Advertisement

Empirical-Measure-Based Identification: Binary-Valued Observations

  • Le Yi Wang
  • G. George Yin
  • Ji-Feng Zhang
  • Yanlong Zhao
Chapter
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

This chapter presents a stochastic framework for systems identification based on empirical measures that are derived from binary-valued observations. This scenario serves as a fundamental building block for subsequent studies on quantized observation data.

Keywords

Brownian Motion Weak Convergence Strong Convergence Asymptotic Distribution Empirical Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

  1. [2]
    J.C. Aguero, G.C. Goodwin, J.I. Yuz, System identification using quantized data, in Proc. 46th IEEE Conf. Decision Control, 4263–4268, 2007.Google Scholar
  2. [8]
    P. Billingsley, Convergence of Probability Measures, John Wiley, New York, 1968.MATHGoogle Scholar
  3. [63]
    M. Loéve, Probability Theory, 4th ed., Springer-Verlag, New York, 1977.MATHGoogle Scholar
  4. [85]
    A.V. Skorohod, Studies in the Theory of Random Processes, Dover, New York, 1982.Google Scholar
  5. [83]
    R.J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley, New York, 1980.MATHCrossRefGoogle Scholar
  6. [53]
    H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory, MIT Press, Cambridge, 1984.MATHGoogle Scholar
  7. [89]
    D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979.MATHGoogle Scholar
  8. [87]
    W.F. Stout, Almost Sure Convergence, Academic Press, New York, 1974.MATHGoogle Scholar
  9. [76]
    D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984.MATHGoogle Scholar
  10. [28]
    S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, John Wiley, New York, 1986.MATHGoogle Scholar
  11. [55]
    H.J. Kushner and G. Yin, Stochastic Approximation and Recursive Algorithms and Applications, 2nd ed., Springer-Verlag, New York, 2003.MATHGoogle Scholar
  12. [108]
    L.Y. Wang, G. Yin, and J.F. Zhang, Joint identification of plant rational models and noise distribution functions using binary-valued observations, Automatica, 42 (2006), 535–547.MATHCrossRefMathSciNetGoogle Scholar
  13. [109]
    L.Y. Wang, G. Yin, J.F. Zhang, and Y.L. Zhao, Space and time complexities and sensor threshold selection in quantized identification, Automatica, 44 (2008), 3014–3024.MATHMathSciNetGoogle Scholar
  14. [110]
    L.Y. Wang, G. Yin, Y. Zhao, and J.F. Zhang, Identification input design for consistent parameter estimation of linear systems with binary-valued output observations, IEEE Trans. Automat. Control, 53 (2008), 867–880.CrossRefMathSciNetGoogle Scholar
  15. [111]
    L.Y. Wang, J.F. Zhang, and G. Yin, System identification using binary sensors, IEEE Trans. Automat. Control, 48 (2003), 1892–1907.CrossRefMathSciNetGoogle Scholar
  16. [47]
    S. Karlin and H.M. Taylor, A First Course in Stochastic Processes, 2nd ed., Academic Press, New York, 1975.MATHGoogle Scholar
  17. [38]
    K. Gopalsamy and I.K.C. Leung, Convergence under dynamical thresholds with delays, IEEE Trans. Neural Networks, 8 (1997), 341–348.CrossRefGoogle Scholar
  18. [41]
    P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York, 1980.MATHGoogle Scholar
  19. [65]
    E. Lukacs, Stochastic Convergence, Academic Press, New York, 1975.MATHGoogle Scholar
  20. [19]
    Y.S. Chow and H. Teicher, Probability Theory, 3rd ed., Springer-Verlag, New York, 1997.MATHGoogle Scholar
  21. [21]
    K.L. Chung, A Course in Probability Theory, John Wiley, New York, 1974.MATHGoogle Scholar
  22. [84]
    G.R. Shorack and J.A. Wellner, Emperical Processes with Applications to Statistics, John Wiley, New York, 1986.Google Scholar
  23. [104]
    L.Y. Wang and G. Yin, Asymptotically efficient parameter estimation using quantized output observations, Automatica, 43 (2007), 1178–1191.MATHCrossRefMathSciNetGoogle Scholar
  24. [13]
    E.R. Caianiello and A. de Luca, Decision equation for binary systems: Application to neural behavior, Kybernetik, 3 (1966), 33–40.CrossRefGoogle Scholar
  25. [18]
    H.F. Chen and G. Yin, Asymptotic properties of sign algorithms for adaptive filtering, IEEE Trans. Automat. Control, 48 (2003), 1545–1556.CrossRefMathSciNetGoogle Scholar
  26. [27]
    C.R. Elvitch, W.A. Sethares, G.J. Rey, and C.R. Johnson Jr., Quiver diagrams and signed adaptive fiters, IEEE Trans. Acoustics, Speech, Signal Process., 30 (1989), 227–236.CrossRefGoogle Scholar
  27. [29]
    E. Eweda, Convergence analysis of an adaptive filter equipped with the sign-sign algorithm, IEEE Trans. Automat. Control, 40 (1995), 1807–1811.MATHCrossRefMathSciNetGoogle Scholar
  28. [33]
    A. Gersho, Adaptive filtering with binary reinforcement, IEEE Trans. Information Theory, 30 (1984), 191–199.MATHCrossRefGoogle Scholar
  29. [73]
    K. Pakdaman and C.P. Malta, A note on convergence under dynamical thresholds with delays, IEEE Trans. Neural Networks, 9 (1998), 231–233.CrossRefGoogle Scholar
  30. [119]
    G. Yin, V. Krishnamurthy, and C. Ion, Iterate-averaging sign algorithms for adaptive filtering with applications to blind multiuser detection, IEEE Trans. Information Theory, 49 (2003), 657–671.MATHCrossRefMathSciNetGoogle Scholar
  31. [17]
    H.F. Chen and L. Guo, Identification and Stochastic Adaptive Control, Birkhäuser, Boston, 1991.MATHGoogle Scholar
  32. [30]
    W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed., John Wiley, New York, 1968.MATHGoogle Scholar
  33. [31]
    W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed., John Wiley, New York, 1971.MATHGoogle Scholar
  34. [62]
    L. Ljung, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, 1987.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Le Yi Wang
    • 1
  • G. George Yin
    • 2
  • Ji-Feng Zhang
    • 3
  • Yanlong Zhao
    • 3
  1. 1.Department of Electrical and Computer EngineeringWayne State UniversityDetroitUSA
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA
  3. 3.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

Personalised recommendations