Skip to main content
SpringerLink
Log in

Distributed Recursive Projection Identification with Binary-Valued Observations

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper investigates a distributed recursive projection identification problem with binary-valued observations built on a sensor network, where each sensor in the sensor network measures partial information of the unknown parameter only, but each sensor is allowed to communicate with its neighbors. A distributed recursive projection algorithm is proposed based on a specific projection operator and a diffusion strategy. The authors establish the upper bound of the accumulated regrets of the adaptive predictor without any requirement of excitation conditions. Moreover, the convergence of the algorithm is given under the bounded cooperative excitation condition, which is more general than the previously imposed independence or persistent excitations on the system regressors and maybe the weakest one under binary observations. A numerical example is supplied to demonstrate the theoretical results and the cooperative effect of the sensors, which shows that the whole network can still fulfill the estimation task through exchanging information between sensors even if any individual sensor cannot.

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. Sayed A H, Tu S, Chen J, et al., Diffusion strategies for adaptation and learning over networks: An examination of distributed strategies and network behavior, IEEE Signal Processing Magazine, 2013, 30(3): 155–171.

    Article  Google Scholar 

  2. Taj M and Cavallaro A, Distributed and decentralized multicamera tracking, IEEE Signal Processing Magazine, 2011, 28(3): 46–58.

    Article  Google Scholar 

  3. Takahashi N, Yamada I, and Sayed A H, Diffusion least-mean squares with adaptive combiners: Formulation and performance analysis, IEEE Transactions on Signal Processing, 2010, 58(9): 4795–4810.

    Article  MathSciNet  Google Scholar 

  4. Zhang Q and Zhang J F, Distributed parameter estimation over unreliable networks with markovian switching topologies, IEEE Transactions on Automatic Control, 2012, 57(10): 2545–2560.

    Article  MathSciNet  Google Scholar 

  5. Sun Y, Fu M, and Zhang H, Performance comparison of distributed state estimation algorithms for power systems, Journal of Systems Science and Complexity, 2017, 30(3): 595–615.

    Article  MathSciNet  Google Scholar 

  6. Xie S and Guo L, Analysis of normalized least mean squares-based consensus adaptive filters under a general information condition, SIAM Journal on Control and Optimization, 2018, 56(5): 3404–3431.

    Article  MathSciNet  Google Scholar 

  7. Gan D and Liu Z, Strong consistency of the distributed stochastic gradient algorithm, Proceedings of the 58th Conference on Decision and Control, Nice, France, 2019, 5082–5087.

  8. Xie S, Zhang Y, and Guo L, Convergence of a distributed least squares, IEEE Transactions on Automatic Control, DOI: https://doi.org/10.1109/TAC.2020.3047989.

  9. Gan D, Xie S, and Liu Z, Stability of the distributed Kalman filter using general random coefficients, Science China Information Sciences, 2021, 64: 172204.

    Article  MathSciNet  Google Scholar 

  10. Kar S, Moura J, and Ramanan K, Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication, IEEE Transactions on Information Theory, 2012, 58(6): 3575–3605.

    Article  MathSciNet  Google Scholar 

  11. Zhu S, Soh Y, and Xie L, Distributed parameter estimation with quantized communication via running average, IEEE Transactions on Signal Processing, 2015, 63(17): 4634–4646.

    Article  MathSciNet  Google Scholar 

  12. Zhu S, Liu S, Soh Y, et al., Performance analysis of averaging based distributed estimation algorithm with additive quantization model, Automatica, 2017, 80: 95–101.

    Article  MathSciNet  Google Scholar 

  13. Zhu S, Chen C, Xu J, et al., Mitigating quantization effects on distributed sensor fusion: A least squares approach, IEEE Transactions on Signal Processing, 2018, 66(13): 3459–3474.

    Article  MathSciNet  Google Scholar 

  14. Wang Y and Zhang J F, Distributed parameter identification of quantized ARMAX systems, Proceedings of the 38th Chinese Control Conference, 2019, 1701–1706.

  15. Tan S, Guo J, Zhao Y, et al., Adaptive control with saturation-constrainted observations for drag-free satellites — A set-valued identification approach, Science China Information Sciences, 2021, 64(10): 202202:1–202202:12.

    Article  MathSciNet  Google Scholar 

  16. Brailsford A, Yussouff M, and Logothetis E, Theory of gas sensors, Sensors and Actuators B: Chemical, 1993, 13(1): 135–138.

