White noise estimators for networked systems with packet dropouts

  • Chunyan HanEmail author
  • Wei Wang
  • Yuan Zhang
Control Theory


This paper studies the optimal and suboptimal deconvolution problems over a network subject to random packet losses, which are modeled by an independent identically distributed Bernoulli process. By the projection formula, an optimal input white noise estimator is first presented with a stochastic Kalman filter. We show that this obtained deconvolution estimator is time-varying, stochastic, and it does not converge to a steady value. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criterion. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.


Convergence analysis networked system packet dropout white noise estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. M. Mendel, “White-noise estimators for seismic data processing in oil exploration,” IEEE Trans. on Automatic Control, vol. 22, no. 5, pp. 694–706, October 1977.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. M. Mendel, “Minimum-variance deconvolution,” IEEE Trans. Geosci. Remote Sensing, vol. 19, no. 3, pp. 161–171, January 1981.CrossRefGoogle Scholar
  3. [3]
    S. Sun, “Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor,” Automatica, vol. 40, no. 8, pp. 1447–1453, January 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    X. Sun, Y. Gao, Z. Deng, C. Li, and J. Wang, “Multi-model information fusion Kalman filtering and white noise deconvolution,” Information Fusion, vol. 11, no. 2, pp. 163–173, 2010.CrossRefGoogle Scholar
  5. [5]
    X. Sun and G. Yan, “Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis,” Digital Signal Processing, vol. 23, no.1, pp. 38–48, 2013.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Z. Deng, H. Zhang, S. Liu, and L. Zhou, “Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems,” Automatica, vol. 32, no. 2, pp. 199–216, February 1996.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    L. Chisci and E. Mosca, “Polynomial equations for the linear MMSE state estimation,” IEEE Trans. on Automatic Control, vol. 37, no. 5, pp. 623–626, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    H. Zhang, L. Xie, and Y. C. Soh, “Optimal and self-tuning deconvolution in time domain,” IEEE Trans. on Signal Processing, vol. 47, no. 8, pp. 2253–2261, 1999.CrossRefzbMATHGoogle Scholar
  9. [9]
    H. Zhang, L. Xie, and Y. C. Soh, “H deconvolution filtering, prediction, and smoothing: a Krein space polynomial approach,” IEEE Trans. on Automatic Control, vol. 48, no. 3, pp. 888–892, 2000.zbMATHGoogle Scholar
  10. [10]
    B. Zhang, J. Lam, and S. Xu, “Deconvolution filtering for stochastic systems via homogeneous polynomial Lyapunov functions,” Signal Processing, vol. 89, no. 4, pp. 605–614, 2009.CrossRefzbMATHGoogle Scholar
  11. [11]
    X. Lu, H. Zhang, and J. Yan, “On the H deconvolution fixed-lag smoothing,” International Journal of Control, Automation, and Systems, vol. 8, no. 4, pp. 896–902, 2010.CrossRefGoogle Scholar
  12. [12]
    B. Chen and J. Hung, “Fixed-order H 2 and H optimal deconvolution filter designs,” Signal Processing, vol. 80, no. 2, pp. 311–331, 2000.CrossRefzbMATHGoogle Scholar
  13. [13]
    A. Cuenca, J. Salt, V. Casanova, and R. Pizá, “An approach based on an adaptive multi-rate smith predictor and gain scheduling for a networked control system: implementation over profibus-DP,” International Journal of Control, Automation, and Systems, vol. 8, no. 2, pp. 473–481, 2010.CrossRefGoogle Scholar
  14. [14]
    A. Cuenca, P. García, P. Albertos, and J. Salt, “A non-uniform predictor-observer for a networked control system,” International Journal of Control, Automation, and Systems, vol. 9, no. 6, pp. 1194–1202, 2011.CrossRefGoogle Scholar
  15. [15]
    B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1453–1464, September 2004.MathSciNetCrossRefGoogle Scholar
  16. [16]
    K. Plarre and F. Bullo, “On Kalman filtering for detectable systems with intermittent observations,” IEEE Trans. on Automatic Control, vol. 54, no. 2, pp. 386–390, 2009.MathSciNetCrossRefGoogle Scholar
  17. [17]
    K. You, M. Fu, and L. Xie, “Mean square stability for Kalman filtering with Markovian packet losses,” Automatica, vol. 47, no. 12, pp. 2647–2657, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    M. Sahebsara, T. Chen, and S. L. Shah, “Optimal H 2 filtering in networked control systems with multiple packet dropout,” IEEE Trans. on Automatic Control, vol. 52, no. 8, pp. 1508–1513, 2007.MathSciNetCrossRefGoogle Scholar
  19. [19]
    S. Sun, L. Xie, W. Xiao, and Y. C. Soh, “Optimal linear estimation for systems with multiple packet dropouts,” Automatica, vol. 44, no. 5, pp. 1333–1342, 2008.MathSciNetCrossRefGoogle Scholar
  20. [20]
    G. Wei, Z. Wang, and H. Shu, “Robust filtering with stochastic nonlinearities and multiple missing measurements,” Automatica, vol. 45, no. 3, pp. 836–841, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    B. Shen, Z. Wang, H. Shu, and G. Wei, “On nonlinear H filtering for discrete-time stochastic systems with missing measurement,” IEEE Trans. on Automatic Control, vol. 53, no. 9, pp. 2170–2180, 2008.MathSciNetCrossRefGoogle Scholar
  22. [22]
    J. Ma, L. Liu, and S. Sun, “White noise filters for systems with multiple packet dropouts,” Proc. of the 30th Chinese Control Conference, Yantai, China, pp. 1586–1590, July 22–24, 2011.Google Scholar
  23. [23]
    C. Yu, N. Xiao, C. Zhang, and L. Xie, “An optimal deconvolution smoother for systems with random parametric uncertainty and its application to semiblind deconvolution,” Signal Processing, vol. 92, no. 10, pp. 2497–2508, 2012.CrossRefGoogle Scholar
  24. [24]
    H. Zhang, X. Song, and L. Shi, “Convergence and mean square stability of optimal estimators for systems with measurement packet dropping,” IEEE Trans. on Automatic Control, vol. 57, no. 5, pp. 1248–1253, 2012.MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Electrical EngineeringUniversity of JinanJinanP. R. China
  2. 2.School of Control Science and EngineeringShandong UniversityJinanP. R. China
  3. 3.Shandong Provincial Key Laboratory of Network Based Intelligent ComputingJinanP. R. China

Personalised recommendations