Skip to main content
SpringerLink
Log in

Distributed bias-compensated normalized least-mean squares algorithms with noisy input

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, we study the problem of distributed normalized least-mean squares (NLMS) estimation over multi-agent networks, where all nodes collaborate to estimate a common parameter of interest. We consider the situations that all nodes in the network are corrupted by both input and output noise. This yields into biased estimates by the distributed NLMS algorithms. In our analysis, we take all the noise into consideration and prove that the bias is dependent on the input noise variance. Therefore, we propose a bias compensation method to remove the noise-induced bias from the estimated results. In our development, we first assume that the variances of the input noise are known a priori and develop a series of distributed-based bias-compensated NLMS (BCNLMS) methods. Under various practical scenarios, the input noise variance is usually unknown a priori, therefore it is necessary to first estimate for its value before bias removal. Thus, we develop a real-time estimation method for the input noise variance, which overcomes the unknown property of this noise. Moreover, we perform some main analysis results of the proposed distributed BCNLMS algorithms. Furthermore, we illustrate the performance of the proposed distributed bias compensation method via graphical simulation results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Golub G H, van Loan C F. An analysis of the total least squares problem. SIAM J Numer Anal, 1980, 17: 883–893

    Article  MathSciNet  Google Scholar 

  2. Feng D Z, Zhang X D, Chang D X, et al. A fast recursive total least squares algorithm for adaptive FIR filtering. IEEE Trans Signal Process, 2004, 52: 2729–2737

    Article  Google Scholar 

  3. So H C. Modified LMS algorithm for unbiased impulse response estimation in nonstationary noise. Electron Lett, 1999, 35: 791–792

    Article  Google Scholar 

  4. Feng D Z, Bao Z, Zhang X D. Modified RLS algorithm for unbiased estimation of FIR system with input and output noise. Electron Lett, 2000, 36: 273–274

    Article  Google Scholar 

  5. Sardellitti S, Barbarossa S. Distributed RLS estimation for cooperative sensing in small cell networks. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICCASP), Vancouver, 2013. 5283–5287

    Book  Google Scholar 

  6. Lorenzo P D, Isufi E, Banelli P, et al. Distributed recursive least squares strategies for adaptive reconstruction of graph signals. In: Proceedings of the 25th European Signal Processing Conference (EUSIPCO), Kos, 2017. 2289–2293

    Google Scholar 

  7. He X K, Xue W C, Fang H T. Consistent distributed state estimation with global observability over sensor network. 2017. ArXiv:1711.04993

    MATH  Google Scholar 

  8. He X K, Hu C, Xue W C, et al. On event-based distributed Kalman filter with information matrix triggers. IFAC-PapersOnLine, 2017, 50: 14308–14313

    Google Scholar 

  9. Lopes C G, Sayed A H. Incremental adaptive strategies over distributed networks. IEEE Trans Signal Process, 2007, 55: 4064–4077

    Article  MathSciNet  Google Scholar 

  10. Mostafapour E, Hoseini A, Nourinia J, et al. Channel estimation with adaptive incremental strategy over distributed sensor networks. In: Proceedings of the 2nd International Conference on Knowledge-Based Engineering and Innovation (KBEI), Tehran, 2015. 803–807

    Google Scholar 

  11. Lopes C G, Sayed A H. Distributed adaptive incremental strategies: formulation and performance analysis. In: Proceedings of IEEE International Conference on Acoustics Speech and Signal Processing Proceedings (ICASSP), Toulouse, 2006. 584–587

    Google Scholar 

  12. Shi L, Zhao H Q. Variable step-size distributed incremental normalised LMS algorithm. Electron Lett, 2016, 52: 519–521

    Article  Google Scholar 

  13. Schizas I D, Mateos G, Giannakis G B. Distributed LMS for consensus-based in-network adaptive processing. IEEE Trans Signal Process, 2009, 57: 2365–2382

    Article  MathSciNet  Google Scholar 

  14. Braca P, Marano S, Matta V. Running consensus in wireless sensor networks. In: Proceedings of the 11th International Conference on Information Fusion (ICIF), Cologne, 2008

    MATH  Google Scholar 

  15. Kar S, Moura J M F. Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. IEEE Trans Signal Process, 2009, 57: 355–369

    Article  MathSciNet  Google Scholar 

  16. Bogdanović N, Plata-Chaves J, Berberidis K. Distributed diffusion-based LMS for node-specific parameter estimation over adaptive networks. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, 2014. 7223–7227

    Book  Google Scholar 

  17. Nassif R, Richard C, Chen J, et al. Diffusion LMS over multitask networks with noisy links. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016. 4583–4587

    Book  Google Scholar 

  18. Lee H S, Kim S E, Lee J W, et al. A variable step-size diffusion LMS algorithm for distributed estimation. IEEE Trans Signal Process, 2015, 63: 1808–1820

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Mateos G, Schizas I D, Giannakis G B. Distributed recursive least-squares for consensus-based in-network adaptive estimation. IEEE Trans Signal Process, 2009, 57: 4583–4588

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  23. Bertrand A, Moonen M, Sayed A H. Diffusion bias-compensated RLS estimation over adaptive networks. IEEE Trans Signal Process, 2011, 59: 5212–5224

    Article  MathSciNet  Google Scholar 

  24. Bertrand A, Moonen M. Consensus-based distributed total least squares estimation in Ad hoc wireless sensor networks. IEEE Trans Signal Process, 2011, 59: 2320–2330

    Article  MathSciNet  Google Scholar 

  25. Bertrand A, Moonen M, Sayed A H. Diffusion-based bias-compensated RLS for distributed estimation over adaptive sensor networks. In: Proceedings of the 19th European Signal Processing Conference (EUSIPCO), Barcelona, 2011. 1025–1029

    Google Scholar 

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

    Google Scholar 

  27. Sayed A H. Adaptive Filters. Hoboken: Wiley, 2008

    Book  Google Scholar 

  28. Haykin S. Adaptive Filter Theory. Englewood Cliffs: Prentice-Hall, 2002

    MATH  Google Scholar 

  29. Nagumo J, Noda A. A learning method for system identification. IEEE Trans Autom Control, 1967, 12: 282–287

    Article  Google Scholar 

  30. Lou J, Jia L J, Tao R, et al. Distributed incremental bias-compensated RLS estimation over multi-agent networks. Sci China Inf Sci, 2017, 60: 032204

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61421001).

Author information

Authors and Affiliations

  1. School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, China

    Lu Fan, Lijuan Jia, Ran Tao & Yue Wang

Authors
  1. Lu Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lijuan Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ran Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yue Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lijuan Jia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, L., Jia, L., Tao, R. et al. Distributed bias-compensated normalized least-mean squares algorithms with noisy input. Sci. China Inf. Sci. 61, 112210 (2018). https://doi.org/10.1007/s11432-018-9461-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-018-9461-3

Keywords

Search

Navigation