    Article  Google Scholar 

  17. Wang L Y, Zhang J F, and Yin G, System identification using binary sensors, IEEE Transactions on Automatic Control, 2003, 48(11): 1892–1907.

    Article  MathSciNet  Google Scholar 

  18. Wang L Y and Yin G, Asymptotically efficient parameter estimation using quantized output observations, Automatica, 2007, 43(7): 1178–1191.

    Article  MathSciNet  Google Scholar 

  19. Godoy B, Goodwin G, Agüero J, et al., On identification of FIR systems having quantized output data, Automatica, 2011, 47(9): 1905–1915.

    Article  MathSciNet  Google Scholar 

  20. Guo J and Zhao Y, Recursive projection algorithm on FIR system identification with binary-valued observations, Automatica, 2013, 49: 3396–3401.

    Article  MathSciNet  Google Scholar 

  21. Wang T, Hu M, and Zhao Y, Convergence properties of recursive projection algorithm for system identification with binary-valued observations, Proceedings of the 2018 Chinese Automation Congress, 2018, 2961–2966.

  22. Guo J and Zhao Y, Identification of the gain system with quantized observations and bounded persistent excitations, Science China Information Sciences, 2014, 57: 1–15.

    MathSciNet  MATH  Google Scholar 

  23. Zhang H, Wang T, and Zhao Y, Asymptotically efficient recursive identification of fir systems with binary-valued observations, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(5): 2687–2700.

    Article  Google Scholar 

  24. Csáji B C and Weyer E, Recursive estimation of ARX systems using binary sensors with adjustable thresholds IFAC Proceedings Volumes, 2012, 45(16): 1185–1190.

    Article  Google Scholar 

  25. Song Q, Recursive identification of systems with binary-valued outputs and with ARMA noises, Automatica, 2018, 93: 106–113.

    Article  MathSciNet  Google Scholar 

  26. Xiao J and Song Q, Recursive identification of quantized linear systems, Journal of Systems Science and Complexity, 2019, 32(4): 985–996.

    Article  MathSciNet  Google Scholar 

  27. Zhang L, Zhao Y, and Guo L, Identification and adaptation with binary-valued observations under non-persistent excitation condition, arXiv: 2107.03588, 2021.

  28. Liu Y, Dong X, Li Q, et al., Integrated strategy for fault-tolerant flight control system design with rate saturating actuators, 2019 IEEE 15th International Conference on Control and Automation, 2019, 136–141.

  29. Godsil C and Royle G, Algebraic Graph Theory, Spring-Verlag, Berlin, 2014.

    MATH  Google Scholar 

  30. Calamai P H and Moré J J, Projected gradient methods for linearly constrained problems, Mathematical Programming, 1987, 39: 93–116.

    Article  MathSciNet  Google Scholar 

  31. Lai T L and Wei C Z, Least squares estimates in stochastic regression models with applications to identification and control dynamic systems, Annals of Statistics, 1982, 10(1): 154–166.

    Article  MathSciNet  Google Scholar 

  32. Chen H F and Guo L, Identification and Stochastic Adaptive Control, Birkhäsuser, Boston, 1991.

    Book  Google Scholar 

  33. Guo L, Time-Varying Stochastic Systems Stability, Estimation and Control, Second Edition, Science Press, Beijing, 2020.

    Google Scholar 

  34. Jing L and Zhang J F, Tracking control and parameter identification with quantized ARMAX systems, Science China Information Sciences, 2019, 62(9): 199203.

    Article  MathSciNet  Google Scholar 

  35. Jing L and Zhang J F, LS-based parameter estimation of DARMA systems with uniformly quantized observations, Journal of Systems Science and Complexity, 2021, DOI: https://doi.org/10.1007/s11424-021-0314-y.

Download references

Acknowledgements

Sincerely thank Miss Die Gan for her valuable discussions.

Author information

Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ying Wang, Yanlong Zhao & Ji-Feng Zhang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ying Wang, Yanlong Zhao & Ji-Feng Zhang

Authors
  1. Ying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanlong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji-Feng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanlong Zhao.

Additional information

The work is supported by National Key R&D Program of China under Grant No. 2018YFA0703800, the National Natural Science Foundation of China under Grant Nos. 61877057 and 62025306, and Open Fund Program of Beijing National Research Center for Information Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Zhao, Y. & Zhang, JF. Distributed Recursive Projection Identification with Binary-Valued Observations. J Syst Sci Complex 34, 2048–2068 (2021). https://doi.org/10.1007/s11424-021-1267-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-021-1267-x

Keywords

Search

Navigation