and optimization over networks. Found. Trends Mach. Learn. 7(4–5), 311C801 (2014)

    Google Scholar 

  24. N. Takahashi, I. Yamada, A.H. Sayed, Diffusion least-mean squares with adaptive combiners: formulation and performance analysis. IEEE Trans. Signal Process. 58(9), 4795–4810 (2010)

    Article  MathSciNet  Google Scholar 

  25. K. Yuan, Q. Ling, W. Yin, On the convergence of decentralized gradient descent. SIAM J. Optim. 26(3), 1835C1854 (2016)

    Article  MathSciNet  Google Scholar 

  26. K. Yuan, B. Ying, X. Zhao, A.H. Sayed, Exact diffusion for distributed optimization and learning-part I: algorithm development. IEEE Trans. Signal Process. 67(3), 708–723 (2019)

    Article  MathSciNet  Google Scholar 

  27. K. Yuan, B. Ying, X. Zhao, A.H. Sayed, Exact diffusion for distributed optimization and learning-part II: convergence analysis. IEEE Trans. Signal Process. 67(3), 724–739 (2019)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by National Key R&D Program of China (2018YFB1402600) and NSFC (61976013).

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  1. School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, 100191, China

    Huining Chang & Wenling Li

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  1. Huining Chang
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  2. Wenling Li
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Correspondence to Wenling Li.

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Chang, H., Li, W. Correction-Based Diffusion LMS Algorithms for Distributed Estimation. Circuits Syst Signal Process 39, 4136–4154 (2020). https://doi.org/10.1007/s00034-020-01363-4

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